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Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C000 Final Proof page i
25.4.2007 7:31pm Compositor Name: BMani
Computational Fluid Dynamics in Food Processing
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C000 Final Proof page ii 25.4.2007 7:31pm Compositor Name: BMani
Contemporary Food Engineering Series Editor
Professor Da-Wen Sun, Director Food Refrigeration & Computerized Food Technology National University of Ireland, Dublin (University College Dublin) Dublin, Ireland http://www.ucd.ie/sun/
1. Computational Fluid Dynamics in Food Processing, edited by Da-Wen Sun
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Computational Fluid Dynamics in Food Processing
edited by
Da-Wen Sun
Boca Raton London New York
CRC Press is an imprint of the Taylor & Francis Group, an informa business
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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8493-9286-1 (Hardcover) International Standard Book Number-13: 978-0-8493-9286-3 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Computational fluid dynamics in food processing / editor Da-Wen Sun. p. cm. -- (Contemporary food engineering series) Includes bibliographical references and index. ISBN-13: 978-0-8493-9286-3 (alk. paper) ISBN-10: 0-8493-9286-1 (alk. paper) 1. Food industry and trade--Fluid dynamics. 2. Food industry and trade--Technological innovations. I. Sun, Da-Wen. TP370.C66 2007 664’.02--dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
2006101711
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Table of Contents Preface to Contemporary Food Engineering Series ................................................................ix Preface...................................................................................................................................xi Editor...................................................................................................................................xiii Contributors .........................................................................................................................xv Chapter 1
An Overview of CFD Applications in the Food Industry ..................................1
Toma´s Norton and Da-Wen Sun Chapter 2
CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets ...........................................................................................43
Jean Moureh Chapter 3
CFD Aided Retail Cabinets Design ..................................................................83
Giovanni Cortella Chapter 4
Improving Performance of a Chilled Multideck Retail Display Cabinet by CFD ................................................................................ 103
Alan M. Foster Chapter 5
CFD Design of Air Curtain for Open Refrigerated Display Cases ................ 129
Homayun K. Navaz, Ramin Faramarzi, and Mazyar Amin Chapter 6
Investigation of Methods to Improve Retail Food Store Environment Using CFD ...................................................................... 143
Savvas Tassou and Weizhong Xiang Chapter 7
CFD Optimization of Air Movement through Doorways in Refrigerated Rooms ........................................................................................ 167
Alan M. Foster Chapter 8
CFD Modeling of Simultaneous Heat and Mass Transfer in Beef Chilling ................................................................................. 195
Francisco Javier Trujillo and Q. Tuan Pham Chapter 9
CFD Prediction of the Air Velocity Field in Modern Meat Dryers ............... 223
Pierre-Sylvain Mirade v
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Chapter 10
CFD Simulation of Spray Drying of Food Products.................................... 249
Han Straatsma, M. Verschueren, M. Gunsing, P. de Jong, and R.E.M. Verdurmen Chapter 11
Three-Dimensional CFD Modeling of a Continuous Industrial Baking Process .............................................................................. 287
Weibiao Zhou and Nantawan Therdthai Chapter 12
Computation of Airflow Effects in Microwave and Combination Heating .......................................................................................................... 313
Pieter Verboven, Bart M. Nicolaı¨, and Ashim K. Datta Chapter 13
Thermal Sterilization of Food Using CFD ................................................... 331
A.G. Abdul Ghani and Mohammed M. Farid Chapter 14
CFD Analysis of Thermal Processing of Eggs .............................................. 347
Sieg fried Denys, Jan Pieters, and Koen Dewettinck Chapter 15
CFD Simulation of Stirred Yoghurt Processing in Plate Heat Exchangers............................................................................................ 381
Joa˜o M. Maia, Joa˜o M. No´brega, Carla S. Fernandes, and Ricardo P. Dias Chapter 16
CFD Modeling of the Hydrodynamics of Plate Heat Exchangers for Milk Processing ....................................................................................... 403
Koen Grijspeerdt, Dean Vucinic, and Chris Lacor Chapter 17
Plate Heat Exchanger: Thermal and Fouling Analysis ................................. 417
Soojin Jun and Virendra M. Puri Chapter 18
CFD Applications in Membrane Separations Systems ................................. 433
Sean X. Liu Chapter 19
Applications of CFD in Jet Impingement Oven............................................ 469
Dilek Kocer, Nitin Nitin, and Mukund V. Karwe Chapter 20
CFD Modeling of Jet Impingement during Heating and Cooling of Foods .......................................................................................... 487
˚ rdh ¨ ga Eva E.M. Olsson and Christian Tra Chapter 21
Use of CFD for Optimization, Design, and Scale-Up of Food Extrusion ......................................................................................... 505
Bharani K. Ashokan, Jozef L. Kokini, and Muthukumar Dhanasekharan
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Chapter 22
Modeling of High-Pressure Food Processing Using CFD ............................ 537
A.G. Abdul Ghani and Mohammed M. Farid Chapter 23
Analysis of Mixing Processes Using CFD..................................................... 555
Robin K. Connelly and Jozef L. Kokini Chapter 24
CFD Simulation of Multiphysical–Multi(bio)chemical Interactions of Tea Fermentation and Infusion ................................................................ 589
Guoping Lian Chapter 25
CFD Prediction of Hygiene in Food Processing Equipment ........................ 603
Bo Boye Busk Jensen and Alan Friis Chapter 26
CFD Design and Optimization of Biosensors for the Food Industry........... 631
Pieter Verboven, Yegermal T. Atalay, Steven Vermeir, Bart M. Nicolaı¨, and Jeroen Lammertyn Chapter 27
Modeling Airflow through Vented Packages Containing Horticultural Products .................................................................................. 649
Maria J. Ferrua and R. Paul Singh Chapter 28
CFD Modeling of Indoor Atmosphere and Water Exchanges during the Cheese Ripening Process ......................................................................... 697
Pierre-Sylvain Mirade Index................................................................................................................................... 727
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Preface to Contemporary Food Engineering Series Food engineering is the multidisciplinary field of applied physical sciences combined with the knowledge of product properties. Food engineers provide technological knowledge essential to the cost-effective production and commercialization of food products and services. In particular, food engineers develop and design processes and equipment in order to convert raw agricultural materials and ingredients into safe, convenient, and nutritious consumer food products. However, food engineering topics are continuously undergoing changes to meet diverse consumer demands, and the subject is being rapidly developed to reflect the market needs. In the development of food engineering, one of the many challenges is to employ modern tools and knowledge, such as computational materials science and nanotechnology, to develop new products and processes. Simultaneously, improving food quality, safety, and security remain critical issues in food engineering study. New packaging materials and techniques are being developed to provide a higher level of protection to foods and novel preservation technologies are emerging to enhance food security and defense. Additionally, process control and automation regularly appear among the top priorities identified in food engineering. Advanced monitoring and control systems are developed to facilitate automation and flexible food manufacturing. Furthermore, energy saving and minimization of environmental problems continue to be important food engineering issues and significant progress is being made in waste management, efficient utilization of energy, and the reduction of effluents and emissions in food production. Consisting of edited books, the Contemporary Food Engineering book series attempts to address some of the recent developments in food engineering. Advances in classical unit operations in engineering applied to food manufacturing are covered as well as such topics as progress in the transport and storage of liquid and solid foods; heating, chilling, and freezing of foods; mass transfer in foods; chemical and biochemical aspects of food engineering and the use of kinetic analysis; dehydration, thermal processing, nonthermal processing, extrusion, liquid food concentration, membrane processes and applications of membranes in food processing; shelf-life, electronic indicators in inventory management, and sustainable technologies in food processing; and packaging, cleaning, and sanitation. These books are intended for use by professional food scientists, academics researching food engineering problems, and graduate level students. The editors of the books are leading engineers and scientists from many parts of the world. All the editors were asked to present their books in a manner that will address the market’s needs and pinpoint the cutting edge technologies in food engineering. Furthermore, all contributions are written by internationally renowned experts who have both academic and professional credentials. All authors have attempted to provide critical, comprehensive, and readily accessible information on the art and science of a relevant topic in each chapter,
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with reference lists to be used by readers for further information. Therefore, each book can serve as an essential reference source to students and researchers at universities and research institutions. Da-Wen Sun Series Editor
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Preface Computational fluid dynamics (CFD) is a state-of-the-art numerical technique for solving fluid flow problems. CFD calculations use a computational grid to solve the governing equations describing fluid flow, i.e., the continuity equation and the set of Navier–Stokes equations, and any additional conservation equations, such as energy balance, across each grid cell by means of an iterative procedure in order to predict and visualize the profiles of velocity, temperature, pressure, etc. Early users of CFD are found in the automotive, aerospace, and nuclear industries. With the enhancement of computing power and efficiency, and the availability of affordable CFD packages, applications of CFD have extended into the food industry for modeling industrial processes, thereby generating comprehensive analyses leading to designing more efficient systems. The implementation of early-stage simulation tools is an international trend so that engineers can test concepts all the way through the development of a process or a system. CFD serves as such a powerful design and analysis tool to the food engineer. In the food industry, many processes such as mixing, drying, cooking, sterilization, chilling, and cold storage involve fluid flow and heat and mass transfer. CFD provides an ideal tool for gaining a qualitative and quantitative assessment of the performance of these processes. With CFD, numerous different combinations of design parameters and working conditions can be experimented on the computer, thus overcoming the need to test the actual design with each modification, leading to the optimization of existing and new processes or systems. Therefore, as the first book in the area of CFD application in food processing, Computational Fluid Dynamics in Food Processing will greatly benefit the food industry in its continual quest for process and product improvement. The book begins with a chapter on overview of technology. The rest of the chapters can be broadly divided into the following three parts: CFD applications in analyzing and optimizing cold-chain facilities (Chapter 2 through Chapter 8); modeling of drying (Chapter 9 and Chapter 10) and heating (Chapter 11 through Chapter 14), processes and analysis of heat exchangers (Chapter 15 through Chapter 17); and other applications in separation (Chapter 18), jet impingement (Chapter 19 and Chapter 20), extrusion (Chapter 21), high-pressure processing (Chapter 22), mixing (Chapter 23), tea fermentation (Chapter 24), equipment hygiene (Chapter 25), biosensor (Chapter 26), packaging (Chapter 27), and cheese ripening (Chapter 28). The chapters in Computational Fluid Dynamics in Food Processing are authored by international peers who have both academic and professional credentials, and this book is intended to provide the engineer and technologist working in research, development, and operations in the food industry with critical, comprehensive, and readily accessible information on the art and science of CFD technology. It should also serve as an essential reference source to undergraduate and postgraduate students and researchers at universities and research institutions. Da-Wen Sun National University of Ireland, Dublin
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Editor Born in southern China, Professor Da-Wen Sun is an internationally recognized figure for his leadership in food engineering research and education. His main research activities include cooling, drying, and refrigeration processes and systems, quality and safety of food products, bioprocess simulation and optimization, and computer vision technology. Especially, his innovative studies on vacuum cooling of cooked meats, pizza quality inspection by computer vision, and edible films for shelf-life extension of fruits and vegetables have been widely reported in national and international media. Results of his work have been published in over 150 peer-reviewed journal papers and in more than 200 conference papers. He received BSc honors and a MSc in mechanical engineering, and a PhD in chemical engineering in China before working at various universities in Europe. He became the first Chinese national to be permanently employed at an Irish university when he was appointed college lecturer at the National University of Ireland, Dublin (University College Dublin) in 1995, and was then continuously promoted in the shortest possible time to senior lecturer, associate professor, and full professor. Dr. Sun is now professor and director of the Food Refrigeration and Computerized Food Technology Research Group at University College Dublin. As a leading educator in food engineering, Professor Sun has significantly contributed to the field of food engineering. He has trained many PhD students, who have made their own contributions to the industry and academia. He has also given lectures on advances in food engineering on a regular basis at academic institutions internationally and delivered keynote speeches at international conferences. As a recognized authority in food engineering, he has been conferred adjunct=visiting=consulting professorships from ten top universities in China including Shanghai Jiaotong University, Zhejiang University, Harbin Institute of Technology, China Agricultural University, South China University of Technology, Southern Yangtze University. In recognition of his significant contributions to food engineering worldwide and his outstanding leadership, the International Commission of Agricultural Engineering (CIGR) awarded him the CIGR Merit Award in 2000 and in 2006; the Institution of Mechanical Engineers (IMechE) based in the UK named him ‘‘Food Engineer of the Year 2004.’’ He is a fellow of the Institution of Agricultural Engineers. He has also received numerous awards for teaching and research excellence, including the President’s Research Fellowship, and twice received the President’s Research Award of University College Dublin. He is a member of the CIGR executive board and honorary vice-president of CIGR, editor-in-chief
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of the newly established Food and Bioprocess Technology—An International Journal (Springer), editor of Journal of Food Engineering (Elsevier), series editor of the ‘‘Contemporary Food Engineering’’ book series (CRC Press=Taylor & Francis), and an editorial board member for the Journal of Food Process Engineering (Blackwell), Sensing and Instrumentation for Food Quality and Safety (Springer), and the Czech Journal of Food Sciences. He is also a chartered engineer registered in the UK Engineering Council.
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Contributors Mazyar Amin Department of Aeronautics and Astronautics University of Washington at Seattle Seattle, Washington
Koen Dewettinck Department of Food Safety and Food Quality Ghent University Ghent, Belgium
Bharani K. Ashokan Department of Food Science and Center for Advanced Food Technology Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Muthukumar Dhanasekharan Fluent Inc. Lebanon, New Hampshire
Yegermal T. Atalay Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium Robin K. Connelly Departments of Food Science and Biological Systems Engineering University of Wisconsin-Madison Madison, Wisconsin Giovanni Cortella Department of Energy Technologies University of Udine Udine, Italy Ashim K. Datta Department of Biology and Environment Engineering Cornell University Ithaca, New York Siegfried Denys Department of Biosystems Engineering Ghent University Ghent, Belgium
Ricardo P. Dias School of Technology and Management Polytechnic Institute of Braganc¸a Braganc¸a, Portugal Ramin Faramarzi Refrigeration and Thermal Test Center Southern California Edison Irwindale, California Mohammed M. Farid Department of Chemical and Materials Engineering The University of Auckland Auckland, New Zealand Carla S. Fernandes School of Technology and Management Polytechnic Institute of Braganc¸a Braganc¸a, Portugal Maria J. Ferrua Department of Biological and Agricultural Engineering University of California Davis, California
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Alan M. Foster Food Refrigeration and Process Engineering Research Center University of Bristol Bristol, UK Alan Friis BioCentrum-DTU, Soltofts Plads Technical University of Denmark Lyngby, Denmark A.G. Abdul Ghani Department of Chemical and Materials Engineering The University of Auckland Auckland, New Zealand Koen Grijspeerdt Institute for Agricultural and Fisheries Research Unit Technology & Food Melle, Belgium M. Gunsing Maritime Research Institute Netherlands Wageningen, The Netherlands Bo Boye Busk Jensen BioCentrum-DTU, Soltofts Plads Technical University of Denmark Lyngby, Denmark P. de Jong NIZO Food Research Ede, The Netherlands
Dilek Kocer Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey Jozef L. Kokini Department of Food Science and Center for Advanced Food Technology Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey Chris Lacor Department of Fluid Mechanics Free University of Brussels Brussels, Belgium Jeroen Lammertyn Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium Guoping Lian Colworth Laboratory Unilever Corporate Research Bedford, UK Sean X. Liu Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Soojin Jun Department of Human Nutrition, Food and Animal Sciences University of Hawaii Honolulu, Hawaii
Joa˜o M. Maia Department of Polymer Engineering University of Minho Guimara˜es, Portugal
Mukund V. Karwe Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Pierre-Sylvain Mirade Department for Science and Process Engineering of Agricultural Products National Institute for Agronomic Research Saint Gene`s Champanelle, France
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Jean Moureh Refrigerating Process Engineering Research Unit Cemagref Antony, France
Virendra M. Puri Department of Agricultural and Biological Engineering The Pennsylvania State University University Park, Pennsylvania
Homayun K. Navaz Department of Mechanical Engineering Kettering University Flint, Michigan
R. Paul Singh Department of Biological and Agricultural Engineering University of California Davis, California
Bart M. Nicolaı¨ Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium
Han Straatsma NIZO Food Research Ede, The Netherlands
Nitin Nitin Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Da-Wen Sun Department of Biosystems Engineering University College Dublin National University of Ireland Dublin, Ireland
Joa˜o M. No´brega Department of Polymer Engineering University of Minho Guimara˜es, Portugal
Savvas Tassou School of Engineering and Design Brunel University Uxbridge, UK
Toma´s Norton Department of Biosystems Engineering University College Dublin National University of Ireland Dublin, Ireland
Nantawan Therdthai Department of Product Development Kasetsart University Bangkok, Thailand
Eva E.M. Olsson Fluid Dynamics FS Dynamics AB Go¨teborg, Sweden
Christian Tra¨ga˚rdh Department of Food Technology, Engineering, and Nutrition Lund University Lund, Sweden
Q. Tuan Pham School of Chemical Sciences and Engineering University of New South Wales Sydney, Australia
Francisco Javier Trujillo Food Science Australia North Ryde, New South Wales, Australia
Jan Pieters Department of Biosystems Engineering Ghent University Ghent, Belgium
Pieter Verboven Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium
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R.E.M. Verdurmen Numico Research B.V. Wageningen, The Netherlands Steven Vermeir Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium M. Verschueren NIZO Food Research Ede, The Netherlands
Dean Vucinic Department of Fluid Mechanics Vrije Universiteit Brussel Brussels, Belgium Weizhong Xiang Hoare Lea Consulting Engineers Bristol, UK Weibiao Zhou Department of Chemistry National University of Singapore Singapore
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An Overview of CFD Applications in the Food Industry Toma´s Norton and Da-Wen Sun
CONTENTS 1.1 1.2
1.3
1.4
1.5
1.6
1.7
Introduction .................................................................................................................. 2 Fundamentals of CFD Modeling.................................................................................. 5 1.2.1 Governing Equations......................................................................................... 5 1.2.1.1 Turbulence Modeling .......................................................................... 8 1.2.1.2 Porous Media and Multiphase Modeling .......................................... 11 1.2.1.3 Non-Newtonian Fluid Modeling ....................................................... 12 1.2.2 Numerical Analysis.......................................................................................... 14 Methods for Improving Modeling Accuracy .............................................................. 14 1.3.1 Convection Schemes ........................................................................................ 14 1.3.2 Unstructured Mesh.......................................................................................... 16 1.3.3 Sliding Mesh .................................................................................................... 16 1.3.4 Multiple Frames of Reference ......................................................................... 17 1.3.5 Spatial Convergence Technique....................................................................... 18 Commercial CFD Codes............................................................................................. 18 1.4.1 CFX (ANSYS, Inc.) ........................................................................................ 19 1.4.2 PHOENICS (CHAM Ltd.) ............................................................................. 20 1.4.3 FLUENT (FLUENT, Inc.) ............................................................................. 20 Performing a CFD Analysis with Commercial Software ............................................ 21 1.5.1 Preprocessing ................................................................................................... 21 1.5.2 Solving ............................................................................................................. 21 1.5.3 Postprocessing ................................................................................................. 22 Applications in the Food Industry.............................................................................. 23 1.6.1 Food Production Facilities .............................................................................. 23 1.6.2 Air Blast and Jet Impingement........................................................................ 25 1.6.3 Cold Storage Facilities..................................................................................... 25 1.6.4 Refrigerated Display Cases.............................................................................. 26 1.6.5 Household and Industrial Refrigeration.......................................................... 26 1.6.6 Sterilization...................................................................................................... 26 1.6.7 Stirred Tanks ................................................................................................... 28 1.6.8 Drying.............................................................................................................. 30 Challenging Issues Confronting CFD Modelers ......................................................... 30 1.7.1 Nonhomogenous Fluid Domain...................................................................... 30 1.7.2 Turbulence Modeling....................................................................................... 31 1
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Computational Fluid Dynamics in Food Processing
1.7.3 y+ Criterion..................................................................................................... 1.7.4 Model Simplification ....................................................................................... 1.7.5 Uneven Meshing .............................................................................................. 1.7.6 Time-Step Selection ......................................................................................... 1.8 Opportunities for Food Industry and Benefits for Consumer .................................... 1.8.1 Software Pricing .............................................................................................. 1.8.2 Processing System Design................................................................................ 1.8.3 Product Quality ............................................................................................... 1.9 Conclusions................................................................................................................. Nomenclature ...................................................................................................................... References ...........................................................................................................................
31 32 32 33 33 33 34 34 34 35 36
1.1 INTRODUCTION Engineers are presently turning to the power of computational fluid dynamics (CFD) to model industrial processes, accomplish comprehensive analyses, and design more efficient systems. The adoption of CFD over the recent years has been inevitable and progressive, as the high costs and time consumption associated with experimentation have often precluded the desire to produce efficient in-depth results. Moreover, associated assumptions, generalizations, and approximations have inhibited analytical models from developing comprehensive flow solutions. By coupling these limitations with the recent advances in the development of numerical solutions for the Navier–Stokes equations, and the enhancement of computing power and efficiency, it is easy to understand why the application of CFD has developed into a viable alternative in the food industry. CFD is maturing into a powerful and pervasive tool with each solution representing a rich tapestry of mathematical physics, numerical methods, user interfaces, and stateof-the-art visualization techniques. In its present-day form, it can be used to efficiently quantify the complex dynamic processes that occur during fluid motion and as a result has developed into a multifaceted industry, generating billions of euros worldwide in a wealth of different disciplines [1,2]. Such disciplines include process engineering, aerospace, hydrology, bioengineering, and meteorology. Among the processes quantifiable by CFD are heat and mass transfer, phase change, solid and fluid interactions, prediction of solid stress, and chemical reactions. These processes and associated industries are summarized in Table 1.1. The links between CFD and the processes associated with the food and beverage industry such as mixing, drying, cooking, sterilization, chilling, and cold storage are profound. Such processes are used regularly to enhance quality, safety, and shelf life of foodstuffs and have been evolving over the years to become more efficient [9]. The adoption of CFD technology by food engineers began in the 1990s, predominately due to the advent of inexpensive powerful computers and CFD software [10]. Today, because of the direct benefits for both the consumer and environment, applications of CFD have become an essential part of system design in the food industry (Figure 1.1). Recent advances in unstructured and adaptive meshing, moving boundaries, and multiple frames of reference now cooperate with physical models to confront the complex phenomena that the food industry has faced over the decades [11]. In addition, CFD can aid food companies to respond to an expanding marketplace by enhancing and developing processing strategies, while endeavoring to maintain high levels of product quality. Table 1.2 highlights the number of CFD modeling applications related to the food industry published by food engineering related journals.
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An Overview of CFD Applications in the Food Industry
TABLE 1.1 Industrial Processes Quantifiable by CFD Dynamic Processes
Industry
Heat and Mass Transfer
Solid and Fluid Interactions
Chemical Reactions
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
Biomedical engineering Food and beverage Agriculture Building simulation Aerospace Chemical
Transport
Phase Change
Examples of CFD Application
Radiation p
p
Visualization of blood flow through heart valves [3] Design and optimization of chillers, ovens, and dryers [1] Design of climate within agricultural buildings [4] Human microclimate studies to aid room design [5] Modeling of space shuttle in ascending flight [6] Complex flow in mixing and reactions at microeddy scale [7] Enhancement of vehicle designs [8]
70
60
Number of papers
50
40
y = 4.7833x1.5351 R 2 = 0.9703
30
20
10
0 1993−1995
1996−1998
1999−2001
2002−2004
2005−2006
Period
FIGURE 1.1 The number of published papers with CFD applications in the food industry.
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Computational Fluid Dynamics in Food Processing
TABLE 1.2 Number of Applied CFD Articles Related to Food Engineering Published in English Journals Period
Journals
1993– 1995
1996– 1998
1999– 2001
2002– 2004
2005– 2006a
% of Total
0 0
1 0
0 0
0 1
0 1
0.71 1.42
D HT, HE
1
1
1
1
2
4.25
ST, DR, HE
1 2
0 0
0 4
0 6
0 7
0.71 12.8
0
1
1
1
0
2.12
0
6
11
18
16
0 0
0 0
0 0
1 0
4 3
3.54 2.12
HT, DR, HE, STER, CH, CR, OV, F, V HE, V, MIX, CH HE, CH, AC
0 0 0
0 1 0
0 0 0
0 0 9
1 0 0
0.71 0.71 6.38
HE HE CH, STER, HT
0
0
2
1
0
2.12
DR, STER
0 0 1 0 0
0 0 1 0 0
1 0 0 0 5
0 1 0 0 7
1 0 4 1 3
1.42 0.71 4.25 0.71 10.64
0
0
0
0
1
0.71
STER
0
0
0
5
2
4.9
0
0
0
0
2
1.42
ST, DR, MIX, FP, CIP, BC STER, CIP
0
1
0
0
0
0.71
CR
0 0
0 0
0 1
2 0
0 0
1.42 0.71
DR CH
0
0
0
1
2
2.12
DR
Computers and Fluids International Journal of Heat and Fluid Flow Computers and Chemical Engineering Food Control Chemical Engineering Science Trends in Food Science and Technology Journal of Food Engineering Applied Thermal Engineering Energy Conversion and Management Journal of Dairy Technology Revue Ge´ne´rale de Thermique Computers and Electronics in Agriculture Chemical Engineering and Processing Chemical Engineering Journal Food Research International Journal of Membrane Science International Dairy Journal International Journal of Refrigeration International Journal of Heat and Mass Transfer Food and Bioproducts Processing Journal of Food Process Engineering Chemical Engineering Research and Design Drying Technology International Journal of Food Science and Technology Le Lait
36.2
Modeling Applications
HT ST, STER, DR, HOM, PF, MIX RS
ST, DR CH MF CH CH, CR, AC
Abbreviations: D, disinfection (UV reaction); HT, heat transfer; HE, heat exchangers; DR, dryers; ST, stirred tanks; STER, sterilization; HOM, homogenization; PF, pneumatic flows; MIX, mixers; CH, chillers; OV, ovens; AC, air curtains; MF, membrane flows; CIP, cleaning in place; CR, clean rooms; BC, Belt cooling; RS, review studies; V, valve; F, fouling. a
Data collected on April 12, 2006.
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1.2 FUNDAMENTALS OF CFD MODELING The CFD codes are developed around numerical algorithms that solve the nonlinear partial differential equations governing all fluid flow, heat transfer, and associated phenomena. If used correctly, CFD provides understanding on the physics of a flow system in detail, and does so through nonintrusive flow and thermal and concentration field predictions. Obtaining accurate CFD solutions requires a large amount of insight into the problem that has to be solved, and the appropriate implementation of both physical models and numerical schemes, either at the user interface or through user-defined codes within the software. Table 1.3 summarizes the modeling techniques used by some recent CFD studies and highlights the attention paid to numerical accuracy. In this section, the governing equations and fundamental principles upon which CFD codes are based will be described followed by a state-of-the-art review on the different CFD codes that exist in the marketplace.
1.2.1 GOVERNING EQUATIONS The governing equations of fluid flow and heat transfer can be considered as mathematical formulations of the conservation laws of fluid mechanics. When applied to a fluid continuum, these conservation laws relate the rate of change of a desired fluid property to external forces and can be considered as 1. The law of conservation of mass (continuity), which states that the mass flows entering a fluid element must balance exactly with the flows leaving it 2. The conservation of momentum (Newton’s second law of motion), which states that the sum of the external forces acting on the fluid particle is equal to its rate of change of linear momentum 3. The conservation of energy (the first law of thermodynamics), which states that the rate of change of energy of a fluid particle is equal to the heat addition and the work done on the particle By enforcing these conservation laws over discrete spatial regions in the flow domain, it is possible to achieve a systematic account of the changes in mass, momentum, and energy as the fluid crosses the region boundaries [21]. The resulting equations of fluid motion are referred to as the Navier–Stokes equations, and can be written as Conservation of mass equation: @r @ þ ruj ¼ 0 @t @xi
(1:1)
@ @ @ @ui @uj ð rui Þ þ rui uj ¼ pdij þ m þ þ rgi @t @xj @xj @xj @xi
(1:2)
Conservation of momentum:
Conservation of energy: @ @ @ @T ð rCa T Þ þ ruj Ca T l ¼ sT @t @xj @xj @xj
(1:3)
Drying Fluent 5.4
Fluent
Kaya et al. [16] 2D
2D
3D
Fluent 6.0
Kocer and Karwe [14]
Mirade [15]
3D
3D
CFX 4.3
Fluent 6.0
Mirade et al. [12]
Dimension
Verboven et al. [13]
CFD Code
Authors
Determining variation of HTC and MTC
Predicting AP in meat dryer
Modeling oven fluid flow and heat transfer
Determining AP, RT, HTC
Predicting AP and temperature in baking tunnel
Objective
Unstructured mesh
NS
None
Conjugate heat transfer
Std. k–«
Reynolds stress model
Rotating BCs
Unstructured mesh
CFD Feature
Laminar, RT
Std. k–«
Turb and Supp Models
Placement of inlet and outlet will improve uniform heating and reduce moisture Heat transfer depends velocity of impinging jets only Predictions accurately show the effect of ventilation cycle on AP homogenity With food products of small-aspect ratios drying time is reduced
CFD was a useful tool
Study Conclusion
No validation with EM although account of model limitations CS ¼ HYBRID, GIS, validation with literature data
GIS, CS ¼ NS, good agreement with EM
CS ¼ NS, GIS ¼ NS, Comprehensive on flow characteristics in oven QUICK CS, good agreement with EM, good GIS
Comments
6
Baking
Process
TABLE 1.3 Recent Publications in CFD Applications
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STAR-CD
CFX 5.7
Foster et al. [20]
CFX
Xu and Burfoot [18]
Jensen and Friis [19]
Fluent 6
Mirade and Picgirard [17]
2D
3D
3D
3D
Determining air curtain velocity
Determining CIP effectiveness
Predicting of HT, MT, and AP in storage rooms
Developing solutions to enhance ventilation
Body-fitted mesh
NS
Std. k–«
NS
None
k–« RNG with OEM in near-wall region
Unstructured mesh
Std. k–«
Effectiveness of air curtain can be enhanced with CFD visualization of flow field
Enhanced indoor environment by modifying ventilation configuration Good agreement with EM. Spatial and temporal quality of the indoor environment was determined Critical shear stress not overcome in the CIP procedure GIS. Good account of limitations of the model and improvement strategies No GIS, CS ¼ NS
Porous media models used, no GIS, good account of model limitations GIS ¼ NS, CS ¼ NS, weight loss and temperature distribution predicted
Abbreviations: turb, turbulence; supp, supplementary; AP, airflow patterns; Std. k–«, standard k–« turbulence model; CS, convection scheme; NS, not specified; GIS, grid independence study; RT, radiative heat transfer; BC, boundary condition; EM, experimental measurements; HTC, heat transfer coefficient; MTC, mass transfer coefficient; OEM, one equation model.
Air curtains
Ventilated room
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There are two ways to model the density variations in the flow field that occur due to buoyancy. The first is to assume that the density differentials in the flow are only required in the momentum equations and are represented by r ¼ rref ½1 bðT Tref Þ
(1:4)
This method is known as Buossinesq approximation and has been used successfully in many food engineering applications [22]. At high-temperature differentials the approximation is no longer valid and another method must be applied [23]. One way is to treat the fluid as an ideal gas and express the density difference by means of the following equation: r¼
rref Wa RT
(1:5)
This method can be considered as a weakly compressible formulation, i.e., the density of the fluid is dependent on temperature and composition, but not pressure. This assumption has also been used successfully in food engineering applications [13,24]. However, modeling buoyancy this way is numerically complex and attaining a converged solution has proved, in some cases, to be more difficult than with the Buossinesq relationship [24]. On their own, the Navier–Stokes equations have a limited amount of applications in many areas of food engineering. This means that the additional processes, which play a major role in influencing the dynamics of a system, must be taken into account in a simulation. In these cases, the governing equations may need to be fortified with additional approximations or physical models to fully represent the modeled flow regime. Important physical models commonly used in food engineering applications include turbulence models, porous media and multiphase modeling, and non-Newtonian modeling. 1.2.1.1
Turbulence Modeling
Turbulence momentum and scalar transport play an essential role in many engineering applications and its simulation has undergone intensive research throughout the years. In the food industry it is often necessary to predict surface heat and mass transfer coefficients, heat-dependent properties of food, and flow characteristics of systems under various scenarios to develop safe and efficient plant processes [9]. These processes are usually associated with turbulent flows, primarily due to the complex geometry and=or high flow rates involved. While the Navier–Stokes equations can be solved directly for laminar flows, the current state of computational capability is unable to resolve the fluid motion in the Kolmogorov microscales associated with turbulent flow regimes [25]. However, in most cases engineers are not interested in the detailed structures of turbulence but need a few specific quantitative features of the flow in order to undertake suitable design strategies. Such details are afforded by the Reynolds-averaged Navier–Stokes (RANS) equations, which are determined by averaging the ergodic processes that typify turbulent flows. Reynolds averaging essentially disregards the stochastic properties of the flow and results in six additional unknowns (i.e., Reynolds stresses) that need to be modeled by a physically well-posed equation system in order to obtain a closure that is consistent with the flow regime. The eddy viscosity hypothesis states that an increase in turbulence can be represented by an increase in effective fluid viscosity, and that the Reynolds stresses are proportional to the mean velocity gradients via this viscosity [23]. The RANS equations can then be written as @r @ þ (ruj ) ¼ 0 @t @xi
(1:6)
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@ @ @ @ui @uj @p0 ( r ui ) þ ( r ui mtot þ þ rgi þ fi uj ) ¼ @t @xj @xj @xj @xi @xi @ @ @ @T ( rCa T) þ ( ruj Ca T) ltot ¼ sT @t @xj @xj @xj
(1:7)
(1:8)
where the effect of turbulence in the total viscosity and heat transfer is given by mtot ¼ mlam þ mturb ltot ¼ llam þ mturb ¼
mturb Ca sturb
@u0i u0j @xj
(1:9) (1:10)
(1:11)
Unfortunately, eddy viscosity models assume isotropic turbulence resulting in diffusion acting in all directions, which is a limitation that has encroached upon its range of applications. Nevertheless, this hypothesis forms the foundation on which many of today’s most widely used turbulence models are based. These range from simple one-equation models based on empirical relationships to variants of the sophisticated but inveterate two-equation k–« model, which describes the eddy viscosity through the production and destruction of turbulence. The commonly used high Reynolds-number standard k–« model can be represented by the following equations: @k @ @ mturb @k þ ( r uj k) mlam þ ¼ Pk r« @t @xj @xj sk @xj @k @ @ m @k « «2 þ ( r uj «) mlam þ turb ¼ C1« Pk C2« r @t @xj @xj k s« @xj k 2 p0 ¼ p rk 3 mtot ¼ rCm
k2 «
(1:12)
(1:13) (1:14) (1:15)
There are many k–« type turbulence models embedded in commercial codes and it is left to the user to assert the model that is appropriate for the application in hand. As illustrated by Bartosiewicz et al. [26] (Figure 1.2), large discrepancies can occur in predictions made by different models, which emphasize the need for validation with experimental measurements. Of all turbulence models available, the standard k–« model still remains an industrial standard and its successful applications are found in recent literature [27,28]. In some cases it has even been found to perform as well as more advanced turbulence models [29,30]. Although, due to the assumptions and empiricism upon which the model is based, there are just as many situations where the k–« model has failed to sufficiently represent the modeled turbulent regime and the predictions have proved inadequate [9,31]. Consequently, engineers have turned to other advanced turbulence models like the renormalization group (RNG) and Reynolds stress-transport models (RSM), which are not so reliant on empiricism and can
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0.995
0.99
P t (MPa)
0.985
k-epsilon k-omega-sst RNG
0.98 20
(a)
30 Secondary nozzle
40 Mixing chamber
X (mm) 1.001 1 0.999 0.998
P t (MPa)
0.997 0.996 0.995 0.994 20
(b)
k-epsilon k-omega-sst RNG
30 Secondary nozzle
40 Mixing chamber
FIGURE 1.2 Predictions by three turbulence models of pressure in an ejector. (From Bartosiewicz, Y., Aidoun, Z., and Mercadier, Y., Appl. Therm. Eng., 26, 604, 2006.)
account for anisotropy of highly strained flows (as shown in Figure 1.3). Yet there have also been cases where the limitations of computational power or convergence difficulties have precluded the use of these models [33,34]. Engineers have also addressed other simulation methodologies such as direct numerical simulation (DNS), detached eddy simulation (DES), and large eddy simulation (LES) to correctly predict turbulent flow and transport phenomena. DNS is a solution to the threedimensional, time-dependent Navier–Stokes set of equations. No turbulence models are involved in the governing equations; consequently, a DNS is conducted on a fine mesh to reproduce all length scales within turbulent flow regime. This obviously necessitates the invocation of intensive computer power, much of which is presently unavailable to the engineer, thereby rendering DNS a research tool for studying turbulence momentum and heat-transfer dynamics. The advantages offered to the food industry by DNS include detailed information regarding turbulent channel flows of dilute polymer solutions [35], the effect of
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(a)
Experiment (1080 measurement points)
(b)
RSM
(c)
High Reynolds k −e model
(d)
LRN k−e Lam−Bremhorst model
11
FIGURE 1.3 Comparison between experimental and predicted results. (From Moureh, J. and Flick, D., Int. J. Refrig., 26, 12, 2005.)
buoyancy on turbulent transfer [36], and information regarding the effective control of turbulence and heat transfer [37]. Large eddy simulation forms a solution given the fact that large turbulent eddies are highly anisotropic and dependent on both the mean velocity gradients and geometry of the flow domain. With the advent of more powerful computers, LES now offers a way of alleviating the errors caused by the use of RANS turbulence models. However, the lengthy time involved in arriving at a solution means that it is an expensive technique of solving the flow [38]. LES provides a solution to large-scale eddy motion in methods akin to those employed for DNS. It also acts as spatial filtering, thus only the turbulent fluctuation below the filter size is modeled. Over recent years, LES has been applied in areas related to food processing [39]. More recently, a methodology has been proposed by which the user specifies a region where the LES should be performed, with RANS modeling completing the rest of the solution; this technique known as DES and is found to increase the solution rate by up to four times [38]. 1.2.1.2 Porous Media and Multiphase Modeling Many large-scale processes in the food industry may have the potential to be grid point demanding in CFD models, owing to the complex geometry of the modeled structures. For example, to predict the detailed transfer processes within a cold store containing stacked foods one must mesh all associated geometry with a complex unstructured or body-fitted system, which is a highly arduous and in many cases inaccessible task. In any case, both
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computational power and CFD algorithms have not yet reached such levels of maturity that these types of computations can be achieved. Therefore, other methods must be used to exploit the physical relationships that exist on a macroscopic level and sufficiently represent the dynamic flow effects that are representative of the modeled material. The porous media assumption, which relates the effects of particle size and shape, alignment with airflow, and void fraction to the pressure drop over the modeled products, has been used in recent studies [40–42]. This method basically applies Darcy’s law to a porous media by relating the velocity drop through the pores to the pressure drop over the material. An extension of this law to account for most commonly encountered nonlinear relationship between pressure drop and velocity is represented by the Darcy–Forchheimer equation [42]: @p m ¼ v þ rC2 v2 @x K
(1:16)
Equation 1.16 is the most common relationship that is used to represent pressure drop through packed beds. In the CFD model, this equation is added as an additional sink term to the momentum equations. The general relationships to determine both the permeability and the inertial loss coefficient can be obtained by inference from the Ergun equation. However, considerable information regarding the detailed flow and transfer processes taking place within the stacked material is lost in this type of modeling strategy. Therefore before modeling a porous media, one must ensure that the parameters in the momentum source terms represent the physical media as closely as possible. Verboven et al. [42] illustrated this point by modifying the Darcy–Forchheimer pressure drop relation using experimental results to accurately represent the resistance to airflow imposed by beds of apples and chicory roots. To organize the model to comprise the main geometry is another means of circumventing detailed meshing while improving upon accuracy of pressure drop relationships, within which lies a subdomain filled with a porous medium to represent the stacked foods. Fluid flow and heat transfer are described by the laws of conservation of mass, momentum, and energy. These particular forms of transport equations in porous media are derived in terms of macroscopic variables. The macroscopic velocity is provided by the volume-averaged Navier–Stokes equations, which are a generalized version of Darcy’s law. This type of computational model can be regarded as a two-phase flow. Because the volume-averaging process causes loss of details regarding the microscopic flow regime, empirical parameters such as the thermal Forchheimer constant, thermal and mass dispersion, and interfacial heat and mass transfer coefficients are required to complete the equation system [44]. Recent studies have used a two-phase modeling technique to predict the environmental conditions of product stores [34]. As shown in Figure 1.4, Zou et al. [43,44] used this method successfully to predict temperature distribution and airflow patterns in ventilated stacked goods. 1.2.1.3
Non-Newtonian Fluid Modeling
Any fluid that does not obey the Newtonian relationship between the shear stress and shear rate is called a non-Newtonian fluid. Many food processing media have non-Newtonian characteristics and the shear thinning or shear thickening behavior of these fluids greatly affects their thermal-hydraulic performance [45]. Over recent years, CFD has provided better understanding of the mixing, heating, cooling, and transport processes of non-Newtonian substances. Indeed, a source of continuous research within this modeling discipline is the effect imposed by the rheological behavior of materials like yoghurt, soup, and milk on equipment design and performance [46,47]. Processing equipment such as heat exchangers, stirred tanks, heaters, and flow conveyors are all connected with the rheological properties of
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Airflow
Airflow
273.8 K 275.8 K 277.8 K 279.9 K 281.9 K 283.9 K 285.9 K 288.0 K 290.0 K 292.0 K
Porous media
Airflow
Bottom layer (XY plane, Z = 1)
Lower middle layer (XY plane, Z = 2)
Upper middle layer (XY plane, Z = 3)
Top layer (XY plane, Z = 4)
Airflow
Solid region (tray)
FIGURE 1.4 (See color insert following page 142.) The modeling of flow through ventilated packaging using a multiphase flow technique. (From Zou, Q., Opara, L.U., and McKibbin, R., J. Food Eng., 77, 1037, 2006; Zou, Q., Opara, L.U., and McKibbin, R., J. Food Eng., 77, 1048, 2006.)
foods, and CFD studies have elucidated numerous methods of equipment optimization [48]. Figure 1.5 illustrates the modeling of a heat exchanger with CFD. Of the several constitutive formulas that describe the rheological behavior of substances, which include the Newtonian model, power-law model, Bingham model, and the Herschel–Bulkley model, the power law is
Corrugations
Velocity (Streamline 1) 0.183 0.137 0.091 0.046 Side channel
Side channel 0.000 [m s−1] z y x
FIGURE 1.5 Modeling of the flow through a heat exchanger. (From Kanaris, A.G., Mouza, A.A., and Paras, S.V., Chem. Eng. Res. Des., 83, 460, 2006.)
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the most commonly used model in food engineering applications [50]. This governs the relationship between shear thinning fluids and the shear rate, and can be shown as . n1 t¼m g
(1:17)
Variants of this model have been incorporated to many non-Newtonian CFD simulations with success. Nevertheless, as shown by Abdul Ghani et al. [51], the complex functions relating fluid viscosity to the performed operation need not always be described, and in some cases the fluid may be treated as Newtonian.
1.2.2 NUMERICAL ANALYSIS A fundamental consideration for CFD code developers is the choice of suitable techniques to discretize the modeled fluid continuum. Of the many existing techniques, the most important include finite difference, finite elements, and finite volumes. Although all of these produce same solution at high-grid resolutions, the range of suitable problems is different for each. Finite difference techniques are of limited use in many engineering flows due to difficulties in their handling of complex geometries. Finite elements can be shown to have optimality properties for some type of equations [23]. However, only a limited number of commercial finite-element packages exist, which is undoubtedly a reflection of the difficulties involved in the programing and implementation of these techniques. Such difficulties are obviated through implementation of finite volume methods. When the governing equations are expressed through finite volumes they form a physically intuitive method of achieving a systematic account of the changes in mass, momentum, and energy as fluid crosses the boundaries of discrete spatial volumes within the computational domain [21]. The ease in the understanding, programing, and versatility of finite volumes has meant that they are now the most commonly used techniques by CFD code developers.
1.3 METHODS FOR IMPROVING MODELING ACCURACY Often times, the details of Navier–Stokes equations are smeared with general assumptions and poor modeling techniques that can impair the quality of CFD simulations. Past examples of this range from inadequate application of turbulence models to the inaccuracies caused by poor quality geometry, meshes, and first-order convection schemes [52]. Fortunately as the acceptance of CFD has grown, emphasis on developing quantitatively accurate solutions for all types of flow applications has increased. Now CFD codes offer a large range of convection schemes, turbulence models, and meshing features such as unstructured mesh, sliding mesh, and multiple frames of reference, which have developed progressively to meet the demands of the food industry [53,54].
1.3.1 CONVECTION SCHEMES As noted previously, the partial differential equations governing fluid flow are solved over discrete volumes within the computational domain. It is therefore necessary to represent these equations as accurately as possible at each location. By increasing the number of volumes on subsequent CFD computations, one would intuitively expect the difference between the solutions to be reduced. However, this leads to an unfavorable increase in
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computational time, especially when using segregated solvers. Over recent years, there has been a continual improvement in the representations of the convection terms in the finite volume equations to reduce the number of grid points involved in a solution. The ultimate accuracy, stability, and boundedness of the solution depend on the numerical scheme used for these terms. A numerical or convection scheme can be perceived as a tool with which the boundary conditions are transmitted into the computational domain and the descretized equations are solved. The performance of a convection scheme is delimited by the ability of the scheme to reduce the error once the mesh is refined. The first-order HYBRID or UPWIND convection schemes are bounded and stable but are predisposed to numerical diffusion and exhibit a sluggish response to grid refinement. Also, owing to their favorable convergence attributes, these schemes are still prevalent in the food engineering literature, which obviously casts serious doubts on the validity of some solutions especially when grid-refinement studies proved unattainable. This point was also confirmed by Harral and Boon [55] when they showed that coarse grid predictions agreed more favorably with experimental measurements than the grid-independent solution. The higher-order scheme QUICK is more accurate and responsive to grid refinement but due to its unbounded nature, it often develops solutions with unphysical under-shoots and over-shoots when strong convection is present. Convergence may also be difficult, especially when nonlinear sources are present in the simulation. Nevertheless, favorable results have been attained when high-order schemes have been used [13,29,56]. Figure 1.6 illustrates the disparity between the velocity predictions of an air jet entering a ventilation room made by a first- and second-order convection schemes at the same grid resolution [57].
Distance from floor (m)
(a)
2.8
2.4 First-order upwind Second-order upwind
2 0
(b)
0.5
1 1.5 Air velocity (m s⫺1)
2
FIGURE 1.6 Prediction of isothermal wall-jet close to the opening. (From Sorensen, D.N. and Nielsen, P.V., Indoor Air, 13, 2, 2003.)
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Cavity wall Outlet Inlet
Rectangular objects
Food surface
FIGURE 1.7 Comparison of unstructured and structured meshes. (From Verboven, P., Datta, A.K., Anh, N.T., Scheerlinck, N., and Nicolai, B., J. Food Eng., 59, 181, 2003; Mirade, P.S., J. Food Eng., 60, 41, 2003.)
1.3.2 UNSTRUCTURED MESH Most commercial CFD codes have emerged from typical Cartesian-type academic programs and for many years the actual geometry criteria of the modeled process could not be fully met and had to be altered to suit the code configuration [52]. One of the major advances to occur in meshing technology over recent years was the ability for hexahedral hybrid meshes to be incorporated into general codes. This allowed a mesh to be fit to any arbitrary geometry, thereby enhancing the attainment of CFD solutions for many industrial applications. A major advantage of unstructured and hybrid meshes is their relaxation of the block structure, a past formal requirement of many general CFD codes. Local mesh refinement can now be achieved more effectively and a solution can be developed to capture all the desired flow features without creating badly distorted cells. The versatility of these meshes has led to an increased take-up by the CFD community and their uses are finding accurate solutions in many applications within the food industry [24]. This form of meshing requires different programing and solution techniques that are not quite as intuitive in implementation as their Cartesian-based counterparts. Therefore, unstructured meshing has not yet fully infiltrated the CFD market, with codes such as PHOENICS remaining faithful to traditional structured methods [51]. Figure 1.7 shows the ability of unstructured mesh to conform to arbitrary geometry without compromising resolution elsewhere within the computational domain.
1.3.3 SLIDING MESH This type of meshing technique is commonly used to model the stirring or moving effect of adjacent geometry and can therefore simulate factory processes such as baking and mixing. This methodology has been used in some areas of food engineering. It allows certain portions of a mesh to slide relative to each other at a common interface, which in the case of a mixing tank is the interface between the tips of the blades and the baffles, and in baking is the continuous movement of the product in the oven [56,58]. Figure 1.8 illustrates the use of the sliding grid technique in a stirred tank.
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f = 0⬚
f = 15⬚
f = 30⬚
f = 45⬚
(a)
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(b)
FIGURE 1.8 Use of sliding mesh in stirred tank application. (From Ng, K., Fentiman, N.J., Lee, K.C., and Yianneskis, M., Chem. Eng. Res. Des., 76, 737, 2006.)
1.3.4 MULTIPLE FRAMES OF REFERENCE This type of meshing introduces an additional assumption that can account for any stationary parts of a flow existing in sliding mesh simulations. Instead of invoking the rotation of the grid directly, the rotation is simulated by inserting suitable body force terms in the momentum equations. By making suitable transformations in the CFD calculations at the interface between rotating and stationary flow regimes, a steady-state simulation can then be conducted on a static mesh [52]. For example, in applying this approach to stirred tanks, which is the most common application in the food industry (illustrated in Figure 1.9), the equations in the flow domain attached to the impeller are solved in a simulated rotating frame of reference whereas the equations in the remaining domain are solved in a frame of reference at rest [60].
T BW
BL H
D/2
b a C
FIGURE 1.9 Simulation of stirred tank using multiple frame of reference technique. (From Li, M., White, G., Wilkinson, D., and Roberts, K.J., Chem. Eng. J., 108, 81, 2005.)
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1.3.5 SPATIAL CONVERGENCE TECHNIQUE When designing a CFD model, one must preconceive potential gradients that may occur so that the computational domain can be suitably meshed. This mesh must then be refined to obtain, as nearest as possible, a grid-independent solution. Unfortunately with today’s computational power, it is not yet possible to obtain a grid-independent solution in some cases [33,57]. Thus the requirements must be relaxed, while still maintaining confidence in the discrete solutions for the governing equations. A spatial convergence technique proposed by Roache [61] based on Richardson extrapolation [62] has been used in many CFD engineering applications [57]. The basic priority of this method is to furnish the CFD user with a conservative estimate of the error (GCI) between the fine grid solution and the unknown exact solution. The requirement is a solution set of the same governing equations from two different grid resolutions. Both CFD solutions must be on a grid, that is, within the asymptotic range of convergence. This means that the fine grid CFD solution must be obtained at, or close to, the upper limit of the available computer power. The coarse grid solution can then be achieved by removing grid lines in each coordinate direction. To ensure that the coarse grid does not fall outside asymptotic range of convergence, the grid refinement ratio (r) between the two grids should be a minimum of 1.1. This also allows the discretization error to be differentiated from other error sources [63]. The GCI can be described as GCI ¼
Fs j«j (rp 1)
(1:18)
where the relative error « between fine and coarse grid solutions is defined as «¼
f2 f1 f1
(1:19)
where Fs is the factor of safety that is usually 3 for two grid comparisons [63], fn is the solution function (i.e., velocity at a location), and p is the formal order of accuracy of the convection scheme (i.e., UPWIND is first order therefore p ¼ 1). This method has recently been used in the food industry to show the convergence of surface-averaged heat-transfer coefficients of food in a microwave oven using QUICK convection scheme [13]. No other recent applications of this technique have been found in the literature pertaining to the food industry. It would, however, seem conceivable that this type of method should take preference in CFD studies, especially where grid independency is unattainable due to computational power, or when first-order convection schemes are used.
1.4 COMMERCIAL CFD CODES Over the last two decades there has been enormous development of commercial CFD codes to enhance their union with the sophisticated modeling requirements of many research fields, thereby accentuating their versatility. These challenges have led to unprecedented competition between developers and have expedited nonuniform development, causing the range of afforded functionalities to vary from code to code. Thus, among the many codes that exist today not all provide the features required by the food engineer. Such requirements include the ability to import grid geometry, boundary conditions, and initial conditions from an external text file as well as the modeling of non-Newtonian fluids, two-phase flows, flow-dependent properties, phase change onset, and flow through porous media [64]. Therefore, functional considerations of a code should be taken into account before selection.
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TABLE 1.4 Commercial CFD Codes with Associated Companies, Cost, and Features Company
Costa
CFD Code b
c
CHAM Ltd. www.cham.co.uk
PHOENICS 3.6.1
ANSYS, Inc. www.ansys.com
CFX 5.1
e1.2 ; e4.8k (þ e0.9k)d; e3.75ke; e14.5kf (þ e2.2k)d e2.4kb; e11.2ke
Fluent, Inc. www.fluent.com
FLUENT 6.1 FIDAP 8.6 STAR-CD 3.2
e3.88kb; e21.5ke,f e3.88kb; e21.5ke,f e2.19kb; e18.33ke,f
FLOW-3D 8.2
$2kb,e; $4kb,e,f; $11kb,c
ANDINA-F CFDþþ
e1.5kb; e17.4kc ~ e7.5kc; APDAg
CD Adapco Group www.cd-adapco.com Flow Science, Inc. www.flow3d.com ADINA, Inc. www.adina.com Meta comp Technologies, Inc. www.metacomptech.com
Features LEVL, SG, FV
USG, LAG þ PT, MPH þ IPH USG, FV, FE CREM Large amount of meshing capabilities Advanced moving obstacle capabilities FE þ FV, SG, ALE UFG
Source: From Kopyt, P. and Gwarek, W., A comparison of commercial CFD software capable of coupling to external electromagnetic software for modeling of microwave heating process. Proceedings of 6th Seminar on Computer Modeling and Microwave Power Engineering, 2004. Abbreviations: FV, finite volume; SG, structured grid; LVEL, wall distance turbulence model; USG, unstructured grid; LAG þ PT, coupled Lagrangian and particle tracker; MPH þ IPH, coupled multiphase and interphase models; CREM, complex rheology and electrohydrodynamic modeling; FE, finite element; ALE, arbitrary Lagrangian and Eulerian formulation; UFG, unified grid for ease of treatment of complex geometries. a b c d e f g
Quotations collected in April 2006. Annual educational. Permanent educational. Technical support. Annual commercial. Permanent commercial. APDA ¼ academic price depends on application.
Most commercial software featured in this chapter incorporate at least a minimum of all these functionalities, employ graphical user interfaces, and support Windows, UNIX, and Linux platforms. The most common general-purpose codes available are elucidated with their associated cost in Table 1.4. Details on three of the most routinely used commercial codes are elaborated below.
1.4.1 CFX (ANSYS, INC.) CFX had long been one of the leading suppliers of CFD software and services to the chemical, food, manufacturing, and power generating industries under its parent company AEA Technology before its $21 million take over by ANSYS, Inc. in 2003. The takeover was seen as an opportunity to broaden the scope of physics and engineering solutions that could be offered to ANSYS, Inc. consumers [65]. Within the framework of ANSYS, Inc., numerous different types of software packages exist that can be used to solve various types of flow problems. ANSYS ICEM CFD offers both unstructured and structured grid generation compliant with the CFX package, postprocessing, and grid optimization tools. ANSYS
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Multiphysics is a coupled physics tool that amalgamates structural, thermal, CFD, acoustic, and electromagnetic tools into one software product. Within the ANSYS CFX workbench contains a large amount of up-to-date fully functional physical models, which include multiphase flow, porous media, heat transfer, combustion, radiation, and moving mesh. Advanced turbulence models are also a feature of ANSYS CFX and it boasts the first commercially available predictive laminar to turbulent flow transition model (Menter–Langtry g–u model). ANSYS CFX also offers a fully parametrical CAD tool with a bidirectional link compatible with most CAD software. The ANSYS CFX software has been used by numerous authors in food engineering including Nahor et al. [34] and Verboven et al. [13].
1.4.2 PHOENICS (CHAM LTD.) PHOENICS is a powerful multipurpose CFD package developed by Brian Spalding, one of the leading pioneers in CFD modeling. PHOENICS simulates a range of processes involving fluid flow, multiphase flows, heat or mass transfer, chemical reaction, and combustion, and has been used successfully by many individuals in the food industry to quantify complex flow processes [66]. It has numerous modeling capabilities that embrace many scenarios faced by the food engineer, of which include Newtonian and non-Newtonian fluid modeling, flow through porous media with direction-dependent resistances, conjugate heat transfer, specification of temperature-dependent sources, and import of CAD geometry. Among the many turbulence models offered, the unique wall distance turbulence (LVEL) model and multifluid model (MFM) are included. The LVEL model circumvents the inaccuracies associated with wall-function computations of most turbulence models by using the knowledge of wall distances (L) and local velocities (VEL) to compute the near-wall flow. The MFM calculates the population distribution of fluids contained within a turbulent mixture and determines its influences on the mean flow. Because the PHOENICS CFD code is based on a structured grid, it necessitates the use of body-fitted coordinates to model complex geometry. This can substantially increase the preprocessing time. In recent months, CHAM in tandem with Symban Power Systems Ltd. have introduced an unstructured grid option in an effort to conform to the needs of the CFD community. Other options that are unique to the PHOENICS software include multiple shared space modeling (MUSES), modeling of objects moving through a Cartesian grid (MOFOR), and modeling curved objects in a Cartesian grid (PARSOL).
1.4.3 FLUENT (FLUENT, INC.) FLUENT, Inc. offers three software packages within the CFD framework that are suitable for the food engineer’s modeling needs. The three packages are FLUENT (general purpose with multiphysics capabilities), FIDAP (for modeling complex physics), and POLYFLOW (polymer modeling). FLUENT, Inc. is presently one of the leading suppliers of CFD software in the world. FLUENT uses unstructured grid technology so that complex geometry can be easily modeled. Among a large range of turbulence models, FLUENT contains large eddysimulation and direct eddy-simulation capabilities, and has a dynamic meshing capability that allows the modeling of different moving parts with the same simulation. The most interesting features of the FLUENT software include models for heat exchangers, discrete phase models for multiphase flows, numerous high-quality reaction models, and the phase change model, which tracks the melting and freezing in the bulk fluid. It also contains a preprocessing tool GAMBIT that employs facilities for the direct import of CAD geometries. FLUENT has recently been used successfully in the food industry by Mirade et al. [41]. FIDAP is finite
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element-based software that offers unique abilities for modeling non-Newtonian flows and free surface flows. It also contains sophisticated radiation, dispersion, and heat transfer models. FIDAP has been used extensively in the food industry [67]. POLYFLOW is a general-purposed finite-element CFD tool for the analysis of polymer processing such as glass forming, thermoforming, and fibre spinning. It has a range of applications that can be extended into the food industry [45].
1.5 PERFORMING A CFD ANALYSIS WITH COMMERCIAL SOFTWARE Undertaking a CFD study demands the use of three predefined environments within the software, with each environment representing an equally important section of the modeling process. The first environment, i.e., the preprocessor, embodies the most important phase of model definition. The ultimate success of the simulation relies upon the modeling constraints and conditions input by the user via mathematical statements to the preprocessor. The second environment, i.e., the solver, takes these mathematical statements, structures them into a solvable arrangement, and solves for the specified boundary conditions by iterative methods. The third environment, i.e., the postprocessor, is used to visualize the solution field. Usually, the stand-alone postprocessing techniques provided by the software are adequate, but in many codes the solution files can be changed into an adequate format and imported by popular spreadsheet or other visualization programs. The following provides an introduction to the different modules comprising a CFD software package.
1.5.1 PREPROCESSING The preprocessor of CFD software holds all the raw data and mathematical statements attributable to the potential success of a modeling exercise. The main tasks facing a user in the preprocessing environment include problem consideration, geometry creation or import, mesh development, physical property set-up, and numerical implementation. As highlighted by Xia and Sun [1], the first important step in a CFD study is to consider the physics of the tackled problem. In doing this, the user determines the physical processes that can be accurately represented in a CFD model and expound suitable mathematical strategies to determine the desired variables. The second stage in model development is geometry design and mesh specification. The geometry is defined by either choosing a predesigned structure from the software database or more commonly by importing the geometry from any standard CAD program. Most packages employ object-orientated automatic grid generation that allows mesh to be defined around the modeled geometry. In a lot of cases specifying a good-quality mesh, a large amount of effort by the user is required. The next step is to define the fluid properties, physical models, and boundary conditions. This phase of preprocessing requires both knowledge regarding the initial status of the model and a preconception of the potential solution. The appropriate selection of convection schemes and relaxation places a large bearing on both the efficiency and accuracy of computations, therefore circumspective choices must be made. Preprocessing is completed once the user finishes all the specified tasks as illustrated in Figure 1.10.
1.5.2 SOLVING The solver environment within CFD software organizes the mathematical input from the preprocessor into numerical arrays and solves them by an iterative method. Iterative methods are commonly used to solve a whole set of discretized equations so that they may be applied
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Structured, BFC's, unstructured
CAD import, predesigned
2. Create mesh
Turbulence, porous media, radiation, reaction
1. Create geometry
3. Specify physical models
Preprocessor
5. Choose numerical options
4. Specify boundary conditions Fluid properties, initial values
Convection scheme, solver type, relaxation
Solve
Postprocessor
Contour plots
Vector plots
Line plots
Animation
FIGURE 1.10 The simulation and analysis within a CFD environment.
to a single-dependent variable. An example of an iterative method used in CFD is the segregated solver, semi-implicit method for pressure-linked equations (SIMPLE), devised by Patankar and Spalding [68], and its descendents, i.e., SIMPLEST, SIMPLER, SIMPLEC, and PISO, which have now become traditional techniques employed by many commercial packages to solve the discretized general equations. These methods determine the pressure field indirectly by closing the discretized momentum equations with the continuity equations in a sequential manner. Consequently, as the number of cells increases, the elliptic nature of the pressure field becomes more profound and the convergence rate decreases substantially [69]. This has led to the development of multigrid techniques that compute velocity and pressure corrections in a simultaneous fashion, thus enhancing convergence rates. The improvement in solver efficiency afforded by multigrid is foiled by memory requirements that increase simultaneously with the number of cells, thus making it difficult in some cases to achieve grid independency with current-computing capabilities. Nevertheless, many CFD packages, even those based on unstructured grids, now successfully employ multigrid as the default solver option. Detailed techniques used by multigrid are available in the literature [69].
1.5.3 POSTPROCESSING The postprocessing environment allows the user to visualize and scrutinize the resulting field solution. Contour, vector, and line plots enhance interpretation of results and are progressively fortified in commercial software packages. Some packages also allow the export of field data to external modeling programs so that it can be processed further. Figure 1.11 illustrates the visualization techniques that can provide sufficient information to move forward in the design process. Animated flow fields have also become increasingly popular and can now accompany peer-reviewed studies on some scientific journal Web sites [29]. Figure 1.12 shows that by examining the progressive development of the flow field a user can gain insight into
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Rear duct
Evaporator
Z Y
Turning vane
X
(a1)
(a2) Y Z
Dead space
Velocity Side of duct 0.8
Rest of duct not modeled
X
Velocity 1.1 0.8
0.5 0.5
110 mm
0.3
0.3
0.0 −1
0.0
[m s ] Y
(b1)
Z
Evaporator moved forward
50 mm
[m s−1] Y X
(b2)
Temperature
15 mm
−0.0
Z
Angle X
60 mm
Temperature −0.0
−0.8
−0.8
−1.5
Product −2.3
Product
−3.0
−3.0
Y
(c1)
Z
Y X
(c2)
Z
X
FIGURE 1.11 (See color insert following page 142.) Visualizations of air curtain used to modify cabinet design. (From Foster, A.M., Madge, M., and Evans, J.A., Int. J. Refrig., 28, 698, 2005.)
the time-dependent features, which can aid in the efficient and accurate development of design solutions.
1.6 APPLICATIONS IN THE FOOD INDUSTRY 1.6.1 FOOD PRODUCTION FACILITIES Food production facilities continuously face challenges in reducing contamination risk by airborne microorganisms. These facilities place heavy demands on ventilation systems to maintain indoor air quality and thermal conditions at near optimal levels for processes to operate successfully. Moreover, food production processes require low air temperatures around food while retaining comfort levels within the workspace, thus rendering the provision of air at a predetermined condition a difficult task. Such difficulties illuminate computational and experimental flow field studies as essential tools in the development of these facilities. CFD coupled with experimental techniques can be used to study airflow behavior and provide ventilation system design as a function of various aspects including room geometry, outdoor climate, and indoor heat and contaminant sources, and have become increasingly popular over recent years [70,71]. A fundamental objective of ventilation is to achieve acceptable levels of indoor air quality. The ventilation system must be satisfactorily effective at removing contaminants, with their distribution directly related to the position of inlets and outlets, strength of pollutant sources, and the ventilation system itself. Both passive and the dynamic transport of contaminants can
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(a)
(b)
(c)
(d)
(e)
(f)
−2 1 4 7 10 13 16 19 22 25⬚C
FIGURE 1.12 Temperature fields at display cabinet taken at 1 s intervals. (From Cortella, G., Comput. Electron. Agr., 34, 43, 2002.)
be studied using CFD [71]. Passive contaminant transport is modeled using a passive scalar (species concentration) transport equation coupled with the equations governing air motion. This is also known as the Eulerian approach and has been recently used to quantify the effectiveness of ventilation systems in clean rooms [72]. Burfoot et al. [70] noted that the complex processes governing the dispersion of contaminant particles may not be fully quantified by the Eulerian approach, and elucidated the advantages of Lagrangian (dynamic) models. These models account for the stochastic treatment of turbulent–particle interactions, inertia, and trajectory crossing and are consequently more difficult to program and implement. Harral and Burfoot [116] studied the ability of two dynamic models to predict the movement of dispersed particles from a contaminant source within a food factory and found a recent random flight model developed by Reynolds [73] to outperform the standard particle tracker of Gosman and Ioannides [74] offered by the ANSYS CFX software package. Ventilation studies generally quantify the efficiency of fresh air delivery and effectiveness of removing contaminants through the use of ventilation scales. These can be computed
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within the framework of CFD and are related to the flow quantities that play an individual part on the quality of the indoor environment. The most regularly used scales in the food industry are a function of the mean age of air. A traditional method of calculating the mean age was to determine the mean turnover time or residence time in a system irrespective of the amount of air recirculation. This led to the development of scales that gave a crude description of the ventilation effectiveness [71]. Another more descriptive method of calculating the local mean age of air is by passively tracking the airflow in the system. This is done by adding another equation to the CFD model, which is derived from a passive scalar that statistically expresses the mean time taken for air to reach any arbitrary point after entering the system: @u @ mlam mturb @u þ rui u þ ¼1 @t @xi slam sturb @xi
(1:20)
This has been used alongside a passive contaminant transport equation in a recent clean room study and has found good agreement with experimental measurements, and has provided insight into system design [75].
1.6.2 AIR BLAST AND JET IMPINGEMENT Heat and mass transfer exchanges between air and food products are proportional to the heat and mass transfer coefficients and therefore affect the surface and core temperatures of food products. Numerous CFD models have been used to calculate the local surface convective heat transfer from the cooling media to food products. These studies have found that k–« turbulence models are generally poor at predicting solutions that closely correspond to experimental data [76–78]. Kondjoyan and Boisson [76] attributed this reason to the misrepresentation of the near-wall flow by the standard wall functions and suggested that this wall treatment be abandoned for heat-transfer calculations. Olsson et al. [78,79] assessed the heat-transfer characteristics of a jet impinging on a cylindrical food product under various conditions with the shear stress transport (SST) turbulence model. Heat-transfer predictions agreed with measurements in the upper part of the cylinder but not in the wake. This was similarly experienced by Kondjoyan and Boisson [76]. Also, heat transfer did not exhibit a relation between jet and cylinder distance, which was in contrast to experimental data. Hu and Sun [77,80,81] have also examined various parameters associated with jet impingement during the air-blast chilling process. Verboven et al. [82] noted that due to the complexities involved in resolving the governing equations in the boundary layer, obtaining appropriate numerical solutions was still an active area of research in thermal analysis.
1.6.3 COLD STORAGE FACILITIES Horticultural produce is commonly cooled by forced air-ventilation through ventilated packaging to achieve efficient and uniform cooling. The cooling rate depends on the rate of heat transfer between the cooling medium and the produce, which is directly related to the air velocity within the packaging. Cost-effective design strategies proffered by CFD have led numerous studies to employ this technique in predicting the environmental variables within ventilated packaging and refrigerated store rooms [34,43,44,83]. The storage process can be simulated in a CFD model by representing the contained goods as a porous medium and employing a predetermined void fraction and average diameter of the produce. This method has yielded reasonable agreement with measurements, although it has been recognized that
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results could further be improved by adding more model details [83]. Other CFD studies have successfully used a two-phase modeling technique to simulate cooling conditions within bulk containers [34,84]. CFD studies of cold storage along with other studies that compute the mass transfer process are summarized in Table 1.5.
