Wind Tunnels: Aerodynamics, Models and Experiments

ENGINEERING TOOLS, TECHNIQUES AND TABLES

WIND TUNNELS: AERODYNAMICS, MODELS AND EXPERIMENTS

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ENGINEERING TOOLS, TECHNIQUES AND TABLES

WIND TUNNELS: AERODYNAMICS, MODELS AND EXPERIMENTS

JUSTIN D. PEREIRA EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2011 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Wind tunnels : aerodynamics, models, and experiments / editors, Justin D. Pereira. p. cm. Includes index. ISBN 978-1-61942-329-9 (eBook) 1. Wind tunnels. I. Pereira, Justin D. TL567.W5W58 2011 629.134'52--dc22 2010047058 Published by Nova Science Publishers, Inc. † New York

CONTENTS vii 

Preface Chapter 1

Chapter 2

Chapter 3

Chapter 4

Design, Execution and Numerical Rebuilding of Shock Wave Boundary Layer Interaction Experiment in a Plasma Wind Tunnel M. Di Clemente, E. Trifoni, A. Martucci, S. Di Benedetto  and M. Marini  The Mainz Vertical Wind Tunnel Facility– A Review of 25 Years of Laboratory Experiments on Cloud Physics and Chemistry Karoline Diehl, Subir K. Mitra, Miklós Szakáll,   Nadine von Blohn, Stephan Borrmann and Hans R. Pruppacher  Modeling and Experimental Study of Variation of Droplet Cloud Characteristics in a Low-Speed Horizontal Icing Wind Tunnel László E. Kollár and Masoud Farzaneh  An Air-Conditioned Wind Tunnel Environment for the Study of Mass and Heat Flux Due to Condensation of Humid Air Akhilesh Tiwari, Pascal Lafon, Alain Kondjoyan and Jean-Pierre Fontaine 

Chapter 5

In-Situ Evaluation for Drag Coefficients of Tree Crowns Akio Koizumi 

Chapter 6

The Pre-X Lifting Body Computational Fluid Dynamics and Wind Tunnel Test Campaign Paolo Baiocco, Sylvain Guedron, Jean Oswald, Marc Dormieux, Emmanuel Cosson, Jean-Pierre Tribot and Alain Bugeau 

Chapter 7 Index

Low-Speed Wind Tunnel: Design and Build S. Brusca, R. Lanzafame and M. Messina 

1 

69 

93 

129 

147 

167 

189  221 

PREFACE This new book presents current research in the study of wind tunnels, including the design, execution and numerical rebuilding of a plasma wind tunnel with the aim to analyze shock wave boundary layer interaction phenomena; the Mainz vertical wind tunnel facility experimenting on cloud physics and chemistry; an air-conditioned wind tunnel environment for the study of mass and heat flux; using wind tunnel studies to evaluate the drag coefficient of the tree crown and Pre-X aerodynamic/aerothermal characterization through computational fluid dynamics and wind tunnels. Chapter 1 - The present chapter reports the design, execution and numerical rebuilding of a plasma wind tunnel experimental campaign with the aim to analyse shock wave boundary layer interaction phenomena in high enthalpy conditions. This particular flow pattern could arise in proximity of a deflected control surface, thus generally causing a separation of the boundary layer and a loss of efficiency of the control surface itself; moreover, high mechanical and thermal loads are generally induced at the flow reattachment over the flap. Therefore, the analysis of this problem is crucial for the design and development of the class of hypersonic re-entry vehicles, considering that, even though it has been widely analyzed in the past, both from an experimental and theoretical point of view, by describing its physical features, only few studies have been carried to analyse the phenomenon in high enthalpy real gas and reacting flow conditions. The activity has been developed by analysing the flow phenomenon of interest in different conditions: i) hypersonic re-entry conditions considering the ESA EXPERT capsule as a workbench, and ii) ground-based facility conditions considering the CIRA Plasma Wind Tunnel “Scirocco”. The aim has been the correlation of the results predicted, by means of a CFD code, and then measured through specific experiments suitably designed, in these two different environments. To this effect, a flight experiment has been designed to be flown on the EXPERT capsule along the re-entry trajectory in order to collect flight data (pressure, temperature and heat flux) on the shock wave boundary layer interaction phenomenon to be used for CFD validation and, additionally, as a reference point for the extrapolation-from-flight methodology developed accordingly. Requirements for the experimental campaign to be performed in the “Scirocco” facility have been derived considering the most critical and interesting points along the EXPERT trajectory. A suitable model, representative of the EXPERT geometry in the zone of interest, i.e. the flap region, has been conceived by defining the main design parameters (nose radius, length, width, flap deflection angle) and an

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experimental campaign has been delineated, the aim being to reproduce on this model the same mechanical and thermal loads experienced ahead and over the EXPERT full- scale flap during the re-entry trajectory. Suitable facility operating conditions have been determined through the developed extrapolation-from-flight methodology; the design and the analysis of shock wave boundary layer interaction phenomenon has been done by focusing the attention mainly to the catalytic effects over the interaction induced by the different behaviour in terms of recombination coefficient of the materials involved in the problem under investigation. Once defined the design loads, the model has been realized and tested in the Plasma Wind Tunnel Scirocco under the selected conditions. The numerical rebuilding, showing a reasonable good level of reproduction, has been also carried out, even though the validation of the entire extrapolation-from-flight and to-flight developed methodology could be completed only after the EXPERT flight currently planned in mid 2011. Chapter 2 - The Mainz vertical wind tunnel is so far a worldwide unique facility to investigate cloud and precipitation elements under conditions close to the real atmosphere. Hydrometeors such as water drops, ice crystals, snow flakes, and graupels are freely suspended at their terminal velocities in a vertical air stream under controlled conditions regarding temperature (between -30°C and +30°C), humidity (up to the level of water saturation), and laminarity (with a residual turbulence level below 0.5%) of the air stream. Cloud processes in warm, cold, and mixed phase clouds have been investigated in the fields of cloud physics and chemistry, aerosol–cloud interactions, and the influence of turbulence. The experiments include the behaviour of cloud and rain drops, ice and snow crystals, snow flakes, graupel grains and hail stones and the simulation of basic cloud processes such as collisional growth, scavenging, heterogeneous drop freezing, riming, and drop-to-particle conversion. Atmospheric processes have been investigated under both laminar and turbulent conditions in order to understand and quantify the influence of turbulence. The results are essential for applications in cloud chemistry models to estimate the atmospheric pathway of trace gases, in cloud and precipitation models to improve the description of the formation of precipitation (growth and melting rates), and in now- and forecasting of precipitation to improve the evaluation of radar and satellite data. Chapter 3 - Variation of the characteristics of aerosol clouds created in icing wind tunnels is studied theoretically and experimentally. The characteristics of interest are the droplet size distribution, liquid water content, temperature, velocity, and air humidity, which are among the most important factors affecting atmospheric icing. Several processes influence the trajectory, velocity, size and temperature of the droplets, such as collision, evaporation and cooling, gravitational settling, and turbulent dispersion. The authors have developed a twodimensional theoretical model that takes these processes into account, and predicts how they influence the changes in the characteristics of the droplet cloud during its movement in the tunnel. The most recent development pays special attention to two of the possible collision outcomes, i.e. coalescence after minor deformation and bounce, together with the transition between them. Indeed, these outcomes are frequent when the relative velocity of the droplets is small, as is the case for a cloud formed after the injection of water droplets in the direction of air flow. An experimental study is also carried out with different thermodynamic parameters at different positions in the test section of the tunnel, which makes it possible to observe the evolution of cloud characteristics under different ambient conditions. The droplet size distribution and liquid water content of the aerosol clouds were measured using an integrated system for icing studies, which comprises two probes for droplet size

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measurements and a hotwire liquid water content sensor. Droplet trajectories were observed using particle image velocimetry. The experimental results are also used to validate the model by comparing them to model predictions. Satisfactory agreement between the experimental and calculated results establishes the applicability of the model to determine the evolution of droplet size distribution and liquid water content in an aerosol cloud in the streamwise direction, together with their vertical variation. Chapter 4 - The development of an artificial ecosystem inside a closed environment is one of the future challenging problems, which is mandatory for the long duration manned space missions like lunar base or mission to Mars. Plants will be essential companion life forms for such space missions, where human habitats must mimic the cycles of life on earth to generate and recycle food, oxygen and water. Thus the optimized growth of higher plants inside the closed environment is required to obtain efficient biological life support systems. The stability and success of such systems lie on the control of the hydrodynamics and on an accurate characterisation of the coupled heat and mass transfer that develop at interfaces (solids, plants,..) within the space habitat. However, very few data can be found on the precise characterization / prediction of the mass transfer at interfaces, and more particularly in space. In most studies the mass flux is deduced from the measured / calculated heat flux by a heat and mass transfer analogy. Hence, the authors have developed a ground based experimental set-up to measure the air flow velocities and concomitant mass transfer on specific geometries under controlled air flow conditions (flow regime, hygrometry, temperature). The final goal is to derive a theoretical model that could help for the prediction of the hydrodynamics and coupled heat/mass transfer on earth, and eventually in reduced gravity. The authors have used a closed-circuit wind tunnel for our experiments, which can produce very laminar to turbulent flows with controlled temperature and hygrometric parameters inside the test cell. The initial experiments have been performed in dry air with an average velocity between 0.5-2.5 m.s-1. The velocity profiles near a clean aluminium flat plate in horizontal or vertical positions have been studied for low Reynolds number flows by hot wire anemometry. The measurements with the horizontal plate showed a boundary layer thickness in agreement with the Blasius’ solutions. Condensation of humid air was induced on an isothermal flat plate, which was cooled by thermoelectricity. The mass transfer on the plate was controlled and recorded with a precise balance. The obtained results are analyzed, and compared to the available data on condensation. Chapter 5 - In order to make a hazard prediction of trees against wind damage, such as stem breakage or uprooting, it is essential to quantitatively estimate the wind force acting on a tree. The drag coefficient of the tree crown, which is necessary to estimate wind force, has been evaluated using wind tunnel studies. Most of the specimens used for wind tunnel studies were dwarf trees, because of the restrictions due to wind tunnel size. However, with regard to the wind-force response, the similarity rule is not applicable to the relationship between dwarf trees and actual-sized trees. In fact, the drag coefficients of small trees were found to be considerably greater than those of actual-sized trees. To estimate the drag coefficients of actual-sized trees accurately and easily, a field test method was developed. Using this method, wind speed and stem deflection were monitored simultaneously. The wind force acting on the tree crown was calculated from the stem deflection; the stem stiffness was evaluated by conducting tree-bending tests. The field tests were conducted on black poplars and a Norway maple; the results showed that the drag coefficients decreased with an increase in wind speed.

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This decrease can be explained mainly by the decrease in the projected area of the crown, because of the swaying movement of the leaves and branches. Although the variation in the drag coefficients was large at low wind speeds because of the swaying behavior of the stem subjected to a variable wind force, the variation at wind speeds above 10 m/s was small. The average drag coefficient for black poplars at a wind speed of 30 m/s was estimated by the curve fitting of a power function to the wind velocity-drag coefficient relationship, and this value was found to be not greater than that of actual-sized conifers previously studied in wind tunnel experiments. These results suggest that the wind permeability of poplar crowns is greater than that of conifer crowns due to the difference in leaf flexibility. Although the drag coefficients in the defoliation season were smaller than those measured in the leaved season at low wind speeds, the difference in drag coefficients became less pronounced at high wind speeds. Chapter 6 - Pre-X was the CNES proposal for demonstrating the maturity of European technology for gliding re-entry spacecraft. The program finished in year 2007 with the end of the phase B and a successful PDR. Then it was stopped with the aim of joining the ESA project IXV. The main goal of this experience is to demonstrate the implementation of reusable thermal protections, perform aero thermo dynamics experiments and efficiency of a suitable guidance navigation and control system. The attitude control is realised by elevons and reaction thrusters overall the hypersonic flight, with a functional and experimental objective. This paper presents the Pre-X aerodynamic / aerothermal characterisation through computational fluid dynamics and wind tunnels tests performed during the phases A and B of the programme. The tests permitted to cover the Mach range from 0.8 to 14 and to investigate the main effects of aerodynamic and aerothermal phenomena. In the preceding phases the aerodynamic shape and centring had been defined. The logic and main results of this activity are presented in this paper. Chapter 7 - In this chapter the authors deal with a procedure for the design and build of a low speed wind tunnel for airfoil aerodynamic analyses and micro wind turbine studies. The designed closed-circuit wind tunnel has a test chamber with a square cross section (500 mm x 500 mm) with a design average flow velocity of about 30 m/s along its axis. The designed wind tunnel has a square test chamber, two diffusers (one adjacent to the test section and one adjacent to the fan to slow the flow), four corners (with turning vanes) to guide the flow around the 90° corners, an axial fan to guarantee the mass flow rate and balance any pressure loss throughout the circuit, a settling chamber with a honeycomb (to eliminate any transverse flow), a series of ever-finer mesh screens (to reduce turbulence) and a nozzle to accelerate flow and provide constant velocity over the whole test chamber. The pressure losses of single components were evaluated as well as the global pressure loss (the sum of pressure losses of all the single components). Once the pressure losses were evaluated, the axial fan was chosen to guarantee the design’s volumetric flow, balance pressure losses and above all maximise its performance. The definitive dimensions of the wind tunnel are 10.49 m x 3.65 m. Once the design targets were defined, the test chamber dimensions, maximum wind speed and Reynolds numbers were calculated. At the end of the design process, the wind tunnel energy consumption was estimated and on-design and off-design performance was evaluated to obtain the wind tunnel circuit characteristics for a defined velocity range (0 – 50 m/s).

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The best circuit and axial fan matches were performed in both the open and closed test section configurations. Using the matching procedure between the fan and wind tunnel’s mechanical characteristics (global pressure loss as a function of wind velocity), the fan operating parameters were set up for optimum energy conservation.

In: Wind Tunnels: Aerodynamics, Models and Experiments ISBN 978-1-61209-204-1 © 2011 Nova Science Publishers, Inc. Editor: Justin D. Pereira

Chapter 1

DESIGN, EXECUTION AND NUMERICAL REBUILDING OF SHOCK WAVE BOUNDARY LAYER INTERACTION EXPERIMENT IN A PLASMA WIND TUNNEL M. Di Clemente1, E. Trifoni1, A. Martucci1, S. Di Benedetto1 and M. Marini1 1

Italian Aerospace Research Centre Via Maiorise – 81043 Capua (CE), Italy

ABSTRACT The present chapter reports the design, execution and numerical rebuilding of a plasma wind tunnel experimental campaign with the aim to analyse shock wave boundary layer interaction phenomena in high enthalpy conditions. This particular flow pattern could arise in proximity of a deflected control surface, thus generally causing a separation of the boundary layer and a loss of efficiency of the control surface itself; moreover, high mechanical and thermal loads are generally induced at the flow reattachment over the flap. Therefore, the analysis of this problem is crucial for the design and development of the class of hypersonic re-entry vehicles, considering that, even though it has been widely analyzed in the past, both from an experimental and theoretical point of view, by describing its physical features, only few studies have been carried to analyse the phenomenon in high enthalpy real gas and reacting flow conditions. The activity has been developed by analysing the flow phenomenon of interest in different conditions: i) hypersonic re-entry conditions considering the ESA EXPERT capsule as a workbench, and ii) ground-based facility conditions considering the CIRA Plasma Wind Tunnel “Scirocco”. The aim has been the correlation of the results predicted, by means of a CFD code, and then measured through specific experiments suitably designed, in these two different environments. To this effect, a flight experiment has been designed to be flown on the EXPERT capsule along the re-entry trajectory in order to collect flight data (pressure, temperature 1

Phone : +39 0823 623577, Fax : +39 0823 623700 Email: [email protected], [email protected], [email protected], [email protected], [email protected]

2

M. Di Clemente, E. Trifoni, A. Martucci et al. and heat flux) on the shock wave boundary layer interaction phenomenon to be used for CFD validation and, additionally, as a reference point for the extrapolation-from-flight methodology developed accordingly. Requirements for the experimental campaign to be performed in the “Scirocco” facility have been derived considering the most critical and interesting points along the EXPERT trajectory. A suitable model, representative of the EXPERT geometry in the zone of interest, i.e. the flap region, has been conceived by defining the main design parameters (nose radius, length, width, flap deflection angle) and an experimental campaign has been delineated, the aim being to reproduce on this model the same mechanical and thermal loads experienced ahead and over the EXPERT full- scale flap during the re-entry trajectory. Suitable facility operating conditions have been determined through the developed extrapolation-from-flight methodology; the design and the analysis of shock wave boundary layer interaction phenomenon has been done by focusing the attention mainly to the catalytic effects over the interaction induced by the different behaviour in terms of recombination coefficient of the materials involved in the problem under investigation. Once defined the design loads, the model has been realized and tested in the Plasma Wind Tunnel Scirocco under the selected conditions. The numerical rebuilding, showing a reasonable good level of reproduction, has been also carried out, even though the validation of the entire extrapolation-from-flight and to-flight developed methodology could be completed only after the EXPERT flight currently planned in mid 2011.

1. INTRODUCTION The high cost of access to space is the main limitation to scientific research and space commercialization, and for this reason all the countries in Europe are thinking how design advanced spacecrafts in order to achieve low launch costs in the near future (Ref. [4],[12]). Spacecrafts like the US Space Shuttle Orbiter represent the first generation of reusable launch systems but several system studies have been conducted during the 80’s to investigate possible future concepts for the next generation of RLVs. In the frame of the ESA-FESTIP Program in late 90’s, system concept studies were carried out and an extensive investigation of a wide range of RLV concepts (more than 10 configurations) was performed (ref. [37]). In the following decade several programmes, at European and national level, were launched to promote the development of some of the identified enabling technologies required for the future generation of reusable space transportation systems that shall be safer and less expensive with respect to the US Space Shuttle. Enabling technologies for such vehicles and derived systems must be inherently reliable, functionally redundant, wherever practical and designed to minimize or eliminate catastrophic failure modes. Reliability could be improved through performance margin that translates to robust design, and this presupposes the maturation of some specific macro-technologies: •

•

Re-entry heating. the aerospace vehicles have to handle the typical large thermal loads encountered during re-entry to Earth from LEO, due to the necessity of reducing the vehicle speed before landing; Hypersonic flight navigation. the future space vehicles will have to fly for large part of their mission to speed much greater that the speed of the sound, and will have to maneuver safely in such conditions;

Design, Execution and Numerical Rebuilding of Shock Wave… •

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Reusability. the most important characteristic from the operational point of view is the tendency to be as much like current airplanes thus translating into the reusability concept.