1.6.4 REFRIGERATED DISPLAY CASES The use of refrigerated display cases allows good visibility and ensures free access to stored food for shop customers. A virtual insulation barrier called the air curtain is developed by the recirculation of air from the top to the bottom of the case [89]. The effectiveness of the air curtain can be impaired by irregularities in the ambient shop environment, thus it is easily understood why display cases may be perceived as one of the weakest links in the chilled food chain [90]. Numerous CFD studies on the ability of the air curtain to maintain food at a predefined temperature have been conducted over recent years [27,29,90]. Because these environmental irregularities cannot be directly incorporated into CFD models, steady-state and two-dimensional assumptions are often made that may in some cases limit solution accuracy [29]. Nevertheless, numerous successful design solutions have been developed on the basis of CFD studies. Foster et al. [27] modeled different regions of a display case to evaluate problems and develop subsequent design solutions. The study highlighted the exacerbating effect of cabinet sidewalls on maintaining design temperature and energy consumption. D’Agaro et al. [29] also found that sidewall effects are the main mechanism for ambient entrainment and thermal losses in refrigerated display cases. Navaz et al. [91] have shown that it is through digital particle image velocimetry (DPIV) and CFD simulations that the entrainment of ambient environment exhibits a linear relationship with the turbulence intensity in the air curtain. The need to maintain turbulence within the air curtain was also studied by Chen and Yuan [92], who proposed a minimum Reynolds number for sealing ability. Their analysis provided a quantitative understanding of the insulation properties of the air curtain as a function of different Grashof, Reynolds, and Richardson numbers.
1.6.5 HOUSEHOLD
AND INDUSTRIAL
REFRIGERATION
The desire for thermal uniformity within household refrigerators has also advanced the application of CFD modeling [93,94]. Fukuyo et al. [94] used CFD to develop a new airsupply system for improving the thermal uniformity as well as the cooling rate experienced within a household refrigerator. A more recent application of CFD was in the study of the flow structure in ejector cycles within commercial refrigerators [95].
1.6.6 STERILIZATION Sterilization is one of the many heat-transfer applications in which CFD is enjoying more widespread use (Table 1.6). In the thermal processing of foods, rapid and uniform heating is desirable to achieve a predetermined level of sterility with minimum destruction of the color, texture, and nutrients of food products [67,99]. Traditionally, mean-temperature approximations have been used in analytical studies to calculate both the sterility and quality of food products. However, CFD studies have proved that both of these parameters are overestimated using this approximation [67]. The ubiquity of canned food has resulted in many numerical studies investigating food quality and sterility. The two main techniques of assessing these parameters with CFD are through the calculation of spore survival rate and temperature history at the slowest heating
Two-phase model
p
New
New
New
New
New
Non-New
Fluid Type
Reasonable agreement with measurements
Successful prediction and optimization Validate LM, optimize ventilation system Prediction of interparticle collisions is important
Successful prediction and optimization
Shapes of corrugations can inhibit fouling
Conclusion
Nahor et al. [34]
Li et al. [88]
Harral and Burfoot [87]
Athanasia et al. [86],
Hu and Sun [80,81]
Jun and Puri [85]
References
Abbreviations: temp, temperature; vel, velocity; FR, fouling rate; FM, fouling model; non-New, non-Newtonian model; HTC, heat-transfer coefficients; CONDIS, contaminant dispersion; LM, Lagrangian model; BFC, body-fitted coordinates; k–«–V, k–« turbulence model variants; New, Newtonian model; PVM, porous vapor model; DEM, discrete element method; HF, heating function.
To validate heat and mass transfer in a cold store
—
p
CFD þ DEM,
vel, CONDIS
Ventilation modeling Solid and fluid conveying in pipes Cold stores
vel, solid deposition, temp vel, temp, weight loss
vel, FR, temp
Spray drying
p
—
3D, unsteady, steady, k–«–V, BFC, PVM 3D, unsteady, LM
To predict chilling process under various conditions To predict operating conditions on FR Dispersion modeling for effective ventilation To predict solid deposition in pipes
vel, HTC, temp
p
Temp Model
3D, unsteady, LM
3D, unsteady, FM
Model Constraints
To predict fouling process in PHE
Objective
temp, FR
Derived Variables
Plate heat exchangers (PHE) Air-blast chilling
System Studied
TABLE 1.5 Comparison of CFD Application of Flows with Combined Mass Transfer
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TABLE 1.6 Comparison of CFD Applications in Combined Flow and Heat Transfer System Studied Mixing jets
Chiller display cabinet Sterilization in food pouches
Derived Variables
Objective
Model Constraints
Mixing index Mixing 2D, steady, characteristics laminar of opposing jets 3D, steady, Std. Temp To enhance k–« design of cabinet Temp To understand 3D, unsteady, sterilization laminar process
Heat-transfer To predict heattransfer coefficients characteristic (HTC), temp Climate in Temp, vel To enhance supermarkets design for costumer comfort Temp, vel To enhance Climate in ventilation refrigerated configuration trucks Heat exchanger
BFC
Steady, Std. k–«
RSM
Fluid Type
Conclusions
Authors
New
Mixing depends on Dt of jets
Wang et al. [96]
New
Successful modifications
Foster et al. [27]
New* Transient nature of SHZ observed New Correlation established with Nusselt number New Optimization parameters proposed New
Abdul Ghani et al. [51]
Rennie and Raghavan [97]
Foster and Quarini [98]
Ventilation duct Moureh and produced more Flick [32] uniform airflow
Abbreviations: vel, velocity; temp, temperature; New, Newtonian model; New*, Newtonian model used to model non-Newtonian fluid; Std. k–«, standard k–« turbulence model; SHZ, slowest heating zone; BFC, body-fitted coordinates; RSM, RSM turbulence model.
zone (SHZ) [100]. CFD has shown the transient nature of the SHZ in the sterilization of a canned food in a stationary position (natural convection) [101]. These studies illustrated the considerable time needed for heat to be transferred throughout the food in a static process. More recent CFD studies have found that uniform heating can be obtained throughout the food by rotating the can (forced convection) intermittently in the sterilization process [102]. Abdul Ghani et al. [22] studied the combined effect of natural and forced convection heattransfer during sterilization of viscous soup and showed that the forced convection was about four times more efficient than natural convection. CFD has recently been used to study the effect of container shape on the efficiency of the sterilization process [103,104]. Conical-shaped vessels pointing upward were found to reach appropriate sterilization temperature the quickest [103]. Full cylindrical geometries performed best when sterilized in a horizontal position [104]. The sterilization of food pouches has also been studied using CFD [51].
1.6.7 STIRRED TANKS Many numerical studies on the mixing of liquids within stirred tanks have been carried out over the last two decades [56]. The main problem facing modelers is in the development of a
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TABLE 1.7 Comparison of CFD Application in Isothermal Flows System Studied
Derived Variables
Stirred tank
Mixing time
Static mixer
Dp
Ventilation of clean room
To analyze impeller design Observe effect of shear thinning
Model Constraints Std. k–«, SM PL
a
To solve problems arising from complex flow field trajectories
NS
Vel, passive contaminant transport
Determine flow patterns in clean room Determine flow patterns in clean room Determine airflow
k–« RNG, contaminant model
Vel, LMA
Airflow in largescale chillers
Objective
Vel
Fluid Type
Conclusions
New
Suitable designs proposed Non-New Pressure drop reduce by shear thinning Non-New Determined striation thinning behavior according to micromixing theory New Proposed design optimization
References Kumaresan and Joshi [53] Liu et al. [48]
Fourcade et al. [108]
Rouaud and Havet [72]
k–« RNG, contaminant model
New
Quantified ventilation effectiveness
Rouaud and Havet [75]
k–«, 2D
New
Optimized chiller layout
Mirade [15]
Abbreviations: vel, velocity; PL, power-law model; New, Newtonian fluid; non-New, non-Newtonian; SM, sliding mesh; Std. k–«, standard k–« turbulence model; a, striation thinning parameter; Dp, pressure drop; k–« RNG, k–« RNG turbulence model; LMA, local mean age of air.
system that proffers the most efficient blending of fluids. This depends on a number of fundamental requirements including correct choice of tank and impeller geometry, rotation speed, and location of fluid inlet and outlets. Table 1.7 summarizes some recent studies on stirred tank development. Essential requirements for tank development are knowledge of power consumption, flow velocity, and mixing characteristics of different stirred tank configurations. This knowledge can be afforded by accurate CFD simulations. Early attempts to solve the flow system and select suitable impeller geometry using CFD were made by Ranade et al. [106]. Unfortunately, the conclusions drawn from their results were questionable and conflicted with other studies [107]. As computer power became increasingly cheaper and CFD techniques rapidly advanced, numerical predictions have found better agreement with experimental data. The blending behavior of stirring tanks for highly viscous flow has been studied by many authors. Kumaresan and Joshi [53] compared the energy consumption of different mixing systems as a function of different impeller parameters. A Newtonian-type pressure drop
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correlation for a shear thinning fluid in a stationary mixing element (SMX) static mixer was devised by Liu et al. [48], who found shear thinning fluids to exhibit better mixing quality than Newtonian fluids. Other studies examine the effects of the modeling approaches such as sliding mesh, moving reference frames, etc. Aubin et al. [56] found that turbulence model had little effect on mean flow compared to effects created by the choice of convection scheme or modeling approach. Song and Han [105] utilized numerical solutions to derive a correlation that expresses the pressure drop characteristic of the Kenic static mixer in terms of the Reynolds number and aspect ratio of the mixing element. More recently CFD has been used to examine the effects of tank and impeller parameters on enzyme deactivation [109].
1.6.8 DRYING Drying of different types of food products has been a challenge faced by the food industry over the centuries. Over recent years, not only have substantial improvements been made to traditional techniques such as tray and spray drying, but also new innovative drying methods like pulse combustion have been developed and optimized using CFD [31]. The nonuniformity of the air-drying process is a common problem associated with batch type drying and CFD modeling techniques are employed to provide design solutions [28,110]. Mathioulakis et al. [110] were one of the first people to use CFD to model airflow in a tray-drying chamber and highlighted the high level of nonuniformity that existed in such processes. Recently, Margaris and Ghiaus [28] used CFD to successfully optimize the tray arrangement and inlet configuration within a tray-drying chamber. Spray drying is another traditional drying technique and is used to derive powders from products associated with the dairy, food, and pharmaceutical industries. The main objective of this technique is to create a product that is easy to store, handle, and transport [111]. Many numerical studies have been conducted to optimize spray driers so that the resultant product has the appropriate rheological properties, particle size distribution, and solubility to achieve its desired function [112,113]. Straatsma et al. [112] developed a drying model based on CFD to calculate flow pattern, temperature, particle trajectories, and particle-drying behavior, and two case studies were presented to illustrate the ability of the model to optimize dryer design. Langrish and Fletcher [31] presented a comprehensive review of the state of the art in spray-drier modeling. Recent numerical studies have focused on investigating the dispersion and fouling rates of particles as well as their evaporation and coalescence within a spray drier [114].
1.7 CHALLENGING ISSUES CONFRONTING CFD MODELERS 1.7.1 NONHOMOGENOUS FLUID DOMAIN As noted above, both Eulerian and Lagrangian techniques can be used to model flows with two or more phases, e.g., water vapor, airborne microbes, and powder. The Eulerian representation treats the particulate phase as a continuum and describes the temporal and spatial concentration of the flow. However, the disadvantages associated with this technique, which include loss of time history of particles, outweigh the potential benefits [115]. Moreover, the Eulerian concept is invalid when particles of size 1 mm are present in the flow regime [73]. Lagrangian stochastic models, i.e., random flight models (using a Lagrangian autocorrelation function) allow particles that are thrown into the near boundary region of the flow stream to experience velocities lower than those sufficient to maintain streamline trajectory. Lagrangian and Eulerian techniques have been used by the spray-drier community, with the former
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allowing far more opportunities for design as it can take into account turbulent structures and inertia crossing [115]. It has been noted in the literature that rigorous random flight models are necessary to ensure accurate predictions [70]. Moreover, a lot of work still has to be done to ensure comprehensive validation of such models [116]. Because CFD models consider the movement of fluid as a continuum, flows involving equal amounts of both fluids and powders cannot be modeled solely by CFD. Other techniques must be employed to account for the complex interactions of the individual particles. A modeling technique called the discrete element method (DEM) has recently been used with good qualitative accuracy to model a large range of granular mixing applications [117]. This method, i.e., DEM, has the ability to take into account powder cohesion and can also be coupled with CFD to simulate the transport of powder materials through pneumatic pipes [60]. DEM is very computationally expensive and often simulations require many days before arriving at a solution. This has meant that the extension of this model to other modes of dense gas–solids flow exhibited by fine powders (particle size less than 100 mm) is impractical. Therefore, it may be some time before such techniques can be incorporated into process design [118].
1.7.2 TURBULENCE MODELING One of the main issues faced by the food industry over the last two decades is the lack of understanding surrounding the efficient discrete quantification of turbulence in fluids and its effect on system performance. Over the years, simplifying assumptions have been made by turbulence modelers to make this problem more approachable. These assumptions have often proved to be unreasonable in many applications. A typical example of this is the Reynolds-number assumption, whereby either a high or low Reynolds-number flow regime is assumed a priori to a simulation. The most outstanding misapplication of this is in studies where turbulent and laminar flow regimes coexist, e.g., clean rooms or food factories. Recent modeling advancements have addressed this issue by developing a predictive laminar to turbulent flow transition model, which has been incorporated in the ANSYS CFX 10.0 software [119]. Unfortunately, as of yet no research employing this model is available. Certainly, modern variants of the k–« model have proved to be more successful than the standard k–« model in similar studies, and in applications involving swirling flow regimes or jet impingement [76]. Nevertheless, from published studies it can be concluded that confidence in k–« model can be upheld in other flow applications provided good agreement is found with measurements under grid-independent conditions [29].
1.7.3
+ Y
CRITERION
Another feature of RANS turbulence models is the near-wall treatment of turbulent flow. Treatment of the near-wall flow in all CFD software packages is specialized according to employed turbulence model. For example, low Reynolds-number turbulence models solve the governing equations all the way to the wall. This requires a high degree of mesh refinement in the boundary layer in order to satisfactorily represent the flow regime, i.e., yþ 1. Conversely, high Reynolds-number turbulence models use empirical relationships arising from the log–law condition that describe the flow regime in the boundary layer of a wall. This means that the mesh does not have to extend into this region; consequently, the number of cells involved in a solution is reduced. The use of this method requires 30 < yþ < 500 [21], although yþ 10 is also acceptable [57]. Generally these wall treatment assumptions do not adversely affect solutions and many studies have employed them with relative impunity provided yþ constraints specific to the turbulence model were adhered.
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Unfortunately, standard wall-treatment functions have failed to satisfactorily predict the phenomenon in applications involving the heat transfer associated with impinging airflow [76]. Recent studies have successfully circumvented this problem by using a blended walltreatment assumption that uses either the low Reynolds number or high Reynolds-number relationship depending on local flow condition in the wall region [78]. Before embarking on CFD modeling, it should be noted that the limitations of the turbulence models available and their associated wall functions must be taken into consideration. Models appropriate for the study should be chosen based on the experiences of similar applications in the literature. Meshing should be then carried out using an iterative procedure that involves repeated CFD solution and mesh adjustment until the yþ criteria is satisfied [21].
1.7.4 MODEL SIMPLIFICATION Large-scale simulations have the potential to be very grid point demanding and can therefore take a large amount of computing time and effort to obtain a detailed field solution. CFD modelers in the food industry have simplified computational models to cut down on both preprocessing and solving time. For example, three-dimensional systems have been modeled in two-dimensions [90], and large-scale models have been reduced in size by modeling only the region of interest [27]. In the physical world, all objects occupy a three dimensional space. Thus to accurately predict the phenomena occurring in any system, each dimension must be represented in a model. This is where CFD has an advantage over many other analytical techniques. However, some applications in the food industry are on such a large scale that modern workstations are not yet capable of efficiently yielding feasible CFD predictions [15]. Moreover, in other applications, such as refrigerated display cases, the interesting features of flow phenomena are not occurring in three dimensions [90]. The two-dimensional modeling technique assumes that the length of a system is much greater than its other two dimensions, and that the flow is normal to the systems length. This assumption essentially disregards the effects of the confining geometry and will therefore hamper the development of an accurate solution, unless it can be explicitly shown through experiments that three-dimensional flows do not impose any effects on the modeled system. Other assumptions used in the literature include those involved when modeling the region of interest of large systems, i.e., refrigeration display cabinets [27], and those used when integrating CFD computations with analytical models and experimental data in optimization of system design, i.e., food chillers [120]. Although these novel techniques may yield predictions in reasonably short time periods, the errors associated with the assumptions may preclude the development of accurate solutions [120]. Precise predictions of the phenomena in large-scale systems may not be achievable until the capacity and calculation power of workstations are developed further. Nevertheless, reasonable solutions can be presently attained provided good modeling practices are enforced including circumspective selections of turbulence model and near-wall treatment, convection scheme, and time-step. The heat and mass transfer must also be taken into account, especially when it is conceived that these processes may influence the flow regime. Additionally, concurrent validation of predictions with experimental measurements is paramount for the future success of simplified CFD modeling.
1.7.5 UNEVEN MESHING To achieve a good level of accuracy one must ensure that the mesh is appropriately refined in areas of interest and in regions where gradients occur in the flow field. Unstructured meshing
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features generally overcome difficulties associated with mesh refinement. Yet, problems can still arise, and even in recent studies the mesh has precluded the use of high-order convection schemes and high-quality turbulence models [33]. In some cases these difficulties are unavoidable, but in many others the problematic regions of the mesh can be diagnosed and repaired. Accurate representations of convective and diffusive fluxes require cells with high aspect ratios or highly skewed cells to be removed from the simulation. Some CFD packages offer means of locating these cells. However, in many cases the CFD modelers often resort to using their experience with a CFD software package to assert the quality of the mesh.
1.7.6 TIME-STEP SELECTION Many of the flow regimes encountered in the food industry are unsteady. Transient processes arise as a result of either moving boundaries, e.g., impeller blades in stirred tanks; unsteady boundary conditions, e.g., variable flow fans; or inherent physical instabilities, e.g., vortex shedding behind obstacle in free-stream flow. In these cases, a steady-state flow regime does not exist and numerical difficulties are often encountered when trying to solve the steady governing equations [29]. Time stepping is an important mechanism that allows a CFD solution to march forward in time. An optimum time-step can be considered as a trade-off between computational efficiency, temporal accuracy, and stability of the employed numerical scheme. Explicit numerical schemes generally require time-steps that are less than or equal to the CFL (Courant–Friedrichs–Lewy) condition in order to retain stability [121]. To uphold this criterion time-steps usually must be very small. Consequently, the computational overhead associated with explicit schemes has impeded their use in industry. The maximum time-step selection of implicit schemes is bounded by the accuracy requirements of the simulation. Therefore, the time-step must be small enough to resolve the frequencies of importance=interinterest in the unsteady phenomenon being modeled. Generally, an appropriate characteristic length and velocity of the problem is necessary to determine the dominant frequency of the flow regime. Sometimes this can be obtained from nondimensional numbers such as the Stroudal number, from experimental data, or from previous computations. An assumption of this frequency does not have to be precise in the first instance, as it can be refined in subsequent computations depending on the desired level of accuracy and what is demanded of the simulation. Using this technique should result in a small number of outer-iterations required to converge each time-step, which has been shown to be the most accurate way of simulating transient flows [122].
1.8 OPPORTUNITIES FOR FOOD INDUSTRY AND BENEFITS FOR CONSUMER 1.8.1 SOFTWARE PRICING The efficacy of modern workstations has been progressing incessantly over the last two decades. This has meant that complex mesh-demanding solutions can now be obtained at the workplace both cost effectively and without recourse to specialized consultancy firms. For example, in a CFD review conducted by Scott and Richardson [123] about a decade ago, price levels for both CFD and a workstation were around e60,000 to e70,000, whereas today e25,000 to e30,000 should be sufficient to purchase a high-end workstation and CFD software for a commercial company with academic prices ranging from 20% to 50% of this cost. Also, the typical processing speeds in workstations today range from 2 to 3.8 GHz with RAM capacities of 1–4 GB. Thus, with this amount of computing power available at
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reasonable prices, CFD studies will become more prevalent in developing cost-effective design solutions for the food industry.
1.8.2 PROCESSING SYSTEM DESIGN Enhancing the design of systems for the production of food products has benefits for both the food industry and consumer alike, and requires research and development of new tools and processing methodologies. Besides the expansion of the food industry, energy and workforce costs are growing rapidly. Consequently, the impetus in recent research has been directed toward the development of processing systems that can integrate multiple operations, which, depending on the requirements of the system, allow the coupling and uncoupling of elementary processes [124]. For example, the development of food powders requires both the drying and transport of ingredients. The governing dynamics in such systems include coupled heat and mass transfer and require in-depth knowledge for optimization and development. CFD modeling can be seen as the next progressive step from expensive laboratory studies and can account for the complex geometries experienced in industry to predict the governing phenomena of the processing system in an unobtrusive manner. As a result of CFD modeling, processing systems have been reduced in size and optimized to become more energy efficient. CFD can then create a climate in which both the industry and consumer can benefit, and food products can be developed with better equipment performance, less pollution impact, faster time to market, and lower design and production costs.
1.8.3 PRODUCT QUALITY Food quality is a critical issue in the food industry. The importance of food quality has heightened over recent years in tandem with the lifestyle changes experienced by many people. Sterilization and hygiene protocols have thus become paramount, and thrust has been toward maintaining high-quality food products from factory to fork. In sterilization applications, CFD modeling has helped to alleviate the difficulties in relating heat transfer in food products to sterility levels and loss of both sensory and nutritional quality. CFD has also changed the way of thinking in the operation of conventional sterilization practices. For example, CFD has proven the high-temperature short-time (HTST) approximation to be invalid under some operating conditions [67]. In addition, CFD has shown the efficacy of the sterilization process to be a function of both food properties and container geometry. Therefore, CFD can assist the understanding of the physical mechanisms that govern the thermal, physical, and rheological properties of foods and benefit the food industry by enhancing confidence and efficiency in sterilization processes [50]. The transport of airborne microbes is significant in high-care food factories and CFD simulations have been used effectively to devise strategies that minimize the movement of contaminated air toward food products [70]. Further advances in physical modeling techniques will allow the dynamic mapping of the airborne particle trajectories to be predicted before implementing cleaning strategies [116].
1.9 CONCLUSIONS The objective of this chapter is to shed light on not only the recent intricacies of fluid flow expounded by leading academics but also the remunerative advantages that CFD can offer in a commercial setting. The literature abounds with captivating and compelling CFD applications in this incessantly expanding industry. CFD has played an active part in system design including refrigeration, sterilization, ventilation, mixing, and drying. This has been aided by
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the ability of commercial companies to conform to the needs of the industry. The recent developments in CFD include greater refinement in areas of adaptive meshing, moving reference frames, and solver efficiency. Physical modeling has also reached higher levels of sophistication with the development of new models and validated by numerous experts and subsequently employed in the chemical and food engineering industry. Notwithstanding this, the CFD modeler must maintain high level of accuracy during the modeling process to uphold confidence of CFD predictions. This means that concurrent experimentation must be carried out to validate predictions, particularly where simplifying assumptions are incorporated into the model. Undoubtedly, with current computing power progressing unrelentingly, it is conceivable that CFD will continue to provide explanations for more fluid flow, heat and mass transfer phenomena, leading to better equipment design and process control for the food industry.
NOMENCLATURE u t g Ca x sT P T R Wa fi k CF K n
velocity component (m s1) time (s) acceleration due to gravity (m s2) specific heat capacity (W kg1 K1) Cartesian coordinates (m) thermal sink or source (W m3) pressure (Pa) temperature (K) gas constant (J kmol1 K1) molecular weight of air (kg kmol1) momentum source (N m3) turbulent kinetic energy (m2 s2) Forchheimer drag coefficient (m1) Darcy permeability (m2) power-law index
GREEK LETTERS r m d b l s « g_ u
density (kg m3) dynamic viscosity (kg m1 s1) Kroneckor delta thermal expansion coefficient (K1) thermal conductivity (W m1 K1) Prandtl number for enthalpy turbulent dissipation rate (m2 s3) shear rate (s1) local mean age of air (s)
SUBSCRIPTS i, j ref turb lam
Cartesian coordinate index reference turbulent laminar
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93. S. Lee, S.J. Baek, M.K. Chung, D.I. Rhee, A. Kaga, and Y. Katsuhito. Study of airflow characteristics in the refrigerator using PIV and computational simulation. Journal of Flow Visualization and Image Processing 6: 333–342, 1999. 94. K. Fukuyo, T. Tanaami, and H. Ashida. Thermal uniformity and rapid cooling inside refrigerators. International Journal of Refrigeration 26: 249–255, 2003. 95. Y. Bartosiewicz, Z. Aidoun, P. Desevaux, and Y. Mercadier. Numerical and experimental investigations on supersonic ejectors. International Journal of Heat and Fluid Flow 26: 56–70, 2005. 96. S.J. Wang, S. Devahastin, and A.S. Mujumdar. Effect of temperature difference on flow and mixing characteristics of laminar confined opposing jets. Applied Thermal Engineering 26: 519– 529, 2006. 97. T.J. Rennie and V.G.S. Raghavan. Numerical studies of a double-pipe helical heat exchanger. Applied Thermal Engineering 26(11–12): 1266–1273, 2006. 98. A.M. Foster and G.L. Quarini. Using advanced modeling techniques to reduce cold spillage from retail display cabinets into supermarket stores to maintain costumer comfort. Proceedings of the I MECH E Part E, Journal of Process Mechanical Engineering 215: 29–38, 2001. 99. J. Tattiyakul, M.A. Rao, and A.K. Datta. Simulation of heat transfer to a canned corn starch dispersion subjected to axial rotation. Chemical Engineering and Processing 40: 391–399, 2001. 100. S. Siriwattanayotin, T. Yoovidhya, T. Meepadung, and W. Ruenglertpanyakul. Simulation of sterilization of canned liquid food using sucrose degradation as an indicator. Journal of Food Engineering 73: 307–312, 2006. 101. A.G. Abdul Ghani, M.M. Farid, X.D. Chen, and P. Richards. An investigation of deactivation of bacteria in a canned liquid food during sterilization using computational fluid dynamics (CFD). Journal of Food Engineering 42: 207–214, 1999. 102. J. Tattiyakul, M.A. Rao, and A.K. Datta. Heat transfer to a canned corn starch dispersion under intermittent agitation. Journal of Food Engineering 54: 321–329, 2002. 103. M.N. Varma and A. Kannan. Enhanced food sterilization through inclination of the container walls and geometry modifications. International Journal of Heat and Mass Transfer 48: 3753–3762, 2005. 104. M.N. Varma and A. Kannan. CFD studies on natural convective heating of canned food in conical and cylindrical containers. Journal of Food Engineering 77(4): 1027–1036, 2006. 105. H.S. Song and S.P. Han. A general correlation for pressure drop in a kenics static mixer. Chemical Engineering Science 60: 5696–5704, 2005. 106. V.V. Ranade, J.B. Joshi, and A.G. Marathe. Flow generated by pitched blade turbines II: simulation using k–« model. Chemical Engineering Communications 81: 225–248, 1989. 107. A.W. Nienow. On impeller circulation and mixing effectiveness in the turbulent flow regime. Chemical Engineering Science 52: 2557–2565, 1997. 108. E. Fourcade, R. Wadley, H.C.J. Hoefsloot, A. Green, and P.D. Iedema. CFD calculation of laminar striation thinning in static mixer reactors. Chemical Engineering Science 56(23): 6729– 6741, 2001. 109. R.S. Ghadge, A.W. Patwardhan, S.B. Sawant, and J.B. Joshi. Effect of flow pattern on cellulase deactivation in stirred tank bioreactors. Chemical Engineering Science 60: 1067–1083, 2005. 110. E. Mathioulakis, V.T. Karathanos, and V.G. Belessiotis. Simulation of air movement in a dryer by computational fluid dynamics: application for the drying of fruits. Journal of Food Engineering 36: 183–200, 1998. 111. J.J. Nijdam and T.A.G. Langrish. The effect of surface composition on the functional properties of milk powders. Journal of Food Engineering 77(4): 919–925, 2004. 112. J. Straatsma, G. Van Houwelingen, A.E. Steenbergen, and P. De Jong. Spray drying of food products: 1. Simulation model. Journal of Food Engineering 42: 67–72, 1999. 113. L.X. Huang, K. Kumar, and A.S. Mujumdar. A parametric study of the gas flow patterns and drying performance of cocurrent spray dryer: results of a computational fluid dynamics study. Drying Technology 21: 957–978, 2003. 114. J.J. Nijdam, B. Guo, D.F. Fletcher, and T.A.G. Langrish, Challenges of simulating droplet coalescence within a spray. Drying Technology 22: 1463–1488, 2004.
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115. D.F. Fletcher, B. Guo, D.J.E. Harvie, T.A.G. Langrish, J.J. Nijdam, and J. Williams. What is important in the simulation of spray dryer performance and how do current CFD models perform? Applied Mathematical Modeling 30(11): 1281–1292, 2006. 116. B. Harral and D. Burfoot. A comparison of two models for predicting the movements of airborne particles from cleaning operations. Journal of Food Engineering 69: 443–451, 2005. 117. F. Bertrand, L.A. Leclaire, and G. Levecque. DEM-based models for mixing of granular materials. Chemical Engineering Science 60: 2517–2531, 2005. 118. J.J. Fitzpatrick and L. Ahrne. Food powder handling properties: industry problems, knowledge barriers, and research opportunities. Chemical Engineering and Processing 44: 209–214, 2005. 119. Anonymous. ANSYS CFX release 10.0 technical specifications. Public notice, ANSYS Inc., Southpointe, Canonburg, PA, 2006. 120. P.S. Mirade, A. Kondjoyan, and J.D. Daudin. Three-dimensional CFD calculations for designing large food-chillers. Computers and Electronics in Agriculture 34: 67–88, 2002. 121. R. Courant, K. Friedrichs, and H. Lewy. Die partiellen differenzengleichungen der mathematischen physik. Mathematische Annalen (Historical Archive) 100: 32–74, 1928. 122. Y. Liu, A. Moser, D. Gubler, and A. Schaelin. Influence of time step length and subiteration number on the convergence behavior and numerical accuracy for transient CFD. In: Proceedings of the 11th Annual Conference of the CFD Society of Canada, Vancouver, 2003, pp. 480–485. 123. G. Scott and P. Richardson. The application of computational fluid dynamics in the food industry. Trends in Food Science and Technology 8: 119–124, 1997. 124. J.C. Charpentier. The triplet ‘‘molecular processes–product–process’’ engineering: the future of chemical engineering? Chemical Engineering Science 67: 4667–4690, 2002.
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets Jean Moureh
CONTENTS 2.1 2.2 2.3 2.4 2.5
2.6
2.7
Introduction ................................................................................................................ Refrigerated Truck...................................................................................................... Numerical Modeling ................................................................................................... Turbulence Models ..................................................................................................... Experimental Device ................................................................................................... 2.5.1 Empty Configuration....................................................................................... 2.5.2 Impermeable Pallets Configuration ................................................................. 2.5.3 Slotted Pallets Configuration........................................................................... Modeling Approach .................................................................................................... 2.6.1 Governing Equations....................................................................................... 2.6.2 Boundary Conditions ...................................................................................... 2.6.3 Numerical Resolution...................................................................................... 2.6.3.1 Modeling the Pallets’ Interstices ........................................................ 2.6.3.2 Modeling the Slotted Wall................................................................. 2.6.3.3 Analysis of Ventilation Efficiency ..................................................... Results and Discussion ............................................................................................... 2.7.1 General Description of the Flow-Field Related to Empty and Loaded Configurations ................................................................................................. 2.7.1.1 Turbulence Behavior ......................................................................... 2.7.1.2 Airflow Rate Evolution through the Truck....................................... 2.7.2 Empty Truck Case ........................................................................................... 2.7.3 Loaded Configuration with Impermeable Pallets ............................................ 2.7.3.1 Airflow Behavior and Velocity Characteristics above the Pallets...... 2.7.3.2 Influence of Airspace Thickness between Wall and Pallets ............... 2.7.3.3 Influence of the Air Duct on Airflow and Temperature Distribution ....................................................................................... 2.7.4 Loaded Configuration with Slotted Pallets ..................................................... 2.7.4.1 Jet Characteristics.............................................................................. 2.7.4.2 Comparing with the Case of Empty Truck ....................................... 2.7.4.3 Comparing with the Case of Impermeable Pallets ............................
44 44 45 46 47 48 48 49 50 50 50 51 51 52 53 55 55 57 58 58 60 60 61 63 65 65 66 67
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2.7.4.4 2.7.4.5
Airflow Characteristics Inside the Pallets .......................................... Interactions between Flows Around and Inside Pallets at the Load Interface ......................................................................... 2.7.4.6 Ventilation Efficiency ........................................................................ 2.7.5 Turbulence Modeling Performance ................................................................. 2.7.5.1 Empty Truck ..................................................................................... 2.7.5.2 Slotted Pallets .................................................................................... 2.8 Conclusions................................................................................................................. Nomenclature ...................................................................................................................... References ...........................................................................................................................
70 71 73 74 74 75 78 79 80
2.1 INTRODUCTION This work is part of a research activity aiming to improve and to optimize air-distribution systems in refrigerated vehicles in order to decrease the temperature differences throughout the palletized cargos. This condition is essential to preserve the quality, safety, and shelf life of perishable products. The present study reports on the numerical and experimental characterization of airflow patterns within a semitrailer. In addition to the empty configuration, two loaded configurations consisting of two rows of impermeable and slotted, but empty pallets, were studied. The experiments were carried out on a reduced-scale (1:3.3) model of a refrigerated-vehicle trailer equipped with a laser Doppler anemometer under isothermal conditions. The numerical modeling of airflow was performed using the computational fluid dynamics (CFD) code Fluent. Two levels of turbulence modeling are performed: the standard k–« and a second-moment closure with the Reynolds stress model (RSM). Comparisons with experimental data obtained allow a critical evaluation of the performance of these models in internal flows. Only the results obtained using the RSM model showed good agreement with the experimental data. Numerical and experimental results make it possible to highlight the confinement effect due to enclosure and the influence of load characteristics on the jet penetration, its development, and hence the overall heterogeneity of ventilation within the truck. In the case of slotted pallets (SPs), results also allow the characterization of airflow patterns around and inside the load, and the analysis of their dynamic interactions.
2.2 REFRIGERATED TRUCK During transportation using refrigerated vehicles, this being an important link in the cold chain, maintaining regular temperature throughout the cargo is essential to preserve quality, safety, and shelf life of perishable foods. In the refrigerated enclosure, heat is transferred primarily by convection; therefore, temperature and its homogeneity are directly governed by the patterns of airflow. Air renewal provided by these airflows should compensate the heat fluxes exchanged through the insulated walls or generated by the products. This process is essential in order to decrease temperature differences throughout the cargo. Within the refrigerated-vehicle enclosure, the air is supplied at relatively high velocities through a small inlet section located adjacent to or near the ceiling. Due to the adherence of the jet on this boundary by the Coanda effect, this design should allow the confined jet to expand while following the room wall surfaces and hence provide a high degree of ventilation throughout the entire enclosure. From an aerodynamic perspective, the key characteristic of transport equipment is the placement of both the air delivery and the return on the same face. This configuration is
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almost universally used as it is practical to place all the refrigerating equipment at one end of the transport unit. The drawback of this asymmetrical design is the presence of a strong pathway between the two sections, implying high velocities in the front of the refrigerated enclosure. In addition, the compactness of the cargo and high resistance to airflow due to narrow airspaces between pallets result in an uneven air distribution in the cargo where stagnant zones with poor ventilation can be observed in the rear part of the vehicle. In these zones, higher temperatures can occur locally within the load [1–5] even though the refrigerating capacity is higher than heat fluxes exchanged by the walls and the products [6]. With an increasing emphasis on the power consumption of refrigeration systems, and an increasing awareness of temperature heterogeneity and its implications for food safety, characterizing and developing effective air-distribution systems will continue to be an important area of research in food refrigeration. Because of the complexity of direct measurement of local air velocities within a refrigerated truck, CFD has become the methodology of choice for the development of airflow models.
2.3 NUMERICAL MODELING Numerical predictions of air velocities and temperature distributions can be obtained by solving sets of differential equations of mass, momentum, and energy written in their conservative form using the finite-volume method. To ensure the accuracy and reliability of CFD simulations, predictions need to be validated against reliable measurements obtained in parametric studies where the influence of all pertinent parameters is investigated separately. In the case of complex 3D systems, comparisons of local velocities and comparisons of global airflow patterns are required. Nonintrusive techniques for velocity measurements such as the laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) provide more reliable data for validation. These measurement technologies also provide a means to improve the reliability of simulations through the imposition of more accurate boundary conditions. Using CFD codes, computers, and processing facilities, complex configurations such as refrigerated transport or storage have been studied by many authors [11–20]. Moureh and Flick [15,16] tested numerous grids and turbulence models to numerically investigate the airflow behavior within an empty enclosure as a function of inlet flow arrangement. The computations were carried out in 3D using Fluent. The governing equations were solved using the finite-volume method in a staggered grid system. The author used the quick scheme, based on the three-point upstream-weighted quadratic interpolation rather than linear interpolation between consecutive grid points. The principal advantage of using the quick scheme is to reduce the number of cells required to yield a grid-independent solution, in comparison to a lower-order scheme. Moureh et al. [17] used Fluent with the Reynolds stress turbulence model (RSM) to predict the airflow pattern within a 3D configuration of a typical refrigerated vehicle loaded with two rows of pallets. The numerical results were validated by experimental measurements of velocity and turbulence obtained using LDV on a 1:3.3 scale model of a trailer under isothermal conditions. The results of this study demonstrated the ability of the RSM to predict the global behavior of the airflow in the highly turbulent wall jet zone and in the narrow air spacings around the pallets. It also provided improved understanding of the mechanisms governing the stability of the confined wall jet on the ceiling and its point of separation. Moureh and Flick [18] used the numerical approach developed previously [17] to characterize the influence of an air-duct system and the narrow airspace separation (1–2 cm) between the pallets and the walls in terms of the ventilation homogeneity throughout the enclosure. The findings underlined the importance of these airspaces, in achieving sufficient
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ventilation around the pallets, to remove infiltration heat and thereby reduce temperature variability. This result agrees with Nordtvedt [19] who also recommended maintaining these airspaces to achieve these outcomes. Tapsoba et al. [20] also used Fluent with the RSM turbulence model to predict the 3D airflow pattern within a refrigerated vehicle, with and without an air-duct system, loaded with two rows of SPs. The Ergun relation was used to express the pressure loss within the pallets. The experimental device was the same as that used previously [18]. The results showed substantial ventilation heterogeneity inside pallets without the air duct, with the rearmost pallet 40 times less ventilated than the fifth pallet. This ratio was reduced to 25 and 8 where the length of the duct was 33% and 66% of the length of the vehicle, respectively. Lindqvist [7,8] used the commercial CFD code Kameleon (SINTEF, Trondheim, Norway) to predict the pressure and velocity distribution in a typical reefer hold filled with pallets in 3D. The aim was to analyze the influence of numerous arrangement factors on the air distribution within the hold. Validation was performed using pressure measurements taken inside a full-scale laboratory model of a section of a reefer hold loaded with pallets. Comparison of predicted and measured pressures showed substantial disagreement. Overall, the air distribution was uneven and thus insufficient for a large number of pallets.
2.4 TURBULENCE MODELS According to the complexity of the airflow in a room, rigorous validation for numerical models is needed before they can be applied to wide ranging air-distribution problems. This validation concerns primarily the choice of turbulence model, for which it is necessary to investigate performance by comparing numerical predictions with experimental data. The selection of the appropriate turbulence model strongly depends on the complexity of the flow. To illustrate the complexity of this selection, this section provides a critical discussion of turbulence models generally used for confined flows encountered in a refrigerated truck. The turbulent wall jet (even with an isothermal co-flowing or stationary external stream) is known to be a difficult flow to predict [21]. An undeniable difficulty arises through the confinement effect induced by wall boundaries, and increased by the compactness of the load, which in turn implies the formation of an adverse pressure gradient along the jet axis. The resulting flow is complicated since it is often the combination of free turbulent shear flows, near-wall effect, and recirculation areas (including high streamline curvature and probably local separation). In addition, the complexity of the system is increased by the presence of the load, which increases the confinement effect and the adverse pressure gradient. Pallets and boxes affect the airflow through surface stresses, porous infiltration, deviations and reattachment, and also turbulence generation. They may create secondary recirculating flows, including stagnant zones, and induce high velocities elsewhere. To predict the turbulent airflow patterns and temperature distribution in such configurations, many authors [7–9,12,13,22–29] have used the Reynolds averaged equations, employing the standard k–« model described by Launder and Spalding [30], since it is easy to program and has broad applicability. However, in the major cases the validation of the turbulence model lacks comparisons with accurate experimental data concerning airflow patterns, especially in 3D cases. According to the complexity of the indoor flows underlined above, different authors [31–35] agree on the inadequacy of the k–« model to predict airflow patterns and underline its limitation by comparison with experimental data. According to Wilcox [31] and Menter [32], the k–« model predicts significantly too high shear–stress levels and thereby delays or completely prevents separation. According to Launder [34], this trend can be more pronounced in the presence of adverse pressure gradient and leads to overprediction of the
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wall shear stress. Aude et al. [35] pointed out the difficulty in accurately predicting the airflow characteristics concerning the velocity levels, the turbulent kinetic energy, its dissipation rate, and the turbulent viscosity in the stagnant regions with the k–« model. In this case, improving predictions can be achieved by taking into account the effect of the turbulence anisotropy by using more advanced turbulence models, such as those based on the second-moment closure, or large eddy simulation. Many authors have reported that the Coanda effect (governing the attachment of the jet on the ceiling) was not well predicted by the k–« model. Moureh and Flick [15,16] observed that the standard k–« model overestimated the Coanda effect of the wall jet and failed to predict its separation under adverse pressure gradient. Verboven et al. [27] pointed out the limitation of this model with respect to the air jet above pallets and near walls in a coolstore. Nady et al. [29] also underlined the inability of the k–« model to predict the detachment of the jet from the ceiling as observed experimentally under nonisothermal conditions. To improve numerical predictions in a ventilated enclosure with a strong Coanda-effect influence, Choi et al. [22] suggested modifying the multiplier coefficient (Cm ¼ 0.09) of the turbulent viscosity given by the standard k–« model. The author recommended Cm ¼ 0.12 or 0.15 if the inlet is near or far from the ceiling, respectively. However, the fact that this modified model cannot be universally applied will discourage further use without comparative experimental data. Although CFD continues to be the modeling methodology most frequently employed for airflow prediction in refrigerated food applications, network models provide an alternative approach for transport systems. Several modeling approaches using electrical analogies to predict the airflow rate in spacing or channels between pallets or boxes were developed [10,36–38]. These approaches could give qualitative information on the air circulation rate and do not require much time or memory capacity. However, these simplified modeling approaches were not able to provide quantitative predictions of airflow patterns, local air velocities, and turbulence levels, which are important in heat transfer phenomena. In addition, predictions cannot take into account the behavior, the stability, and the diffusion of the supplied forced air jet.
2.5 EXPERIMENTAL DEVICE According to the complexity of direct measurement of local air velocities in the truck, the experiments were carried out on a scale model of a trailer built with a length scale ratio of 1=3.325 with respect to the adimensional Reynolds number (Re ¼ rW0DH=m). Airflow inlet and outlet were located in the front face of the parallelepiped as shown in Figure 2.1 where the full-scale geometry is represented. All dimensions and results in this paper are given in connection with the full-scale geometry using the Reynolds analogy. The walls of the scale model were composed of wood except one side constructed of glass to allow internal air velocity measurement using 1D LDV system (Laservec) manufactured by TSI. The LDV consists of an LDP-100 probe and the raw data are processed by an IFA 600 signal processor. This system does not interfere with the flow and is able to correctly resolve the sign as well as the magnitude of velocity and to determine mean velocity and its fluctuation. It comprised a 50 mW laser diode emitting a visible red beam at 690 nm wavelength, a beam splitter, a Bragg (acousto-optic) cell, a focusing and receiving lens to collect scattered light from the measurement point, and a photomultiplier. Since the basic input to the processor is a frequency, this permits a very wide potential range of velocities from millimetre per second to over 1000 m s1. The accuracy is considered to be less than 1%. The air supplied to the model was seeded with atomized oil particles of 4 mm mean diameter that scatters light as the flow carries them through the measurement volume. The probe was carried on an automatic displacement system that provides a resolution of +0.5 mm in three directions.
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y
AA
z x L = 13.3
D = 0.0 or 0.18
0.14
Inlet 1 Walls H = 2.5 BB
0.18 0.15 1.22
Outflow Wd = 2.46
FIGURE 2.1 Dimensions of the truck enclosure (m).
The scale model was supplied with air from a fan, which can go up to 5800 m3=h. The airflow was introduced in the enclosure perpendicular to the front face with a mean velocity of U0 ¼ 11.5 m s1, i.e., a Reynolds number of 1.9 105. The two inlet arrangements studied were the ceiling-slotted case (D ¼ 0, D is the distance of the jet inlet slot below the ceiling) and the downward displace slot case (D ¼ 0.18 m). Excepting the Coanda effect at the ceiling level, these two cases lead to similar results. Unless otherwise stated, D ¼ 0 was considered. Three configurations were investigated, which are discussed below.
2.5.1 EMPTY CONFIGURATION According to the complexity of factors affecting the homogeneity of ventilation, it is of great interest, as a first step, to study the case of an empty semitrailer container not loaded with pallets. The comparison between the loaded and unloaded configurations allows to better understand and to quantify separately the influence of the geometrical factors related to the enclosure (L=H > 5) and to the presence of inlet and outlet sections on the same side, from those related to the load: stowing patterns, pallet dimensions and porosity, and spaces between pallets.
2.5.2 IMPERMEABLE PALLETS CONFIGURATION Impermeable pallets (IPs) represent the case of frozen foods and they are considered as obstacles. Inside the scale model, closed glass boxes are used to represent pallets. The loaded configuration consists of two rows of 16 pallets. The dimensions of this device, expressed using the actual scale are represented in Figure 2.2. This configuration was investigated in two cases: Without air ducts. The whole airflow rate is blown at the front of the truck. In this case, two airspaces distances between pallets and walls are considered: the reference case with e ¼ 2 cm and e ¼ 1 cm. With air ducts. The airflow rate was blown on three positions: z ¼ 0 (front), z ¼ L=3, and z ¼ 3L=4 with 35%, 50%, and 15% as flow rate repartition, respectively (Figure 2.3).
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Shift-slotted case: D = 0.18
Ceiling-slotted case: D = 0 Jet axis
y 1.7 z 0.02
0.1
0.8
Wood blocks
(a) 0.02 x
1.2
0.02 z 0.02
(b)
0.1
0.1
FIGURE 2.2 Configuration of the load in the enclosure. (a) Side view of the load (section AA of Figure 2.1) and (b) top view of the load (section BB of Figure 2.1).
2.5.3 SLOTTED PALLETS CONFIGURATION Porous pallets represent the case of fresh products where bulk ventilation is needed to evacuate heat fluxes and gas concentration generated by the products. Given the difficulties concerning direct air velocity measurements inside filled pallets, this study will consider the case of slotted but empty pallets. This allows obtaining reliable velocity measurements with the LDV system within SPs and therefore to validate the numerical model within these enclosed pallets. This configuration also allows studying airflow around and inside pallets and to analyze their dynamic interactions. The enclosure was loaded with two rows of 32 polystyrene SPs of size 1.7 0.8 1.2 m as shown in Figure 2.2. The slots were spread out over the six faces of each box and allowed air to go through 15% of the surface (Figure 2.4). The pallets were set resting on wooden blocks of dimension 0.1 0.1 0.1 m, allowing air circulation under them. Small gaps of 0.02 m were maintained between the pallets.
35%
50%
15%
FIGURE 2.3 Schematization of air ducts and airflow distribution in the truck.
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FIGURE 2.4 Photograph of a SP.
To allow velocimetry measurements within the load, one box had been equipped with a slotted Plexiglas wall. This box was displaced in the enclosure to investigate each position.
2.6 MODELING APPROACH 2.6.1 GOVERNING EQUATIONS The time-averaged Navier–Stokes differential equations for steady, high-Reynolds numbers, and incompressible flows expressed in their conservative form for mass and momentum conservation were solved by a finite-volume method using the Fluent solver. Turbulence was predicted with the standard k–« turbulence model and RSM, which is an advanced model for which an individual transport equation is derived for each shear-stress component. The RSM was used as the default turbulence model.
2.6.2 BOUNDARY CONDITIONS The computational domain may be surrounded by inflow and outflow boundaries in addition to symmetry and solid walls. At the inlet, uniform distribution is assumed for velocity components, kinetic energy of turbulence k0, and the energy dissipation rate «0. The numerical values are specified as .
(U ¼ V ¼ 0; W ¼ W0 ¼ 11.5 m s1 representing the mean longitudinal velocity, giving an inlet flow rate Q0 ¼ 5500 m3 h1,
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets .
.
.
51
pffiffiffiffiffiffi k0 ¼ 3=2 (U0I0z)2; where I0z ¼ 10% (I0z ¼ w2 =W0 ) represents the turbulence intensity of the z-component of velocity at the inlet as obtained from experiments, «0 ¼ (Cm0.75 k01.5=0.07DH) where DH represents the hydraulic diameter of the inlet section, and For the RSM model, turbulence is assumed to be isotropic: ui uj ¼ 2=3 k0 dij .
According to these conditions, the Reynolds number is considered as being equal to 2 105 in experiments and numerical simulations. At the outflow, pressure is supposed to be uniform and zero gradient is applied for all transport variables. The turbulence models are only valid in fully turbulent regions. Close to the wall, where viscous effects become dominant, the model is used in conjunction with wall functions. For this study, the conventional equilibrium logarithmic law governing the wall is used [30]. At the symmetry plane, zero normal velocity and zero normal gradients of all variables are assigned. For thermal simulations, the following boundary coefficient conditions were assumed: . . . .
External temperature (Te): 308C. Blowing temperature (T0): 288C. Overall heat transfer through the insulating wall: 0.3 W m2 K1. The pallets are considered to be adiabatic. Only convective exchange between the truck wall and the air is taken into consideration.
2.6.3 NUMERICAL RESOLUTION The computations were carried out using Fluent, a commercial CFD code on a 3D configuration. The governing equations are solved using the finite-volume method in a staggered grid system. A nonuniform grid was implemented, with a high-density mesh in regions near the inlet, outlet, and walls where high gradients were expected. In these simulations, the quick scheme, based upon three-point upstream-weighted quadratic upstream interpolation was used instead of a linear interpolation between consecutive grid points [39]. The principal objective in using the quick scheme is to reduce the number of cells required to yield a grid-independent solution, in comparison to a lower-order scheme. In order to test the influence of the number of cells used in the solution, many grid sizes comprised between 240,000 and more 106 cells were used. However, simulations show for greater than 450,000 cells that the predicted values are grid-independent. Unless otherwise stated, the presented numerical data are grid-independent. 2.6.3.1 Modeling the Pallets’ Interstices As there was a big difference between pallet dimensions and the small gaps between them (Figure 2.2b), direct meshing of all these gaps would lead to very large grid size (exceeding the memory capacity) and a high computing time, especially if a gradual grid refinement is applied where the size ratio between two consecutive cells should not exceed 20%. To avoid this difficulty, we replaced thin airspaces between pallets along the vehicle by a fictitious, aerodynamically equivalent, porous medium for which the permeability coefficient was chosen so as to ensure the same airflow resistance as the actual medium. This approach was made possible because air velocity measurements showed that laminar flow was dominant between pallets (Re < 500) [11]. Consequently, there is a linear
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relationship between airflow rate and pressure gradient as in a porous medium governed by Darcy’s law. In the proposed method, the permeability coefficient for this fictitious porous medium was chosen in order to ensure that for a given pressure gradient, the same flow rate as for the actual medium is obtained. Consequently, the analogy between the laminar flow between two parallel plates separated by a distance e and a flow in a porous medium between two parallel plates separated by a distance e0 are related as follows:
0
(Umean e)actual medium ¼ (Umean e )porous medium )
Kp dp 0 dp e2 e e¼ dx 12m m dx
(2:1)
Thus the equivalent permeability is equal to Kp ¼
e3 12e0
(2:2)
The use of this analogy allows the reduction in grid size because airspaces separating pallets were represented by relatively large porous cells (e0 ¼ 0.06 m) with a permeability coefficient that was calculated from Equation 2.2. Figure 2.5 illustrates the effect of this analogy on grid refinement and consequently on grid size. 2.6.3.2
Modeling the Slotted Wall
Fluid flow was sensitive to the slotted wall effect by the means of the normal pressure jump through the wall, which is characterized by C1 the pressure loss coefficient: 1 DP ¼ C1 rU? 2 2
(2:3)
where DP is the total pressure drop and U? is the mean velocity normal to the wall. The pressure drop for a single slotted wall was measured and the coefficient C1 equals 80. Direct meshing
Palette n
Porous media analogy
Palette n + 1
e
Palette n
Pallet domain
Palette n + 1
e⬘
Porous media Grid Free zone
FIGURE 2.5 Analogy between laminar flow and porous medium flow on the grid refinement.
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2.6.3.3 Analysis of Ventilation Efficiency The overall ventilation efficiency is often characterized by the number of times the enclosure’s air volume is replaced during one time unit: t0 ¼
Inlet flow rate (m3 h1 ) Enclosure volume (m3 )
(2:4)
An extension of this concept is proposed here in order to characterize the local ventilation _ , flowing in and out of the volume efficiency of the pallets. Thus we analyze the flow rate m _ can be (Vp) of one pallet of surface S (Figure 2.6a) . According to numerical simulations, m computed by the following integration: _ out ¼ _ ¼m _ in ¼ m m
1 2
ð
~~ r U ndS
(2:5)
S
where ~ n is the unit normal vector of the elementary surface dS. For each pallet, a local ventilation efficiency can be written as t¼
_ 1 m r Vp
(2:6)
However, air flowing in the volume of a pallet is not only composed of fresh injected air at temperature T0 but also of heated air from the surrounding pallets (Figure 2.6b). If ventilation is used to extract heat that is generated in the enclosure, only the fresh
. m , Tin (mixed air entering the pallet) . m , Tout (a) . m eq, T0 (fresh air from the inlet)
. m , Tout . . Useless air, (m eq −m ) Tout (b)
FIGURE 2.6 Introducing the concept of equivalent fresh air renewal for one pallet. (a) Heat balance on the considered pallet and (b) heat balance with the concept of equivalent fresh air.
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injected air is efficient. In order to characterize the quantity of the fresh air part entering a pallet, a fictitious and uniform volumetric heat load per unit volume, q, is applied throughout the pallet domain. This simulates for example heat generation due to respiration of a load of fruit or vegetable. In steady state, the heat balance of a pallet can be expressed using bulk average air temperatures of the air flowing in and out, named Tin and Tout, respectively. _ Cp (Tout Tin ) U ¼ qVp ¼ m
(2:7)
Moreover, the incoming airflow can be considered as the mixing of a quantity of fresh air _ m _ eq) at temperature Tout _ eq at temperature T0 and a recirculating air flow rate (m named m (Figure 2.6b). Thus the heat balance can be rewritten: _ eq Cp (Tout T0 ) U ¼m
(2:8)
This means that, in terms of heat extraction capacity, the process gives rise to an equivalent _ eq entering the volume. The additional airflow part: m _ m _ eq flow rate of fresh injected air m flows in a circular manner and does not affect the heatÐ balance. From the simulations, the following quantity A ¼ S rj~ v ~ njTdS can be computed: A¼
ð
ð rj~ v ~ njT dSin þ rj~ v ~ njT dSout Sin Sout ð ð ¼ Tin rj~ v ~ nj dSin þ Tout rj~ v ~ nj dSout
rj~ v ~ njT dS ¼
S
ð
Sin
Sout
_ ¼ (Tin þ Tout )m
(2:9)
From Equation 2.7 and Equation 2.9, the temperatures Tin and Tout can be calculated and _ eq can be obtained from Equation 2.10: finally m U A Cp 1 U Aþ ¼ _ 2m Cp
1 Tin ¼ _ 2m Tout
_ eq ¼ m
U Cp (Tout T0 )
_ ¼m
(2:10) Tout Tin Tout T0
We can then define a local ventilation efficiency based on the equivalent fresh air renewal: t eq ¼
_ eq 1m r Vp
(2:11)
A heat load of 50 W m3 was applied in the simulations. Adiabatic boundary conditions were applied on the enclosure walls and free convection was not taken into account in order to point out only the effect of forced convection inside the enclosure. For these conditions, a dimensional analysis showed that t and teq are independent of the heat load.
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2.7 RESULTS AND DISCUSSION 2.7.1 GENERAL DESCRIPTION CONFIGURATIONS
OF THE
FLOW-FIELD RELATED
TO
EMPTY AND LOADED
Figure 2.7 presents a comparison between loaded and empty enclosures showing the behavior of the streamlines related to the mean flow-field in the symmetry plane. These streamlines are obtained from 1080 (24 45) measurement points made using the LDV system for empty and SPs and numerically for IPs. On the same plane, Figure 2.7 presents the velocity decay along the jet axis for the different studied cases.
Height (m) 2.5 2 1.5 1 0.5 0 0
2
4
6
8
10
12
14
Length (m) (a) y/H 1 0.90
0.44
0.22
0.07
0.02
8
10
0.01
Loaded with SPs, experimental 0 (b) Height (m) 2.5 2 1.5 1 0.5 0 0
2
4
6
12
14
Length (m) 11.5 m s−1
0 m s−1 Air velocity (m s−1) (c)
FIGURE 2.7 Influence of the load on the streamline behavior in the symmetry plane. (a) Empty configuration: experimental data (1080 LDV measurement points); (b) slotted configuration: experimental data (LDV measurement points); (c) loaded with IPs: numerical data with RSM model.
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For the empty configuration, Figure 2.7a clearly shows that the wall jet separates from the ceiling at approximately 8.5 m (z=L ¼ 65%). This separation splits the jet into two regions dominated by two vortices of opposite circulation. The primary recirculation located in the front part of the enclosure delimits the reach and the action of the inlet jet. Conversely, the secondary flow located in the rear part is poorly supplied by the primary jet. In addition, the velocities are very low. This type of airflow is highly undesirable because the stagnant zone aspect is related to the secondary recirculating area, where high levels of temperature and contaminant could be expected due to the poor mixing with the primary recirculating air. Concerning the IPs case (Figure 2.7c), the impermeability of the load increases the confinement effect, which in turn causes a more pronounced adverse pressure gradient. This limits the jet development and strongly affects its stability. As a consequence, the separation point is located more upstream at z=L ¼ 40% in the case of the loaded configuration instead of z=L ¼ 65% for the empty configuration. This trend was also confirmed on Figure 2.8 showing that the jet penetration decreased as the load permeability decreased.
1 Empty enclosure SPs IPs
0.8
W/ W0
0.6 0.4 0.2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z /L
−0.2 (a)
11 Exp.-empty truck Exp.-loaded truck Model-empty truck Model-loaded truck
W (m s−1)
9 7 5 3 1 −1 0
2
4
6 8 Length of the truck (m)
10
12
14
(b)
FIGURE 2.8 Decay of the jet velocity along the truck in empty and loaded configurations. (a) Experimental data, (b) empty and loaded with IPs. (continued)
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1 Experiment
W/ W0
0.8
RSM
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
z /L (c)
FIGURE 2.8 (continued) (c) Loaded with SPs.
In the case of SP (Figure 2.7b), the velocity tended asymptotically to zero but remained positive on the jet axis. The separation point is transformed to a stagnation point at z=L ¼ 0.5. This means that no recirculating pattern occurred in the symmetry plane. Another common characteristic of confined configuration concerns the apparition of an adverse pressure gradient preceding the stagnant zone [11,15]. 2.7.1.1 Turbulence Behavior Figure 2.9 shows comparisons between numerical and experimental data concerning the evolution of the mean-square of the turbulent velocity in the z direction (w2 ) through the inlet section along the enclosure in an empty configuration. Similar trend of w2 was obtained for loaded configurations (data not shown). As it can be seen on Figure 2.9, w2
4
RSM Experiment
3.5 3 2.5 2 1.5 1 0.5 0 0
2
4
6
8
10
12
14
Length of the enclosure (m)
FIGURE 2.9 Evolution of the mean-square of the longitudinal fluctuating velocity (w2 ) along the jet axis: comparison between experiment and numerical results.
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numerical and experimental data experience two peaks. The first peak is a common characteristic of turbulent jet expansion due to diffusion of the turbulence from the edge to the core of the jet. The second peak located near the separation area of the jet from the wall reflects the extra amount of turbulence generated in this region where high gradients of velocities were locally present. Even if the trend of numerical and experimental values is similar, the RSM seemed to overestimate the diffusive character of the turbulence. This could be explained by the complexity of the flow at the separation point where the wall shear stress vanishes and the logarithmic law of the wall is not valid. 2.7.1.2
Airflow Rate Evolution through the Truck
Figure 2.10 shows a comparison between empty and loaded configurations concerning the longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0), obtained using numerical data. For a given cross-section along the enclosure, the circulating flow rate Q(z) was calculated as follows: ð Q(z) ¼ 0:5 (2:12) jW j ds Sz
where Sz represents the cross-section considered at z coordinate and W represents the local velocity. This comparison also shows that the presence of pallets significantly increases the confinement effect and reduces the development of the jet and the entrainment phenomena with the surrounding ambience. Consequently, the evolution of dimensionless airflow rate (Q(z)=Q0) in the loaded configuration is lower than in the empty configuration. According to Figure 2.10, the maximum values of (Q(z)=Q0) are 1.5 for loaded configuration and 3 for empty configuration and they are reached at 1 and 3.5 m, respectively. The following section discusses separately the main aspects related to the different configurations.
2.7.2 EMPTY TRUCK CASE Figure 2.11 and Figure 2.12 present velocity profiles in the symmetry and the inlet centered plane and turbulence profiles in the symmetry plane. 3 Model-loaded truck Model-empty truck
Q (z )/Q 0
2
1
0 0
2
4
6
8
10
12
14
Length of the truck (m)
FIGURE 2.10 Longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0) in empty and loaded configurations (IP).
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2.5
Height: y (m)
2.25 2 1.75
1m 2m 6m 9m
1.5 1.25 1 −2
0
2
4 W (m
6
8
10
s−1)
(a) 1.25
Width: x (m)
1.00
0.05 m
0.5 m
1m
2m
5.5 m
6.5 m
7.5 m
8m
12 m
0.75
0.50
0.25
0.00 −1
0
1
3
5
7
9
11
13
−1)
W (m s (b)
FIGURE 2.11 Experimental longitudinal velocity component (W ). (a) Vertical profiles along the symmetry plane at 1, 2, 6, and 9 m and (b) horizontal profiles in the inlet centered at 0.05, 0.5, 1, 2, 5.5, 6.5, 7.5, 8, and 12 m.
Just after the inlet, the jet attached to the ceiling by Coanda effect and flowed along it until its separation while entraining the surrounding fluid. Between the inlet (z ¼ 0) and up to z ¼ 4 m, the airflow rate increased (Figure 2.10) and the jet decay is similar to an unbounded 2D wall jet [16]. The confinement effect due respectively to the interaction with the lateral enclosure wall and with the reverse flow (Figure 2.11) tends to reduce the entrainment of the jet with its surroundings and causes the stabilization of dimensionless airflow rate: Q(z)=Q0 (Figure 2.9). Owing to the airflow rate stabilization, the mixing process causes the velocity profile to flatten with distance (Figure 2.11) and in turn implies the decreasing of the total flux of
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2.5
Height: y (m)
2
1.5 2m 3m 4m 9m
1
0.5 0
0.5
1
1.5
2
2.5
3
3.5
Mean square of horizontal turbulent velocity: w 2 (m2 s−2)
FIGURE 2.12 Vertical profiles of the mean-square of the longitudinal fluctuating velocity (w2 ) along the symmetry plane.
momentum. This decay can only be compensated for by an adverse pressure gradient that causes the separation of the wall jet at 8.5 m. Consequently, a stagnant zone with low velocities and a quasiuniform pressure is present at the rear between the end wall and the zone of separation.
2.7.3 LOADED CONFIGURATION 2.7.3.1
WITH IMPERMEABLE
PALLETS
Airflow Behavior and Velocity Characteristics above the Pallets
In order to illustrate the overall behavior of the airflow above the pallets, experimental and numerical contours of velocity fields are presented and compared in Figure 2.13 in three cross-sections at L=4, L=2, and 3L=4 of the vehicle. Each figure is obtained with 90 experimental points. At L=4 (Figure 2.13a) velocity fields show that the wall jet moves along the ceiling, where it is maintained by the Coanda effect, and returns along the side walls and above the pallets. Near side walls velocities are very low. At L=2, in the middle of the vehicle (Figure 2.13b), located downstream of the separation of the wall jet, the behavior of the airflow is completely different. After its separation from the wall, the jet reattaches on the top of the pallets where velocities become positive. Simultaneously, the jet returns along the ceiling where the velocities are negative. At 3L=4 (Figure 2.13c), velocities are still positive above the pallets and negative on the ceiling where the returning airflow occupies the whole width. Figure 2.14 shows a comparison between numerical and experimental data concerning the w2 field values in a cross-section at L=4 above the pallets. High turbulence near the jet boundaries of the mixing area and low values for the returning flow under the jet and near the wall boundaries can be seen. Figure 2.15 shows numerical data concerning contours of air velocities and temperatures for the external planes of the truck. However, the predicted temperatures should be interpreted with caution because it cannot be verified experimentally on the isothermal reduced-scale model.
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Ceiling
Y
W (m s−1)
Top of pallets
X
−2.5 −1.1 Numerical results
2.8
1
Y
W (m s−1) −0.5 −0.3 Numerical results
4.9
3.8
X
0
−0.2 - 0
0.2
−0.4 - −0.2
2 – 4 m s−1 0 – 2 m s−1
0.1
0.3
m s−1
m s−1
−2 – 0 m s−1 0 - 0.2 m s-1
−4 – −2 ms−1
0.2 - 0.4 m s-1 Experimental results
Experimental results
(a)
(b)
Y
W (m s−1) −0.02
−0.01
X 0
0.01
0.02
Numerical results
−0.2 - 0.1 m s-1 -0.1 - 0 m s-1
0 - 0.1 m s-1 0.1 - 0.2 m s-1 Experimental results
(c)
FIGURE 2.13 (See color insert following page 142.) Velocity field above the loading at (a) L=4, (b) L=2, and (c) 3L=4: comparisons between numerical and experimental data.
2.7.3.2 Influence of Airspace Thickness between Wall and Pallets The thin airspace (ew ¼ 1 – 2 cm) located between the lateral wall and pallets (Figure 2.2) represents the most sensitive area in the load. As regards the low velocities between the wall and the pallets, heat fluxes exchanged through the insulated wall with the
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w2 (m 2 s −2)
0
0.1
1
2
3
4
(a) 3 − 4 m2 s−2 1 − 2 m2 s−2
2 − 3 m2 s−2
0 − 1 m2 s−2
(b)
FIGURE 2.14 (See color insert following page 142.) Contours of the mean-square of the turbulent velocity in the z direction (w2 ) above the loading at L=4. (a) Numerical values and (b) experimental values.
0
0.2
0.4
0.6
0.8
1
(a)
−10 −12 −13 −15 −16 −18 −19 −20 −22 −24 −25 −26 −28
(b)
FIGURE 2.15 (See color insert following page 142.) Numerical contours of velocity and temperature in the most sensitive planes of the truck: (a) velocity contours: W=W0, (b) contours of temperature (8C); T0 ¼ 288C; Te ¼ þ308C.
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Velocity magnitude (m s−1)
4 Exp.− e w = 1 cm Exp.− e w = 2 cm Model− e w = 1 cm Model− e w = 2 cm
3
2
1
0 0
5
10
15
Length of the truck (m)
FIGURE 2.16 Evolution of air velocity magnitude between the lateral wall and pallets at the medium level of pallets along the truck for e ¼ 1 and 2 cm.
surrounding atmosphere are difficult to remove in this space and high temperatures are expected locally. Figure 2.16 presents a comparison between numerical and experimental data concerning velocity magnitude at the medium level along the enclosure for two airspaces: 1 and 2 cm. This figure clearly shows that in these spaces the air velocity magnitudes are governed by the behavior of the air wall jets. Downstream from the separation of the jet, beyond 6 m from the inlet, the velocities are very low and close to zero. Conversely, high velocities correspond to the zone of primary recirculation. It is interesting to note that for ew ¼ 2 cm, velocities are overall higher than obtained with ew ¼ 1 cm. This underlines the importance of this separation to improve the ventilation efficiency in this area and thus reduce temperature levels. We also noted the qualitative good agreement between numerical and experimental data. 2.7.3.3 Influence of the Air Duct on Airflow and Temperature Distribution Figure 2.17 shows a comparison with and without the use of air ducts concerning (from numerical data given by the RSM model) the longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0), obtained by numerical data. This result clearly shows that ventilation of the rear of the truck is improved by the use of air ducts. In this area, the flow rate is increased from 100 to 1000 m3=h approximately. Conversely, it is reduced at the front of the truck. This reflects a better uniformity of the ventilation in the truck. Figure 2.18 presents a comparison between experimental and predicted values of air velocities at medium level between the wall and pallets with and without an air duct. These figures clearly show that in these spaces the air velocity magnitudes are governed by the behavior of the overall airflow rate. As observed in numerical and experimental results, the use of air ducts improves air circulation and its homogeneity along this sensitive plane. Most importantly, the occurrence of low velocities and a stagnant zone in the rear part of the truck is avoided. Air velocities here are maintained at around 1 m s1 instead of 0.1 m s1, as would have occurred without this device.
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2 1.75 With air ducts Without air ducts
1.5
Q (z)/Q 0
1.25 1 0.75 0.5 0.25 0 0
2
4
6 8 Length of the truck (m)
10
12
14
FIGURE 2.17 Longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0) with and without air ducts.
To evaluate the benefit of an air duct on temperature levels and their uniformity, Figure 2.19 presents a numerical comparison concerning the contours of air temperatures in this most sensitive plane with and without this device. As can be seen, when air ducts are used, the zones of higher temperature move from the rear of the truck to the middle position located between two air-duct nozzles where lower velocity is expected. The use of an air duct makes it possible to decrease the higher temperature (Tmax) from 168C to 208C. In addition, the dispersion of the air temperature, defined as (Tmax Tmin), decreases from 128C for a vehicle without air ducts to 88C for a vehicle with air ducts.
4 Model-with air ducts
Velocity magnitude (m s−1)
3.5
Model-without air ducts Exp.-without air ducts
3
Exp.-with air ducts 2.5 2 1.5 1 0.5 0 0
2
4
6 8 Length of the truck (m)
10
12
14
FIGURE 2.18 Evolution of air velocity magnitude between lateral wall and pallets on the medium level with and without air ducts.
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets
T (⬚C)
−28
−26
−24
−22
−20
−18
65
−16
(a)
(b)
FIGURE 2.19 (See color insert following page 142.) Numerical results concerning contours of isotemperatures in the most sensitive plane of the truck located between lateral wall and pallets with and without air ducts. (a) Without air duct and (b) with air duct.
2.7.4 LOADED CONFIGURATION
WITH
SLOTTED PALLETS
2.7.4.1 Jet Characteristics Figure 2.20 plots the downshifted case (D ¼ 0.18 m), the contour levels of longitudinal normalized velocity W=W0 in the symmetry plane, and in the inlet-centered horizontal plane, respectively. They lead to several conclusions on the general pattern of the jet. Due to the confinement effect, two lateral vortices structures were induced by the jet intrusion into the enclosure as can be seen in Figure 2.20b (negative values of W). These structures controlled the initial growth of the jet and limited its diffusion in the transverse direction. In the inlet region z=L 2 [0, 0.15], the jet attaches rapidly to the ceiling by the Coanda effect and the decay of the maximal velocity followed the characteristic decay of the theoretical 2D unbounded wall jet until z=L ¼ 0.2 [40]. In the intermediate region z=L 2 [0.15, 0.5], due to the confinement effect, the jet vanishes at z=L ¼ 0.5 approximately (Figure 2.8c) and attaches the top of pallets at row 8 and flows over it to the rear (Figure 2.23). In the rear region (z=L 2 [0.5, 1]), flow is weak; W velocity levels were less than 0.2 W0 (Figure 2.8 and Figure 2.20), from z=L > 0.7 these levels did not even exceed 5% of W0.
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0.2
0 0.
0.4
0.5
1 0.
0.9
0.80.6 9 . 0 0.7
0.3
1.0
Computational Fluid Dynamics in Food Processing
0.0
0.1
0.1
0.0
0.8
y /H
0.2 0
0.7
0.2
0.4
0.6
0.8
1 z /L
0.6
0.5
0.4 Vector reference: 1 (a)
Vector reference 0.6
−0.2 −0.1 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
1
0.4 -0.1 0 0 0. .7 8
0. 9
0
0.5 0.6
x /W d
0.2
0.1
Jet boundary
0.2
0.4
0.3
−0.2 −0.4 0
0.2
0.4
0.6
0.8
1
z/L (b)
FIGURE 2.20 Velocity contours above the SPs. (a) The symmetry plane and (b) inlet centered plane.
2.7.4.2
Comparing with the Case of Empty Truck
Figure 2.21 plots the contour of W=W0 on the inlet centered horizontal plane and shows a major difference in jet diffusion between the empty and the loaded case. In the empty enclosure there was a head-on flow moving forward and occupying the full width of the enclosure from z=L ¼ 0.1 to z=L ¼ 0.5. But in the SPs case, the geometrical confinement effect due to the presence of the load was reinforced dynamically by the two lateral vortices, which tended to reduce the jet diffusion and lead to a centered flow. As a consequence, the inlet decay of the jet (z=L 2 [0, 0.15]) in the empty case is higher than in the loaded case. For z=L 2 [0.15, 0.5] the tendency was inversed; the decay in the loaded case was higher than in the empty case. The load limited the entrainment flow and hence tended to decrease the velocity level on the jet axis.
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0.5
0.1
0
0.3
0.4
0.4
0.2
1 0.
0.3
0.8
0.2
0.9
0
0.5 0.6
(a)
0.1
0.1 0.2 0.3
0 0.7
0
0.2
0.2
0.4
0.6
0
0.8
1
0.5 −0.1 0
0.1
0
5
(b)
0.2
0.
0.8 7 0. 9
0.6
0.
0.2
0.4
0.3
0.4
0.6
0.8
1
FIGURE 2.21 Velocity contours W=W0 in the inlet centered plane. (a) Empty truck and (b) loaded truck (SP).
Another comparison concerning velocity profiles between the empty enclosure and the enclosure loaded with SP is shown in Figure 2.22. 2.7.4.3 Comparing with the Case of Impermeable Pallets To highlight the load porosity effect on the airflow pattern and the jet behavior, experimental longitudinal velocity concerning SPs and IPs is compared in Figure 2.23. These comparisons concern three cross-sections of the enclosure above the pallets: z=L ¼ 1=4, z=L ¼ 1=2, and z=L ¼ 3=4. Contours of W=Wmax are presented and Wmax is the maximum of jW j in each section. In the three sections, higher positive velocities were observed in the SPs case. In the first quarter, for example, the values of Wmax=W0 are 50% and 30% for SPs and IPs, respectively. This clearly indicates that the pallets’ porosity contributes to a better wall jet development along the enclosure by enabling the airflow entrainment through the load. In addition, the impermeability of the load (IPs case) tends to confine the return flow principally above the pallets where higher negative velocity values are observed in the IPs case. For this configuration there are higher velocity gradients between the two opposed streams and consequently more aerodynamic interaction and friction between them. This aspect also limits the wall jet development in the IPs case. As a consequence, the jet axis moves from the ceiling and attaches to the top of the pallets in the IPs case at z=L ¼ 1=2. On the contrary, in the SPs case, the jet progressively occupies the full width above the pallets and can be seen at z=L ¼ 3=4. Obviously, the return flow took place partially within the load in the SPs case. Other local aspects concerning airflow patterns observed in Figure 2.23 could be noticed: . .
At z=L ¼ 1=4, the two cases presented a reverse flow on the wall sides. At z=L ¼ 1=2 in the IPs case, due to the wall jet separation, the velocity varied principally from the top of the pallets, where the wall jet attached by Coanda effect flowed to the rear, and then to the ceiling (W > 0), where reverse flow took place
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RSM: slotted boxes Experiment: slotted boxes
0.5
0.1
−0.1 -0.1
0.3
0.3
0.3
−0.5 -0.5
0.5
x /Wd
0.5
x /Wd
x /W /Wd
Experiment: empty enclosure
0.1
W/W0 0
0.5
1
−0.4
−0.2 0 −0.1
-0.3 −0.3
0.1
W/W0 0.2
0.4
0.6
0.8
−0.4
−0.2
−0.1
0.4
0.6
-0.5 −0.5
-0.5 −0.5
z/L = 1/13.3
0.2
−0.3
−0.3 -0.3
−0.5 -0.5
W/W0 0
z/L = 2/13.3
z /L = 4/13.3
0.8
y/H
1
y/H
y/H y/H
(a) 1
1
0.8
0.8 Top of the pallets
Top of the pallets
Top of the pallets
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2 W/W0
W/W0 −0.2 -0.2
W/W0 0
0
0 0
0.2 0.2
z/L = 1/13.3
0.4
0.6
0.8 0.8
1
−0.2
0
z/L = 2/13.3
0.2
0.4
0.6
0.8
−0.2
0
0.2
0.4
0.6
z /L = 4/13.3
(b)
FIGURE 2.22 Experimental longitudinal velocity component (W=W0) at z=L ¼ 1=13.3, 2=13.3, and 4=13.3. (a) Horizontal profiles in the inlet centered plane and (b) vertical profiles along the symmetry plane.
.
(W < 0). This reveals a vertical recirculation bubble, which occupies the full width of the enclosure. With the SPs, the velocity varied principally from the centre, where W > 0, to the lateral side, where W < 0. This reveals a horizontal recirculation bubble, which occupies the full height above the pallets. At z=L ¼ 3=4, with the IP, air was almost stagnant; the maximum W velocity was very low (Wmax=W0 ¼ 0.5%). With the SP the velocity levels remained significant (Wmax=W0 ¼ 4.5%) without reverse flow (W > 0). This confirmed a better wall jet development and penetration into the enclosure for SP case.
These conclusions clearly embody the importance of load porosity on the jet behavior. Figure 2.24 shows the approximate outlines of air patterns for the different configurations.
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets
1
y /H
.6
1
0
2
0.4 .2 0 0 0.
0.75 Section z/L = 0.25; W max /W 0 = 51%; W max = 6.4 m s−1
0.75
−0 .6
0.8
−0.2
−0.4
0.2 0.0
−0 .
0.4
0.8
0. 8
y /H
Section z /L = 0.25; W max /W 0 = 31%; W max = 3.6 m s−1
−0.4 −0.6
.4 −0 2 − 0. 0.0 0.2
0.4
0.6
0.8
0.6
0.0
.6
0.0
0.6
0.2
0.0
(a)
−0
4
0.2
Section z/L = 0.75; W max /W 0 = 4.5%; W max = 0.6 m s−1
−0. 4
Section z /L = 0.5; W max /W 0 = 3.1%; W max = 0.36 m s−1
0.
0.2
0.8
Section z /L = 0.5; W max /W 0 = 7.5%; W max = 0.86 m s−1
0.0 0.4
0.2
−0 .2
−0.2
−0.6 Section z /L = 0.75; W max /W 0 = 0.5%; W max = 0.06 m s−1 (b)
FIGURE 2.23 Velocity contours above the load at z=L ¼ 0.25, z=L ¼ 0.5, z=L ¼ 0.75. (a) SPs and (b) IPs.
Symmetry plane. Side view
Inlet-centered horizontal plane. Top view
(a) Empty enclosure
(b) Loaded with slotted boxes
(c) Loaded with impermeable boxes
FIGURE 2.24 Approximate outlines of air patterns, comparison between the empty enclosure and the loaded cases.
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Vector reference 0.5 m s−1
V W
Inlet
1
2
3
4
5
6
7
8
15
16
Outlet
Vector reference 0.2 m s−1
V W
9
10
11
12
13
14
FIGURE 2.25 Velocity vectors of V and W inside the middle plane of SPs (6 10 LDV measurement points per pallet).
2.7.4.4
Airflow Characteristics Inside the Pallets
Velocity profiles were measured in the middle longitudinal plane of the pallets (6 10 measurement positions per pallet). The components V and W have been captured separately. The mean velocity of components V and W is plotted in Figure 2.25. The z-component of velocity is plotted in plain vectors and y-component of velocity is plotted in dashed lines. Figure 2.26 shows air velocities in the middle plane of pallets 3, 6, 8, and 10 measured with a fine grid (11 21 measurement positions per pallet). With the exception of the top, W was negative everywhere in the load (Figure 2.25) and the mean values of W were much higher than those of V from pallets 2 to 16. This demonstrates that the general trend of flow in the load was horizontal from the rear to the front exit. The mean value of W was the lowest at the rear; it increased from pallets 16 to 6 and decreased from pallets 4 to 2. This was a consequence of mass balance, i.e., of the exchanges between the headspace (above the pallets) and the load; the downward flow (coming into the load) in the rear half of the enclosure explains the increasing flow rate in the load (from box 16 to 6) whereas the upward entrainment flow induced by the inlet jet explains the decreasing flow rate (from pallets 4 to 2). The maximum W vector is always located at the fourth position from the top in pallets 8 to 14. This location corresponds to the bottom of the vortices, which have all almost the same position in these pallets. Pallet 1, which is the closest to the exit, is particularly unique compared to the others. Flow direction in this box was mainly vertical; there was very strong aspiration at the outlet leading to a short circuit from inlet to outlet throughout the first box.
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Reference vector 0.5 m s−1 y = 1.7
Reference vector 0.5 m s−1
V2 + W2 (m s−1) 0.45 0.43 0.40 0.38 0.35 0.33 0.30 0.28 0.25 0.23 0.21 0.18 0.16 0.13 0.11 0.08 0.06
Slots
Plain walls
V2 + W2 (m s−1) 0.52 0.49 0.46 0.43 0.39 0.36 0.33 0.30 0.27 0.24 0.20 0.17 0.14 0.11 0.08 0.05 0.01
Zoom in figure 10
y = 0.2 0.56 m
Pallet 3
Pallet 6
Reference vector 0.5 m s−1
Reference vector 0.5 m s−1
V2 + W2 (m s−1)
V2 − W2 (m s−1)
0.51 0.48 0.45 0.42 0.39 0.36 0.34 0.31 0.28 0.25 0.22 0.19 0.16 0.13 0.11 0.08 0.05
Pallet 8
0.41 0.39 0.38 0.34 0.31 0.29 0.26 0.24 0.21 0.19 0.16 0.14 0.11 0.09 0.07 0.04 0.02
Pallet 10
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FIGURE 2.26 Velocity vectors and magnitude ( V 2 þ W 2 ) in the middle plane of the pallets: 3, 6, 8, and 10 (11 21 LDV measurement points).
2.7.4.5 Interactions between Flows Around and Inside Pallets at the Load Interface In the load next to the top faces, the flow pattern was strongly affected by the main flow developed by the turbulent wall jet in the headspace. From W velocity vectors in Figure 2.25, one can notice that next to the top face, W < 0 from box 1 to 7 and W > 0 from box 8 to 16. This could be easily explained by the flow behavior above the pallets; it notably has been
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shown that the jet in the symmetry plane started to deflect from the ceiling at z=L ¼ 0.3 (fourth box position) and reattached by Coanda effect at the top faces of the pallets at z=L ¼ 0.5 approximately (eighth box position) where it flows to the rear. Due to this reattachment, a vertical shear appeared at the top of pallets from 8 to 16, which were located downstream of the jet reattachment and the internal flow was entrained by the external flow developed in the headspace. A horizontal shear zone was also observed at the top of each box from position 6 to 16 on the vertical velocity profiles (Figure 2.25); W was positive (upward) at the left side and negative at the right side (the effect was less distinct from pallets 13 to 16). Concerning airflow patterns, these shearing flows developed vertically and horizontally revealed the presence of vortices created at the top of pallets from 8 to 16 and framed between the vertical slotted walls. This phenomenon is highlighted by the recirculating pattern at the top of pallets 8 and 10 in Figure 2.25. We assumed that such vortices also exist for pallets 6 and 7 but the vortex centres were on the top of these pallets (which could explain that W was everywhere negative in these pallets). So it seems that there were vortices near the top of pallets 6–16 and that the position of the vortex centres followed the same trend that the jet, which attached the load top approximately at box 8. This is schematized in Figure 2.27. These vortices highlight the aerodynamic interaction that occurred through the top slotted wall between the external main flow developed by the inlet jet and the secondary return flow developed inside the pallets. By increasing velocities and turbulence, these aerodynamic structures improve the transfer mechanisms between the pallets and the external flow. The presence of a recirculation bubble between a jet and the reattachment wall, represented by the top of the pallets, is a well-known phenomenon in fluid dynamics. However, two aspects highlight the principal characteristics of the studied configuration. The first denoted the aerodynamic influence exerted by the separations between the pallets and rows of pallets, which obviously lead to split this theoretical global recirculation in many individual structures related to different pallet zones (Figure 2.26 and Figure 2.27). The second concern is the ‘‘aerodynamic permeability’’ of the top slotted wall of the pallets, which enables to y z Ceiling coanda effect
Vortices in the shear zone
Top faces coanda effect
Jet entrainment
1
4
8
Short-circuit to the exit
FIGURE 2.27 Outline of air path lines inside the load.
12
16
Main horizontal flow in the boxes
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0.2
Mean velocity (m s−1)
0.1
1
2
3
4
5
6
7
8
9
10
11
12
−0.1
13
14
15
16
Pallet number
−0.2
Mean W Mean V
−0.3
−0.4
FIGURE 2.28 Mean values of V and W components in SPs.
develop vortices inside the pallets that are located downstream the reattachment point of the jet, i.e., after the eighth position (Figure 2.25). From pallets 2 to 5, the vertical velocity was always positive near the top (Figure 2.25 and Figure 2.28). This revealed the air entrainment coming from the load and supplying the inlet jet. 2.7.4.6 Ventilation Efficiency Figure 2.29 and Figure 2.30 respectively present the evolution of the local ventilation efficiency and the fresh air renewal obtained numerically in each of the 16 pallets. The results show a high degree of ventilation heterogeneity along the vehicle, especially between the rear and the front sides. As it can be seen from Figure 2.8, the local ventilation efficiency tendency 1400 1200
t (h−1)
1000 800 600 400 200 0 1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 Pallet number
FIGURE 2.29 Local ventilation efficiency within pallets: t numerical data.
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180 160 140
teq (h−1)
120 100 tn
80 60 40 20 0 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Pallet number
FIGURE 2.30 Equivalent fresh air renewal efficiency: teq numerical data.
shows a plateau for the five first pallets at 1200 h1 approximately. From pallet 6 to pallet 16, ventilation efficiency decreases progressively. The flow rate throughout the last pallet is about 35 times smaller than for the five first pallets. Concerning the fresh air renewal distribution (Figure 2.30), the ratio between the pallets placed in the front part and in the rear of the vehicle is smaller than that observed for the ventilation in Figure 2.8. The value of teq obtained for the last pallet is only six times smaller that the highest value obtained for pallet 4. This figure also indicates that the fresh air renewal for the last pallets is three times smaller than the overall value. This means that maintaining the appropriate temperature for the last pallets necessitates an air flow rate three times higher than the global heat balance of the truck. This is important to take into account for refrigerated-vehicle design and for temperature regulation, because often refrigeration control is only based on an outlet temperature sensor. For the first pallets, the equivalent fresh air flow rate is about eight times smaller than the total air flow rate. This means that the air flowing into one of these pallets contains only about one-eighth of fresh air (coming directly from the enclosure inlet at T0). The rest was warmed up by flowing first throughout other pallets or by mixing in the different flow structures (jet mixing layer, lateral vortices above the load, etc.). Because of the low flow rate encountered in the rear of the vehicle, large temperature differences between air currents flowing in and out of the last pallets are observed. In fact, free convection is also expected in the last pallets (which are not taken into account in these simulations) and this increases air flow rate and limits temperature rise.
2.7.5 TURBULENCE MODELING PERFORMANCE 2.7.5.1
Empty Truck
The comparisons concerning streamline behavior (Figure 2.31) show that only RSM is able to correctly predict the separation of the wall jet and the general behavior of the motion of air related to the primary and to the secondary recirculations. The same figure also shows the poor predictions given by the k–« turbulence model and underlines its inability to predict flow separation.
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Experiment
RSM
k−e Model
RSM with a coarse grid (3e)
FIGURE 2.31 Influence of the turbulence model and the grid size on the flow pattern at the symmetry plane.
The good predictions given by the RSM with 624,000 cells were altered by using a more coarse grid (238,560 cells). In this case, the detachment point was located further downstream and in turn the second recirculation area was reduced and the primary recirculation enlarged. The altered RSM predictions were similar to those of the k–« based models. This behavior can be explained by increased numerical diffusion resulting from the coarser grid. 2.7.5.2 Slotted Pallets 2.7.5.2.1
Above the Pallets
Figure 2.32 shows that the standard k–« turbulence model and the RSM give similar results. However, the major difference observed between the two models concerns the jet behavior rather than local velocity values. As observed in Figure 2.33, the jet trajectory predicted by the k–« model was still close to the ceiling whereas experimental data showed a detachment from this wall followed by a deflection toward the top faces of the pallets by Coanda effect. This clearly indicates that the k–« model lacks sensitivity with respect to the adverse pressure gradient, overpredicts the ceiling Coanda effect, and hence increases the jet penetration distance into the enclosure. This could explain the higher velocities obtained by this model, notably in the rear. On the contrary, the RSM better performed the partial jet detachment from the ceiling and its progressive deflection toward the top of the pallets. However, the aerodynamic interaction between the jet and the slotted wall need to be improved by taking into account the horizontal
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Computational Fluid Dynamics in Food Processing W/W0 1
0.90
0.44
0.07
0.02
0.01
0.22
1.00 0.90 0.56 0.44 0.22 0.07 0.02 0.01 0.00 −0.05 −0.08 −0.12 −0.23 −0.34
Experiment 0 1 0.90
0.44
0.22
0.02
0.01
0.00
y/H
0.07
Simulation, RSM
0 1 0.90
0.44
0.22
0.07
0.02
0.01
Simulation, k−e
0 0
0.5 z /L
1
FIGURE 2.32 Velocity contours (W=W0) in the symmetry plane above the pallets: Comparison between experiments and turbulence models.
frictional resistance exerted by the top of the pallets against the jet. Although this horizontal friction could be neglected in terms of pressure losses compared with the perpendicular effect, it becomes essential for the numerical model to be able to predict the jet attachment on the top of the pallets by Coanda effect as it can be seen experimentally in Figure 2.32 and Figure 2.33. Experimental and RSM predictions showed that the area of the lateral vortex structures, delimited by the zero velocity contour, is confined near the inlet section in the front part of the enclosure (Figure 2.34). The k–« model predicts more stretched structures covering the whole side wall from the front to the rear. This could be explained by the high rate of entrainment
Experiment Simulation, RSM Simulation, k −e 1
y /H = 1 Ceiling
y /H
0.9 0.8 y/H = 0.72 Top of pallets
0.7 0
0.2
0.4 z /L
0.6
0.8
1
FIGURE 2.33 Jet trajectory in the symmetry plane (downshifted case: D ¼ 0.18 m).
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0.5 −0.10
0.01 0.10
0.71 0.89
0
0.03
W/W0
0.05
0.15 0.46
1.00 0.89 0.71 0.46 0.34 0.15 0.10 0.00 −0.01 −0.10 −0.16 −0.22
0.34
Experimental 0.5 −0.01
x /Wd
−0.16 −0.10
0.00 0.01
0.15
0
0.89 0.71
0.10
0.003 0.002
0.46 0.34
Simulation, RSM 0.5
−0.16
−0.10
0.00
−0.01
0.15
0.10
0.46 0.34 0.89 0.71
0
0.03 0.05
0.003
0.002
Simulation, k−e 0
0.5 z /L
1
FIGURE 2.34 Contour levels of longitudinal normalized velocity W=W0 in the inlet centered horizontal plane (downshifted case: D ¼ 0.18 m).
flow predicted by this model (data not shown) due to its greater, but not physical, jet stability and penetration along the enclosure. However, it should be stated that neither model agrees closely with the shape of the contours. Although experiments show that lateral vortices affect and slightly predominate jet diffusion, both models display an inversed tendency. Another aspect displayed by experimental data concerns the evolution of the horizontal velocity contours along the enclosure. These contours show that the maximum of the jet velocity is still in the symmetry plane up to z=L ¼ 0.5. Further downstream, the jet tends to deviate toward the lateral walls and brings out a curved velocity profile on the axis as shown in Figure 2.34. RSM reflects qualitatively this tendency, whereas the k« fails to predict this deviation. 2.7.5.2.2
Flow Inside the Load
Figure 2.35 presents the longitudinal velocity profile on the vertical center line of four pallets (namely 3, 5, 12, and 16). In pallet 3 and pallet 5, air flows toward the front face, where the outlet is located, along the whole height with a rather uniform velocity. The measured values are about 0.3 m s1, the predicted ones are slightly lower. In pallet 12 and pallet 16, velocity is very low. At the top of these pallets, measurements as well as simulations display positive values. This means that air flows toward the rear in the upper part of the load. This can be explained by the drag exerted by the air flow just above the load, which is also directed toward the rear. There are clearly some differences, particularly with the results for the pallets 12 and 16 where numerical results, in contrast to the measured results, reveal air velocity profiles very close to zero. The slotted wall effect was only taken into account through a normal pressure drop (with a uniform pressure drop coefficient), whereas there were other effects: alternation of slotted and plain zones, tangential drag, turbulence production, turbulent stresses redistribution, etc.
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y (m)
2
Experiment RSM
Experiment RSM
W (m s−1) −1.5 −1
2
y (m)
W (m s−1) −0.4
0 −0.5
0
0.5
Pallet 3
0 −0.2
0
Pallet 5 2
2
W (m s−1) −0.4 −0.2 Pallet 12
y (m)
y (m)
Experiment RSM
Experiment RSM
0 0
0.2
W (m s−1)
0.4 Pallet 16
−0.05
0 0
0.05
FIGURE 2.35 Longitudinal velocity inside the load on the vertical center line of the pallets.
To improve predictions, there is a need to take into account tangential frictions, especially at the top slotted walls where strong interactions between the main flow above the load and the return flow in the pallets were observed.
2.8 CONCLUSIONS In this study, experiments and numerical simulations performed using the CFD code Fluent were carried out in order to characterize velocities and airflow patterns within a typical refrigerated truck in empty and loaded configurations. The experiments were carried out on an isothermal reduced-scale model with laser-Doppler velocimetry.
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Experiments and simulations highlight the importance of the load and confinement effect in reducing the reach of the jet within the truck, which in turn maintains a high degree of ventilation heterogeneity between the front and the rear where stagnant zones and low velocities are present. The main conclusions were as follows: .
.
.
The load modified strongly the flow patterns but the velocity levels remained similar in all cases: jet velocity decreased rapidly in the first half and in the rear half the velocity was low. The jet penetration and the main recirculating flow were reduced as the load porosity decreased. The sideways diffusion was reduced as the porosity of the load decreased. The loaded cases presented a back flow on the sides of a centered jet.
In the case of IP, the simulations show the ability of the RSM model to accurately predict the overall behavior of the airflow patterns and velocity characteristics. The good predictions also concern the thin airspace separation (1–2 cm) between pallets and walls, which constitute the most sensitive plane in the load. The results also underline the importance of these separations in maintaining the ventilation around the pallets in order to better remove the heat exchanged through insulated walls and thus to decrease the higher temperatures reached locally in this most sensitive area. Numerical and experimental results show that the use of air-duct systems improves the overall homogeneity of the ventilation in the truck and avoids the occurrence of stagnant zones and low velocities in the rear part of the load. In this zone, velocities are maintained at around 1 m s1 instead of 0.1 m s1 without this air duct. These aspects contribute to a decrease in the temperature differences throughout the palletized cargo and thus to the preservation of the quality, safety, and shelf life of perishable products. In the case of the SPs, the results clearly show the predominance of the return flow directed from the rear toward the outlet inside the SPs. The result also shows a high rate of shear on the top of the pallets, revealing strong interactions with the main flow developed outside the pallets. This denotes the presence of individual vortices delimited by pallet separations and caused by the deflecting of the wall jet and its reattachment on the top of the pallets. The results also show a high degree of ventilation heterogeneity inside the load. The velocity level was lowest at the rear, and maximum near the fourth pallet. There was a short circuit from inlet to exit throughout the first box. The numerical results show a qualitatively good agreement with experimental data. The RSM better performed predictions than the k–« model especially on the top faces of the pallets where strong aerodynamic interactions are observed with the main flow. Velocity levels were overall underestimated within pallets and there was a lack of sensitivity in shearing zones. However, the Coanda effect at the top of the pallets could be better predicted if the model includes the wall friction on the slotted walls.
NOMENCLATURE C1 Cp D DH e ew H
pressure drop coefficient specific heat of air (J kg1 K1) ceiling-inlet distance (m) hydraulic diameter of the inlet section (m) airspaces separation pallets (m) airspaces separation between wall and pallets (m) height of the enclosure (m)
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I K k Q L _ m p Re T U, V, W u, v, w Wd x, y, z
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turbulence intensity (%) porous media permeability (m2) kinetic energy of turbulence (m2 s2) flow rate (m3 s1) length of the enclosure (m) flow rate flowing in and out of one pallet (m3 s1) static pressure (Pa) Reynolds number, Re ¼ rW0DH=m temperature (K) lateral, vertical, and longitudinal mean velocity components (m s1) lateral, vertical, and longitudinal fluctuating velocity components (m s1) width of the enclosure (m) lateral, vertical, and longitudinal coordinates (m)
GREEK SYMBOLS « m n r t ?
turbulence energy dissipation rate (m2 s3) dynamic viscosity (kg m1 s1) kinematic viscosity (m2 s1) density (kg m3) ventilation efficiency (h1) normal
SUBSCRIPTS 0 eq in out p t i, j, k
inlet equivalent in term of fresh air flowing in the considered pallet flowing out the considered pallet porous medium turbulent vector directions in x, y, and z
REFERENCES 1. Lenker, D.H., Wooddruff, D.W., Kindya, W.G., Carson, E.A., Kasmire, R.F., and Hinsch, R.T. Design criteria for the air distribution systems of refrigerated vans. American Society of Agricultural Engineers, 28(6): 2089–2097, 1985. 2. Go¨gus, A.Y. and Yavuzkurt, S. Temperature pull-down and distribution in refrigerated trailers. In: Proceedings I.I.F–I.I.R commissions D2, Wageningen, pp. 189–193, 1974. 3. LeBlanc, D., Beaulieu, C., Lawrence, R., and Stark, R. Evaluation of temperature variation of frozen foods during transportation. The Refrigeration Research Foundation Information Bulletin (Bethesda, MD), December 1994. 4. Bennahmias, R. and Labonne, G. Etude de la distribution de l’air et de la dispersion des tempe´ratures dans une semi-remorque frigorifique, Re´union des commissions C2, D1 et D2=3 de l’IIF, Fez (Morocco), pp. 241–256, 1993. 5. Meffert, H.F.Th. and Van Nieuwenhuizen, G. Temperature distribution in refrigerated vehicles. In: Proceedings I.I.F.–I.I.R. Commissions D1, D2, and D3, Barcelona, Spain, pp. 131–135, 1973. 6. Billiard, F., Bennahmias, R., and Nol, P. Nouveaux de´veloppements dans les transports a` tempe´rature dirige´e routiers. In: Proceedings I.I.F–I.I.R. Commissions B2, C2, D1, D2=3, Dresden, Germany, pp. 793–802, 1990.
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7. Lindqvist, R. Reffer hold distribution, Preprint Conferences. I.I.F.–I.I.R., Cambridge, UK, 1998. 8. Lindqvist, R. Air distribution design for controlled atmosphere in reefer cargo holds, 20th International Congress of Refrigeration, I.I.R.–I.I.F., Sydney, 1999. 9. Wang, H. and Touber, S. Simple non-steady state modelling of a refrigerated room accounting for air flow and temperature distributions. In: Proceedings of I.I.F.–I.I.R. Commissions B1, B2, C2, D1, D2=3, Wageningen, pp. 211–219, 1988. 10. Meffert, H.F.Th. and Van Beek, G. Basic elements of a physical refrigerated vehicles, air circulation and distribution. In: 16th International Congress of Refrigeration, I.I.F–I.I.R., Paris, pp. 466–475, 1983. 11. Me´nia, N.Z. Etude nume´rique et expe´rimentale de l’ae´raulique dans un ve´hicule frigorifique, The`se INA-PG, 2001. 12. Wang, H. and Touber, S. Distributed dynamic modelling of a refrigerated room. International Journal of Refrigeration, 13: 214–222, 1990. 13. Van Gerwen, R.J.M. and Van Oort, H. Optimization of cold store using fluid dynamics models. In: Proceedings I.I.F.–I.I.R. Commissions B2, C2, D1, D2=3, Dresden, Germany, 4: pp. 473–480, 1990. 14. Hoang, M.L., Verboven, P., De Baermaeker, J., and Nicolaı¨, B.M. Analysis of air flow in a cold store by means of computational fluid dynamics. International Journal of Refrigeration, 23: 127–140, 2000. 15. Moureh, J. and Flick, D. Wall air-jet characteristics and airflow patterns within a slot ventilated enclosure. International Journal of Thermal Sciences, 42: 703–711, 2003. 16. Moureh, J. and Flick, D. Airflow characteristics within a slot-ventilated enclosure. International Journal of Heat and Fluid Flow, 26: 12–24, 2005. 17. Moureh, J., Menia, N., and Flick, D. Numerical and experimental study of airflow in a typical refrigerated truck configuration loaded with pallets. Computer and Electronics in Agriculture, 34: 25–42, 2002. 18. Moureh, J. and Flick, D. Airflow pattern and temperature distribution in a typical refrigerated truck configuration loaded with pallets. International Journal of Refrigeration, 27: 464–474, 2004. 19. Nordtvedt, T. Cold air distribution in refrigerated trailers used for frozen fish transport, I.I.F.– I.I.R. Commissions B1, B2, D1, D2=3, Palmerston North (Nouvelle Ze´lande), 2: pp. 539–544, 1993. 20. Tapsoba, M., Moureh, J., and Flick, D. Airflow pattern in an enclosure loaded with pallets: the use of air ducts. Eurotherm seminar 77, Heat and Mass Transfer in Food Processing, June 20–22, Parma, Italy, 2005. 21. Craft, T.J. and Launder, B.E. On the spreading mechanism of the three-dimensional turbulent wall jet. Journal of Fluid Mechanics, 435: 305–326, 2001. 22. Choi, H.L., Albright, L.D., and Timmons, M.B. An application of the k–« turbulence model to predict how a rectangular obstacle in a slot-ventilated enclosure affects air flow. Transactions of the American Society of Agricultural Engineers, 33: 274–281, 1990. 23. Chen, Q., Comparison of different k–« models for indoor air flow computations. Numerical Heat Transfer Part B, 28: 353–369, 1995. 24. Awbi, H.B. Application of computational fluid dynamics in room ventilation. Building and Environment, 24: 73–84, 1989. 25. Davidson, L., Ventilation by displacement in a three-dimensional room: a numerical study. Building and Environment, 24: 263–272, 1989. 26. Hoang, M.L., Verboven, P., De Baermaeker, J., and Nicolaı¨, B.M. Analysis of air flow in a cold store by means of computational fluid dynamics. International Journal of Refrigeration, 23: 127–140, 2000. 27. Verboven, P., Hoang, M.L., and Nicolaı¨, B. Numerical computation of air moisture and heat transfer in chicory root cool stores, Ae´raulique et Industries Alimentaires, ENSIA France, 2001. 28. Mariotti, M., Rech, G., and Romagnoni, P. Numerical study of air distribution in a refrigerated room. Proceedings of the 19th International Congress of Refrigeration, pp. 98–105, 1995. 29. Nady, A., Saı¨d, M., Shaw, C.Y., and Zhang, J.S. Computation of room air distribution. ASHRAE Transactions: Symposia, 101: 1065–1077, 1995. 30. Launder, B.E. and Spalding, D.B. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3: 269–289, 1974.
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31. Wilcox, D.C. Turbulence modeling for C.F.D. DCW Industries, Inc., La Can˜ada, California, 1994. 32. Menter, F.R. Eddy viscosity transport equations and their relation to the k–« model. ASME Journal of Fluids Engineering, 119: 876–884, 1997. 33. Nallasamy, M. Turbulence models and their applications to the prediction of internal flows: a review. Computers and Fluids, 151–194, 1987. 34. Launder, B.E. On the modeling of turbulent industrial flows, Proceedings of Computational Methods in Applied Sciences, Hirsch, C., et al. (ed.), Elsevier, Amsterdam, pp. 91–102, 1992. 35. Aude, P., Be´ghein, C., Depecker, P., and Inard, C. Perturbation of the input data of models used for the prediction of turbulent air flow in an enclosure. Numerical Heat Transfer Part B, 34: 139–164, 1998. 36. Smale, N.J. Mathematical modelling of airflow in shipping systems: model development and testing. PhD Thesis, Massey University, New Zealand, 2005. 37. De Kramer, J., Kelder, J., Canters, R. Airflow and climate distribution in reefer containers—a network model. Poster presented at Model-IT, Katholieke Universiteit, Leuven, Belgium, 2005. 38. Me´nia, N.Z., Moureh, J., and Flick, D. Mode´lisation simplifie´e des e´coulements d’air dans un ve´hicule frigorifique. International Journal of Refrigeration, 25: 660–672, 2002. 39. Leonard, B.P. A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering, 19: 59–98, 1979. 40. Mitoubkieta, T. Etude expe´rimentale et nume´rique de l’ae´raulique dans un ve´hicule frigorifique, The`se INA-PG, 2006.
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CONTENTS 3.1 3.2
Introduction ................................................................................................................ Retail Cabinet ............................................................................................................. 3.2.1 Classification ................................................................................................... 3.2.1.1 Storage Temperature ......................................................................... 3.2.1.2 Geometry........................................................................................... 3.2.1.3 Refrigeration Equipment ................................................................... 3.2.1.4 Air Circulation .................................................................................. 3.2.1.5 Energy Consumption......................................................................... 3.2.2 Standardized Temperature Tests ..................................................................... 3.2.3 Air Curtains..................................................................................................... 3.3 Applications of CFD to Display Cabinets.................................................................. 3.3.1 Modeling Product Temperature Distribution.................................................. 3.3.2 Modeling Airflow ............................................................................................ 3.3.2.1 Air Curtains....................................................................................... 3.3.2.2 Shelves ............................................................................................... 3.3.2.3 Evaporator and Rear Ducts .............................................................. 3.3.3 Modeling the Influence of Air Humidity......................................................... 3.3.4 Modeling Interactions with the Ambient Conditions ...................................... 3.3.4.1 Radiation........................................................................................... 3.3.4.2 Ambient Air Movement .................................................................... 3.3.5 Glass Doors Fogging and Defogging .............................................................. 3.3.6 Mist Cooling—Humidification ........................................................................ 3.4 CFD Codes ................................................................................................................. 3.4.1 Methodology ................................................................................................... 3.4.1.1 Preprocessing ..................................................................................... 3.4.1.2 Solving ............................................................................................... 3.4.1.3 Postprocessing ................................................................................... 3.4.2 Turbulence Models .......................................................................................... 3.4.3 Mass Transfer .................................................................................................. 3.4.4 Validation ........................................................................................................ 3.5 Conclusions................................................................................................................. References ...........................................................................................................................
84 84 84 84 85 86 87 87 87 89 90 91 92 92 93 93 94 94 94 94 95 95 95 96 96 97 97 97 97 98 99 99
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3.1 INTRODUCTION In retail stores, refrigerated cabinets are used to display perishable food. For merchandizing purposes, the main function of such equipment is the effective display of products to make them visible and easily accessible to customers. At the same time, food should be maintained at the prescribed temperature, and preserved from radiant heat. The safety and quality of perishable foodstuffs are strongly affected by inappropriate storage temperature and by uneven temperature fluctuations, which are regrettably encountered to a large extent in display cabinets [1]. For this reason, from the point of view of storage conditions, retail cabinets are considered to be one of the weakest links in the cold chain, and only the typical short-residence time of food in such appliances reduces the risk of quality loss. It is therefore essential that the efficacy of retail cabinets in terms of food preservation is improved. The people who can play an important role in this improvement are the manufacturer, the person in charge of installation and maintenance, and the shop manager. The cabinet is certified by the manufacturer to comply with the testing standards currently in place for a specified climate class defined by ambient temperature and relative humidity. Actually, the performance of display cabinets in terms of food temperature is strongly affected by ambient conditions, particularly air velocity and direction, and radiative heat load [2–5]. For this reason, particular care is necessary for the installation; and furthermore, accurate maintenance and operation are essential to accomplish correct food storage conditions. The manufacturer is the only person who can take advantage from the use of computational fluid dynamics (CFD). Thus, the contents of this chapter will mainly focus on problems related to the design of retail cabinets, giving only some suggestions about installation and proper use.
3.2 RETAIL CABINET The main features of a retail cabinet can be summarized with the following statements: . .
Food should be displayed in the most efficient way to promote selling. Correct food storage temperature should be ensured, with temperature fluctuations reduced as much as possible.
The preservation and the display functions are contrasting requirements, because the best way to protect the product from temperature fluctuations is to keep it as far as possible from the shop environment; thus keeping it out of sight of customers. Furthermore, the manufacturer must operate an optimization process aiming to fulfill another important requirement, which is low energy consumption. In fact, while retaining the preserving function, a better display function usually requires higher energy consumption. Low energy consumption is becoming increasingly important, and the manufacturer should make huge efforts trying to cope with all these requirements.
3.2.1 CLASSIFICATION Retail cabinets are classified according to various criteria [2–4,6]. Among them, the most important are the storage temperature and the cabinet geometry, which are the key factors for the choice of the most suitable unit. Another important classification can be made according to the kind of air circulation, which is crucial for certain food. Finally, a further classification can be made according to energy consumption. 3.2.1.1
Storage Temperature
Retail cabinets are intended to host almost every kind of perishable food, from frozen food at 188C to some kind of fruits and pastry at þ108C. For this reason, they are usually classified
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as ‘‘low temperature’’ cabinets in the case of storage and display of frozen food, and ‘‘medium temperature’’ cabinets in the case of storage and display of chilled food. A more detailed classification is defined in the testing standards currently in place and will be discussed in Section 3.2.2. 3.2.1.2 Geometry As regards geometry, retail cabinets can be [2] . .
.
Closed (in the presence of doors or sliding covers=glasses) or open Vertical multideck (Figure 3.1), horizontal single deck (Figure 3.2), or horizontal serve-over counters A combination of these, e.g., a horizontal open-top cabinet combined with a vertical multideck closed cabinet
Of course, the various geometries of cabinets are not suitable for all foods and temperatures. As an example, closed cabinets are the most suitable for frozen food, in order to reduce heat
FIGURE 3.1 Vertical multideck display cabinet.
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FIGURE 3.2 Horizontal display cabinet.
infiltration from the ambient; in this case, horizontal open-top cabinets are to be preferred, while vertical open cabinets are to be avoided. 3.2.1.3
Refrigeration Equipment
Display cabinets are designed only to maintain the correct storage temperature of food. Therefore, they are not capable of reducing the temperature of products if they are too warm when loaded [2,6]. However, the cabinets’ refrigeration equipment is forced to perform heavy duty because of the huge amount of heat due to air infiltration, radiative heat transfer, and product manipulation by the customers. Depending on the refrigerating equipment, display cabinets can be classified as incorporated condensing units and remote condensing units. In the cabinets with incorporated condensing units, also named ‘‘stand alone,’’ the whole vapor compression refrigerating equipment is contained within the cabinet, which only needs a power supply connection and a drainage piping. In the remote condensing units, the cabinet is connected to a refrigerating unit that usually supplies several cabinets, both at low and medium temperatures. The remote condensing units can be further distinguished depending on the refrigerating system as a compression-type refrigerating system or an indirect-type refrigerating system. In the cabinets of the first category only the expansion valve and the evaporator are contained in the cabinet, which is fed with liquid refrigerant from a centralized refrigerator. Because the compression-type refrigeration system is complex and affords limited flexibility under changes to supermarket layout, it is typically used only in medium to large size stores. However, this configuration is preferable because of its enhanced energy efficiency. The recent issue about halocarbon refrigerants is pushing interest toward employing systems of the second category, in which a secondary refrigerant circulating system is installed between a central refrigerating system (usually placed in an outbuilding) and the cabinets. This configuration reduces dramatically the amount of refrigerant circulated, and allows to use toxic or flammable refrigerants with lower environmental impact (e.g., ammonia) at the expense of a more complicated circuitry.
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3.2.1.4 Air Circulation A further classification can be made with reference to air circulation inside the cabinet. Cold-air distribution can be ensured by forced or natural circulation, the choice depending mostly on the kind of foodstuff. As a general rule, forced air circulation is preferable, because it is much more effective in transferring the refrigerating power, thus enabling the correct operation of almost every kind of display cabinet. Natural air convection should be preferred for the display of unwrapped sensitive food like meat, pastry, and ice cream, where water loss coupled with heat transfer on the food surface can give rise to significant quality damage due to dehydration. It is mostly used on horizontal serve-over units, where air stratification helps in reducing warm-air infiltration inside the load volume. 3.2.1.5 Energy Consumption Supermarkets are intensive users of energy in all countries. Electricity consumption in large supermarkets represents a substantial share of about 4% of the national electric energy use, either in the US or in France. A large part of this consumption, varying from 50% to 70%, is due to air conditioning and refrigeration [7,8]. In the US, typical supermarkets with approximately 3700 to 5600 m2 of sales area consume about 2 to 3 million kWh annually for total store energy use [9]. The national average electricity intensity (the annual electricity use divided by the size of the facility) of a grocery store in the US is about 565 kWh m2 per year [8,10], and 400 kWh m2 per year for Europe [7]. These figures are a real challenge for energy savings, and the supermarket chains are spending a substantial proportion of money on the yearly energy consumption compared to the investment costs. For this reason, the evaluation and certification of the energy consumption of display cabinets is becoming an essential step in the future development of such equipment. In Europe, 15 national associations of manufacturers of air handling, air conditioning, and refrigeration equipment joined Eurovent–Cecomaf, which represents more than 800 companies. Eurovent–Cecomaf set up a voluntary certification program also for retail display cabinets, whose performance and daily energy consumption have been certified and classified. A list of the certified cabinets is freely available on the web site [11]. The decision maker of the supermarket chain is thus given the chance to be aware of the energy costs and compare different solutions.
3.2.2 STANDARDIZED TEMPERATURE TESTS Various testing standards for retail display cabinets are currently in place, e.g., the EN standard 23953 [12,13] in Europe, and the ASHRAE standards 72–2005 [14] in the US. The objective of such standards is to specify requirements for the construction, characteristics and performance of refrigerated display cabinets used in the sale and display of foodstuffs, . . . . to specify test conditions and methods for checking that the requirements have been satisfied, as well as classification of the cabinets, their marking and the list of their characteristics to be declared by the manufacturer [13].
Apart from the requirements about construction, the main scope of these standards includes classifying retail cabinets as a function of their storage temperature, and giving instructions for measuring their energy consumption. Specific conditions for the ‘‘temperature test’’ are thus defined in the standards. The cabinet is loaded with packages made of a specified composition of water, cellulose, and
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FIGURE 3.3 A display cabinet during a standardized temperature test.
additives; it is placed in a test room (Figure 3.3) where air temperature and humidity, and air velocity and radiant heat are controlled; and the temperature of a certain number of ‘‘measure packages’’ is recorded over a period of 24 hours after having reached steady state. Various temperature classes are identified, depending on the load temperature measured during such tests. The European standard identifies the temperature classes through the definition of the highest and lowest temperatures of the warmest and coldest packages, as reported in Table 3.1 [13]. The test room conditions are identified through the definition of the ambient psychrometric conditions (climate classes), as reported in Table 3.2 [13]. For all of them, air velocity and radiant heat are the same. In particular, air velocity should be equal to 0.2 m s1 parallel to the plane of the cabinet display opening and to the longitudinal axis. Radiant heat is controlled by the prescription of the wall temperature and emissivity, and the level of illumination. It should be noted that compliance of a retail cabinet with the standards does not mean that the correct storage temperature will be kept during normal operation in the retail store, even if the cabinet has been set up and situated in accordance with the recommendations of the manufacturer (normal conditions of use). This is almost due to the dissimilar thermal properties of foodstuffs and test packages, and to some differences in ambient conditions (i.e., air velocity, air temperature, radiative heat load). The EN standard 23953-2 [13] highlights this argument in the Annex C ‘‘Comparison between laboratory and in-store conditions.’’ It states thus:
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TABLE 3.1 Temperature Classes according to the EN Standard 23953 Highest Temperature of the Warmest Package (8C)
Class
Lowest Temperature of the Coldest Package (8C)
15 12 12 þ5 þ7 þ10 þ10 Special classification
L1 L2 L3 M1 M2 H1 H2 S
Lowest Temperature of the Warmest Package (8C) 18 18 15 — — — —
— — — 1 1 þ1 1
The complete range of various climate conditions and various ways of loading in stores cannot be simulated in the laboratory. For these reasons, specific climate classes and loading are defined for tests in the laboratory to classify cabinets and to make comparisons. For open refrigerated display cabinets, test results in laboratory cannot be directly transposed in stores.
For this reason, it is crucial that the cabinet is installed and operated with awareness. For the same reason, designers can make use of the great advantage offered by the use of CFD, because the designers can check different configurations, thereby saving the huge amount of time required for the standardized tests (at least a couple of days each), and can predict the performance of the apparatus at operating conditions different from the standardized ones.
3.2.3 AIR CURTAINS In an open cabinet, refrigerated air curtains are established at the cabinet opening when cooling of the load is achieved via forced air distribution. The reason for the choice of this
TABLE 3.2 Climate Classes according to the EN Standard 23953 Test Room Climate Class 0 1 2 3 4 5 6 7 8
Dry Bulb Temperature (8C)
Relative Humidity (%)
20 16 22 25 30 40 27 35 23.9
50 80 65 60 55 40 70 75 55
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position is the need of reducing heat transfer from the external environment by creating a barrier between the load volume and the external ambience. Heat transfer through the solid walls surrounding the load volume can be effectively cut by means of adequate insulating material. On the contrary, load is subject at the opening to both radiative and convective heat transfer from the ambient. Both of them cause heating of the food surface. Radiative heat transfer takes place between the load surface and the room walls, lights, and all other objects surrounding the opening. It plays an important role, since emissivity of the food packaging and of the surrounding objects is usually high (in the range 0.8–0.9). It has been measured that the temperature of the exposed surface of frozen food can increase up to 5–10 K due to the absorption of radiant heat. Radiant heat can be reduced by using low emissivity materials for food packaging, high efficiency (low temperature) lights in the environment, and shielding coatings on the glass door surfaces, if any [15]. Convective heat transfer is due to the temperature difference between the load volume and the environment. Air movement caused by natural convection unavoidably causes infiltration of warm air through the opening, which is enhanced in the presence of even slight air movements in the room. The air curtain is capable of effectively restraining the convective heat transfer and the warm-air infiltration, in the meantime reducing the surface heating due to radiation. In the case of open cabinets, more than one air curtains are used, the temperature of the external air curtain being higher than that of the internal one for the sake of a better flow stability. Air from the curtains is then extracted through a grille and forced by fans through a finned cooling coil where heat is removed. The surface temperature of the cooling coil is usually below the dew-point temperature of air; thus water condensation takes place. In the frequent case of surface temperature of the coil below 08C, frost formation takes place, which requires cyclical coil defrosting operations. Finally, refrigerated air is supplied to a plenum and then, through a honeycomb, to the supply grille, thus creating the air curtains. In the case of closed cabinets, usually only one air curtain is established, which flows close to the internal surface of the door. When the door is open, the air curtain helps prevent warm-air infiltration. When the door is closed, the air curtain extracts heat from the load volume and particularly from the food surface, which is still subject to radiant heat. Air curtains will be discussed more in detail in Section 3.3.2.1 and in Chapter 4 and Chapter 5.
3.3 APPLICATIONS OF CFD TO DISPLAY CABINETS CFD is a successful tool for the designer of display cabinets, who can take advantage from this tool to improve load temperature distribution, predict the airflow pattern and its efficacy, reduce warm-air entrainment, and improve product refrigeration. As previously mentioned, the main concern arises from the necessity to ensure an effective display, while preserving the optimal storage conditions and achieving the lowest energy consumption. The manufacturer must face this challenge and find the solution that better fits such requirements. Air movement inside the cabinet plays the key role in this challenge, essentially because it is in charge of product refrigeration. The thorough comprehension of the phenomena associated with airflow in display cabinets is in turn a difficult task, almost due to the various interdependent factors that act simultaneously. Often a trial and error process has to be established, requiring numerous experimental tests that entail spending a huge amount of time and money. Numerical modeling performed by a skilled person can be a viable alternative, once its reliability has been validated against experimental data. Sensitivity analyses can be easily executed, efforts can be directed to optimize the most critical components, and improvements in the performance of the whole cabinet can be achieved in a much shorter time than through
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experimental testing. Furthermore, the performance of the cabinet at different ambient conditions (e.g., temperature, humidity, air velocity) or operating conditions (e.g., load arrangement) can be predicted with sufficient accuracy, thus leading to a better awareness of the possible performance of the unit in the actual conditions at the retail store. In the following, the most important applications of CFD to retail cabinets are briefly described and the possible advantages of numerical modeling are discussed.
3.3.1 MODELING PRODUCT TEMPERATURE DISTRIBUTION Product temperature inside a display cabinet suffers from an uneven distribution, both from left to right and from back to front of the shelves. Temperature differences up to about 5 K for chilled food and about 10 K for frozen food can be encountered, which can be unacceptable. The difference from the left to the right side is often due to uneven air distribution, and will be discussed later on. The main reasons for the difference from back to front are the proximity of the cooling coil to the back or bottom of the load volume and the effect of radiant heat on the front surface. Radiant heat can account for up to 12% [16] of the total load, and therefore cannot be neglected. Furthermore, as radiation is concentrated on the surface, it leads to a significant local temperature increase. Experimental tests [17] showed a reduction of up to 10 K of the surface temperature of the upper layer of products in a horizontal frozen-food cabinet, thanks to the application of a low emissivity shield. This is because food packaging has an average emissivity of about 0.9, which is also the value required by the EN standard for the test packages. The main problem when simulating the product temperature distribution resides on the necessity to adopt a transient state model. In fact, heat exchanges through radiation and with the cooling coil are both time-dependent phenomena, linked to the shop opening time, to the presence of covers or night curtains, to the on–off cycling of the refrigerating equipment, and to the defrosting operations. Figure 3.4 reports as an example the temperature of the warmest and the coldest test packages measured at different locations in a frozen-food cabinet. Further to the influence of the location, the temperature fluctuation due to the defrosting operations is also clearly visible. The defrosting operations can be performed by heating the coil or simply by switching-off the refrigerating equipment. The missed refrigerating power leads to a step increase in food temperature, which requires a few hours to completely recover.
Temperature (°C)
−12 −14 −16 −18 −20 −22
0
4
8
12
16
20
24
Time (h)
FIGURE 3.4 Temperature of the warmest and coldest packages during a temperature test.
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For this reason, modeling the product temperature distribution inside a cabinet should be performed via a transient state simulation adopting a reliable model of radiation. In this case, it is not convenient to model concurrently the airflow pattern in the air curtains because of the great disparity between the time constants of the two phenomena. A satisfactory transient model of the airflow should require a time step of a few hundredths of a second, whereas for the food temperature a few minutes could be enough. When modeling the load temperature distribution, the air curtain could be simulated as a convective boundary condition with an average convective coefficient evaluated by means of previous simulations or through classical correlations. In this case, the CFD model becomes a much simpler coupled conduction–convection model that can also be easily solved with in-house codes [17,18].
3.3.2 MODELING AIRFLOW From the point of view of the designer, the effective simulation of the airflow pattern inside the whole display cabinet is the most interesting result. However, there are too many factors regarding the geometry of the cabinet, the operating conditions of the cabinet, and the ambient conditions, which interact and influence the performance of the unit. This would require a very complex model with an almost unpredictable accuracy that probably could not fit the actual operating conditions well [19]. A solitary paper is present in the literature with a simulation of a whole vertical open chilled cabinet in 3D, with the purpose of obtaining steady-state temperature distribution in the product [20]. The whole cabinet including the load, the air curtains, the air ducts, and a portion of the ambient is included in the domain, and the authors claim reasonable agreement with the load temperature distribution obtained from spot thermocouple measurements and infrared camera images. It is much more effective to split the whole flow course into a few sections, and set up simplified models where some variables can be disregarded, after verification by means of a sensitivity analysis. With such models, it will become almost impossible to closely reproduce the operation of the whole cabinet, however they will be much more effective for a quick comparison of various configurations [19,21–23]. The most widely used simplified models relate to the air curtain, the air distribution between two shelves, the airflow at the evaporator, and the airflow in the rear ducts. In all of them, load surface can be considered as an adiabatic surface at the storage temperature. The effect of radiation on the load surface can be considered through a suitable increase in the food surface temperature. Usually, simulations are performed for a cabinet fully loaded, because this operating condition is required for the standard test and it is the most common in supermarkets. 3.3.2.1
Air Curtains
The function of the air curtain has already been introduced, and will be further detailed in Chapter 4 and Chapter 5. It is indeed the most investigated part of the display cabinet, because of its crucial influence in the performance of the unit, in terms of both product temperature and energy consumption. This is almost due to the warm-air infiltration, which accounts for 60%–75% of the total refrigeration load [2,24]. In fact, as soon as the air curtain leaves the air discharge, entrainment of warm air takes place due to the increase in the width of the curtain. Because of the necessity to maintain the mass balance, a portion of the flow rate will be lost at the air return and will overspill at the bottom of the cabinet, thus causing the so-called ‘‘cold feet effect.’’
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The induction factor a is defined for a single air curtain as the ratio of the mass flow rate of ambient air entrained to the total mass flow rate at the return grille [2,23]: a¼
_ ambient treturn tdischarge m ffi _ return tambient treturn m
(3:1)
It can be computed also in the case of multiple air curtains, through the calculation of the average values of air temperature weighed with the respective mass flow rates. The induction factor is commonly considered for the evaluation of the effectiveness of the air curtain, especially because the variables required for its calculation are easily measurable. It has been found to depend upon several factors, among which the most important are the initial turbulence intensity, the Reynolds number, and the velocity profile at the air discharge [25]. Early simulations of the air curtains were performed using in-house codes in 2D domains. As an example, Cortella [26] utilized a finite element code based on the stream functionvorticity formulation, with a turbulence model similar to an LES procedure. Transient simulations were performed in a 20,000 grid-points domain of a vertical open cabinet for chilled food. The induction factor and the refrigerating power were found to be in good agreement with experimental values, and some suggestions could be given to enhance curtain stability. Also, Ge and Tassou [27] used an in-house code based on finite differences, which also took into account the moisture content in the air curtain. From this model, the authors derived some correlations for the estimation of the heat flow rate and of the return air temperature at various conditions. The employment of commercial codes made simulations much easier, because the main problems of computational efficiency and user friendliness of in-house codes were overcome. In the last decade, many authors published 2D simulations of air curtains in horizontal and vertical cabinets, with the aim of the prediction of the airflow pattern and of the evaluation of the curtain efficacy at various conditions [22,28–34]. A 3D simulation of air curtains has been developed by D’Agaro et al. [23] and will be discussed in more detail in Section 3.3.4.2. In all the studies mentioned here, CFD has always proved to be a successful tool for the optimization of the air curtain. 3.3.2.2 Shelves In open vertical cabinets, air curtains are deeply influenced by the shape, length, and loading of shelves. As regards loading, the best air-curtain efficacy is encountered when the cabinet is fully loaded, which is the standard test and design condition and also the most common condition in retail stores. As regards geometry, at the design stage a lot of experimental tests or CFD simulations are required to minimize air-curtain disruption at the front of the shelves [35]. 3.3.2.3 Evaporator and Rear Ducts Uneven distribution of air at the evaporator ducts is crucial because it could lead to an uneven air-curtain velocity at the air discharge, thus causing differences in product temperature from left to right in the load volume. Foster et al. [35] investigated the flow of air as it exited the evaporator and entered the rear duct. The effects of a dead space were identified and modifications were suggested in order to reduce the formation of vortices and to improve air distribution in the back plenum. Similar simulations can be performed on different geometries of cabinets, and not only the shape of the rear ducts, but also the position of the evaporator and of the fans can be investigated. More details are given in Chapter 4.
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3.3.3 MODELING
THE INFLUENCE OF
AIR HUMIDITY
Commercial codes give the user the opportunity to include moisture content in the airflow models, in order to investigate both heat and mass entrainment in the cabinet. Some authors did use this feature when performing their simulations [20,27,28]. Actually, presence of humidity is crucial for the cabinet performance, because humidity entrainment leads to performance detriment due to evaporator frosting. However, the increase in computer power requirements due to the inclusion of moisture content in the CFD model can be avoided by estimating the latent heat from a mass balance on the water vapor content of the air curtain, once the induction factor and the humidity ratio of the ambient air are known, and assuming that air is saturated at the evaporator outlet. More details about the numerical methodology are given in Section 3.4.3.
3.3.4 MODELING INTERACTIONS
WITH THE
AMBIENT CONDITIONS
Display cabinets operation, especially for open cabinets, is crucially influenced by ambient conditions. Radiant heat, ambient air velocity, and direction are only the most important variables that must be considered when designing such units. 3.3.4.1
Radiation
In the previous section, the effect of radiant heat has been described, and some suggestions have been given on how to reduce radiant heat gain on the load surface. As regards simulations, it has been clarified that radiation has to be accounted for only when simulations of the load temperature distributions are being performed, whereas it is unnecessary for the evaluation of airflow patterns when load surface can be considered as a constant temperature surface. 3.3.4.2
Ambient Air Movement
Air velocity in the ambient environment and its direction are also crucial for the performance of the cabinet, and for this reason standard tests prescribe both of them. Furthermore, airflow visualizations performed on the air curtains during cabinet testing showed that 3D effects take place and can be significant, even with still air in the ambient. For these reasons, we realize that it is necessary to investigate more thoroughly the 3D effects in the air curtains. Typically, almost all papers in the literature describe 2D simulations, for the sake of CPU time and memory requirement reduction, assuming that simulations are performed on the median section and that end effects can be negligible. In fact, especially for short length cabinets, end effects can be significant, and lead to uneven air-curtain velocity and food temperature distribution. D’Agaro et al. [23] performed 3D simulations on a 2.44 m long vertical cabinet for frozen food, and investigated the effect of longitudinal air movement. The authors report that 3D flow structures that may originate from slow air movements in the ambient are responsible for 20% decay in the performance of the unit between a 2 m and a 1 m long cabinet, thus underlining the importance of 3D simulations in the design of short to medium cabinets. Another important interaction between the cabinet and the ambient is the accumulation of cold air, which overspills the return air grille and accumulates on the floor in front of the unit. This situation is named cold feet effect because of the unpleasant sensation on the customer who walks close to vertical open cabinets. Some authors [36] tried to simulate the whole sales area of a store, but the model was too complex and time consuming. For this reason, they moved to a simplified model of a chilled aisle, simulated on the three symmetry
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planes, and investigated different ventilation and heating strategies. More details on the topic are reported in Chapter 4.
3.3.5 GLASS DOORS FOGGING
AND
DEFOGGING
On closed display cabinets with doors, mist deposition occurs on the internal side of the door each time it is open, especially for frozen-food cabinets. In the case of transparent doors, a quick defogging must be achieved to recover product visibility through the glass. For this purpose, an air curtain is established flowing along the internal glass surface, and an electric heater is sometimes embedded in the multiglazed door. Demisting time can be estimated through the application of CFD. Croce et al. [37] and D’Agaro et al. [38] coupled a CFD commercial code with an in-house code for the evaluation of the airflow pattern and of the water layer evolution, respectively. More details on the numerical procedure are given in Section 3.4.3. The computation enables the prediction of the water layer height during condensation when the door is open, and also during evaporation in the presence of electrical heaters. Various parameters of the refrigerated cabinet (e.g., geometry, air-curtain velocity, and temperature) and the glass door (e.g., geometry, global heat transfer coefficient, and presence of electrical heaters) can be considered. The model also takes into account condensation as a thin film or a collection of water droplets. Results showed the model to be reliable for the evaluation of the entity of defogging time reduction that might be expected with different solutions.
3.3.6 MIST COOLING—HUMIDIFICATION Unwrapped food products like fruits and vegetables are subject to dehydration when displayed in open cabinets. This is due to air dehumidification that takes place on the cooling coil surface, especially when forced convection cabinets are employed. The importance of relative humidity on the shelf life of products is well known, and all efforts are made to limit quality decay and weight loss when it is possible. In display cabinets, air dehumidification can be limited by choosing appropriate air velocity and temperature at the design stage, however the solution is not fully satisfactory. Another approach is derived from the air-conditioning plants, and from some vegetable refrigerated storage rooms, where air humidification is sometimes exploited through water spray. This technique has the only disadvantage of being a possible way to bacteria growth, and therefore requires strict control from the microbiological point of view. Tests have been performed on humidification equipment that use water-mist sprayed over the products’ surface above each shelf and the well [39]. Results were encouraging, since weight loss was reduced, at the expense of a slightly higher refrigeration load requirement. This device is already commercially available, and supplied upon request by display cabinet manufacturers, however it has not yet been thoroughly investigated. Commercial codes are available to treat heat and mass transfer, and some research has been performed in the similar field of weight loss during blast chilling [40]. Thus, in the near future some research work will be probably devoted to this interesting topic.
3.4 CFD CODES CFD is based on the solution of the governing flow (i.e., the continuity and the Navier– Stokes) equations, the energy conservation equations, and sometimes on the conservation of other factors (e.g., water moisture). It has become popular only recently, when the availability
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of more powerful and affordable computers made it possible to investigate practical problems that were previously too computationally expensive. When applied to display cabinets, CFD can model fluid flow; conductive, convective, and radiative heat transfer; and moisture transfer. In addition to numerous in-house codes, there are a number of commercial codes that can now cope with a high level of complexity. However, most of them are general purpose software designed for use in many different research fields. Therefore, robustness sometimes is enhanced to the detriment of accuracy, which still needs to be improved [41].
3.4.1 METHODOLOGY Every CFD simulation can be split into three consecutive phases: preprocessing, solving, and postprocessing [41]. 3.4.1.1
Preprocessing
Preprocessing starts with the choice of the computational domain to be simulated, includes the mesh generation, the definition of material properties, and ends with the application of boundary conditions. It is a crucial phase for obtaining reliable results. The users must be fully aware of the physics of the problem, because in this phase they set up the model of their practical problem. The choice of the domain to be investigated needs to be carefully considered in order to include all possible effects on the object of investigation. As an example, CFD simulation of an open display cabinet requires a portion of the external ambient to be included in the computational domain, in order to evaluate correctly the warm-air entrainment and the coldair overspill. Two dimensional or three dimensional domains can be considered for display cabinets. Until now, almost all the simulations about air curtains have been performed in 2D because of the necessity to reduce the computational load. However, D’Agaro et al. [23] have shown that in short length cabinets the end effects cannot be disregarded, thus demonstrating that in certain cases 3D simulations could be necessary. For the simulation of air ducts (e.g., rear ducts, evaporator, and fans), 3D simulations are usually indispensable because of their complicated geometry. The dimension of the elements in the grid influences the level of accuracy of the solution. Usually, the dimension must be reduced in the portions of domain where an accurate solution is required (e.g., in the presence of turbulence or of high velocity gradients) or close to solid boundaries, where the requirements of the turbulence model must be satisfied. Of course the computational time increases with the number of elements in the domain, thus suggesting the limiting of grid refinements to those areas where it is strictly necessary. For an accurate simulation, it should be necessary to check that the solution is not ‘‘grid dependent,’’ i.e., it does not depend on the dimension of the elements. Otherwise, mesh refinements are still required. Once all the properties of the various solid and fluid substances have been identified, the boundary conditions must be defined. This is another important step in the simulation, whose effect in the solution can be significant. Usually it is necessary to introduce assumptions at this step, because the available boundary conditions do rarely match the actual conditions. In many cases, different boundary conditions must be checked, the results compared, and a sensitivity analysis performed for the identification of the best conditions. More specific information about different boundary conditions used to simulate display cabinets is reported in Chapter 4.