Starting from the necessity of a proper level of maturity of these high level technologies, some guidelines and critical points to be developed at lower level, in order to match the particular requirements for the RLV design, were identified by past space systems and technological programs. Among the others, can be identified: • • • •

Configuration Design Extrapolation to Flight Transition Prediction Control Surface Aerothermodynamics

It is clear that many other technological areas are being involved and ask for other significant developments (propulsion, flight mechanics, stability and control, guide and navigation, configuration optimization, etc.) but, in any case, to develop the future space transportation system a considerable work should be devoted to the aeroshape definition in order to improve performance, flyability and controllability, propulsion integration, heat load reduction, stage separation, coupling between forebody aeroelasticity and propulsion system, coupling between viscous drag and heat loads. The aerodynamic efficiency (E=CL/CD) should be increased since they will experiment large part of flight at moderate altitude at high Mach number, strongly asking for more efficient aerodynamic design. Also the transition process from laminar to turbulent boundary layer should be predicted with greater accuracy since it plays an important role in the design of aerospace planes thermal protection system, and the currently available theoretical know-how (i.e. the stability theory) could not yet guarantee for a safe and reliable transition prediction (Ref. [18], [19], [20]). Among the others, the study of aerodynamic efficiency of control surfaces plays a role of primary importance (Ref. [17]). In fact, the necessity of manoeuvrability and high cross-range during ascent or re-entry phase requires the capacity to increase control surfaces aerodynamic efficiency whose analysis is strictly connected to the study of shock wave boundary layer interaction (SWBLI) occurring around them. The increase of knowledge must regard, especially in the SWBLI phenomenon in high enthalpy conditions, the prediction, with a good level of approximation, of its behaviour in flight conditions. In a classical approach, the design of space vehicles (e.g. the Space Shuttle) is based heavily upon experimental data although, due to the inherent limitations of similarity laws, ground based facilities cannot simulate completely the physics of flows experienced by such vehicles during re-entry. To overcome these limitations different strategies could be adopted: in US data obtained from in-flight experiments, particularly with the X-series vehicles, have been used to complement the test data obtained from ground-based facilities; on the other hand, since the times of Hermes Program, Europe chose to complement the knowledge available from the cold wind tunnels, which are not able to model the high-temperature and real gas effects typical for higher speeds and altitudes, by means of high enthalpy or hot-flow facilities. ESA, therefore, supported the updated of existing cold flow wind tunnels, and also the construction of facilities with new capabilities, as for example the PWT Scirocco of

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CIRA, to investigate the heat loads and gas surface interactions on materials and large size structures (ref. [10], [38]). In any case, the prediction of hypersonic flows, both for the complexity of the required physical modelling and for the impossibility to duplicate in wind tunnels real flight conditions due to the high energy required, is still one of the main problem related to the development of the new class of space vehicles. Moreover, high efficiency space vehicles require complex investigations because of the large contribution of the viscous effects to the aerodynamic forces and heating, while the effects of the gas modelling are important since the small blunt nose, necessary to increase the aerodynamic efficiency, does not shield the rest of the vehicle, thus implying the presence of large chemical effects on most of the vehicle surface. The main data sources for the aerothermodynamic design of a space vehicle are computational fluid dynamics, wind tunnel tests and flight experiments, generally on simplified geometries: •

•

•

wind tunnel tests are important because they allow carrying on “controlled” simulations and therefore to better understanding the flow-physics phenomena; although ground-based facilities provide fundamental information for flight, no one facility can provide all of the aerothermodynamic information required for the design of a vehicle. As today it is well recognised, duplication of all flight characteristic parameters (Mach, Reynolds, Damkhöler, state of the gas) in a ground facility is not possible, particularly flight Reynolds number and high enthalpy effects are critical and difficult to be reproduced at ground; flight experiments data represent the “truth” to be predicted, i.e. they show the real performance of the vehicle in representative conditions and, therefore, they are unique for vehicle qualification although they are quite costly, require considerable time and have uncertain repeatability and accuracy. Many phenomena can not be directly measured and de-coupling of effects is not always an easy task; numerical simulations still play a fundamental role in the study of aerothermodynamics; moreover, the highest confidence in any ground-based or flight data set occurs when the results obtained with CFD are in agreement with them, the socalled extrapolation-to-flight technique. Even if today CFD is contributing significantly to the aerothermodynamic design of advanced vehicles, it still suffers from lack of physical modelling, robustness and accuracy of the mathematical algorithms, grid generation flexibility and hardware limitations; thus good windtunnel and flight data are still necessary for validation and/or calibration of CFD codes used to predict surface and flow field variables for the full-scale vehicle at reentry flight conditions.

The best approach for improving confidence in aerothermodynamic design tools, from a computational and ground-based experimental point of view, is to validate those tools and design approaches with respect to flight experiments. As matter of fact, although in the last years Europe has dedicated significant effort to improve the quality and reliability of aerothermodynamic predictions, due to their key importance in the design and development of any hypersonic space vehicle, and a considerable effort has been devoted to the realization of ground based plasma facilities and development of advanced numerical tools with the state

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of the art physical model, in-flight experimentation is still needed to validate the computational codes and to establish meaningful and reliable ground-to-flight extrapolation methodology. Above Mach 10, where in particular high-temperature effects become dominant, CFD represents the only prediction tool, and therefore the appropriate validation of numerical codes is a great concern. Generally it is achieved, by comparing data measured in hightemperature facilities with those obtained by numerical prediction and in many cases a numerical approach is used to define the experimental test cases and for the interpretation of the measured data. CFD codes are subsequently being used for flight simulations above Mach 10 even if this ‘extrapolation method’ assumes that the physical models enabling good results for the simulation of the experimental test cases, provide good results also for free flight. Therefore, free-flight data are required to remove any doubt about the validity and accuracy of the CFD predictions, and to confirm the extrapolation methodology as well. The main argument for the in-flight experimentation is therefore the need for realistic and combined loads levels which are representative for the operational environment of a RLV. Such tests must be performed complementarily to on-ground testing for validating critical enabling technologies of the reference RLV concept. The analysis of this phenomenology is complicated by the fact that, in hypersonic regime, scaling laws have not yet been found. Plasma Wind Tunnels, which allow the same energy levels of the real flight, are in fact characterized by the test chamber flow rather dissociated conditions, and this has a large influence on the flow-field around the test article, while cold hypersonic wind tunnels, where the simulation is focused on the duplication of Mach and Reynolds numbers, permit only to reproduce the classical aerodynamic forces and the related coefficients even though with strong limitations. The influence of real gas effects and viscous interaction effects on control flap efficiency and heating is one of the main aerothermodynamic issues for the next generation RLV design, together with the qualification testing of the thermal protection system in ground-based facility and the consequent extrapolation to flight for experimental results. In order to assess these issues, a numerical approach has been followed to define a windtunnel experimental campaign on a representative model to reproduce the in-flight expected values of mechanical and thermal loads acting on a typical control device, in interpreting the measured data and finally for the extrapolation to the flight conditions of the experimental results, as the local conditions in the wind tunnel facility only partially duplicate those in flight. Moreover, a flight experiment whose results could be used as point of reference for such phenomena has been also designed. As matter of fact, aerothermodynamic design issues, as the analysis of flap efficiency for control and navigation, has been addressed using advanced numerical codes, ground-based facilities and flight testing. Following the previous considerations, it arises the need to develop an extrapolationfrom-flight and to-flight methodology able to combine and mutually validate the flight and ground data on the problem of interest. Even though the prediction of mechanical and thermal loads acting on the control surfaces of hypersonic vehicles is crucial for the design of their aerodynamic shapes and thermal protection system, at the moment the lack of hypersonic flight data that can serve as a point of reference for the validation process, makes it impossible, especially for some of the most challenging hypersonic problems.

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Figure 1. Extrapolation from flight and to flight procedure.

The issue of an extrapolation-to-flight methodology for high enthalpy flow must be in the light of a progressive building up of confidence in the design of a space vehicle. The development of such methodology, whose rationale is shown in Figure 1, has been carried out referring to the ESA EXPERT capsule (ref. [40]), which has the indubitable advantage to be a simple geometry, conceived as an experimental test-bed for in-flight experimentation and designed to avoid degradation and flow contamination. In order to develop the methodology and to extrapolate plasma facility results to real flight conditions, it is necessary, first of all, to characterize by means of CFD simulations the flight conditions in the flap region and design a flight experiment in order to instrument the vehicle and to collect flight data during the reentry mission, to be used for the post-flight analysis to validate the entire procedure. On the other hand it is necessary to design, perform and numerically rebuild a number of experimental tests in a plasma wind tunnel facility that can be representative of the flight conditions with respect to the SWBLI phenomenon over the flap. Finally, plasma wind tunnel results must be correlated, by means of the relevant parameters of the interaction as viscous interaction parameter and rarefaction parameter, with those predicted (and then measured) during the flight, the goal being to understand the test conditions necessary to reproduce (simultaneously or separately) the mechanical (pressure) and thermal (heat flux, temperature) loads acting on the control surface device.

1.1. EXPERT Capsule The development of the extrapolation to flight methodology has been carried out referring to the ESA EXPERT capsule whose in-flight test program focuses on a generic capsule-like configuration designed in such a way to enhance the most interesting aerothermodynamic phenomena of a typical re-entry vehicle performing a sub-orbital ballistic hypersonic flight. The main objective of the project is to collect in-flight data on the most critical aerothermodynamic phenomena via dedicated classical and advanced flight test measurement assemblies (i.e. EXPERT Scientific Payloads), and this in order to improve the knowledge about the differences between ground experiments and real flight conditions; each particular phenomenon related with the high energy re-entry mission (gas-surface interaction, induced and natural laminar-to-turbulence transition, real gas effects on shock wave boundary

D Design, Execuution and Num merical Rebuilding of Shocck Wave…

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laayer interactio on, shock layyer chemistryy) has been separately annalyzed, and a specific exxperiment hass been designned for each of them in the t frame of the Technicaal Research Prrogram related d to the capsuule developmeent. The scienttific data will then be used to validate sttate-of-the-art numerical toools for aeroothermodynam mic applicationns and grounnd-to-flight exxtrapolation prrocedures (Reef. [39]). Each Paylo oad will be qualified q accoording to thee relevant Asssembly, Integgration and V Verification Plan; P in paraallel a numbber of experrimental activvities in thee field of aeerothermodynamics are carrried out to acqquire all necessary pre-flight information on specific phhenomena allo owing for an optimized posst-flight phasee. Among the others, speciaal attention haas been given n to the Shockk Wave / Bounndary Layer Innteraction pheenomenon whhose effects onn the open flapps are being innvestigated with w two differeent Scientific Payloads, i.e. Payload 6, thhrough instrum mentation of flaps f and caviities with maiinly classical sensors, and Payload 7, thhrough the chaaracterization of the boundaary layer apprroaching the flap, f whose deevelopment haas been carried d out in the fraame of the preesent research activity. The referen nce geometry of the EXPER RT capsule iss a body of revvolution with an ellipsecllothoid-cone two-dimensionnal longitudinaal profile cut by b 4 planes annd equipped with w 4 fixed oppen flaps. Thhe elliptical nose n has a raadius of 600 mm at the stagnation s point and an ecccentricity of 2.5. The fixedd flaps have a deflection off 20 deg, a widdth of 400 mm m and an xaxxis projected length l of 300 mm m (see Figurre 2).

Fiigure 2. EXPER RT capsule.

2 MATHEM 2. MATICAL MODEL t developm ment of the The analyssis of shock wave boundaary layer inteeraction, for the exxtrapolation-frrom-flight meethodology, haas been carriedd out considerring the CIRA A numerical coode H3NS which w allowss for the aeerothermodynaamic analysiss over compplex threediimensional geeometries andd suitable to simulate s com mpressible flow w at high entthalpy (ref. [228]). One of the main charactteristics of hyppersonic flows is that, due to the high temperatures exxperienced beehind the bow w shock, thee gas cannot be considereed as a perffect gas as coommonly assu umed for low w speed flows;; air moleculees at temperattures higher thhan 800 K sttart to vibratee and for tempperatures arouund 1500 K the t dissociatioon of oxygen molecules beegin whereas for higher tem mperature also nitrogen moolecules dissoociate. The moodelling of hiigh temperatu ure phenomeena is quite difficult beccause of the difference among a the

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M. Di Clemente, E. Trifoni, A. Martucci et al.

characteristic time of fluid-dynamics and that of chemical reactions and vibration. This situation generally leads to the thermochemical non-equilibrium. In fact, there are many problems in high-speed gas dynamics where the gas doesn’t reach the equilibrium state; a typical example is the flow across a shock wave, where the pressure and temperature are rapidly increased within the shock front. By the time equilibrium properties have been approached, the fluid element has moved a certain distance downstream of the shock front. The modelling of these phenomena cannot be limited to a calculation of equilibrium conditions at a certain temperature and pressure, but a number of equations must be added to the classical Navier-Stokes formulation, one for each vibrating or dissociated species. In the code considered for numerical computations, governing equations have been discretized using a finite volume technique with a centred formulation over structured multiblock meshes. This approach is particularly suitable to the integral form of the equations; in fact, in a first order approximation, it is simply obtained by integrating the equations for each cell and considering the variables constant inside each volume. The integral formulation ensures that mass, momentum and energy are conserved at the discrete level. Suitable models have to be taken into account to define the thermodynamics, the transport coefficients and turbulent variables as reported in detail in Appendix 1. The inviscid fluxes at cell interfaces are computed using a Finite Difference Splitting (FDS) Riemann solver, which is especially suitable for high speed problems (Ref.[3]). This method solves for every mesh interval the one-dimensional Riemann problem for discontinuous neighboring states (the states at both sides of the cell face). The second order approximation for FDS is obtained by means of a higher order ENO (Essentially Non Oscillatory) reconstruction of interface values. The viscous fluxes are calculated by central differencing, i.e. computing the gradients of flow variables at cell interfaces by means of Gauss theorem. Time integration is performed by using an Euler forward scheme with a semi-implicit pre conditioner based on the derivative of the source chemical and vibrational terms.

3. PWT SCIROCCO EXPERIMENT PRELIMINARY DESIGN A number of experiments to be performed in the CIRA Plasma Wind Tunnel “Scirocco”, representative of the capsule flight conditions with respect to the shock wave boundary layer interaction phenomenon occurring around the 20 deg flap, has been designed: PWT driving conditions, model configuration and attitude and model instrumentation have been defined, by means of a massive CFD activity performed by using the CIRA code H3NS. These experiments have been designed in order to allow for the duplication of characteristic parameters (viscous interaction parameter, rarefaction parameter, reference pressure and heat flux) of the interaction to reproduce on a full-scale flap model both pressure and heat flux levels estimated in critical re-entry flight conditions. The final goal has been to develop an extrapolation-to-flight methodology for such flows since the full duplication of flow characteristic numbers (Mach, Reynolds, Damkhöler) and state of the gas is not feasible in ground facilities. A parametric analysis of the facility operating conditions and model characteristic dimensions (nose radius, length, flap dimensions, etc.) has been carried out in order to define the operating conditions and experimental set up that permit a simultaneous reproduction of

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9

mechanical and thermal loads acting on flap in flight conditions over the selected model. The rest of the activity has been devoted mainly to the choice of the different protection materials, its equipment (sensors distribution) and the experimental tests at the selected flow conditions. The final model configuration reproduces the full-scale EXPERT 20 deg flap, mounted on a holder composed by a flat plate with a rounded leading edge (made of copper and actively cooled) and lateral edges. The flap has been realized in C-SiC, which is the same material foreseen for the realization of the EXPERT capsule flap, whereas for the flat plate it has been used Haynes 25 whose main thermo-mechanical characteristics are quite similar to PM1000 which is the material foreseen on the capsule. The effects of catalysis jump, due to the coupling of different materials, have been analysed by considering the available recombination coefficients for the materials of interest, or modelling the different parts as fully or not catalytic.

3.1. PWT “Scirocco” Facility Description The CIRA Plasma Wind Tunnel “Scirocco” is devoted to aerothermodynamic tests on components of aerospace vehicles; its primary mission is to simulate (in full scale) the thermo-fluid-dynamic conditions suffered by the Thermal Protection System (TPS) of space vehicles re-entering the Earth atmosphere. “Scirocco” is a very large size facility, whose hypersonic jet has a diameter size up to 2 m when impacts the test article and reaches Mach number values up to 11. The jet is then collected by a long diffuser (50 m) and cooled by an heat exchanger. Seventy MW electrical power is used to heat the compressed air that expands along a convergent-divergent conical nozzle. Four different nozzle exit diameters are available: 0.9, 1.15, 1.35 and 1.95 m, respectively named C, D, E and F. The overall performance of “Scirocco” in terms of reservoir conditions is the following: total pressure (P0) varies from 1 to 17 bar and total enthalpy (H0) varies from 2.5 to 45 MJ/kg. Facility theoretical performance map in terms of reservoir conditions produced by the arc heater is shown in Figure 3. Lower enthalpy values are obtained by using a plenum chamber between the arc heater column exit and the nozzle inlet convergent part, which allows transverse injection of high pressure ambient air to reduce the flow total enthalpy.

Figure 3. Arc heater theoretical performance map.

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M. Di Clemente, E. Trifoni, A. Martucci et al.

The energetic heart of the facility is the segmented constricted arc heater, a column with a maximum length of 5.5 m and a bore diameter of 0.11 m. At the extremities of this column there are the cathode and the anode between which the electrical arc is generated. A power supply feeds the electrical DC power to the electrodes for the discharge. A compressed air supply distributes dry compressed air to the various segments of the arc heater column, being able to supply a mass flow rate ranging from 0.1 to 3.5 kg/s, heated up to 10000 K. The last important subsystem of “Scirocco” is the vacuum system, which generates the vacuum conditions in test chamber required by each test. The system consists of ejectors that make use of high pressure water steam as motor fluid (30 bar and 250 °C). The achievement of the operating conditions (P0, H0) in test chamber is assured by the presence, before the insertion of the model, of a 100mm-diameter hemi-spherical calibration probe made of copper, cooled, that measures radial profiles of stagnation pressure (Ps) and stagnation heat flux (Qs) at a section 0.375 m downstream of the conical nozzle exit section, by means of high precision pressure transducers and Gardon-Gage heat flux sensors, respectively. Facility regulations (mass flow, current) are tuned in order to measure on the calibration probe a certain couple of values (Ps, Qs) which correspond to the desired set point in terms of the couple (P0, H0).

3.2. Facility Performance Evaluation The definition of a representative experiment in the CIRA Plasma Wind Tunnel “Scirocco” has been done by considering the most interesting points of the EXPERT reference trajectory, i.e. point P1, that is the point characterized by the highest stagnation point heat flux, and point P2, characterized by high heat flux and a relatively low pressure, potentially critical for passive/active oxidation transition of the C-SiC, which is the material of the nose and the flaps of the capsule. A preliminary analysis of PWT Scirocco capabilities for the duplication of SWBLI flows has been carried out, the aim being to understand what it is possible to reproduce in this plasma facility in terms of the characteristic parameters of the interaction as pressure and heat flux (peak values and reference values, upstream of the separation), viscous interaction parameter,

(χ

L

)

(

)

≈ M ∞3 / Re ∞L , rarefaction parameter, VL ≈ M ∞ / Re ∞L , separation

length experienced during the flight that has been preliminary predicted through CFD simulations. Even if in this phase preliminary flight values have been used, it was important only to develop an extrapolation from flight methodology that allowed to set the facility operating parameters necessary to duplicate assigned flight values, that have been then updated through three-dimensional non equilibrium computations. Starting from the nominal operating envelope of PWT facility, considering the conical nozzle D (length 3.1 m from the throat section, exit diameter 1.15 m) and assuming fully laminar flows, a certain number of numerical simulations has been performed, basing on the currently explored region of the envelope, where qualification and validation tests have been already executed in order to have a clear idea of what can be simulated in terms of SWBLI interesting parameters inside the facility; in particular, the effects of total pressure (at low, medium and high total enthalpy) and total enthalpy (at low, medium and high total pressure) have been investigated. Then, additional computations have been performed in order to

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duplicate the estimated flight values of the interesting parameters of the interaction around the body-flap. The complete CFD test matrix, for this preliminary phase, is reported in Table 1 in terms of total pressure (P0) and total enthalpy (H0), while in Figure 4 these points have been shown inside the PWT Scirocco theoretical envelope. Table 1. CFD Matrix for preliminary computations P0 (bar) 2.45 2.45 2.40 4.70 5.20 5.20 7.90 7.90 7.90 13.00 12.00 10.00 7.90 10.00

PWT-1 PWT-2 PWT-3 PWT-4 PWT-5 PWT-6 PWT-72 PWT-8 PWT-9 PWT-10 PWT-111 PWT-121 PWT-13 PWT-14

H0 (MJ/kg) 11.90 15.00 18.80 10.40 15.00 18.80 11.00 15.00 18.80 11.00 15.00 15.00 17.90 11.00

45

40

35

PWT Operating Envelope Preliminary Computations

H0, MJ/kg

30

Additional Computations

25

20

15

10

5

0 0

2

4

6

8

10

12

14

16

18

P0, bar

Figure 4. PWT envelope and operating conditions.

For each of the considered points, the PWT nozzle flow has been simulated in the hypothesis of fully laminar thermo-chemical non equilibrium flow, then the centreline conditions at X = Xnozzle exit + 0.15m (= 3.25 m) have been taken as free stream conditions to perform the simulation of flow around the model (located preliminarily 0.15 m downstream of the nozzle exit section). 2 For these conditions an angle of attack of the model equal to 10 deg has been also considered

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M. Di Clemente, E. Trifoni, A. Martucci et al.