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3.4.1.2 Solving The solution of the governing equations requires their discretization and an iterative process to obtain an approximation of the value of each variable at specific points in the domain. Calculation is stopped when the residuals in the calculation of the balance of one or more properties are below a specified value, and the solution is said to converge. Reaching convergence is not trivial, and also the choice of the threshold value of residuals is not easy. Some suggestions are given in Chapter 4. Another main concern about solving in CFD simulation is the choice between steady state or transient calculations. The choice depends on the phenomena to be investigated, and some suggestions have been given in the previous sections depending on the object of the simulation. In general, transient simulations should be performed only in the case where the time evolution of a phenomenon is under investigation, because convergence must be reached at each time step, and therefore they are much more time consuming. 3.4.1.3 Postprocessing When the solution reaches convergence, a distribution of the values of all the variables throughout the whole domain is produced. Such values must be processed to obtain visualizations and some required numerical results (e.g., the induction factor, the refrigerating power). The postprocessing phase is thus essential for the evaluation of the simulation results, and it is also an important tool for their most thorough understanding. In fact, the postprocessor also performs calculations and balances, thus giving further precious information.
3.4.2 TURBULENCE MODELS Turbulence models must be adopted to take into account the turbulence effects, which cannot be evaluated through a direct simulation. In fact, direct simulation of turbulence in large domains as those used for display cabinets would require a really huge amount of memory and CPU time. There are many turbulence models available, and unfortunately the choice of the model significantly affects the results. Literature works can be helpful with this respect, however experience is fundamental. The basic turbulence models are the so-called ‘‘two equations models,’’ which are the default choice for many commercial codes. Among these, the k–« and the RNG k–« models are the most widely used. Although easy to implement, they require the previous evaluation of the turbulence kinetic energy and dissipation rate, which is a matter of difficult measurements or experience. Furthermore, they are not considered as the best choice because of the poor accuracy sometimes encountered. Other models are those based on the Reynolds stresses and the large Eddy simulation. The former was found to be accurate [42] even if it required a quite fine mesh. The latter was successfully used by Cortella et al. [26] in the framework of a stream function-vorticity in-house code. Some more suggestions, particularly on the initial turbulence intensity, will be given in Chapter 4, while a deeper discussion of turbulence models is left to specific literature.
3.4.3 MASS TRANSFER It has already been pointed out in Section 3.3.3 that the moisture content of the air is a critical factor influencing the performance of display cabinets, because humidity entrainment
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involves an additional latent heat that shall be removed at the cooling coil. Furthermore, also in the case of chilled cabinet, the surface temperature of the cooling coil is often below 08C, thus leading to frost formation and to the need for cyclical defrosting operations. The evaluation of the latent heat does not strictly require a coupled heat and mass transfer simulation. The induction factor can be once again considered from the evaluation of the water mass balance in the air curtain: a¼
_ ambient xreturn xdischarge m ffi _ return xambient xreturn m
(3:2)
where x is the humidity ratio (kgvap=kgdry air). The ambient humidity ratio is known, while the discharge humidity ratio can be easily estimated by assuming saturation for the discharge air [2,23]. On the contrary, there are some particular cases where coupled heat and mass transfer must be simulated, like for example the simulation of door fogging and defogging in closed display cabinets. This topic has already been introduced in Section 3.3.5. In the following, more details are given on the numerical procedure, which involves coupling of two different codes, for the dry heat or flow and for the mass transfer [38]. The problem is split into two phases, the first regarding the dew deposition on the internal face of the glass when the door is open and the second regarding the defogging operation once the door is closed. As regards the heat transfer, the evaluation of the local heat transfer coefficient for the airflow on the internal face of the glass is performed with a single phase solver. In fact, the phase change during evaporation is limited to a thin layer on the solid surface, and therefore it is accounted for through proper boundary conditions. Conductive heat transfer through the multiglazed glass can be solved by means of a steady-state network of thermal resistances, which can also take into account radiation in the air cavities, thus leading to a very simple conduction problem easily solvable with simple in-house codes. Finally, the external heat transfer coefficient can be effectively estimated by means of the classical empirical correlations for steady-state natural convection on a vertical plate. The different domains and solvers are coupled through an exchange of boundary conditions, thus leading to a more flexible algorithm. As regards the mass transfer, an in-house code was used, where the latent heat contribution due to condensation or evaporation appeared as a heat source or sink, respectively, and the code was placed at the interface between the solid and the fluid domain. Thermal and mass balances can be established at the interface and solved taking advantage of the heat and mass transfer analogy. A detailed description of this procedure is given in Ref. [38]. It is interesting to note that in this model the water layer can be considered as a continuous film or as a number of droplets, whose geometry changes during the condensation and evaporation processes. Furthermore, the effect of electric heaters can be accounted for, in order to speed up the demisting process. The simulation showed to be reliable when compared to experimental tests, especially using the droplet model.
3.4.4 VALIDATION It is common opinion that CFD simulations must be validated, and this is especially true in the case of display cabinets, where the simulation of such a complex problem requires a number of assumptions to set up the model. Usually, validation is performed against experimental tests at controlled conditions, like those in accordance with the standards in force. The variables that can be compared are essentially load temperature, air temperature, and air velocity.
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Measurements of load temperature can be easily performed, and the effect of radiative heat transfer can be highlighted by means of infrared thermal imaging systems. Measurements of air temperature can be easily performed at the discharge and return grille, although it is quite complicated to measure air temperature along the air curtain. Infrared systems cannot visualize air temperature, because it is transparent under infrared radiation. Some images taken with infrared cameras and willing to show air temperature are actually infrared visualization of the cabinet end-wall temperature. Accurate measurements of air velocity are difficult, especially along the air curtain. At the discharge and return grille, the use of hot wire anemometers allows for a sufficiently accurate evaluation of the velocity distribution, even if important information about direction and turbulence is lost. Anemometers placed along the air curtain are susceptible to disturb the airflow pattern, thus giving place to an incorrect evaluation. Axell [43] reported a strong influence of the distance and shape of the sensors, and claimed to have measured values in ‘‘good qualitative agreement’’ with the numerical results. Much more reliable results can be obtained using the particle image velocimetry (PIV), which is a very accurate method for flow pattern measurements. Air has to be seeded; the field of investigation is lighted with a laser sheet; and a number of subsequent images are taken by a digital video camera placed perpendicular to the laser plane. Processing of the images allows for the identification of the movement of each seeding particle, thus leading to the complete flow pattern recognition. Rather than for CFD validation, this is a valuable tool for the adoption of the best CFD boundary conditions, especially at the discharge air (air velocity and direction, turbulence intensity), which are crucial to obtain reliable results [44].
3.5 CONCLUSIONS Retail display cabinets design can take great advantage of CFD, in terms of both time and money savings. It is rather difficult to replicate experimental results, due to flow complexity and difficulties in reproducing the actual ambient conditions. However, CFD is very effective for sensitivity analyses, and can be very helpful to compare the performance at different operating conditions and find the optimal design of the unit. In the near future, CFD will surely grow in popularity, and probably it will be much easier to perform even complicated simulations due to the increasing computational power. Three dimensional simulations will be more affordable, and larger computational domains will permit a more thorough evaluation of the influence of ambient air, as an example. Nevertheless, a lot of critical assumptions or choices must be made to perform a CFD simulation, and the outcomes will always depend on the judgment of the operator. Furthermore, commercial codes tend to improve robustness at the expense of accuracy every time convergence is difficult, thus leading to incorrect results. For these reasons, CFD must be always operated by skilled people, the results accurately assessed and, whenever possible, boundary conditions and results of some reference cases should be validated by comparison with experimental tests.
REFERENCES 1. Spiess W.E.L., Boehme T., and Wolf W. Quality changes during distribution of deep-frozen and chilled foods: distribution chain situation and modeling considerations. In: Food Storage Stability, Taub I.A. and Singh R.P. (eds.), CRC Press, Boca Raton, FL, pp. 399–417, 1997. 2. Rigot G. Meubles et vitrines frigorifiques, Pyc Edition, Paris, 1990. 3. Gac A. and Gautherin W. Le froid dans les magasins de vente de denree´s pe´rissables, Pyc Edition, Paris, 1987.
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28. Van Oort H. and Van Gerwen R.J.M. Air flow optimisation in refrigerated display cabinets. In: Proceedings of the 19th International Congress of Refrigeration, IIR=IIF, The Hague, the Netherlands, pp. 446–453, 1995. 29. Bale´o J.N., Guyonnaud L., and Solliec C. Numerical simulation of air flow distribution in a refrigerated display case air curtain. In: Proceedings of the 19th International Congress of Refrigeration, IIR=IIF, The Hague, the Netherlands, pp. 681–688, 1995. 30. Laguerre O., Moureh J., Srour S., Derens E., and Commere B. Predictive modelling for refrigerated display cabinets. In: Proceedings of IIR International Conference Advances in the Refrigeration Systems, Food Technologies and Cold Chain, Sofia, Bulgaria, pp. 480–487, 1998. 31. Cortella G., Manzan M., and Comini G. Computation of air velocity and temperature distributions in open display cabinets. In: Proceedings of IIR International Conference Advances in the Refrigeration Systems, Food Technologies and Cold Chain, Sofia, Bulgaria, pp. 617–625, 1998. 32. Wu Y., Xie G., Chen Z., Niu L., and Sun D.W. An investigation on flowing patterns of the airflow and its characteristics of heat and mass transfer in an island open display cabinet with goods, Applied Thermal Engineering, 24: 1945–1957, 2004. 33. Cortella G. and D’Agaro P. Air curtains design in a vertical open display cabinet. In: Proceedings of IIR International Conference New Technologies in Commercial Refrigeration, Hrnjak P.S. (ed.), Urbana, USA, pp. 55–63, 2002. 34. Cui J. and Wang S. Application of CFD in evaluation and energy-efficient design of air curtains for horizontal refrigerated display cases, International Journal of Thermal Sciences, 43: 993–1002, 2004. 35. Foster A.M., Madge M., and Evans J.A. The use of CFD to improve the performance of a chilled multi-deck retail display cabinet, International Journal of Refrigeration, 28: 698–705, 2005. 36. Foster A.M. and Quarini G.L. Using advanced modelling techniques to reduce the cold spillage from retail display cabinets into supermarket stores to maintain customer comfort. In: Proceedings of the Institution of Mechanical Engineers, Part E—Journal of Process Mechanical Engineering, 215: 29–38, 2001. 37. Croce G., Nonino C., and Della Mora F. Numerical simulation of defogging conditions. In: Proceedings of the 3rd ICCHMT, Banff, Canada, 2003. 38. D’Agaro P., Croce G., and Cortella G. Numerical simulation of glass doors fogging and defogging in refrigerated display cabinets, Applied Thermal Engineering, 26: 1927–1934, 2006. 39. Brown T., Corry J.E.L., and James S.J. Humidification of chilled fruit and vegetables on retail display using an ultrasonic fogging system with water=air ozonation, International Journal of Refrigeration, 27: 862–868, 2004. 40. Hu Z. and Sun D.W. CFD simulation of heat and moisture transfer for predicting cooling rate and weight loss of cooked ham during air-blast chilling process, Journal of Food Engineering, 46: 189– 197, 2000. 41. Xia B. and Sun D.W. Application of computational fluid dynamics in the food industry: a review, Computer and Electronics in Agriculture, 34: 5–24, 2002. 42. Moureh J. and Flick D. Airflow characteristics within a slot-ventilated enclosure, International Journal of Heat and Fluid Flow, 26: 12–24, 2005. 43. Axell M., Fahlen P.O., and Tuovinen H. Influence of air distribution and load arrangements in display cabinets. In: Proceedings of the 20th International Congress of Refrigeration, IIR=IIF, Sydney, Australia, paper 152, 1999. 44. Casarsa L. and Arts T. Experimental investigation of the aerothermal performance of a high blockage rib roughened cooling channel, Journal of Turbomachinery, 127: 580–588, 2005.
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Improving Performance of a Chilled Multideck Retail Display Cabinet by CFD Alan M. Foster
CONTENTS 4.1 4.2
Introduction ............................................................................................................... 104 Description of Cabinet............................................................................................... 104 4.2.1 Air Curtain ..................................................................................................... 105 4.2.2 Defrost............................................................................................................ 107 4.3 Standard Testing ........................................................................................................ 108 4.4 CFD Analysis ............................................................................................................ 108 4.4.1 Experimental Investigation ............................................................................. 109 4.4.2 Setting Up the CFD Model ............................................................................ 109 4.4.2.1 Two or Three Dimensional............................................................... 109 4.4.2.2 Mesh Size.......................................................................................... 111 4.4.2.3 Turbulence Model ............................................................................ 111 4.4.2.4 Buoyancy .......................................................................................... 112 4.4.2.5 Steady State or Transient? ................................................................ 113 4.4.2.6 Humidity .......................................................................................... 113 4.4.2.7 Boundary Conditions ....................................................................... 113 4.4.3 Convergence and Mesh Independence............................................................ 116 4.4.4 Postprocessing ................................................................................................ 117 4.5 Results from Typical Simulations .............................................................................. 118 4.5.1 Air Curtain ..................................................................................................... 118 4.5.2 Modeling of the Duct ..................................................................................... 119 4.5.3 Shelving .......................................................................................................... 120 4.5.4 Cold Feet Effect.............................................................................................. 121 4.5.4.1 Whole Store ...................................................................................... 121 4.5.4.2 Aisle.................................................................................................. 123 4.6 Verification ................................................................................................................ 124 4.7 Conclusions................................................................................................................ 125 Nomenclature ..................................................................................................................... 126 References .......................................................................................................................... 126
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4.1 INTRODUCTION In the UK, retail sales of frozen and prepared chilled food were worth £118 billion per annum between 2005 and 2006. The majority of which was sold from refrigerated display cabinets. Being able to maintain the temperature of this food is of vital importance to retailers to ensure optimal food quality, safety, and shelf life [1]. It has been shown that mean food temperatures between chilled multideck cabinets can range from 18C to þ168C [2]. This range causes food manufacturers problems when defining the shelf life of products and results in shelf lives that are either unduly cautious or potentially risky. Open display cabinets are one of the weakest links in the chilled food chain [3] and large (>5 K) temperature differences are found in most cabinets. This is due to the technical difficulties in reducing the difference between the lowest temperature packs, which are usually sited at the rear of the cabinet, and the highest temperature packs sited at the front of the cabinet. Technical problems in the even supply of air from the evaporator and the design of the air curtain can result in uneven temperatures across the cabinet (left to right) and too much entrainment of ambient air at the front of the cabinet. Multideck cabinets are extremely sensitive to ambient conditions. Small changes in ambient temperature, humidity, or airflow can have a large impact on food temperature. This is not a problem during the setting up and testing of a cabinet where it is kept in a temperature-controlled test room. However, in reality the ambient conditions are unlikely to be controlled. Many authors [4–9] have shown computational fluid dynamics (CFD) modeling to be a valuable tool to rapidly provide design options to improve airflow within display cabinets. Due to the speed that a variety of scenarios can be predicted, CFD provides the ideal means to improve the performance of display cabinets. The aims of this chapter are to provide a CFD user with an understanding of retail display cabinets and a retail display cabinet designer with an understanding of CFD. This chapter is specific to multideck chilled cabinets and the use of commercial CFD codes. It is hoped that this chapter will further stimulate the use of CFD to improve the design and more cost-effective testing of the multideck chilled retail display cabinets.
4.2 DESCRIPTION OF CABINET In the majority of multideck retail display cabinets, the evaporator is in the base of the cabinet (although it is becoming more common for them to be in the rear duct) and the fans draw air through the evaporator and up the duct at the rear of the cabinet. Air exits the duct through holes or slots in the cabinet rear grille and also through a slot or honeycomb grille placed at the front of the cabinet canopy, termed the discharge grille (Figure 4.1). The purpose of the discharge grille is to create a vertical air curtain from the front of the cabinet canopy to a grille placed at the front of the cabinet well (termed the return grille). The air curtain creates a nonphysical barrier between the cold air in the cabinet and the ambient air outside. Due to the air from the curtain being colder than the surrounding air it will also fall due to buoyancy. As the air curtain falls from the cabinet discharge grille, the curtain entrains cold air from inside the cabinet (entered through the rear grille) and warm air from the environment. The entrainment of warm air from the environment causes the air curtain to become warmer as it passes down the cabinet. Entrainment causes the mass flow rate of the air curtain to increase as it moves down the front of the cabinet. Due to conservation of mass flow, not all of the air in the air curtain will be taken away by the return grille: a significant portion will overspill onto the floor. As this air will be colder and denser than the ambient air, it stays on the floor, causing a customer comfort issue which is commonly termed the ‘‘cold feet effect.’’
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Rear duct Rear grille
Discharge grille
Fan Shelf
Return grille Evaporator
FIGURE 4.1 Vertical section of multideck display retail cabinet with the evaporator fan in the rear duct.
The purpose of the rear grille is to provide cold air over the products and to provide a pressure in the display area that counteracts the deflection of the air curtain into the display area caused by the stack effect (discussed in detail in Chapter 7).
4.2.1 AIR CURTAIN The air curtain is by far the most researched element of multideck display cabinets. It is essentially a turbulent recirculated plane air curtain. Setting up of the air curtain is critical in the correct operation of the cabinet and also because infiltration through the air curtain is by far the largest heat load. It has been reported to be between 60% and 70% of the heat load on the cabinet by Axell and Fahlen [10], 73% by Faramarzi [11], and 76% by Van Baxter [12]. Turbulent recirculated plane air curtains were studied by Howell and Shibata [13]. They showed that .
.
.
.
There will be a break in the air curtain if the deflection modulus is not reached. (The deflection modulus is used to describe the sealing ability of the air curtain. It is the ratio of initial momentum in the air curtain jet to the transverse forces (buoyancy forces) that the air curtain is attempting to seal against. This is fully described by Hayes and Stoecker [14] and also in Chapter 7 of this book.) Initial turbulence intensity has a significant effect on the rate of heat transfer through the air curtain, as long as the initial velocity is large enough to maintain a continuous air curtain. The total heat transfer through the air curtain is directly proportional to the initial jet velocity and the temperature difference across it. There is a value of the deflection modulus, which exists for each air curtain configuration that minimizes the rate of heat transfer across it.
Finding the value of the deflection modulus that minimizes the rate of heat transfer across it is the holy grail of display cabinet designers. It is mainly found by trial and error, if at all. CFD offers the opportunity to predict the values of jet temperature, velocity, and turbulence that will minimize heat transfer across the curtain.
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There are two important dimensionless numbers which are used to categorize the air curtains. The Reynolds number (Re) is the ratio of momentum to viscous forces: Re ¼
ruD m
(4:1)
As display cabinet air curtains are refrigerated, they are negatively buoyant. The Richardson number (Ri) is the ratio of gravitational to momentum forces: Ri ¼
bgDTH u2
(4:2)
As the air leaves the discharge grille it starts to entrain air from both inside the cabinet and the ambient. This entrainment causes mixing in the jet. The air jet can be separated into distinct regions from the jet outlet at the discharge grille to the jet return at the return grille [15] (Figure 4.2). In the flow development region, the centerline velocity and temperature remain constant. Ambient air is unable to cross the curtain and enter the cabinet in this region. As the jet travels beyond this region, the jet centerline velocity will decrease and the temperature increases as air entrained from the ambient mixes through the curtain. Even though the momentum of the curtain remains constant (if we ignore buoyancy), the width and volume flow rate of the air curtain increase. This increase in flow rate is called entrainment. The level of entrainment can be defined by the entrainment ratio or coefficient: e¼
QRG QDG QDG
(4:3)
Potential core Discharge grille
Flow development region
Fully developed flow
Center line
FIGURE 4.2 Plane turbulent jet.
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In a retail display cabinet, air curtains are more complicated than the idealized jet described. Buoyant forces in a refrigerated air curtain mean that the air curtain will deflect from its path. The curtain will also probably impact on food and shelves on its way to the discharge grille. These factors will likely increase the level of entrainment. The sum of the mass flow rate through the discharge grille and rear grille will return through the return grille. The extra mass flow rate caused by entrainment cannot enter the return grille. Therefore, the entrained air from inside the cabinet will spill back into the cabinet warming the cabinet and entrained air from outside the cabinet will spill out of the cabinet causing the environment to cool (cold feet effect). A dimensionless number is commonly used to characterize the thermal influence of this entrainment: a¼
TRG TDG Tamb TDG
(4:4)
This number will always be between 0 and 1. A value of 0 means no entrainment (return temperature equals discharge temperature) and 1 is complete entrainment (return temperature equals ambient temperature). Navaz et al. [16] have established three phenomena which affects the level of entrainment. These are: (a) turbulence intensity, (b) Reynolds number (based on discharge grille width), and (c) velocity profile at the discharge grille. Chen and Yuan [17] measured the effect of the environment on air curtain heat loads. They showed that both increases in ambient temperature and relative humidity cause heat gain through the curtain to rise.
4.2.2 DEFROST The vast majority of multideck display cabinets will require defrosting of the refrigerant heat exchanger (evaporator coil). This is because ambient air of high moisture content will mix with the air curtain as explained above and some of this moisture will condense on the heat exchanger. In almost all cases the heat exchanger will be running below 08C and therefore the water will turn to ice. This ice needs to be removed from the heat exchanger before it becomes blocked. As ice builds up the velocity of the air passing through the heat exchanger drops, this can have a significant impact on product temperatures. There are three common methods of removing the ice: 1. With off cycle defrost, the ice is melted during the off cycle. When there is no demand for cooling, refrigerant is not passed through the heat exchanger. However, the heat exchanger fan is allowed to run until the heat exchanger rises to a set temperature above 08C. 2. Electric heaters in front of the heat exchanger or in the heat exchanger block are used to (generally at set time intervals) melt the ice. 3. Hot or warm gas defrost involves using either hot refrigerant gas from the compressor discharge or warm gas from the top of the receiver. The important thing to remember when modeling a display cabinet is that moisture buildup and defrosts cause a transient effect, where temperatures in the cabinet and the velocity through the discharge grille cycle up and down. Therefore, it is important to know when defrosts are taking place, so that boundary condition and verification measurements can be made at appropriate times.
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4.3 STANDARD TESTING Most retail display cabinets within Europe are tested to the European testing standard, EN441 [18–21]. This has recently been superseded by BS EN ISO 23953-1:2005, Part 1 and 2 [22,23] that has similar tests but slightly more stringent test room requirements. Within EN441-6 [20] chilled cabinets are described as M1 if all the temperatures of test packs are maintained between 18C and 58C, M2 if between 18C and 78C, or H if between 18C and 108C. A further, more stringent, temperature classification M0 is often used in the UK to describe cabinets that maintain the temperature of all the test packs between 18C and 48C. At present few cabinets conform to the M0 classification. A database of cabinets sold in the UK, which comply with the enhanced capital allowance scheme (ECAS) (a UK government scheme to allow incentives for purchasing energy efficient products [24]) contained 56 integral multideck cabinets that were classified as M1 or M2; however, only three cabinets were classified as M0. The airflow in the test room may be an important factor in the performance of the cabinet. Chen and Yuan [17] showed that increases in air speed parallel to the cabinet had a small effect on infiltration. D’Agaro et al. [25] showed that ambient air entrains preferably at the upstream side, which is estimated to increase the required refrigerating power by 30%. For the European standards the airflow must be parallel to the plane of the cabinet display opening and to the longitudinal axis. The velocity of this parallel flow should be in the range 0.1–0.2 m s1. This environmental flow is in the other plane to the cabinet flow and therefore to accurately model the display cabinet and the environment in an EN441 test requires a three-dimensional (3D) model. Testing in the US is carried out to a slightly different standard (ASHRAE 72-193). In this standard, ambient air currents must be parallel to the cabinet display opening but must not be more than 0.25 m s1. This means that the airflow could be the same as the European standard (0.1–0.2 m s1). There are other differences between the two standards in relation to the dummy product, loading of product, lighting level, etc. Testing of a display cabinet is very time-consuming. The cabinet needs to be loaded with test packs (either 1 or 0.5 kg). A typical cabinet will require over 300 of the 1 kg and 150 of the 0.5 kg packs. At least 50 of the 0.5 kg packs will require a thermometer inserted into their geometric center (m-packs). It is important to load the cabinet to a set specification as cabinet loading will greatly affect the performance of the cabinet. A logging system is required to record the temperature of all of the m-packs during a 24 h test. The cabinet will have to be left (generally for 24 h) to stabilize after any changes have been made. A major benefit of CFD modeling is the ability to reduce the amount of time required for cabinet testing.
4.4 CFD ANALYSIS Many authors [4–9] have shown CFD modeling to be a valuable tool to rapidly provide design options to improve airflow within display cabinets. Due to the speed that a variety of scenarios can be predicted, CFD provides an ideal means to both understand the airflow within the cabinet as well as determine which design options would provide improvements to the cabinet. These improvements may be required to meet the intended classification or to meet a tighter classification which may allow a premium price to be charged for CFD studies. There are a number of commercially available CFD codes that can be used; four popular codes are ANSYS CFX, FLUENT, STAR-CD, and PHOENICS. Modern codes are easier to use than codes in the past. Features such as automatic mesh generation can reduce the time
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to create a mesh from days to seconds. Moreover, today’s standard desktop PCs are easily capable of running these models. Other more specific codes have been used to good effect. For example, Axell et al. [26] have used a code designed for the simulation of fires in enclosures (SOFIE) successfully in the modeling of retail display cabinets.
4.4.1 EXPERIMENTAL INVESTIGATION Currently it is not feasible to create a CFD model of a whole cabinet that includes the necessary detail with which to troubleshoot all the cabinet performance failings. Instead, it is more appropriate to generate predictive models of different regions of the cabinet where problems have already been identified during the standard testing. Examples of problem areas found by the author in past testing are as follows: .
.
.
.
Large temperature gradients between the back and front of the cabinet, i.e., product at the back of the shelf will be too cold and product at the front too warm. This is either due to too little air entering from the holes in the rear grille and=or that the air curtain is ineffective. Temperatures too warm at the top of the cabinet—this is most likely to be caused by an air curtain that is being bent in towards the top shelves. Temperatures too warm at the bottom of the cabinet—this is often caused by too little air entering from the holes in the rear grille, specifically near the bottom. One side of the cabinet warmer than the other—this may be caused by an uneven geometry inside the cabinet, e.g., evaporator extends further on one side than the other. It may also be the consequence of the test standard, i.e., EN standards require air to flow across the face of the cabinet and this can cause uneven temperatures.
Once a problem area has been found, further testing with thermocouples and smoke visualization will lead to a better understanding of the problem. It is possible that this level of investigation is all that is required to fix the problem. However, if it is not, CFD has the potential to increase the understanding further and allows you to try ‘‘what-if ’’ scenarios.
4.4.2 SETTING UP
THE
CFD MODEL
Howell [27] assigned generic operating variables for the range of display cabinets in operation (Table 4.1). These data are a useful means of specifying boundary condition data if measured data is not available. Although modern CFD software has removed some of the required fluid dynamics knowledge of the user, some understanding of fluid dynamics is still required. An expert CFD user also needs an understanding of the physics of the problem they are trying to model. It is not currently possible to create a CFD model of a retail display cabinet that simulates everything perfectly. Assumptions will have to be made that will simplify the model, reducing its complexity and the computer resources required to solve the relevant equations. Below are some of the assumptions which will need to be considered. 4.4.2.1 Two or Three Dimensional Historically it has been commonplace to model the air curtain of a display cabinet in two dimensions (2D), this is very efficient in computer resources as a 3D model would require many times more memory and processor time. As the air curtain is long, a 2D model of the
22
24
Source: From Howell, R.H., Trans. ASHRAE, 99, 667, 1993. Note: Converted from imperial to metric units.
2 2 5 3 4 4 22 28 18
4 4 2 0 2 2 25 31 21 70 75 75 110 100 40 70 65 65 65
19
Discharge Thickness (mm)
1 1 8 6 7 7 19 26 15
Return Temperature (8C)
2.0
1.0 1.1 0.9 0.9 0.6 0.6 1.0 1.0 2.0
Discharge Velocity (m s21)
1.5
0.8 1.0 1.4 1.3 1.0 1.2 0.8 0.8 1.5
Distance from Discharge to Return (m)
Vertical
Horizontal Vertical Vertical Vertical Horizontal Vertical Horizontal Horizontal Vertical
Orientation of Air Curtain
110
Single shelf meat Multishelf meat Multishelf dairy Multishelf deli Single shelf produce Multishelf produce Single shelf frozen Single shelf ice cream Glass door reach-in frozen food (with=air curtain) Glass door reach-in ice cream (with=air curtain)
Case Description
Case Temperature (8C)
Discharge Temperature (8C)
TABLE 4.1 Generic Operating Variables for the Range of Display Cabinets in Operation
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central plane is commonly taken. As CFD codes are generally 3D, creating a model in 2D requires modeling of the third dimension with only one grid cell in that direction and using symmetry boundaries either side of the cell. Recently, increases in computer power have allowed 3D models of the air curtain to be produced. D’Agaro et al. [25] showed that the extremity effects caused by the side walls in reduced length cabinets lead to inaccurate results unless a 3D simulation tool is used. Axell et al. [26] produced a 3D model just for one shelf of a display cabinet to allow the flow from the pattern of holes in the rear grille to be predicted. 4.4.2.2 Mesh Size In the past, creating a computational mesh was a very time-consuming task. Since the advent of unstructured meshing, most CFD codes are able to create a mesh that fits the geometry efficiently. It is sometimes necessary to refine this mesh in specific areas to provide the best accuracy for given computer resources. If computer resources are large and the problem to be meshed small, the simple solution is to create lots of small grid cells. This is often not the case and it is more appropriate to have a finer mesh in certain areas than others. The areas which require a fine mesh will be the areas which are of most interest and have the largest velocity and temperature gradients. If vortices are likely, a mesh in the area of the vortex needs to be fine enough to resolve it. In the case of air curtain predictions, it is usual to have the finest mesh covering the likely position of the air curtain as it drops down the cabinet and the coarsest mesh in the ambient space outside the cabinet. The number of cells required will vary depending on whether the simulation is 2D or 3D, the overall size of the geometry, the size of the smallest element in the geometry, and the type of turbulence model used. The amount of mesh points available will depend on the computer hardware and the central processing unit (CPU) time available. The amount of random access memory (RAM) required for the meshing will depend on the CFD code, 100,000 mesh cells will require between 40 and 300 Mb of RAM. It is obvious from the literature that computer resources limit the accuracy and resolution of CFD results. For example, Cortella et al. [28] restricted their mesh to 20,000 grid points to reduce CPU time on a Hewlett-Packard (HP) C100 workstation using a large-eddy simulation (LES) turbulence model. 4.4.2.3 Turbulence Model Turbulence consists of fluctuations in the flow field in time and space. It is a complex process, mainly because it is 3D, unsteady, and consists of many scales. It can have a significant effect on the characteristics of the flow and the magnitude of heat transfer. Turbulence occurs when the inertia forces in the fluid become significant compared to viscous forces, and is characterized by a high Reynolds number (Equation 4.1). It is possible to directly predict turbulence using the Navier–Stokes equations that form the basis of CFD, however, the range of length scales and timescales required to do this requires enormous computer resources. Instead, turbulence models can be used, which account for the effects of turbulence without requiring a prohibitively fine mesh. The simplest of these are the statistical turbulence models. When looking at timescales much larger than the timescales of turbulent fluctuations, turbulent flow could be said to exhibit average characteristics, with an additional time-varying component. The Navier– Stokes equations are modified to produce the Reynolds averaged Navier–Stokes (RANS) equations. These equations model the mean flow quantities only. The averaging procedure introduces additional unknown terms containing products of the fluctuating quantities, which
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act like additional stresses in the fluid. These terms, called ‘‘turbulent’’ or ‘‘Reynolds’’ stresses, are determined using the turbulence model. Two-equation turbulence models are the most commonly used. This is because they offer a good compromise between numerical effort and computational accuracy. The k–« model [29] is the industry standard model and the most commonly used turbulence model found in the literature [6,8,9,30,31]. It uses two variables, the turbulent kinetic energy, k, and turbulence dissipation rate, «. It is, however, reputed to overestimate the air entrainment at the edge of the jet [4]. Navaz et al. [7] used the k–« model for the core flow, in combination with Cebeci–Smith algebraic model near the wall region, to avoid a high-resolution grid near the wall. There is another form of the k–« model called the renormalization group (RNG) k–« model. It is basically the same as traditional k–« model, the transport equations for turbulence generation and dissipation are the same, but the model constants differ. This model offers little improvement over the standard model and other authors [3] have obtained almost identical results with the two models. The biggest problem that the k–« model provides to the CFD user is that both k and « need to be defined at the inlets. To define k requires a knowledge of the turbulence intensity. Turbulence intensity can be measured using a very fine hot-wire anemometer. This equipment is expensive (>£2500), delicate, and generally not in the hands of retail display cabinet manufacturers, because of this, k is often estimated. Modern CFD codes offer reasonable default values and advice on how it can be estimated. « can be estimated using k and an appropriate length scale. If the level of turbulence is unknown and cannot be measured, a sensitivity analysis could be performed. This analysis could be used to see the effect of high and low levels of turbulence on the system, if the level of turbulence does not significantly affect the results then it is not important to know it accurately. Because the length to width ratio of a display cabinet air curtain is high, Ge and Tassou [31] suggested that the effect of initial turbulence intensity will be quite small. Stribling [9] compared the k–« and Reynolds stress model. The Reynolds stress model does not use the eddy viscosity hypothesis, but solves an equation for the transport of Reynolds stresses in the fluid and is therefore more computationally intensive. The difference between the two models was found to be less than that found between predicted and measured velocities. Statistical models are satisfactory in steady-state conditions; however, they can lead to errors in transient simulations. LES estimates the turbulent fluxes on the basis of vorticity theory. Cortella and D’Agaro [3] have found very different results when comparing LES and k–« models. 4.4.2.4
Buoyancy
The purpose of the air curtain is to provide a momentum force to oppose the buoyant force caused by the difference in density=temperature between the air inside and outside of the cabinet. The buoyant force therefore requires modeling to predict the system. One way of doing this is to model air as an ideal gas where its density is linked to the temperature by the ideal gas law: p ¼ rRT
(4:5)
However, this is numerically more complex and generally unnecessary given the limited temperature differences experienced with display cabinets. A numerically simpler approach is to use the Boussinesq approximation: r rref ¼ rref b(T Tref )
(4:6)
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This model uses a constant density fluid, but applies a local gravitational body force throughout the fluid, which is a linear function of fluid thermal expansivity and the local temperature difference with reference to a datum. The Boussinesq approximation is appropriate only if density variations are small, e.g., a few percent or less. Buoyant flow is more difficult to solve than nonbuoyant flow. The flow is likely to be unstable and can cause the CFD solver to crash or fail to reach an acceptable answer. It may be better to use a transient model and accept that there is no steady-state solution. If the model is of the ducting rather than the air curtain, the temperature differences are low and the forced convection component high and therefore a buoyant model will have little benefit over a nonbuoyant model. 4.4.2.5 Steady State or Transient? The airflow in the cabinet can generally be modeled as steady state. There will be a reduction of flow rate between defrost cycles as the evaporator coil ices up but this can be examined by carrying out steady-state models at both the higher and lower flow rate condition. Although turbulence is a transient phenomenon, statistical turbulence models allow a steady-state mean flow to be predicted. Food temperature will vary between defrost cycles and this effect could be modeled using a transient model. However, mean food temperatures could be predicted using a steady-state model. If using LES turbulence models the numerical solutions do not achieve a steady state, Cortella et al. [32] stopped their calculations when the time-averaged value of return air temperature stopped varying with time. 4.4.2.6 Humidity Humidity of the air has a significant effect on the display cabinet. A higher humidity in the ambient air will increase the heat load on the cabinet due to latent heat exchange through infiltration and will cause the evaporator to frost. Van Oort [8] and Ge and Tassou [31] have incorporated moisture content of the air into their CFD models. However, it is possible to solve the flow field for dry air and calculate the increase in load caused by the humidity using _ Lw Q1 ¼ awa m
(4:7)
4.4.2.7 Boundary Conditions The first stage of creating a CFD model is defining the domain to model. This can be deduced after careful consideration of the results gathered from the experimental investigation. The most common area of investigation is the air curtain. The boundaries of this domain are the discharge and return grille, rear grille, and the outside environment (ambient). A description of these boundary conditions follows. If another domain was chosen, e.g., the air inside the ducting of the cabinet, a different set of boundary conditions would be chosen. 4.4.2.7.1
Discharge Grille
The boundary condition used for the discharge grille is generally termed an ‘‘inlet.’’ A simple assumption used for the flow from the discharge grille is a constant velocity across the grille. This can be obtained by using a vane anemometer with a measurement head of similar size to the grille. In real cases, the air velocity from the grille is probably not uniform. Figure 4.3 shows measured velocities from a discharge grille, both before and after defrost. A more accurate profile can be entered into the model only if there are enough mesh cells covering this boundary to resolve it.
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1 0.9
Vertical velocity (m s−1)
0.8 0.7 0.6 0.5 0.4 0.3 Just after defrost Just before defrost
0.2 0.1 0 0
20
40
60
80
100
Distance from front of discharge grille (mm)
FIGURE 4.3 Velocity profile exiting discharge grille.
Turbulence will vary along the length of the jet, with the highest at the interface [16]. An accurate model of entrainment requires both setting the velocity and turbulence profiles at the outlet or predicting them by modeling the flow further upstream in the duct. 4.4.2.7.2
Rear Grille
The boundary condition for the rear grille is also set as an inlet. The rear grille usually comprises an array of holes punched out of a plate. To model the air flowing through each of the holes in the rear panel while also modeling the air curtain would require far too many grid cells and therefore would be too computer intensive. It would also require a 3D model unless the holes were modeled as slots. It is common to assume that all of the flow enters the rear grille through one large hole that covers the entire area of the rear grille. This assumption is probably correct a few hole diameters downstream of the rear panel, as all of the small highvelocity jets would entrain together to form one large low-velocity jet. Axell et al. [26] carried out simulations using three different assumptions for the round holes: (a) square holes (with the same hydraulic diameter as the circular holes), (b) thin slots (with the same opening area as a whole row of circular holes), and (c) wide slots (the width of a slot was the same as the diameter of the holes). The square-shaped holes gave the most accurate flow profile. However, by the time the flow had reached the front of the shelf, the profiles for all three assumptions were similar. 4.4.2.7.3
Return Grille
The return grille can be set as an ‘‘outlet’’ where the mass flow rate through the outlet is equal to the mass flow rate through all of the inlets (discharge grille and rear grille). 4.4.2.7.4
Ambient
If the entrainment of air from the surroundings is to be investigated, a boundary condition that simulates the ambient is required. Placing an ‘‘opening’’ type boundary, a few meters in front of the cabinet can be used. This opening boundary allows air to travel out or in depending on the pressure at that position.
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Product
As the primary function of a display cabinet is to keep food cold and not to cool it down, modeling the product temperature is often not necessary. The product may be modeled as an adiabatic or constant temperature obstruction to the flow and a steady-state solution carried out. The ability of the cabinet to keep the product cold can be derived from the air temperatures around the product. In reality the product will be warmer than the air around it because it gains heat via radiation. Faramarzi [11] showed the radiation load on the cabinet to be 12% and Madireddi and Agarwal [33] showed this to be 10% of the total load and therefore significant. The product temperature can be predicted by a combination of convection from the air to the product surface, conduction from the food surface into the body of the product, and radiation between the food surface and other surfaces in view. There are a number of radiation models available in CFD code. In the situation of modeling the radiation between surfaces of a display cabinet, the air is transparent to radiation. In this case, the radiation only affects the air by heating or cooling the surfaces of the domain, with no radiant energy transfer directly to the air. For this particular case the Monte Carlo model is the most appropriate. The Monte Carlo method simulates the physical interactions between photons and their environment. There is a computational overhead associated with tracking the photons across the domain and therefore a coarser mesh is used for the radiation field. In addition to the surface temperatures, the emissivity will also be required. Hawkins et al. [34] have carried out a study of the effects of low emissivity materials on display cabinets; this paper is a useful source to establish product emissivities. However, if none of the surfaces are shiny it is safe to assume all surfaces have an emissivity of 0.9. Heat transfer through the product (conjugate heat transfer (CHT)) requires that only the energy equation is solved in these regions, so compared with the same number of nodes in a fluid region CPU usage is reduced. Cortella [5] separated the prediction of load temperature and airflow due to the very different time constants of the transient phenomena involved. He used a finite element model to predict the product temperature and coupled this with a CFD code to predict fluid properties. 4.4.2.7.6
Walls
Walls of the cabinet can be modeled as nonslip walls, either adiabatic or constant temperature, if the temperature is known. It is of course possible to model the heat load through the walls of the cabinet given a known thickness and thermal conductivity. However, the heat load from conduction is only 4% of the total heat load [11] and therefore generally ignored. 4.4.2.7.7
Rear Duct
It is possible to extend the model of the air curtain to an entire circuit, i.e., for the flow to be modeled from the return grille through the evaporator and out through the discharge grille. In this case, the discharge return grille and rear grille would not be specified as inlet and outlet boundary conditions; instead the velocities and temperatures through these grilles would be predicted. Lan et al. [6] have carried out such a simulation. They used a porous region to simulate the rear grille. The advantage of this method is that the effect of holes within the plate (porous plate) can be modeled without the need for a complex mesh. The porous region effectively acts as a resistance to flow. Two parameters are required, the volume porosity and the Darcy coefficient. Lan et al. measured a volume porosity (the ratio of area of holes to total area) of 0.036.
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They used a Darcy coefficient of 0.2 to calculate the flow resistance in the direction through the holes. They used a large value for the Darcy coefficient for the direction perpendicular to this, as flow through the rear grille is unidirectional. They treated the perforated return grille and the evaporator in the same way. The evaporator is also a thermal sink. Heat can be removed from the volume to simulate the cooling of the evaporator. Lan et al. [6] adjusted the magnitude of the heat loss until it matched experimental measurements of temperature at the exit.
4.4.3 CONVERGENCE AND MESH INDEPENDENCE The level of accuracy of the predictions is defined by the residual error. This residual error should decrease with each iteration; if this happens, the solution is said to be converging. When the residual error has converged to a satisfactory level, the predicted values can be taken as the output and viewed by a graphical viewer. It is at this point where the CFD user who has knowledge of the fluid dynamics of the system he or she is trying to model will hopefully spot any errors or misjudged assumptions in the predictions. It is likely the first predictions may contain errors, may not have converged to the necessary accuracy, or the mesh was not fine enough. After corrections have been made to the model, the numerical error should be assessed. Judgment of convergence is a bit of a black art, however, the following rules [35] are a guide. The size of the maximum residual if .
. . .
.
.
>5 104 is very poor, global balances will be poor and quantitative data is largely unreliable (this is good enough for getting a rough idea of flow phenomena or making pretty pictures) 5 104 is loose convergence, but good enough for most engineering applications 1 104 is good convergence, often sufficient for most engineering applications 5 105 is tight convergence (if geometry and boundary conditions are not well defined, then this may be more than necessary (since errors in the geometry=boundary undary conditions will be greater than this) and it is often not possible to achieve this level of convergence) 1 105 or lower is very tight convergence, sometimes required for geometrically sensitive problems 1 106 to 1 107 is machine round-off (this level of convergence is not possible without double precision, in most cases and convergence this tight is only of academic interest)
Typically root mean square (RMS) residuals are about a factor of 10 smaller than the maximum residual, and so the above guidelines for maximum residuals can also be applied to RMS residuals, with the targets reduced appropriately. If the solution is still converging beyond your specified residual level, it is valuable to converge to a lower solution to establish whether further convergence will change your results appreciably. If a buoyant model is being used, which will be the case if the air curtain is being studied, convergence will be more difficult. A solution to this problem is to reduce the size of the time step; this will make the model take longer to run, but will increase its accuracy. Cortella and D’Agaro [3] used a time step of 0.01 s and RMS residual of 104 for transient simulation of the air curtain. Opening boundaries, which have both inflow and outflow, may be required in modeling the ambient entrainment for the air curtain. These boundaries can lead to instabilities that
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impede convergence to the desired residual level. By keeping these boundaries a distance from the area of interest, e.g., the air curtain, it is less likely that they will effect it. By monitoring the result of interest, e.g., a product or return grille temperature, etc., during the convergence it will be possible to assess whether the desired result has reached a constant value. Once the solution has converged satisfactorily, a check will need to be made that the solution is mesh independent. This means that if the mesh is refined, the solution will not change. This can happen if the mesh that has been applied to the problem is not small enough to resolve the physics, e.g., to pick up recirculation zones. If heat transfer is being predicted from a wall to the air it is important to ensure that wall boundary layers have adequate mesh resolution. The mesh resolution in a boundary layer affects the prediction of convective heat transfer and the temperature gradient near the wall. For walls without a specified temperature, e.g., the surface of the product, the temperature gradient near the wall affects the calculated surface temperature and, consequently, the amount of radiation emitted (if radiation is being modeled).
4.4.4 POSTPROCESSING Visualization of the results is arguably the most exciting part of the CFD analysis. It is at this point where it may become obvious that the CFD model is an error and the reasons why may or may not be obvious. If the model is correct, the results may reinforce what is already known. This may not be a bad thing since one of the advantages of CFD is its ability to convey knowledge of how a retail display cabinet works. The author has shown CFD visualization to people who have worked with display cabinets for many years but had never seen the airflow represented in such a clear manner as with CFD. It is also possible that the visualization will show something unexpected; this can be very exciting, especially if it can be experimentally verified. A personal example of this was when a CFD model predicted an unexpected vortex in the corner of display cabinet, which was later verified using laser doppler anemometry (LDA) [36]. Modern CFD software has a multitude of colorful ways of representing the predictions. For 2D models of display cabinets, color contours representing the temperature and vectors representing the air velocity are most commonly used (Figure 4.4). For 3D models the contours and vectors can be plotted in representative planes. It is sometimes necessary to visualize the flow through the whole 3D region without being confined to 2D planes. This can be achieved by plotting streamlines (Figure 4.6). The airflow from a region, e.g., from the air discharge grille, can be followed through the 3D domain and out through another boundary, e.g., through an ambient opening. Postprocessing is an important step in the CFD analysis process. CFD generates large quantities of data and this must be clearly presented. The postprocessing tool allows the user to qualitatively visualize flow and also to extract quantitative numbers for direct comparison with experimental data and assessment of performance. These postprocessors are normally built into the CFD suite of software and often not available when the results are to be presented to an external audience. Exporting graphical images of areas of interest and displaying in Microsoft PowerPointß are a common ways of disseminating the results. Postprocessors often allow animations to be exported so that transients can be more easily represented and these can be imported into Microsoft PowerPoint. The problem with this type of dissemination is that 3D models cannot be rotated, which can be very useful for visualizing the flow. If data is exported in virtual reality modeling language (VRML) output, this holds the 3D geometry and using a VRML viewer this geometry can be rotated.
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Temperature
15 mm
−0.0
−0.8
−1.5
−2.3
Product
−3.0 [°C] Y
z
X
CFX
FIGURE 4.4 (See color insert following page 142.) Velocity vectors predicted by CFD in a vertical plane at the top of the cabinet. The length of the vector is proportional to the air velocity, the color represents the temperature (air curtain 1.5 m s1 and 15 mm).
Presenting CFD visualization in scientific publications is difficult as they are generally grayscale. Although CFD visualization can be output in grayscale, it is not easy conveying all the information in a grayscale figure. Many publications now have a Web-based version and this will usually allow color figures.
4.5 RESULTS FROM TYPICAL SIMULATIONS The following section shows results from typical simulations, which have been published by this author.
4.5.1 AIR CURTAIN A multideck cabinet originally designed to meet the EN441 M2 (18C to 78C) classification was required to perform to the M0 (18C to 48C) temperature classification. CFD was used as a tool to recommend design improvements to achieve this. The cabinet was lightly loaded (in accordance with the requirements for loading a cabinet intended for storage of sensitive products) with gaps present between shelves that enabled vortices to be generated. Prior to modifications the temperature of all ‘‘m’’ packs was above 18C and below 78C. However, only 42 m-packs (out of 54) spent the entire test period between 18C and 48C. A maximum temperature of 6.98C was measured in the m-pack positioned at the top right front of the well. A minimum temperature of 18C was recorded in the m-pack situated at the top rear left of the well. The area of most concern in terms of high temperatures was located at the center and right front of shelf 1 and the front edges of the well. The flow of air as it exited the discharge grille and traveled down the cabinet was simulated. To reduce complexity of the model and concentrate on the area of interest, the air curtain for only the top shelf was modeled. The existing air curtain exiting the discharge
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60 mm
Temperature −0.0
−0.8
−1.5 Product −2.3
−3.0 [°C]
Y Z
X
CFX
FIGURE 4.5 Velocity vectors predicted by CFD in a vertical plane at the top of the cabinet. The length of the vector is proportional to the air velocity; the color represents the temperature (air curtain 0.375 m s1 and 60 mm).
grille had a velocity of 1.5 m s1 and a temperature of 18C, with the jet pointing vertically downwards. The width of the air curtain was 15 mm. The problem was considered to be 2D as the cabinet and air curtain were very long; therefore, end effects could be ignored. Turbulence was likely to be an important factor and was therefore modeled using the k–« model. Buoyancy was also another important factor as it is the difference in density caused by temperature difference between inside and outside the cabinet, which causes deflection of the air curtain. The CFD model predicted that the air curtain would be bent towards the product and hit the outer corner of the product (Figure 4.4). A vortex was then created, which draws warmer air over the front of the product. The air curtain would also be disrupted bringing warmer air onto the shelves below. CFD modeling was used to investigate the effect of a number of modifications including changing the width and angle of the curtain. Increasing the width of the air curtain to 60 mm, while keeping the volume flow rate through the air curtain constant, was predicted to remove the vortex. This was likely to keep the product cooler and also maintain a better air curtain for the next shelf down (Figure 4.5). The CFD predictions also showed that there were benefits in angling the air curtain away from the shelves, and that the optimum angle depends on the width and velocity of the curtain.
4.5.2 MODELING OF
THE
DUCT
The cabinet used in the previous section also had an uneven temperature left to right, which could not be attributed to the airflow in the room. Asymmetries within the duct were examined. It is not possible for the evaporator to run the full width of the cabinet due to the turns at the ends of the evaporator; these are often greater on one side of the evaporator than the other. These problems can lead to both a 3D and unsymmetrical flow within the duct.
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Rear duct
Evaporator Z Y
X
Dead space CFX
FIGURE 4.6 Streamlines predicted by CFD from the exit of the evaporator for the unmodified cabinet.
The cabinet presented in the previous section had a 110 mm gap between each end of the duct and the evaporator. Air, which exited the evaporator, had therefore to change in direction by 908 to enter the edge of the duct. CFD was used to model the flow of air as it exited the evaporator and entered the rear duct. Only the bottom edge of the cabinet was considered, where air from the evaporator was required to fill the dead space previously identified at the edges of the cabinet. Figure 4.6 shows streamlines predicted by CFD from the exit of the evaporator for the unmodified cabinet. The predictions show that as air leaves the evaporator it moves out to the side to fill the dead space and then travels up the rear duct. In doing so the air spirals up the rear duct at the edge. This type of airflow was likely to result in vortices as the air entered the cabinet rather than the uniform flow required. To address this problem the following design solutions were proposed: 1. Make the evaporator as wide as possible (reducing the length of the dead space). 2. Move the evaporator towards the front of the cabinet and create an angle such that the air would more easily move to the edge of the duct. 3. Insert an angled plate at the bottom of the duct to increase the pressure and even-out the flow. Figure 4.7 shows streamlines predicted by CFD from the exit of the evaporator for the modified cabinet (length of evaporator extended such that there was only a 50 mm dead space at each end of the cabinet, evaporator moved forward by 80 mm, angle to expand air to the edge of the duct and a turning vane). With these modifications the CFD predicted that no vortex would develop.
4.5.3 SHELVING To minimize disruption of the air curtain it is ideal to have the front of the shelves present as flat a face as possible [37]. Shelves fully loaded with product to the edge of the shelf help
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Turning vane
Z Y
X
CFX
FIGURE 4.7 (See color insert following page 142.) Streamlines predicted by CFD from the exit of the evaporator for the modified cabinet.
achieve this. As the product is removed from the shelves during the buying process a larger gap appears for the air curtain to negotiate. This causes the air curtain to bend inwards, causing more entrainment (Figure 4.8). Infiltration rates with varying shelving=product were predicted using the CFD model. These infiltration rates were put into a refrigeration model to predict energy consumption of the compressor. They showed that when the cabinet was fully loaded the energy consumption was least (570 W per meter length of cabinet). The energy consumption increased to a maximum when all shelves=product were removed (653 W per meter length of cabinet).
4.5.4 COLD FEET EFFECT The cold feet effect is caused by mixing between the air curtain and environment as discussed in Section 4.2. Foster and Quarini [38] studied the cold feet effect. The aim of the work was to quantify the effect in three supermarket chains and use CFD to investigate ways of alleviating it. Two different scales of CFD model were used. 4.5.4.1 Whole Store The first was of the whole store sales area; this was run on a Silicon Graphics R10000 workstation with 256 Mb RAM. The store was ventilated by inlet diffusers, which forced air out in four directions (towards the front, back, and both sides of the store). Because of this, each of the 13 diffusers had to be modeled as 4 separate inlets, giving a total of 52 inlets in the model. The inlets were modeled as constant velocities of 4.2 m s1 at an angle of 458 to the ceiling. The temperature of the air at the inlet was 268C. These data were taken from measurements carried out at the store. The eight return diffusers were modeled as mass flow boundaries. By design, only half the air that entered the store, left through these diffusers.
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FIGURE 4.8 (See color insert following page 142.) 2D model of a multideck display cabinet showing velocity vectors and temperature contours. The air curtain is bent in toward the cabinet where shelves have been removed.
This was to keep the store at a slightly higher pressure than outside to avoid ‘‘dirty’’ air entering the store. It was considered that most of this air would exit through doorways. Putting each of the doorways into the model would have made it too complex (in terms of the number of mesh points). Therefore, a mass flow boundary was set along the bottom of the four side walls. The cabinets and shelving were modeled as solid blocks to restrict flow around the store. For the refrigerated cabinets (chilled and frozen) a heat sink was set in front of the blocks. This simulated the quantity of heat removed from the store. The values were chosen from ASHRAE [39] and varied for the different types of refrigerated cabinet. The store had a heated floor in the chilled and frozen aisles during the winter. The heated floor was simulated by setting a constant temperature boundary condition of 198C and a heat transfer coefficient of 9.3 W m2 K1. The internal dimensions of the store were 64 m 37 m 24 m. The geometry was divided into a grid of 130,000 cells, with a resolution of between 30 and 600 mm. This number of grid cells was quite large when the work was carried out in 1997 and needed to be run on a UNIX workstation. This is now considered to be a small number of grid cells and could easily be run on a desktop personal computer (PC). Figure 4.9 shows predicted and measured temperatures of the supermarket store at two heights. Although the temperatures predicted were not the same as measured, the trends were very similar. The model clearly showed that the level of stratification reduced significantly between the chilled and ambient aisles. It showed that the temperature at floor level was dictated by the location of the chilled cabinets. At a height of 2 m the model showed that the cabinets had little effect and that the temperature range was small. The model also showed that warm air from the inlets did not spread very far.
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19.1
21.7
19.6
22.1
21.9
21.5
21.8
22.1
22.0
18.0
22.0
18.1 16.7
> 2.9000E + 02 2.8773E + 02 2.8462E + 02 2.8150E + 02 2.7838E + 02 2.7527E + 02 < 2.7300E + 02
22.4
18.2
> 2.9800E + 02 2.9720E + 02 2.9610E + 02 2.9500E + 02 2.9390E + 02 2.9280E + 02 < 2.9200E + 02
13.3
13.3 14.3 12.6
0.25 m above floor
21.8
21.6
21.1
21.7 22.2 22.4 22.4
16.5
23.3
2 m above floor
FIGURE 4.9 (See color insert following page 142.) Plan view of store at a height of 0.25 m and 2.0 m. Colors show predicted temperatures (K) and values of measured temperature (8C) are superimposed.
4.5.4.2 Aisle The computer model of the whole store was too large to model detail in the store and the time taken for convergence was too long to carry out many what-if scenarios in a limited time. To reduce the complexity of the model, just a chilled aisle was modeled. Three symmetry planes were used to reduce the number of grid cells further. The cabinet was modeled as a solid object with an inlet boundary at the top face blowing cold air vertically downward. An outlet boundary was positioned at the bottom of the cabinet. The temperature and velocity at the inlet were 28C and 1.0 m s1, respectively. Warm ambient air was required to enter and leave the domain. Previous modeling and experiment showed that cold air escaped at floor level out of the aisle and warm air entered at high level. Because of the positions of the symmetry planes, the floor and ceiling of the model, there was only one boundary face that could exchange this air and it was at the end of the aisle. A constant pressure boundary was chosen to simulate the air entering and leaving the aisle. The temperature of air entering the aisle was 228C and the temperature of the floor wall–boundary was 148C (these were taken from measurements). Predicted and measured temperatures in chilled aisles in three different supermarkets are shown in Figure 4.10. The simulation was found to be a good approximation of the three different stores. The temperature near the floor, the gradient of the temperature stratification, and the constant temperature region above the cabinet were all predicted accurately. This model was then used to predict the effect of different heating and ventilation strategies. These were heated floors, air mixing, which drew cold air from under the cabinet and projected it upwards between the cabinets and high velocity vertically blowing fans in the center of the aisle. The CFD model was able to predict the effect of these strategies and relay them back to the supermarket heating and ventilation engineers. Tassou and Xiang [40] carried out a very similar study. They also found the complexity of modeling the entire store too great and chose to model an aisle using the same symmetry planes. However, with more modern hardware, they were able to model the food within the
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25 23
Temperature (°C)
21 19
Safeway center Sainsbury center ASDA center CFD center Safeway end Sainsbury end ASDA end CFD end
17 15 13 11 9 7 0.0
1.0
2.0
3.0
4.0
5.0
Distance from floor (m)
FIGURE 4.10 Temperatures measured at two positions in three different stores in the coldest aisles and temperatures predicted from the numerical model.
cabinet. They showed that under-floor heating had little effect on air temperatures in the aisle (18C or 28C in the center of the aisle); this is in agreement with the work by Foster and Quarini. It is important to note that although the cabinet has an effect on the store environment, the store environment also has an effect on the cabinet. As Tassou and Xiang’s model included the product they were able to simulate this. They showed that the heated floor causes a temperature rise on the surface of the products facing the aisle of around 2.28C and a rise at the core of the product of approximately 0.88C. This was due to heat transfer by radiation between the floor and the chilled products in the cabinet. Increasing the heat flux on the floor would reduce cold discomfort but would have a detrimental effect on the chilled products in the cabinet.
4.6 VERIFICATION Verification is an important part of any type of simulation. Navaz et al. [7] state that CFD needs to be calibrated. It is all too easy to accept the simulation as correct because it looks right. Only through verification of your simulation will you gain the confidence to trust further simulations. Due to the complexities of the flow within retail display cabinets, many assumptions are used to create a CFD simulation. Verification will provide the only real proof of the accuracy of these assumptions. If verification shows the model to be inaccurate these assumptions will need to be reviewed and a more accurate simulation attempted. Verification can range in complexity and there are a number of methods that can be used to validate a CFD model. These extend from the simplest methods that may provide just one important value by which to validate the model, to highly complex experimental methods that provide transient values at many positions. Measurement of temperature is the easiest method of validation, as this can be measured simply and cheaply using thermocouples at multiple positions. Madireddi and Agarwal [33]
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used an infrared (FLIR Systems) thermal imaging camera to compare temperature contours of the air curtain with those predicted by CFD, although the method in which this was done has not been reported. Measurement of velocity is more expensive and complicated. As velocity is a vector quantity, a direction as well as a magnitude needs to be measured. Vane anemometers can be used; however, they need to be lined up with the direction of the flow, which needs to be ascertained if not known. They are also large and therefore give an average velocity over a relatively large area. Hot-wire anemometry is another method by which to measure velocity. They are less susceptible to the direction of flow and measure over a much smaller area. A large number of hot-wire anemometer measurements are required to build up a picture of the airflow of a refrigerated display cabinet and their use can disrupt the already turbulent airflow. Axel et al. [26] showed that hot-wire anemometers should not be installed too close to each other. They showed that disturbances between sensors can be created by natural convection and by the size and shape of the sensor. If it is connected to a traverse, as used by Howell and Shibata [13] to study heat transfer through turbulent recirculated plane air curtains, the velocity at known positions in the air curtain can be measured without too much disruption. If the hot wire is fine enough and connected to a high-frequency data logger, the turbulence of the jet can also be measured. Direction of the velocity is a more difficult value to measure; it can be done using smoke or tufts of tissue paper. Recording the flow direction at multiple points requires some image analysis. If infiltration through the curtain is the important value you are trying to validate, then validating the air curtain velocity is an indirect way of doing this. A better and more direct way to do this would be to measure the infiltration by tracer gas techniques. Axell and Fahlen [10] have used a tracer gas to study infiltration through the air curtain. There are many types of gases which can be used. Sulfur hexafluoride (SF6) is advantageous as it can be detected at extremely low concentrations; however, it requires expensive mass spectrometry to do this. Carbon dioxide (CO2) has disadvantages in that there is a fine line between high enough concentrations to measure and low enough to be safe. However, it can be detected using much cheaper infrared meters. Particle image velocimetry (PIV) offers an ideal method of verifying CFD simulations, as it can provide a similar level of resolution of the flow field as the simulation. PIV has been used by Navaz et al. [41] together with LDA and CFD to study the flow field of an air curtain in a fully loaded open vertical display cabinet with horizontal shelves. Particle image velocimetry provides noninvasive velocity measurements and visualization in a cross section of airflow. The velocity vectors are derived from the movement of seeding particles between two light pulses. The target area for the measurements is illuminated with a light sheet and a digital camera is used to image the target area onto a charge-coupled device (CCD) array. The CCD is able to capture each light pulse in separate image frames. Once a sequence of two light pulses is recorded, the images are divided into small subsections called interrogation areas. The interrogation areas from each image frame are cross-correlated with each other thus identifying a common particle displacement and hence velocity. This is repeated for each interrogation area, creating a vector map of the complete target area.
4.7 CONCLUSIONS Chilled multideck retail display cabinets are a common mechanism for displaying chilled food. Getting these cabinets to meet the tight temperature standards required by supermarkets and also to be energy efficient is expensive by conventional means.
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CFD modeling has been proved by many authors to be an invaluable tool in understanding the heat transfer mechanisms of retail display cabinets. Although CFD modeling in this industry is still in the hands of academics, whose project timescales are an order of magnitude longer than industrial project timescales, this is beginning to change. CFD software has become more user-friendly, operates on standard desktop PCs, and reasonable predictions can be obtained in days rather than months (total timescale of generating the model to final conclusions ready to test). However, it should be remembered that anybody can obtain a colorful picture that looks correct, it is still necessary to have a user with an understanding of the physics and to experimentally validate test results. CFD is not yet at the stage and may never be, where testing and validation can be eliminated. For this reason CFD should be considered as a tool to allow the reduction of testing not its elimination.
NOMENCLATURE D e g H QDG QRG Re Ri DT TRG TDG Tamb Tref u
Hydraulic diameter (m) Entrainment ratio, dimensionless Acceleration due to gravity (9.81 m s2) Height (m) Mass flow rate at the discharge grille (kg s1) Mass flow rate of the jet at the return grille (kg s1) Reynolds number, dimensionless Richardson number, dimensionless Temperature difference (K or 8C) Temperature at return grille (K or 8C) Temperature at discharge grille (K or 8C) Temperature at ambient (K or 8C) Reference temperature (K or 8C) Velocity (m s1)
GREEK SYMBOLS a b r rref m
Thermal entrainment coefficient, dimensionless Coefficient of expansion, dimensionless Density (kg m3) Reference density (kg m3) Viscosity (kg m1 s1)
REFERENCES 1. P Olsson. Chilled cabinet surveys. In: Processing and Quality of Foods. Vol. 3. London: Elsevier Applied Science, 1990, pp. 279–288. 2. SJ James, JA Evans. Temperatures in the retail and domestic chilled chain. In: Processing and Quality of Foods. Vol. 3. London: Elsevier Applied Science, 1990, pp. 273–278. 3. G Cortella, P D’Agaro. Air curtains design in a vertical open display cabinet. In: Proceedings of International Institute of Refrigeration, Urbana, 2002, pp. 57–65. 4. JN Baleo, L Guyonnaud, C Solliec. Numerical simulations of air flow distribution in a refrigerated display case air curtain. In: Proceedings of International Institute of Refrigeration, The Hague, 1995, pp. 681–687. 5. G Cortella. CFD aided retail cabinets design. Computers and Electronics in Agriculture 34: 43–66, 2002.
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6. TH Lan, DHT Gotham, MW Collins. A numerical simulation of the air flow and heat transfer in a refrigerated food display cabinet. In: Proceedings of the European Thermal Sciences, Rome, 1996, pp. 1139–1146. 7. HK Navaz, R Faramarzi, M Gharib, D Dabiri, D Modaress. The application of advanced methods in analyzing the performance of the air curtain in a refrigerated display case. Transactions of the American Society of Mechanical Engineers, Journal of Fluids Engineering 124(3): 756– 764, 2002. 8. H Van Ort, RJM Van Gerwen. Air flow optimisation in refrigerated cabinets. In: Proceedings of International Institute of Refrigeration, The Hague, 1995, pp. 446–453. 9. D Stribling, SA Tassou, D Marriot. A two dimensional CFD model of a refrigerated display case. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 103(1): 88–95, 1997. 10. M Axell, P Fahlen. Climatic influence on display cabinet performance. In: Proceedings of International Institute of Refrigeration, Urbana, 2002, pp. 175–184. 11. R Faramarzi. Efficient display case refrigeration. Ashrae Journal 41(11): 46–54, 1999. 12. Van Baxter. Energy-efficient supermarket display cases. IEA Heat Pump Newsletter 22(3): 14–16, 2004. 13. RH Howell, M Shibata. Optimum heat transfer through turbulent recirculated plane air curtains. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 86(1): 188–200, 1980. 14. FC Hayes, WF Stoecker. Heat transfer characteristics of an air curtain. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 2120: 168–180, 1969. 15. N Rajaratnam. Turbulent Jets. Amsterdam: Elsevier Scientific, 1976. 16. HK Navaz, BS Henderson, R Faramarzi, A Pourmovahed, F Taugwalder. Jet entrainment rate in air curtain of open refrigerated display cases. International Journal of Refrigeration 28(2): 267–275, 2005. 17. YG Chen, XL Yuan. Experimental study of the performance of single-band air curtains for a multi-deck refrigerated display cabinet. Journal of Food Engineering 69(3): 261–267, 2005. 18. EN441-4:1995. Refrigerated Display Cabinets. General Test Conditions. CEN, European Standard. 19. EN441-5:1996. Refrigerated Display Cabinets. Temperature Test. CEN, European Standard. 20. EN441-6:1995. Refrigerated Display Cabinets. Classification According to Temperature. European Standard. 21. EN441-9:1995. Refrigerated Display Cabinets. Electrical Energy Consumption Test. European Standard. 22. BS EN ISO 23953-1:2005. Refrigerated Display Cabinets–Part 1: Vocabulary. 23. BS EN ISO 23953-2:2005. Refrigerated Display Cabinets–Part 2: Classification, Requirements and Test Conditions. 24. Enhanced Capital Allowance Scheme, The Carbon Trust, http:==www.eca.gov.uk, London, UK. 25. P D’Agaro, G Croce, G Cortella, P Schiesara. Investigation on air curtains behavior in display cabinets by means of 3-d computational fluid dynamics. In: Proceedings of International Institute of Refrigeration, Vicenza, 2005, pp. 71–78. 26. M Axell, PO Fahlen, H Tuovinen. Influence of air distribution and load arrangements in display cabinets. In: Proceedings of International Institute of Refrigeration, Sydney, 1999, paper 152. 27. RH Howell. Effects of store relative humidity on refrigerated display case performance (rp-596). Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 99(1): 667–678, 1993. 28. G Cortella, M Manzan, G Comini. CFD simulation of refrigerated display cabinets. International Journal of Refrigeration 24(3): 250–260, 2001. 29. BE Launder, DB Spalding. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289, 1974. 30. W Xiang, SA Tassou. A dynamic model for vertical multideck refrigerated display cabinets. In: Proceedings of International Institute of Refrigeration, Sofia, 1998, pp. 637–644. 31. YT Ge, SA Tassou. Simulation of the performance of single jet air curtains for vertical refrigerated display cabinets. Applied Thermal Engineering 21(2): 201–220, 2001.
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32. G Cortella, M Manzan, G Comini. CFD simulation of refrigerated display cabinets. International Journal of Refrigeration 24(3): 250–260, 2001. 33. S Madireddi, R Agarwal. Computation of three-dimensional flow field and heat transfer inside an open refrigerated display case with an air curtain. In: Proceedings of International Institute of Refrigeration, Vicenza, 2005, pp. 79–86. 34. AC Hawkins, CA Pearson, D Raynor. Advantages of low emissivity materials to products in commercial refrigerated open display cabinets. In: Proceedings of Institute of Refrigeration, London, 1973, pp. 54–64. 35. ANSYS CFX User Manual, online. 36. Application of CFD and 3 component LDA to refrigerated cabinet flows. FPERC Newsletter, University of Bristol, 16: 4–5, 1997. 37. AM Foster, SJ James. Using CFD in the design of food cooking, cooling and display plant equipment. In: Second European Symposium on Sous vide, Leuven, 1996, pp. 43–57. 38. AM Foster, GL Quarini. Using advanced modelling techniques to reduce the cold spillage from retail display cabinets into supermarket stores to maintain customer comfort. Proceedings of the Institution of Mechanical Engineers Part E. Journal of Process Mechanical Engineering 215(1): 29–38, 2001. 39. ASHRAE (American Society of Heating, Refrigeration and Air Conditioning Engineers), Handbook, Applications, 1991, pp. 2,3. 40. SA Tassou, W Xiang. Interactions between the environment and open refrigerated display cabinets in retail food stores-design approaches to reduce shopper discomfort. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 109(1): 299–306, 2003. 41. HK Navaz, R Faramarzi, M Gharib, D Dabiri, D Modarress. The application of advanced methods in analyzing the performance of the air curtain in a refrigerated display case. Transactions of the American Society of Mechanical Engineers Journal of Fluids Engineering 124(3): 756–764, 2002.
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CFD Design of Air Curtain for Open Refrigerated Display Cases Homayun K. Navaz, Ramin Faramarzi, and Mazyar Amin
CONTENTS 5.1 5.2 5.3
Background................................................................................................................ 129 Introduction ............................................................................................................... 130 Model Description ..................................................................................................... 131 5.3.1 Outside Domain ............................................................................................. 134 5.3.2 Inside Domain ................................................................................................ 136 5.4 Conclusion ................................................................................................................. 139 Acknowledgment................................................................................................................ 140 Nomenclature ..................................................................................................................... 140 References .......................................................................................................................... 140
5.1 BACKGROUND Open vertical refrigerated display cases are widely used in supermarkets and grocery stores to maintain the food products at a prescribed temperature while allowing the customers to easily reach for the food products. The operation and main features of all contributors to the dynamics of an air curtain are shown in Figure 5.1. The cold air is supplied to the case through a discharge air grille (DAG) at the top and in some cases through a perforated back panel (BP). A fan located at the lower portion of the case pulls the air flow toward a return air grille (RAG) that is recirculated after coming into contact with cold coils. The air curtain is referred to the region of air flowing from the DAG to the RAG. The existence of a momentum gradient between the air curtain and its surrounding air causes an entrainment of the outside warm air that will partially mix with the cold air forming the air curtain. Therefore, the temperature of the air curtain as it travels down toward the RAG increases. Since the total air flow rate inside the display case is constant, a portion of the entrained air will overspill from the case after mixing with the cold air curtain. The overspill air temperature is higher than the cold air temperature originating from the DAG and lower than the room temperature. Similarly, the temperature of the air at the RAG is between the cold air and warm air temperatures. The magnitude of the air temperature at the RAG and also for the overspill air is a function of the amount of entrained air and turbulence-enhanced mixing
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Discharge air grille (DAG) or honeycomb
Entrained air
Overspilled air (mixture of warm and cold air)
Air curtain
Return air grille (RAG)
Coil
Back panel (BP)
Fan
Coils
FIGURE 5.1 Main features of an open refrigerated display case.
of cold and warm air along the air curtain flow. The portion of the warm air that is mixed with the cold air and is going through the RAG is referred to as the infiltration rate. It appears that the infiltration rate is directly proportional to the entrainment rate; however, this may not be a sufficient condition, i.e., higher entrainment rate does not necessarily result into an increase in infiltration rate. The ‘‘effectiveness’’ of mixing and structural integrity of the air curtain thereafter has also a significant effect on the infiltration of the warm air into the display case.
5.2 INTRODUCTION The motion of fluids is controlled by the mass and momentum conservation differential equations referred to as the Navier–Stokes (NS) equation. In many engineering applications a flow of heat (energy) also is accompanied by the transport of mass and momentum. The NS equations are usually augmented by adding the energy conservation equation, resulting from the first law of thermodynamics. Therefore, referring to NS equations usually includes the energy conservation equation. Before the advent of computers, the solution to these nonlinear set of equations could have only been obtained for a limited number of simple problems involving fluid flow and heat transfer. In the past, most of the equations developed for engineering applications mostly relied on dimensional analysis (similitude) and calibration of such correlations based on experimental data and curve fitting. Although this provided a very practical tool for engineers in terms of a global approach, it lacked the detailed information needed for close examination of a system leading to an optimized design. Obtaining solutions to NS equations became more of a reality with the development of faster computers during the 1980s and gave birth to the computational fluid dynamics (CFD) area in engineering and mathematical sciences. One of the first NS solvers was developed at Los Alamos National Laboratory called VNAP [1] and was based on MacCormack explicit predictor–corrector scheme. A semi-implicit algorithm for incompressible flow was developed by Qin and Spalding [2] and a family of semi-implicit commercial codes [3–5] was spun off the
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original algorithm thereafter, and all of them are commercially available through different vendors. A more detailed discussion of the CFD genesis is given by Navaz and Berg [6]. However, it was not until mid-1990s that the commercial industry felt comfortable with CFD applications mainly due to the difficulties that were usually encountered in tedious process of setting up a model for a CFD run including the mesh generation. Introducing interactive front end (IFE) for data entry and advances in grid generation somewhat simplified this process. In recent years, using CFD application has become an integrated part of most design processes involving fluid flow or heat transfer. In spite of all the progress in the field of CFD, care should be taken in using and interpreting the results of a CFD code. The numerical solution to NS equations is still an approximation; they still rely on embedded models such as turbulence, evaporation, etc., and last but not least the existence of multiple solutions for a problem is a possibility. So, it is fair to state that the CFD technique is still evolving and at this point they are not independent of validation and verification tests. For several years CFD tools were mainly used in aerospace industry for finding solutions to rocket engine and shock layer flows. It was not until 1990s that CFD found its way into the automotive industry due to the ongoing progress in the field of numerical techniques. During late 1990s CFD applications found their way into analyzing mainly the air flow, heating and=or cooling in food industry [7,8]. A comprehensive review of the previous literature demonstrates that CFD is a powerful tool that can be implemented for parametric study of air flow as applied to air curtains or refrigeration systems [8,9]. Such studies, if performed in a systematic and meaningful way, can lead to design optimization of such systems. The intention of this work is not only to demonstrate that CFD can be used as a viable design tool, but also to lay out a methodology of implementing it in a systematic and cohesive manner to ensure reliable results. Before attempting such extended and comprehensive studies a protocol should be designed and followed. The purpose of this research was to develop such a protocol or methodology to show the effectiveness of CFD tools in performing parametric studies to lower infiltration of the warm air into the air curtain leading to the design of more energy-efficient open refrigerated display cases.
5.3 MODEL DESCRIPTION CFD provides detailed local information about the fluid flow, therefore, giving insight into ways to alter a design for better performance. Furthermore, when validated, it can be used as a tool to perform parametric studies with a high level of confidence leading to optimization of a design. Generally, in open refrigerated display cases, it is desired not only to reduce the entrainment of warm and moist air onto the air curtain air flow stream, but also to minimize its mixing rate with the cold air. Achieving these two goals will reduce the infiltration of the warm moist air into the display case through the RAG. It is important to quantify the amount of entrained warm and moist air and its partial infiltration into the cold air curtain as a function of design parameters. To accomplish this, it is preferred to decouple the flows inside and outside of the display case. This approach will eliminate the need for the modeling of the fan by only considering the end result of its operation, i.e., the total air flow rate inside the display case. However, this approach requires a priori knowledge of velocity profile, volumetric flow rate, and turbulence intensity at certain boundaries of the domain. This information can only be achieved by direct measurements at these boundaries referred to as boundary conditions that are needed for the CFD applications. To clarify the proposed two-domain approach, the schematics of ‘‘inside’’ and ‘‘outside’’ domains are shown in Figure 5.2. The cold air exits from the DAG and the BP and after mixing with the outside warm air, it enters the display case through the RAG. Since the problem is divided into two
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BPF
DAG
Shelf
BPF Outside domain Shelf
BPF
Inside domain
Constant temperature open boundary
Wall
Wall
Shelf
BPF
RAG Plexiglas Coils Wall
FIGURE 5.2 Schematic of the inside and outside domains with boundary conditions.
domains, care must be taken in implementing the boundary conditions for the CFD analysis. This is important because the boundary conditions set the process of information propagation throughout the domain and the final solution thereafter. Experimental methods are used to properly specify the boundary conditions that are required for each domain as discussed later. Experimental methods can also be used to validate and verify the computational procedure. Accurate definition of boundary conditions for the DAG is even more important than other boundaries because it is the origin of the air curtain and its characteristics will affect the behavior of an air curtain. The boundaries that need to be specified are shown in Figure 5.2 and they will be discussed further. Earlier studies [10] have indicated that for the range of Reynolds number considered in this work (>2000), the temperature gradient across the air curtain does not contribute to the entrainment and infiltration as much as the momentum gradient. Therefore, temperature will not be considered as a major contributor to the infiltration rate in this work. An open vertical refrigerated display case manufactured by Hill Phoenix was used to vary the Reynolds number and the velocity profile at the DAG. Dummy food products filled with test packages (or product simulator) were put on shelves to simulate the presence of food product in the display case according to ASHRAE Standard 72-1983. The food products are composed of 80% to 90% water, fibrous materials, and salt. A plastic container completely filled with a sponge material that is soaked in a brine solution of water and salt (6% by mass) was used to simulate the product. Air flows in three-dimensional space requiring excessive computational resources for parametric studies. On the other hand, since the length of DAG and RAG is much greater than their width, a two-dimensional analysis can be justified if the velocity profile maintains the same basic shape along the DAG grille. The velocity and temperature profiles across the RAG should also be known by measurements. The first quantity is used to find the total mass
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LDV at 1.22 m from one end (middle) PIV at 1.22 m from one end (middle) LDV at 1.83 m from one end (1/4 distance from one end)
Vertical velocity (m s−1)
−0.2 −0.4 −0.6 −0.8 −1 −1.2 −1.4 −1.6 0.01 0.02 0.03 0.04 0.05 0.06 Distance across the DAG from inside to outside (m)
FIGURE 5.3 Vertical velocity profiles along the display case by LDV and PIV measurements. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
(or volumetric) flow rate inside the display case and the latter measurement will determine the average temperature at the RAG. This average temperature is needed to calculate the infiltration rate based on the enthalpy method described in Ref. [11]. Two experimental methods that can effectively yield information about the velocity and turbulence intensity profiles are the laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) techniques. Both methods can be used in parallel (for more reliability) or independently to define the velocity and turbulence intensity profiles at the DAG and RAG. The velocity profile exiting the DAG is maintained somewhat unchanged to about 5 cm of the two ends. Figure 5.3 shows some of the measurements made about 0.6 m (2 ft) apart, with one being the center of the display case. It is seen that the basic characteristics of the vertical velocity profile are unchanged as predicted by both LDV and PIV measurements. This finding justifies a two-dimensional CFD modeling that is more feasible and practical approach. Generally, three-dimensional flow fields are more complex and computationally more demanding. Therefore, a two-dimensional CFD modeling can be used to proceed to the next step. It should also be noted that these measurements are performed at about 2.5 cm below the DAG plane. To model the BP geometry in two dimensions, the number of perforations and their area were measured and they were incorporated as eight longitudinal slots along the display case representing an identical area in two dimensions. The flow distribution through these perforations was not equal. The mass outflow rate through these slots was changed until the temperature distribution inside the case became similar to that of an infrared (IR) measurements as will be pointed out later. To have an accurate measurement of the display case total air mass flow rate, the front of the RAG was replaced by a Plexiglas to allow the laser beam to go through the RAG for velocity measurements as indicated in Figure 5.2. The velocity profile across the RAG was measured and was similar to a typical turbulent profile and remained the same along the display case. The average velocity at the RAG provided an accurate measurement of the total volumetric air flow rate that is needed for the two-domain analysis [11]. This preliminary
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study was necessary to understand the individual flow situation and to provide justification for the two-dimensional CFD model.
5.3.1 OUTSIDE DOMAIN It is necessary to develop a model for this portion of the flow because it defines the characteristic of flow and the mixing level that is present along the air curtain. It also specifies the amount of entrained air and infiltration rates because both are a part of this domain. Due to elliptic nature of the flow in any display case the incorrect specification of boundary conditions will propagate into the domain resulting in erroneous prediction of entrainment and infiltration rates. Furthermore, parametric studies will be reliable after the validation of the CFD code. It should be noted that the validation and specification of proper boundary conditions to a certain extent are analogous. For instance, measuring the velocity profile at the DAG not only serves as a boundary condition for the outside domain, but also can be compared to the velocity profile resulting from the CFD solution of the inside domain for validation. Basically, the presence of significant turbulence intensity at the DAG will trigger more mixing from the origination point of the air curtain (or jet). The development of turbulence will speed up the existence of a high shear segment in the profile. When Figure 5.3 is examined, the velocity profile at the DAG has two distinct maxima. Figure 5.4 shows the turbulence intensity at the DAG as predicted by LDV and PIV. The turbulence intensity increases significantly at the interface of the two velocity peaks due to an increase in shear stress. At this point we can define the following boundary conditions for this domain: 1. Velocity profile, turbulence intensity at the DAG as specified by LDV and PIV and shown in Figure 5.3 and Figure 5.4. The temperature is assumed to be constant for the air at DAG. 2. Left wall at room pressure and temperature. 3. No-slip wall at the bottom, top, and back wall. 4. Display case walls and shelves are defined as no-slip adiabatic wall.
Turbulence intensity (% of the mean flow)
DPIV LDV
30
25
20
15
10 0
0.06 0.02 0.04 Distance across and 2.5 cm below the DAG (m)
FIGURE 5.4 Experimental turbulence intensity at the DAG. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
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5. Specified exiting mass flow rate (also display case total mass flow rate) at RAG as specified by LDV and PIV measurements through the Plexiglas. 6. By knowing the display case total (measured at RAG) and DAG mass flow rates, the total mass flow rate through the BP can be found. The temperature of the exiting air from the BP is constant and equal to that of DAG, and by knowing the total area of the perforated spots, the velocity can be calculated. Now the question is how to distribute the _ RAG ¼ Total ¼ m _ DAG þ m _ BP) among slots? To accomplish this, remaining mass flow rate (m an IR camera mapped the temperature distribution throughout the outside domain then the mass was distributed arbitrarily until the CFD generated the same temperature field. It was found that the flow of mass through the perforated BP reduces from bottom to top. The computational analysis for the inside domain further verified this proposed approach and is discussed in the next section. The temperature fields obtained by CFD and mapped by IR camera are forced to match in boundary condition (6) as seen from Figure 5.5 by varying the mass distribution among shelves. The data for velocity field and streamlines taken by PIV match with those of the simulation analysis as seen in Figure 5.6. The agreement between the calculated and observed IR image defines the air distribution among shelves. These values will serve to specify the exit boundary conditions excluding DAG for the inside domain (boundary condition (2) in the inside domain). The verification of the simulation with experiment for the final result, i.e., the infiltration rate is necessary. To accomplish this, the amount of entrained air is calculated from Figure 5.6 for the CFD and PIV results by extracting the data in front of the display case and integrating
Temperature (⬚C) 25 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 −1 −2.2
88.75 80.70 72.64 64.59 56.53 48.48 40.42 32.36 24.30
FIGURE 5.5 Comparison between the CFD and IR image for temperature field. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
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Vertical velocity (m s−1) 0.65 0.55 0.45 0.35 0.25 0.15 0.05 −0.05 −0.15 −0.25 −0.35 −0.45 −0.55 −0.65 −0.75 −0.85 −0.95 −1.05 −1.15 −1.25
1.5
1
0.5
Vertical velocity (m s−1)
Y
2
Distance in y-direction (m)
Distance in y-direction (m)
2
X
1
0.65 0.55 0.45 0.35 0.25 0.15 0.05 −0.05 −0.15 −0.25 −0.35 −0.45 −0.55 −0.65 −0.75 −0.85 −0.95 −1.05 −1.15 −1.25
0 0
1.5 0.5 1 Distance in x-direction (m)
(DPIV)
2
0
1 2 Distance in x-direction (m)
(CFD)
FIGURE 5.6 Vertical velocity contours and streamlines by PIV and CFD. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
it over the area. It was found that the entrainment rates predicted by CFD and PIV were, respectively, 9.20 m3 min1 (325 CFM, cubic feet per minute) and 9.06 m3 min1 (320 CFM). Again, it is important to realize that the entrainment and infiltration rates are two different parameters and it should be understood that an increase in entrainment does not necessarily translate directly to an increase in infiltration rate. This correlation only exists under enhanced mixing conditions throughout the air curtain necessitating calculation or direct measurement of the infiltrated outside air through the RAG. For this particular case, the infiltrated amount of warm air was calculated by using the enthalpies as shown in the previous work [11]. The enthalpy method derived in Ref. [11] requires the average temperature at the Ð RAG to evaluate the infiltration rate. The average temperature can be obtained _ , where y and m _ are the local vertical velocity and the total mass flow fromT ¼ RAG ryTdA=m rate, respectively. Based on the enthalpy method, the amount of infiltrated warm air was calculated to be about 35% of the entrained air that is about 3.20 m3 min1 (114 CFM). The amount of infiltrated warm air by collecting the condensate from the coil and relating it to the room humidity was measured to be 3.00 m3 min1 (100 CFM). Although these quantities are close, a direct measurement of the infiltrated warm air through other methods will be advantageous and is a part of the scope of the ongoing research. The meticulous validation and verification that is laid out increases the confidence in any parametric study. Any parameter such as the turbulence intensity, velocity at the DAG, and=or dimensions of the display case can be altered for the outside domain and the entrained and=or infiltrated air can be calculated to examine the effects of each parameter on the infiltration.
5.3.2 INSIDE DOMAIN The prior research [12] has indicated that the velocity profile (shape) affects the mixing and entrainment rate. In principle, the two-peak shape that was shown in Figure 5.3 should be
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0
Height (cm)
Vertical velocity (m min−1)
−50
−100
200 150 100 50 0 −50 −100 −150 −200 −250 −300
0 50 Horizontal distance (cm)
FIGURE 5.7 Vertical velocity contours and vectors at the DAG (inside domain).
avoided. This shape or the velocity profile is a function of the geometry inside the display case particularly the DAG region. Now the question is how to perform reliable parametric studies to obtain the desired velocity profile at the DAG by altering the DAG geometry before its exit plane. For this purpose, a CFD model is built for the interior region of the display case. The evaporator coil is modeled as an obstruction and the honeycomb at the DAG is modeled as series of small slots. The actual geometry of the DAG is taken from the computer-aided design (CAD) files. The following boundary conditions are imposed: 1. Inlet velocity (or mass flow rate) at the RAG is specified as measured by LDV. 2. The velocity through the BP was specified as outlets with the values obtained from boundary conditions of the outside domain. 3. DAG was specified as a jet with no specified velocity and room pressure. The total volumetric flow rate in the display case was about 32.8 m3 min1 (930 CFM) that generated the RAG average velocity of about 100 m min1 (300 ft min1). The velocity contours and vectors at the DAG are shown in Figure 5.7. The velocity profile at the DAG is the outcome of the modeling solution and it should resemble the experimental data. This velocity can be extracted from Figure 5.7 and is shown and compared with experimental PIV and LDV measurements in Figure 5.8a. Considering that the PIV and LDV data are taken about 2.5 cm below the exit plane of the DAG whereas the velocity profile for the inside domain model is extracted exactly at the DAG exit, some ‘‘spreading’’ can be expected. Figure 5.8a clearly demonstrates this fact therefore, it can be concluded that this is an excellent agreement. For further validation, the geometry of the DAG is altered to a 208 slanted surface shifting the more pronounced peak toward the outside of the display case. Figure 5.8b shows this new geometry with its corresponding turbulence kinetic energy as the flow approaches the exit plane of the DAG. It can be seen that the turbulence intensity has somewhat decreased inside the DAG. The 208 slanted nozzle caused the flow to have a more
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8 6 4 2 0 0
5 10 Horizontal distance (cm)
0.84000 0.50622 0.30507 0.18385 0.11079 0.06677 0.04024 0.02425 0.01461 0.00881 0.00531 0.00320 0.00193 0.00116 0.00070
0 −50
−20
−100 −40 −150 −60
−80
−200 CFD prediction PIV LDV
−250
−20 Vertical velocity (m min−1)
Vertical velocity at the DAG (m min−1)
0
Vertical velocity at the DAG (ft min−1)
Vertical distance (cm)
Turbulent kinetic energy (J kg−1)
−60 −80
−100
CFD LDV 2.5 cm below the DAG
−120
6 8 2 4 Distance from outside to inside at the DAG (cm)
(a)
−40
2 3 4 5 6 7 8 9 Distance from outside to inside (cm)
(b)
FIGURE 5.8 Two DAG geometries with corresponding experimental and analytical exit velocities. (Courtesy of Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., ASHRAE Trans., 111(Part 1), 1084, 2005. With permission.)
pronounced peak toward the outside of the display case as seen in Figure 5.8b. From these results it can be concluded that the model for the inside domain is fairly robust and it can be used for further studies. In an attempt to eliminate the two-peak configuration to postpone turbulence development along the air curtain, and also trying to avoid a ‘‘sharp’’ velocity peak responsible for large velocity gradients that can contribute to the turbulence intensity development, another configuration was considered in the modeling. This configuration had a 578 slanted surface with widen throat before the air curtain exit. Figure 5.9 shows this geometry and its corresponding velocity at the exit as compared to the previous validated cases. This appeared to be an improvement over the other two cases. In fact the 208 slanted nozzle produced a sharp peak toward the outside of the display case that will create an increased shear stress and it is expected to increase the entrainment rate. Furthermore, the peak of the velocity should be more toward the inner section of the display case to enhance mixing in the colder region and not the outside of the case. Therefore, the latter case should yield the least entrainment rate. Parametric studies reveal that this is the case at all turbulence levels as seen from Figure 5.10. It is also seen that the entrainment rate for the 208 slanted surface has a more pronounced entrainment rate than the original case, as expected.
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Vertical velocity across the DAG (m min−1)
Turbulence kinetic energy (J kg-1) 578 Slanted surface
0.84000 0.41339 0.20344 0.10012 0.04927 0.02425 0.01193 0.00587 0.00289 0.00142 0.00070
0
0
−50
−20
Vertical velocity across the DAG (ft min−1)
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−100
−40
−150
−60
−200 −250
−80
−300
−100
Original DAG design 20⬚ Slanted surface 57⬚ Slanted surface
−120
−350 −400 −450
−140 0
1 2 3 4 5 6 7 8 Distance across the DAG from outside to inside (cm)
−500
FIGURE 5.9 The improved DAG geometry and its vertical velocity profile compared to previous cases. (Courtesy of Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., ASHRAE Trans., 111(Part 1), 1084, 2005.)
5.4 CONCLUSION
surface 578 Slanted
7 6 5 4 3 2 1 0
0
0.1 0.2 0.3 0.4 0.5 Entrainment rate/ total case flow rate
8
0
n
Original desig
9
Entrainment rate (ft3 min-1)
Entrainment rate (m3 min-1)
10
50
11
0
ce 208 Slanted surfa
12
100 150 200 250 300 350 400
A methodology that is based on a hybrid experimental=computational approach was developed to study the air curtain of a refrigerated display case. The experimental data were used to not only specify the correct boundary conditions for the CFD analysis, but also they were compared to the analytical results for the purpose of validation. It was also shown that how the two-domain approach, if posed correctly, can eliminate the need for inclusion of a fan model that introduces a significant uncertainty to the overall problem. A protocol was also developed for using CFD to generate accurate and meaningful results for entrainment, infiltration, and temperature field that are dictated by the velocity and turbulence distribution
10 5 15 20 Turbulence intensity at the discharge air grille
FIGURE 5.10 Entrainment for three geometries as a function of turbulence intensity at the DAG. (Courtesy of Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., ASHRAE Trans., 111(Part 1), 1084, 2005. With permission.)
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within the flow applicable to any open refrigerated display case configuration. It was also demonstrated that a calibrated CFD tool can be used to conduct parametric studies that can lead to an optimized display case, i.e., minimizing the infiltration of warm air.
ACKNOWLEDGMENT This work was partially sponsored by the US Department of Energy, Office of Building Technology, State and Community Programs under contract DE-AC05-00OR22725 with UT-Battelle, LLC. The authors wish to thank Southern California Edison (SCE) Company for allowing us to use their RTTC facilities for our testing and also Mr. Van D. Baxter from the Oak Ridge National Laboratory for monitoring the project and providing us with his support and advice.
NOMENCLATURE back panel flow (m3 min1) computational fluid dynamics cubic feet per minute (ft3 min1) discharge air grille digital particle image velocimetry pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 turbulence intensity, for isotropic fluctuations: I ¼ 2k=3Vmean , dimensionless turbulence kinetic energy (m2 s2 or J kg1) mass flow rate (kg s1) particle image velocimetry return air grille Reynolds number, based on DAG width, Re ¼ rVw=m, where r is the density, w is the DAG width, m is the viscosity, and V is the average discharge velocity, dimensionless IR infrared RTTC refrigeration and thermal test center SCE Southern California Edison T temperature (K or 8C) u0 horizontal velocity fluctuation (m s1) v0 vertical velocity fluctuation (m s1) w DAG width (m)
BPF CFD CFM DAG DPIV I k _ m PIV RAG Re
GREEK SYMBOLS r m
density (kg m3) molecular viscosity (N s m2)
REFERENCES 1. Cline, M.C., VNAP2: A Computer Program for Computation of Two-Dimensional, TimeDependent Compressible Turbulent Flow, LANL Report LA-8872, August 1981. 2. Qin, H.Q., and Spalding, D.B., The Lagrangian hydrodynamical calculations in PHOENICS code, Computational Fluid Dynamics Unit, Imperial College, London, UK, 1989. 3. CFD-ACE, Theory Manual, CFD Research Corporation, Version 1.0, Huntsville, AL, 1993. 4. The Fluent Code, Users Manual, Fluent, Inc.
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5. STAR-CD Code, Users Manual, Adapco Corp. 6. Navaz, H.K. and Berg, R.M., Numerical treatment of multi-phase flow equations with chemistry and stiff source terms, Journal of Aerospace Science and Technology, 2(3): 219–229, 1998. 7. Stribling, D., Tassou, S.A., and Mariott, D., A two-dimensional CFD model of a refrigerated display case, ASHRAE Transactions, 103(Part 1): 88–94, 1997. 8. Modarress, D., Gharib, M., Dabiri, D., and Navaz, H.K., Experimental and computational analysis of an air curtain display case, Technical Report Prepared for the Southern California Edison Company, Contract No. K1069006, December 1999. 9. Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., Past, present, and future research towards air curtain performance optimization, ASHRAE Transactions, 111(Part 1): 1084–1088, 2005. 10. Navaz, H.K., Faramarzi, R., Dabiri, D., Gharib, M., and Modarress, D., The application of advanced methods in analyzing the performance of the air curtain in a refrigerated display case, Journal of Fluid Engineering, ASME Transactions, 124: 756–764, 2002. 11. Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Jet entrainment rate in air curtain of open refrigerated display cases, International Journal of Refrigeration, 28(2): 267–275, 2005. 12. Navaz, H.K., Amin, M., Srinivasan, C.R., and Faramarzi, R., Jet entrainment minimization in air curtain of open refrigerated display cases, International Journal of Numerical Methods for Heat and Fluid Flow, 16(4): 417–430, 2006.
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Investigation of Methods to Improve Retail Food Store Environment Using CFD Savvas Tassou and Weizhong Xiang
CONTENTS 6.1 6.2 6.3 6.4
Introduction ............................................................................................................... 143 Model of Vertical Multideck Display Cabinet........................................................... 144 Modeling a Display Cabinet Zone in Retail Food Stores.......................................... 146 Display Cabinet Zone without Accessory Heating System........................................ 146 6.4.1 Effect of Distance between Free Boundary and Display Cabinets ................. 146 6.4.2 Modeling the Display Cabinet Zone without Heating System ....................... 147 6.5 Factors that Could Influence the Simulation Results ................................................ 151 6.5.1 Ambient Air Temperature .............................................................................. 151 6.5.2 Cabinet Air Circulation Rate ......................................................................... 151 6.5.3 Air Supply (Evaporator Coil Air off ) Temperature ....................................... 152 6.6 Display Cabinet Zone with Hot Air Heating System ................................................ 152 6.7 Display Cabinet Zone with Underfloor Heating System ........................................... 154 6.8 Extract and Supply System ........................................................................................ 155 6.8.1 Top Suction and Bottom Supply System........................................................ 157 6.8.2 Bottom Extract System................................................................................... 159 6.8.3 Bottom Extract and Top Supply .................................................................... 160 6.9 Conclusions................................................................................................................ 165 References .......................................................................................................................... 166
6.1 INTRODUCTION Food display cabinets are the main refrigerated fixtures in modern food retail stores. The refrigeration systems that serve the refrigerated cabinets and other refrigerated fixtures, such as walk-in coolers, consume close to 50% of the total energy consumption of the store and so their efficiency and food storage integrity are critical to the economic viability of the store and to the impact of retail food stores on the environment. The most common type of cabinet, certainly for medium temperature applications, is the open vertical multideck display cabinet. This design has become popular due to its large display area and ease of access for customers. An air curtain is normally used to reduce the heat and moisture exchange between the cabinet and the store environment. However, irrespective of the design and efficiency of the air curtain, there is always an interaction between the air curtain and the environment, causing entrainment and mixing of warm air 143
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from the environment with cold air in the display cabinet. As a result of the additional air drawn in from the ambient, there is a corresponding quantity of cold air spilling out of the cabinet into the aisles formed between rows of display cabinets. This cold air spillage causes discomfort to customers shopping in the retail food store. In order to improve thermal comfort, measures should be taken to raise the air temperature at low level in the aisles without affecting the product temperature and refrigeration load. To investigate ways to improve thermal comfort in retail food stores, the computational fluid dynamics (CFD) technique was employed to study the effect of different approaches in heating the air at low level within the aisles located in the refrigerated food area of the store. The study involved the development and validation of a vertical multideck chilled food display cabinet model. This cabinet model was then used to develop a model of a display cabinet zone in a food retail store, which incorporated a row of cabinets and the aisle between the cabinets. The model considered the interactions between the display cabinet air and the air in the aisle as well as the effect of different heating approaches on the air in the cabinet zone, product temperature, and display cabinet thermal load. The heating systems that were investigated included a hot air system, an underfloor heating system, and thermal destratification systems (bottom extract and top supply and top extract and bottom supply).
6.2 MODEL OF VERTICAL MULTIDECK DISPLAY CABINET The open vertical multideck display cabinet was first modeled and validated against test results obtained in an environmental test chamber. A cross section of the cabinet and measuring points during tests in the chamber are shown in Figure 6.1. Construction details and the geometric characteristics of the cabinet as well as modeling and test procedures are described in Ref. [1]. The flow in the environmental chamber and the display cabinet was
Temperature sensor Relative humidity sensor Air velocity sensor 20 20 Product temperature sensor arrangement 20
20
1500
Sensor arrangement at return grille 500
500 100
FIGURE 6.1 Display cabinet and measuring points in the environmental test chamber.
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modeled using the Renormalization Group (RNG) k« model. The products in the cabinet were assumed to be of rectangular shape and stacked uniformly, which made it possible to model them as a conducting solid. With this approach, the solid region was not taken as a boundary but calculated as a part of the fluid that has infinite viscosity. The heat transfer between the fluid and solid can then be solved using the equation proposed in Ref. [2]. To model the radiative heat transfer between the display cabinet and the environment the discrete transfer radiation model (DTRM) was used [3,4]. The perforated back panel and the honeycomb of the air curtain outlet were modeled using the porous media approach [5]. The solution of the conservation equations for mass, momentum, energy, species, and turbulent quantities is based on the control volume technique. This consists of . .
.
Division of the domain into discrete control volumes using a general curvilinear grid Integration of the governing equations on the individual control volumes to construct the algebraic equations for discrete unknowns (velocities, pressure, scalars) Solution of the discretized equations
To achieve accurate representation of the flow, when meshing the computational geometry, grids are concentrated in the positions where the temperature and velocity gradients are high, such as the air supply tunnel, the air curtain outlet, and the air return grille. Following this principle, the cabinet and test chamber geometry was meshed as 51 72 30 (i, j, k) grids. Grid independence tests were carried out to ensure that the grid chosen provided the best compromise between speed and solution accuracy. Figure 6.2 shows the baseline mesh scheme of the computational domain. A detailed comparison of simulation and test results was carried out to validate the CFD model [1]. It was found that the model could predict product and air temperatures in the cabinet with a maximum error of 1.08C.
FIGURE 6.2 Meshing scheme of the display cabinet in the environmental chamber.
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6.3 MODELING A DISPLAY CABINET ZONE IN RETAIL FOOD STORES Display cabinets in retail food stores are linked to the store environment system by the mass and heat transfer between the display cabinets and the surrounding air. To model display cabinets in the store, ideally the whole store together with the display cabinets and the products in the cabinets should be taken into consideration. For this purpose, for a medium size store, the grid size will be very large. However, if it is assumed that the display cabinet only exchanges heat and moisture with the local environment (air surrounding the display cabinets), and the store air movement is not very strong, then the display cabinet zone can be treated in isolation from the rest of the store. The effect of air movement caused by the operation of the display cabinets and heating terminal devices within the display cabinet zone and the interactions between adjacent zones can be accounted for by treating the boundaries between zones as pressure boundaries. Previous studies have shown that the display cabinet in the environmental chamber under the effect of low side airflow could be modeled as a display cabinet in open space with free boundaries [1]. That is, the walls of the environmental chamber could be replaced by pressure boundary conditions. The display cabinet zone modeled consisted of two rows of cabinets facing each other as shown in Figure 6.3. The velocity distribution on the pressure boundary is unknown but the total pressure on the boundary can be assumed to be 0 Pa (gauge) if the airflow through the boundary is low. The distance between the free boundary and display cabinet should be large enough to eliminate the effect of the position of the boundary on the simulation results. To investigate this, simulations were carried out to determine the minimum distances X and Y between the free boundary and display cabinets. Because the display cabinet zone is symmetrical in two directions, only a quarter of the zone was modeled.
6.4 DISPLAY CABINET ZONE WITHOUT ACCESSORY HEATING SYSTEM 6.4.1 EFFECT
OF
DISTANCE
BETWEEN
FREE BOUNDARY AND DISPLAY CABINETS
Simulations were carried out to assess the effect of distance between the free boundary and the display cabinets. The inputs to the model can be seen in Table 6.1. Two cases were Symmetrical surface Free boundary Free boundary
H
X Y
L
1000 W 1000
Y
X
FIGURE 6.3 Two rows of display cabinets in the retail food store (dimensions in mm).
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TABLE 6.1 Model Inputs for Display Cabinet Zone without Accessory Heating System Length of the display cabinet zone (m) Store floor to the ceiling height (m) Distance between display cabinet rows (m) Ambient air temperature (8C) Ceiling and wall surface temperature (8C) Ambient air moisture content (g=kg) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet airflow rate per meter length (m3 s1 m )
12 3.5 2.5 21 21 8 2 2.6 0.1
investigated, for Case 1, X ¼ 1:0 m and Y ¼ 1:2 m, and for Case 2, X ¼ 2:0 m and Y ¼ 2:0 m. The resulting average velocity and air temperature at low level (0.3 m above floor level), product temperature on top, third, and bottom shelves, and cooling load are compared in Table 6.2. It can be seen that increasing X and Y from 1.0 and 1.2 m to 2.0 m had only a very small effect on the air temperature, product temperature, and cooling load, so it was concluded that it would be safe to use 2.0 m for X and Y for the simulations.
6.4.2 MODELING THE DISPLAY CABINET ZONE WITHOUT HEATING SYSTEM In this section, the results from modeling the store at summer conditions are presented. The inputs to the model are given in Table 6.1. To validate the model, results from measurements of temperature, velocity, and humidity carried out at five stores from three supermarket chains by Foster and Quarini [6] were used. The results from one of the stores (Supermarket A, store 2) are shown in Table 6.3. Figure 6.4 shows the air temperature distribution on a horizontal plane 0.3 m above floor level. It can be seen that the air temperature in the aisle between the display cabinets is around 7.58C. Towards the edges of the zone, section A in Figure 6.4, the temperature increases slightly as the air leaving the zone is replaced by warmer air entering from outside the zone.
TABLE 6.2 Effect of Distance between Free Boundary and Display Cabinets Comparison Items Average velocity at low level (m s1 ) Air temperature at low level (8C) Average product temperature (8C) at positions indicated in Figure 6.1
Cooling load (kW m1 )
Top shelf Third shelf Bottom shelf
Case 1
Case 2
X ¼ 1:0, Y ¼ 1:2 (m)
X ¼ 2:0, Y ¼ 2:0 (m)
0.31 7.20
0.30 7.30
3.10 2.10 3.80 1.14
3.10 2.00 3.80 1.12
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TABLE 6.3 Measurements at One Supermarket Store floor to ceiling height (m) Length of the display cabinet zone (m) Distance between display cabinet rows (m) Mean highest temperature in all aisles (8C) Minimum temperature (8C)
Winter Summer Winter (heated by floor heating) Summer (floor heating off)
3.5 12 2.5 21.5 21 10.7 8.5
Source: From Foster, A.M. and Quarini, G.L., IIF-IIR-Commission D2=3, Cambridge, UK, 217–225, 1998.
Figure 6.5 shows the temperature contours on sections A, B, C, and D (only the display cabinet on the left hand side plotted). It can be seen that the zone is divided into two areas: the low-temperature area close to the floor and the high-temperature area at high level. The height of the boundary from the floor is a function of the position along the aisle. In the middle of the aisle, section D, the height of the low temperature region is highest and at the end of the aisle, section A the height is lowest. The minimum temperature predicted in the aisle is 7.58C compared to a minimum of 8.58C in an actual store measured by Foster and Quarini [6]. Figure 6.6 shows the velocity vectors at section D in the aisle. It can be seen that the cold air overspill from the cabinet descends to the floor and leaves towards the center of the aisle where it meets with the overspill from the opposite row of cabinets. The air then rises and turns back towards the display cabinet, forming local recirculation. Figure 6.7 shows temperature-coded velocity vectors on horizontal planes: (a) 0.3 m above the floor and (b) 2.0 m above the floor. It can be seen that the air leaves the display cabinet zone at low level at both ends of the aisle and warm air enters the zone at high level. The velocity at low level is high (0:30:5 m s1 ) and at high level is much lower (0:050:1 m s1 ). 2.94E + 02 2.93E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.91E + 02 2.90E + 02 2.90E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.88E + 02 2.87E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.85E + 02 2.84E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.82E + 02 2.81E + 02 2.81E + 02 2.80E + 02 2.80E + 02 2.79E + 02
2m 2m 2m
Section A Section B Section C Section D
FIGURE 6.4 Temperature contours (K) on a horizontal plane 0.3 m above floor level (without HVAC system).
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1350 mm
2.90E + 02 2.89E + 02
1100 mm
2.88E + 02 2.87E + 02 2.87E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02
Section B
Section A
2.82E + 02 2.81E + 02 2.80E + 02 2.80E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02
1600 mm
1650 mm
2.75E + 02 2.74E + 02 2.74E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section C
Section D
FIGURE 6.5 Temperature contours (K) at sections A, B, C, and D (without HVAC).
The air temperature at high level is maintained constant and equal to the store temperature due to air entering the zone from the rest of the store. Figure 6.8 shows air temperature, moisture content, and relative humidity along the aisle centerline. It can be seen that the moisture content distribution mirrors well the air temperature distribution. At low level in the aisle, the moisture content is quite low and the relative humidity is of the order of 70%. The relative humidity reduces as the temperature increases to a value of 50% just outside the cold temperature zone. Figure 6.9 shows the variation of product temperature in the display cabinets. The average temperatures are 3.18C on the top shelf, 2.18C on the third shelf, and 3.88C on the bottom shelf (the measurement positions are shown in Figure 6.1). The cooling load was found to be 1:05 kW m1 .
2.94E+02 2.93E+02 2.92E+02 2.91E+02 2.91E+02 2.90E+02 2.89E+02 2.88E+02 2.87E+02 2.87E+02 2.86E+02 2.85E+02 2.84E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.80E+02 2.80E+02 2.79E+02 2.78E+02 2.77E+02 2.76E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.73E+02 2.72E+02 2.71E+02
FIGURE 6.6 Temperature-coded velocity vectors (K) at section D (without HVAC).
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0.3 m above floor
2.0 m above floor
FIGURE 6.7 Temperature-coded velocity vectors (K) on two horizontal planes (without HVAC system). 8.00E−03 7.88E−03 7.77E−03 7.65E−03 7.53E−03 7.42E−03 7.30E−03 7.18E−03 7.07E−03 6.95E−03 6.83E−03 6.72E−03 6.60E−03 6.48E−03 6.37E−03 6.25E−03 6.13E−03 6.02E−03 5.90E−03 5.78E−03 5.67E−03 5.55E−03 5.44E−03 5.32E−03 5.20E−03 5.09E−03 4.97E−03 4.85E−03 4.74E−03 4.62E−03 4.50E−03 2.94E+02 2.94E+02 2.93E+02 2.93E +02 2.92E +02 2.92E +02 2.91E +02 2.91E +02 2.90E +02 2.90E +02 2.89E +02 2.89E +02 2.88E +02 2.88E +02 2.87E +02 2.87E +02 2.87E +02 2.86E +02 2.86E +02 2.85E +02 2.85E +02 2.84E +02 2.84E +02 2.83E +02 2.83E +02 2.82E +02 2.82E +02 2.81E +02 2.81E +02 2.81E +02 2.80E +02
50% (RH)
75% (RH)
72% (RH)
70% (RH)
72% (RH) 75% (RH)
Moisture content (kg kg−1)
Air temperature (K)
FIGURE 6.8 Variation of temperature and moisture content along the aisle centerline (without HVAC system).
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2.78E+02 2.78E+02 2.78E+02 2.77E+02 2.77E+02 2.77E+02 2.77E+02 2.76E+02 2.76E+02 2.76E+02 2.76E+02 2.75E+02 2.75E+02 2.75E+02 2.75E+02 2.75E+02 2.74E+02 2.74E+02 2.74E+02 2.74E+02 2.73E+02 2.73E+02 2.73E+02 2.73E+02 2.72E+02 2.72E+02 2.72E+02 2.72E+02 2.71E+02 2.71E+02 2.71E+02
FIGURE 6.9 Product temperature distributions (K) in the display cabinets (without HVAC system).
6.5 FACTORS THAT COULD INFLUENCE THE SIMULATION RESULTS 6.5.1 AMBIENT AIR TEMPERATURE To investigate the effect of ambient temperature on the thermal environment in the aisles, two simulations were carried out for ambient temperatures of 218C and 238C. Inputs to the CFD model are listed in Table 6.4. The results given in Table 6.5 show that increasing the ambient air temperature from 218C to 238C caused a small increase in the minimum air temperature in the zone from 7.58C to 8.38C, and a small increase in the cooling load of the cabinets from 1:05 to 1:14 kW m1 .
6.5.2 CABINET AIR CIRCULATION RATE The air circulation rate in the cabinet will vary due to frost formation on the evaporator coil. This will in turn influence the product temperature and the thermal environment in the display cabinet zone. To investigate these effects, simulations were carried out for two air circulation rates of 0:07 and 0:1 m3 s1 using the data in Table 6.6 as inputs to the CFD model.
TABLE 6.4 Inputs to the Display Cabinet Zone Model Length of the display cabinet zone (m) Store floor to ceiling height (m) The distance between display cabinet rows (m) Ambient air temperature (8C) Ambient air moisture content (g kg1 ) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate per meter length (m3 s1 m )
12 3.5 2.5 21 or 23 8.0 2 2.6 0.1
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TABLE 6.5 Cooling Load and Product Temperature Ambient Temperature 218C 238C
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 0.98
3.1 4.2
2.1 2.6
3.8 4.7
7.5 8.3
The results are given in Table 6.7. It can be seen that as the air circulation rate is reduced, the cooling load of the cabinet reduces slightly and the product temperature increases by approximately 1.08C. The minimum air temperature in the display cabinet zone also increases from 7.58C to 8.88C due to reduced cold air overspill in the zone.
6.5.3 AIR SUPPLY (EVAPORATOR COIL AIR
OFF)
TEMPERATURE
The air temperature at the outlet of the evaporator coil will have an impact on the product temperature in the cabinet, the temperature of the air overspill from the cabinet, and the air temperature in the aisle. To investigate these effects, simulations were carried out with evaporator coil air off temperatures of 2 C and 4 C. The inputs to the model are given in Table 6.8 and the results in Table 6.9. It can be seen that reducing the evaporator coil supply temperature by 28C causes, on average, a 1.08C reduction in the product temperature. The temperature of the air overspill from the cabinet also reduces and this causes a reduction in the minimum temperature in the aisle from 7.58C to 6.88C. The lower product and air temperatures in the cabinet cause an increase in the heat transfer between the cabinet and the surrounding environment, which leads to a slight increase in the cooling load of the cabinet.
6.6 DISPLAY CABINET ZONE WITH HOT AIR HEATING SYSTEM The last two sections demonstrated that the aisle temperature would be too low if no heating system is employed in the zone. Hot air heating systems can be found in some supermarkets but their effects on product temperature and aisle temperature need to be
TABLE 6.6 Inputs to the Display Cabinet Zone Model—Air Circulation Length of the display cabinet zone (m) Store floor to ceiling height (m) The distance between the display cabinet rows (m) Ambient air temperature (8C) Ambient moisture content (g kg1 ) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate for per meter length (m3 s1 m )
12 3.5 2.5 21 8 2 2.6 0.1 or 0.07
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TABLE 6.7 Cooling Load and Product Temperature at Different Air Circulation Rates Air Circulation Rate (m3 s1 m1 ) 0.07 0.10
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.81 0.91
4.1 3.1
2.8 2.1
5.0 3.8
8.8 7.5
assessed. In this section, the results of simulations to investigate the effect of an air heating system to increase the temperature at low level in the aisle are presented. The hot air was assumed to be supplied through diffusers at ceiling level, 3.5 m above floor level. The diffuser positions are shown in Figure 6.10. For the hot air heating system, one of the main concerns is whether the hot air can reach the low level of the display cabinet zone. For this reason, simulations were carried out for 1 vertical air velocities of 2 and 3 m s1 corresponding to flow rates of 1.6 and 2:4 m3 s , respectively, and supply temperature of 308C. Figure 6.11 shows temperature-coded velocity vectors at section C when the air supply velocity was 2 m s1 . It can be seen that the hot air jet reaches the floor level just under the diffusers. However, in other areas in the zone the temperature remains quite low as can be seen from Figure 6.12, which presents the temperatures in the zone 0.3 m above the floor surface. Figure 6.13 shows temperature-coded velocity vectors at section C for a hot air supply 1 velocity of 3 m s1 (air supply flow rate 2:4 m3 s ), and Figure 6.14, temperature contours on a horizontal plane 0.3 m above floor level. It can be seen that at section C, below the diffuser, the cold aisle effect disappears but the temperature remains low in most other areas of the zone. These results indicate that hot air supply systems are quite inefficient in eliminating the cold aisle effect in the display cabinet zone. With the heat input required for 1 1 an air supply system flow rate of 1:6 m3 s of 16.2 kW and for 2:4 m3 s of 24.3 kW, hot air systems are also inefficient in terms of energy usage. The effect of the hot air system on product temperature and cooling load is shown in Table 6.10. It can be seen that the cooling load and product temperature increase with increasing supply airflow rate. For the higher flow rate the product temperature increases by 0.88C compared to the case where no heating system is used. The minimum
TABLE 6.8 Inputs to the Display Cabinet Zone Model—Air Supply Temperature Length of the display cabinet zone (m) Store floor to ceiling height (m) The distance between the display cabinet rows (m) Ambient air temperature (8C) Ambient air moisture content (g kg1 ) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate per meter length (m3 s1 m )
12 3.5 2.5 21 8 2 or 4 2.6 0.1
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TABLE 6.9 Cooling Load and Product Temperature at Different Air Supply Temperatures Coil Air Off Temperature (8C) 2 4
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 1.03
3.1 1.9
2.1 1.0
3.8 3.1
7.5 6.8
air temperature in the aisle also increases by 2.58C but it is not enough to eliminate the cold aisle effect.
6.7 DISPLAY CABINET ZONE WITH UNDERFLOOR HEATING SYSTEM Floor heating systems can be found in some supermarkets [6]. In this section, the effect of underfloor heating systems on the aisle temperature, cooling load, and product temperature is investigated. In the simulations, a heat flux of 150 W m2 was employed [7]. Figure 6.15 shows the resulting air temperature distribution at low level in the display cabinet zone. It can be seen that the air temperature is low and only slightly higher than the zone without any heating system. Figure 6.16 shows temperature contours at different sections in the zone. They are very similar to those for no heating in the zone. From the simulation results the average heat transfer coefficient (not including the radiation element) from the floor surface was determined to be 5:94 W m2 K and the average floor surface temperature 308C, giving a heat input to the zone air of 3.87 kW. Increasing the heat flux to 200 W m2 increased the floor surface temperature to 388C but had only a very small effect on the aisle temperature. A comparison of cooling load, air, and product temperature of a zone with the underfloor heating system and zone without heating is given in Table 6.11. It can be seen that the underfloor heating system causes a 0.88C rise in product temperature and increases very slightly the cooling load of the cabinet. Its effect on increasing the air temperature is quite small. A floor surface temperature of 308C and a heat flux of 150 W=m2 only lead to a 1.58C rise in the minimum aisle temperature from 7.58C to 9.08C. It can thus be concluded that underfloor heating systems are not effective in reducing the cold aisle effect in the display cabinet zone. Section C Section D 3510
2120
3510
Air supply grille, 640 ⫻ 570, 2 off
6000
6000
FIGURE 6.10 Diffuser positions in the display cabinet zone (dimensions in mm).
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FIGURE 6.11 Temperature-coded velocity vectors (K) at section C (hot air, V ¼ 2 m s1 ).
6.8 EXTRACT AND SUPPLY SYSTEM The results in the previous sections indicate that when no heating is used in the aisles, temperature stratification occurs from floor to around 1.65 m above floor level. A hot air system with air supplied from ceiling diffusers can increase the air temperature at low level in
3.02E+02 3.01E+02 3.00E+02 2.99E+02 2.98E+02 2.98E+02 2.97E+02 2.96E+02 2.95E+02 2.95E+02 2.94E+02 2.93E+02 2.92E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.89E+02 2.88E+02 2.87E+02 2.86E+02 2.85E+02 2.85E+02 2.84E+02 2.83E+02 2.82E+02 2.82E+02 2.81E+02 2.80E+02 2.79E+02 2.79E+02
Section A 2m Section B 2m Section C 2m Section D
12 m
2.5 m
FIGURE 6.12 Temperature contours (K) on a horizontal plane 0.3 m above floor level (hot air system, V ¼ 2 m s1 ).
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3.03E+02 3.02E+02 3.01E+02 3.00E+02 2.98E+02 2.97E+02 2.96E+02 2.95E+02 2.94E+02 2.93E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.87E+02 2.86E+02 2.85E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.80E+02 2.79E+02 2.78E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.72E+02 2.71E+02
FIGURE 6.13 Temperature-coded velocity vectors (K) at section C (hot air, V ¼ 3 m s1 ).
the aisles but the effect is localized and at the expense of high-energy consumption. A way of reducing or eliminating the temperature stratification in the aisles is to recirculate the air in the aisles. Two ways of achieving this are: (1) top suction and bottom supply and (2) bottom suction and top supply system.
3.02E+02 3.01E+02 3.01E+02 3.00E+02 2.99E+02 2.98E+02 2.98E+02 2.97E+02 2.96E+02 2.95E+02 2.94E+02 2.94E+02 2.93E+02 2.92E+02 2.91E+02 2.91E+02 2.90E+02 2.89E+02 2.88E+02 2.87E+02 2.87E+02 2.86E+02 2.85E+02 2.84E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.81E+02 2.80E+02 2.79E+02
FIGURE 6.14 Temperature contours (K) on a horizontal plane 0.3 m above floor level (hot air system, V ¼ 3 m s1 ).
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TABLE 6.10 Cooling Load, Product and Aisle Temperature for Hot Air Heating System Hot Air Supply Flow Rate (m3 s1 )
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 0.94 1.09
3.1 3.5 3.6
2.1 2.3 2.4
3.8 4.3 4.6
7.5 9.0 10.0
0 (No heating) 1.6 2.4
6.8.1 TOP SUCTION
AND
BOTTOM SUPPLY SYSTEM
In top suction and bottom supply, air can be extracted from close to the ceiling of the supermarket, heated if necessary, and returned at low level in the display cabinet zone. This arrangement is shown in Figure 6.17. The geometry modeled is shown in Figure 6.18. The extract grille is at the center of the zone and the supply grille is at the bottom of the display cabinet, 100 mm above floor level. In order to achieve good performance, the supply grille is the same length as the display cabinet row. The inputs to the model are listed in Table 6.12. Figure 6.19 shows the resulting temperature contours at low level in the display cabinet zone. It can be seen that air temperature at low level is divided into two different areas: the low-temperature area near the display cabinets and the higher temperature area near the center of the aisle. In the low-temperature area, the air temperature is around 138C–148C and in the high-temperature area, the air temperature is around 168C–178C. Figure 6.20 shows temperature contours at different sections in the display cabinet zone. It can be seen that the temperature distribution in the aisle is different from the previous cases
2.95E+02 2.94E+02 2.93E+02 2.93E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.89E+02 2.88E+02 2.87E+02 2.86E+02 2.85E+02 2.85E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.81E+02 2.80E+02 2.79E+02 2.78E+02 2.77E+02 2.77E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.73E+02 2.72E+02 2.71E+02
2m
Section A Section B
2m Section C 2m Section D 12 m
2.5 m
FIGURE 6.15 Temperature contours (K) on a horizontal plane 0.3 m above floor level for underfloor heating system.
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Section A
Section B
Section C
Section D
FIGURE 6.16 Temperature contours (K) at different sections (underfloor heating system).
studied. The temperature in the aisle is not stratified into two zones. This is due to the fact that the warm air supplied at low level mixes with the cold air overspill from the cabinet and the mixture is extracted from the zone at high level by the extract grille. At sections A and B, the air temperature is around 168C and at sections C and D the air temperature is around 158C. From Figure 6.20 it can be also seen that the air temperature close to the air curtain is lower than the store temperature by between 38C and 58C. This reduction in temperature causes a reduction in the sensible cooling load of the display cabinet. For the display cabinet zone without heating system, the sensible cooling load was 0:63 kW m1 whereas that for the top extract and bottom supply system is 0:59 kW m1 , representing a 7% reduction. For an average air temperature at the top extract grille of 19.48C and a supply temperature to the zone of 218C, the heating power required by the system is around 7.5 kW. Figure 6.21 shows the moisture content at different sections of the display cabinet zone. It can be seen that the moisture content contours mirror the temperature contours in Figure 6.20. The moisture content around the air curtain (warm side) reduces due to the operation of the top extract and bottom supply system. The moisture content at sections A and B is about 7 g kg1 and at sections C and D is around 6:5 g kg1 . This gives a latent load
TABLE 6.11 Cooling Load, Product and Aisle Temperature for Underfloor Heating System Heat Flux (W m--2 ) 0 (No heating) 150 200
Product Temperature (8C)
Cooling Load (kW m--1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 0.93 0.96
3.1 3.7 3.9
2.1 2.5 2.6
3.8 4.7 4.9
7.5 9.0 9.5
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Heat from main refrigeration rack
0.1 m3 s−1 m−1
Dehumidifying cooling coil
Evaporator
0.1 m3 s−1 m−1
FIGURE 6.17 Display cabinet zone with top extract and bottom supply system.
of 0:24 kW m1 compared to 0:28 kW m1 latent load for the case of no heating in the aisle, which represents a 14% reduction.
6.8.2 BOTTOM EXTRACT SYSTEM With this system air is removed from the low level in the cabinet zone and no air is supplied at high level in the store. The position and dimensions of the return grille are the same as those of the supply grille in Figure 6.18. The extract flow rate used in the simulations was 0:1 m3 s1 m1 , which is the same as the air circulation rate in the cabinets. Figure 6.22 shows air temperature contours on a horizontal plane 0.3 m above floor level. It can be seen that the air temperature is quite uniform at around 158C, approximately 78C above the minimum zone temperature without a heating system.
6000
Bottom supply
Suction grille 720 ⫻ 630
Y
1250 Suction grille
Supply grille 12000⫻ 100 X
FIGURE 6.18 Scheme of top suction and bottom supply system (dimensions: mm).
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TABLE 6.12 Inputs to the Display Cabinet Zone with Destratification Unit (Top Extract and Bottom Supply System) Length of the display cabinet zone (m) Store floor to ceiling height (m) Distance between display cabinet rows (m) Ambient air moisture content (g kg1 ) Ambient air temperature (8C) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate per meter length (m3 s1 m ) 1 3 1 Air supply rate for suction and supply system (m s m ) Air supply temperature for suction and supply system (8C)
12 3.5 2.5 8 21 2 2.6 0.1 0.1 21
Figure 6.23 shows air temperature distribution at sections A, B, C, and D. It can be seen that the zone air is stratified into two distinct zones with the height of the low temperature zone being approximately 0.6 m from the floor. The bottom extract system has significantly reduced the height of the low temperature zone and increased the minimum air temperature. Although the minimum temperature in the display cabinet zone is still low, it is possible to increase the minimum air temperature by increasing the suction flow rate or supplying warm air from the top of the display cabinet zone.
6.8.3 BOTTOM EXTRACT
AND
TOP SUPPLY
With this system the air removed at low level is heated to 218C and supplied back into the zone from an air supply slot (200 12,000 mm) at high level along the center of the display cabinet 2.94E+02 2.94E+02 2.93E+02 2.93E+02 2.93E+02 2.92E+02 2.92E+02 2.92E+02 2.91E+02 2.91E+02 2.91E+02 2.90E+02 2.90E+02 2.90E+02 2.89E+02 12 m 2.89E+02 2.89E+02 2.88E+02 2.88E+02 2.88E+02 2.87E+02 2.87E+02 2.87E+02 2.87E+02 2.86E+02 2.86E+02 2.86E+02 2.85E+02 2.85E+02 2.85E+02 2.84E+02
Section A 2m Section B 2m Section C 2m Section D
2.5 m
FIGURE 6.19 Temperature contours (K) on a plane 0.3 m above floor level (top suction and bottom supply system).
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2.94E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.81E + 02 2.80E + 02 2.79E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02 2.76E + 02 2.75E + 02 2.74E + 02 2.73E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section A
Section C
Section B
Section D
FIGURE 6.20 Temperature contours (K) at different sections of the zone (top extract and bottom supply).
zone. The supply velocity is 1:0 m s1 . It can be seen from Figure 6.24 that the temperature at low level is quite uniform with the minimum temperature at around 178C. Figure 6.25 shows temperature contours at sections A, B, C, and D. It can be seen that the air temperature distribution on different sections is similar and the low temperature zone is pushed very close to the floor. The interaction between the air curtain and the warm air
8.00E − 03 7.79E − 03 7.58E − 03 7.37E − 03 7.16E − 03 6.94E − 03 6.73E − 03 6.52E − 03 6.31E − 03 6.10E − 03 5.89E − 03 5.68E − 03 5.47E − 03 5.25E − 03 5.04E − 03 4.83E − 03 4.62E − 03 4.41E − 03 4.20E − 03 3.99E − 03 3.78E − 03 3.57E − 03 3.35E − 03 3.14E − 03 2.93E − 03 2.72E − 03 2.51E − 03 2.30E − 03 2.09E − 03 1.88E − 03 1.67E − 03
Section A
Section C
Section B
Section D
FIGURE 6.21 Moisture content (kg kg1 ) at different sections (top extract and bottom supply).
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Section A 2m Section B 2m Section C 2m Section D 12 m
2.5 m
FIGURE 6.22 Temperature contours (K) on a horizontal plane 0.3 m above floor level (bottom extract system).
stream can be seen in Figure 6.26. A recirculation area between the air curtain and the warm air stream can be observed. The impact of this, however, on the product temperature is quite small (see Table 6.14). The display cabinet zone model predicted the air temperature at the 1 bottom suction grille to be around 11.48C. Because the total air suction flow rate is 2:4 m3 s for the zone, the heating load for heating the air up from 11.48C to 218C is 28.5 kW. This load
2.94E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.81E + 02 2.80E + 02 2.79E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02 2.76E + 02 2.75E + 02 2.74E + 02 2.73E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section A
Section C
Section B
Section D
FIGURE 6.23 Temperature contours (K) at different sections (bottom extract system).
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Section A 2m Section B 2m Section C 2m Section D
12 m
2.5 m
FIGURE 6.24 Temperature contours (K) on a horizontal plane 0.3 m above floor level (bottom extract and top supply system).
is quite high but can be satisfied by using the heat rejected from the central refrigeration equipment. Figure 6.27 shows the moisture content distribution in the display cabinet zone. The moisture content at the bottom suction grille was predicted to be 0:004 kg kg1 and this was used as the top supply moisture content. It can be seen that the moisture content close to the
2.94E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.81E + 02 2.80E + 02 2.79E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02 2.76E + 02 2.75E + 02 2.74E + 02 2.73E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section A
Section B
Section C
Section D
FIGURE 6.25 Temperature contours (K) at different sections (bottom extract and top supply system).
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2.94E+02 2.93E+02 2.92E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.89E+02 2.88E+02 2.87E+02 2.86E+02 2.86E+02 2.85E+02 2.84E+02 2.83E+02 2.83E+02 2.82E+02 2.81E+02 2.80E+02 2.79E+02 2.79E+02 2.78E+02 2.77E+02 2.76E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.73E+02 2.72E+02 2.71E+02
FIGURE 6.26 Temperature-coded velocity vectors (K) at section D (bottom extract and top supply system).
air curtain is only 0:005 kg kg1 , much lower than the ambient moisture content of 0:008 kg kg1 . This can significantly reduce the latent load and therefore reduce the defrost energy of the display cabinets. A comparison between the cooling load of the display cabinet zone with bottom suction and top supply and a zone without any heating is shown in Table 6.13.
8.00E− 03 7.82E− 03 7.64E− 03 7.46E− 03 7.28E− 03 7.10E− 03 6.92E− 03 6.74E− 03 6.56E− 03 6.38E− 03 6.20E− 03 6.02E− 03 5.84E− 03 5.66E− 03 5.48E− 03 5.30E− 03 5.12E− 03 4.94E− 03 4.76E− 03 4.58E− 03 4.40E− 03 4.22E− 03 4.04E− 03 3.86E− 03 3.68E− 03 3.50E− 03 3.32E− 03 3.14E− 03 2.96E− 03 2.78E− 03 2.60E− 03
Section A
Section B
Section C
Section D
FIGURE 6.27 Moisture content (kg kg1 ) at sections A, B, C, and D (bottom extract and top supply system).
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TABLE 6.13 Latent and Total Cooling Load for Different Systems Zone Type
Latent Cooling Load (kW m1 )
Total Cooling Load (kW m1 )
0.28 0.24 0.16
0.91 0.82 0.84
No heating Top suction and bottom supply Bottom suction and top supply
It can be seen that the bottom suction and top supply system can reduce the latent cooling load by about 40% and this will greatly reduce the defrost energy of the display cabinets and improve energy efficiency of the display cabinet refrigeration systems. A comparison between the bottom extract system, bottom extract and top supply system and no heating on product temperature, and minimum air temperature is given in Table 6.14. It can be observed that the bottom suction and top supply system is much more effective in reducing the cold aisle effect with only a very small impact on product temperature.
6.9 CONCLUSIONS The cold aisle effect, low temperatures at low level between rows of open vertical multideck refrigerated display cabinets in food retail stores, is a problem that has not, as yet, been satisfactorily resolved. The low temperatures in the refrigerated aisles cause discomfort to customers and may influence sales of refrigerated foods. A number of approaches have been employed over the years to address the problem with variable levels of success. This chapter, through the technique of CFD has investigated the effectiveness of some early approaches to reduce the cold aisle effect, such as the use of HVAC systems to supply hot air from ceiling diffusers to the display cabinet zone, and underfloor heating systems. Results from actual store measurements and simulations indicate that both methods are unable to eliminate the cold aisle effect. A hot air system can provide localized heating at low level in the aisle but not uniform heating over the whole cabinet zone. High temperatures and air velocities can also have an impact on the cabinet performance and product temperature and require high thermal energy inputs. Underfloor heating, although has the ability to provide uniform heating of the air at low level in the aisle, is unable to destratify the air and thus its impact in reducing the cold aisle effect is limited.
TABLE 6.14 Comparison between Bottom Suction System, Bottom Suction and Top Supply System, and No Heating System Zone Type Bottom extract Bottom extract and top supply No heating
Temperature Top Shelf (8C)
Temperature Third Shelf (8C)
Temperature Bottom Shelf (8C)
Zone Minimum Air Temperature (8C)
3.6
2.4
4.7
13
3.7 3.1
2.4 2.1
4.7 3.8
17 7.5
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More effective approaches in reducing the cold aisle effect are through the elimination of thermal stratification in the aisle. Ways of achieving this are through the removal of cold air in the aisle and replacing it with warmer air from the rest of the store with or without supplemental heating. Three possible systems were investigated: (a) simple removal of air from low level in the aisle and discharging it at high level outside the cabinet zone; (b) removal of air at low level, heating it using heat generated, for example, by the condensers of the refrigeration plant, and supplying at high level in the display cabinet zone, and (c) removing warm air at high level in the aisle, heating it and supplying at low level in the aisles. These three destratification approaches are more effective in reducing the cold aisle effect than hot air or underfloor heating systems. The most effective of the three approaches was found to be the bottom extract and top supply system. This system can lead to acceptable air temperatures in the aisles and lower latent loads on the cabinets. The lower latent load should lead to a reduction in evaporator coil frosting and defrosting losses.
REFERENCES 1. Xiang, W. Performance improvement of multideck display cabinets and reduction of their impact on the store environment. PhD thesis, Brunel University, England, 2003. 2. Hinze, J.O. Turbulence. McGraw-Hill, New York, NY, 1975. 3. Shah, N.G. A new method of computation of radiant heat transfer in combustion chambers. PhD thesis, Imperial College of Science and Technology, London, England, 1979. 4. Carvalho, M.G., Farias, T., and Fontes, P. Predicting radiative heat transfer in absorbing, emitting and scattering media using the discrete transfer method, Fundamental of Radiation Heat Transfer, ASME HTD, American Society of Mechanical Engineers, New York, Vol. 106, pp. 17–26, 1991. 5. Stribling, D., Tassou, S.A., and Marriott, D. Optimization of the design of refrigerated display cases using computational fluid dynamics. Proceedings of the Institute of Refrigeration, 92, 7.1–7.7, 1996. 6. Foster, A.M. and Quarini, G.L. Using advanced modeling techniques to reduce the cold spillage from retail cabinets into supermarket stores, IIF-IIR-Commission D2=3, Cambridge, UK, pp. 217–225, 1998. 7. Faber, O. Advanced supermarket refrigeration and HVAC systems, Notes of Discussion, January 2000. 8. European Standard EN 441-4. Refrigerated display cabinets. General test conditions, CEN, European Standard, 1995.