This CFD-based procedure was also successfully applied to previous experiments design, where it was clearly shown that the same test chamber flow is predicted by means of the uncoupled (single simulation of nozzle flow with geometrical extension to the model stagnation point section) as done in this work and coupled (complete simulation of flow through PWT facility, with test chamber details) simulations, thus assessing the accuracy of the overall experimental test design. The preliminary geometry, which can be considered representative of the EXPERT geometry around the body-flap region (scale 1:2), was a 0.60 m long blunted flat plate with a 0.15 m long flap forming a 20 deg angle with the plane and a cylindrical nose whose radius was equal to 0.25 m as schematically reported in Figure 5.

Figure 5. Preliminary shape of the test article.

All the computations have been performed in non-equilibrium fully laminar conditions, assuming a fully catalytic wall with a fixed temperature equal to 300 K or the radiative equilibrium condition, considering the symmetry plane of the model with a two dimensional approach. For numerical reasons a horizontal plate has been considered at the flap trailing edge; the effect of this plate, that could fix the reattachment at the end of the flap, has been analyzed for the conditions PWT-7 and PWT-3 of Table 1, that are the conditions, respectively, characterized by the highest and the lowest Reynolds number. This effect seems to be negligible (see Figure 6 and Figure 7) being the reattachment mechanism not “driven” by the expansion at the flap trailing edge, but it occurs on the flap “far enough” from its trailing edge. From the computed results of the present analysis, and from considerations about the complexity of baseflow (useless) prediction, it can be concluded that the geometry model with the flat plate extension behind the flap can be always employed for present simulations. mach 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 -0.5

1.2

Y (m)

1

0.8

0.6

0.4

0.3

Y (m)

1.4

0.2

0.1 0.5

0.6

0.7

0.8

0.9

1

X (m)

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

X (m)

Figure 6. Mach contours for the condition PWT-7 with base flow.

Design, Execution and Numerical Rebuilding of Shock Wave…

200000

200000 180000

1000

140000

800

120000 600

100000 80000

400

60000

Pressure (Pa)

160000

Heat Flux (W/m2)

Pressure (Pa)

1000

1200

180000

Pressure Pressure - Base Heat Flux Heat Flux - Base

800

140000 120000

600

100000 80000

400

40000

200

160000

Pressure Pressure - Base Heat Flux Heat Flux - Base

60000 40000

200

20000 0

0.4

0.6

20000

0

0.8

Heat Flux (W/m2)

1200

13

0

0.4

0.6

X (m)

0

0.8

X (m)

Figure 7. Pressure and Heat Flux distribution for PWT-7 (left) and PWT-3 (right).

The pressure distribution along the wall for all the computations is reported in Figure 8 (left); after the rapid expansion starting from the stagnation point, a quasi-constant pressure region is observed along the flat plate up to the zone of shock wave boundary layer interaction induced by the presence of the flap; at the separation location there is a pressure jump due to the separation shock, then pressure reaches a plateau in the recirculation region and a peak after the reattachment on the flap followed by a sharp expansion at the end of the flap. The overall distribution is typical of such SWBLI interaction. Pressure levels on the model are mainly influenced by the value of the total pressure being negligible the effect of the total enthalpy; therefore, it is clear that higher values of the pressure in the interaction zone can be achieved with higher values of the total pressure (or additionally giving an incidence to the model in the test chamber). In the same figure (right) it is reported the wall heat flux distribution for the same computations; in this case both the total pressure and total enthalpy influence wall heat transfer, that increases as these two variables increase (following roughly the dependency upon the product

p 0 H 0 ).

8000

1E+06

Pressure (Pa)

4000

P0=2.45 P0=2.45 P0=2.40 P0=4.70 P0=5.20 P0=5.20 P0=7.90 P0=7.90 P0=7.90

800000

Heat Flux (W/m2)

H0=11.90 H0=15.00 H0=18.80 H0=10.40 H0=15.00 H0=18.80 H0=11.00 H0=15.00 H0=18.80

6000

H0=11.90 H0=15.00 H0=18.80 H0=10.40 H0=15.00 H0=18.80 H0=11.00 H0=15.00 H0=18.80

600000

P0=2.45 P0=2.45 P0=2.40 P0=4.70 P0=5.20 P0=5.20 P0=7.90 P0=7.90 P0=7.90

400000

2000 200000

0

0

0.2

0.4

X (m)

0.6

0.8

0

0

0.2

0.4

0.6

0.8

X (m)

Figure 8. Wall pressure (left) and heat flux (right) distributions in PWT operating conditions.

In the recirculation region there is a decrease of the heat flux, typical of fully laminar interactions, followed by an increase on the flap and a peak just immediately after the reattachment point, where boundary layer thickness reaches the minimum value.

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M. Di Clemente, E. Trifoni, A. Martucci et al.

For some of the computations, the effect of the wall temperature has been estimated by considering the radiative equilibrium condition. The results of these computations are reported in Figure 9 for pressure (left) and heat flux (right) wall distribution. As general trend, with the radiative equilibrium temperature at the wall, the separation bubble is larger (except for the condition PWT-3 where the effect is negligible) and the peak loads over the flap (both thermal and mechanical) are lower than those predicted with a fixed wall temperature equal to 300K. This is due to the higher temperatures in the boundary layer in the case of the radiative equilibrium condition, and then to the lower values of density causing an increase of the boundary layer thickness; the upstream propagation of pressure disturbances is enhanced in the case of radiative equilibrium and, consequently, an early separation is predicted. The effects on mechanical loads is a reduction of ∼4% with the condition of equilibrium radiative wall whereas is ∼3% for thermal loads as reported also in Table 2. It can be concluded that in these conditions surface temperature has only a small effect on thermal and mechanical loads acting on the flap.

1600

Pressure (Pa)

1200 1000

400000 H0=11.90 H0=11.90 H0=18.80 H0=18.80 H0=15.00 H0=15.00 H0=11.00 H0=11.00 H0=18.80 H0=18.80

P0=2.45 P0=2.45 P0=2.40 P0=2.40 P0=5.20 P0=5.20 P0=7.90 P0=7.90 P0=7.90 P0=7.90

T=300K T=Tradeq T=300K T=Tradeq T=300K T=Tradeq T=300K T=Tradeq T=300K T=Tradeq

300000

Heat Flux (W/m2)

1400

800 600 400

H0=11.90 P0=2.45 H0=11.90 P0=2.45 H0=18.80 P0=2.40 H0=18.80 P0=2.40 H0=15.00 P0=5.20 H0=15.00 P0=5.20 H0=11.00 P0=7.90 H0=11.00 P0=7.90 H0=18.80 P0=7.90 H0=18.80 P0=7.90

T=300K T=Tradeq T=300K T=Tradeq T=300K T=Tradeq T=300K T=Tradeq T=300K T=Tradeq

200000

100000

200 0 0.2

0.4

0.6

0 0.2

0.8

0.4

X (m)

0.6

0.8

X (m)

Figure 9. Twall effects on wall pressure (left) and heat flux (right) distributions.

Table 2. Tw effects: comparison of the peak values on the flap Tw=300K

PWT – 1 PWT – 3 PWT – 5 PWT – 7 PWT – 9

Ppk (Pa) 331.7 328.8 680.4 1093.7 949.0

Tw=Trad.eq. qpk (kW/m2) 78.8 131.6 171.2 146.9 293.2

Ppk (Pa) 306.5 328.7 639.8 1054.3 907.2

qpk (kW/m2) 72.9 129.7 167.0 142.8 286.5

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15

3.3. Definition of PWT Model The wide amount of CFD results obtained in different PWT conditions has permitted the development of the extrapolation-from-flight procedure: it allows to determine the experimental test conditions (P0, H0 and model attitude) able to duplicate the representative mechanical and thermal loads ahead and over the flap. However, in order to give the final requirements for the detailed model design and then for the execution of the tests, it has been necessary to consider also different aspects of the problem, not only the aerothermodynamic ones. A detailed numerical analysis has been carried out to analyse the effects of geometric variation of the model on the flow variables, in particular, the effects of the nose radius, the flap dimension and the model’s finite span have been considered. Sensitivity analysis has been carried out considering the PWT operating condition characterized by a reservoir enthalpy H0=15MJ/kg and a reservoir pressure P0=10 bar, being this condition the one determined for the duplication of the point P1 flight conditions over the model as it will be described hereinafter.

3.3.1. Nose Radius Computations with the radiative equilibrium wall assumption have shown that temperature in the nose region could reach 2000 K. If there will be the possibility to have an active cooling system (at least in the nose region) the size of the nose could be decreased in order to not exceed the model weight limit for the “Scirocco” Model Support System (MSS). A sensitivity analysis to the nose radius has been then carried out for one of the selected operating conditions inside the PWT operating envelope, by considering three different models with the same length of the plate ahead the flap and three different nose radii, equal to 0.25 m (the first hypothesis), 0.1 m and 0.05 m; it has been found that the influence of nose radius is small in terms of mechanical loads (see Figure 10, left) even if a slight decreases of about 5% is predicted in the reference and peak values whereas, for what concerns the thermal loads (see Figure 10, right ), a slight increase of the values in front of the flap and a small decrease of the peak values is predicted as also reported in Table 3. H0=15 MJ/kg P0=10 bar AoA=12 deg

8000

H0=15 MJ/kg P0=10 bar AoA=12 deg

1.5E+06

Heat Flux (W/m2)

Pressure (Pa)

6000 Rnose = 25 cm Rnose = 10 cm Rnose = 5 cm

4000

Rnose = 25 cm Rnose = 10 cm Rnose = 5 cm

1E+06

500000 2000

0

0.2

0.4

0.6

0.8

0

X (m)

Figure 10. Effects of nose radius on wall pressure and heat flux.

0.2

0.4

X (m)

0.6

0.8

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M. Di Clemente, E. Trifoni, A. Martucci et al.

Table 3. Nose radius effects: mechanical and thermal loads ahead and over the flap Rnose (m) 0.25 0.10 0.05

Pref (Pa) 1024.91 1002.02 890.92

Qref (kW/m2) 120.85 152.36 167.18

Ppk (Pa) 2226.34 2095.86 2004.07

qpk (kW/m2) 266.34 252.26 239.16

The reduction of the nose radius causes a decrease of the separated region mainly due to the movement towards the flap hinge line of the separation point whereas the reattachment point is located more or less in the same position for all the analyzed configurations (see Figure 11).

H0=15 MJ/kg P0=10 bar AoA=12 deg

Skin Friction Coefficient

0.03

Rnose = 25 cm Rnose = 10 cm Rnose = 5 cm

0.02

0.01

0

0

0.2

0.4

0.6

0.8

X (m)

Figure 11. Nose radius effects: skin friction distribution.

From this analysis it results that the model with the nose radius equal to 0.1m seems to be the best solution for the model configuration, also considering the fact that a lower value of the radius could make difficult the handling and positioning of model instrumentation whereas the model with the biggest value of the nose radius could result in a too heavy model difficult to sustain during the test execution with the MSS.

3.3.2. Flap Dimensions Another variation that has been considered with respect to the preliminarily selected model has been done by considering the full scale flap dimensions, thus exploring the possibility to test in PWT “Scirocco” the actual EXPERT open flap before the flight, whose overall dimensions are 0.30 m in length and 0.40 m in width. The effect of this variation has been examined with respect to the model with the nose radius of 0.10 m, considering the same total length of the previous one since the extension of the flat plate has been decreased from 0.35 m to 0.20 m. The results are shown in Figure 12; considering the full scale EXPERT flap the size of the separation bubble decreases and the thermal and mechanical loads over the flap increase. The effects in terms of wall pressure are evident (Ppk increases of ∼24%) whereas are modest in terms of heat flux (qpk increases of ∼5%).

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H0=15 MJ/kg P0=10 bar AoA=12 deg 8000

1200

Flap 1:2

1000

800

pressure Flap 1:1 pressure Flap 1:2 tot. wall flux Flap 1:1 tot. wall flux Flap 1:2 Geometry

4000

600

400

2

Flap 1:1

Heat Flux [kW/m ]

Pressure [Pa]

6000

200

2000

0

0.2

0.4

0.6

0.8

1

0

X [m]

Figure 12. Effects of flap dimensions.

3.4. Final Configuration and Materials The final configuration of the model, whose characteristic dimensions are Rnose = 0.10 m, Lplate = 0.20 m (the flap hinge is located at X=0.30m starting from the nose), Lflap = 0.30 m (projection on the X-axis), corresponding to the full scale 1:1 flap and flap deflection angle = 20 deg is shown in Figure 13.

MATERIALS Nose : TBD

0.4

Plate : PM1000 Flap : C-SiC 0.3

Y (m)

Lplate = 0.20 m

Lflap = 0.30 m (scale 1:1)

0.2

δflap = 20 deg

0.1

R nose = 0.10 m 0

-0.1 0

0.1

0.2

0.3

0.4

0.5

0.6

X (m)

Figure 13. Final model configuration.

The final geometrical configuration of the model to be tested in the plasma wind tunnel “Scirocco” is a trade-off between the aerothermodynamic requirements necessary to reproduce the flight characteristic parameters of the interaction in PWT conditions, and the thermo-mechanical design issues that have taken under consideration also different aspects of the problem. The model reproduces the EXPERT capsule flap (scale 1:1) characterized by 20 deg deflection angle; it is mounted on an holder with a flat plate ahead the flap with rounded leading and lateral edges. In Figure 14 it is reported a schematic representation of the model. To be consistent with the EXPERT capsule, the model will be built by using as much as possible the same materials to manufacture its different parts: the leading edge is a GLIDCOP AL-15 copper cylinder with an active cooling system; the upper part is covered by a flat plate of PM1000 equipped with pressure taps, thermocouples and combined heat flux/pressure

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M. Di Clemente, E. Trifoni, A. Martucci et al.

sensors; the flap is covered by a 4mm thick plate of C-SiC with a deflection angle of 20 deg with respect to the flat plate, and it is equipped with pressure taps and thermocouples. The lateral rounded panels, the entire lower panel and the parts below the PM1000 flat plate will be realized in PROMASIL 1100; the wedge underlying the C-SiC flap will be realized in amorphous carbon. For what concerns the dimensions of the model, the cylinder leading edge has a radius of 100mm and a length of 400mm, the flat plate is 400m wide and 200mm long, the flap is 400mm wide and 300mm long. All the lateral edges are rounded with a radius of 50mm in order to avoid localized over heating, whereas the flap plate has a radius of curvature at the lateral edges equal to 4mm (i.e. its thickness). The model will be installed on the PWT Model Support System (MMS) by means of a proper interface that consists of a commercial steel circular beam built with AISI 316L; the interface is covered by proper thermal insulator of PROMASIL 1100 to avoid any critical solicitation due to the plasma interaction with the model surface. Such a covering has a cylindrical shape for the proper alignment of the upper and lower parts of the test article with the MSS body surface. It is realised to avoid the presence of gaps between the surfaces and the possibility of any peak heating occurrence.

Figure 14. Model for PWT tests.

4. EXTRAPOLATION FROM FLIGHT PROCEDURE The definition of representative experiments in PWT has been done by considering the most interesting points of the EXPERT reference trajectory: point P1 (M∞=13.40, h=37Km), characterized by the highest stagnation point heat flux, and point P2 (M∞=18, h=50Km) characterized by high heat flux and a relatively low pressure, potentially critical for passive/active oxidation transition of the C-SiC.

4.1. Facility Operating Conditions In par. 0, requirements for the execution of the PWT test campaign will be shown: according to the extrapolation from flight procedure, those requirements must be duplicated

Design, Execution and Numerical Rebuilding of Shock Wave…

19

inside the facility on the representative model that has been defined and dimensioned. To this purpose, it is necessary to define the facility operating conditions and model positioning and attitude within the test chamber to achieve the goal. The wide amount of CFD results obtained in different operating conditions has permitted the development of the extrapolation-from-flight procedure, in such a way to determine the experimental test conditions (P0, H0 and model angle of attack) that allow for the duplication of the representative mechanical and thermal loads ahead and over the flap of the model. For each of the computations carried out in PWT conditions, considering the effect of facility operating conditions, of the angle of attack of the model, wall temperature, radius of the nose and length of the flap, different variables of interest have been analyzed: • •

Boundary layer edge variables at the separation location: M, Re, V and ρ Reference values at the separation location: χ, V, Pref and qref

The comparison between the characteristic SWBLI parameters estimated in flight conditions and the results obtained in PWT for the selected test conditions, is shown, in terms of reference pressure (Pref) and heat flux (qref), in Figure 15 and Figure 16, respectively. For the range of trajectory around the maximum stagnation point heat flux (Point P1, H0∼13.2 MJ/kg), it seems not possible to duplicate the reference values of pressure and heat flux which instead could be well enough duplicated for points at higher enthalpy, that it clearly means at higher altitudes (Point P2, H0∼18 MJ/Kg, h∼50 Km). 2.50E+05

2.00E+05

CFD Flight 2D Qref Flight 2D Qref Flight 3D Point P1 Point P2 Qref - PWT Qref - PWT Additional Runs

Qref (W/m2)

1.50E+05

1.00E+05

5.00E+04

0.00E+00 0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

1.40E+07

1.60E+07

1.80E+07

2.00E+07

H0 (J/Kg)

Figure 15. Comparison between qw ahead the flap in flight and PWT conditions. 1.00E+05

CFD Flight 2D Pref - FLIGHT 2D Pref FLIGHT 3D Point P1 Point P2 Pref - PW T Pref - PW T Additional Runs

Pref (Pa)

1.00E+04

1.00E+03

1.00E+02

1.00E+01 8.00E+06

1.00E+07

1.20E+07

1.40E+07

1.60E+07

1.80E+07

2.00E+07

H0 (J/Kg)

Figure 16. Comparison between Pw ahead the flap in flight and PWT conditions.

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M. Di Clemente, E. Trifoni, A. Martucci et al.

As it is clear from the comparison between the estimated reference values in flight conditions and the computed values on the selected model in PWT conditions, there is still a difference in the range of trajectory around the point with the maximum stagnation point heat flux (a factor ∼10 for the pressure, ∼1.5 for the heat flux), but the “Scirocco” facility seems to be able to duplicate the reference values (Pref and qref) at an higher value of the altitude (h∼50 Km, M∼18).

4.1.1. Pressure and Heat Flux Reference Values In Figure 17 it is reported the variation of Pref as function of the reservoir pressure P0; as it is expected the dependence is linear, and it has been found that the reference pressure is slightly affected by the reservoir enthalpy. The best approximation (obtained by a least square method) is reported in Equation 2.3 1200 1000

Pref [Pa]

800 600 Pref Eq. 25

400 200 0 0.00

2.00

4.00

6.00

8.00 P0 [bar]

10.00

12.00

14.00

Figure 17. Pref variation as function of P0.

Pref = 4.44H 0 + 51.81P0 − 38.24

(1)

The variation of the reference heat flux (for a fixed wall temperature equal to 300 K) is reported in Figure 18; in this case it has been found that the reference heat flux is a linear function of the parameter

p0 H 0 ; the best approximation is reported in Equation 2. 50000 45000 40000

2

q ref [W/m ]

35000 30000 25000 20000

Qref

15000

Eq. 26

10000 5000 0 10.00

15.00

20.00

25.00

30.00 (P0)

Figure 18. qref variation as function of 3

35.00 1/2

40.00

45.00

50.00

55.00

60.00

H0

P0 H 0 .

In all the curve-fits reported in the present paragraph the following units are used: H0 in MJ/kg and P0 in bar, whereas the results are expressed in Pa and W/m2 respectively for pressure and heat flux (both reference and peak values).