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CFD Optimization of Air Movement through Doorways in Refrigerated Rooms Alan M. Foster
CONTENTS 7.1 7.2 7.3
Introduction ............................................................................................................... 168 Natural Convention through an Opening.................................................................. 168 Cold Stores................................................................................................................. 170 7.3.1 Chilled Stores.................................................................................................. 170 7.3.2 Frozen Stores.................................................................................................. 170 7.3.3 Door Protection.............................................................................................. 171 7.3.3.1 Strip Curtain..................................................................................... 171 7.3.3.2 Loading Docks and Vestibules ......................................................... 172 7.3.3.3 Flexible Fast-Opening Doors ........................................................... 172 7.3.3.4 Air Curtains...................................................................................... 172 7.4 Prediction ................................................................................................................... 172 7.4.1 Analytical and Empirical Models ................................................................... 172 7.4.2 Computational Fluid Dynamics ..................................................................... 174 7.4.2.1 Theory .............................................................................................. 174 7.4.3 Applications.................................................................................................... 175 7.4.3.1 Cold Stores ....................................................................................... 176 7.4.3.2 Air Curtains...................................................................................... 178 7.5 Validation .................................................................................................................. 185 7.5.1 Temperature Measurement............................................................................. 185 7.5.2 Velocity Measurement .................................................................................... 186 7.5.2.1 Vane Anemometry............................................................................ 186 7.5.2.2 Hot-Wire Anemometry..................................................................... 186 7.5.2.3 Laser Doppler Anemometry............................................................. 186 7.5.2.4 Digital Particle Image Velocimetry................................................... 187 7.5.3 Infiltration ...................................................................................................... 188 7.5.3.1 Flow Rates ....................................................................................... 188 7.5.3.2 Gas Decay ........................................................................................ 188 7.6 Conclusions................................................................................................................ 189 Nomenclature ..................................................................................................................... 190 References .......................................................................................................................... 191
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7.1 INTRODUCTION Most unwrapped meat, poultry, fruits, and vegetables and all types of wrapped foods are stored in large air-circulated rooms. Specific rooms are used for the storage of chilled or frozen foods. A reduction in the average storage temperature can significantly increase the length of retention and quality of many chilled foods. Bacterial counts will decrease, leading to an increase in safety and shelf life of the product. Olafsdottir et al. [1] found that reducing the storage temperature of cold fillets from 0.58C to 1.58C increased the minimum sensory life from 12.5 to 15 days. The weight loss from unwrapped foods will reduce, thus increasing quality and productivity. Reduced temperature cycling in frozen storage rooms reduces the moisture drawn from the foods, which reduces in-pack frosting and freezer burn. Improvements such as the introduction of state-of-the-art refrigeration systems with advanced controls that include subcooling, floating head pressures, high-efficiency evaporators, condensers, and motors, and also variable speed drives, can help reduce energy usage and temperature control [2]. However, in any refrigerated store, entrances are required for loading and unloading raw materials or finished products and they are a major source of heat infiltration. Air infiltration can account for more than half the total heat load for refrigerated stores [3]. Refrigerated stores are one of the highest consumers of electric energy in the commercial building sector [4]. The electric usage of these refrigerated stores often ranges from 400 to 600 kW h m2 per year, with refrigeration accounting for more than 70% of overall electric usage [2]. Infiltration of warm moist air through doorways into refrigerated rooms during loading and unloading causes many problems to the operators. These include . .
.
.
Increased costs for running [3] and defrosting the refrigeration system Safety problems associated with the mist formed in the doorway, as the cold air mixes with the ambient air [5] Safety problems associated with ice forming around the door opening (of freezer rooms), on the floor, and on the ceiling [5] Food quality, safety, and weight loss caused by temperature fluctuations
The design of an entrance in a temperature-controlled space is always a conflict between operators, who would prefer a completely unrestricted access, and the needs of temperature control, which would prefer no doors or openings. The positioning and design of entrances are often decided on ease of use criteria with temperature control and interaction with the refrigeration system as a secondary consideration. Azzouz et al. [6] measured a heat infiltration of 3.4% between the cold store and ambient during a door opening. The cold air leaves at the bottom and warm moist air enters at the top. However, this is only true if one door is opened. If more than one door is opened in the same room at the same time, then air will flow in through one door and leave out of the other depending on the atmospheric pressure differences around each door. There are a limited number of computational fluid dynamics (CFD) modeling studies carried out on natural convection through cold store entrances. By far, the majority of CFD studies of air curtains have been on refrigerated display cabinets, which are of a much smaller scale (less height and lower velocity) and recirculating. This chapter details the work carried out in this area and other relevant areas.
7.2 NATURAL CONVENTION THROUGH AN OPENING The theory of natural convection through an opening has been developed by a number of authors; the actual models are described in Table 7.1. Natural convection through an opening
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169
TABLE 7.1 Analytical Models of Infiltration Rate through an Open Door due to Natural Convection "
Brown and Solvason (1963)
I
Tamm (1966)
I
Fritzsche and Lilienblum (1968)
I
Gosney and Olama (1975)
I
Pham and Oliver (1983)
I
#0:5 ( ri ro ) b ¼ 0:343 A(gH) 1 0:498 ravg H 1:5 ( ri ro ) 0:5 2 ¼ 0:333 A(gH)0:5 ri 1 þ (ro =ri )0:333 0:5 1:5 ( ri ro ) 2 ¼ 0:333 Kf,L A(gH)0:5 0:333 ri 1 þ (ro =ri ) 0:5 1:5 ( ri ro ) 2 ¼ 0:221 A(gH)0:5 ri 1 þ (ri =ro )0:333 0:5 1:5 ( ri ro ) 2 ¼ 0:226 A(gH)0:5 ri 1 þ (ro =ri )0:333 0:5
is caused by the temperature difference and thus density difference between the air inside and outside the room. This effect is commonly known as the stack effect. Eighty years ago Emswiler [7] expressed the basic theory for natural convection through openings in a partition separating fluids at different densities. His investigation concentrated on multiple openings and his theory was based on the Bernoulli equation for ideal flow and introduced the concept of the neutral level. This is the height at which the pressure is the same either side of the partition. Brown and Solvason [8] developed a theory of natural convection through single vertical rectangular openings in partitions. They showed that a pressure profile is developed in the opening that is caused by the difference in density due to temperature difference between the environments on either side of the partition. This velocity profile generated from this pressure distribution is shown in Figure 7.1. They assumed that the neutral height was half the height of the entrance. Tamm [9] improved on this model, calculating the height of the neutral level and using inside and outside densities for inflow and outflow, respectively, where appropriate, instead of an average value. Fritzsche and Lilienblum [10], who conducted experiments using vane
Cold store To
Ti
u
Entrance
Pressure = Po
hn
FIGURE 7.1 Schematic showing natural convection through a refrigerated room entrance.
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anemometers, added a correction factor to Tamm’s equation. The correction factor takes into account the contraction of the flow, friction, and thermal effects. Fritzsche and Lilienblum’s equation assumed that the volume flow rate into and out of the room were the same. This is only the case if the air entering the room does not cool. This may be a good approximation for a small room, where infiltration through the door causes the air in the refrigerated room to rise in temperature. If the room is large and the air entering the room cools to the refrigerated room air temperature, the mass flow rate into and out of the room will be the same but not the volume flow rate. Gosney and Olama [11] provided an equation for constant mass flow rate and by fitting measurements with their model provided a different correction factor. Pham and Oliver [12] conducted experiments on airflow through refrigerated room doors and produced a factor of 0.68 that should be applied to Tamm’s equation to fit their experimental data. Whereas Jones et al. [13] investigated moisture transfer through openings and showed that the mass transfer of water vapor could be adequately described by the air convection currents at the opening, which is much greater than the diffusion.
7.3 COLD STORES Refrigerated rooms are primarily used for the storage of food. To give an idea of size and layout of cold storage rooms, Pham and Oliver [12] studied rooms covering volumes of 177–37,000 m3 , heights of 3.8–21.2 m, and temperature differences between room and ambient from 19.58C to 348C. Door sizes ranged from w h ¼ 1.08 1.98 m to 3.0 3.6 m. Cold stores are generally constructed from prefabricated insulated panels and contain floor-to-ceiling racking or pallets. Usually, the doors of large cold stores are pneumatically actuated, horizontally sliding, insulated doors. Smaller storage rooms may have manually activated hinged or sliding doors. There are two main types of cold storage room—chilled and frozen—each having different problems associated with infiltration.
7.3.1 CHILLED STORES The chilled cold store will usually run between 08C and 58C and the food within it will usually be stored for short periods of time (days). However, meat may be aged (matured) in chill rooms for up to 7 weeks and vacuum-packaged products can be stored for up to 16 weeks in chill rooms operating at 1 + 0.58C. Because the chilled store is often used for shorter storage times it is often quite small and product is moved in and out regularly. As the food in chilled stores is close to temperatures where bacteria can grow, hygiene and temperature control is the major consideration. Heat infiltration will raise air and inevitably product temperatures. It is an accepted crude approximation that bacterial growth rates can be expected to double with every 108C rise in temperature [14]. However, below 108C, the effect is far more pronounced and chilled storage life is halved for each 28C to 38C rise in temperature. In the normal temperature range of 1.58C and 58C for chilled meat, there can be as much as an eightfold difference in growth rate between the upper and lower temperatures [15]. Door openings can therefore have a critical impact on product temperature and storage life.
7.3.2 FROZEN STORES The frozen cold store will usually run below 188C and the food within it will be stored for long periods of time. Storage times are dependent on enzymic and oxidative reactions,
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which are a function of temperature. They range from 3 to 4 months for shrimps at 188C [16] to 2.5 years for lamb stored at 258C [15]. As long as the food remains below 128C, there will be no growth of pathogenic or spoilage microorganisms and so the food will remain safe [17], therefore, hygiene and temperature control is not the major consideration. The energy required to keep the food at this very low temperature for a longtime is now one of the prime considerations. Another important consideration is the moisture entering the store. This moisture quickly turns into ice. The ice can be found around the door, above the door, and on the evaporators. The ice causes a slip hazard to personnel and forklift trucks and also a falling hazard as large lumps of ice can fall from above the door onto personnel. This ice may need regular removal, which is also expensive. Condensing moisture in the doorway causes a mist (fogging) that is another safety hazard as visibility of the forklift drivers is impaired. Boast [18] states that snow, ice, and frost are responsible for over 90% of accidents in cold storage areas, from slippage and damage caused by and to the mechanical-handling equipment.
7.3.3 DOOR PROTECTION To reduce infiltration while the door is open, cold stores often contain one or more infiltration-reducing devices. The ability of these devices to reduce infiltration is defined as the effectiveness and is derived by the following equation: E¼
Qb Qa Qb
(7:1)
An effectiveness of 1.0 means that infiltration is totally eliminated, 0 means that there is no effect on the infiltration, and a negative value indicates that the infiltration is worse. Measured values of the static effectiveness of infiltration devices by a wide range of authors are shown in Table 7.2. 7.3.3.1 Strip Curtain The traditional, and most common, equipment for reducing infiltration is the strip curtain. This consists of a number of overlapping transparent PVC strips. Chen et al. [3] found that TABLE 7.2 Reported Effectiveness Values for Infiltration Protection Devices Device
Type
Strip curtain
Air curtain
Combined air and strip curtains Fast doors
Dual Vertical nonrecirculating
Vertical double nonrecirculating Vertical recirculating Horizontal recirculating Horizontal double recirculating Horizontal air curtain
Effectiveness 0.86 to 0.96 static 0.83 to 0.93 traffic 0.92 to 0.98 0.44 to 0.83 1.58 to 0.54 negative pressure 0.6 to 0.93 0.36 to 0.8 0.59 to 0.82 0.74 0.9 to 0.92 0.63 to 0.93
Source [12,21,44] [44] [6,37,38,44,45,46]
[47] [45] [12,45,46] [21] [12] [44]
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strip curtains in good condition reduce infiltration by 0.92; however, for a damaged strip curtain the infiltration was about three times higher. Ligtenburg and Wijjfels [5] claim that the strip curtains are generally considered unsafe, are not particularly efficient, are unhygienic, and require much maintenance. It is possible that this equipment may be banned in the future. 7.3.3.2
Loading Docks and Vestibules
Loading docks are commonly seen on large frozen storage depots. They allow the movement of food between the cold store and refrigerated motortruck without interaction with the ambient air. The motortruck backs up to the loading dock (of which there will probably be more than one) and seals restrict-air infiltration between the ambient and the loading dock. The store door directly feeds into the dock. These loading docks are normally refrigerated to a temperature between that of the outside ambient and the store and may also be dehumidified. Air lock vestibules can also be used for personnel or forklift access; however, they have their own problems in that they restrict access, are difficult to fit to existing sites, can be bulky, and have a high capital cost. 7.3.3.3
Flexible Fast-Opening Doors
Flexible, fast-opening doors can be a replacement to normal insulated doors. They operate much faster than normal insulated doors ( 2 m s1 ) and therefore limit the time that the door is partially open to a minimum. The reasons for low take-up of these devices are that they have heavy maintenance requirements, can jam, and are known to reduce vision of forklift truck operators, which result in accidents. 7.3.3.4
Air Curtains
An air curtain is effectively a plane turbulent jet of air forming a barrier between the cold air in the store and the warm ambient air. The theory of air curtains are described in more detail in Chapter 4. Air curtains reduce infiltration without taking up as much space as vestibules and without impeding traffic. Their origin dates back to a patent applied for by Van Kennel in 1904 and they have been popular for around 50 years. Air curtains consist of a fan unit that produces a jet of air forming a barrier to heat, moisture, dust, odors, insects, etc. In the case of cold store air curtains, the fan unit is usually above the door, blowing a jet of air vertically downward. Some air curtains recirculate their air via a return duct but it is simpler and more common not to do so. The effectiveness of air curtains has been shown to vary considerably (Table 7.2). Micheal [19] and Foster et al. [20] have shown that incorrect specification, installation, set-up, and adjustment can have an adverse effect on effectiveness of the air curtains.
7.4 PREDICTION 7.4.1 ANALYTICAL
AND
EMPIRICAL MODELS
The equations for the analytical models, which have been outlined in Section 7.2, are given in Table 7.1. All of these analytical models are based on ideal flow theory, and the later models contain an empirical coefficient to account for viscous and thermal effects. Hendrix et al. [21] have compared these models against real measurements and found that they generally overpredict the volume flow rate through the door. The Gosney and Olama [11] model exhibited the ability to predict experimentally observed values for volume flow rate, mass flow rate, and heat infiltration. The deviations were less than 25% for volume and mass flow
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rates. Chen et al. [3] found that Tamm’s model overpredicted the air infiltration rate through an open door by 30%. Chen suggested that further measurements were needed to be carried out on a wider range of cold stores, door sizes, and operating conditions to confirm results and establish the generality of the empirical factors. When Foster et al. [22] compared analytical models to measurements they concluded that the Brown–Tamm models substantially overpredict the infiltration for all of the measurements (between 52% and 123% overprediction). Tamm’s modified model predicts the measurements much more closely than the original (it was within the experimental error for a cold store at 08C). Taking all of the experiments into account, the Gosney model performed best (maximum of 39% overprediction), followed by the Fritzsche model (maximum of 43% overprediction). Most air curtains are essentially plane turbulent jets and the physics of these jets are also well documented [23–25]. Solving the equations for natural convection through openings and also for turbulent jets allows the interaction between the air curtain and infiltration through the entrance to be evaluated. Hayes and Stoecker [26,27] developed an analytical model to predict heating and cooling loads across nonrecirculatory air curtains (Equation 7.2). Their model allows the calculation of the ‘‘deflection modulus,’’ which is the ratio of air curtain momentum to transverse forces, caused by temperature difference on either side of the curtain (stack effect). The stack effect is created by the difference in air densities on the two sides of the doorway and results in a linear variation in pressure from the top to the bottom of the opening:
Dm ¼ gH 2
bu2 ro bu2 ¼ 2 To To gH ðrc rw Þ Tc Tw
(7:2)
They also presented a chart showing the minimum outlet momentum required to maintain an unbroken curtain (Figure 7.2). 0.24
0.20
gH 2(rc − rw)
(ro bu 2) min
15⬚ toward cold side 0.16 0⬚ 15⬚ toward warm side 30⬚ toward warm side
0.12
0.08 0
0
20
40
60
80
100
H /bo
FIGURE 7.2 Minimum outlet momentum required to maintain an unbroken curtain. (Design Data for Air curtains, 1969 ß ASHRAE Inc. (www.ashrae.org). With permission.)
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From the chart and equation it is possible to calculate the minimum air curtain velocity to provide an unbroken curtain. However, because this velocity is at the borderline of stability, a higher outlet velocity must be selected to provide a factor of safety. They showed that the heat transfer through the curtain is proportional to the jet velocity for velocities above the borderline of stability and it is not therefore beneficial to have too high a safety factor. The literature suggests a range of safety factors between 1.3 and 2.0 to use in this model [27]. Foster et al. [22] compared this analytical model to measured data. Using this range of safety factors, a number of velocities could be chosen from 11 to 17 m s1 . Using these velocities resulted in an experimental effectiveness of the air curtain varying from 0.37 to 0.70. A higher safety factor of 2.2 yielded the best effectiveness in these tests.
7.4.2 COMPUTATIONAL FLUID DYNAMICS Many authors have used CFD to predict heat and mass transfer inside refrigerated rooms [28–31], but it has been used far less to predict natural convection through cold store entrances. 7.4.2.1
Theory
The time-averaged continuity, momentum, and energy equations for a constant property incompressible fluid in absence of volumetric heating and neglecting the effects of viscous dissipation can be written as follows in their conservative form: rw¼0 r
@w þ rr (w w) ¼ rp þ mr2 w þ rb T Tref g r rw0 w0 @t
(7:3) (7:4)
@T þ rcp r wT ¼ lr2 T r rw0 T 0 (7:5) @t The unknown Reynolds stresses rw0 w0 and Reynolds fluxes rw0 T 0 appear on the right-hand sides of Equation 7.4 and Equation 7.5, respectively. If the temperature variations are small, then the Boussinesq approximation can be used to simulate buoyancy. Following such an approximation, the density is assumed constant in the transient and convective terms, while it is linearly dependent on temperature in the buoyancy term rb T Tref g. By far the most common turbulence model used is the k« turbulence model; this is adopted to model the Reynolds stresses and fluxes. As it uses an eddy-viscosity hypothesis, the Reynolds stresses can be linearly related to the mean velocity gradients as follows: rcp
2 2 rw0 w0 ¼ rkd mt r wd þ mt r w þ ðrwÞT 3 3
(7:6)
where mt is the turbulent viscosity, k ¼ 1=2(w0 )2 is the turbulent kinetic energy, and d is the identity matrix. Analogously, the Reynolds fluxes are linearly related to the mean temperature gradient as (7:7) rw0 T 0 ¼ rcp at rT with at ¼
mt rst
(7:8)
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where at and st are known as the turbulent diffusivity and the turbulent Prandtl number, respectively. As we are now dealing only with mean quantities, we shall drop the over bar for the sake of simplicity. In the k« model, it is assumed that the turbulence viscosity is linked to the turbulence kinetic energy and dissipation via the following equation: mt ¼ Cm r
k2 «
(7:9)
where Cm is a constant. The values of k and « come directly from the differential transport equations for the turbulence kinetic energy and turbulence dissipation rate: @rk mt þ r (rwk) r m þ rk ¼ P r« @t sk @r« mt « þ r (rw«) r m þ r« ¼ ðCe1 P Ce2 r«Þ @t k se
(7:10) (7:11)
where P is the shear production defined by 2 P ¼ mt rw rw þ rwT r wðmt r w þ rkÞ 3
(7:12)
where Ce1 , Ce2 , sk , and se are constants.
7.4.3 APPLICATIONS Many of the investigations of natural convection through openings are not for cold storage rooms but for other types of building, e.g., warehouses, offices, retail outlets, etc. It is more common for the building to be at a warmer temperature than the environment and therefore the airflow through the opening is the reverse of that found in a cold store. Wind effects are a common problem with natural convection in buildings. This is also true for refrigerated rooms where the door opens into the environment; however, many refrigerated rooms are within factories where wind effects are negligible. Probably, Schaelin et al. [32] carried out the first CFD study of the airflow pattern through large openings that allow bidirectional flow. They simulated airflow through large openings in buildings with and without an external wind. The airflow pattern was calculated where warm air leaves a room through the upper part of the large opening and rises as a thermal plume. Although this work was done for a heated room, the same effect can be seen in a cold store where warm air enters the top of the door and rises to the ceiling of the cold store. They found that both twodimensional (2D) and three-dimensional (3D) CFD models agreed well with analytical models [33] and the predictions were supported by experiments [27,34]. In addition to investigating the thermal plume outside of the room, they also investigated the velocity and temperature field inside the room and through the opening, with and without wind effects. They showed that the CFD prediction of the doorway velocity profile was more realistic than that obtained by an analytical Bernoulli model. The 3D model yielded about 20% more flow through the doorway with wind than the 2D model, and the suggested reason for this was that the heater (used to heat the room) was wider than the full width of the door. A common problem with CFD modeling of flow through an
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entrance is the extent of the ambient environment that should be included in the computational domain. This issue is important with 3D models where the computational resources required can be prohibitive. Schaelin et al. [32] showed that in free convection cases, the length of the ambient domain can be set to about half of the opening height. It is becoming more common to design natural convection ventilation systems in buildings due to their environmental impact (zero fan power). These systems use a chimney (with or without an extraction fan) for their ventilation. While the stack effect is the enemy in the cold storage industry, it is the friend in modern building design. Wong and Heryanto [35] studied the stack effect to enhance natural ventilation using wind tunnel experiments and CFD. Their study revealed that external wind effect is still the most important factor that determines natural ventilation performance. It is therefore important not to ignore the wind effect when studying cold storage rooms, which open into the environment. 7.4.3.1
Cold Stores
There are very few studies where CFD has been used to predict infiltration through an unprotected cold store entrance. In the studies of Foster et al. [36], CFD studies were carried out on a purpose-built refrigerated test room of internal dimensions 5 6 4 m high. The room had a large single opening, 2.3 m wide 3.2 m high. The room was constructed within a large hall to avoid wind effects and to keep the ambient air temperature steady. The entire cold store, as well as a region outside, was modeled. The initial conditions (time ¼ 0) of the air were zero velocity, 208C inside the room, and 208C outside the room. A full buoyancy model was not used, instead the Boussinesq model was used. Turbulence of the air was modeled using the k–« turbulence model. A thermal energy model was used to model the change in temperature of the air once the door was opened. Air flowing out through the door was a transient effect and there was no steady state. The model was run for a period of 30 s from the moment the door was opened and a solution obtained every second. To simplify the model, a number of assumptions were made. These were as follows: 1. There was no heat flow through the walls of the test room. 2. The test room had no thermal mass. 3. Humidity had no effect on the flow rate through the door (it does, however, have an effect on heat transfer through the door). 4. The evaporator had no effect on the airflow. 5. How the door was opened did not affect the airflow through it. 6. The simplification of outside-room conditions had no effect. 7. The room was leak proof, i.e., air can only move through the entrance. 8. The initial conditions of constant temperature and velocity inside and outside the room before the door is opened were true. The geometry was discretized with a tetrahedral mesh. The mesh size was 113,188 tetrahedral elements and 21,626 nodes. Vane anemometer measurements, carried out at different heights in the door opening, and CFD predictions showed that the airflow decreased with time. Velocities measured by the top and bottom vanes and predicted velocities in the same positions for a period between 10 and 30 s post door opening are shown in Figure 7.3. The predicted velocity into the room at the top and its decay with time is well within the repeatability of the measurements. The predicted velocity out of the room at the bottom was 0:30:5 m s1 lower than the measured velocity.
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Velocity (m s−1)
1.5 1 0.5 0 −0.5 −1 −1.5 10
15
20
25
30
Time (s)
FIGURE 7.3 Velocities measured by both the top (triangular marker) and bottom (square marker) vane anemometer (mean of six replicates, error bars represent +1 standard deviation) and predicted velocities (dashed lines) in the same positions (room temperature 208C) during a period 10 to 30 s after opening. A positive velocity is out of the room.
Vane anemometry measurement and CFD prediction both showed that air flows out (positive) of the bottom of the entrance and in (negative) through the top. The highest velocity out of the room was near the floor and the highest velocity in the room is close to the top. The velocity profile with height, one-third of the width of the entrance from the left-hand end after 20 s, is shown in Figure 7.4. The shape of the profile was well predicted by the CFD. However, the CFD underpredicted the velocity of the air leaving the chamber at the bottom of the opening. Foster et al. [22] also used CFD to predict infiltration rates. A tracer gas technique was used to measure the rate of infiltration against the length of time the door was open and the resulting data were compared to the CFD predictions (Figure 7.5). Two CFD models were used, one that had the domain boundary 3 m from outside the walls of the cold room and one
1.5 Velocity (m s−1)
1 0.5 0 −0.5 −1 −1.5 0
0.5
1
1.5
2
2.5
3
Height (m)
FIGURE 7.4 Velocities measured inside the large entrance 20 s post door opening at each anemometer position (six replicates) plotted against height. The CFD predicted velocity profiles are represented by the dashed lines.
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Infiltration (m3)
150
100
50 Measured CFD CFD extended boundaries
0 0
10
20
30
40
50
Door-opening times (s)
FIGURE 7.5 Measured and predicted infiltration through the 2.3 m wide door for different dooropening times. The CFD predictions are for both the standard and extended boundary models.
with the boundary 6 m away. Both CFD models predict a similar infiltration rate to that measured. However, both models, especially the model without the extended boundary predicted a reduction of infiltration rate with time, which was not apparent in measurements. The reason for this was probably due to the region outside the cold store reducing in temperature faster (and therefore reducing the driving force) in the model than in reality. This was because the region outside was finite in the model and effectively infinite in reality. The predictions also showed that infiltration varied with time and that the predictions could be split into three separate stages. The first stage was the lag stage covering the time required before the flow became fully developed. This was followed by a steady-state stage where there was a constant flow rate through the entrance. The final stage was the tail-off stage, where the temperature difference (driving force) between the cold store and the surroundings was reducing. The lag stage was predicted to be between 0.3 and 1.6 s for the different models. This lag stage has been measured by Azzouz et al. [6] to be of the order of 1.5 s. For long dooropening times of 30 s, a 1.5 s lag time will reduce the infiltration by only 5% compared to no lag, while for shorter door-opening periods of, for example 10 s, the infiltration will be reduced by 15%. 7.4.3.2
Air Curtains
There have been many academic studies using CFD to simulate the air curtains used for refrigerated display curtains (Chapter 3 through Chapter 6). Fewer studies have been carried out on air curtains used on buildings. Perhaps the first reported study in this area was by SenterNovem (an agency of the Dutch Ministry of Economic Affairs), TNO (a Dutch Research Institute), and the University of Groningen, together with Biddle Air curtains in the early 1990s [37]. They used the PHOENICS code to develop the CFD model using the k« model to predict turbulence and fullscale testing to validate. Their 3D model contained about 25,000 grid cells, which took about 300 h to converge; however, this is a very small mesh by today’s standard.
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The predictions showed that there was a 3D effect not seen with the 2D model, whereby air leaks through the side of the curtain. They also showed that the air curtain is not effective when there is a ventilation rate through the entrance. This ventilation rate is often a necessary design requirement to allow air changes within the building. The predictions concluded that air curtains used in shop doorways should condition the incoming air (heat it to a comfortable temperature) rather than try to reduce it. This is not, however, the case for cold room curtains on sealed cold stores, where the flow through the entrance is buoyant and there is no net ventilation rate (equal flow in and out). A major conclusion of the CFD studies was that the incoming air is conditioned most effectively at the lowest applicable air velocity, which was contradictory to past popular belief. The Building Services Research and Information Association (BSRIA) used specialpurpose CFD software, FLOVENT (developed by BSRIA and Flomerics Limited), for the analysis of air movement, temperature distribution, and airborne contaminant dispersion in the context of the built environment [38]. They studied the effect of building leakage on air curtain performance. They showed that for leaky buildings, when air curtains are subjected to large wind forces, there will be a significant pressure difference retained across the doorway and the net volume flow rate through the doorway will hardly be affected by the operation of the air curtains. Ligtenburg and Wijjfels [5] from Biddle bv (Netherlands) in collaboration with TNO Environment and Energy used CFD to study an air curtain used on frozen-food stores. They used the PHOENICS code and verified with experimental data obtained from a mock-up. The air curtain modeled had three jets blown downward at the same velocity (5 m s1 ). The inside jet (cold store side) was drawn from the cold store (308C to 208C, 80%–100% RH). The outside jet (ambient side) was drawn from the ambient (08C to 208C, 60%–100% RH). The middle jet was drawn from the cold store and heated, giving a very low relative humidity and thus reducing any condensation mist between the other two jets (perhaps 58C, 23% RH). The CFD predictions indicated that an effectiveness of 0.84 can be achieved with this air curtain. Foster et al. [20] simulated a 1.0 m long air curtain with a 30 mm slot, which was fitted centrally above the door on the outside of a cold store. For this study, a 2D model was created to allow accurate prediction of the narrow (30 mm) air curtain jet while still allowing all of the cold store and some of its surroundings to be modeled. The 2D model was created using CFX (ANSYS Inc.) 3D finite-volume code and by fixing only one numerical mesh cell over the width of the domain and applying symmetrical boundary conditions to the faces at either side. The domain of the model contained the volume inside the cold store for the width of the air curtain (initially at 208C) and a much larger volume outside the cold store (initially at þ208C), to provide a source of warm air for exchange. The volume outside the cold store was between four and eight times larger than the volume inside the cold store. This gave a good compromise between accuracy and numerical speed. The jet from the air curtain was modeled as an inlet into the domain with a constant velocity, temperature, and turbulence intensity. The magnitude of the inlet velocity was varied from 0 to 18 m s1 and the direction was taken to be normal to the boundary. The temperature of the jet was set at 208C, which was the initial temperature of the ambient, and the turbulence intensity was 10%. An opening boundary condition was set at the top side of the air curtain, removing an identical mass of air that entered from the inlet. All boundaries except the inlet and outlet of the air curtain were modeled as nonslip walls where the velocity of the fluid at the wall boundary was set to zero. The wall-function approach was an extension of the method of Launder and Spalding [39]. In the log–law region, the near-wall tangential velocity is related to the wall-shear-stress
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by means of a logarithmic relation (Equation 7.13 through Equation 7.15). In the wallfunction approach, the viscosity affected sublayer region is bridged by employing empirical formulas to provide near-wall boundary conditions for the mean flow and turbulence transport equations. These formulas connect the wall conditions (e.g., the wall-shear-stress) to the dependent variables at the near-wall mesh node, which is presumed to lie in the fully turbulent region of the boundary layer: uþ ¼
U 1 ¼ ln ( yþ ) þ C uf k
(7:13)
rDyuf m
(7:14)
12 tw uf ¼ r
(7:15)
where yþ ¼ and
The numerical mesh was at its finest (8 mm) at the entrance of the door and around the air curtain nozzle. This was in order to accurately resolve the large shear created by the air jet at the nozzle exit. The total number of grid nodes for the problem was 42,000. The k« turbulence model was used to predict turbulence effects. The hardware used to run the model was a Viglen Genie PC with an Intel Pentium 4 processor running at 1.6 GHz with 1 GB RAM. The CFD model was used to predict the effectiveness of the air curtain at differing jet velocities; this is shown against measured values in Figure 7.6. The maximum predicted effectiveness (0.84) was higher than that measured (0.72). The air curtains–measured effectiveness
Measured
1.0
Predicted 2D
Predicted 3D
Effectiveness
0.8
0.6
0.4
0.2
0.0 5
10
15
20
25
Jet velocity (m s−1)
FIGURE 7.6 Measured and predicted effectiveness of the air curtain for different air jet velocities for both 2D and 3D models.
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CFX 80 Velocity (vector 1) 6
Temperature (contour 1) (10) 20 (9) 16 (8) 12
5
3
2
(7)
8
(6)
4
(5) −0 (4) −4
7 6 5 4
(3) −8 (2) −12
3
(1) −16
0
Y
[m s−1] 2
1
X
FIGURE 7.7 (See color insert following page 142.) CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 6 m s1 .
was still increasing when it reached the maximum obtainable velocity (18 m s1 ) of the air curtain. The optimum jet velocity (velocity at which maximum effectiveness is obtained) was predicted (10 m s1 ) to be lower than the measured velocity (>18 m s1 ). As discussed earlier, 2D models tend to predict a higher effectiveness than measured, as end effects allow air to leak around the edge of the air curtain, causing increased infiltration. Also, a higher measured optimum velocity is required than predicted to counteract this effect. Figure 7.7 through Figure 7.9 show the predicted velocity vectors and temperature contours for air jet velocities of 6, 10.4, and 18 m s1 , and these correspond to a lower than optimum, optimum, and above optimum velocity, respectively. For a jet velocity of 6 m s1 (Figure 7.7), the air curtain is bent into the cold store such that it does not reach the floor and therefore does not seal the entrance. For a jet velocity of 10:4 m s1 (Figure 7.8), the air curtain is vertical providing optimum sealing. For the jet velocity of 18 m s1 (Figure 7.9), the increased entrainment caused by the high velocity air curtain causes a pressure buildup inside the cold store, which forces the air curtain outward reducing its effectiveness. Foster et al. [40] extended their CFD model to a 3D model. The geometry of the modeled air curtain was an approximation of the real air curtain (Figure 7.10); the exact geometry would have required a finer mesh than was possible with the given computing resources, when used in conjunction with such a large domain. Important geometrical dimensions, such as the nozzle thickness and its relative position to the fan body, were modeled as accurately as possible. The air return grille on the air curtain was modeled as being at the top of the air curtain. This was because the real return grille characteristics were complex and attempts at modeling it with the size of mesh used in the model caused unrealistic flows. The door rail obstructed entrainment to the room side
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CFX 80 Temperature (contour 1) (10) 20
Velocity (vector 1) 10
(9) 16 (8) 11
8
5
(7)
7
(6)
3
(5) −1 (4) −6
3
(3) −10 (2) −14 (1) −18
0 [m s
Y
−1]
1
2345
X
FIGURE 7.8 (See color insert following page 142.) CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 10:4 m s1 .
CFX 80 Velocity (vector 1) 18
2
1 Temperature (contour 1) (10) 20 (9) 17
14
(8) 14 (7) 11 (6) 8
9 (5) 5 (4) 2 5
(3) −1 (2) −4
0 [m s
−1]
(1) −7 Y
z
X
FIGURE 7.9 (See color insert following page 142.) CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 18 m s1 .
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Return air 60
1000 620
100
Simplified door rail
120
100 30
Fan body
Air curtain jet
Air curtain jet Cold store entrance
Cold store entrance
1360
FIGURE 7.10 Front and side elevations of the modeled air curtain device and air curtain inlet and outlet boundaries. Dimensions are in millimeters.
of the outlet nozzle and so a simplified geometry was created to give the same effect (shown as the block labeled ‘‘simplified door rail’’ to the left of the outlet and return ducts in Figure 7.10). The numerical mesh ranged from 30 mm at its finest point to 500 mm at its largest point, with an expansion factor of 1.2 between these mesh sizes. The width of the air jet boundary is the same as the minimum cell size, thus there is only one cell across the width of the air jet. In the plane of the door entrance, and for a radius of 0.5 m from this plane, the mesh was 100 mm with an expansion factor of 1.2 outside the radius of influence. The total number of grid nodes for the model was 383,945. To test the convergence of the mesh, finer meshes were used on a ‘‘cut down’’ geometry. This ‘‘cut down’’ geometry was essentially the same, except a symmetry plane was used to reduce the number of mesh points. Mesh sizes of 100, 70, and 40 mm in the plane of the door entrance were produced. In this model, computer resources did not allow meshes smaller than 40 mm within the entrance. Computer simulation times were approximately 22 h for a transient run of 30 s with a mesh size of 100 mm to a normalized residual of 1 104 . For each solution variable, w, the normalized residual, rw0 , is given in general by the following equation: [rw0 ] ¼
[rw ] ap Df
(7:16)
where rw is the raw residual control volume imbalance, ap is representative of the control volume coefficient, and Df is a representative range of the variable in the domain. Figure 7.6 shows that the predicted effectiveness was always lower than measured (0.10 lower at the minimum and 0.15 lower at the maximum measured velocity). This
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model was more accurate than the 2D model, which overpredicted the effectiveness of the curtain. The trends of the predicted and measured data are similar up to the maximum measured velocity, in that they had a similar, positive gradient that reduced with jet velocity. The predicted effectiveness reached a maximum of 0.66 at a jet velocity of 22 m s1 . It was not possible to increase the measured jet velocity above 18 m s1 in these experiments due to limitations in the installed system. However, the only data found in the literature [41] show the shape of the predicted curve to be accurate, essentially a polynomial curve with one maximum effectiveness at a specific velocity. It is not possible to predict from the data at what jet velocity the maximum effectiveness would be. However, the (average) positive gradient between the highest two measured velocities indicates that the maximum effectiveness would be greater than 0.72, at a jet velocity above 18 m s1 . Figure 7.11 shows predicted velocity vectors for a vertical elevation in the central plane of the entrance. Although the air curtain leaves the nozzle pointing straight down, the air is very soon deflected away from the room by the Coanda effect due to the proximity of the fan body. It is not possible to see the 3D effects of this flow from a single 2D plane and therefore 3D isovelocity plots for three different views are shown in Figure 7.12. The isovelocity plots show the direction of airflow for all positions at 3 m s1 . The front elevation shows that the jet narrows in the plane of the entrance. The side elevation highlights that the center of the jet is bent out away from the room but the sides are folded back into the room. The plan view shows that the central part of the jet is deflected out of the room
CFX
Temperature (contour 1) 22
Velocity (vector 2) 18
17 12
14
7 2 −2
9
−7 −12
5
−17 −22 [C]
0 [m s−1]
FIGURE 7.11 Predicted velocity vectors and temperature contours in the plane of the entrance for a jet velocity of 18 m s1 .
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FIGURE 7.12 Velocity vectors at a isovelocity of 3 m s1 in the region of the entrance for a jet velocity of 18 m s1 . Front elevation (left), side elevation (right), and plan view (bottom).
(upwards in the figure) and narrows, but that the sides of the jet are drawn into the room and cross one another.
7.5 VALIDATION Validation of CFD models is a difficult task, but is extremely important [42]. A numerical discrepancy between predicted and measured data is often put down to the measured conditions not being the same as the predicted conditions [12]. This is often due to an inability to accurately measure all of the boundary conditions for the model. Validation of the CFD models has been carried out using a number of different experimental methods.
7.5.1 TEMPERATURE MEASUREMENT Azzouz et al. [6] used an array of 16 temperature probes to measure the air temperature in the entrance of a cold room while the door was open. Hendrix et al. [21] used 28 type T
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thermocouples mounted on four separate strings, three of these were hung from cold store and loading bay ceilings (4.5 m high with four equally spaced thermocouples and 9 m high with seven equally spaced thermocouples) and the fourth was mounted on a 3 m stand in the entrance with 10 thermocouples. This data were rapidly passed to a personal computer via an RS232 link.
7.5.2 VELOCITY MEASUREMENT 7.5.2.1
Vane Anemometry
Fritzsche and Lilienblum [10] used vane anemometers to measure velocity across an entrance. Similarly, Foster et al. [36] used an array of 16 minivane-anemometer heads (diameter of 25 mm) (2 columns 8 vanes) on movable frames to determine airflow through door openings. The advantage of this system was that it was a cheap way of measuring transient air velocity in multiple positions at the same time. However, the vanes were not accurate at low velocity (below 0:3 m s1 the vanes would intermittently stop spinning giving a reading of 0 m s1 ). Vane anemometers measure velocity in only one direction. This is fine where the direction of velocity is known (in this case perpendicular to the face of the entrance, in at the top and out at the bottom). However, if there are external forces on the flow, e.g., wind or an air curtain, direction of the flow will need to be first determined and the vanes aligned. If the wind is erratic this will not be possible.
7.5.2.2
Hot-Wire Anemometry
Hendrix et al. [21] used eight hot-wire anemometers in a ‘‘tree’’ support structure with a data acquisition system to measure one-dimensional velocities through the entrance. These devices were constant temperature devices and therefore required steady-state air temperatures to allow accurate velocity measurement. Placement of these devices before door opening was critical such that a step change in temperature of the device did not happen when the door was opened (this would happen if the lower anemometers were initially placed outside of the cold room). 7.5.2.3
Laser Doppler Anemometry
Laser Doppler anemometry (LDA) has the advantage that it can measure velocity in all three dimensions, is nonintrusive to the airflow, and allows rapid measurement and will therefore measure turbulence. LDA was used by Foster et al. [36] to measure velocity closer to the walls than was practical using vane anemometry. The LDA used was a threecomponent, fiber-optically coupled system using a 5 W argon ion laser, with precision three-axis traversing gear. Unlike the array of vane anemometers, the LDA was unable to measure the velocity at multiple points simultaneously. Due to the length of time for an LDA measurement to be taken and then to traverse to the next position (approximately 30 s), the data could not be taken sequentially in a single run. Measurements were taken at a single point before the door was closed and the room equalized in temperature before moving to the next position. The size of the entrance also had to be reduced such that a steady-state flow was measured, i.e., the temperature change (driving force) between the room and ambient must not change significantly over the measurement period.
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Velocity (m s−1)
1 0.5 0 −0.5 −1
0
0.2
0.4
0.6
0.8
Height (m) CFD
LDA mean
Velocity (m s−1)
0.8 0.6 0.4 0.2 0 0
0.1 0.2 Distance from left-hand side (m) LDA mean
0.3
CFD
FIGURE 7.13 Velocities measured using LDA and predicted using CFD through the small entrance against height. Vertical line 0.143 m from the left-hand edge of the entrance (top chart); horizontal line at a height of 0.134 m (bottom chart).
Measurements were made along a vertical line and a horizontal line; these measurements were compared to CFD predictions and are shown in Figure 7.13. CFD predictions of the velocity profile along the vertical line were accurate; however, predictions of the horizontal line were not so. The reason for this was that there were not enough grid cells around the entrance for the CFD to capture the vena contracta caused by the door sides. The vena contracta is caused at a sudden contraction where the flow contracts to a diameter smaller than the contraction. This vena contracta can be seen from the LDA measurements as a region of zero flow near the sidewall (Figure 7.13, bottom chart). However, due to the coarseness of the mesh in the entrance, the CFD model predicted higher velocities near the side of the door. 7.5.2.4 Digital Particle Image Velocimetry Digital particle image velocimetry (DPIV) offers an ideal method of verifying CFD simulations, as it can provide a similar level of resolution of the flow field to that of the simulation. This author has no knowledge of this technique being used for cold room entrance infiltration. However, it has been used comprehensively for refrigerated display cabinet air curtains (more details in Chapter 4). The reason for this may be that the size of plane required to
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capture the flow through the entrance is much larger than for a refrigerated display cabinet, and therefore will require a more powerful laser to illuminate it.
7.5.3 INFILTRATION It is more valid to verify infiltration caused by the door opening, as this is the parameter by which the effect of door opening on cold rooms is assessed. To verify the infiltration caused by door opening requires either measuring the flow rates in and out of the entrance, or measuring the decay of a gas that is at a higher concentration in the room than outside. 7.5.3.1
Flow Rates
Hendrix et al. [21] showed that air velocities at as few as eight heights in the doorway were required for calculating volume flow rates. This small number of points was found to be adequate, since the air velocities at the floor and neutral level are known to be zero and the air velocity profile at the top of the door is approximately flat. The volume flow rate into the room and out of the room can be calculated by integrating the velocity profile above and below the neutral level, respectively. To establish the mass flow rate involves integrating the velocity density profile. The density is calculated from the temperature using the ideal gas law (Chapter 4, Equation 4.5). It is an important point to note that the mass of air entering and leaving the room may not be the same. This will be the case if the cold room warms during the door opening; the density of the air in the cold room will decrease, and as the cold room is of fixed volume, a net mass of air must leak from the room. 7.5.3.2
Gas Decay
Tracer gas techniques can been used to measure the infiltration through a cold store. There is a standard tracer gas technique [43] applicable with many types of tracer gas. As shown in Equation 7.17, concentrations measured immediately before and after the door opening can be used to calculate the infiltration: c ln ¼ rt co
(7:17)
This method assumes that the tracer gas is fully mixed with the air in the room. Sulfur hexafluoride (SF6 ) has been used successfully [3,12] to measure infiltration. Chen et al. [3] had a system, which included a gas chromatograph and electron-capture detector with an automatic tracer gas SF6 delivery, and sampling system to monitor tracer gas concentration simultaneously at three locations. The differences between the three sampling locations were small, suggesting that it was reasonable to assume the air in the cold store was well mixed. For trials with large rates of infiltration there was a slight delay between the start of the door-opening regime and detection in changes in the tracer gas concentration. This was attributed to the partitioning effect described by Pham and Oliver [12]. They showed that the presence of product racking tends to divide the room into several zones, so that some of the air entering the building goes out without thoroughly mixing with the air in the rest of the room. Carbon dioxide (CO2 ) is another gas that can be used; its disadvantage over SF6 is that it can only be detected at much larger concentrations; however, its advantage is that it can be detected with infrared absorption equipment rather than the much more expensive electroncapture gas chromatograph.
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Foster et al. [22] used CO2 to determine the volume of air exchange in the test room during a period with the door open. The concentration of CO2 was recorded before and after a set door-opening time. Carbon dioxide was released into the room and mixed using the evaporator fans to give a concentration of approximately 0.5% (5000 ppm). This was measured using a CO2 infrared analyzer (accuracy 5% of full scale). The room was small and contained no product racking and therefore partitioning effects were not considered important. Immediately before each door-opening test, the evaporator fans were switched off to allow the air movement to settle for 30 s. The door was fully opened for the set door-opening time and then closed. All trials were carried out with an initial cold room temperature of 208C. The concentration of CO2 immediately before opening the door and immediately after closing the door was used to calculate the infiltration rate.
7.6 CONCLUSIONS CFD models of the velocity profile through cold store entrances presented in this chapter have been shown to be generally accurate; however, there are areas where the accuracy is less than satisfactory. Reasons for this can usually be put down to limitations in the number of mesh cells allowed due to the computer hardware (memory). The mesh cells need to be small around the entrance to capture the vena contracta, but larger away from the entrance to reduce the overall number of cells. Control of the ambient conditions is also an important consideration, wind effects have been shown to be very important and therefore either need to be included in the model or known to be insignificant in reality. The extent of the ambient domain that needs to be modeled is another important consideration. If the ambient is small and the door is opened for a longtime, the ambient temperature may rise, causing a drop-off in the driving force, which may not be apparent in reality, where the ambient may be effectively infinite. CFD predictions have been shown to give a significant improvement in accuracy over the fundamental analytical equations (Brown and Tamm); however, the empirical coefficients added by Gosney and Fritzsche gave more accurate predictions than the CFD models. More detailed CFD models with more grid cells in the entrance may give a better prediction. CFD models show a lag time that analytical predictions ignore, however, unless the door-opening time is very short this reduction in flow is quite insignificant. A 2D CFD model was unable to accurately predict the optimum jet velocity of an air curtain. However, it predicted a value equivalent to that predicted by an analytical model with a low safety factor. The CFD model showed how the shape of the air curtain varied with different jet velocities as the air curtain traveled down the entrance and how these different jet velocities affected the effectiveness of the curtain. The analytical model of Hayes and Stoecker predicts optimum jet velocity of an air curtain on a cold store; however, it does not predict effectiveness of the air curtains. The model only gives a guide to the optimum jet velocity; depending upon the safety factor chosen, a large range of air curtain effectiveness can therefore be achieved. A 2D CFD model can predict the effectiveness of an air curtain; however, the predictions were higher than measured. This is because end effects will allow air to leak around the edge of the air curtain, causing increased infiltration, which are not predicted in 2D. Higher jet velocities will to some extent negate this problem and this is a probable explanation for the increased optimum jet velocity of the real air curtain compared to the 2D CFD model. A 3D CFD model was able to provide a better prediction of effectiveness and optimum jet velocity than the 2D model. The predicted effectiveness was lower and optimum jet velocity higher than measured, the opposite to the 2D model. The model showed that the flow from
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an air curtain cannot be considered as 2D. For the air curtain studied a complex 3D flow pattern was apparent. Many different experimental approaches have been used to provide data to verify these CFD models. These include thermometry, arrays of minivane anemometers, hot-wire anemometry, LDA, and tracer gas techniques, which include both SF6 and CO2 . Each approach has its own advantages and disadvantages and therefore a complete validation may be better carried out using a range of these methods. A more complete validation of the 3D interaction between the air curtain and the natural convection in the entrance requires a tool such as DPIV. This has been used in refrigerated display air curtains but not yet with cold store air curtains. Current computer power is still a limitation for accurate 3D predictions. Future increases in computer power, especially with the advent of 64-bit hardware and parallel processing should allow more accurate predictions.
NOMENCLATURE at A b c cp C Cm Ce1 Ce2 E g k Kf,L H p P Q r t T u uþ U yþ
turbulent diffusivity (m2 s1 ) area of entrance (m2 ) wall thickness (m) concentration 1 specific heat at constant pressure (J kg1 K ) log layer constant k« turbulence model constant (0.09) k« turbulence model constant (1.44) k« turbulence model constant (1.92) effectiveness, dimensionless acceleration due to gravity (9:81 m s2 ) turbulent kinetic energy per unit mass (J kg1 ) correction factor height of entrance (m) static pressure (Pa) 3 shear production of turbulence (kg m1 s ) 3 infiltration (m ) air change rate, dimensionless time (s) temperature (K) velocity (m s1 ) near-wall velocity (m s1 ) velocity tangent to the wall at a distance Dy from the wall (m s1 ) dimensionless distance from the wall
GREEK SYMBOLS b d « k l r se
coefficient of thermal expansion (K1 ) identity matrix, dimensionless 3 turbulence dissipation rate (m2 s ) von Karman constant 1 thermal conductivity (W m1 K ) 3 density (kg m ) k« turbulence model constant (1.3)
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sk st t m
191
k« turbulence model constant (1.0) turbulent Prandtl number shear stress (N m2 ) 1 dynamic viscosity (kg m1 s )
SUBSCRIPTS a with air curtain avg average b without air curtain f friction i inside n neutral o outside ref reference t turbulent 0 initial
SUPERSCRIPTS — 0
T w
turbulent mean quantities turbulent fluctuating quantities inverse matrix wall
REFERENCES 1. G. Olafsdottir, H.L. Lauzon, E. Martinsdottir, J. Oehlensschlager, and K. Kristbergsson. Evaluation of shelf life of superchilled cod (Gadus morhua) fillets and the influence of temperature fluctuations during storage on microbial and chemical quality indicators. Journal of Food Science 71: 2 S97–S109, 2006. 2. R. Faramarzi, B.A. Coburn, and R. Sarhadian. Showcasing energy efficiency solutions in a cold storage facility. Energy Efficiency in Buildings; Teaming for Efficiency 3: 107–118, 2002. 3. P. Chen, D.J. Cleland, S.J. Lovatt, and M.R. Bassett. Air infiltration into refrigerated stores through rapid-roll doors. In: Proceedings of International Institute of Refrigeration, Sydney, 1999. 4. D. Leue and P. Eilert. Industry transformation in refrigerated warehouses. In: Proceedings of the American Council for an Energy Efficient Economy, Washington, DC, 2000. 5. P.J.J.H. Ligtenburg and D.J. Wijjfels. Innovative air curtains for frozen food stores. In: Proceedings of International Institute of Refrigeration, The Hague, 1995, pp. 420–437. 6. A. Azzouz, J. Gosse, and M. Duminil. Experimental determination of cold loss caused by opening industrial cold room doors. International Institute of Refrigeration 16(1): 57–66, 1993. 7. J. Emswiler. The neutral zone in ventilation. Journal of the American Society of Heating and Ventilating Engineers 32(1): 1–16, 1926. 8. W.G. Brown and K.R. Solvason. Natural convection in openings through partitions-1, vertical partitions. International Journal of Heat and Mass Transfer 5: 859–868, 1963. 9. W. Tamm. Kalterveluste durch kuhlraumoffnungen. Kaltetechnik-Klimatisierung 18: 142–144, 1966. 10. C. Fritzsche and W. Lilienblum. Neue messengun zur bestimmung der kalterluste an kuhlraumturen. Kaltetechnik-Klimatiserung 20: 279–286, 1968. 11. W.B. Gosney and H.A.L. Olama. Heat and enthalpy gains through cold room doorways. Proceedings of the Institute of Refrigeration 72: 31–41, 1975. 12. Q.T. Pham and D.W. Oliver. Infiltration of air into cold stores. In: Proceedings of the International Institute of Refrigeration, Paris, 1983, 4: pp. 67–72.
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13. B.W. Jones, B.T. Beck, and J.P. Steele. Latent loads in low humidity rooms due to moisture. ASHRAE Transactions 89: 35–55, 1983. 14. C.O. Gill. The microbiology of chilled meat storage. In: Proceedings of the 24th Meat Industry Research Conference, Hamilton: MIRINZ Publication, 1986, pp. 210–213. 15. S.J. James and J.E. Evans. Frozen storage of meat and meat products. FAIR Concerted Action PL95–1180, 1997. 16. G. Londahl and C.E. Danielson. Time temperature tolerances for some meat and fish products. In: Proceedings of International Institute of Refrigeration, Warsaw, 1972. 17. S.J. James and C. James. Microbiology of refrigerated meat. In: Meat Refrigeration. Cambridge: Woodhead Publishing Limited, 2002. 18. M. Boast. Frost free operation of large and high rise cold storage. Proceedings of the Institute of Refrigeration 6: 1–11, 2003. 19. W.R. Micheal. Air curtains for use on cold stores. In: Proceedings of International Institute of Refrigeration, Marseille, 1960, pp. 489–495. 20. A.M. Foster, M.J. Swain, R. Barrett, P. D’Agaro, and S.J. James. Effectiveness and optimum jet velocity for a plane jet air curtain used to restrict cold room infiltration. International Journal of Refrigeration 29(5): 692–699, 2006. 21. W.A. Hendrix, D.R. Henderson, and H.Z. Jackson. Infiltration heat gains through cold storage room doorways. ASHRAE Transactions 95(2): 1158–1168, 1989. 22. A.M. Foster, M.J. Swain, R. Barrett, and S.J. James. Experimental verification of analytical and CFD predictions of infiltration through cold store entrances. International Journal of Refrigeration 26(8): 918–925, 2003. 23. G.N. Abramovitch. The Theory of Turbulent Jets. Cambridge, MA: The MIT Press, 1963. 24. N. Rajaratnam. Turbulent Jets. Amsterdam: Elsevier Scientific, 1976. 25. C.J. Chen and W. Rodi. Vertical Turbulent Buoyant Jets—A Review of Experimental Data. Oxford: Permagon Press, 1980. 26. F.C. Hayes and W.F. Stoecker. Heat transfer characteristics of the air curtain. ASHRAE Transactions 2120: 153–167, 1969. 27. F.C. Hayes and W.F. Stoecker. Design data for air curtains. ASHRAE Transactions 2121: 168–180, 1969. 28. H.W. Wang and S. Touber. Simple non-steady-state modeling of a refrigerated room taking account air flow and temperature distributions. In: Proceedings of the International Institute of Refrigeration, Wageningen, 1989, pp. 211–219. 29. M. Mariotti, G. Rech, and P. Romagnoni. Numerical study of air distribution in a refrigerated room. In: Proceedings of the International Institute of Refrigeration, The Hague, 1995, pp. 98–105. 30. M.L. Hoang, P. Verboven, J. de Baerdemaeker, and B.M. Nicolai. Analysis of the air flow in a cold store by means of computational fluid dynamics. International Journal of Refrigeration 23: 127–140, 2000. 31. H.H. Nahor. CFD model of the airflow, heat, and mass transfer in cool stores. Revue internationale du froid 28(3): 368–380, 2005. 32. A. Schaelin, J. van der Maas, and A. Moser. Simulation of airflow through openings in buildings. ASHRAE Transactions 2: 319–328, 1992. 33. W. Schmidt. Turbulente Ausbreitung eines Stromes erhizter Luft. Zeitschrift fu¨r Angewandte Mathematik und Mechanik 21(5): 264–278; 21(6): 351–363, 1941. 34. W. Rodi. Turbulent Buoyant Jets and Plumes. Oxford: Permagon Press, 1982. 35. N.H. Wong and S. Heryanto. The study of active stack effect to enhance natural ventilation using wind tunnel and computational fluid dynamics (CFD) simulations. Energy and Buildings 36(7): 668–678, 2004. 36. A.M. Foster, R. Barrett, S.J. James, and M.J. Swain. Measurement and prediction of air movement through doorways in refrigerated rooms. International Journal of Refrigeration 25(8): 1102–1109, 2002. 37. P. Ligtenburg and P. Waldron. Open door trading: Cutting out the energy waste. Heating and Ventilating Engineer 65(713): 14–20, 1992. 38. F. Alamdari. Air curtains: Commercial applications. BSRIA Application Guide 2=97, Berkshire, 1997.
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39. B.E. Launder and D.B. Spalding. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289, 1974. 40. A.M. Foster, M.J. Swain, R. Barrett, P. D’Agaro, L.P. Ketteringham, and S.J. James. Threedimensional effects of an air curtain used to restrict cold room infiltration. Applied Mathematical Modelling 31(6): 1109–1123, 2007. 41. G.R. Longdill, L.F. Frazerhurst, and L.G. Wyborn. Air Curtains—MIRINZ Report Number 385. Hamilton: Meat Research Institute of New Zealand, 1974. 42. M.N.A. Said, C.Y. Shaw, J.S. Zhang, and L. Christianson. Computation of room air distribution. ASHRAE Transactions 101(1): 1065–1077, 1995. 43. A.S.T.M. Standard practice for measuring air leakage rate by the tracer dilution method. ASTM standard E741–83, Annual Book of ASTM Standards. Philadelphia: American Society for Testing and Materials, 1983. 44. C.C. Downing and W.A. Meffert. Effectiveness of cold-storage door infiltration protective devices (rp-645). Transactions of the ASHRAE: 99–356, 1993. 45. K. Takahashi and M. Inoh. Some measurements on air curtain efficiency for cold rooms. In: Proceedings of the International Institute of Refrigeration, Munich, 1963, 2: pp. 1035–1039. 46. G.R. Longdill and L.G. Wyborn. Performance of air curtains in single-storey cold stores. In: Proceedings of the International Institute of Refrigeration, Venice, 1978, 4: pp. 77–88. 47. J. Van Male. A new vertical air curtain design for cold-storage doors. In: Proceedings of the International Institute of Refrigeration, Paris, 1983, 4: pp. 74–82.
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8
CFD Modeling of Simultaneous Heat and Mass Transfer in Beef Chilling Francisco Javier Trujillo and Q. Tuan Pham
CONTENTS 8.1 8.2
Introduction ............................................................................................................... 195 CFD Modeling of Heat and Mass Transfer on a 2D Model of a Beef Leg—A Rigorous Approach .............................................................................. 197 8.2.1 Problem Statement ......................................................................................... 197 8.2.2 Mathematical Model ...................................................................................... 198 8.2.2.1 Transport Equations in the Air ........................................................ 198 8.2.2.2 Transport Equations in the Meat ..................................................... 200 8.2.2.3 Boundary Conditions and CFD Modeling....................................... 200 8.2.2.4 Initial Conditions.............................................................................. 202 8.2.2.5 Boundary Layer Treatment .............................................................. 202 8.2.3 Details of Numerical Solution ........................................................................ 202 8.2.4 Results and Analysis....................................................................................... 204 8.3 CFD Modeling of Heat and Mass Transfer on a Three Dimensional Model of a Beef Carcass—The Three-Step Method .................................................. 205 8.3.1 Mathematical Model ...................................................................................... 207 8.3.2 Validation ....................................................................................................... 209 8.4 A Simplified Combined CFD-Conduction Model for Beef Chilling ......................... 214 8.5 Conclusions................................................................................................................ 217 Nomenclature ..................................................................................................................... 218 References .......................................................................................................................... 219
8.1 INTRODUCTION Refrigeration is the most widely used method for preserving the quality of fresh meat. In industrial beef processing, after the animal is killed, it is de-hided, eviscerated, sawn into halves (called sides), then chilled in an air chiller for 16 h or more. During this process, cooling and water movement proceed together and interact to influence surface water activity, microbial growth, weight loss, meat temperature, and meat tenderness, all of which have important economic consequences. As the meat cools, heat is conducted through the product and carried away by the air. The meat surface is warmer and more humid than the air, resulting in surface evaporation. Water from inside diffuses towards the surface to make up for the evaporation. The balance between evaporation and diffusion governs the water activity near the surface, which together with temperature determines the potential for
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microbial growth. It is therefore important to be able to calculate the evolution of temperature and moisture during this chilling process in order to optimize it, or at least to ensure that the quality standards to the consumer are maintained. Both heat and mass transfer are affected by the flow characteristics and the development of the momentum, heat, and mass boundary layers. They are the function of air properties, the geometry of the product, that of the chiller room, and the flow characteristics (temperature, humidity, velocity, and turbulence). Therefore, local variations in the heat and mass transfer coefficients are expected along the surface [1], producing local differences in temperature and water activity. These variations are important because they may cause hot or moist spots where unacceptable microbial growth takes place. Early numerical models of meat chilling [2–7] have focused on solving the equations for conduction and=or diffusion in the meat. A common shortcoming of these methods is that they use empirical equations to determine the average heat and mass transfer coefficients. These equations have been developed for airflow around simple geometries but do not necessarily apply to the complex flow pattern around real carcasses. It is known that the value of the surface heat transfer coefficients (HTC) varies along the surface of the product, depending on the development of the boundary layer. Kondjoyan and Daudin [8] showed that the convective transfer coefficient value varies from 40% to þ40% of the mean value around a circular cylinder. Variations in the case of real food geometries, such as a pork hindquarter [9], are even more complex. Recently, computational fluid dynamics (CFD) has been used to model the chilling process of beef carcasses in order to determine local variations of heat and mass transfer coefficients around real food geometries. Nguyen and Pham [10] used CFD to simulate the heat transfer process in beef carcass chilling. The complex geometry of the beef carcasses was represented in three dimensions by a grid of about 100,000 nodes. Nguyen and Pham took into account heat conduction inside the meat and heat convection in the air phase, but they did not take into account evaporation and mass transfer. Hu and Sun [11] modeled the heat and mass transfer on the air side during the cooling of cylindrical-shaped cooked meat. They used the CFD software CFX to calculate the average heat transfer coefficient ht but did not predict local (ht ) variations. Hu and Sun [12] improved the previous model by calculating the local heat transfer coefficient cell by cell around a 3D model of the surface, but the mass transfer was not treated rigorously via CFD modeling. For example, the Lewis relationship was used to calculate mass transfer from heat transfer, and the surface water activity of the meat was assumed to be equal to the relative humidity of the air (on a scale of 0 to 1), which is not necessarily true. Most models calculate the average mass transfer coefficient hm using the Lewis relationship and assume a constant value for water activity [5,6,11,12]. A source of difficulty is that heat and mass transfer happen on vastly different scales due to the big difference in heat and mass diffusivity in the meat. By the time the whole product is cooled, only the surface layer (a few mm) loses water. This makes it difficult to model the two processes efficiently and accurately using a homogeneous grid. To solve this problem, Pham and Karuri [13] used a secondary grid for moisture calculations, but they solved the transport equations only for the solid phase and not for the air phase, relying instead on an empirical ht and the Lewis relationship to calculate the hm . A complete and rigorous approach for the simultaneous heat and mass transfer on a 2D model of a beef leg was presented by the authors [14] using Fluent 6.0. Special techniques were used to solve the heat and mass transport equations for both the air and meat phases, due to some limitations in the software. In the air, turbulent flow was modeled with the renormalization group (RNG) k–« model and the boundary layer was fully solved using the Fluent’s enhanced wall treatment. This model predicted local variations in the heat and mass transfer
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coefficients and temperature and water activity around the elliptical surface. The model was then extended [15] to a complete 3D beef carcass model and it was able to predict weight loss, heat load, surface and center temperatures. For the complex carcass geometry, a three-step method was used to simulate the simultaneous heat and mass transfer process in order to reduce the computational time. In the first step, a steady-state simulation of the flow field was conducted. In the second step, the local heat and mass transfer coefficients were calculated. Finally, the third step consisted of the simultaneous heat and mass transfer process simulation in the meat carcass only using the previously obtained transfer coefficients as boundary conditions. A separate 1D grid was used to calculate the moisture diffusion in the meat. The model allowed calculating and predicting the heat load, temperatures, weight loss, and water activity. Local variations in the heat and mass transfer coefficients, temperature, and water activity were found around the beef carcass. The CFD model gave temperature predictions that agree with experimental data better than any previous model. This chapter is divided into three main sections. Section 8.2 describes the rigorous approach for the simultaneous heat and mass transfer [14] and its implementation in Fluent. This model is implemented in a 2D geometrical representation of a beef leg cross section. Section 8.3 explicates a three-step method applied to the complex 3D carcass geometry. Finally, Section 8.4 illustrates the use of CFD to calculate local heat and mass transfer coefficients and their subsequent incorporation into faster simplified models.
8.2 CFD MODELING OF HEAT AND MASS TRANSFER ON A 2D MODEL OF A BEEF LEG—A RIGOROUS APPROACH A numerical simulation of the simultaneous unsteady heat and mass transfer in an elliptical model of a beef leg is carried out using Fluent 6.1. Special programming techniques are used to solve the heat and mass transport equation for both the air and meat phases, due to some limitations in the software. The meat was treated as a fluid subregion where the heat and mass transport equations are modeled by different scalar variables, which are however linked at the interface with the heat and mass transfer modeling of the air phase. In the air, turbulent flow was modeled with the RNG k–« model and the boundary layer was fully solved using Fluent’s ‘‘enhanced wall treatment.’’ The model predicts local variations in the heat and mass transfer coefficients and temperature and water activity around the ellipse’s surface.
8.2.1 PROBLEM STATEMENT A beef leg undergoing chilling is modeled as an ellipse [6] with minor and major diameters of 0.22 and 0.29 m, respectively, placed inside a wind tunnel 1.5 m wide by 2.3 m long (Figure 8.1). Air enters the tunnel at 277.95 K, 98% relative humidity, atmospheric pressure, 0:54 m s1 normal to the inlet plane, and with a turbulence intensity of 10%. The product is initially at 315.15 K with a moisture content of 75% wet basis. The properties of air were assumed constant except the density that was expressed as function of temperature and pressure. For the meat, we assume a density of 1111 kg m3 , specific heat of 3407 J kg1 K1 , and thermal conductivity of 0:397 W m1 K1 . The moisture diffusivity can be calculated with the equation obtained by curve-fitting drying data for lean beef meat samples [16]: Dm ¼ 4:67 105 exp(3757:26=T) m2 s1
(8:1)
In the drying tests for determining moisture diffusivity (Dm ), it was found that the effective diffusivity varied with time. The above equation corresponds to the initial drying period,
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Moisture Heat
FIGURE 8.1 Representation of the beef leg as an ellipse.
where the meat shrinkage of the samples is less than 10%. It was expected that the initial drying period simulates best the conditions in carcasses chilling, where shrinkage of the meat is negligible and water diffusion from inside the meat constantly rewets the meat surface. The effect of the external fat cover on the water diffusivity was neglected in the model.
8.2.2 MATHEMATICAL MODEL 8.2.2.1
Transport Equations in the Air
In the air, a set of six transport equations are solved: a. The Continuity Equation @r v ¼ 0 þ r r~ @t
(8:2)
v is the mean velocity vector. where r is the density, t is the time, and ~ b. The Momentum Equation @( r~ v) þ r r~ v~ v ¼ rp þ r ( teff ) @t
(8:3)
where p is the pressure and teff the effective stress tensor given by teff ¼ meff
h i T vI v þ r~ v 2 r ~ r~ 3
with meff being the effective viscosity.
(8:4)
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c. The Energy Transport Equation @(rE ) v (rE þ p) ¼ r þr ~ @t
leff rT
X
Jj þ teff Hj ~
! v ~
(8:5)
j
where leff is the effective thermal conductivity, Hj the enthalpy of the species j, ~ Jj the diffusion flux of species j, E the specific energy of the fluid defined as p v2 E ¼ H þ r 2
(8:6)
where H is the enthalpy and v2 =2 represents the kinetic energy. d. The Water Transport Equation @(rY ) vY ¼ r ~ þ r r~ Jw @t
(8:7)
~ Jw ¼ rDeff rY
(8:8)
where Deff is the effective water diffusivity and Y the water mass fraction. e. The Turbulent Kinetic Energy Equation X @ X @ @ @k ð rk Þ þ rkvj ¼ ak meff þ Gk þ Gb r« YM @t @xj @xj @xj j j
(8:9)
f. The Turbulent Dissipation Rate Equation X @ X @ @ @« « «2 (r«) þ r«vj ¼ a« meff þ C1« ðGk þ C3« Gb Þ C2« r R« @t @xj @xj @xj k k j j
(8:10)
The RNG k–« model [17,18] was used to calculate the turbulent kinetic energy, k, and its rate of dissipation, « (Equation 8.9 and Equation 8.10). In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients. Gb is the generation of turbulence kinetic energy due to buoyancy. YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C1« , C2« , and C3« are constants. The quantities ak and a« are the inverse effective Prandtl numbers for k and «, respectively. The scale elimination procedure in RNG theory results in a differential equation for turbulent viscosity: 2 r k y^ d pffiffiffiffiffiffi ¼ 1:72 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d^ y «m y^3 1 þ Cy where y^ ¼ meff =m Cy 100
(8:11)
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Equation 8.11 is integrated to obtain the effective viscosity turbulent viscosity meff . It gives an accurate description of how the effective turbulent viscosity varies with the effective Reynolds number, allowing the model to better handle low Reynolds number and near-wall flows [18]. The effective thermal conductivity is calculated from leff ¼ aCp meff
(8:12)
a 1:3923 0:6321 a 2:3923 0:3679 m
¼
a 1:3929
a 2:3929
m 0 0 eff
(8:13)
where a is calculated from [17]
and a0 ¼ 1=Pr ¼ k=mCp . The effective diffusivity Deff is calculated in a manner that is analogous to the method used for heat transport. For this case, the value of a0 in Equation 8.13 is a0 ¼ 1=Sc, where Sc is the ‘‘molecular Schmidt number.’’ 8.2.2.2
Transport Equations in the Meat
In the meat, only the transport equations for thermal energy and moisture need to be solved. The energy transport equation is @ rm cp,m T ¼ r(lm rT) (8:14) @t where rm , cp,m , lm , and T are the density, heat capacity, thermal conductivity, and temperature of the meat, respectively. The moisture transport equation is @(rm W ) ¼ r(rm DmrW ) @t
(8:15)
where W is the water mass fraction in the meat (wet basis) and Dm the water diffusivity. 8.2.2.3
Boundary Conditions and CFD Modeling
Conditions at the inlet of the wind tunnel containing the beef leg are as given under ‘‘Problem specifications.’’ At the tunnel outlet, zero normal gradients are assumed for all variables: v, T, Y, «, k. At the walls of the tunnel, zero velocity, zero heat flux, and zero water flux are assumed. At the meat surface, thermal and species equilibrium, and conservation of heat and mass apply. With regard to conservation of heat and mass, special computational techniques have to be applied to balance the heat and mass fluxes coming out of the solid (beef carcass) with those entering the air phase; the heat and moisture leave the beef region to enter the air region. If the mesh is fine enough to get into the thermal and mass boundary sublayers, the water flux that enters the air can be calculated cell by cell using the concentration profile in the air control volume next to the solid surface, using the equation Jw ¼ rD
Ys Yc ds
(8:16)
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where Jw is the local water flux on a particular surface element, Ys and Yc are the water mass fraction in the air at the meat surface and center of the volume element, respectively, ds is the distance between the meat surface and the center of the volume element. The heat flux (q) entering the air was calculated as the sum of convection (qconv ), evaporative (qevap ), and radiative (qrad ) components: q ¼ qconv þ qevap þ qrad
(8:17)
qevap ¼ Jw DHvap qrad ¼ s«r Ts4 Ta4
(8:18) (8:19)
where DHvap is the latent heat of vaporization of water, Ts the temperature on the meat surface, and Ta is the bulk temperature of the air. qconv was calculated using the temperature gradient of the air control volume next to the surface: qconv ¼ l
Ts Tc ds
(8:20)
where Ts and Tc are the air temperate on the meat surface and center of the volume element, respectively. The following equilibrium conditions between the air in contact with meat and the meat surface must also hold: a. Thermal Equilibrium Ts ¼ Ta,s ¼ Tm,s
(8:21)
where Ta,s is the temperature of the air phase on the meat surface and Tm,s is the temperature of the meat at the surface. b. Chemical Potential or Water Activity Equilibrium aw ¼ aw,m,s ¼ aw,a,s
(8:22)
where aw,m,s and aw,a,s are the superficial water activity of the meat and air, respectively. As a consequence of Equation 8.22, the absolute humidity (water mass fraction dry basis) of the air on the meat surface (Ys ) can be calculated from the following equation: Ys ¼
aw PV =PT 18 1 aw PV =PT 29
(8:23)
The surface water activity aw is calculated as a function of the water content of the meat at the surface using the Lewicki equation [19]: Xm ¼
0:0488 0:0488 34:7794 (1 aw )0:8761 1 þ aw
(8:24)
where Xm is the dry basis water content of the meat at the surface (g water g dry solid1 ). The Lewicki equation was chosen for its applicability to the high water activity range. This equation fits well the moisture sorption isotherm data at high humidities and predicts that the water content Xm tends to infinity when aw ! 1, as expected. Other models, such as
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the Guggenheim–Anderson–de-Boer (GAB) or Peleg equations, are inaccurate in the high water activity range. For instance, the GAB equation is applicable to a wide range of aw (0.1–0.9) but it has been reported that the error increases sharply for values of aw above 0.9. The surface water activity during meat cooling has been found to be in the high range [20] caused by continuous moisture diffusion from inside the meat to the surface. Thus, the Lewicki model is considered more appropriate. The model neglects the effect of the external fat cover on the water activity. 8.2.2.4
Initial Conditions
At zero time, the meat temperature and moisture content are uniform as per ‘‘Problem Statement.’’ It was also assumed that the airflow was fully developed. Thus, a steady-state solution for the air phase was done as a preliminary step before starting the transient simulation, with the air temperature near the meat surface kept at 315.15 K and the humidity corresponding to equilibrium with the meat. 8.2.2.5
Boundary Layer Treatment
The temperature and concentration gradients next to the surface must be accurately known because they are used to calculate the mass and heat fluxes between the meat surface and the air. Therefore, we used the Fluent’s enhanced wall treatment [18] in order to model the fluid all the way to the wall. This near-wall modeling method combines the two-layer model, where the viscosity affected near-wall region is completely resolved all the way to the viscous sublayer, using enhanced wall functions. In this approach, the whole domain is subdivided into a viscosity-affected region and a fully turbulent region. The demarcation of the two regions is determined by a wall-distance-based turbulent Reynolds number [18]. In the fully turbulent region the k–« model is used. The turbulent viscosity in the viscosity-affected nearwall region is determined with the one-equation model of Wolfstein [21]. The turbulent viscosities in the two regions are smoothly blended using a blending function. To extend its applicability throughout the near-wall region, Fluent formulates the law of the wall (enhanced wall function) as a single expression for the entire wall region by blending the linear (laminar) and logarithmic (turbulent) laws of the wall using a function suggested by Kader [22]. The latter is a near-wall modeling method that combines a two-layer model (the viscosity affected near-wall region is completely resolved all the way to the viscous sublayer) with enhanced wall functions. The near-wall mesh must be fine enough to resolve the transport equations down to the laminar sublayer. This is also important given that the wall functions (Fluent adapted them from Ref. [23]) are valid for fully developed turbulent flows (high Reynolds numbers) and this is not the case for carcass chilling. Therefore, it is not recommended to use the common simplification of using a gross mesh altogether with wall functions to accurately model beef chilling processes.
8.2.3 DETAILS
OF
NUMERICAL SOLUTION
The equations were solved using Fluent’s segregated method, where the governing equations are solved sequentially. In that method, each discretized transport equation is linearized implicitly with respect to the equation’s dependent variable. Because the equations are nonlinear and coupled, iterations must be performed before a converged solution is obtained. A point implicit (Gauss–Seidel) linear equation solver is used by Fluent in conjunction with an algebraic multigrid (AMG) method. The pressure–velocity coupling method used was pressure-implicit with splitting of operators (PISO), which is recommended for unsteady
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problems. Time steps of 1 s were used at the beginning, gradually increasing up to 10 min at the end of the simulation. Up to 40 iterations were done for each time step. If the meat is defined in Fluent as a solid region, the mass transfer processes cannot be solved because Fluent cannot solve the mass transfer equation in a solid. Thus, the meat had to be defined as a fluid phase. However, the heat and mass transfer modeling obtained by Fluent in that ‘‘meat fluid region’’ is not valid because Fluent adds convective and other extra terms that are not part of the transport equations in the meat. To overcome this problem, Fluent allows the user to define new field variables called user-defined scalars (UDS). The moisture and temperature inside the meat are considered as new field variables or UDS with their own associated transport properties (diffusivity and density). Defining a UDS simply involves specifying whether there are convective, diffusive, and transient terms in the transport equations, and specifying expressions for the transport properties mentioned above. The Fluent default menu allows only fixed boundary conditions. Because the boundary conditions at the air–meat interface change with time and are dependent on the values of the field variables, they have to be modeled using user-defined functions (UDFs), which are functions programmed by the user in Cþþ that can be automatically linked with the Fluent Solver. With a UDF, we can take the present values of the local field variables (temperature, moisture content, etc.) and use them to calculate the boundary conditions at that particular instant. The UDFs are incorporated in the set of equations solved by the segregated solver, such that the values they predict are updated in each new time step iteration. There are four UDFs representing the moisture balance, the heat balance, moisture equilibrium, and thermal equilibrium at the interface: 1. DEFINE_PROFILE (mass_flux_meat, tm, j): Calculates the moisture flux leaving the meat at the interface by convection, using Equation 8.16. It is used as a boundary condition of the UDS2 that represents the mass transport equation in the meat. 2. DEFINE_PROFILE (heat_flux_meat, tm, j): Calculates the heat flux leaving the meat at the interface by convection, radiation, and evaporation according to Equation 8.17. It is used as a boundary condition of the UDS1 that represents the energy transport equation in the meat. 3. DEFINE_PROFILE (temperature_air_interf, t, n): Makes the air temperature at the meat interface equal to the meat surface temperature (Equation 8.21). It is used as a boundary condition of the air phase energy equation. 4. DEFINE_PROFILE (water_air_interf, t, n): Calculates the moisture concentration in the air at the interface by the following procedure: . Read the meat surface temperature (Equation 8.21). . Read the moisture concentration at the meat interface and calculate the water content. . Calculate the water activity with Equation 8.24 using the Newton–Raphson method. . With the water activity and the meat surface temperature, calculate the moisture content of the air using Equation 8.23. This UDF is used as a boundary condition of the mass equation of the air phase. In each iteration the segregated method solver does the following: . . .
Solve the linearized discretized momentum equation in the air phase. Solve total mass conservation in the air phase and update velocities. Solve energy equation in the air phase—this involves calls to UDF3 for a boundary condition.
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. . .
.
. .
Solve moisture equation in the air phase—this involves calls to UDF4 for a boundary condition. Solve for turbulent kinetic energy in the air phase. Solve for eddy dissipation in the air phase. Solve energy (UDS1) equation in the meat phase. This involves calls to UDF2 for the boundary condition. Solve moisture (UDS2) equation in the meat phase. This involves calls to UDF1 for the boundary condition. Update all properties. Check for convergence.
For each time step, this procedure is carried out until convergence is obtained or 40 iterations have been done. In order to enhance the stability of the procedure, the UDFs 1 to 4 were calculated after getting convergence in the previous time step.
8.2.4 RESULTS
AND
ANALYSIS
Figure 8.2 shows the changes of the surface temperature with the position over the elliptical cylinder (given by the angle) after 1 and 5 h. As can be seen in the figure, the temperature varies by up to 58C around the ellipse at a particular time. Local variations of the water activity with position can be seen in Figure 8.3. Figure 8.4 shows the water concentration profile deep inside the meat at 08 (the impact or stagnation point), indicating that the mass transfer inside the meat is noticeable only in a 25 mm surface layer (about one-fifth of the mean radius). The heat transfer on the other hand affects the entire domain inside the meat, as seen in Figure 8.5, which shows the temperature profiles at time 0 min, 30 min, and 5 h. This modeling proved that it is feasible to conduct a rigorous unsteady-state simulation of the simultaneous heat and mass transfer process during beef chilling. However, the computational cost is very high. To model 20 h of chilling on this simple 2D object took about 6 days on a Pentium 1.5 GHz computer, making it unpractical for normal industrial calculations.
296 Temperature 1 h Temperature 5 h
294 Temperature (K)
292 290 288 286 284 282 280 0
20
40
60
80 100 Angle (⬚)
120
140
160
FIGURE 8.2 Surface temperature profile as a function of the angle at 1 and 5 h.
180
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0.978
aw 1 h aw 5 h
0.976
Water activity
0.974 0.972 0.97 0.968 0.966 0.964 0.962 0.96 0.958 0
20
40
60
80 100 Angle (⬚)
120
140
160
180
FIGURE 8.3 Surface water activity as a function of the angle at 1 and 5 h.
8.3 CFD MODELING OF HEAT AND MASS TRANSFER ON A THREE DIMENSIONAL MODEL OF A BEEF CARCASS—THE THREE-STEP METHOD In this section the unsteady heat and mass transfer process is modeled on a 3D beef carcass geometric model. The 3D geometry of the carcass was constructed from the set of 2D crosssectional data of Davey [5,24]. The geometric generation procedure is similar to the one used by Nguyen and Pham [10] (details of the geometric construction are explained in Ref. [15]). The beef side was placed inside a wind tunnel of dimensions 650 1100 2775 mm height. This apparatus, used by Davey, was placed inside a small industrial beef chiller to conduct experimental trials. Both phases, air and beef, were meshed with Gambit using tetrahedral unstructured meshes. The mesh on the air side next to the beef surface was constructed in a fine manner in order to solve the transport equations in the fluid all the way to the wall as explained before. The mesh on the meat side needs to be very fine close to the surface in order to model the water diffusion on the meat, which takes place only near the surface. Unfortunately, it cannot
80
Water fraction (%)
75 70 65 60 55 Water concentration 20 h Water concentration 10 h Water concentration 1 h
50 45 0
5 10 15 20 25 Distance deep inside the ellipse (mm)
30
FIGURE 8.4 Water concentration profile deep inside the meat at 08 (stagnant point) at 1, 10, and 20 h.
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3.15e+02 3.11e+02 3.08e+02 3.04e+02 3.00e+02 2.97e+02 2.93e+02 2.89e+02 2.85e+02 2.82e+02 2.78e+02 Aug 04, 2003 Contours of Static Temperature (k) (Time = 0.0000e+00) FLUENT 6.0 (2d, dp, segregated, spe2, rngke, unsteady)
Temperature profile at time 0 min 3.15e+02 3.11e+02 3.08e+02 3.04e+02 3.00e+02 2.97e+02 2.93e+02 2.89e+02 2.85e+02 2.82e+02 2.78e+02 Aug 04, 2003 Contours of Static Temperature (k) (Time = 1.8000e+03) FLUENT 6.0 (2d, dp, segregated, spe2, rngke, unsteady)
Temperature profile at time 30 min 3.15e+02 3.11e+02 3.08e+02 3.04e+02 3.00e+02 2.97e+02 2.93e+02 2.89e+02 2.85e+02 2.82e+02 2.78e+02 Aug 04, 2003 Contours of Static Temperature (k) (Time = 1.8000e+04) FLUENT 6.0 (2d, dp, segregated, spe2, rngke, unsteady)
Temperature profile at time 5 h
FIGURE 8.5 Temperature profile inside the meat time 0 min, 30 min, and 5 h.
be made sufficiently fine due to the constraints of the software and the hardware. Thus, in order to solve the water transport equation inside the meat, a separate set of supplementary 1D grids was constructed using the idea of Karuri and Pham [13]. The main 3D volume elements are used by Fluent to solve the heat transfer inside the meat. The secondary grid in 1D is implemented in an additional piece of code programmed via a Fluent UDF to solve the water diffusion equation. Each instance of this grid is ‘‘attached’’ to one of the face centroids
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Wind tunnel Unstructured mesh
Gy
Beef phase mesh Gy
Beef
Gx
Air phase mesh
Gz
Gx
Boundary layer mesh
Beef
Boundary layer mesh
Fine 1D mesh normal vector
Triangular base
Fine boundary layer mesh
Face centroid
Air
Prismatic volume element Beef surface
Meat 3D cell element
FIGURE 8.6 Details of the generated mesh.
around the beef surface, penetrating the meat in the direction perpendicular to the surface. The mesh goes 24 mm into the meat. Twenty elements of different lengths were placed in that distance. Close to the surface, where the concentration gradients are greater, the elements are shorter. Deeper in the meat, where the mass flux is very small, the elements are longer. The mesh was made 1D because the mass transfer only occurs a few centimeters next to the surface of the meat and hence the mass flux direction is almost perpendicular to the meat surface. Figure 8.6 displays details of the generated mesh.
8.3.1 MATHEMATICAL MODEL The same set of equations as in Section 8.2.2 applies and in theory it is also possible to simultaneously model the unsteady heat and mass transfer process for the 3D carcass model. However, given the high computational time required (especially in three dimensions), a threestep method [12,25] was followed to simplify and accelerate the simulation. The steps consist of firstly conducting a CFD steady-state simulation only in the air phase, secondly, determining the local heat and mass transfer coefficients, and thirdly, doing the unsteady-state simulation on the meat only using the heat and mass transfer coefficients from the previous step. Three runs were completed and the heat load, weight loss, surface and center leg, loin and shoulder temperatures were compared with the experimental data obtained by Davey [5,24]. The three-step process is valid if the heat and mass transfer coefficients are constant during the chilling period. The forced convection heat and mass transfer coefficients depend on the Reynolds number and the turbulent intensity. If buoyancy effects are taken into
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TABLE 8.1 Initial and Boundary Conditions for Runs 14, 18, and 32
Weight (kg) Fat thickness (mm) at Aus-Meat P8 (rump) position Aus-Meat fatness grade Air relative humidity (%RH) Air temperature (8C) Air tunnel velocity (m s1 ) Slaughter floor time (min) Initial beef temperature (8C)
Run 14
Run 18
Run 32
113.5 14 4 98.5 6.02 0.99 90 42.4
108 6 2 98 4.88 0.538 120 42.4
140 12 3 99.9 6.57 0.69 85 42.4
account, the transfer coefficients will also depend on the wall temperature, air temperature, and water content. However, the effects of buoyancy on the heat and mass transfer coefficients for air velocities higher than about 0:5 m s1 may be considered unimportant [26]. Thus, the heat and mass transfer coefficients can be considered constant during each computational run if the air velocity ( 0:5 m s1 ) and the turbulence intensity are constant. The experimental runs number 14, 18, and 32 by Davey [24] were modeled via CFD with the three-step technique. The initial and boundary conditions for those runs are listed in Table 8.1. The local heat and mass transfer coefficients in the chilling period were determined via CFD knowing the air velocity, temperature, and the turbulence intensity. The following boundary conditions were applied in order to calculate the heat and mass transfer coefficients in the first step: at the tunnel’s inlet the air velocity, humidity, and temperature must be known. The boundary conditions for the k–« model were specified with the turbulence intensity and the hydraulic diameter. At the tunnel outlet, zero normal gradients are assumed for all variables: v, T, Y, «, k. At the walls of the tunnel, zero velocity, zero heat flux, and zero water flux are assumed. Finally, at the beef surface, zero velocity was assumed and initial values were applied for surface temperature and air moisture content. With the boundary conditions defined, a steady-state CFD simulation was conducted for the air phase only. After the transport equations have been solved, the heat and mass transfer coefficients can be calculated cell by cell using the concentration profile in the air control volume next to the solid surface. The near-wall mesh must be fine enough to resolve the transport equations down to the laminar sublayer. Thus, the water flux at the beef surface can be calculated cell by cell using the concentration profile in the air control volume next to the solid surface by using Equation 8.16. Subsequently, the local mass transfer coefficient can be calculated from the local water flux: hm ¼
Jw (Ys Ya )
(8:25)
where Ya is the bulk water content of the air. Similarly, the convective heat flux qconv is calculated using Equation 8.20 and the local heat transfer coefficient can be obtained from ht ¼
qconv (Ts Ta )
(8:26)
The transfer coefficients calculated with the chilling room specifications cannot be used to model the slaughter floor period given that the flow patterns are different. Thus, another
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steady-state CFD modeling of the slaughter floor was conducted to determine the local heat and mass transfer coefficients in this stage [15]. The local heat and mass transfer coefficients during the slaughter and chilling periods can be used to conduct the unsteady-state simulation on the meat side. The slaughter floor period is modeled first. At zero time, the product is initially at 42.48C with a moisture content of 75% wet basis. After modeling this initial period, the obtained temperature and moisture profiles are used as the initial conditions for the chilling stage. The boundary conditions at the carcass surface are defined as follows: for the water transport equation, a convective boundary condition is defined as Jw ¼ hm (Ys Ya )
(8:27)
where the moisture content of the air on the meat surface (Ys ) is assumed to be in equilibrium with the meat surface and is calculated from Equation 8.23. For the energy transport equation the boundary conditions 8.17–8.19 apply and the convective heat flux is calculated from qconv ¼ ht (Ts Ta )
(8:28)
The three-step method enables the first 20 h of chilling plus the slaughter period to be simulated for 5 days using a 2.5 GHz Pentium 4 computer. The method is accurate if the heat and mass transfer coefficients are constant during each of the stages (slaughter floor and chilling). This assumption is largely valid if the air velocity and turbulent intensity are constant and if buoyancy effects can be ignored.
8.3.2 VALIDATION Figure 8.7 shows the experimental and CFD-calculated heat loads for Davey’s Run 32 and compares it with the 1D finite difference (FD) [5] and the 2D finite element (FE) [6] models of Davey and Pham. It can be seen that the values predicted by all the three models are in good agreement with the experimental data. Figure 8.8 shows the calculated and experimental leg
1000 900
CFD FD FE Exp
800 Heat load (W)
700 600 500 400 300 200 100 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.7 Comparison of the heat load profiles calculated with the CFD, FE, and FD models with experimental data for run 32.
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50 CFD FE FD Exp
45 Temperature (⬚C)
40 35 30 25 20 15 10 5 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.8 Comparison of leg center (top) and leg surface (bottom) temperatures calculated with the CFD, FE, and FD models with experiment for run 32.
center, and surface temperature histories. The CFD center temperature prediction is quite accurate during the 20 h of chilling. A slight under-prediction during the peak may be due to the use of an average initial temperature at slaughter, which is a value that can change between particular runs. The leg surface temperature is also very well predicted, matching almost perfectly the experimental values. Figure 8.9 shows the shoulder center and surface temperature profiles for run 14. CFD predicts very well both the shoulder center and surface temperatures. Figure 8.10 shows the center and surface loin temperatures for run 18. The CFD and FE models underpredict both center and surface temperatures during the first 10 h of chilling. A similar trend was observed in all the runs. Since the same discrepancy appears at both the surface and the center, it seems that the error in the CFD prediction is due to overestimation of the effective surface
45 CFD FE FD Exp
40
Temperature (⬚C)
35 30 25 20 15 10 5 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.9 Comparison of the shoulder center (top) and shoulder surface (bottom) temperatures calculated with the CFD, FE, and FD models with experiment for run 14.
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35
CFD FE FD Exp
Temperature (⬚C)
30 25 20 15 10 5 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.10 Comparison of the loin center (top) and loin surface (bottom) temperatures calculated with the CFD, FE, and FD models with experiment for run 18.
heat transfer coefficient rather than an error in loin thickness or composition. A possible factor is that the insulating effect of surface fat, for both heat and mass transfer, has not been taken into account. The average root mean square percentage difference (%RMS) between the experimental and calculated data for the center and surface leg, loin and shoulder temperatures showed that in general, the 3D CFD model gives the best temperature predictions, closely followed by the 2D FE model [15]. The highest %RMS in all cases is obtained with the 1D FD model, showing its inaccuracy for predicting temperatures. This better performance was also confirmed by analyzing the relative value residuals (RVR) and the cumulative residual distribution of the three models (CFD, FE, and FD); both the FE and CFD models exhibit normal shape residual distributions [15]. The temperature predictions improved from the FD to the FE model because of the better geometrical representation: the FD model is a composite of 1D objects while the FE model is a composite of 2D objects. The slight improvement from the FE to the CFD can be attributed to improvements in geometrical representation (from 2D to 3D), in the local heat and mass transfer coefficient calculations by CFD, and in the more accurate modeling of mass transfer. CFD modeling can also predict local variations on the surface temperature, water activity, and heat and mass transfer coefficients. Figure 8.11 displays the temperature distribution over the carcass surface after 5 h of chilling, showing local temperature differences of up to 98C. Figure 8.12 displays the heat transfer coefficient distribution over the carcass leg, showing a peak in the regions where the air directly impacts the carcass surface. For instance, the heat transfer coefficient changes from 4.1 to 8:8 W m2 K1 around the leg in the reference plane in the graphic. Figure 8.13 shows the weight loss in run 18. All the models underpredict the weight loss of run 18 but overpredict it in runs 14 and 32 [15]. The overprediction may be caused by external fat that acts as a resistance to mass transfer. For run 18, the fat cover is just 6 mm while for runs 14 and 32 it is 14 and 12 mm, respectively. Figure 8.14 shows the calculated water activity profile (around the positions in Figure 8.11) for run 18. Local variations of up to 0.09 in aw can be seen, caused by local differences in heat and mass transfer coefficients. It is also seen that the water activity drops to a minimum value during the initial period with its high
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2.95e+03 2.94e+03 2.93e+03 2.92e+03 2.91e+03 2.90e+03
Leg a
2.89e+03 2.88e+03 2.87e+03 2.86e+03 2.85e+03 2.84e+03
Loin c
2.83e+03 2.82e+03 2.81e+03 2.80e+03 2.79e+03 2.78e+03
Sho b
2.77e+03 2.76e+03 2.75e+03
Temperature (K) External view
Internal view
FIGURE 8.11 Temperature profile around the carcass for run 32 after 5 h of chilling.
1.20e+01 1.15e+01 1.10e+01
Airflow
1.04e+01 9.90e+00 9.38e+00 8.85e+00 8.33e+00 7.81e+00
Reference plane
7.28e+00 6.76e+00
Higher h t
6.23e+00 5.71e+00 5.18e+00 4.66e+00 4.14e+00 3.61e+00 3.09e+00 2.56e+00 2.04e+00 1.51e+00
h t (W m–2 K–1)
FIGURE 8.12 Heat transfer coefficient around the carcass leg for run 18.
Lower h t
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1.8 1.6
Weight loss (kg)
1.4 1.2 1.0 0.8 0.6 Weight loss CFD Weight loss FD Weight loss FE Weight loss exp
0.4 0.2 0.0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.13 Weight loss calculated with the CFD, FE, and FD models for run 18.
cooling and evaporation loads, then increase again as the rate of evaporation drops off and the surface is rewetted by water diffusion from inside the meat carcass [13,27]. The water activity changes with position depending on the local heat and mass transfer coefficients. The water activity is higher in the loin than in the leg and shoulder, because the loin cools faster given its small thickness and hence the surface water vapor pressure reduces faster, slowing down the evaporation process. The leg on the other hand is the thickest part of the carcass. The meat at that location cools more slowly; therefore, the surface vapor pressure remains higher, enhancing the evaporation. Overall, the water activity remains in the range 0.89–0.98 during the chilling period. Lovatt and Hill [20] reported experimental water activity values mostly between 0.88 and 0.94, which agrees with the CFD predictions.
1.000
Water activity
0.980 0.960 0.940 0.920 Sho b Loin c Leg a
0.900 0.880 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.14 Surface water activity profiles around leg (Leg a), loin (Loin c), and shoulder (Sho b) for run 18. Positions are marked on Figure 8.11.
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8.4 A SIMPLIFIED COMBINED CFD-CONDUCTION MODEL FOR BEEF CHILLING A rigorous CFD model (Section 8.2) and even the three-step simplification (Section 8.3) are still too time consuming for routine use. We have therefore developed a simplified combined model in which CFD was used to estimate the local heat and mass transfer coefficients, assuming uniform surface temperatures, and applying these values to Davey and Pham’s composite 2D finite element model [6] to solve the heat transfer equation in the product, which has an elongated shape. The 2D model was enhanced by adding another set of 1D grids [13] to solve the water transport equation near the surface of the meat. The local surface transfer coefficients were calculated by CFD for various combinations of air orientations and speeds, and summarized in a set of regression equations. Fluent was used to calculate heat transfer coefficients as explained in Section 8.2.1. A series of calculations was carried out at all combinations of three different approach velocities (0.07, 0.7, and 1:7 m s1 ), eight different airflow directions (shown beside the carcass in Figure 8.15), and three different turbulence intensities (10%, 20%, and 60%), making a total of 72 runs. The air velocity and turbulence values were chosen to coincide with the 5%, 50%, and 95% percentiles of experimental data gathered across a number of industrial chillers. The heat and mass transfer coefficients vary from one cross section to another and within each cross section. Therefore, the perimeter of each cross section was divided into subsections, as shown in Figure 8.16, and the transfer coefficients were averaged over each subsection. A regression equation was found to calculate the htc and mtc in each section and subsection as a function of velocity and turbulence intensity. To allow the equations to be
Section 1 Section 2 Section 3 8 7
Section 4 Section 5 Section 6
1 2
6 5
3 4
Section 7 Section 8 Section 9 Section 10 Section 11
Section 12
FIGURE 8.15 Cross sections of a beef side and numbering of airflow directions. The air velocity is always in the front-to-back plane of the beef side.
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Section 3-2 Section 9-3 Section 3-1
b/4
b/4
b/4
Section 9-4
Section 9-2
b/4
Section 3-3 Section 9-1
Section 9-6 Section 9-5
Section 3-4
FIGURE 8.16 Details of two cross sections showing subdivisions of boundary. Sections i–j refer to the j-th division of the i-th cross section of Figure 8.15. Arrow or segments show boundaries between subdivisions.
used over a wide range of temperature and carcass sizes, they were expressed in terms of dimensionless numbers: Nu ¼ C Rem Pr1=3 TuA
(8:29)
Sh ¼ F Rer Sc1=3 TuN
(8:30)
The exponents of Pr and Sc are chosen according to Chilton and Colburn [28]. The length scale used for Re and Nu is the total length of the carcass, as it is a less ambiguous and more readily measurable quantity than, say, the mean diameter of the cross section, which may be physically more significant. Since only one carcass shape is being modeled, this will not affect the scientific validity of the approach. Using any other dimensions as basis will lead to the same results. C, m, A, F, r, and N are empirical constants that depend on airflow direction, section, and subsection. There were a total of 472 combinations of air directions, sections, and subsections, i.e., 472 pairs of equations such as the above. The simplified combined model takes only a few minutes, rather than hours or days, to simulate a chilling run. It was verified with data from Davey’s [24] chilling tests. Calculated and measured total heat loads are compared in Figure 8.17, total weight losses in Figure 8.18,
Calculated heat load (kJ)
15,000
10,000
5,000
0 0
5,000
10,000
15,000
Measured heat load (kJ)
FIGURE 8.17 Comparison of calculated and measured total heat loads for wind tunnel tests.
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Calculated weight loss (kg)
2
1.5
1
0.5
0 0
0.5
1
1.5
2
Measured weight loss (kg)
FIGURE 8.18 Comparison of calculated and measured total weight losses for wind tunnel tests.
deep meat temperatures after 10 h chilling in Figure 8.19, and surface temperature after 5 h in Figure 8.20. Reasonable agreement was obtained in most cases. The surface temperature at 5 h and deep meat temperature at 10 h were chosen because at those respective times these temperatures are changing quickly, and so any discrepancy would show up most clearly. The scatter is rather large for surface temperatures (discrepancy of 48C in one case), but these are always difficult to measure accurately and surface temperatures will vary from one location to another on the surface anyway. In most cases the errors are within 28C. The agreement is also good for heat loads and weight losses, except for one case; there is an outlier in the weight loss plot (Figure 8.18), the calculated loss being 30% lower than the measured loss. This point represents a run with a carcass that is unusually lean, with P8 fat thickness of
Calculated center temperature (⬚C)
40 35 30 25 20 15 10
Leg Loin y=x
5 0 0
5 10 15 20 25 30 35 Measured center temperature (⬚C)
40
FIGURE 8.19 Comparison of calculated and measured deep meat temperatures after 10 h for wind tunnel tests.
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Surface temperature after 5 h Calculated surface temperature (⬚C)
15
10
5 Leg Loin y=x 0 0
5 10 Measured surface temperature (⬚C)
15
FIGURE 8.20 Comparison of calculated and measured surface temperatures after 5 h for wind tunnel tests.
only 1 mm (all others have P8 thicknesses 7 mm or more). This fact was not taken into account as we assumed an average fat cover for all carcasses.
8.5 CONCLUSIONS The rigorous unsteady-state simulation of the simultaneous heat and mass transfer process during beef chilling is not straightforward. Many difficult practical problems are caused by the coupling of several transport equations, the existence of a solid phase and a fluid phase, the species and thermal balances and equilibria at the interface of these phases, the simultaneous heat and mass transfer that occur on vastly differing scales inside the meat, and the complexity of the geometry. Special techniques, using Fluent’s UDS and UDF, have to be applied to model the simultaneous heat and mass transfer across two phases. Fluent’s enhanced wall treatment combined with a very fine grid near the wall must be used in order to accurately model the fluid all the way to the wall and calculate the convection fluxes. Given the present state of computer hardware, a fully rigorous unsteady-state simulation could only be carried out for a 2D geometry. For the complex 3D carcass geometry, a threestep method has been used to reduce the computational time. In the first step, a steady-state flow field was simulated. In the second step, the local heat and mass transfer coefficients are calculated cell by cell around the beef surface with the information obtained on step 1. Finally, the third step consists of the simultaneous heat and mass transfer process simulation only on the meat carcass. The mass transfer was simulated using a secondary 1D mesh to reduce the computational cost, caused by mass and heat transfer occurring on different scales. Local variations on the heat and mass transfer coefficients were found around the beef carcass surface caused by the development of the momentum, heat and mass boundary layers. CFD predicted local temperature variations of up to 98C, and water activity variations of up to 0.09, around the beef surface. The model also shows that the water activity decreases to a minimum value during the first chilling hours followed by an increase (rewetting). The water activity changes with position depending on the local heat and mass transfer coefficients, which depend on the geometry, air velocity, and turbulent intensity.
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For industrial applications, where faster simulations are needed, we have developed a simplified combined model in which CFD is used to estimate the local heat and mass transfer coefficients, assuming uniform surface temperatures, and a finite element model using a set of 2D grids is used to solve the heat transfer equation in the product. Such simplifications will continue to be needed in industrial simulation at least for the next few years.
NOMENCLATURE aw aw,a,s aw,m,s cp,m ds D Deff Dm E Gb Gk H hm hm ht ht I ~ Jj Jw k Nu p Pr PT PV q qconv qevap qrad Re Sh Sc t T Ta Ta,s Tc Tm,s Ts Tu v
water activity superficial water activity of the air superficial water activity of the meat meat specific heat (J kg1 K1 ) distance from the superficial face node to the cell center node (m) water diffusivity in air (m2 s1 ) effective diffusivity of water in air (m2 s1 ) water diffusivity in meat (m2 s1 ) specific energy of fluid (J kg1 ) generation of turbulence kinetic energy due to buoyancy generation of turbulent kinetic energy due to mean velocity gradients enthalpy (J kg1 ) local mass transfer coefficient (kg dry air m2 s1 ) average mass transfer coefficient (kg dry air m2 s1 ) local heat transfer coefficient (W m2 K1 ) average heat transfer coefficient (W m2 K1 ) unit tensor diffusion flux of species j (kg m2 s1 ) water mass flux (kg m2 s1 ) turbulent kinetic energy (m2 s1 ) Nusselt number pressure (Pa) Prandtl number total pressure (Pa) vapor pressure of pure water (Pa) heat flux (W m2 ) convective heat flux (W m2 ) evaporative heat flux (W m2 ) radiative heat flux (W m2 ) Reynolds number Sherwood number Schmidt number time (s) temperature (K) bulk air temperature (K) temperature of the air phase on the meat surface (K) temperature at the center of the air volume element besides the meat surface (K) temperature of the meat at the surface (K) temperature at the meat surface (K) turbulence intensity velocity (m s1 )
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~ v T ~ v W Xm Y Ya Yc Ys YM
219
mean velocity vector (m s1 ) transposed mean velocity vector (m s1 ) water mass fraction in the meat (kg water kg total1 ) water content at the meat surface (kg water kg dry solid1 ) water mass fraction in the air (kg water kg dry air1 ) bulk water mass fraction in the air (kg water kg dry air1 ) water mass fraction of the air at the center of the volume element besides the meat surface (kg water kg dry air1 ) water mass fraction of air at the meat surface (kg water kg dry air1 ) contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
GREEK SYMBOLS a« ak DHvap « «r l leff lm m meff r rm s teff y^
inverse effective Prandtl numbers for « inverse effective Prandtl numbers for k latent heat of vaporization of water (J kg1 ) turbulent energy dissipation rate radiation emissivity air thermal conductivity (W m1 K1 ) effective thermal conductivity (W m1 K1 ) meat thermal conductivity (W m1 K1 ) air viscosity (kg m1 s1 ) effective viscosity of air (kg m1 s1 ) air density (kgm3 ) meat density (kg m3 ) Stefan–Boltzmann constant effective stress tensor (N m2 ) ¼ meff =m
SUBSCRIPTS a c conv evap s m rad
air phase cell node convective evaporation at the meat surface meat radiation
REFERENCES 1. P. Verboven, B.M. Nicolai, N. Scheerlinck, and J. De Baerdemaeker. The local surface heat transfer coefficient in thermal food process calculations: A CFD approach. Journal of Food Engineering 33: 15–35, 1997. 2. S.J. Lovatt, Q.T. Pham, A.C. Cleland, and M.P.F. Loeffen. A new method of predicting the timevariability of product heat load during food cooling—Part 1. Theoretical considerations. Journal of Food Engineering 18: 13–36, 1993. 3. A. Kuitche, J.D. Daudin, and G. Letang. Modeling of temperature and weight loss kinetics during meat chilling for time-variable conditions using an analytical-based method—I. The model and its sensitivity to certain parameters. Journal of Food Engineering 28: 55–84, 1996.
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4. S. Chuntranuluck, C.M. Wells, and A.C. Cleland. Prediction of chilling times of foods in situations where evaporative cooling is significant—Part 1. Method development. Journal of Food Engineering 37: 111–125, 1998. 5. L.M. Davey and Q.T. Pham. Predicting the dynamic product heat load and weight loss during beef chilling using a multi-region finite difference approach. International Journal of Refrigeration 20: 470–482, 1997. 6. L.M. Davey and Q.T. Pham. A multi-layered two-dimensional finite element model to calculate dynamic product heat load and weight loss during beef chilling. International Journal of Refrigeration 23: 444–456, 2000. 7. P. Mallikarjunan and G.S. Mittal. Heat and mass transfer during beef carcass chilling—Modeling and simulation. Journal of Food Engineering 23: 277–292, 1994. 8. A. Kondjoyan and J.D. Daudin. Determination of transfer coefficients by psychrometry. International Journal of Heat and Mass Transfer 36: 1807–1818, 1993. 9. A. Kondjoyan and J.D. Daudin. Heat and mass transfer coefficients at the surface of a pork hindquarter. Journal of Food Engineering 32: 225–240, 1997. 10. A.V. Nguyen and Q.T. Pham. A computational fluid dynamic model of beef chilling, in 20th International Congress of Refrigeration, IIR=IIF. Sydney, 1999. 11. Z. Hu and D.-W. Sun. CFD simulation of heat and moisture transfer for predicting cooling rate and weight loss of cooked ham during air-blast chilling process. Journal of Food Engineering 46: 189–197, 2000. 12. Z. Hu and D.-W. Sun. Predicting local surface heat transfer coefficients by different turbulent k–« models to simulate heat and moisture transfer during air-blast chilling. International Journal of Refrigeration 24: 702–717, 2001. 13. Q.T. Pham and N.W. Karuri. A computationally efficient technique for calculating simultaneous heat and mass transfer during food chilling, in 20th International Congress of Refrigeration, IIR=IIF, Sydney, 1999. 14. F.J. Trujillo and Q.T. Pham, CFD modeling of heat and moisture transfer on a two-dimensional model of a beef leg, in 21st International Congress of Refrigeration, Washington, DC, 2003. 15. F.J. Trujillo and Q.T. Pham. A computational fluid dynamic model of the heat and mass transfer during beef chilling. International Journal of Refrigeration 29: 998–1009, 2006. 16. F.J. Trujillo, C. Wiangkaew, and Q.T. Pham. Drying modeling and water diffusivity in beef meat. Journal of Food Engineering 78: 74–85, 2007. 17. V. Yakhot and S.A. Orszag. Renormalization group analysis of turbulence. I. Basic Theory. Journal of Science Computing 1: 3–51, 1986. 18. Fluent Inc., Modeling turbulence, in FLUENT 6.2 user’s guide, Vol. 2. F. Inc., Editor. 2005, Fluent Inc., Lebanon, NH. 19. F.J. Trujillo, P.C. Yeow, and Q.T. Pham. Moisture sorption isotherm of fresh lean beef and external beef fat. Journal of Food Engineering 60: 357–366, 2003. 20. S.J. Lovatt and H.K. Hill. Surface water activity during meat cooling, in IIR Proceedings Series Refrigeration Science and Technology, Sofia, Bulgaria, 1998. 21. M. Wolfshtein. The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient. International Journal of Heat and Mass Transfer 12: 301–318, 1969. 22. B.A. Kader. Temperature and concentration profiles in fully turbulent boundary layers. International Journal of Heat and Mass Transfer 24: 1541–1544, 1981. 23. B.E. Launder and D.B. Spalding. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289, 1974. 24. L.M. Davey, Measurement and prediction of product heat load and weight loss during beef chilling, PhD thesis, 1998, School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney, p. 299. 25. A.V. Nguyen and Q.T. Pham. Mean convective heat transfer coefficient of beef carcases computed by a computational fluid dynamic model, in FOODSIM 2000: International Conference on Simulation in Food and BioIndustries, Nantes, France, 2000.
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26. F.J. Trujillo, A computational fluid dynamic model of heat and moisture transfer during beef chilling. PhD thesis, 2004, School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney, p. 352. 27. L.S. Herbert, D.A. Lovett, and R.D. Radford. Evaporative weight loss during meat chilling. Food Technology in Australia 30: 145–148, 1978. 28. T.H. Chilton and A.P. Colburn. Mass transfer (absorption) coefficients. Industrial and Engineering Chemistry 26: 1183–1186, 1934.
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CFD Prediction of the Air Velocity Field in Modern Meat Dryers Pierre-Sylvain Mirade
CONTENTS 9.1 9.2 9.3
Introduction ............................................................................................................... 223 Operation of Modern Meat Dryers ........................................................................... 224 Air Velocity Fields in Modern Meat Dryers.............................................................. 227 9.3.1 Experimental Investigation ............................................................................. 227 9.3.2 Steady-State Numerical Investigation............................................................. 227 9.3.3 Unsteady Numerical Investigation ................................................................. 232 9.3.3.1 Features of Unsteady Modeling ....................................................... 233 9.3.3.2 Influence of the Amplitude of the Ventilation Cycle........................ 234 9.3.3.3 Influence of the Form of the Ventilation Cycle................................ 237 9.3.3.4 Consequences of Dissymmetry in the Ventilation Cycle .................. 238 9.4 Modern Meat Dryers of Large Height ...................................................................... 240 9.4.1 Problematic..................................................................................................... 240 9.4.2 Mean Age of Air ............................................................................................ 241 9.5 Conclusion ................................................................................................................. 245 References .......................................................................................................................... 246
9.1 INTRODUCTION No other technology creates such an aromatic and desired flavor of meat products as fermentation and drying [1]. Dry sausages are one of the most important fermented meat products. In Europe, total production of nonsmoked molded dried sausages is about 350,000 tonnes a year, a significant proportion of which comes from southern European countries including Italy, Spain, and France (90,000 tonnes a year). In northern European countries such as Germany, Denmark, Sweden, and Norway, almost all dry sausages produced are smoked during processing. In Hungary, the traditional salami is even smoked in a first drying step, before being molded in a second ripening step [1]. In the successive operations involved in the manufacture of dry sausage, namely grinding of lean meat and fat, mixing with additives, stuffing in casings, and drying, the drying process is crucial. Indeed, to obtain a well-balanced drying of all sausages, airflow patterns and indoor climate (temperature and relative humidity) should be homogeneous throughout the drying room. In practice, water loss differences between sausages are observed in the dryer, which result from local heterogeneities in the air velocity distribution. This problem is
223
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partially addressed through the rearrangement of the trolleys of sausages in the room during the drying process. Nevertheless, many authors have reported that poor control of drying conditions is the main raison for low quality [2,3]. During drying, the water content of the sausages should decrease homogeneously. When the rate of water evaporation from the surface of the sausage is higher than the rate of water migration from inside the sausage, a dry crust (also called ‘‘dry rim’’) is formed, which adversely affects sausage texture and flavor. Conversely, when the evaporation rate is lower, the surface remains too moist, which favors the growth of undesirable molds that can impair product texture, flavor, and safety. Hence, the drying process consists in continuously fitting the drying rate to a product undergoing perpetual biochemical and biological evolution, and maintaining water activity at the product surface at an ideal value in order to develop the desirable flora. In other words, ripening has an influence over the main physical, chemical, and microbiological transformations that take place inside the products and which define the final organoleptic properties of dried products. As water exchanges at the product surface are directly related to the characteristics of the surrounding air (temperature, velocity, and relative humidity), it is of paramount importance to identify global airflow patterns inside the dryer. In Europe, dry sausage and especially ham were originally manufactured in mountainous highlands, since the outside air could be used inside the meat dryers almost all year round without conditioning, due to the fresh temperature and high relative humidity. More recently, static dryers equipped with cooling batteries level with the ceiling and heating batteries level with the floor have appeared in geographic areas with a less favorable natural climate. They operate by mixing descending fresh air volumes with ascending hot air volumes, thus generating natural ventilation with very low air velocity. Hygrometric control was achieved by condensation of water on the cooling batteries. This type of meat dryer was used to manufacture hams and low-diameter dry sausages [3]. To reduce ripening time, fans were introduced into the meat dryers to force air to circulate around the products at a velocity of 0:1 m s1 . At the very beginning, blowing ducts were placed level with the floor while suction ducts were placed level with the ceiling. Although the direction of air movement could be inverted in this type of dryer, heterogeneity in air distribution remained in the full volume filled with the products, causing strong heterogeneity in drying between the upper and lower part, thus compelling professionals to regularly move their products. To even out the drying conditions, and thereby product processing, throughout the entire volume of the plant, modern meat dryers were created where air distribution was time-dependent. This chapter reports on scientific studies aimed at analyzing the significance and effects of the specific operation of modern meat dryers through numerical modeling, with particular emphasis on dryers of large height, which are currently increasingly used in industry.
9.2 OPERATION OF MODERN MEAT DRYERS Figure 9.1 shows the layout of a typical modern meat dryer with a schematic description of the airflow pattern. The geometry of this type of meat dryer is simple; the airflow is generally supplied through two stainless steel ducts of rectangular cross section fitted with plastic conical jets placed on each side of the plant, and is extracted level with the ceiling by means of two or three stainless steel ducts fitted with adjustable plastic extraction apertures. These modern meat dryers are characterized by a main upward airflow generated by two downstream airflows generated by conical jets, which merge over the plant floor. As indicated earlier, when attempting to create homogenous drying conditions throughout the entire volume of a plant, it is important to take into account the fact that the operation of a modern meat dryer is time-dependent, and this is due to two reasons.
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Extraction ducts fitted with extraction apertures
Height: from 2 to 6m
Blower ducts fitted with conical jets
Area of filling with meat products About 0.5 m
Width: from 2 to 7 m (Length: from 2 to 20 m)
FIGURE 9.1 Layout of a typical modern meat dryer according to a vertical section with a schematic description of the airflow patterns (black arrows).
Firstly, as regards air distribution, the airflow supplied by two lateral blower ducts ranges from a high to a low rate in the first duct in a few tens of seconds while it reciprocally ranges from a low to a high rate in the second duct, thus giving rise to a periodic ventilation cycle (Figure 9.2). However, the overall blower airflow rate remains steady at any given time, at 100%. Figure 9.2 highlights that the ventilation cycle has a sinusoidal form, since the distribution of airflow rate in the two blower ducts is generally set by adjusting a regulation valve placed on the duct supplying air to the two blower ducts. The two inlet airflows are then directed downstream, descending along the lateral room walls before merging over the floor in a location that depends on the value of the ventilation cycle. The more unbalanced the ventilation cycle, the more distant the location of the merging area from the middle of the dryer. Once merged, the airflow then moves upward toward the extraction ducts, at the same time bathing the meat products filling the plant and exchanging heat and moisture with them. This ventilation cycle means that the merging location of the upward airflow moves cyclically over the drying floor. All meat products are consequently bathed by the same airflow during full periods of the ventilation cycle, and a priori are thus dried in a homogeneous way.
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Percentage of overall blower airflow rate (%)
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Left-hand blower duct
Right-hand blower duct
High
50
Low One period of the ventilation cycle 0
15
30
45
60
75
Time (s)
FIGURE 9.2 Description of the airflow rate evolution between each of the two blower ducts during one period of the ventilation cycle in a modern meat dryer (the sinusoidal form is truly representative of what occurs in industrial plants).
Furthermore, during ventilation, air velocity ranges from 5 to 20 m s1 at the output of the conical jets of the blower ducts, and is on average 0:4 m s1 around the products. Secondly, the specific ventilation pattern previously described and which is intended to supply air to the dryer alternates rapidly with a rest sequence in which there is no ventilation, depending on the level of relative humidity in the volume filled with the products; this relative humidity increases due to water evaporating from the surface of the sausages. Ventilation is reactivated once a high level of relative humidity is reached in order to reduce relative humidity until a low level is reached. Periods of ventilation generally correspond to around one-third of the total ripening time (Figure 9.3). 90 Air relative humidity of the dryer (%)
Periods with ventilation 85 80 75 70 65 60 Rest periods (no ventilation) 55 3500
4500
5500
6500
Time (s)
FIGURE 9.3 Evolution in air relative humidity during the operation of a modern meat dryer according to the ventilation and rest periods.
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A modern meat dryer therefore works by a series of ventilation cycles and rest sequences (Figure 9.3) managed by an operator who generally uses empirical rules to adjust the drying conditions. In practice, these rules are known to be affected by the design (dimensions, location of the blower and extraction ducts, etc.), and filling level of the dryer, as well as by the amplitude of the ventilation cycle. In other words, both the design of modern meat dryers and the optimal process conditions are based more on the practical experience accumulated by plant designers and dried meat manufacturers over the years than on the results of academic research.
9.3 AIR VELOCITY FIELDS IN MODERN MEAT DRYERS The majority of research on the processing of dried sausages or hams reported in the literature deals with fermentation, transfers from inside the product, or drying kinetics as a function of air properties [1,4–11]. For example, Daudin et al. [8] highlighted steep gradients in water content in the first 10 mm close to the surface of drying sausages; they also indicated that accurate control of the air characteristics around the sausages was essential in order to control water activity at the sausage surface [8].
9.3.1 EXPERIMENTAL INVESTIGATION There are few experimental and numerical studies available on the overall operation of modern meat dryers [12–16]. Experimental analyses carried out in modern meat dryers are understandably rare since the measurements are particularly laborious and time-intensive due to the natural unsteadiness of the airflows and especially the ventilation cycle, which continuously modifies the air velocities at the output of the conical jets. The only method that can be used to measure air velocities in this kind of plant is the standard average procedure that consists in averaging velocity measurements over a sufficiently long length of time (over one or several ventilation cycles at each measurement point) to obtain a constant value for mean velocity [12,14]. In a 134 m3 small-scale sausage dryer filled with 108 objects made of polystyrene (1:70 0:25 0:15 m) arranged in six rows in order to reproduce industrial filling levels, Mirade and Daudin [14] measured air velocity distribution in five configurations corresponding to two different steady distributions of the ventilation cycle, namely 50%=50% and 20%=80% per blower duct. The first airflow distribution gave a large area with air velocities reaching 2 m s1 in the middle of the dryer, but a wider airflow than expected as a result of slow and slight time variations in the blower airflow rate from each duct. Moreover, the authors noted that changing the distribution of the airflow rate from 50%=50% to 20%=80% completely disrupted airflow patterns, with the appearance of a poorly ventilated area at the center of the dryer and air velocities of about 1:5 m s1 close to the blower ducts. In the 20%=80% configuration, the authors concluded that the large airflow blown in from the right-hand side duct to the floor moved along the floor and up the opposite wall, drawing in the airflow from the left-hand side duct.
9.3.2 STEADY-STATE NUMERICAL INVESTIGATION Numerical studies of airflows in modern meat dryers have often been performed using CFD techniques. With the development of cheaper, more powerful computers and commercial packages, over the years CFD has been increasingly applied to assess airflow patterns in modern meat dryers [13–16], ever since the pioneering studies performed by EDF, the French producer of electricity, and cited by Dabin and Jussiaux [3] that aimed to optimize air circulation inside the drying room in order to obtain more regular product drying.
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From two calculations using steady-state boundary conditions and corresponding to two different distributions of airflow rate between the two blower ducts of the room (50%=50% and 30%=70%), these original studies indicated a complex air circulation pattern including two swirls that shifted laterally as a function of the air distribution between the two blower ducts. Consequently, the velocities of air in contact with dried sausages ranged from 0.4 to 0:6 m s1 , and were threefold to fivefold higher than the theoretical velocity determined from the total airflow rate blown in the room divided by its surface [3]. A similar approach, namely three steady-state and two-dimensional CFD simulations corresponding to airflow rate distributions between the two blower ducts of 50%=50%, 59%=41%, and 67%=33%, respectively, identified a strong heterogeneity in airflow pattern in a salami dryer, with air velocities ranging from 0.2 to 0:8 m s1 in the volume filled with the products [13]. The heterogeneity in air velocity magnitudes in the volume filled with the products was confirmed by 3D numerical results obtained by Mirade and Daudin [14] using the commercially available CFD code Star-CD [17], in the case of a 134 m3 small-scale sausage dryer for two steady-state ventilation cycle configurations between the two blower ducts (50%=50% and 20%=80%). Calculations were made on a Sun Sparc 10=41 workstation with 128 Mb of RAM. Airflow was considered as steady, incompressible, and isothermal. Main flow turbulence was taken into account using the tried and tested k« model [18] when far from the walls—which were assumed to be smooth—and where the standard wall function was applied [19]. Even though the k« model is known to perform poorly in a variety of important cases, such as some unconfined flows or flows with large extra strains, it is currently widely used for turbulence modeling since it is robust, time-efficient, and fairly accurate. The SIMPLE algorithm [20] was chosen for coupling pressure and velocity and to introduce pressure into the continuity equation. A first-order upwind differencing scheme was incorporated into the computational model as discretization scheme for the convection terms of each governing equation. First-order schemes are known to increase numerical diffusion due to discretization errors, especially when the flow is not aligned with the grid [19]. Although they therefore yield less accurate results, first-order schemes give better convergence of calculation than secondorder schemes. Complete convergence of the discretized differential equations ranged from 5 to 8 days, reaching 8 days when using 300,000 vertices for meshing the 134 m3 small-scale sausage dryer [14]. Figure 9.4a and Figure 9.4b show the distribution of the simulated air velocity patterns according to a vertical section located approximately in the middle of the dryer for inflow distributions of 50%=50% and 20%=80%, respectively [14]. When the distribution of the airflow rate was balanced between the two blower ducts (50%=50%), calculations revealed that the higher air velocities were located level with the floor and in the middle of the dryer. On either side of this central area, poorly ventilated areas with air velocities lower than 0:6 m s1 were highlighted (Figure 9.4a). Conversely, unbalancing the distribution of the airflow rate from 50%=50% to 20%=80% completely disrupted the airflow patterns, as illustrated in Figure 9.4b, where the lower air velocities were concentrated in the middle of the dryer whereas the higher air velocities were found close to the two blower ducts. Using 2D CFD modeling, Mirade and Daudin [14] also highlighted a very unsteady airflow pattern when the airflow rate was closer to 50%=50%. An imbalance of only 4% between the left- (54%) and the right-hand side (46%) blower ducts greatly modified the location of the wellventilated central area, which shifted over 60 cm toward the right, as indicated in Figure 9.4c, thus confirming the findings of the original study carried out by EDF [3]. Furthermore, and again using the Star-CD code, Mirade and Daudin [21] studied the effect of changes in airflow structure in relation to amplitude from 50%=50% to 10%=90% and dissymmetry of +5% in the ventilation cycle; it was assumed that the ventilation cycle was
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linear and that this non-steady-state problem (due to the ventilation cycle) could be numerically approached as a series of steady-state problems. By integrating the air velocities simulated between a low level and a high level during one period of the ventilation cycle, they identified 60%=40% as the amplitude giving the most homogeneous airflow inside the
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FIGURE 9.4 Distribution of the air velocities calculated from 3D CFD modeling on a vertical section located at half-length of a 134 m3 small-scale sausage dryer corresponding to three steady-state configurations of the ventilation cycle: (a) 50%=50%, (b) 20%=80%, and (continued)
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FIGURE 9.4 (continued) (c) 54%=46%.
area filled with the sausages despite the fact that there was a gradient in air velocity distribution in relation to the height within the plant (Figure 9.5a). They also highlighted the need for controlled regulation of the ventilation cycle in modern meat dryers since a slight variation of +5% in the airflow rate at a distribution of around 60%=40% markedly disrupted the airflow pattern, which became strongly dissymmetric (Figure 9.5b). On account of the simplicity of the system regulating and distributing airflow between the two blower ducts and due to the marked unsteadiness of the airflow around the 50%=50% blower conditions, dysfunction in the ventilation cycle frequently occurs in industrial settings, leading to slight variations around the low and high levels with no change in the overall blower airflow rate. Hence, in practice, there is greater heterogeneity in sausage product treatment between different locations in the plant. Figure 9.5b indicates the appearance of a poorly ventilated area with velocities lower than 0:4 m s1 on the left-hand side of the sausage dryer, i.e., where the air velocities at the output of the conical jets were the highest. The slight variation in airflow rate distribution between the two blower ducts globally increased the air velocity gradients. All these simulations were performed using the same modeling procedure as previously [14], i.e., the k–« model [18] for modeling turbulence, the SIMPLE algorithm [20] for coupling pressure and velocity, and a first-order upwind differencing scheme [19] as discretization scheme for the convection terms in the governing equations. Without using CFD, Rizzi [22] developed a parametric model to rapidly predict airflow velocity patterns in ascending flow ripening chambers, with the idea of improving the operation and design of these industrial plants by means of dynamic ripening simulation software coupling a fluid dynamics model to a numerical model of the sausage drying process. The fluid dynamics model was built to give the air velocity module as output and to give direction as a function of the geometrical characteristics of the drying chamber (dimensions, location of the blower and extracting ducts, number and location of the products loaded) and of the inlet airflow conditions (overall mass flow rate and inflow sharing ratio between the two blower ducts).
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FIGURE 9.5 Distribution of the air velocity means calculated from 2D CFD modeling on a vertical section of a 134 m3 small-scale sausage dryer for a ventilation cycle of linear form at amplitude 60%=40%: (a) without dissymmetry and (b) with a dissymmetry of +5% between the left- and righthand side blower ducts (the ventilation cycle was discretized in a series of steady-state configurations so as to be taken into account in the CFD modeling).
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Several assumptions (incompressible fluid, steady and uniform motion) have been made in order to construct an accurate, flexible, and computationally ‘‘light’’ fluid dynamics model. Moreover, the main idea upon which this model is based consisted in defining an imaginary 2D pipe network inside the drying room, thus assuming all parameters to be constant along the room depth. Once both geometrical and fluid dynamics parameters have been set, the pipe network was then solved using an iterative technique specially developed to solve hydraulic problems, i.e., the Hardy–Cross method [23,24]. This specific method makes it possible to determine the airflow rates in each network duct as defined by the room walls and product surfaces from the mass flow rate at the boundary conditions. However, as the Hardy–Cross method neglected fluid momentum and considered that pressure gradients were the basic driving forces within the network, a customization of pressure drop coefficients was set up in order to avoid the solving of additional partial differential momentum equations, which would have compromised both the computational simplicity and the rapidity of the model. Indeed, as it was well known that in some areas of a modern ripening chamber—above all the inlet and downward areas and level with the room floor and the extraction region—fluid momentum took precedence over pressure gradients, this phenomenon had to be taken into account when modeling the evolution of the airflows. The customization of pressure drop coefficients amounted to introducing factors to artificially increase or decrease certain head drop coefficients to force the airflows to follow preferential paths inside the pipe network. The first step in using the fluid dynamics model consists in defining the degree of precision required and assessing both the main geometrical and fluid dynamic characteristics of each duct in the pipe network as a function of the room’s geometrical characteristics and of the type, number, and relative location of the products. Pressure drop coefficients are then calculated from the classical rules of hydraulics and calibrated by means of corrective factors determined from relations established on the basis of general information obtained from experimental data processing. For each mesh of the pipe network, the model checks whether the energy balance equation is satisfied with a degree of precision lower than that actually required, and if necessary adds a corrective mass flow rate. The process is iterated throughout the entire pipe network until the energy balance equation is satisfied for every mesh with the required degree of precision. When considering a network configuration corresponding to a single rack filled with 18 salamis (three rows per six columns) with degree of precision set to 50 Pa, Rizzi [22] indicated that the resulting network made of 90 nodes and 72 cells was solved in about 600 iterations, with an average computation time of about 5 s when using a Pentium II 400 MHz processor. The fluid dynamics model satisfactorily predicted air velocity distribution as a function of overall mass flow rate entering the drying room and, above all, as a function of steady-state sharing of the airflow rate between the plant’s two blower ducts [22]. Together, these numerical studies [13,14,21,22] have provided useful information on air circulation during the ventilation cycle, but have not accurately analyzed the dynamic operation of the meat dryers since only steady-state numerical models were built.
9.3.3 UNSTEADY NUMERICAL INVESTIGATION The ability of CFD to dynamically predict airflow patterns inside a modern sausage dryer by means of 2D numerical models using time-dependent boundary conditions (i.e., an unsteady model) to accurately reproduce real operating conditions was recently assessed [15,16]. Mirade [15,16] studied the effect on ventilation homogeneity of modifying amplitude (four levels tested: 80%=20%, 70%=30%, 65%=35%, and 60%=40%) and form (linear [15] or sinusoidal [16]) during one period of the ventilation cycle. In the case of a sinusoidal form,
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Mirade [16] also numerically evaluated the change in airflow structure due to dissymmetry of 2%, 5%, or 10% of the ventilation cycle due to a dysfunction of the plant, which could occur in industry due to the simplicity of the system regulating airflow rate distribution between the two blower ducts and the marked unsteadiness of the airflow around a 50%=50% distribution. The layout of the small industrial sausage dryer used in the studies of Mirade [15,16] for building the dynamic CFD model was absolutely identical to that of Figure 9.1, with a height of 2.96 m and a width of 2.45 m. In this plant, the air was blown in through two stainless steel ducts placed on each side that were fitted with eight plastic conical jets 0.195 m long and 0.063 m in diameter. The air was extracted at the top through two other stainless steel ducts set 0.50 m apart and fitted with ten plastic extraction apertures of 0.08 m in diameter. The height of the free space from the ends of the conical jets to the floor was 2.32 m and the air velocity at the output of the jets was 5 m s1 when the ventilation corresponded to a 50%=50% configuration. The filling of the dryer in the numerical models was represented using 24 sausages of rectangular cross section (0:50 0:05 m), with eight sausages set 0.15 m apart at each of the three heights. The distance between two consecutive heights was 0.3 m, and the distance between the first rack of sausages and the floor was 0.35 m. 9.3.3.1 Features of Unsteady Modeling Starting with the geometrical configuration presented in Figure 9.1, the CFD code Fluent v.5.1.1 and 5.4.8 [25] was used to build a numerical model based on an unstructured 2D mesh of 25,500 tetrahedral cells. From the previous mesh, several variants of the 2D numerical model were constructed that corresponded to different forms and amplitudes of the ventilation cycle [15,16]. Given that 2D modeling was used, the results had to be viewed with caution, not due to the 2D representation of a presumably 3D airflow blown by the conical jets, but rather due to the representation of the objects filling the device. Indeed, in 2D calculations, objects can act as a barrier, since the airflow cannot skirt around them as it does in reality, which almost certainly contributes to an increase in the heterogeneity of the airflow patterns. On the other hand, despite being performed in 2D, an unsteady CFD model has to be particularly useful for assessing the dynamic operation of modern meat dryers. To account for time-dependent boundary conditions due to the ventilation cycle, specific user-defined functions (UDF) were written in Cþþ programming language and applied to the inlet areas of the CFD models. In all calculations [15,16], airflow was considered as incompressible, isothermal and—unlike the previous studies [13,14,21,22]—unsteady. From preliminary tests, the time step increment was evaluated at 0.02 s so that the convergence of the calculations obtained for residuals lower than 103 needed no more than 25–30 iterations at each time step [15]. A total 3000 time steps was therefore required to fully simulate just one period of the ventilation cycle that lasted 60 s. More complex and costly—in terms of computation time—modeling procedures were used than in the previous studies [13,14,21,22]. Indeed, main flow turbulence was taken into account by means of the Reynolds-stress model [26], which needed the resolution of six equations instead of two for the k« model [18]—far from walls and objects, where a ‘‘nonequilibrium’’ wall function was applied. Moreover, a second upwind-differencing scheme [19] and the PISO algorithm [27], instead of the SIMPLE algorithm, were also necessary in order to obtain accurate results. Calculations were performed either on a 266 MHz Pentium II PC with 384 Mb of RAM or on a 2.2 GHz Pentium IV PC with 1.5 Gb of RAM. Calculation time ranged from 55.2 to 59.6 h on the Pentium II PC and from 8.3 to 9 h on the Pentium IV PC, depending on the variant of the numerical model being solved.
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Given that unsteady modeling was used, an initialization of the calculations, i.e., the air velocity patterns at time zero, was required; this was obtained from a preliminary calculation where the inlet boundary conditions were steady and equal to 50% of the overall airflow rate in each of the two blower ducts. However, as this preliminary calculation needed unsteady modeling to reach convergence owing to the strong unsteadiness of the airflow in a 50%=50% configuration, it generated many air velocity patterns, thus forcing the author to check that the mean airflow structure determined over the full period of the ventilation cycle was not sensitive to initial conditions [16]. To do this, Mirade [16] performed three different simulations corresponding to different initial conditions and noted that the three mean airflow patterns obtained on the full period were the same. 9.3.3.2
Influence of the Amplitude of the Ventilation Cycle
Regardless of the form of the ventilation cycle, i.e., whether linear or sinusoidal, the influence of the ventilation cycle on airflow patterns can be summed up as follows [15,16]: (i) air velocity distribution truly varies with the amplitude of the ventilation cycle; consequently, modern meat dryer has an optimum amplitude depending on its geometry (dimensions and location of the blower and extraction ducts) and filling level; (ii) above this optimal amplitude, there appears a marked heterogeneity in the ventilation, mainly according to the height between the lower part that is poorly ventilated and the upper part of the plant; and (iii) below the optimal amplitude, the heterogeneity also exists, but more according to the width of the plant, with high velocities concentrated toward the center. Figure 9.6a through Figure 9.6d give the distribution of the air velocity means calculated on a vertical section of the dryer for a ventilation cycle of linear form, thus illustrating the 2750 2450 2150
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FIGURE 9.6 Distribution of the air velocity means calculated from 2D unsteady CFD modeling on a vertical section of a small sausage dryer over one period of ventilation cycle of linear form, at amplitudes of: (a) 80%=20%,
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FIGURE 9.6 (continued) (b) 70%=30%, (c) 65%=35%, and (continued)
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FIGURE 9.6 (continued) (d) 60%=40% (given the unsteady modeling, the ventilation cycle was directly incorporated into the CFD model by means of a user-defined function. The black rectangle in the figures outlines the area usually filled with sausages.).
influence of the amplitude of the ventilation cycle on airflow patterns [16]. Before analyzing Figure 9.6a through Figure 9.6d, it should be noted that the symmetrical air velocity distribution in relation to the median plane of the plant proves that the unsteady CFD models correctly took into account the dynamic operation of the dryer induced by the ventilation cycle. Comparison of Figure 9.6a through Figure 9.6d shows large differences in the distribution of air velocity means according to the linear ventilation cycle studied, with the best homogeneity corresponding to an amplitude of 65%=35% (Figure 9.6c), even though air velocity means ranged from 0.6 to slightly higher than 1:2 m s1 in the area filled with objects and despite the fact that a significant stratification of air velocities with height appeared in the plant, with air velocities higher than 1:2 m s1 for widths ranging from 975 to 1475 mm and for heights ranging from 1050 to 2250 mm [16]. These findings are consistent with numerous industrial observations indicating that, in this type of dryer, the driest meat products are very often located in the upper part. Over and above this amplitude considered as an effective value to even out the air velocity distribution in the dryer, numerical results accounted for a marked heterogeneous distribution of air velocities with means ranging from 0.3 to more than 1:2 m s1 , as well as poorly ventilated areas in the lower part of the plant and at half-height at the left and right of the area filled with the objects, together with a highly ventilated upper part of the dryer, with air velocity means peaking at 1:5 m s1 locally. Below the amplitude of 65%=35%, air velocity means higher than 0:9 m s1 appeared in the lower part of the dryer (Figure 9.6d) compared with the three other cases (Figure 9.6a through Figure 9.6c), thus giving rise to heterogeneity in ventilation according to the width of the dryer, with an area in the middle that was more ventilated than on either side.