Design, Execution and Numerical Rebuilding of Shock Wave… q ref = 791 .54 P0 H 0 + 2443 .5

21 (2)

In Figure 19 and Figure 20 are reported, respectively, the iso-lines of reference pressure and reference heat flux inside the PWT envelope. 45 40

SCIROCCO-PWT Envelope Map Numerical Computations

H0 (MJ/kg)

35 30 25

Pref

20 15 10 5 0 0

5

10

15

P0 (bar)

20

25

Figure 19. Iso-Pref lines inside the PWT envelope. 45 40

SCIROCCO-PWT Envelope Map Numerical Computations

H0 (MJ/kg)

35 30 25 20

qref

15 10 5 0 0

5

10

P0 (bar)

15

20

25

Figure 20. Iso-qref lines inside the PWT envelope.

4.1.2. Pressure and Heat Flux Peak Values The same procedure described in the previous paragraph has been repeated for the peak values of pressure and heat flux reported, for all the performed computations, in Figure 21 and Figure 22. In Figure 21 it is reported the variation of Ppeak as function of the reservoir pressure P0; the best approximation in terms of reservoir pressure and enthalpy is reported in Equation 3.

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M. Di Clemente, E. Trifoni, A. Martucci et al.

2500

Ppeak [Pa]

2000

1500

1000

Ppeak Eq. 29

500

0 0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

P0 [bar]

Figure 21. Ppeak variation as function of P0. Ppeak = 175.91P0 + 8.2711H 0 − 3.3385 P0 H 0 − 90.476

(3)

The variation of the peak value of heat flux (for a fixed wall temperature equal to 300 K) is reported in Figure 22; in this case it has been found that the reference heat flux is a linear function of the parameter

p0 H 0 ; the best approximation is reported in Equation 4.

250000

2

qpeak [W/m ]

200000

150000 Qpeak

100000

Eq. 30 50000

0 10.00

15.00

20.00

25.00

30.00 (P0)

Figure 22. qpeak variation as function of

q peak = 4529.9 P0 H 0 − 34262

35.00 1/2

40.00

45.00

50.00

55.00

60.00

H0

P0 H 0 4

(4)

In Figure 23 and Figure 24 it is reported, respectively, the variation inside the PWT envelope of the peak values of pressure and heat flux.

Design, Execution and Numerical Rebuilding of Shock Wave…

23

45 40

SCIROCCO-PWT Envelope Map Numerical Computations

H0 (MJ/kg)

35 30 25 20

ppeak

15 10 5 0 0

5

10

P0 (bar)

15

20

25

Figure 23. Iso-Ppeak lines inside the PWT envelope.

45 40

SCIROCCO-PWT Envelope Map Numerical Computations

H0 (MJ/kg)

35 30

qpeak

25 20 15 10 5 0 0

5

10

P0 (bar)

15

20

25

Figure 24. Iso-qpeak lines inside the PWT envelope.

4.1.3. Angle of Attack The reported curve-fits allow to determine the values of reference and peak values of pressure and heat flux on the model starting from the reservoir conditions of the PWT facility; these relationships refer to the case of the model attitude α=0 deg. In order to consider also the effect of the angle of attack on these parameters, it is possible to take into account the conditions reported in Table 1 with α≠0 deg, and to determine the ratios of pref, qref, ppeak and qpeak with respect to the case of α=0 deg. The ratios, which have been considered to be independent from the reservoir conditions, have been expressed as linear function of the angle of attack; they are reported in Equations 5,6, 7 and 8, respectively for the reference and peak values of pressure and heat flux: Rp ref =

pref |α ≠ 0°

Rp peak =

p peak |α ≠0°

pref |α =0°

p peak |α =0°

= 0.0842 α + 1

(5)

= 0.0641 α + 1

(6)

24

M. Di Clemente, E. Trifoni, A. Martucci et al. Rqref =

qref |α ≠0°

Rq peak =

q peak |α ≠ 0°

qref |α =0°

q peak |α = 0°

= 0.0483α + 1

(7)

= 0.0382 α + 1

(8)

4.2. Definition of the Experimental Conditions The analysis of shock wave boundary layer interaction in flight conditions, along the EXPERT capsule re-entry trajectory, has been done in order to derive the requirements for the design of the experimental campaign to be performed in the CIRA PWT Scirocco (ref. [32]). In particular, two characteristics points along the EXPERT reference trajectory have been taken into account: • Point P1 (M∞=13.4, h=37km) that is the point when the capsule experiences the highest stagnation point heat flux along the re-entry; • Point P2 (M∞=18, h=50km) that is a high altitude point potentially critical for the passive/active oxidation of the C-SiC, which is the material used of the nose cap and the flap, characterized by high heat flux and a relatively low pressure. The requirements for the design of the experimental campaign have been determined considering three-dimensional numerical computations performed along the re-entry trajectory in thermo-chemical non-equilibrium conditions (ref. [34]). In Figure 25 wall heat flux contours over the capsule surface are shown; wall temperature is fixed over the nose and the PM1000 cone (extracted from a thermal analysis of the TPS) whereas it has been considered in radiative equilibrium conditions over the flaps. It is evident, by the skin-friction pattern, the highly three-dimensional separation of the boundary layer ahead the flap and the consequent reattachment. In Figure 26 heat flux and pressure distribution along the symmetry plane of the capsule for the point P1 is shown whereas in Figure 27 the same plot for point P2 is shown.

Figure 25. Heat flux over the EXPERT capsule: M∞=13.99, AoA=0 deg.

Design, Execution and Numerical Rebuilding of Shock Wave…

25

Figure 26. Point P1 heat flux and pressure distribution.

Figure 27. Point P2 heat flux and pressure distribution.

According to the precious results, requirements for the PWT experimental campaign are extracted in the following Table 4: Table 4. PWT experiment requirements condition Target P1 Target P2

Variable Pflap (Pa) Qflap (kW/m2) Pref (Pa) Qref (kW/m2)

Flight Estimation 19573.7 250.0 511.9 80.8

In order to determine the facility operating conditions that guarantee the achievement of a certain value of the couple (Pref,qref) or (Ppeak,qpeak) it is necessary to solve, respectively the system of Equations 1, 2, 3, and 4 in terms of P0 and H0. As already said these relationships refer to the case of α=0 deg but, if the solution the couple (H0,P0) falls outside of the operating envelope of the facility is it necessary also to take into account the possibility to have an incidence of the model different from zero and then to consider also Equations 5, 6,

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M. Di Clemente, E. Trifoni, A. Martucci et al.

7 and 8. In particular, for point P1 the operating conditions of the facility have been determined in order to duplicate the peak values of pressure and heat flux over the flap estimated in flight conditions whereas for the point P2 the reference values ahead of the flap of pressure and heat flux have been considered as target of the experimental test.

4.2.1. Point P1-PWT Concerning point P1 (M∞=13.4, h=37Km), the selected PWT condition is H0=15 MJ/Kg and P0=10 bar, and the model is set with a 12 deg angle of attack (the flap is in the wind side part), as graphically shown in Figure 28. As it will be clarified hereinafter, for this point, it is not possible to duplicate inside the PWT facility the peak value of pressure over the flap therefore the operating conditions have been determined to duplicate only the peak value of heat flux with a degradation of the test objectives. 45 SCIROCCO-PWT Envelope Map Numerical Computations Iso-qpeak=250 kW/m2 P1-PWT

40

H0 (MJ/kg

35 30 25 20 15 10 5 0 0

5

10

15

P0 (bar)

20

25

Figure 28. Definition of point P1-PWT.

4.2.2. Point P2-PWT Regarding the duplication of the reference values of pressure and heat flux estimated at the trajectory point P2 (M∞=18, h=50Km), the following PWT test condition has been determined: H0=11 MJ/kg, P0=10 bar, α=5 deg, as graphically shown in Figure 29. 45 SCIROCCO-PWT Envelope Map Numerical Computations Iso-Pref=511.9 Pa Iso-qref=80.8 kW/m2 Point P2-PWT

40

H0 (MJ/kg

35 30 25 20 15 10 5 0 0

Figure 29. Definition of point P2-PWT.

5

10

15

P0 (bar)

20

25

Design, Execution and Numerical Rebuilding of Shock Wave…

27

5. MODEL THERMO-STRUCTURAL DESIGN Test article conceived in the preliminary phase consists of a steel frame covered by thermal protection panels: the leading edge is a water cooled copper alloy cylinder, the upper part of the model is covered by a metallic panel of PM1000 whereas the flap is covered by a C/SiC panel and it is installed with a deflection angle equal to 20 deg with respect the PM1000 panel. Hence, the model is mounted on the facility MSS by means of a proper interface. Such a model is conceived to be applied for several types of tests. All the components of the test article are easily removable, in order to be replaced by others, with different characteristics (in terms for example of surface properties as catalysis and emissivity). Each part of the model has been analyzed through thermal and structural analysis to define thickness and insulator to keep temperature in the internal part of the model below certain limits.

5.1. Flat Plate The flat plate in front of the flap has an overall thickness equal to 25 mm: it is formed by an upper panel made of PM1000, whose thickness is 2.5 mm (as on the EXPERT capsule), and a lower insulator made of PROMASIL of 22.5 mm thickness. For what concerns the mechanical interface between PM1000 panel and the insulator, different hypotheses have been analyzed in the design phase: the best solution has been identified considering the possibility of PM1000 panel to expand without any constrains with the insulator and by avoiding only the detachment of the panel from the model. In this way it has been possible to reduce the generation of critical thermal stresses on the surface and, therefore, to preserve the structural integrity of the panel under high heat flux conditions.

5.1.1. Thermal Analysis To avoid the establishing of the reported dangerous stress field, the lesson learned is to let the PM1000 expand freely with respect to the underlying PROMASIL insulator; flat plate has been conceived as a 2.5 mm thick PM1000 panel jointed to the 22.5 mm thick PROMASIL 1100 panel through six PM1000 M3 bolts free to move; the sandwich was bonded to the metal frame by a 0.5 mm layer of high temperature commercial silicone rubber. Two dimensional ANSYS transient thermo-structural analyses have been performed to assess this concept design considering the most stressed section. The PM1000 panel was sketched as a semi-infinite panel at an initial temperature equal to 323 K, subjected, on the upper face, to the heat flux distribution numerically determined (fully catalytic wall, total hemispherical emissivity equal to 0.85), and adiabatic on the lower face; an unsteady thermal simulation has been carried out assuming a test duration equal to 150 sec. Temperature distribution, after 150 sec, in the PM1000 and PROMASIL panels is reported in Figure 30.

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M. Di Clemente, E. Trifoni, A. Martucci et al.

Figure 30. PM1000 panel thermal transient.

In Figure 31 the temperature transient is shown for different points of the model according to the following legenda: TEMP_2 is PM1000 leading edge surface temperature; TEMP_3 is PM1000 trailing edge surface temperature; TEMP_4 is PM1000-PROMASIL leading edge interface temperature; TEMP_5 is PM1000-PROMASIL trailing edge interface temperature; TEMP_6 is PROMASIL-frame leading edge interface temperature; TEMP_7 is PROMASIL-frame trailing edge interface temperature

Figure 31. PM1000 panel thermal transient.

At the end of the test PM1000 panel maximum temperature (TEMP_2) is lower than 1500 K, that is its melting temperature, while promasil-frame maximum interface temperature (TEMP_6) is lower than 500 K that is suitable with the maximum service temperature of the model internal components.

5.1.2. Structural Analysis With the last thermal transient analysis as input, a two-dimensional structural transient analysis was performed on the PM1000 panel considered unbound. At the end of the test the longitudinal free expansions of the panel, indifferently at the upper surface and at the

Design, Execution and Numerical Rebuilding of Shock Wave…

29

PM1000-PROMASIL interface, result in the order of ± 2 mm, while the vertical movements are negligible; consequently, longitudinal and transversal gaps of 2 mm were imposed to the borders of the panel flat plate in order to avoid thermal stress occurrence.

Figure 32. PM1000 panel longitudinal expansion field at t=150 sec.

5.2. Deflected Flap The flap has been conceived as a closed flap with the same dimensions of the flaps installed on the EXPERT capsule. In order to identify the best solution, different concepts have been analyzed through thermal analysis: • • •

massive flap made of SiC, directly connected to the metal frame; self-sustaining flap, a 4 mm thick SiC structure, directly connected to the frame; composite flap, a 4 mm thick C-SiC panel supported by an insulating wedge having a trapezoidal section.

The final concept has been selected and analyzed more in detail through thermal and structural analysis. The plate is made of Keraman C/SiC panel bonded through 0.15 mm layer of ceramic adhesive to an amorphous Carbon wedge which is connected to the frame.

5.2.1. Thermal Analysis Thermal analysis has been carried out under two dimensional hypothesis considering the most loaded section of the model; temperature distribution, after 150 sec, is shown in Figure 33 whereas thermal transient is shown in Figure 34.

30

M. Di Clemente, E. Trifoni, A. Martucci et al.

Figure 33. Keraman C/SiC and amorphous Carbon wedge temperature field at t=150 sec.

Figure 34. Keraman C/SiC and amorphous Carbon wedge temperature transient.

In Figure 34: TEMP_2 is leading edge C/SiC surface temperature; TEMP_3 is leading edge C/SiC-Amorphous Carbon interface temperature; TEMP_4 is leading edge Amorphous Carbon-frame interface temperature; TEMP_5 is trailing edge C/SiC surface temperature; TEMP_6 is trailing edge C/SiC-Amorphous Carbon interface temperature; TEMP_7 is trailing edge Amorphous Carbon -frame interface temperature. TEMP 8 is Amorphous Carbon-frame interface temperature, 110 mm downstream the leading edge At the end of the test amorphous Carbon-frame interface temperature attains about 800 K at the leading edge (TEMP_4), about 400 K at 110 mm downstream the leading edge (TEMP_8) and remains practically cold at the trailing edge (TEMP_7); the highest Keraman C/SiC temperature (TEMP_5) exceeds 85% of temperature transient, not achieving radiative equilibrium. Being the frame designed as a cold structure, it is necessary to limit its temperature to at least 420 K; finally, the wedge leading edge will be 110 mm cantilever respect to the frame and the frame area between the wedge leading edge and 110 mm downstream will be thermally protected by PROMASIL insulating material at least 10 mm thick. Two-dimensional ANSYS transient thermal analysis carried out in this condition

Design, Execution and Numerical Rebuilding of Shock Wave…

31

confirmed the protective effect of the additional PROMASIL insulator with respect to the metallic frame.

5.2.2. Structural Analysis With the last thermal transient analysis as input, a two dimensional structural transient analysis was performed and the conservative hypothesis of C/SiC-amorphous Carbon perfect interface has been made. At the end of the test, after 150 sec, von Mises stress fields in C/SiC and amorphous Carbon result both lower than their ultimate strength (see Figure 35); in detail, stress field in the bonding area is in the order of 10 MPa, that is critical for the ceramic adhesive but anyway of the same order of magnitude of the flexural strength reported (10÷15 MPa).

Figure 35. Keraman C/SiC von Mises stresses at t=150 sec.

The maximum longitudinal and vertical expansions of the panel resulted respectively in the order of +0.3/-0.4 mm and +0.2/-0.4 mm as shown in

Figure 36. Keraman C/SiC flap longitudinal (left) and vertical (right) expansion field x20 at t=150s.

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M. Di Clemente, E. Trifoni, A. Martucci et al.

5.3. Lower and Lateral Panels These parts of the test article, shown in Figure 37, are realised with PROMASIL. The lower panel has rectangular shape of 399 mm wide, 480.5 mm long and 25 mm thickness. It is stuck by a proper thermal resistant stick to the lower part of the frame, in order to protect the frame itself and the instrumentation installed on the test article from the very high thermal fluxes coming from the surrounding plasma during the development of the test run. The thickness of 25 mm of the lower panel has been evaluated in a conservative way by considering the highest value of the heat flux generated during the test runs. Thus, such a thickness is larger than necessary, because it is considered that the surface is not directly exposed to the plasma, but it is in the shadow region of the test article where the aerothermal loads are lower. Some little gaps of 0.5 mm between the lower panel and laterals are maintained on both the sides of the panel in order to permit the free thermal expansion of the material during the test. Such gaps will be full of proper thermal resistant stick such as silicones, in order to avoid any critical penetration of hot plasma fluid into the model.

Figure 37. Lower and lateral panels.

The laterals are also stuck to the frame of the test article. They are sized to resist to the high heat flux transferred to the model due to its geometry. In fact, at the extremities of the PM1000 panel, the heat flux value increases due to the finite size of the model. In order to reduce the aerothermal load at the extremities, a radius of 50 mm has been considered and such lateral panels of the model are sized to resist to that heat flux value. Panels have a length of 480.5 mm, a flat part of 100 mm and two radiuses at the top and the bottom of 50 mm for each one. By this way, the frame of the model and its instrumentation are well protected by thermal loads coming from the plasma.

5.4. Water Cooled Leading Edge This component, shown in Figure 38, is the most critical of the test article. It was chosen, during the design phase, to realize this component with copper in order to avoid any contamination of the boundary layer in the downstream part of the model, where the shock wave boundary layer interaction experiment takes place. The high temperatures foreseen on this part make it necessary to consider also a water cooling system. The geometry of the leading edge is very complex. It consists of inner and outer parts of copper. About the outer

Design, Execution and Numerical Rebuilding of Shock Wave…

33

part its thickness is 5 mm. It is cylindrical for the main length of the body, with a diameter of 200 mm and a length of 400 mm. At the extremities the body has two shoulders to guarantee the geometrical connection to the main cylindrical body surface. On this component, very high values of heat flux are foreseen.

Figure 38. Water cooled leading edge.

The inner part of the leading edge is a massive solid of copper with the same geometrical components of the outer part. Its overall length is 490 mm, and the diameter of the cylindrical body is 182 mm. On its back, a flat surface of copper with a thickness of 4 mm allows to fix the body to the outer part of the leading edge, by means of proper welding. Thus between these parts a cooling jacket is realised, with a thickness of 4 mm and cooling water is introduced into the jacket, then it flows through the cooled jacket along the length of the leading edge body, from a shoulder to the other and viceversa, and it is driven by means of proper copper dams which are properly realized on the surface of the inner body.

5.5. Model Frame The frame is a cage made by a plurality of 30 x 30 x 3 mm L-beams AISI 316L (see Figure 39). The ends of the horizontal anglers are welded together at 45°, in order to obtain a continue surface without steps. On the upper and lower vertical parts of the front cage anglers, 8 holes M13 will be applied at a horizontal and vertical distance of 16.5 mm from the frame edge.

Figure 39. Model frame.

34

M. Di Clemente, E. Trifoni, A. Martucci et al.

At the back of the cage, two vertical beams are welded to the upper and lower anglers to bolt the MSS interface. Such an interface will be installed by proper bolts and nuts M12. In fact, the two vertical beams and anglers at the back part of the cage will be drilled for the realization of the 8 holes with a diameter of 13 mm. Thus, 8 nuts M12 will be welded at the inside part of the beams and anglers, in order to permit the screwing of the corresponding bolts of the interface. The frame can be outlined in a conservative way as a structure of just 8 cantilever Lbeams (I =1,40×10-8 m4, ℓ=0.456 m) loaded on the edge by a transverse load F of 1979 N at 20° angle of attack. Under these assumptions the structure constitutes a system of 8 stiffeners acting in parallel, each cantilever having the same deflection of the others and being loaded by 1/8 of the transverse load F; the frame edge deflection results of 2.9×10-3 m while the normal stress at the joint is 174 MPa, the yield safety factor is 1.18.

5.6. Final Material Selection As described in the present section, the material selected for the realization of the flat plate is PM1000 that is the same material foreseen for the TPS of the EXPERT capsule. In any case, due to some problem in the provision of this material, whose production has been suspended during the development of the design phase, it has been replaced by Haynes 25 which has been selected due to the fact that its thermo-mechanical properties are very similar to those of PM1000. The same thermal and structural analysis have been carried out considering this material and they provided practically the same results already presented.

6. PWT SCIROCCO EXPERIMENT DETAILED DESIGN Once the model dimensions and the materials have been defined, and the test operating conditions allowing for the duplication ahead and over the flap of the mechanical and thermal loads estimated along the EXPERT re-entry flight trajectory have been defined accordingly to the developed extrapolation-from-flight procedure, detailed two- and three- dimensional numerical analyses have been carried out to analyse, mainly, the effects of the finite spanwise dimension of the model itself.

6.1. Computational Grids Computational grids for the simulations of the flow over the model have been generated by means of the grid generator commercial software package ICEMCFD®. Numerical simulations have been made by neglecting the presence of the MMS of the facility, thus avoiding to simulate the base flow region. However, it has been verified with a 2D simulation that this assumption has no significant impact on the predicted values over the model, and results will be shown in Sec. 0. An O-grid topology turning around the body and projected on the symmetry and outlet planes has been built around the model, while a quarter O-grid topology has been created on the flap lateral part. The block decomposition is shown in Figure 40. Due to the symmetry of the flow (inside the PWT test chamber) with respect to the

Design, Execution and Numerical Rebuilding of Shock Wave…

35

longitudinal symmetry plane of the model, the computational grid has been generated only for a half of the model. It is composed of hexahedral elements obtained with a block-structured approach; the total number of blocks is 62 and the total number of cells is about 1.5 millions for the finest grid level.

Figure 40. Block decomposition.

Figure 41. Computational grid.

Computational grid over model surface and in the symmetry and outlet planes is shown in Figure 41. The mesh has been stretched in correspondence of the flap hinge line (i.e. the interface between Haynes 25 and C-SiC, where flow separation takes place), and normally to the model surfaces in order to properly predict the different boundary layers developing around the geometric configuration. The minimum spacing normal to the wall for the fine grid level is 5.9⋅10-6 m at the geometrical stagnation point (with a correspondent aspect ratio of about 1200), and is 4⋅10-6 m at the hinge line (with an aspect ratio of 2.5). A factor 8 exists between the number of cells of the fine grid level and that of the coarse grid level: each edge of the coarse grid level has been split in two parts to obtain the fine grid level, while a medium grid level has been properly created to verify the grid independence of the computed results on the fine grid. Table 5 reports the total number of cells, blocks and faces of the mesh for the three different grid levels employed for the computations.

36

M. Di Clemente, E. Trifoni, A. Martucci et al. Table 5. Computational grid characteristics GRID LEVEL coarse medium fine

CELLS 189088 771803 1512704

BLOCKS

FACES

62

234

6.2. Two-Dimensional Numerical Results In order to analyze different aspects of the problem, in particular the effects of some assumptions that have been made in the 3D calculations, several 2D flow simulations have been made by considering the flow in the centreline of the model. Even though this is a rather good approximation for plane surfaces for which the flow exhibits a quasi-two-dimensional structure, these computations have been used only for parametric and qualitative analysis, considering the 3D computations as dimensioning cases. This approximation allowed us to perform a wide amount of computations with a reasonable CPU-time consuming. The symmetry plane of the full 3D grid around the model has been extracted and used for the two-dimensional computations. This grid is composed by about 20000 cells (fine level). The complete CFD matrix considered for the 2D computations is shown in Table 6. The following effects on the SWBLI over the model have been analyzed: 1) the effects of the Haynes 25 and C-SiC catalytic recombination coefficients; 2) the effects of the nose wall temperature assumption; 3) the effects of the base flow. Table 6. 2D CFD Matrix4 Wall Temperature # ID

Nose

Plate/Flap

Catalytic Recombination Coefficients Haynes 25

Notes

C-SiC

γO

γΝ

γO

γΝ 1

1

373

Rad.Eq.

1

1

1

2

373

Rad.Eq.

1

1

0

0

3

Rad.Eq.

Rad.Eq.

1

1

0

0

4

373

Rad.Eq.

0

0

0.05

0.015

5

373

Rad.Eq.

0.001

0.001

0.05

0.015

6

373

Rad.Eq.

0.01

0.01

0.05

0.015

7

373

Rad.Eq.

0.1

0.1

0.05

0.015

8

373

Rad.Eq.

1

1

0.05

0.015

9

373

Rad.Eq.

1

1

1

1

Base Flow

Regarding points 1) and 2) of the present analysis, it is useful to remind that when the preliminary requirements have been given, the model surface was assumed to be fully catalytic and in radiative equilibrium without any interface between different materials. For 4

The conditions of run #9 have been applied for two computations whose model differs for the geometry of the flap trailing edge, as it will be shown when the effects of the base flow region on the model will be discussed.

Design, Execution and Numerical Rebuilding of Shock Wave…

37

all these computations the nose and the lower part of the model have been always considered as fully catalytic.

6.2.1. Wall Catalycity Effects Several 2D computations have been performed to analyze the effects of the catalytic recombination coefficients of both Haynes 25 and C-SiC over the characteristic parameters of the SWBLI flow. For what concerns the effects of Haynes 25 recombination coefficients over the interaction, the analysis has been performed considering a parametric variation of γO and γN, between 0 and 1, and keeping constant the recombination coefficients of C-SiC (γO=0.05, γN=0.015, from ref. [30]). The analysis and comparison of results can be done considering the computations #4, #5, #6, #7 and #8 of Table 6, for which the nose temperature has been imposed equal to 373K whereas on the Haynes 25 flat plate and the C-SiC flap the wall radiative equilibrium temperature has been considered. The effect of Haynes 25 catalytic behaviour on the results over the flap is negligible, the peak values of pressure and heat flux are almost the same for all the conditions that have been considered, as it results from Figure 42 and Figure 43 where, respectively, the wall distributions of pressure and heat flux are reported. Of course, the main effect has been found on the flat plate especially for what concerns heat flux and temperature distributions that increase as the recombination coefficients increase (see, respectively, Figure 43 and Figure 44). Note that computation #4 corresponds to a Haynes 25 non catalytic and computation #8 to a Haynes 25 fully catalytic. Finally, the effect of catalysis on the size of the flow separation, induced by the presence of the SWBLI around the hinge-line, is to slightly enlarge the separation region in the case of non-catalytic Haynes 25 as can be seen in Figure 45 where the skin friction coefficient distribution is reported. As a general remark, the catalytic effect seems to be more important with respect to the influence estimated on the EXPERT capsule, due to the fact that in PWT conditions the flow is more dissociated (either due to the expansion nozzle flow either due to the lower pressure levels) therefore the effects of wall catalycity are more evident.

Figure 42. Haynes 25 catalysis effects: wall pressure distribution.

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Figure 43. Haynes 25 catalysis effects: heat flux distribution.

Figure 44. Haynes 25 catalysis effects: wall temperature distribution.

Figure 45. Haynes 25 catalysis effects: skin friction distribution.

In the same way, the effect of the C-SiC recombination coefficients over the SWBLI flow has been analyzed. This analysis has been done considering the Haynes 25 as a fully catalytic material and by changing the recombination coefficients of C-SiC. Wall temperature has been considered equal to 373 K for the nose and equal to the radiative equilibrium temperature for the flat plate and the flap as done in the previous analysis. The simulations used for this

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39

comparison correspond to the computations #1, #2 and #8 of Table 6; computation #1 corresponds to a fully catalytic flap, computation #2 corresponds to a non catalytic flap, while computation #8 corresponds to a partially catalytic flap with constant recombination coefficients (γO=0.05, γN=0.015). For all these computations the Haynes 25 has been considered as fully catalytic. As already found for the analysis of Haynes 25 catalysis effects on the predicted interaction flow, pressure distribution over the model is not significantly affected by the catalytic behavior of C-SiC flap as it results from the wall pressure distribution shown in Figure 46.

Figure 46. C-SiC catalysis effects: wall pressure distribution.

The effects of C-SiC catalysis on heat flux and temperature distribution over the model are much more evident, as shown, respectively, in Figure 47 and Figure 48. It is interesting to note that the catalytic recombination coefficients of C-SiC do not affect the results only over the flap itself but also on the Haynes 25 flat plate. In particular, when the C-SiC is considered as a non-catalytic material (i.e. no recombination at the wall is forced), a strong increase of the heating on Haynes 25 has been found: following the flow direction inside the separation bubble, the particles composing the air mixture “feel” a discontinuity at the hinge-line, between a low and a high catalytic material, thus forcing a sudden recombination with a strong energy release and a consequent heat flux (and temperature) increase. Of course, this effect is more evident when the flap is non catalytic rather than in partially catalytic conditions, when a certain recombination of the atomic oxygen and nitrogen over the C-SiC is allowed. This effect will be also treated when analyzing the 3D computations because the phenomenon is highly influenced by the three-dimensional effects of the interaction around the flap, as it will be described in sec. 0. It is also interesting to note that the partially catalytic condition over the flap, assuming the coefficients γO=0.05 and γN=0.015, causes a little reduction of the heat flux (see Figure 47) and temperature (see Figure 48) over the flap with respect to the fully catalytic condition.

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Figure 47. C-SiC catalysis effects: heat flux distribution.

Figure 48. C-SiC catalysis effects: wall temperature distribution.

The effects of C-SiC catalysis over the size of the separation bubble are negligible (as well as those of the Haynes 25 catalysis) as it results from Figure 49, where the skin-friction coefficient distribution over the model is reported.

Figure 49. C-SiC catalysis effects: skin friction distribution.

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6.2.2. Nose Temperature Effects The preliminary requirements for the design of the model for SWBLI experiments were given considering the radiative equilibrium temperature at wall for all the parts of the model. However, the design phase of the model itself highlighted the necessity to cool the copper cylindrical leading edge whose surface temperature has to be maintained lower than 2000 K thus, during the experimental tests, it will be used a demineralised water active cooling system to keep the temperature constant at a value of about 373 K (∼100 °C). Since the aim of the experimental activities is to duplicate in PWT conditions some characteristic parameters of the interaction encountered in EXPERT flight conditions, it is necessary to verify that: 1) the nose wall temperature does not affect the estimated values of pressure and heat flux over the flat plate and the flap and 2) that the operating conditions determined, in the preliminary activity, to duplicate these parameters, considering the wall radiative equilibrium temperature, are still valid. The nose wall temperature effects over the flat plate and the flap can be analyzed by comparing the computations #2 and #3 of Table 6 where the Haynes 25 has been considered as fully catalytic and the C-SiC flap as non catalytic. The results have been reported in terms of wall pressure, wall heat flux and wall temperature distributions, respectively, in Figure 50, Figure 51 and Figure 52. As it is clear, the effects over the pressure are negligible along the entire geometry (Figure 50), whereas nose temperature has an effect on the heat flux (Figure 51) and temperature (Figure 52) distributions over the flat plate whereas the influence over the flap is negligible. It must be noted that the effect of the cooled nose is positive for the nose/Haynes 25 interface (see Figure 52): in fact, a decrease of about 100 °C is predicted at the beginning of the Haynes 25 flat plate, whose estimated temperature, in the case of radiative equilibrium wall temperature on the nose, was too much close to the maximum allowable temperature for this material. Note, in Figure 51 and Figure 52, the phenomenon described in the previous paragraph of peak heating at the Haynes 25 plate/C-SiC flap catalytic interface due to the re-circulating flow inside the separation bubble. Another effect of the nose temperature is the influence on the size of the flow separation; in particular, the separation point moves slightly upstream whereas the reattachment point is almost the same, as it is possible to see from the skin friction coefficient distribution reported in Figure 53.

10000

0.7

8000 0.6 RUN #2 - T nose=373 K RUN #3 - Tnose=Trad.eq. Geometry

Pressure [Pa]

4000

0.5

0.4 2000

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

X [m]

Figure 50. Tnose effects: wall pressure distribution.

0.5

0.6

0 0.7

y [m]

6000

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M. Di Clemente, E. Trifoni, A. Martucci et al.

1500

0.7

1000

0.5

0.4

y [m]

Heat Flux [kW/m2 ]

0.6 RUN #2 - Tnose=373 K RUN #3 - Tnose=Trad.eq. Geometry

0.3 500 0.2

0.1

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.7

X [m]

Figure 51. Tnose effects: wall heat flux distribution.

2200

RUN #2 - T nose=373 K RUN #3 - Tnose=Trad.eq. Geometry

2000

0.7

0.6 1800 0.5

1400 0.4

1200 1000

y [m]

Temperature [K]

1600

0.3

800 0.2

600 400

0.1 200 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.7

X [m]

Figure 52. Tnose effects: wall temperature distribution.

0.05

0.7

0.6 RUN #2 - T nose=373 K RUN #3 - T nose=Trad.eq. Geometry

0.03

0.5

0.4 0.02

y [m]

Skin Friction Coefficient

0.04

0.3 0.01 0.2 0

-0.01

0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.7

X [m]

Figure 53. Tnose effects: skin friction coefficient distribution.

6.2.3. Base Flow Effects Three-dimensional numerical computations have been made avoiding to consider the presence of the base flow region in order to reduce the number of points and speed up the convergence (see Figure 41). Also the majority of the two-dimensional computations, whose grid has been extracted from the 3D mesh, have been performed without the base flow. Even if the effect of the base flow region on the results over the model has been already analyzed

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for the preliminary configuration of the model (see par.0) it is important to verify also in this case that the assumption to neglect the simulation of this region does not affect significantly the numerical predictions over the model, therefore a couple of computations with the base flow region has also been performed (run #9 of Table 6). The grid used for this comparison is showed in Figure 54. In the forward part it is exactly the same grid used for the computations without the base; at flap trailing edge three blocks have been added to simulate the base flow region whose length is equal to 1.5 Lflap, that has been estimated sufficient to allow for the closure of the base vortex.

0.8

0.6

Y [m]

0.4

0.2

0

-0.2 0

0.2

0.4

0.6

0.8

1

X [m]

Figure 54. Grid for 2D base flow computations.

Two different flap trailing edge shapes have been considered and are shown in Figure 55: the sharp and the rounded one, the latter with a 2mm radius of curvature. Computations have been performed in the hypothesis of radiative equilibrium temperature and fully catalytic base. Mach number contours of simulation with sharp flap trailing edge are reported in Figure 56, showing clearly that the selected length of the computational domain in the base region is sufficient to allow for the closure of the vortex.

0.215 Sharp

Y (m)

0.21

0.205

0.2

Rounded R=2 mm

0.195

0.19 0.565

0.57

0.575

0.58

X (m)

Figure 55. Sharp and rounded flap trailing edge.

0.585

0.59

0.595

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0.7 Mach_number: 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

0.6 0.5 0.4

Y [m]

0.3 0.2 0.1 0 -0.1 -0.2 -0.3 0

0.2

0.4

0.6

0.8

1

X [m]

Figure 56. Base flow effects: Mach number contours.

In Figure 57 wall pressure distribution for the computation without the base flow region (run #1 of Table 6) is compared with the results obtained considering the base flow region; as it is clear, the presence of the base region, independently from the shape of the flap trailing edge, causes a reduction of the separation length and a slight decrease of the pressure load over the flap. For what concerns the thermal loads, the reduction of the separation length causes an increase over the flap as shown in terms of wall heat flux and temperature distributions, respectively, in Figure 58 and Figure 59. For a quantitative estimation, the values at the reattachment point of heat flux and temperature have been reported in Table 7: the increase is equal to ∼5% in terms of wall heat flux and ∼1% in terms of wall temperature. The effect of the trailing edge geometry is negligible for the values of heat flux and temperature over the flap being important only very close to the trailing edge itself; the maximum temperature, in the case of base flow calculation, is ∼25 K higher in the case of the sharp trailing edge with respect to the case with a rounded trailing edge, as reported in Figure 59. In Figure 60 the skin-friction coefficient distribution over the model is reported; it is clear from this figure the reduction of the separation length in the case of base flow calculations; the effect of the base flow affects both the separation point location and the reattachment point one. The exact positions of separation and reattachment in the cases with or without the presence of the base region are reported in Table 7, and show a reduction of about 15% of the separation length due to base flow effects, independently of the shape of the flap trailing edge. Table 7. Base flow effects: thermal loads and separation

# ID

Geometry

Tflap

qflap 2

Tmax

Xsep

Xreat

Lsep

[K]

[kW/m ]

[K]

[m]

[m]

[m]

1

No base

1367

171

1367

0.1504

0.4857

0.3353

9

Sharp TE

1386

180

1605

0.1639

0.4467

0.2828

9

Rounded TE

1387

181

1580

0.1637

0.4459

0.2822

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RUN #1 - No Base RUN #9 - Baseflow - Rounded flap trailing edge RUN #9 - Baseflow - Sharp flap trailing edge

3000

Pressure [Pa]

2500

2000

1500

1000

500

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X [m]

Figure 57. Base flow effects: wall pressure distribution.

RUN #1 - No Base RUN #9 - Baseflow - Rounded flap trailing edge RUN #9 - Baseflow - Sharp flap trailing edge

600

Heat Flux [kW/m2 ]

500

400

300

200

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X [m]

Figure 58. Base flow effects: wall heat flux distribution.

RUN #1 - No Base RUN #9 - Baseflow - Rounded flap trailing edge RUN #9 - Baseflow - Sharp flap trailing edge

1800 1600

Temperature [K]

1400 1200 1000

800 600 400 0.1

0.2

0.3

0.4

0.5

0.6

0.7

X [m]

Figure 59. Base flow effects: wall temperature distribution.

0.8

0.9

1

45

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0.04

Skin Friction Coefficient

0.03

0.02

0.01

0

-0.01

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X [m]

Figure 60. Base flow effects: skin friction coefficient distribution.

6.3. Three-Dimensional Numerical Results The complete CFD matrix for 3D computations is reported in Tab. 8. The computations have been performed for the two test chamber conditions, defined in sec. 0, that allow for the duplication in PWT of characteristic parameters of the shock wave boundary layer interaction ahead and over the flap estimated during the EXPERT capsule re-entry trajectory. Tab. 8. 3D CFD Matrix P0 [bar]

H0 [MJ/kg]

AoA [deg]

nose

Temperature plate lateral/bottom

P1-PWT

10

15

12

373 K

rad. eq.

P2-PWT

10

11

5

373 K

rad. eq.

Catalysis lateral/bottom

flap

nose

plate

rad. eq.

rad. eq.

FC

FC

FC

rad. eq.

rad. eq.

FC

FC

FC

flap FC NC FC NC

Note that, as reported in Table 4, for point P1 the peak loads acting on the flap are reported as targets (to be duplicated in PWT experiments), while for point P2 the targets are represented by the reference values ahead of the flap, upstream of the boundary layer separation front. Temperature at the cylindrical leading edge of the model has been imposed for all the computations equal to 373 K (100°C) due to the presence of the active cooling system, whereas for all the other parts of the model the hypothesis of wall radiative equilibrium has been made. For what concerns the catalytic behaviour of the different materials, all the parts have been considered as fully catalytic, in order to provide a conservative estimation of the heat flux, whereas for the C-SiC flap the two limit conditions of fully catalytic and non catalytic wall have been considered. This latter condition has been chosen since the twodimensional sensitivity analysis of Sec. 0 has shown that assuming a non catalytic flap causes an unexpected overheating at the Haynes 25 plate/C-SiC flap interface, i.e. at the hinge line. In order to completely describe the predicted results on the test article, a series of planes cutting the model have been defined, along which the surface distributions of the interesting aerothermodynamic variables as pressure, heat flux and temperature have been plotted. These cutting planes are shown in Figure 61. The extraction of the numerical surface results will be performed on three longitudinal planes corresponding to the symmetry plane

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(Z=0 m), to a middle plane in the spanwise direction (Z=0.1 m) and to a plane near the model lateral edge (Z=0.195 m), and six transversal planes located on the Haynes 25 flat plate (X=0.125 m, X=0.200 m and X=0.275 m) and on the C-SiC flap (X=0.350 m, X=0.450 m and X=0.550 m). Moreover, the predicted flow features will be described in detail also by means of contour maps on the model surface (pressure, temperature, heat flux) and skin-friction lines.

Figure 61. Cutting planes for surface data extraction.