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9.3.3.3 Influence of the Form of the Ventilation Cycle Unlike the cycle of linear form, with a sinusoidal form of the ventilation cycle that is certainly closer to industrial reality, a large poorly ventilated area with means lower than 0:6 m s1 appears in the lower part of the plant (Figure 9.7a) at an amplitude of 65%=35%, i.e., the value identified as the best amplitude for evening out the drying conditions in the case of a linear ventilation cycle. The airflow structure given by Figure 9.7a resembles that of a linear ventilation cycle of 70%=30% (Figure 9.6b). In view of the marked heterogeneity in the distribution of the airflow, an amplitude of 65%=35% was not optimal for a sinusoidal ventilation cycle [16], meaning that, in addition to amplitude, the form of the ventilation cycle also has an influence on airflow patterns inside modern meat dryers. Scaling down the amplitude of the ventilation cycle from 65%=35% to 60%=40% (Figure 9.7b) made the airflow patterns more homogeneous, as the poorly ventilated area in the lower part of the plant disappeared, leading to an airflow structure identical to the best one obtained for a linear ventilation cycle (Figure 9.6c). The best results in terms of ventilation homogeneity were obtained for an amplitude of 65%=35% with a ventilation cycle of linear form, and for an amplitude of 60%=40% with ventilation cycle of sinusoidal form. This difference due to the form of the ventilation cycle can be explained from the findings of a previous 2D CFD study [14]. Indeed, in an empty sausage dryer of similar geometry, Mirade and Daudin [14] demonstrated that for steadystate conditions of ventilation, (i) slight variations of +4% around 50%=50% in the low and high levels of the ventilation cycle provided adequate ventilation of the whole width of the dryer where the products are usually placed, and (ii) a strong imbalance between the airflow 2750 2450 2150
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FIGURE 9.7 Distribution of the air velocity means calculated from 2D unsteady CFD modeling on a vertical section of a small sausage dryer over one period of ventilation cycle of sinusoidal form, at amplitudes of: (a) 65%=35% and (continued)
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FIGURE 9.7 (continued) (b) 60%=40% (given the unsteady modeling, the ventilation cycle was directly incorporated into the CFD model by means of a user-defined function. The black rectangle in the figures outlines the area usually filled with sausages.).
rates of the two blower ducts caused poor ventilation around the sausages. As the sinusoidal form leads rapidly to stronger imbalances than the linear form, the same ventilation homogeneity thus logically occurred with a ventilation cycle of lower amplitude [16]. 9.3.3.4
Consequences of Dissymmetry in the Ventilation Cycle
As mentioned earlier, dysfunction in the ventilation cycle frequently occurs in industry as a result of the simplicity of the system distributing the airflow between the two blower ducts and due to the marked unsteadiness of the airflow around the 50%=50% blower conditions. Figure 9.8a through Figure 9.8c show the unsteady numerical model results achieved for a sinusoidal ventilation cycle of amplitude 60%=40% when a dissymmetry of 2% (Figure 9.8a), 5% (Figure 9.8b), or 10% (Figure 9.8c) is taken into account. The air velocity means were calculated over five full ventilation cycles, i.e., for a length of time (5 min) that is truly representative of what occurs in a real industrial setting when the ventilation is activated [16]. Figure 9.8a through Figure 9.8c can be compared with Figure 9.7b to evaluate the change in airflow patterns due to dissymmetry. According to Figure 9.8a, a dissymmetry of 2% did not really affect the airflow distribution since the results were quite similar to those of the numerical model with no dissymmetry. The higher air velocities were still concentrated at half-width and half-height in the modern sausage dryer. The only significant difference was an increase in air velocity means in the lower part of the dryer, for widths ranging from 1175 to 1275 mm and heights ranging from 450 to 850 mm. Increasing the dissymmetry of the ventilation cycle from 2% to 5% clearly affected airflow patterns, leading to the appearance of dissymmetry between the two sides of the plant together
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FIGURE 9.8 Distribution of the air velocity means calculated from 2D unsteady CFD modeling on a vertical section of a small sausage dryer over five periods of ventilation cycle of sinusoidal form and amplitude 60%=40%, with a dissymmetry equal to: (a) 2%, (b) 5%, and (continued )
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FIGURE 9.8 (continued) (c) 10% (given the unsteady modeling, the ventilation cycle was directly incorporated into the CFD model by means of a user-defined function. The black rectangle in the figures outlines the area usually filled with sausages.).
with poorly ventilated areas with means lower than 0:6 m s1 in the lower part on each side (Figure 9.8b). The stratification of air velocity means according to height in the dryer also increased, almost certainly contributing to heterogeneity in product drying not only between top and bottom but also between the left and the right of the dryer. Predictably, a further increase in the dissymmetry of the ventilation cycle strongly disrupted means distribution for air velocity (Figure 9.8c). In the area filled with objects, air velocity means ranged from 0:3 m s1 in the lower part, where they formed a large area, to over 1:2 m s1 in the upper part. According to Figure 9.8a through Figure 9.8c, beyond 2% dissymmetry in the high and low levels of the ventilation cycle, it is essential to carefully regulate the ventilation cycle in order to prevent unwanted changes in airflow patterns that will almost certainly impair meat product drying.
9.4 MODERN MEAT DRYERS OF LARGE HEIGHT 9.4.1 PROBLEMATIC In the race to increase the competitiveness of dried meat products, production has been mechanized excessively in recent years with the introduction of robots to automatically move the trolleys filled with products from the manufacturing area to the drying area, and then, when dried, from the drying area to the packaging area. Consequently, modern meat dryers
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have become higher, reaching and sometimes exceeding 6 m, thus allowing the manufacture of the same quantity of dried meat products with a lower floor surface. Many manufacturers have reported poor meat drying in this type of dryer, particularly in the upper half just above the lateral blower ducts, where sausages appear too moist and too molded during the drying process, thus revealing insufficiently ventilated areas. To cope with this problem, some plant designers have installed a specific system in order to invert airflows during the ventilation periods. Some systems blow air with a steady airflow rate without ventilation cycle via the ducts placed level with the ceiling and extract it via ducts fixed to the lateral walls of the plant. All the difficulty lies in adjusting the duration of the periods where the airflow is inverted in relation to the periods where the air is introduced through the lateral blower ducts according to the ventilation cycle. Chanteloup [28] recently studied the airflow patterns in two modern 6 m-high industrial sausage dryers based on unsteady 2D CFD modeling performed with the CFD code Fluent [25], highlighting heterogeneity in airflow patterns in the case of standard dryer configurations. With the aim of evening out the airflow distribution, the author then tested the effects of modifying the amplitude and duration of the ventilation cycle, changing the height of the blower ducts, adding deflectors to force the air to penetrate inside the area filled with the sausages, adding a third extraction duct level with the ceiling, and inverting the airflow inlet.
9.4.2 MEAN AGE
OF
AIR
To investigate the effect of the previous modifications on the airflow patterns, the notion of mean age of air (MAA) was introduced into the CFD models. MAA, which is widely used in building or clean-room ventilation sciences, can be defined as the average lifetime of air at a particular location, giving an indication on the ‘‘freshness’’ of the air. In the framework of a ventilated room with a single inlet and a single outlet, local MAA corresponds to the average time it takes for air to travel from the inlet to any point inside the room [29–33]. Moreover, MAA can be solved by CFD codes as an additional user-defined transported scalar following the equation corresponding to steady-state configurations: @ @t rui t Gt ¼ St @xi xi
(9:1)
where t is the MAA scalar, rui is the mass flow rate (r is the air density and ui is the air velocity), G is the diffusion coefficient of t for the air mixture, and St is the source term of t, which depends on the density of the air mixture. Several authors have reported that the diffusion coefficient and the source term of t could be written following the two equations [29–34]: G t ¼ 2:88r 105 þ St ¼ 1
mEFF 0:7
(9:2) (9:3)
where mEFF is the effective viscosity, which is related to both molecular viscosity and turbulent viscosity. The boundary conditions for the solution of Equation 9.1 are zero value at the air inlet and zero gradient at the air outlet and wall surfaces. Furthermore, age of air is a passive quantity that does not affect airflow patterns; hence, the local MAA is obtained from the solution of the airflow equation [34].
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By solving this scalar transport equation by means of a user-defined function incorporated into the Fluent code, Chanteloup [28] calculated MAA distribution in different configurations of two modern sausage dryers of large heights with the aim of identifying a technical solution that evens out at best ventilation. In the standard dryer configuration, i.e., for one period of the ventilation cycle (amplitude of 90%=10%) and without air inlet inversion, the calculations indicated a lack of ventilation in the upper half of the plants compared with the lower half, with air velocities locally lower than 0:1 m s1 and an MAA peaking at 80 s at the level of the two rows immediately located just above the lateral blower ducts. Air velocities in the lower half of the dryer were higher, ranging from 0.3 to 0:6 m s1 , and the MAA values were lower, ranging from 58 to 70 s. These findings undoubtedly corroborate the observations made in industry, i.e., the appearance of overmoist and excessively molded sausages just above the lateral blower ducts during the drying process in modern sausage dryers of large height. Figure 9.9 displays the local MAA calculated in a 4.3 m-wide sausage dryer, taking into account an air inlet inversion of 2 min (Figure 9.9a), 3 min (Figure 9.9b), 4 min (Figure 9.9c), or 5 min (Figure 9.9d) during 10 min of ventilation [28]. Even though numerical results revealed few differences in the air velocity distribution between the four configurations (air velocity means ranged from 0.17 to 0:24 m s1 in the area filled with the sausages), analysis of Figure 9.9 shows marked differences in local MAA distribution. Increasing the inversion of the air inlet led to marked gradients in MAA distribution in relation to height; 531 477 423
315 261
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369
207 153 99
57 (a)
121
185
249
313
45 377
Area of filling with sausages
Mean age of air (s) >105 95–105 85–95 75–85 65–75 55–65 <55
Width (cm)
FIGURE 9.9 Distribution of the local mean age of air (MAA) calculated from 2D unsteady CFD modeling on a vertical section of a 6 m-high and 4.3 m-wide industrial sausage dryer over 10 min of ventilation corresponding to: (a) 8 periods (then 8 min) of ventilation cycle of sinusoidal form and amplitude 90%=10%, without dissymmetry, and 2 min where the air inlet was inverted and then blown by the extraction ducts.
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57 (b)
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45 57 (c)
121
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>105 95–105 85–95 75–85 65–75 55–65 <55
Width (cm)
FIGURE 9.9 (continued) (b) 7 periods of ventilation cycle and 3 min of air inlet inversion; (c) 6 periods of ventilation cycle and 4 min of air inlet inversion; and (continued)
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207 153 99 45 57 (d)
121
185
249
313
377
Mean age of air (s) >105 95–105 85–95 75–85 65–75 55–65 <55
Width (cm)
FIGURE 9.9 (continued) (d) 5 periods of ventilation cycle and 5 min of air inlet inversion (in this unsteady modeling, two user-defined functions were used: the first to take into account the form and amplitude of the ventilation cycle, and the second to calculate the local MAA).
when the inversion reached 5 min (Figure 9.9d), local MAA values ranged from less than 55 s level with the ceiling near the extraction ducts to over 105 s (exactly 130 s) in the lower part of the dryer (giving a mean of 79 s with a standard deviation of 27 s), whereas the heterogeneity of MAA distribution was much lower when using an inversion time of 2 min (Figure 9.9a), i.e., a mean of 67 s and a standard deviation of below 5 s between the top and bottom of the dryer. In light of these results, local MAA seems to be a better and a more sensitive parameter than air velocity for highlighting pockets of inadequate ventilation and thus for assessing ventilation efficiency in industrial food plants. From the analysis of the local air velocity in combination with the local MAA distribution, Chanteloup [28] numerically demonstrated that changing the height of the lateral blower ducts between 2 and 4.1 m had a very poor effect in evening out the ventilation in the area filled with the sausages, whatever the width of the dryer, 4.3 or 5.3 m. The air velocity means ranged from 0.38 to 0:44 m s1 (with a standard deviation of 0:19=0:20 m s1 ), and MAA means ranged from 33 to 35 s with a standard deviation below 5 s in all cases. Halving the duration of the ventilation cycle from 60 to 30 s combined with the addition of a third extraction duct level with the ceiling slightly affected airflow patterns inside the large-height dryers studied. As indicated in Figure 9.9, inverting the air inlet in the dryer significantly modified air distribution in the plant, even improving ventilation homogeneity around the sausages compared with a standard operation without air inlet inversion, provided that the inversion time did not exceed one-fifth of the total ventilation time. On the other hand, scaling down the amplitude of the ventilation cycle from 90%=10% to 60%=40% without inverting the
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349 Area of filling with sausages
Height (cm)
448
250
151
52 66
132
198
264
330
396
462
Mean age of air (s) >20 18–20 16–18 14–16 12–14 10–12 <10
Width (cm)
FIGURE 9.10 Distribution of the local mean age of air (MAA) calculated from 2D unsteady CFD modeling on a vertical section of a 6 m-high and 5.3 m-wide industrial sausage dryer over 10 min of ventilation (8 periods of ventilation cycle of sinusoidal form and amplitude 90%=10%, without dissymmetry, and 2 min of air inlet inversion) and where two 0.35 m-long horizontal deflectors were fitted just above each blower duct (in this unsteady modeling, two user-defined functions were used: the first to take into account the form and amplitude of the ventilation cycle, and the second to calculate the local MAA).
air inlet during ventilation logically led to an increase in air velocities around the sausages located in the lower half of the plant to the detriment of the upper half, thus increasing the height stratification phenomenon, particularly in terms of local MAA distribution. Finally, the numerical investigation carried out revealed that the best distribution of local MAA (mean value of 18 s and standard deviation below 1 s) was obtained when a 0.35 m-long horizontal deflector was fitted just above each lateral blower duct in the 5.3 m-wide modern sausage dryer, for an air inlet inverted for 2 min for every 10 min of ventilation (Figure 9.10). On the other hand, the air velocities were not homogeneously distributed around the sausages since standard deviation reached 0:17 m s1 for a mean of 0:37 m s1 . In addition, the strong impact on the homogeneity of MAA distribution was much lower when the same deflectors were added in the numerical model corresponding to the second sausage dryer, which was less wide. Taken together, these numerical conclusions confirm that airflow patterns are very difficult to assess a priori; they also underline that numerical results absolutely must be validated by experimental results.
9.5 CONCLUSION This chapter clearly shows that CFD techniques can be very useful tools for assessing and improving airflow patterns in modern industrial meat dryers of medium or large height,
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particularly those operating due to the ventilation cycle. The effect of the amplitude and form of the ventilation cycle on the homogeneity of the distribution of the air velocity means has been illustrated, together with the effect of a dissymmetry in the ventilation cycle. The results obtained confirmed the industrial observations on poor process efficiency in some parts of the plants, such as, for example, that the driest products are often located in the upper part of medium-height meat dryers. The need for controlled regulation of the ventilation cycle was also highlighted. Calculations performed in modern sausage dryers of large height proved that local MAA distribution was a highly promising and very useful parameter for assessing ventilation efficiency compared with the usual air velocity, even if numerical results needed to be validated by experimental data. With CFD techniques, the significance and effects of operating conditions and design parameters can therefore be analyzed to gain a better understanding of the dynamics of the meat drying. Furthermore, more recent studies assessing airflow patterns via unsteady modeling will shortly provide professionals with a rational approach to help them in the operation and design of modern dryers, once they will have been validated by experimental data. However, a full numerical model of how a modern meat dryer operates would be ideal, i.e., a model describing the homogeneity of the drying conditions and the interaction between the meat products being dried and the indoor atmosphere (velocity, turbulence, temperature, and relative humidity). This remains difficult because very refined meshes will need to be constructed, yielding 3D numerical models requiring immense memory size. However, further progress can be expected in the years to come as the CFD codes become more and more flexible in use while the calculating power of computers currently used in practice continues to increase.
REFERENCES 1. V. Kottke, H. Damm, A. Fischer, and U. Leutz. Engineering aspects in fermentation of meat products. Meat Science 43(Supplement S): 243–255, 1996. 2. C. Noel. Etude du processus de se´chage des saucissons en vue d’e´viter le crouˆtage, accident de fabrication pre´judiciable a` la qualite´. DESS report, University of Bourgogne, Dijon, France, 1991. 3. E. Dabin and R. Jussiaux. Le Saucisson Sec. Paris: Erti e´diteur, 1994, pp. 120–127. 4. J. Lenges, A. Sterckendries, and A. Drouet. Etude des processus de se´chage des saucissons. In: Proceedings of CERIA Conference. Brussels, 1973, 6 p. 5. P. Baldini. De´termination de l’activite´ de l’eau aw des produits ensache´s crus en fonction de la teneur en eau. Viandes et Produits Carne´s 2: 8–14, 1981. 6. A. Stiebing and W. Rodel. Influence of the pH on the drying pattern in dry sausage. Fleischwirtschaft 70: 1039–1043, 1990. 7. F. Lucke and H. Hechelmann. Starter cultures for dry sausages and raw ham. Fleischwirtschaft 71: 307–313, 1991. 8. J.D. Daudin, A. Kondjoyan, and J. Sirami. Water and salt transfers analysis in drying of sausages. In: Proceedings of the 38th International Congress of Meat Science and Technology. ClermontFerrand, 1992, pp. 1199–1202. 9. P. Baldini, E. Cantoni, F. Colla, C. Diaferia, L. Gabba, E. Spotti, R. Marchelli, A. Dossena, E. Virgili, S. Sforza, P. Tenca, A. Mangia, R. Jordano, M.C. Lopez, L. Medina, S. Coudurier, S. Oddou, and G. Solignat. Dry sausages ripening: influence of thermohygrometric conditions on microbiological, chemical and physicochemical characteristics. Food Research International 33: 161–170, 2000. 10. T. Bolumar, P. Nieto, and J. Flores. Acidity, proteolysis, and lipolysis changes in rapid-cured fermented sausage dried at different temperatures. Food Science and Technology International 7: 269–276, 2001. 11. A.I. Andre´s, R. Cava, J. Ventanas, V. Thovar, and J. Ruiz. Sensory characteristics of Iberian ham: Influence of salt content and processing conditions. Meat Science 68: 45–51, 2004.
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12. P.S. Mirade and J.D. Daudin. Analyse expe´rimentale de l’ae´raulique d’un se´choir a` saucisson. In: Proceedings of 5th French Congress on Chemical Engineering. Lyon, 1995, pp. 83–88. 13. R. Braconnier, J.R. Fontaine, and J. Gillet. Etude des e´coulements d’air dans une e´tuve de se´chage de charcuterie. National Symposium on Qualite´ de l’air dans les IAA, Cemagref, Rennes, France, 1997. 14. P.S. Mirade and J.D. Daudin. A numerical study of the airflow patterns in a sausage dryer. Drying Technology 18: 81–97, 2000. 15. P.S. Mirade. Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach. In: Proceedings of the 1st International Conference on Simulation in Food and Bio-Industries. Nantes, 2000, pp. 43–47. 16. P.S. Mirade. Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models. Journal of Food Engineering 60: 41–48, 2003. 17. Anonymous. Star-CD Manuals. London: Computational Dynamics Limited, 1994. 18. B.E. Launder and D.B. Spalding. Mathematical Models of Turbulence. New York: Academic Press, 1972, pp. 90–109. 19. C. Hirsch. Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows. Chichester: John Wiley, 1988, pp. 408–517. 20. S.V. Patankar and D.B. Spalding. A calculation procedure for heat, mass, and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer 15: 1787– 1806, 1972. 21. P.S. Mirade and J.D. Daudin. Etude nume´rique en 2 dimensions du cycle de ventilation d’un se´choir a` saucisson moderne. Entropie 226: 54–62, 2000. 22. A. Rizzi. Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber. Journal of Food Engineering 58: 151–171, 2003. 23. J.M. Martinez-Benet and L. Puigjaner. A powerful improvement on the methodology for solving large-scale pipeline networks. Computers and Chemical Engineering 12: 261–265, 1988. 24. M. Djuric and M. Novakovic. Numerically oriented improved Hardy–Cross method. Software for Engineering Workstations 5: 54–64, 1989. 25. Anonymous. Fluent 6: User’s Guide. Lebanon, NH: Fluent Inc., 2001. 26. Z.U.A. Warsi. Fluid Dynamics: Theoretical and Computational Approaches. Boca Raton, FL: CRC Press, 1993, pp. 540–552. 27. R.I. Issa. Solution of the implicitly discretized fluid flow equations by operator-splitting. Journal of Computational Physics 62: 40–65, 1985. 28. V. Chanteloup. Imple´mentation de la notion d’aˆge moyen de l’air a` l’aide d’une ‘‘User-Defined Function’’ dans le code Fluent. Master report, Blaise Pascal University, Clermont-Ferrand, France, 2005. 29. W.J. Fisk, D. Faulkner, D. Sullivan, and F. Bauman. Air change effectiveness and pollutant removal efficiency during adverse mixing conditions. Indoor Air 7: 55–63, 1997. 30. C.C. Federspiel. Air-change effectiveness: theory and calculation methods. Indoor Air 9: 47–56, 1999. 31. J. Abanto, D. Barrero, M. Reggio, and B. Ozell. Airflow modeling in a computer room. Building and Environment 39: 1393–1402, 2004. 32. Z. Lin, T.T. Chow, K.F. Fong, C.F. Tsang, and Q. Wang. Comparison of performances of displacement and mixing ventilations. Part II: Indoor air quality. International Journal of Refrigeration 28: 288–305, 2005. 33. O. Rouaud and M. Havet. Numerical investigation on the efficiency of transient contaminant removal from a food processing clean room using ventilation effectiveness concepts. Journal of Food Engineering 68: 163–174, 2005. 34. G. Gan. Effective depth of fresh air distribution in rooms with single-sided natural ventilation. Energy and Buildings 31: 65–73, 2000.
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CFD Simulation of Spray Drying of Food Products Han Straatsma, M. Verschueren, M. Gunsing, P. de Jong, and R.E.M. Verdurmen
CONTENTS 10.1 10.2
10.3 10.4
10.5
10.6
10.7
Introduction ............................................................................................................. 250 Flow Field Calculation ............................................................................................ 252 10.2.1 Transient versus Steady State ..................................................................... 252 10.2.2 Turbulence .................................................................................................. 252 10.2.3 Gas Flow Solving........................................................................................ 252 Particle Tracking ...................................................................................................... 252 Particle Drying Models ............................................................................................ 254 10.4.1 Introduction ................................................................................................ 254 10.4.2 Transport Phenomena................................................................................. 254 10.4.3 Drying Model Approaches ......................................................................... 256 10.4.4 Drying Model based on Diffusion Concept................................................ 256 10.4.4.1 Introduction ................................................................................ 256 10.4.4.2 Internal Moisture Transport ....................................................... 257 10.4.4.3 External Moisture Transport ...................................................... 258 10.4.4.4 External Heat Transport ............................................................. 259 10.4.4.5 Shrink of Particles ....................................................................... 260 10.4.5 Sorption Isotherms ..................................................................................... 261 10.4.5.1 Introduction ................................................................................ 261 10.4.5.2 GAB Relation ............................................................................. 261 10.4.5.3 Determination of Sorption Isotherms ......................................... 262 10.4.6 Diffusion Coefficient Relations................................................................... 263 10.4.6.1 Introduction ................................................................................ 263 10.4.6.2 Expression 1 ................................................................................ 263 10.4.6.3 Expression 2 ................................................................................ 264 10.4.6.4 Determination of Diffusion Coefficient ...................................... 264 Submodels for Thermal Reactions ........................................................................... 265 10.5.1 Introduction ................................................................................................ 265 10.5.2 Forming of Insoluble Material ................................................................... 266 Submodel for Stickiness ........................................................................................... 267 10.6.1 Introduction ................................................................................................ 267 10.6.2 Glass Transition Temperature .................................................................... 268 10.6.3 Relation between Glass Transition and Sticky-Point Temperature ............ 271 Fouling of Equipment .............................................................................................. 271
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10.8
Interparticle Collision Models................................................................................ 272 10.8.1 Introduction ............................................................................................ 272 10.8.2 Sampling Statistical Data ........................................................................ 272 10.8.3 Collision Probability ............................................................................... 273 10.8.4 Rebound after Collision .......................................................................... 274 10.8.5 Other Postcollision Events ...................................................................... 274 10.9 Coalescence and Agglomeration Model ................................................................. 275 10.9.1 Introduction ............................................................................................ 275 10.9.2 Classification of Collision Partners ......................................................... 275 10.9.3 Types of Collision Events........................................................................ 276 10.9.4 VD–VD=DRY Collision Type ................................................................ 276 10.9.5 DRY–DRY Collision Type..................................................................... 277 10.9.6 Properties of Agglomerates ..................................................................... 277 10.9.7 Conservation of Mass after Agglomeration ............................................ 278 10.10 Implementation of a CFD Model for Spray Dryers .............................................. 278 10.10.1 Introduction ............................................................................................ 278 10.10.2 Spray-Dryer Simulation .......................................................................... 279 10.11 Conclusions ............................................................................................................ 283 Nomenclature ..................................................................................................................... 283 References .......................................................................................................................... 284
10.1 INTRODUCTION Spray drying is an essential unit operation for the manufacture of many consumer food products, such as milk and whey powders, infant formula powders, coffee creamers, and other powders with proteins, fats, and sugars from animal (e.g., milk) or vegetable origin, egg powders, and coffee powders. In a spray dryer, the feed of a solution or suspension is atomized and the droplets are dried with a hot gas. The dryer can have one or more gas inlets and atomizers. Some dryers have one outlet for the gas as well as for the product. In that case the product has to be separated from the gas by a cyclone or bag filter. However, most dryers are provided with a product outlet, for example at the bottom of the dryer and one or more separate gas outlets. These gas outlets are placed in such a position (e.g., at the top of the dryer) so that minimal quantities of product leave through them. Simultaneous to the drying process, coalescence or agglomeration of droplets can also take place. The highest probability of agglomeration is in the neighbourhood of the atomizers. In practice, agglomeration is stimulated by using multiple atomizers spraying toward each other or by injecting fine particles (e.g., separated from the outlet gas) near the atomizers. Figure 10.1 shows an example of an industrial two-stage dryer consisting of a spray drying chamber and a vibrating fluid bed. The spray dryer is provided with one hot air inlet, which is constructed in such a way that a strong swirl component is added to the gas velocity. The dryer has one atomizer placed in the center of the air inlet and has one air outlet, which is placed in the center of the dryer. Because of the swirl of the gas, this is a suitable place for an air outlet. Fines, separated from the outlet gas of the drying chamber and the fluid bed, are returned near the atomizer. The layout of the equipment and the operating conditions play a major role in processrelated aspects as well as product-related aspects. Process-related aspects are, for example,
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Atomizer wheel/nozzles
Hot air inlet
Fines return
Spray chamber
Cyclone
Bag filter
Concentrated product Vibrating fluid bed
Warm air
(Agglomerated) powder
Cold air
FIGURE 10.1 An industrial two-stage spray dryer with fines return. (Courtesy of Anhydro A=S.)
fouling of the equipment and product losses with the outlet gas. Fouling of equipment is a serious practical problem when droplets reach the wall while they are still very sticky. Other aspects such as the thermal load, the retention of volatile components, and the agglomeration are product related. As food products are heat sensitive, the thermal load during drying is of great importance for the final quality. A too-high thermal load can lead to degradation of valuable components such as proteins and vitamins, brown coloring, forming of insoluble material, or other undesired components. High-quality instant powders require optimal free-flowing properties, absence of dust, and quick dissolution or dispersion in water or other solvent without the formations of lumps. The degree of agglomeration is an important factor for these properties. By agglomeration, small particles are combined to form larger particles in which the original particles are still identifiable (see Figure 10.2). In this way the characteristics of a single particle are maintained while the bulk powder properties are improved. Agglomeration of particles can be carried out as a separate process after drying, but it is more convenient to combine it with the drying process. It is clear that a good simulation technique is very valuable for the design of spray dryers, solving process-related problems, and finding conditions to get the best product properties.
200 µm
FIGURE 10.2 SEM-photograph of spray-dried and agglomerated powder. (From Verdurmen, R.E.M., Menn, P., Ritzert, J., Blei, S., Nhumaio, G.C.S., Sonne Sørensen, T., Gunsing, M., Straatsma, J., Verschueren, M., Sibeijn, M., Schulte, G., Fritsching, U., Bauckhage, K., Tropea, C., Sommerfeld, M., Watkins, A.P., Yule, A.J., and Schønfeldt, H., Dry. Technol., 22, 1403, 2004.)
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A full 3D simulation of a spray drier is possible with CFD. With almost all basic CFD software packages it is possible to simulate the flow pattern of the gas in the dryer and the trajectories of the particles. For food processing these basic techniques alone are not enough. The value of these simulations increases when these basic techniques are extended with additional submodels such as a drying model, kinetic models of thermal reactions, submodels describing the stickiness of the product, an agglomeration model, and so on. In this chapter several submodels will be discussed in more detail.
10.2 FLOW FIELD CALCULATION 10.2.1 TRANSIENT
VERSUS
STEADY STATE
Often transient as well as steady-state flow field calculations are possible with CFD software packages. In transient calculations, the changes during the run time of an instationary process are simulated. For spray drying this would, for example, be useful to study the dynamic behavior of the dryer during the start-up or shutdown of the installation. Normally, spray drying is a continuous process and the steady-state situation will be of most interest. However, it is useful to make some marginal notes here. When looking through the peep window of an industrial dryer, it can be seen that the flow pattern is rather chaotic and permanently fluctuating like the wind in our earthly atmosphere. It seems that a pure steady state can never be reached. For some engineers, this is a reason to do transient simulations instead of steady-state simulations for spray dryers. However, steady-state simulation is a good approximation for most spray dryers and in the remainder of this chapter the steady-state approach will be assumed.
10.2.2 TURBULENCE The gas flow in a spray dryer is turbulent. To simulate the flow field, several turbulence models are available to approximate the influence of turbulent fluctuations on large-scale flow behavior [1]. A popular turbulence model is the k« model [1]. This model uses a specific relation to determine the local value of the eddy viscosity from the turbulent kinetic energy (k) and its dissipation («). It assumes that the turbulence is isotropic (the same in all directions). This assumption strongly reduces the required CPU-time of the calculation. That is why the k« model is currently one of the most popular turbulence models for technical calculations. The assumption of an isotropic turbulence is not permitted for strongly swirling flows (e.g., in cyclones). The k« model is suitable for most spray-dryer simulations, because the swirling motion is not so strong that the accuracy is reduced. In some designs of spray dryers a strong swirling motion is introduced. In such cases another turbulence model such as the Reynolds stress turbulence model is a better choice.
10.2.3 GAS FLOW SOLVING To predict the profiles of the gas flow velocity, temperature, and pressure, a calculation grid is set up for the spray-dryer volume. For each volume cell in the grid, the equations describing the fluid flow are solved in an iterative process. After each iteration a better solution of the equations will be reached. The iterative procedure will be continued until sufficient convergence has been reached.
10.3 PARTICLE TRACKING In spray drying, the flow consists of a continuous gas phase and dispersed phase in the form of liquid or solid particles. The motion of the particles will be influenced by that of the gas
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phase and vice versa via displacement and interphase momentum, mass, and heat transfer effects. Moreover, gravitational forces also act on the particles. The strength of the interactions will depend on the particle’s size, density, and number density. The particle trajectories can be calculated by solving the momentum conservation equations for droplets. A widely used approach is the Lagrangian=Eulerian method. With this method the residence time of a particle is divided into small time steps. After each time-step a new position and velocity of the particle is calculated. In this way the whole trajectory from injection point to outlet is calculated. This time-step method should not be confused with transient calculation mentioned in Section 10.2.1. In fact, the Lagrangian method describes the place-dependent particle behavior in a steady-state situation. Indispensable is the inclusion of the phenomena that occur when a droplet strikes a wall. In the simplest case, the result is an elastic or inelastic bounce. Optional submodels can be added that describe the effects of phenomena such as sticking or shattering at the wall, interparticle collisions followed by rebounding, break up, coalescence, or agglomeration. In industrial spray dryers, billions of particles are atomized each second. It is extremely time consuming to calculate all these trajectories for large-scale dryers, so a more statistical approach is more suitable. In this approach, the total population of droplets is represented by a finite number of computational parcels, each of which represents a group of particles having the same properties. Each parcel has its own initial properties, such as injection point, velocity, diameter, density, temperature, and so on. Of course, the number of parcels must be large enough so that the properties of the full population are well represented. This can be assessed, in the absence of any other measures, by performing calculations with different numbers of parcels and comparing the results. In turbulent flows, the random walk technique is employed to introduce the fluctuating nature of the turbulent velocity gas field. This means that the gas velocity that the particle feels is not the local mean velocity, but the mean value added with a random turbulent contribution. In general, the flow field and particle trajectories are calculated separately. The gas flow solver and particle tracker are then alternately run in a calculation loop, as shown in Figure 10.3. The gas flow solver calculates the gas conditions, such as temperature, moisture, velocity, and degree of turbulence, in each volume cell of the grid. The particle tracker reads in these data in order to calculate the trajectories. When the parcel passes a cell of the grid the amounts of energy, mass, and momentum transferred to the gas are calculated and added to the source terms of that cell. In this way all trajectories are calculated one by one. In the next iteration, the gas flow solver uses these source terms for a new calculation. The calculation loop is repeated until sufficient convergence is achieved. Gas flow solver
Gas conditions
Source terms for energy, mass, and momentum Particle tracker
Particle trajectories
FIGURE 10.3 Calculation flowchart.
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It can occur that a lot of volume cells are not visited within one particle tracking loop with a limited number of parcels, especially when the grid is fine. Caused by the random nature of the turbulence, in the next particle tracking loop the parcels will follow other trajectories and other volume cells will be or will not be visited. This results in inhomogeneous source terms over the entire domain. A good strategy to smooth these inhomogeneities is averaging the source terms over multiple iterations.
10.4 PARTICLE DRYING MODELS 10.4.1 INTRODUCTION Many CFD software packages support particle tracking combined with heat and mass transfer. However in most packages, the transport limitations within a particle are not taken into account. These packages are suitable for evaporation of pure solvent droplets, but are not suitable for spray drying of food products, because the internal mass transport determines the drying rate of these products. For that purpose, a package is needed that can be called a drying model during particle tracking.
10.4.2 TRANSPORT PHENOMENA For mass and heat transport during spray drying, external and internal phenomena can be distinguished. External transport phenomena take place from the particle surface to the surrounding air and internal transport phenomena from the inner to the outer side of the particle. The heat of evaporation is withdrawn from the particle by evaporation of water, so there is a coupled heat and mass transfer. The external transport rate can be described by a transfer coefficient and a driving force. The transfer coefficient is strongly determined by the Reynolds number based on the velocity difference between particle and surrounding air. The driving force for mass transfer is the difference in water concentrations (or vapor pressure) in the gas phase at the droplet’s surface and the bulk of the air. So, a relation is needed to describe the equilibrium vapor pressure of the product as a function of its moisture content and temperature. The internal transport rate is strongly determined by the effective diffusion coefficient (for mass) or thermal conductivity (for heat). In most cases, water concentration gradients are the driving force for internal moisture transport. However, when the particle temperature exceeds the boiling temperature, a vapor pressure gradient becomes the driving force. Internal heat transport (conduction) takes place faster in comparison with internal mass transport (diffusion). For droplets with small diameters, such as for spray drying, the assumption of a uniform temperature within the particle is a valid approximation. An example of a calculated time evolution of moisture and temperature during drying of a single skim-milk droplet with a diameter of 100 mm in an ideal mixed volume of air is shown in Figure 10.4. When the initial moisture content of the particle is high, in the first stage of drying, the external mass transport is the rate-limiting factor. The water evaporation rate is high and the particle temperature will approach the wet-bulb temperature. The wet-bulb temperature depends upon the temperature and moisture content of the surrounding air but is typical in the range of 408C–508C. Figure 10.4 shows that this drying stage is very short (0.01 s). When the outer shells of the particle get dry, the internal mass transport becomes dominant and the water evaporation rate strongly decreases. The particle temperature approaches the temperature of the surrounding air and the moisture content of the outer shell will approach equilibrium with the surrounding air. In this stage there is a sharp moisture gradient within the particle, which equalizes gradually. After a drying time of 30 s, the mean moisture content
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Air Particle Boiling T
Temperature (⬚C)
160
120
80
40 0.00
0.02
0.04 0.05
0.45
0.85
1
11
21
Time (s) 1.0
Mean Inner shell Outer shell Equilibrium
Moisture (kg kg −1)
0.8
0.6
0.4
0.2
0.0 0.00
0.02
0.04 0.05
0.45 0.85 Time (s)
1
11
21
FIGURE 10.4 Calculated drying of a single skim-milk particle (100 mm) in an ideal mixed volume of air. Mass ratio dry solids=dry air: 0.05; relative particle velocity: 0:1 m s1 ; initial conditions: particle moisture: 1 kg kg1 dry solids; particle temperature: 708C; air moisture: 8:5 g kg1 dry air; air temperature: 1808C. Top: Air temperature (Tair ), particle temperature (Tp ), and boiling temperature (Tboil ) as a function of time. Bottom: Moisture content (average, inner shell, outer shell) and equilibrium moisture content as a function of time.
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of the particle has approached but not yet reached the equilibrium value. In the figure, the boiling point of the inner of the particle (wettest part) is also plotted. Although the air-inlet temperature is far above the water-boiling temperature, the highest particle temperature remains just below its boiling point. The particle behavior strongly depends on the type of the product and the process conditions. During drying, a particle can shrink, but full shrink is not very likely. In general, the particle becomes porous by the forming of vacuoles or open channels. Under certain conditions, for example, when the feed contains a high amount of dissolved gas or when the droplet exceeds the boiling point, the particle can be inflated like a balloon and dry further as a hollow particle or burst into small pieces.
10.4.3 DRYING MODEL APPROACHES Many particle drying models have been developed with various approaches of the drying kinetics. An example is the approach to describe the rate of evaporation as the rate of the unhindered evaporation (without internal transport limitations), multiplied by a factor which decreases with the particle’s moisture content [2]. The factor is based on a characteristic drying rate curve of the specific product. Another approach is based on a reaction-engineering concept, assuming drying as a competitive process between an evaporation and a condensation reaction [3]. Both approaches consider only the course of the overall moisture content of the drying particle. In more extended models, the differential equation that describes the instationary diffusion process in a spherical particle [4] is solved numerically [5,6]. In this approach the time evolution of the moisture gradients within the particle is included. Other variants add special particle behavior to the model, for example, for particles that are inflated to hollow spheres [7,8]. Each model has its advantages and disadvantages and is more or less suitable for a specific product. In this chapter, a model that describes the drying kinetics by the diffusion concept will be worked out. The advantage of this concept is the inclusion of the moisture gradients within the particles. For particle collisions with the wall or with other particles, the moisture content of the outer shell of the particles is relevant, while for thermal reactions during drying the local moisture content in combination with the temperature is needed. A disadvantage is that the effective diffusion coefficient as a function of moisture content and temperature must be known. Advanced experiments are needed to obtain that information.
10.4.4 DRYING MODEL 10.4.4.1
BASED ON
DIFFUSION CONCEPT
Introduction
In this section, a particle drying model is worked out. The internal moisture transport is described by the diffusion concept, the external heat and mass transport by the theory of a turbulent boundary layer. A number of assumptions are made: . . .
Particles are spherical. Temperature within the particle is homogeneous. No effect of exceeding the boiling temperature.
The drying model can be applied to Lagrangian particle tracking in CFD calculations or to batch drying of one or more particles in a fixed quantity of air. The latter is equivalent to continuous drying in a cocurrent process.
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10.4.4.2
Internal Moisture Transport
Within a powder particle the moisture is transported by diffusion. For a thin spherical shell (thickness dr) the mass balance of water can be set up as Fin ¼ Fout þ Fac
(10:1)
where F is the mass flow of water going into, going out of, and accumulated in the shell. Working out this balance gives dcp Fin ¼ 4p r2 D (10:2) dr r 2 dcp Fout ¼ 4p r D (10:3) dr rþdr Fac ¼ V
dcp dcp ¼ 4pr2 dr dt dt
(10:4)
Finally, this leads to the common differential diffusion equation: @cp 1 @ 2 @cp r D ¼ 2 r @r @t @t
(10:5)
where cp is the moisture content (kg m3 ) and D the (local) water diffusion coefficient. This differential equation cannot be solved analytically. For simplicity, a numerical solution according to a first-order method is chosen. In general, a disadvantage of a firstorder method is that it needs smaller calculation steps than a higher-order method. An advantage of this method is that it is much easier to implement and that it can more easily be combined with effects like shrink and agglomeration: for example, the time-step sizes can be varied depending on the transport rate so that instabilities can be avoided; shell radii need not to be equidistant and can be varied during the drying process. The particle is divided in a number of shells. Equation 10.2 through Equation 10.4 are written in the differential form for each shell i, where 1 is the innermost and n the outermost shell: Fin, 1 ¼ 0 Fin, i ¼
(Di þ Di1 ) (cp,i cp,i1 ) 4pr20,i (i > 1) (rm,i rm,i1 ) 2
(10:6) (10:7)
Fout,i ¼ Fin,iþ1 (i < n)
(10:8)
Fout , n ¼ Fev
(10:9)
Fac,i ¼ Mdp,i
Dcdp,i Dt
(10:10)
where Fev is the rate of evaporation at the outside of the particle (kg s1 ), Mdp,i the dry solids mass of shell i, cdp,i the moisture content (kg kg1 ) of shell i based on the dry solids mass, r0,i the outer radius of shell i. rm,i is defined as rm,i ¼
r0,i þ r0,1þi 2
(10:11)
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cp and cdp are related as cp ¼ r p
cdp 1 þ cdp
(10:12)
where rp is the density of the particle (kg m3 ). The rate of evaporation (Fev ) is determined by the external mass transport from the particle to the surrounding air (see Section 10.4.4.3). With these equations the new moisture content of each shell after a time-step Dt can be calculated. In case of a CFD calculation, the total amount of mass transferred to the surrounding air is obtained by summation of Fev Dt for each Lagrangian time-step that the particles reside in the volume cell. The value obtained by summation is saved in a source term for that cell and is used in the next iteration of the flow solver to calculate the new moisture content of the air in that volume cell. In case of batch drying of one or more particles in a fixed quantity of dry air, the new air moisture content can be calculated with dxa Fev,total ¼ dt Mda
(10:13)
where xa is the moisture content of air based on dry air, Fev,total is the total water flow transferred from the particles to the surrounding air, and Mda the mass of dry air. 10.4.4.3
External Moisture Transport
The external moisture transport from the particle j to the surrounding air can be written as [11] Fev, j ¼ kj Aj ca, j ca
(10:14)
where kj is the mass transfer coefficient (m s1 ), Aj the surface area of the particle (m2 ), ca, j the water concentration in air (kg m3 ) at equilibrium with the particle surface, and ca the water concentration in the bulk of the surrounding air. The water concentration in air (ca ) is related to the partial water pressure ( pa ) according to the ideal gas law pa ¼
ca RT Mw
(10:15)
where Mw is the molecular weight (kg mol1 ) of water, R the ideal gas constant (J mol1 K1 ), and T the absolute temperature (K). Equation 10.14 can be rewritten as Fev, j
Mw pa, j pa ¼ kj Aj R Tp Ta
(10:16)
where Tp is the particle temperature and Ta the bulk air temperature. pa, j can be calculated with the sorption isotherms of the product (see Section 10.4.5).
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In drying practice, the moisture content of air is usually expressed as kg water=kg dry air (xa ). This content is related to pa by pa ¼
xa pt xa pt ¼ Mw 0:622 þ xa þ xa Ma
(10:17)
where pt is the total pressure and Ma the molecular weight of dry air. The mass transfer coefficient (k) can be calculated from the Sherwood number (Sh) obtained from empirical relations for spherical particles, for example, the Ranz–Marshall equation [10,11]: Sh ¼ 2 þ 0:58Re0:5 Sc0:33
(10:18)
where Re is the Reynolds number and Sc the Schmidt number. The Sherwood number is defined as Sh ¼
kd D
(10:19)
where d is the particle diameter and D the diffusion coefficient of water vapor in air. 10.4.4.4
External Heat Transport
Heat transport from particle to the surrounding air takes place due to temperature differences. Besides that, heat is withdrawn from the particles by water evaporation. The heat balance of the particle can be written as Qout þ Qev þ Qac ¼ 0
(10:20)
where Qout is the heat flow transferred to the surrounding (J s1 ), Qev the heat flow withdrawn by evaporation, and Qac the accumulated heat flow. Working out the balance gives Qout ¼ aA Tp Ta
(10:21)
Qev ¼ Fev Hev þ Tp Cp,wv
(10:22)
Qac ¼ Mdp
dHdp dt
(10:23)
where a is the heat transfer coefficient (W m2 K1 ), T the temperature (8C) of the particle (p ) or air (a ), Cp the specific heat capacity of water vapor (wv ), Hev the heat of evaporation (J kg1 ) of water at 08C, Mdp the total dry mass of the particle, and Hdp the total enthalpy of the particle based on the mass of dry solids. Hdp can be written as Hdp ¼ Tp Cp,p ¼ Tp Cp,dp þ Cp,w cdp
(10:24)
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where Cp is the specific heat capacity of the dry solids (dp) or water (w) and cdp is the overall moisture content of the particle based on the dry solids mass. In analogy with the mass transfer, the heat transfer coefficient (a) can be calculated from the Nusselt number (Nu) obtained from empirical relations for spherical particles, for example, the Ranz–Marshall equation: Nu ¼ 2 þ 0:58Re0:5 Pr0:33 where Re is the Reynolds number and Pr the Prandtl number. The Nusselt number is defined as ad Nu ¼ l
(10:25)
(10:26)
where d is the droplet diameter and l the thermal conductivity of the surrounding air. With these equations the new enthalpy of the particle (Hdp,tþDt ) after a time-step Dt can be calculated. When the new enthalpy and the new overall moisture content of the particle are calculated, the new particle temperature can be calculated with Tp,tþDt ¼
Hdp,tþDt Cp,dp þ Cp,w cdp,tþDt
(10:27)
In case of a CFD calculation, the total amount of heat transferred to the surrounding air is obtained by summation of Qout Dt for each Lagrangian time-step that the particles reside in the volume cell. The value obtained by summation is saved in a source term for that cell and is used in the next iteration of the flow solver to calculate the new air temperature in that volume cell. In case of batch drying of one or more particles in a fixed quantity of air, the following equations can be used to calculate the new air temperature. The change of the enthalpy of air based on the mass of dry air (Hda ) is dHda Qout,total ¼ dt Mda
(10:28)
where Qout,total is the summed heat flow (J s1 ) transferred from the particles to the surrounding air and Mda the mass of dry air. The enthalpy of air is defined as Hda ¼ Ta Cp,a þ xa Cp,wv þ xa Hev (10:29) First, the new enthalpy after a time-step Dt is calculated with Equation 10.28 and Equation 10.29. When the new enthalpy (Hda, tþDt ) and moisture content of air (xa, tþDt ) are known, the corresponding temperature of the air can be calculated with Ta,tþDt ¼ 10.4.4.5
Hda,tþDt xa,tþDt Hev Cp,a þ xa,tþDt Cp,wv
(10:30)
Shrink of Particles
During drying the particles will shrink. On the other hand, vacuoles or open pores can be formed during drying, so there is no full shrink. It is not easy to predict the shrink behavior. One approach is to define a shrink factor (Sf ) as Vp ¼ Sf Vmassive þ (1 Sf)Vini
(10:31)
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where V is the actual (p ), massive (massive ) (no vacuoles), and initial (ini ) volume of the particle. According to this equation, the volume of the particle is a linear combination of the massive and the initial volume. The shrink factor is a value between 0 (no shrink, constant volume) and 1 (full shrink). The volume of the massive-product changes with the moisture content and can be calculated from the actual density of the massive product and the actual particle weight. The density of the massive product can be approximated as 1 rmassive
¼
mp 1 mp þ rw rds
(10:32)
where mp is the moisture content based on total mass (kg kg1 ), rw the density of water (kg m3 ), and rds the density of dry solids. When the (local) particle volume is known, the radii of the particle’s shells can be recalculated.
10.4.5 SORPTION ISOTHERMS 10.4.5.1
Introduction
For modeling of the external moisture transport from a drying particle to the surrounding air (see Section 10.4.4.3), an equilibrium relation is needed to obtain the water vapor pressure of the wet product as a function of its temperature and moisture content. For this purpose, mainly sorption isotherms are used. With a sorption isotherm, the moisture content of the product is related to the water activity. The water activity (aw ) is defined as the ratio between the partial water vapor pressure of the air that is in equilibrium with the product (pa ) and the water vapor pressure of pure water (p0w ) at one and the same temperature: aw ¼
pa p0w
(10:33)
The advantage of the use of sorption isotherms is that a great part of the temperature dependence of the water vapor pressure is described by the well-known relation for pure water. In spite of that, the water activity is not fully temperature independent. The sorption isotherms determined at room temperature are not sufficient for drying purposes. A sorption isotherm at elevated temperature is needed and sometimes it is necessary to determine sorption isotherms at different temperatures. In literature several physical or mathematical models are presented to describe the sorption isotherms as reviewed in Ref. [12]. For food products the GAB (Guggenheim, Anderson, de Boer) equation is widely used, which is worked out in the next section. 10.4.5.2
GAB Relation
The GAB relation has the following form: " W ¼ Wm
# cg 1 Kaw Kaw þ 1 þ cg 1 Kaw 1 Kaw
(10:34)
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where aw is the water activity, W the powder moisture content, and Wm , cg , and K productspecific constants. To calculate the water activity at given moisture content, the GAB equation can be rewritten as
aw ¼ where
and
H1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H12 4H2 2H2
(10:35)
Wm H1 ¼ K cg 1 2 W
(10:36)
H 2 ¼ K 2 1 cg
(10:37)
These GAB constants can be temperature dependent. There are some mathematical expressions available to describe the temperature dependence of these constants (e.g., Arrhenius alike relations). Alternatively, the water activity as a function of temperature can be obtained by interpolation between experimental sorption isotherms at a limited number of temperatures. 10.4.5.3
Determination of Sorption Isotherms
There are several ways to determine sorption isotherms. A common complication for food products with a high content of carbohydrates is the crystallization during determination [15]. As spray drying is a fast process, there is no time for crystallization and the carbohydrates generally remain in the amorphous state. However, when the powders are rewetted during experiments to determine the sorption isotherms, crystallization can occur after some time. The sorption behavior of crystallized product is rather different from that of amorphous product [16], so data are not representative for the spray drying process. In practice this can mean that the sorption properties cannot be determined above a critical moisture content. The value of the critical moisture content depends on the type of product and the method of determination. In many cases, the sorption data beyond the critical point is not relevant for spray drying. In cases that it is relevant, it is possible to extrapolate valid data beyond the critical moisture content. Several methods to determine sorption isotherms are described in literature [13]. A widely used method is bringing the sample with known weight and moisture content in a vacuum desiccator over a saturated salt solution with known relative humidity. After equilibrating for about 24 h, the sample is weighed again and the equilibrium moisture content is calculated [14,15]. Kockel et al. [12] have presented a method where fresh powder is brought to equilibrium with conditioned air in a stirred fluidized bed. With this method, the time to reach equilibrium is reduced to about 3 h. A more direct method is described by Hols et al. [16]. Here, a laboratory scale dryer is applied to produce powder samples with a range of moisture contents. The samples are placed in a closed holder with a small headspace, supplied with a humidity sensor. After 10–90 min the equilibrium air humidity can be measured. Several researchers have reported experimental sorption data [8,12,15,16]. In Figure 10.5 the sorption isotherms of milk powder are shown as an example. The experimental data are fitted with the GAB relation (see Section 10.4.5.2). The moisture content is based on the fat-free dry matter. Because fat has no interaction with water, the same sorption
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1.0
Water activity (−)
0.8
Sorption isotherms milk powder 23⬚C 45⬚C 75⬚C
0.6
0.4
0.2
0.0 0.00
0.05 0.10 0.15 0.20 Moisture content in fat-free dry matter (kg kg−1)
0.25
FIGURE 10.5 Sorption isotherms of milk powder [16]. GAB constants: 238C: Wm ¼ 0.059, cg ¼ 11.4, k ¼ 1.04; 458C: Wm ¼ 0.043, cg ¼ 9.8, k ¼ 1.10; 758C: Wm ¼ 0.019, cg ¼ 8.2, k ¼ 1.19.
data can be applied for milk powders with various fat contents (and the same nonfat dry-matter composition).
10.4.6 DIFFUSION COEFFICIENT RELATIONS 10.4.6.1
Introduction
As explained in Section 10.4.2, diffusive transport of water from the inner to the outer side of the drying particle plays a major role in internal transport phenomena. The water diffusion coefficient strongly depends on the moisture content. The diffusion coefficients should be determined experimentally. Numerous forms of a mathematical expression to describe the diffusion coefficient are reported in literature [8]. Two mathematical expressions are worked out in the next sections. 10.4.6.2
Expression 1
The diffusion coefficient (D) as a function of the moisture content (W ) and the temperature (T ) is described with the equations ln DW ¼ a1,T
b1,T c1,T þ W
(10:38)
b2,W T
(10:39)
and ln DT ¼ a2,W þ
where a1 , b1 , c1 , a2 , and b2 are product-specific model constants. When the model constants a1 , b1 , and c1 are known at two temperatures (T1 and T2 ), both moisture and temperature
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dependence can be expressed in the following equation, which is in fact a linear interpolation between two points with coordinates (1=T1 , ln DT1,W ) and (1=T2 , ln DT2,W ): ln DT,W ¼
½ln DT2 ,W ln DT1 ,W 1 1 þ ln DT1 ,W 1 1 T T1 T2 T1
(10:40)
So, for a given moisture content ln DT1,W and ln DT2,W can be calculated with Equation 10.38. After that ln DT,W can be calculated at given temperature T with Equation 10.40. For this model six parameters (a1 , b1 , and c1 at two temperatures) have to be obtained by fitting to experimental data. Users have to be aware that extrapolation to temperatures out of the experimental range can lead to unrealistic diffusion coefficients. 10.4.6.3
Expression 2
A good alternative description of the diffusion coefficient has been developed and described in Ref. [9]. In this description, the whole temperature and moisture dependence is fit with only two parameters a and b. The diffusion coefficient is described by the following expression, which is a modification of the expression suggested in Ref. [8] and used for skim milk: b þ cW DH 1 1 DT,W ¼ exp exp 1 þ aW R T 303
(10:41)
where W is the moisture content based on total mass; and a, b, c, and DH are product-specific parameters. To restrict the degrees of freedom of Equation 10.41, but keep getting good fits with various products, the parameters are reduced as b ¼ 38:912 (constant) c ¼ 323:29a bþc a ¼ 16:84 1 b þ 323:39 DH ¼ 1:799 104 bW 0:445 The constants are obtained by fitting data reported by Wijlhuizen et al. [8] for skim milk. For that data set a and b are set to 1. The moisture dependence and the temperature dependence are adapted especially with a and b, respectively. This expression is applied to various food products (not published) and values of a and b are found in the range of 0.6–1.6 and 1.0–1.2, respectively. 10.4.6.4
Determination of Diffusion Coefficient
Diffusion coefficients can be determined in single droplet drying experiments, for example, in an acoustic levitator [17,18]. In that experimental setup, a vertical standing acoustic wave is generated. A drying droplet is levitated within the pressure node of the standing wave. The vertical position is recorded from which the droplet mass can be derived. The droplet contour is recorded with a camera that yields the droplet volume. By comparing the experimental
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T = 70⬚C T = 30⬚C
Diffusion coefficient (m2 s−1)
10−10 10−11 10−12 10−13 10−14 10−15 0
20
40 60 Moisture content (% m/m)
80
100
FIGURE 10.6 Diffusion coefficient of skim-milk powder as a function of temperature and moisture content according to Wijlhuizen et al. [8]. (From Wijlhuizen, A.E., Kerkhof, P.J.A.M., and Bruin, S., Chem. Eng. Sci., 34, 651, 1979.)
results at different temperatures with theoretical model calculations for a drying droplet, the diffusion coefficients can be derived [9]. In Figure 10.6 the diffusion coefficient of skim-milk powder is shown as an example.
10.5 SUBMODELS FOR THERMAL REACTIONS 10.5.1 INTRODUCTION Because food products are heat sensitive, the thermal load during drying is of great importance for the final quality. When submodels for the thermal reactions are available, they can be used in combination with the particle drying model (see Section 10.4). In general, the history of the particles’ temperature and moisture gradients are stored during the simulation of CFD. In that case the submodels can be applied subsequently in the postprocessing step. During the heat treatment of food products (thermization, pasteurization, sterilization) heat-induced reactions such as destruction of food nutrients, inactivation of enzymes, denaturation of proteins, destruction of microorganisms, and formation of new components take place. Most of these reactions can be described by simple nth-order (often first-order) reaction kinetics, where the reaction rate constant is dependent on the temperature according to the Arrhenius relation. In general, such a simple approach cannot be applied for spray drying. The reaction rate constant will strongly change with the dry solids content as a consequence of the change in the mobility of the molecules. Therefore, additional experiments and research are needed to describe the heat-induced reactions. One example of a thermal reaction during spray drying is the formation of insoluble material, which is undesirable especially for instant powders. In the next section we demonstrate how to carry out experiments in order to derive a kinetic model for this reaction during the drying of concentrated milk [19]. This method is also suitable for other food products or other thermal reactions.
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10.5.2 FORMING
OF INSOLUBLE
MATERIAL
The forming of insoluble material during the spray drying of concentrated milk is studied in the previous work [19]. The method and results are briefly described in this section. The mechanism by which insoluble material is formed is not yet fully understood. The current view is that the mechanism involves the unfolding of b-lactoglobulin, followed by aggregation with casein. It appears that other mechanisms also play a role. It is known that high-pressure atomization causes considerable amounts of insoluble material with a relatively high fat content. However, a kinetic model based on quantitative data can be set up, without knowing the exact mechanism. The easiest way to get quantitative data is by doing heating tests. Samples are prepared in a range of moisture contents, placed in a holder with a high area to volume ratio, and heated in a water bath for a certain time and temperature and cooled. Finally, the insolubility index is determined. Such heating tests with milk indicated that concentrates with a moisture content higher than 50% and powders with a moisture content lower than 10% needed several minutes more heating time at a temperature of 958C to form insoluble material. These heating times are much higher than the residence time in a spray dryer (20–40 s). Samples with moisture contents in the range of 10%–50% were difficult to homogenize and difficult to handle in heating tests. Samples with moisture content in the range of 12%–35% already had a high insolubility index directly after preparation without any heat treatment, probably caused by gelation of proteins. Another restriction of the heating tests is that short heating times (<7 s) are difficult to realize. Therefore, additional experiments were carried out on a pilot-scale spray dryer. The feed flow was kept very low with respect to the airflow, so that the air temperature and humidity hardly changed during the drying process. The concentrated milk feed was atomized with a pneumatic nozzle to obtain a large variety of droplet sizes. Experiments were done at air outlet temperatures in the range of 778C–1148C. The powder produced was sieved into three size fractions. The insolubility index of each size fraction was determined. The drying history of the particles was simulated with the drying model, as described in Section 10.4.4, and a CFD simulation is not needed for this purpose. Because the air conditions remain constant during the experiments, a simple simulation of batch drying of a particle in a quantity of air will do. The time that a particle needs to traverse the critical moisture range during drying depends on the particle diameter. So, in fact the variation of particle diameters generates a variation in heating times. A simple kinetic model is assumed: .
. .
Insoluble material is formed during spray drying only when the moisture content is between 10% and 30%. In this range, the rate of formation is independent of the moisture content. The rate of formation exhibits zero-order kinetic behavior with temperature dependency according to Arrhenius.
The rate of formation (rISi ) is described by the equation rISi
Ea 1 1 ¼ k0 exp R T T0
(10:42)
where k0 is the reaction rate constant, Ea the energy of activation (J mol1 ), R the universal gas constant (J mol1 K1 ), T the temperature, and T0 the reference temperature (K).
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10 7
3
Insolubility index (mL)
4
1 2
0.7 0.4
1
0.10 0.07 0.04 20
40
60
80
100
120
140
160
180
Diameter (µm)
FIGURE 10.7 Insolubility index (ISi) versus particle diameter. Experimental results (symbols) and model calculation (lines). Temperatures: 868C (1, *), 968C (2, &), and 1148C (3, ~). Model constants: k0 ¼ 0:054 mL s1 ; Ea ¼ 2:7 105 J mol1 ; T0 ¼ 348 K.
The kinetic constants k0 and Ea were determined by regression analysis. Figure 10.7 shows the experimental results and the model fits.
10.6 SUBMODEL FOR STICKINESS 10.6.1 INTRODUCTION The stickiness of particles plays a major role in the fouling of the equipment and in the agglomeration of colliding particles during spray drying. In general, the stickiness depends on the products’ dry solids composition, the moisture content, and temperature. Agglomeration or fouling takes place when a sticky particle collides with another object (wall or another particle) and forms a liquid bridge that is strong enough to resist mechanical deformations. Various researchers have calculated the critical viscosity for sticking during contact times of a few seconds by applying various models. The critical viscosity is in the range of 106 –108 Pa s. This value has been confirmed experimentally by various investigators [20–25]. At a viscosity higher than the critical value the particles will not stick. The critical viscosity occurs at a temperature that is called the sticky-point temperature. Especially, food products with a high content of carbohydrates are known as sticky products. During the fast spray drying process, carbohydrates do not crystallize, but get in an amorphous state with a liquid-like rubbery structure, which gradually changes to a glassy state. For this type of product, the sticky-point temperature can be related to the glass transition temperature.
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10.6.2 GLASS TRANSITION TEMPERATURE At the glass transition temperature (Tg ) the amorphous material changes from a liquid-like rubbery structure to a glassy state or vice versa. The Tg values of amorphous compounds and food materials are usually experimentally determined by differential scanning calorimetry (DSC), although other methods, such as nuclear magnetic resonance (NMR) can be applied as well [27]. DSC detects a characteristic change in specific heat (DCp ) at Tg . The glass transition temperature (Tg ) values may differ slightly depending on the applied analytical method, and also because of their thermal history. Roos [27,28] determined Tg and DCp for various sugars experimentally. These are given in Table 10.1, together with experimental data TABLE 10.1 Glass Transition Temperatures and Specific Heat Changes for Pure Compounds Compound Water
Mw 18
Pentoses Arabinose Ribose Xylose Hexoses Fructose Fucose Galactose Glucose Mannose Rhamnose Sorbose Disaccharides Lactose Maltose Melibiose Sucrose Trehalose
180 180 180
342 342 342
Alditols Maltitol Sorbitol Xylitol Maltodextrinsa DEb 36 DE 25 DE 20 DE 10 DE 5 Starch a b c
500 (370) 720 900 (504) 1800 (640) 3600 (991)
Tg (8C) Onset
Midpoint
135
DCp ( J=g)
Reference
3+0.5
[27,29]
2 20 6
3 13 14
0.66 0.67 0.66
[27,28] [27,28] [27,28]
5 26 30 31 25 7 19
10 31 38 36 31 0 27
0.75 — 0.50 0.63 0.72 0.69 0.69
[24,27,28] [27,28] [27,28] [24,27,28] [27,28] [27,28] [27,28]
101 87 85 62 100
92 91 67 107
0.45 0.61 0.58 0.60 0.55
[27,28] [27,28] [27,28] [24,27,28] [27,28]
39 9 29
44 4 23
0.56 0.96 1.02
[27,28] [27,28] [27,28]
0.58
[25,29] [25] [25,29] [25,29] [25,29] [25]
100 121 141 160 188 243c
0.45 0.40 0.30
Molecular weight according to manufacturer, effective molecular weight in parenthesis. Dextrose equivalent. Predicted.
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for maltodextrins [25]. Often Tg is reported as midpoint value, but Roos argues that the onset value is more important as most mechanical properties change above the onset value of Tg [28]. A decrease in viscosity is already observed above the onset value of Tg , which is particularly important for carbohydrate materials with respect to stickiness or crystallization. In spray drying, often mixtures of components are dried instead of the pure compounds. The Tg of these mixtures, containing two or more components and water can be estimated with the equation of Couchman and Karasz [25,26]: P wi DCp,i Tg,i Tg ¼ i P (10:43) wi DCp,i i
where wi is the mass fraction of component i, DCp,i the specific heat change of component i at Tg,i , and Tg,i the glass transition temperature of the pure component i. This equation is applied to multicomponent mixture systems. It proved to fit very well for data at higher concentration of solids (>70 m=m%), which means that it can be applied under spray drying conditions [25]. From this equation it can be derived that the presence of moisture decreases the glass transition temperature, as Tg for water is 1358C. Already, at very low moisture contents Tg decreases significantly. As an example, in Figure 10.8, the glass transition temperature of lactose is plotted against the moisture content. For a binary mixture the Couchman–Karasz equation can be rewritten as the simpler Gordon–Taylor equation: Tg ¼
w1 Tg1 þ kgt w2 Tg2 w1 þ kgt w2
(10:44)
DCp2 DCp1
(10:45)
where kgt ¼
The glass transition temperature (Tg ) values of many anhydrous high molecular weight food polymers cannot be experimentally determined as the Tg values of these are usually high, and materials tend to decompose at temperatures below Tg . In that case an estimate has to be made, 110
Temperature Tg (⬚C)
90
70
50
30
10 0
2
4 Moisture content (% m/m)
6
8
FIGURE 10.8 Glass transition temperature of lactose as a function of the moisture content according to the Couchman and Karasz equation. Tg,lactose ¼ 1018C; DCp,lactose ¼ 0.45 J g1; Tg,water ¼ 1358C; DCp,water ¼ 3.0 J g1:
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based on the Tg for homopolymers. It was observed that for glucose polymers, such as maltodextrins, Tg increases with the molecular weight in a similar way as for synthetic polymers. Therefore, Tg can be predicted for high molecular weight compounds according to the Fox and Flory relationship: Kg (10:46) Tg ¼ Tg1 M where Tg1 is the limiting Tg at high molecular weight, Kg a constant, and M the molecular weight. For maltodextrins Tg1 ¼ 243 C and Kg ¼ 52:8 K kg mol1 [25–27]. Also, Tg values for complex food mixtures have been determined experimentally. The Tg values of a number of dry products are listed in Table 10.2. TABLE 10.2 Glass Transition Temperature for Food Products Product Good start
Prosobee
Fish protein hydrolysate
Fish protein hydrolysate FPH 1 Fish protein hydrolysate FHP 2 Fish protein hydrolysate FHP 3 Whey protein hydrolysate LE 80-BT
Whey protein hydrolysate WE 80-M
Whey protein hydrolysate WE 80-BG
Casein hydrolysate CAS 90-STL
Casein hydrolysate CAS 90-GBT
a
Specifications
Tg (8C)
Reference
Lactose=maltodextrin: Carbohydrate 59% Protein 13% Fat 28% Corn syrup solids Carbohydrate 55% Protein 16% Fat 29% Molecular weight average: 10.5 kDa DCp ¼ 0:44 J g1 High molecular weight fraction 89.2% High molecular weight fraction 65.4% High molecular weight fraction 70.4% Molecular weight average: 1.95 kDa Free amino acids 35% Degree of hydrolysis: 41 Molecular weight average: 3 kDa Free amino acids 2% Degree of hydrolysis: 16 Molecular weight average: 0.47 kDa Free amino acids 4% Degree of hydrolysis: 30 Molecular weight average: 0.81 kDa Free amino acids 17% Degree of hydrolysis: 44 Molecular weight average: 0.35 kDa Free amino acids 13% Degree of hydrolysis: 23
74
[32]
82
[32]
71.9
[33]
49.2a 30.1a 42.2a 58.3a
[31] [31] [31] [31]
84.0a
[31]
69.9a
[31]
60.9a
[31]
87.3a
[31]
Tg extrapolated from measurements at various aw in Ref. [31].
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1012 1011
Viscosity (Pa s)
1010 109 108 107 106 105 0
5
10
15
20
25
30
Temperature difference T – Tg (⬚C)
FIGURE 10.9 Viscosity above glass transition temperature according to WLF relation. c1 ¼ 17.44; c2 ¼ 51.6; viscosity at Tg : 1012 Pa s.
The moisture content of a food polymer also determines the water activity. So, the glass transition temperature can also be related to the water activity instead of the water content. It appears that in many cases Tg decreases linearly with increasing water activity [29,30].
10.6.3 RELATION
BETWEEN
GLASS TRANSITION
AND
STICKY-POINT TEMPERATURE
For amorphous products, at temperatures below Tg the viscosity is higher than 1012 Pa s and no viscous flow will occur. At temperatures above Tg the molecular mobility is greatly increased while the viscosity rapidly decreases. The decrease in viscosity above the glass transition temperature and below the melting temperature can be described very well with the WLF relationship [27]: h log hg
!
c1 T T g ¼ c2 þ T T g
(10:47)
where h is the dynamic viscosity at temperature T, hg the viscosity at Tg , and c1 and c2 are constants. The most commonly used values of c1 and c2 are 17.44 and 51.6, respectively. This relation is plotted in Figure 10.9. As stated above (see Section 10.6.1), the critical viscosity for stickiness is 106108 Pa s. As the figure shows, this viscosity occurs at 158C–278C above the glass transition temperature.
10.7 FOULING OF EQUIPMENT The submodel for stickiness (see Section 10.6) can be used to get the fouling pattern of the dryer equipment. During particle tracking of a CFD simulation, when a parcel collides with a wall the sticky state of that particle can be determined. When it is in the sticky state and some other criteria with respect to velocity and angle of impact are satisfied, the particle sticks to the wall. Monitoring the locations where particles stick to the wall gives a good impression of the fouling pattern.
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10.8 INTERPARTICLE COLLISION MODELS 10.8.1 INTRODUCTION In a spray dryer, locations can exist where the particle concentration is so high that collisions between particles are probable. These interparticle collisions can have several consequences such as