6.3.1. Condition P2-PWT In this paragraph, only the numerical results related to the conditions PWT-P2 are reported being the condition realized during the first test of the experimental campaign whose results will be shown in sec. 0. The condition P2-PWT has been determined to reproduce the reference values (ahead of the separation point) of pressure and heat flux experienced by the EXPERT capsule flap during the re-entry trajectory at the so-called point P2, a flight condition where the transition between passive and active oxidation of the C-SiC could take place. The facility operating conditions able to duplicate such values correspond to a reservoir enthalpy H0=11 MJ/kg and a reservoir pressure P0=10 bar, with the model positioned at an angle of attack equal to 5 deg (flap is in the windside part), and 0.375 m behind the PWT conical nozzle D exit section. Pressure contours are shown in Figure 62 whereas in Figure 63 and Figure 64 the skinfriction lines over the model are shown. It is clear the presence of the bow shock in front of the model; the pressure is maximum on the cylinder leading edge then it decreases regularly on the model; furthermore, pressure field seems largely two-dimensional on the cylindrical leading edge, the flat plate and the region around the hinge line (where a flow recirculation occurs), whilst evident spanwise effects are present on the flap surface with a clear flow expansion at the flap lateral edge. A separation of the boundary layer in front of the flap is predicted, followed by a recirculation bubble and a flow reattachment over the flap, as clear from the skin friction lines shown in Figure 63; it is clear the three-dimensionality of the flow around the model, that is stresses in Figure 64 by the view from the top of the model. Longitudinal extent of the separated area decreases moving from model centreplane to the lateral edge due to the effect of the finite spanwise dimension: the flow expansion at the model edge causes a strong spanwise flow inside the recirculation bubble with consequent boundary layer thinning. A certain two-dimensionality of the flow on the cylindrical leading

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edge and the flat plate is predicted whereas it is almost completely lost over the flap, where finite span effects are larger due to the stronger flow expansion at flap lateral edge (transversal pressure gradient is stronger over the flap, behind the reattachment shock).

Figure 62. P2-PWT: pressure contours.

Figure 63. P2-PWT: skin-friction lines.

Figure 64. P2-PWT: skin-friction lines (top view).

Temperature contours in the case of fully catalytic C-SiC flap are shown in Figure 65, whereas in Figure 66 it is reported an enlargement of the flap region. Temperature on the

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leading edge is imposed at 373 K whereas on the rest of the model the radiative equilibrium is assumed. On the flap, temperature reaches values of about 1200 K on the symmetry plane with an increase at the lateral edge due to the thinning of the boundary layer caused by the flow expansion. In Figure 66 an enlargement of the flap region is shown; in the same figure is also visible the pattern of the skin-friction lines in the lateral flap region. Separation vortex in front of the flap turns around the flap itself, and a double-vortex structure on the lateral part of the model takes place. Two separation lines and two attachment lines are clearly visible, thus evidencing a typical corner flow structure with a inner vortex and a outer main vortex, this latter separating just below the flap lateral edge and attaching on the rounded lateral protection of the model. In particular, along the attachment line of the main vortex an local peak of temperature up to values of about 1300 K has been predicted.

Figure 65. P2-PWT, FC flap: skin-friction lines and temperature contours.

Figure 66. P2-PWT, FC flap: skin-friction lines and temperature contours in the flap region.

In Figure 67 pressure transversals distribution on the Haynes 25 flat plate are reported at the three different X=const planes selected for analysis purposes. Pressure decreases moving along the plate up to the separation location where a sharp increase due to the separation shock is predicted, and finite span effects are again evident at all X=const sections. Heat flux distributions over the plate are shown in Figure 68; in the zone of attached flow (sections X=0.125 m and X=0.200 m), a rather constant distribution in the central part of the model is predicted, then it decreases moving towards the lateral edge up to a sharp increase

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due to the rounded lateral edge of the model. At the section X=0.275 m, that is inside the separation bubble, heat flux distribution is almost constant on the plate up to the lateral edge where a sudden increase is predicted. The same behaviour is found, of course, in terms of wall temperature whose transversal distributions are shown in Figure 69. The threedimensional effects over the plate are enhanced in the separation bubble as it results from the increase of heat flux and temperature at the lateral edge of the model with respect to the values on the model symmetry plane predicted at X=0.275 m, rather than the same increase at the location X=0.125 m and X=0.200 m.

Figure 67. P2-PWT: pressure distributions along Z axis on the Haynes 25 flat plate.

Pressure distribution over the flap is not affected by the catalytic behaviour of the material as shown clearly from Figure 70, where pressure transversal distributions at three different X=const planes over the flap itself are plotted. Two-dimensionality of the flow in terms of pressure seems better moving towards the flap trailing edge, where pressure levels are higher. On the contrary, as expected, heat flux (see Figure 71) and temperature (see Figure 72) distributions over the flap are strongly influenced by the catalytic properties of C-SiC. In the case of non catalytic C-SiC, even though the heat flux and temperature values over the flap are clearly lower than the fully catalytic results, the increase at the lateral edge of the flap is much higher. This is due to the combined effect of three-dimensionality (flow expansion at the flap lateral edge) and the catalytic interface between the top of the flap, modelled as non catalytic, and the lateral side of the flap, that is always considered as fully catalytic. It must be also underlined that predicted heat flux and temperature remain constant in the spanwise direction for most of the flap width, and at all transversal planes, and that the strong increase of thermal loads at the flap lateral edge is confined in very small regions (1 to 2 cm).

Figure 68. P2-PWT: heat flux distributions along Z axis on the Haynes 25 flat plate.

Design, Execution and Numerical Rebuilding of Shock Wave…

Figure 69. P2-PWT: temperature distributions along Z axis on the Haynes 25 flat plate.

Figure 70. P2-PWT: pressure distributions along Z axis on the C-SiC flap.

Figure 71. P2-PWT: heat flux distributions along Z axis on the C-SiC flap.

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Figure 72. P2-PWT: temperature distributions along Z axis on the C-SiC flap.

Wall pressure longitudinal distributions are shown in Figure 73 along the three different Z=const planes for the non catalytic and fully catalytic flap. Distributions are typical of a shock wave boundary layer interaction phenomenon in laminar regime: downstream of the strong expansion around the blunted leading edge, pressure slightly decreases on the flat plate up to the separation location where the separation shock causes an increase of pressure to a plateau value. On the flap, flow reattaches through the reattachment shock thus causing a local peak of pressure in correspondence of the minimum thickness of the boundary layer, just downstream of the reattachment point. By the way, three-dimensional effects are present along the entire geometry of the model with the exception of the cylindrical leading edge, thus indicating that the model is not sufficiently wide to inhibit the influence of finite span effects on the shock wave boundary layer interaction phenomenon. Furthermore, these effects are stronger over the flap than over the flat plate, this being due to the greater transversal pressure gradients which establish at the flap lateral edge. The small kink of pressure at X=0.1 m is caused by the thermal interface between the cooled nose (Tw=373 K) and the Haynes 25 plate assumed at the radiative equilibrium, that causes a sudden change of boundary layer thickness. Note that the effects of three-dimensionality become stronger just in correspondence of such (geometrical and thermal) interface. In Figure 74 and Figure 75, respectively, heat flux and temperature distributions over the model for fully catalytic and non catalytic flap conditions are reported. As expected, a strong catalytic effect is observed over the flap (at all longitudinal sections), with a significant reduction of both heat flux and temperature in non catalytic conditions. The threedimensional effects result in an increasing of the thermal loads in the lateral part of the model (section Z=0.195 m), and are clearly independent of the catalytic flap condition, being induced exclusively by the pressure gradient which establishes at the flap lateral edge and causes a flow expansion and a boundary layer thinning. Inside the separation bubble the classical cuspid-like distribution is predicted, with heat flux and temperature that decrease due to the increasing of the boundary layer thickness, and the reduction of the gradients at wall, whereas a local peak of thermal loads at the reattachment point is predicted (where boundary layer thickness is minimum).

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Figure 73. P2-PWT: pressure distributions along X axis.

Figure 74. P2-PWT: heat flux distributions along X axis.

Figure 75. P2-PWT: temperature distributions along X axis.

An interesting flow feature predicted in the present simulations is the localized effect of the catalytic interface at the hinge line, between the fully catalytic Haynes 25 flat plate and the non catalytic modelled C-SiC flap, on the flow separated region. This effect has been anticipated also in the two-dimensional sensitivity analysis of Sec. 0.

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In Figure 76 it is shown a detail of the recirculation zone and atomic oxygen field at the interface described above, in the case the C-SiC flap is modelled as non catalytic (top), and the heat flux distributions at model centreplane in both cases of fully catalytic (FC) and non catalytic (NC) flap (bottom). In the case of non catalytic C-SiC hypothesis a strong heat flux peak on the Haynes 25 plate just before the hinge line is predicted as a consequence of the sudden recombination of dissociated species over the plate. In fact, the atoms that do not recombine on the non catalytic flap, following the re-circulating streamlines, encounter a fully catalytic surface and suddenly recombine, with a consequent strong energy release which reflects on a localized peak heating (however, in an extent less than 1 cm). This sudden recombination of atomic oxygen and nitrogen over the PM1000 flat plate inside the recirculation bubble is clearly shown also in Figure 77 and Figure 78, where O and N mass fraction contour maps are shown respectively, in the case of non catalytic C-SiC flap.

Figure 76. P2-PWT: atomic oxygen mass fraction and heat flux in the recirculation region.

Figure 77. P2-PWT, NC flap: atomic oxygen mass fraction contours.

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Figure 78. P2-PWT, NC flap: atomic nitrogen mass fraction contours.

6.4. Model Instrumentation In order to collect a meaningful amount of data for comparison with CFD results and flight measurements taken during the EXPERT re-entry mission, a certain distribution of sensors over the model has been considered. The interesting parameters to be measured are pressure, temperature and heat flux. Sensors (pressure taps, combined heat flux/pressure and thermocouples) are mainly located on the centreline of the model, but some pressure taps are also located away from the symmetry plane to measure three dimensional effects on the interaction due to the finite spanwise dimension. A few thermocouples are located in some positions on the model in order to check the temperature map provided by the I/R thermograph. The proposed location of the sensors is shown in Figure 79.

Figure 79. Sensors location on the model.

Pressure measurements have been performed by the “Scirocco” PWT ESP (Electronic Scanner Pressure) System by PSI Engineering, used also for previous experimental campaigns carried out in the PWT facility. Temperature measurements have been performed through type-K (flat plate) and type-B (flap) thermocouples whose signals have been acquired by the “Scirocco” LBDS Data Acquisition System. The acquisition rate has been 10 Hz for pressure and 25 Hz for temperature.

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During the test, facility I/R thermograph system has been also used in order to acquire a spatially well resolved temperature map with a data rate of about 15Hz. In this context the two thermocouples on the Haynes 25 flat plate have been used only as support and verification of the data coming from the IR system. Three dual-color pyrometers have been pointed, during the test, at specific locations of the model surface to compare the measurements with the acquisition carried out through the I/R system (see Figure 79). Dualcolor pyrometers measure in the 2-color principle in which two adjacent wavelengths are used to calculate the temperature by rationing the radiation intensities of the two wavelengths. This technique offers the advantage, with respect conventional one-color pyrometer, to measure temperature independently of the emissivity of the object in wide ranges. Additionally, these pyrometers have been switched to one-color mode and used like a conventional pyrometer to calculate the emissivity of the material (combined with the TC acquisition) during the post run analysis. Two sensors for a combined heat flux/pressure (CFP) measurement have been placed on the Haynes 25 flat plate; this choice has allowed a pre-flight verification and qualification in plasma wind tunnel conditions of both sensors and related mechanical interfaces with the model TPS material and structure, that is fundamental for the EXPERT flight being these sensors the same which will be used on the real capsule.

Figure 80. Instrumentation on the flat plate (left) and the flap (central, right).

In Figure 81, Figure 82 and Figure 83 the sensors positions are shown on the model together with the predicted contour maps of the model surface properties to be measured in the test conditions P1-PWT and P2-PWT. The proposed distributions are able to properly

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characterize all the aspects (flow separation, pressure plateau, peak loads over the body-flap, etc.) of the shock wave boundary layer interaction phenomenon in the flap region and the boundary layer characteristics ahead of the flap.

Figure 81. Pressure distribution and PT sensors location.

Figure 82. Temperature distribution and TC sensors location.

Figure 83. Heat flux distribution and CFP sensors location.

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7. TEST EXECUTION The first test of the experimental campaign was performed in July 2008 considering the facility condition able to duplicate the thermal and mechanical loads foreseen at point P2 of the EXPERT re-entry trajectory.

Figure 84. Test article ready to be tested.

During the development of the test, the arc-heater was ignited and driven to the planned set point. Flow conditions into the test chamber were qualified by the probe insertion. Test Article was then inserted into the plasma flow and removed as planned at the end of the test whose duration was equal to about 92s. Test has been performed considering also the variation of the angle of attack from 0 deg (at the beginning of the test) to 5 deg for the central part of the test, to 0 deg again before the extraction of the model. This movement has allowed to evaluate the effect of the angle of attack on the separation due to the interaction. Some of the results acquired during the test are shown in the following figures. In Figure 85 temperature measurement on the flat plate acquired through the two thermocouples is shown; at the end of the test, the plate reaches a temperature of about 500° C; the two thermocouples measured more or less the same value for the entire test duration. In Figure 86, pressure measurement on the plate is shown: after the insertion in the plasma flow, at 0 deg of angle of attack, the model is tilted to 5 deg and a increase of pressure, which remains almost constant during the entire duration, is predicted. Before the extraction the angle of attack is reduced to 0 deg and pressure is back to the same values predicted at the beginning of the test.

Figure 85. Temperature measurements on the flat plate.

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Figure 86. Pressure measurements on the flat plate.

The same trend, from a qualitative point of view, is predicted on the flap (see Figure 87). In this case it is interesting to highlight the variation in the measurement of pressure PT10 whose value decreases during the test: this is due to the increase of separation bubble extension (due to the effect of temperature of the flap) and the movement of the reattachment shock.

Figure 87. Pressure measurements on the flap.

Figure 88. Temperature field maps from I/R camera, t=20 sec (left) and t=80 sec (right).

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Temperature maps, at two different instants of the test, respectively t=20 sec and t=80 sec, are shown in Figure 88. The presence of the separation bubble produces a reduction of temperature in the flat plate near the corner and a peak, at the reattachment, clearly visible on the flap. Heat flux on the flat plate has been measured through two combined heat flux / pressure sensors; these sensors are built with a copper calorimeter equipped with two thermocouples, to derive heat flux measurement, and with a central hole connected to a pressure transducer to measure pressure at the same point where heat flux evaluation is carried out. During the test execution the time evolution of temperature inside the two CFP sensors has been measured through the thermocouples installed at the top and the bottom of the copper calorimeter; the results are reported in Figure 88 for the CFP1 (left) and CFP2 (right).

Figure 88. Temperature measurement in CFP1 (left) and CFP2 (right) sensors.

Starting from these measurements the heat flux acting on the calorimeter itself has been derived by means of the following relation: q' =

dT Q' ⎛ m ⋅ c ⎞ dT =⎜ = Ccal ⋅ ⎟⋅ dt A ⎝ A ⎠ dt

(9)

where Ccal is a constant depending on the material and the dimension of the calorimeter. The results obtained for the CFP1 and CFP2 are reported in following Figure 89: as it is clear the two sensors are able to measure the heat flux over the flat plate and also to capture the different phases of the test (model injection in the plasma, increase/decrease of the angle of attack, extraction from the plasma). The computed results have been obtained after a smoothing on temperature measurements, in order to guarantee the continuity of the time derivative.

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Figure 89. CFP heat flux results.

8. POST TEST ANALYSIS AND NUMERICAL REBUILDING The experimental test has been numerically rebuilt considering the real conditions realized in the test chamber, which were slightly different from those predicted in the pre-test phase. In detail, two different time instants have been considered for this rebuilding and, for these computations, wall temperature imposed as boundary condition on the flat plate and the flap has been derived from the thermocamera results, presented in the previous section, at t=20 sec and t=80 sec. Moreover, another refinement introduced with respect the pre-test phase has been to consider the angularity of the flow induced by the conical shape of the Scirocco expansion nozzle. As matter of fact, from a practical point of view, the simulation of the flow around a model inside the test chamber is generally divided in two phases: firstly, the simulation of the nozzle flow is carried out, then the conditions at nozzle exit section are considered as freestream conditions for the simulation around the model. These conditions, evaluated at the nozzle centreline, are imposed as constant conditions along the entire inlet boundary of the mesh around the model. In this case, due to the dimension of the model, it has been important to consider also the angularity of the flow at the nozzle exit, which has a conical shape. In the results presented hereinafter it is clear this effect and the consequent differences on the results computed over the model in the two cases, especially for what concerns wall pressure distribution, show in Figure 90. A general decrease of wall pressure over the model is predicted in the case of conical inlet profile. The effect is less evident for what concerns heat flux distribution, shown in Figure 92: also in this case the comparison with the experimental results evaluated through the combined heat flux/pressure sensors is rather good. The effect of wall temperature has been analyzed by comparing two computations carried out by assuming the wall temperature equal to the thermocamera measurements at two different time instants, t=20sec and t=80 sec. The results are shown in Figure 93: wall pressure (left) is exactly the same in the two cases being the angle of attack the same whereas heat flux decreases at t=80 sec due to the increasing of imposed wall temperature on the flat plate and the flap (i.e. the model is being heated). As a consequence, the extension of the separation bubble, as detached also from the experimental results, slightly increases.

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Figure 90. Experiment rebuilding: wall pressure distribution.

Figure 92. Experiment rebuilding: heat flux distribution.

Figure 93. Experiment rebuilding: effect of wall temperature.

8.1. Comparison with Pre-Test and Flight Data The distributions of pressure and heat flux on the model symmetry plane predicted in the pre-test and the rebuilding phase have been compared with those predicted in flight conditions, to verify that the extrapolation-from-flight methodology was correctly developed

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and applied, and with the experimental results measured during the test, to verify the reliability of the numerical tool used for all the computations. It is useful to remind here the working hypotheses on which are based the thermochemical non equilibrium laminar flow simulations performed for the present activity: 3D simulations for the pre-test and rebuilding phase have been performed by assuming all the parts of the model as fully catalytic and in radiative equilibrium (except for the nose where a cold wall condition has been imposed). Wall pressure distributions are shown in Figure 91: the comparison between the flight expected results and the measured/computed results in PWT conditions in front of the flap, i.e. the reference value of pressure, is rather good, even though in flight conditions a larger extension of the separation bubble is predicted. Heat flux distributions are shown in Figure 92: on the flat plate, heat flux levels computed in flight and PWT conditions, before the separation, compare rather well and agree also well with the experimental results. On the flap, the determined conditions for the test execution allowed to duplicate well the target values, i.e. the heat flux distribution expected in flight conditions. From the analysis of these distributions, it can be concluded that point P2 targets, extracted from the computations carried out in flight conditions, have been reasonably achieved in PWT conditions and correctly duplicated in the post test activity. Therefore, it can be concluded that the developed extrapolation from flight methodology allowed for the achievements of the requirements over the designed model, also accepting the facts that the (maximum possible) model width is not sufficient to avoid finite span effects on the shock wave boundary layer interaction around the flap and over the entire model.

Figure 91. P2 pressure distribution: comparison between test, flight and exp. Conditions.

Figure 92. P2 heat flux distribution: comparison between test, flight and exp. Conditions.

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9. CONCLUSION Shock wave boundary layer interaction in real gas, high enthalpy conditions have been analyzed through a numerical and experimental activity. In detail, different, but strictly connected, directions have been followed, the aim was to develop an extrapolation from flight methodology in order to reproduce, in a realistic plasma environment, on a representative model the same conditions, in terms of wall pressure and heat flux distribution, expected on the EXPERT capsule in the region of the interaction in critical points along the re-entry trajectory. The followed approach is justified by the consideration that the prediction of hypersonic flows, both for the complexity of the required physical modelling and for the impossibility to duplicate in wind tunnels real flight conditions due to the high energy required, requires the necessity to take into account, and mutually validate, different sources of data as flight and wind tunnel experiments, and combining them by means of a numerical activity. This methodology has been developed and applied to the analysis of shock wave boundary layer interaction in high enthalpy flow conditions being the understanding of this phenomenon, which takes place for example in proximity of a deflected control surface, crucial for the design of the next generation of RLV. Predicted reference and peak values of pressure and heat flux (estimated in some characteristics points along the flight trajectory) have been considered to design the experimental campaign, whose first test has been presented and critically discussed, performed in the CIRA Plasma Wind Tunnel “Scirocco” on a representative model, with the aim to duplicate those levels in a realistic plasma environment. For a meaningful design of such experimental test campaign a massive use of CFD has been carried out to analyze several aspects of the problem which must be necessarily taken into account. The model considered is constituted by a cylindrical leading edge followed by a flat plate and the 1:1 scale 20 deg deflected EXPERT flap with rounded lateral edges to minimize local heating effects. During the preliminary phase, based on two dimensional analysis on the model symmetry plane, the main design parameters of the model (leading edge radius of curvature, length of the flat plate and flap dimensions) have been chosen to duplicate on the model itself pressure and heat flux levels encountered in flight conditions. Moreover, different facility operating conditions (in terms of reservoir enthalpy, H0, and pressure, P0) and model positioning/attitude within the test chamber have been determined, considering some laws determined on the basis of the performed computational activity, and this in order to duplicate either the shock wave boundary layer interaction phenomenon occurring around the flap either the associated thermo-mechanical loads acting on it during the EXPERT re-entry flight. It has been demonstrated, through the experimental results and the numerical rebuilding activity that the selected operating conditions were able to produce on the model a shock wave boundary layer interaction around the flap qualitatively similar to the one occurring in flight. Moreover, heat flux and pressure are duplicated ahead and over the flap in the experimental test corresponding to the point P2. Anyhow, differences in terms of wall pressure over the model, with respect to the levels estimated in flight conditions, combined with the fact that necessarily in PWT conditions the flow arrives over the model in dissociated conditions play a role also on the catalysis effects over the interaction that have been analyzed through a parametric analysis. In particular, it

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can be concluded that the differences in terms of catalytic behaviour between the plate and the flap causes local overheating phenomena at the junction location due to the discontinuity that the flow within the recirculating bubble feels in the recombination coefficients, and these effects could be significant when the flap is less catalytic than the forward plate. The effects have been analyzed from a quantitative point of view through two- and three-dimensional computations over the model design for the PWT experiments, and through qualitative analysis in EXPERT flight conditions where it has been found that catalysis has a strong effect on the heating rates but a negligible effect on the interaction main parameters (upstream influence and reattachment). An instrumentation layout and sensor positioning over the model conceived for the experimental campaign, combined with non intrusive instrumentation available, have also allowed for the measurements of the interesting variables as temperature, pressure and heat flux, whose values compares well with the post test numerical results, to properly characterize all the aspects (flow separation, pressure plateau, peak loads over the body-flap, etc.) of the shock wave boundary layer interaction phenomenon in the flap region and the boundary layer characteristics ahead of the flap.

REFERENCES [1]

Anderson J.D., “Hypersonic and High Temperature Gas Dynamics”, McGraw-Hill, 1989. [2] Bertin J.J., “Hypersonic Aerothermodynamics”, AIAA Education Series. [3] Borrelli S., Pandolfi M., “An Upwind Formulation for the Numerical Prediction of Non Equilibrium Hypersonic Flows”, 12th International Conference on Numerical Methods in Fluid Dynamics, Oxford, United Kingdom, 1990. [4] Caporicci M., “European Crew and Logistic Vehicles For ISS and Exploration Missions”, AIAA Paper 2005-3252. [5] Chanetz B., “Study of axi-symmetric shock wave/boundary layer interaction in hypersonic laminar flow”, ONERA Technical Report TR No. 42/4362, February 1995. [6] Chanetz B., “ONERA hypersonic test-cases in the framework of the Working Group”, 18th Hypersonic experimental and computational capability, AGARD Advisory Report 319, Vol. 2, 1996. [7] D’Ambrosio D., “A Study on Shock Wave- Boundary Layer Interactions in High Speed Flows”, 4th European Symposium on Aerothermodynamics for Space Vehicles, October 2001. [8] Davis J. P., Sturtevant, B., “Separation Length in High-Enthalpy Shock/Boundary Layer Interaction”, Physics of Fluids, Vol. 12,No. 10, 2000, pp. 2661–2687. [9] Delery J. M., “Shock Interference Phenomena in Hypersonic Flows”, Third Joint Europe/U.S. Short Course in Hypersonics, Univ. of Aachen, Germany, October 1990. [10] De Filippis F., Caristia S., Del Vecchio A., Purpura C., “The Scirocco PWT Facility Calibration Activities”, 3rd International Symposium Atmospheric Re-entry Vehicle and Systems, Arcachon, France, March 2003. [11] Dujardin A., Guelhan A., Longo J.M.A., Mack A., “Numerical/Experimental Investigation of a Wedge-Compression Corner with a Gap-Flow under Cold-

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M. Di Clemente, E. Trifoni, A. Martucci et al. Hypersonic Conditions”, Proceedings of the 4th European Symposium on Aerothermodynamics for Space Vehicle, October 2001. Enzian A., Devezeaux D., et al., “Flight Experiments to Address Unsolved Aerothermodynamic Issues for a Future European Reusable Space Launcher”, Proceedings of the 4th European Symposium on Aerothermodynamics for Space Vehicle, October 2001. Grasso F., Falconi D., “High-Speed Turbulence Modelling of Shock-Wave/BoundaryLayer Interaction”, AIAA Journal, Vol. 31, No. 7, 1993, pp. 1199–1206. Grasso F., Bellucci V., “Thermal and Chemical Non-Equilibrium Hypersonic Flow Computations”, Agard CP-514, Theoretical and Experimental Methods in Hypersonic Flows, April 1993. Grasso F., Leone, G., “Chemistry Effects in Shock Wave Boundary Layer Interaction Problems,” Proceedings of the IUTAM Symposium on Aerothermochemistry of Spacecraft and Associated Hypersonic Flows, Jouve, Paris, 1992, pp. 220–227. Grasso F., Marini M., “Analysis of Hypersonic Shock-Wave Laminar Boundary-Layer Interaction Phenomena”, Computers and Fluids, Vol.25, No. 6, 1996. Hirschel E.H., “Aerothermodynamic Phenomena and the Design of Atmospheric Hypersonic Airplanes”, Advances in Hypersonics, Defining the Hypersonic Environment , Vol. 1, Birkhauser, Boston, 1992, pp. 1–39. Holden M. S., “Two-Dimensional Shock Wave–Boundary Layer Interactions in High Speed Flows. Part II, Experimental Studies on Shock Wave–Boundary Layer Interaction”, AGARDograph AG-203, June 1975, pp. 41–110. Holden M. S., “A Study of Flow Separation in Regions of on Shock Wave-Boundary Layer Interaction in Hyper sonic Flow”, AIAA Paper 78-1169, Seattle, Wash. , 1978. Longo J. M., Radespiel R., “Flap Efficiency and Heating of a Winged Re-Entry Vehicle”, Journal of Spacecraft and Rockets, Vol. 33, No. 2, 1996, pp. 178–184. Mallinson S. G., Gai S. L., Mudford, N. R., “The Interaction of a Shock Wave with a Laminar Boundary Layer at a Compression Corner in High-Enthalpy Flows Including Real Gas Effects,” Journal of Fluid Mechanics, Vol. 342, 1997, pp. 1–35. Mallinson S. G., Gai, S. L., Mudford, N. R., “High-Enthalpy, Hypersonic Compression Corner Flow,” AIAA Journal, Vol. 34, No. 6, 1996, pp. 1130–1137. Marini M., “Effects of Flow and Geometry Parameters on Shock-Wave BoundaryLayer Interaction Phenomena”, AIAA Paper 98-1570. Marini M., “Analysis of hypersonic compression ramp laminar flows under sharp leading edge conditions”, Aerospace. Science and Technology, No. 5, 2001. Marini M., “Body-Flap Efficiency Prediction of a FESTIP Concept Vehicle”, 2nd International Symposium Atmospheric Reentry Vehicles and Systems, Arcachon, France, March 2001. Muylaert J., Berry W., “Aerothermodynamics in Europe: Achievements and Challenges”, Proceedings of the 2nd European Symposium on Aerothermodynamics for Space Vehicle, February 1995. Nasuti F., Barbato M., Bruno C., “Material-Dependent Catalytic Recombination Modeling for Hypersonic Flows”, Journal of Thermophysics and Heat Transfer, Vol. 10, No.1, 1996. Ranuzzi G., Borreca S., “H3NS: Code Development Verification and Validation”, CIRA-CF-06-1017.

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[29] Stewart D. et al., “Surface characterization of Candidate Metallic TPS for RLV”, AIAA Paper 99-3458. [30] Stewart D. et al., “Surface Catalytic Efficiency of Advanced Carbon Carbon Candidate Thermal Protection Materials for SSTO Vehicles”, NASA TM-110383. [31] Di Clemente M., Marini M., Schettino A., “Shock Wave Boundary Layer Interaction in EXPERT Flight Conditions and Scirocco PWT”, AIAA Paper 2005-3411, 13th AIAA/CIRA International Space planes Conference, Capua, May 2005. [32] Di Clemente M., Marini M., Schettino A., “Shock Wave Boundary Layer Interactions in SCIROCCO Plasma Wind Tunnel”, East-West High Speed Flows Conference, Pechino, October 2005. [33] Di Clemente M., Marini M., Di Benedetto S., Schettino A., Ranuzzi G., “Numerical Prediction of Aerothermodynamic Effects on a Reentry Vehicle Body Flap Configuration”, Acta Astronautica, 65, 2009 221–239. [34] Schettino A., Votta R., Roncioni P., Di Clemente M., “Aerodynamic and Aerothermodynamic Database of EXPERT Capsule”, East-West High Speed Flows Conference, Moscow, November 2007. [35] Di Clemente M., Sellitto C., Vigliotti A., Martucci A., Marini M., “Shock Wave Boundary Layer Interaction Measurement Assembly on the EXPERT Capsule”, 16th AIAA/DLR International Space Planes Conference, Bremen, November 2009. [36] Di Clemente M. “Numerical studies for the realization of aerodynamic systems for guide and control of re-entry vehicles”, Ph.D. Dissertation, University of Rome “La Sapienza”, February 2008. [37] Dujarric C., "Possible Future European Launchers – A Process of Convergence", ESA Bulletin No. 97, 1999. [38] Russo G., De Filippis F., Borrelli S., Marini M. and Caristia S., “The SCIROCCO 70MW Plasma Wind Tunnel: A New Hypersonic Capability”, F.K. Lu and D.E. Marren Editors, Advanced Hypersonic Test Facilities, Progress in Astronautics and Aeronautics Series, published by AIAA, September 2002. [39] Thoemel J., Muylaert J., Ratti F., Gavira J., “In-Flight Testing of Critical Technologies and Experimentation of Aerothermodynamic Phenomena”, 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, AIAA Paper 2009-7232, Bremen, November 2009. [40] Ratti F., Gavira J., Passarelli G., Massobrio F., “EXPERT. The ESA experimental reentry test-bed: System overview”, 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, AIAA Paper 2009-7224, Bremen, November 2009.

In: Wind Tunnels: Aerodynamics, Models and Experiments ISBN 978-1-61209-204-1 © 2011 Nova Science Publishers, Inc. Editor: Justin D. Pereira

Chapter 2

THE MAINZ VERTICAL WIND TUNNEL FACILITY– A REVIEW OF 25 YEARS OF LABORATORY EXPERIMENTS ON CLOUD PHYSICS AND CHEMISTRY Karoline Diehl1, Subir K. Mitra1, Miklós Szakáll1,*, Nadine von Blohn1, Stephan Borrmann1,2 and Hans R. Pruppacher1 1

Institut für Physik der Atmosphäre, Johannes Gutenberg-Universität Mainz, Germany 2 Max-Planck-Institut für Chemie, Mainz, Germany

ABSTRACT The Mainz vertical wind tunnel is so far a worldwide unique facility to investigate cloud and precipitation elements under conditions close to the real atmosphere. Hydrometeors such as water drops, ice crystals, snow flakes, and graupels are freely suspended at their terminal velocities in a vertical air stream under controlled conditions regarding temperature (between -30°C and +30°C), humidity (up to the level of water saturation), and laminarity (with a residual turbulence level below 0.5%) of the air stream. Cloud processes in warm, cold, and mixed phase clouds have been investigated in the fields of cloud physics and chemistry, aerosol–cloud interactions, and the influence of turbulence. The experiments include the behaviour of cloud and rain drops, ice and snow crystals, snow flakes, graupel grains and hail stones and the simulation of basic cloud processes such as collisional growth, scavenging, heterogeneous drop freezing, riming, and drop-to-particle conversion. Atmospheric processes have been investigated under both laminar and turbulent conditions in order to understand and quantify the influence of turbulence. The results are essential for applications in cloud chemistry models to estimate the atmospheric pathway of trace gases, in cloud and precipitation models to improve the description of the formation of precipitation (growth and melting rates), and in now- and forecasting of precipitation to improve the evaluation of radar and satellite data.

*

E-mail: [email protected]; Tel.: (+49) 6131 3925102; Fax: (+49) 6131 3923532

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Keywords: vertical wind tunnel; laboratory experiments; cloud physics; cloud chemistry.

1. INTRODUCTION Clouds play an important role in the climate system of the earth. They affect the energy budget of the atmosphere by reflecting, scattering, and absorbing the short-wave radiation coming from the sun and the long-wave radiation from the earth surface. By scavenging aerosol particles and trace gases, cloud particles and raindrops are involved in wash-out processes of the atmosphere and affect the partitioning of particles and gases between the phases and their pathway in the atmosphere. In the initiation of clouds, the growth of cloud droplets or ice crystals by the deposition of water vapor and by collision and coalescence is essential. At temperatures below the freezing point, ice nucleation processes and, afterwards, processes in mixed phase clouds such as riming are important. In later stages of cloud development, the further growth of cloud drops and ice particles to larger sizes affects the initiation of precipitation. To improve the knowledge of all these cloud and rain processes, laboratory experiments are essential. They demand the reliable simulation of processes under atmospheric conditions and became more and more important during the last century. Harsh atmospheric and climatic processes, such as acidic rain, severe hailstorms, hurricanes, floods, or even droughts have not only environmental but also serious social impacts. Thus, in order to reliably forecast weather and climate changes and to avoid possible destructive effects, the thorough understanding of chemical and physical processes of clouds and precipitation is of great importance. The correct interpretation of measured meteorological parameters using different platforms (e.g., radars or satellites, radiosondes) requires the accurate knowledge of cloud processes as well. To forecast weather and climate variations, one has to correctly describe the processes within clouds in model simulations. Thus, modeling requires reliable input parameters in order to generate reasonable outputs. On the other hand, to verify theoretical models, repeatable measurements under different but well-controlled conditions are required which can be performed only under laboratory conditions. So far, there exist a number of laboratory facilities to simulate atmospheric cloud processes such as cloud chambers (e.g., Möhler et al., 2003), flow tubes (e.g., Bertram et al., 1996, Stratmann et al., 2004), continuous flow diffusion chambers (e.g., DeMott and Rogers, 1990), fall shafts (Beard et al., 1991), free-fall freezing tubes (Wood et al., 2002), drop levitators (e.g., Carleton et al., 1997; Ettner et al., 2004; Diehl et al., 2009), and vertical wind tunnels. In contrast to other constructions such as the cloud chamber AIDA (Möhler et al., 2003) or the cloud simulator LACIS (Stratmann et al., 2004), vertical wind tunnels are restricted to processes after the formation of cloud droplets or ice particles as the relative humidity is always below saturation. On the other hand, in vertical wind tunnels hydrometeors are freely floated at their terminal velocities so that all microphysical and chemical processes taking place in clouds or with raindrops can be simulated not within a large cloud but with single drops or ice particles. There are three main types of wind tunnels used in atmospheric simulation applications. In the open L-type wind tunnels a blower maintains the continuous air flow through the tunnel (e.g., Blanchard, 1950; Kamra and Ahire, 1989; Saylor and Jones, 2005). A

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backpressure plate at the upper end of the construction ensures a velocity minimum at the centre of the tunnel so that hydrometeors can be freely floated in the wind tunnel. The disadvantages are turbulences produced by the blower and the backpressure plate and maintaining temperature and humidity at constant values is not possible because of the open region where the drop is suspended. In the O-type wind tunnels the air is circulated by a blower (e.g., List, 1966). Although this construction manages to keep the temperature and humidity at near constant values, it is impossible to achieve turbulence-free conditions because of the placement of the blowers in the flow path. In the layout for wind tunnels of the Z-type the air is sucked through the tunnel by a vacuum pump at the upper downstream end of the construction through a sonic nozzle which avoids turbulence in the tunnel air stream. Furthermore, the air can be conditioned in the lower (upstream) section of the tunnel. The Mainz vertical wind tunnel is so far a worldwide unique representative of the Z-type tunnel. It allows the observation of individual hydrometeors freely floating at their terminal velocities in a laminar or controlled turbulent environment. Temperature, humidity as well as the aerosol and trace gas content of the air, in which the hydrometeors are suspended, are exactly controlled during the measurements. For further physical or chemical analysis, the suspended hydrometeors are investigated in-situ and/or extracted from the wind tunnel.

2. DESCRIPTION OF THE MAINZ VERTICAL WIND TUNNEL 2.1. History A wind tunnel specially built for investigations in the area of cloud physics with a Z-type layout was first constructed by Prof. Hans R. Pruppacher in 1968 at the University of California at Los Angeles (UCLA wind tunnel; e.g., Beard and Pruppacher, 1969). This tunnel was the forerunner type of the Mainz vertical wind tunnel which was built in 1986 also under the supervision of Prof. H. R. Pruppacher at the University of Mainz in Germany, and funded by the German Federal Ministry of Science and Technology (BMBF). This second generation tunnel has improved performance in areas of range of speeds, stability of environmental conditions and ease of operation. This allows the free suspension of larger water drops, graupels and hailstones as well as snowflakes and smaller drops at their respective terminal velocities. For nearly 25 years the Mainz vertical wind tunnel has been utilized in various investigations in the fields of cloud physics and chemistry.

2.2. Construction The schematic drawing of the Mainz vertical wind tunnel can be seen in Figure 1. The wind tunnel consists of three main sections: In the lower horizontal part of the Z-construction the air is modified according to the requirements of the experiment: It can be filtered to remove unwanted aerosol particles and trace gases, dried and possibly warmed or cooled. For the cooling of the air a three stage air conditioning system with a double feedback loop temperature control is available consisting of a dehumidifier unit and two cooling units. Post-

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cooling humidification of the tunnel air is performed by a steam generator. Also small droplets can be introduced into the wind tunnel using a set of ultrasonic fog generators. In addition, several aerosol and gas inlets allow achieving the necessary environmental characteristics in the wind tunnel as required. The temperature of the tunnel air can be adjusted to any value between -30°C and +30°C while the humidity can be set up to the level of water saturation. A bypass inlet allows laboratory air to enter the wind tunnel if air conditioning is not required for experiments, e.g., for the investigation of shape of raindrops in ambient air at the ground level.

Figure 1. Schematic drawing of the Mainz vertical wind tunnel. The air conditioning and experimental parts of the wind tunnel are located on the first floor, while the pumps and valves on the second floor of the laboratory.

The vertical part of the wind tunnel represents the experimental and observation section. There in the lowest part, the settling chamber, the air stream changes its direction from horizontal to vertical. Afterwards, the tunnel air flow is laminarized by a honeycomb followed by a set of sieves. The laminar air stream passes through a contraction section which is essential for the freely floating of the hydrometeors. It creates a uniform vertical velocity profile across the tunnel with a weak minimum in its center. Subsequently, the air enters the observation section. For different experimental requirements, there are a number of sections available with different cross sections and built from different materials as needed. The most frequently used observation section has a cross section of 17 cm × 17 cm. The walls are made of transparent material to allow direct observation of the freely suspended hydrometeors. Air

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lock type enclosures can be mounted on the walls of the experimental sections to facilitate insertion and retrieval of hydrometeors. In the upper horizontal section of the construction flow control and drive units are located. Two vacuum pumps are used to suck the air through the tunnel. The velocity of the air stream is controlled by a sonic valve which allows very fast variations of the wind speed. Inside the sonic nozzle the flow speed increases reaching the speed of sound at the throat of the valve immediately followed by a sonic barrier downstream in the flow. This barrier prevents any pressure fluctuations at the inlet of the pumps from moving upstream and disturbing the flow in the observation section. As the flow speed in the sonic valve is the same, the mass flow is directly proportional to the cross sectional area of the sonic throat which can be varied to change the flow speed in the tunnel. Wind speeds up to 40 m/s in the observation section are possible so that freely floating hydrometeors of all sizes between 30 µm and a few centimeters can be investigated in the tunnel. For vertical air speeds typically used in the wind tunnel the air stream shows a uniform velocity distribution over the whole cross section area up to the boundary layer. This ensures that hydrometeors are floating in a more or less stable fashion in the tunnel. The unmodified air stream is laminar with a residual turbulence level below 0.5% (Vohl et al., 1999). To investigate the influence of turbulence on microphysical processes this can be changed. The low level of the unmodified background turbulence allows the production of a well-defined turbulent flow which is generated by positioning obstructing objects upstream of the experimental section (e.g., Vohl et al., 1999; Diehl et al., 2000). In those experiments, the energy dissipation rate in the turbulent wind tunnel air stream has to be measured in order to ensure that it lies in the range of the turbulent kinetic energy spectrum found in natural clouds.

2.3. Experiments Experiments performed so far in the Mainz vertical wind tunnel during the last 25 years are classified by several criteria: laminar or turbulent air stream; cloud physical or chemical processes or aerosol―cloud interactions; warm, cold, or mixed phase clouds.

2.3.1. Experiments in Laminar Air Stream A large number of experiments were performed in an unmodified laminar air stream. These serve as references for similar studies in a turbulent environment, they also help to understand the principles of those processes. 2.3.1.1. Basic Cloud Physical Processes In a laminar air stream in the vertical wind tunnel some basic cloud physical processes were investigated in warm, mixed phase, and cold conditions. Internal Circulation, Shape, and Oscillation of Raindrops One of the most important parameters of raindrops from the point of view of meteorological applications are the axis ratio, i.e., the ratios of the largest vertical and horizontal chords, the variation of the shape, the frequency of this variation (i.e. the

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oscillation frequency), and the internal circulation inside the drops. Cloud droplets and small raindrops (< 1 mm in diameter) have spherical form so that they can be considered as rigid spheres in fluid dynamical and cloud microphysical modeling. Raindrops larger than 1 mm in diameter are deformed and the shape distortion increases with the equivalent diameter of the drop. Their shapes can be approximated by oblate spheroids and their sizes are given as volume-equivalent diameter, which is the diameter of a water sphere having the same volume as the raindrop. The hydrodynamic behavior of raindrops with volume-equivalent diameters between 1 and 7 mm were investigated. The drops were injected into the tunnel as the air speeds were adjusted to be equal to their terminal velocity so that they were freely floating. Their motions were recorded using a high-speed digital or analogue video camera. From the individual images the change of the raindrop shape, the amplitude and frequency of oscillation were determined with high accuracy, and the internal circulation was characterized. As an example, the high-speed images of one oscillation period of a water drop with 6 mm equivalent diameter freely floating in the Mainz wind tunnel are shown in Figure 2.

Figure 2. High-speed images of an oscillating water drop with 6 mm equivalent diameter freely floating in the Mainz vertical wind tunnel. The image sequence represents one oscillation period. The single frame size is mm 10.4×7.8 mm, the total time of the shown sequences is 38 ms.

The static axis ratios in equilibrium were evaluated and compared to different models (Szakáll et al., 2009; Szakáll et al.; 2010). It was shown that the experimental data for raindrops with different sizes fit very well to the following polynomial (Beard and Chuang, 1987; Chuang and Beard, 1990):

α = 1.01668 − 0.09806 D 0 − 2.52686 D 02 + 3.75061D 03 − 1.68692 D 04

(1)

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Excellent agreement was also found comparing the contours of shapes for different drop sizes calculated according to Beard and Chuang (1987), the images of drops in equilibrium recorded in the Mainz vertical wind tunnel, and the experimental field data from a novel 2Dvideo disdrometer (Thurai et al., 2009). Figure 3 shows a direct comparison of two different drop shape models – the force-balance model of Beard and Chuang (1987) and the simple ellipsoid raindrop shape model of Green (1975) – with a freely floating water drop photographed in the Mainz vertical wind tunnel.

Figure 3. The theoretical shapes from the force balance model of Beard and Chuang, 1987 (solid line), the simple ellipsoid model of Green, 1975 (dashed line) and the shadow image of a raindrop with 6 mm diameter. The scale of the polar graph is in mm. The original photo of the raindrop recorded in the Mainz vertical wind tunnel can be seen in the right lower corner of the figure.

Nevertheless the raindrop shape is not static but changes continuously as the drops larger than 1 mm are oscillating. This is most probably caused by eddy shedding from the downstream side of the raindrops (Pruppacher and Klett, 1998). The oscillation amplitude is a very important parameter in several applications in the areas of microphysical and chemical models. The size dependence of the oscillation amplitude of water drops was parameterized by Szakáll et al. (2010) by the following polynomial fit to their measurement data:

Aα = 3.6 ⋅ 10 −3 D0 + 2.13 ⋅ 10 −2 D0 2

(2)

where Aα is the amplitude of the axis ratio and D0 is the equivalent drop diameter in mm. The equation shows that the oscillation amplitude is increasing with drop size. The oscillation frequency is also determined by the drop size as the wavelength of the oscillation mode is directly related to the geometry of the drop (Feng and Beard, 1991). The frequency of the

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main oscillation mode (n=2,m=0) can be calculated using the Rayleigh formula (Pruppacher and Klett, 1998):

f

R 2

⎛ 2σ ⎞ ⎟ = ⎜⎜ 2 3 ⎟ ⎝ π ρ w a0 ⎠

1/ 2

(3)

Feng and Beard (1991) showed that the deformed drop shape leads to a removal of degeneracy between the fundamental (n=2, m=0) mode and the higher associated modes (n=2, m=1,2) and introduced a correction term into the Rayleigh formula which gives the frequencies of the different oscillation modes. This asymptotic analysis was used for a comparison of frequencies of different oscillation modes experimentally determined at the Mainz wind tunnel and remarkable agreement was found (Szakáll et al.; 2009) between the model results and the observations. Furthermore, wind tunnel observations indicated a sizedependence of the (n=2,m=1), (n=2,m=2) and (n=3,m=1) oscillation modes besides the fundamental mode (n=2,m=0) for each water drop falling at terminal velocity (Szakáll et al.; 2009). To visualize the internal circulation inside raindrops, small insoluble particle tracers were added to the drops. Their density was close to that of water so that the trajectory of the particle tracers closely followed that of a fluid element without any significant gravitational separation within the drops. The experimentally determined average internal circulation velocities fit considerably well to the theoretical curve of LeClair et al. (1972) who numerically solved the Navier-Stokes equation for water spheres falling in air and found that the mean circulating speed is proportional to the terminal speed of the drops (Szakáll et al., 2009). Earlier observations that drops with diameters less than 1 mm - which are spherical and do not significantly oscillate - have a regular flow pattern inside (e.g., LeClair et al., 1971) were confirmed and it was shown that in larger drops - which are deformed and oscillate with observable amplitudes – the internal circulation is irregular and turbulent. Furthermore, the internal circulation speed changes continuously between zero and maximum values: The circulation comes almost to a standstill and afterward it builds up again (Szakáll et al.; 2009). These findings are of great importance for the trace gas uptake by raindrops.

Collisional Drop Growth and Riming An essential process to form precipitation-sized drops is the collisional growth of cloud droplets. The collision efficiency of drops is the main factor affecting the drop collection rate and rain formation in liquid water clouds. It is defined as the ratio of the number of drops colliding with a larger collector drop to the total number of drops lying within the geometrical volume of interaction. It depends strongly on the sizes of the collision partners and lies in general between values close to zero (no collisions) and one. During experiments in the vertical wind tunnel a single collector drop was injected into the tunnel at a wind speed matching the terminal velocity of the drop. Thus, it was suspended freely within the observation section of the tunnel. The radius of this collector drop was between 70 and 170 µm. Downstream of the floating drop a cloud of smaller droplets was produced by a battery of sprayers so that the larger collector drop grew by collision with the droplets. The droplet radii

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were 1 to 7 µm. The growth rate of the collector drop was determined from the change in terminal velocity while it was kept continuously suspended in the observation section. Theoretically the drop growth rate is described by the following equation (Pruppacher and Klett, 1997):

r12

dr1 1 = ∫ K (r1 , r2 ) r32 n(r2 ) dr2 dt 3

(4)

with

K (r1 , r2 ) = E π (r1 + r2 ) 2 v1 − v 2

(5)

where K is the collection kernel, r1 and r2 are the radii of the collector and the colliding droplet, respectively, v1 and v2 the corresponding terminal velocities. E = Ecoll Ecoal is the collection efficiency with the collision efficiency Ecoll and the coalescence efficiency Ecoal. It was assumed that the coalescence efficiency equals 1 meaning that all colliding drops stay together and form a new drop. Earlier, collision efficiencies of drops with values of the pratio: p=r2/r1 (r2 the radius of the smaller collision partner, r1 the radius of the collector drop) as low as 0.05 was not available in the literature. These have been determined from the wind tunnel experiments by an empirical approach. For details see Vohl et al. (1999) and Vohl et al. (2007). Previously existing tabulated values of the collision efficiency were interpolated and completed in such a way that drop growth rates calculated with these collision efficiencies matched with observed growth rates. The new tables provide collision efficiencies for a wide range of drop sizes and radius ratios p. This is highly important for small p-ratios where the collision efficiency changes significantly. The empirically derived collision efficiencies are available for use in cloud models. The analogous process to collisional drop growth in a mixed phase cloud is riming, i.e. the growth of ice particles by the deposition of liquid droplets. This is an important process to form precipitation in mixed phase clouds which are the most abundant ones in mid-latitudes. The experiments were performed in the way that a single spherical ice particle with 290 to 390 µm radius was freely suspended in the wind tunnel within a cloud of supercooled droplets with radii between 10 and 20 µm. The experiments were performed in a temperature range between -8 and -12°C where riming proceeds in the atmosphere. The collection kernels Kice were calculated from the mean mass increase dm/dt of the rimed ice particles and the average liquid water content LWC during the experiments according to the following equation (Pflaum and Pruppacher, 1979):

K ice =

dm / dt LWC

(6)

The results of this experiment together with earlier studies on collection kernel are plotted in Figure 4. Parameterizations were derived from new and earlier wind tunnel experiments describing the collection kernel of ice particles as function of the collector momentum m×v (mass × fall velocity) (v. Blohn et al., 2009):

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K ice _ 6 = 10.06 (m v) 0.847

(7)

K ice _ 10 = 10.22 (m v) 0.738

(8)

Kice _ 15 = 10.72 (m v)0.728

(9)

Collection kernel, (cm3 s-1)

3

1

0.1 0.001

0.01

0.1

Momentum of collector, m×v (g cm s-1) Figure 4. Collection kernel of rimed graupel as a function of momentum of collector. Experimental data are plotted for 15 µm, 10 µm and 6 µm cloud droplet radii by dots, triangles and asterisks, respectively. The solid, dashed, and dotted lines represent theoretical calculations for liquid-liquid drop collisions.

The indices stand for the mean size of the supercooled droplets in µm. In theory, the collection kernel K is given by Eq. 5; however, efficiencies for interactions between spherical collector ice particles of differing densities (resulting from riming) and droplets are not available so far. Therefore, the measured ice collection kernels were compared to corresponding collection kernels of liquid drops as determined in earlier wind tunnel experiments (Vohl et al., 1999; Vohl et al., 2007). It was found that the collection kernels of ice particles were slightly higher than the collection kernels of liquid drops (see Figure 4). An empirical factor depending on the cloud droplet radii was derived so that for the investigated size ranges of ice particles and droplets corrected collection kernels of ice particles can be incorporated in cloud models.

Melting of Snow Flakes A topic of great importance in cloud and precipitation microphysics is the phase change of water. In mid-latitudes, precipitation is often initiated via the ice phase, i.e. rain on the ground is the result of the melting of ice particles. The melting time and the fall behavior of

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melting snow flakes were investigated in wind tunnel experiments. Natural and laboratorymade aggregates of ice crystals were melted under free falling conditions while the wind tunnel was warmed up at rates typical for falling snow flakes in the atmosphere (1.5°C per min, corresponding to an average warming rate of approximately 0.8°C per 100 m). The diameters of the snow flakes were around 10 mm with masses between 2 × 10-3 g and 11 × 10-3 g and corresponding densities of 0.005 g cm-3 to 0.02 g cm-3. They melted into drops of diameters between 1.5 and 2.6 mm. The variation of the fall mode, the fall velocity, and the percentage of ice melted was recorded with a film camera (Mitra et al., 1990). Dry snow flakes exercised spinning, helical, shaking or swing motions with frequencies dependent on the size and the porosity of the snow flake and the number of component crystals. As soon as melting started, the frequencies of movements changed abruptly to values of a wide spread without correlation to any parameter. From irregular sideways motions of the melting snow flakes it was concluded that aggregation by collision of ice crystals and snow flakes continues in natural cloud even in the upper part of the melting layer. At the time when the ice lattice of the snow flake collapsed uncontrollable erratic downward acceleration began. Based on these observations, the melting of snow flakes was divided into four stages. The wind tunnel observations served as a basis for the polarimetric model of Russchenberg and Lighthart (1996) for snow flakes passing through the melting layer. The determined melting rates were used by several authors to model the development of the atmospheric melting layer, e.g. Szyrmer and Zawadzki (1999), Barthazy et al. (1998), Phillips et al. (2006) and are still the only ones which are available for such model simulations.

2.3.1.2. Cloud Chemistry Processes Rainwater samples show the content of trace gases in the liquid phase indicating that scavenging by water drops is an essential process to remove trace gases from the atmosphere. To realistically investigate the scavenging of trace gases the process of gas uptake has to be performed with water drops freely floating at their terminal velocities. Only in this case the air stream around the drop corresponds with the situation in the atmosphere and the gas uptake will proceed as in natural raindrops. During experiments at the Mainz vertical wind tunnel drops were suspended in the wind tunnel while the air was mixed with trace gases in various concentrations. The experiments were performed partly with raindrops with radii of 2.9 mm and partly with smaller drops with radii of 360 µm. After defined exposition times in the range of some minutes the drops were captured and taken out from the wind tunnel, fixed in sample bottles, and analyzed by means of ion chromatography to determine their trace gas content. The investigations concentrated on the uptake and desorption of sulfur dioxide (SO2) and ammonia (NH3). Scavenging of Sulfur Dioxide by Large and Small Raindrops Besides from natural sources like volcanic emissions and aeolian formation of particulate sulfate, sulfur dioxide (SO2) enters the atmosphere mainly from anthropogenic sources, e.g. the combustion of fossil fuels and the smelting of metals (Warneck, 2000). Measured sulfate in raindrops can originate from in-cloud SO2 oxidation or from the uptake of sulfate particles. The proportioning of these could be clarified by theoretical models which were verified by laboratory experiments at the Mainz vertical wind tunnel. Besides pure water drops also drops were investigated which contained oxidants or catalysts supporting the SO2 oxidation in the

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liquid phase. As oxidant H2O2 was used and as catalysts the heavy metals manganese (Mn) and iron (Fe) in ionic forms. The uptake of SO2 gas by raindrops of 2.9 mm radius was investigated with various concentrations in the gas phase between 50 to 500 ppbv while the drops contained H2O2 in concentrations of 1× 10-6 to 1× 10-3 M (Waltrop et al., 1992). The studies with small drops of 360 µm radius were undertaken with SO2 gas concentrations of 100 ppbv with 1× 10-3 M H2O2 present in the liquid phase (Diehl et al., 2000). In cases where heavy metals were used as catalysts the SO2 gas concentration was 100 ppbv, and the drops (radii 2.9 mm and 360 µm) contained a Mn2+ concentration of 1 × 10−5 M or a Fe3+ concentration of 2 × 10−6 M. The exposure times were up to 220 s. Desorption of SO2 from water drops was studied with drop radii from 250 µm to 2 mm. In all cases it was found that oxidants and catalysts significantly enhance the uptake rates in agreement with theoretical models (Waltrop et al., 1991; Diehl et al., 2000; HeuselWaltrop et al., 2003). On the other hand, theoretical studies based on wind tunnel experiments indicated that for typical concentrations of sulfate inside raindrops significant amounts of SO2 will desorb from the drops unless oxidants like H2O2 are present in the liquid phase (Mitra and Hannemann, 1993).

Scavenging of Ammonia by Raindrops Ammonia (NH3) is one of the most important trace gases in liquid phase chemistry as it is the only inorganic base of major abundance in the atmosphere. Ammonia is mainly emitted from livestock waste, application of fertilizer, and biomass burning (e.g., Schlesinger and Hartley 1992). As it is highly soluble in water it plays an important role in the acid-baseinteractions of cloud and rain water (Warneck 2000). The experiments at the Mainz vertical wind tunnel showed that ammonia is taken up very efficiently by water drops. As in the atmosphere not only a single species is present also the simultaneous uptake of two or more species was studied: NH3 together with CO2, and NH3 together with SO2 and CO2. Drops with radii of 2.9 mm were freely suspended in the wind tunnel air which contained between 195 and 430 ppbv NH3 gas and 350 ppmv CO2, or, in other cases, 280 to 390 ppbv NH3 gas, 95 to 110 ppbv SO2 gas, and 350 ppmv CO2. Exposure times were up to 180 s. The experimental results were compared to gas uptake models, i.e. convective diffusion models. The application of these models showed that the NH3 uptake is significantly overestimated when aqueous CO2 kinetics is not included (Hannemann et al., 1995). This is also presented in Figure 5, where the experimentally determined NH3 uptake (symbols) is compared with three different formulations for aqueous CO2 chemistry. Under the assumption of solution and ionization equilibrium (solid line) the NH3 uptake is significantly overestimated in comparison to full kinetic treatment (dashed line). By neglecting the chemical reaction CO 2 (aq) + OH - ↔ HCO 3- in the CO2 hydration treatment, the uptake of NH3 is significantly underestimated (dotted line). Simulations with a pollution washout model with realistic SO2, NH3, and CO2 gas profiles indicated that the SO2 uptake is strongly dependent on the NH3 concentration in the atmosphere and on the rain rate. Furthermore, it was found that small drops contribute more towards the washout of these gases and that in case of simultaneous presence of NH3 and SO2, desorption of these gases was strongly reduced (Hannemann et al., 1996).

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22 20 18

-5

[NH3]tot (10 mol/l)

16 14 12 10 8 6 4 2 0 0

20

40

60

80

100

120

140

160

Time (s) Figure 5. Comparison between the results of three different aqueous chemistry formulations on the NH3 uptake by a 5.76-mm diameter water drop at 15 °C [NH3]g = 195 ppbv; [CO2]g = 350 ppmv (Hannemann et al., 1995). Symbols: experimentally determined NH3 uptake; solid line: CO2 assumed to be in thermodynamically equilibrium; dashed line: full kinetic treatment; dotted line: kinetic treatment but neglecting the chemical reaction

CO 2 (aq) + OH - ↔ HCO 3- .

Cloud chemistry processes were also performed in the ice phase not at the vertical wind tunnel but in flow tubes placed inside a walk-in cold chamber. Therefore, these experiments are not described here. However, the results indicate that the uptake of trace gases in the liquid phase is significantly enhanced in comparison to the uptake in the ice phase (Mitra et al., 1990; Diehl et al., 1995; 1998; Hoog et al., 2007). Therefore, it can be concluded that the direct scavenging of trace gases via the ice phase will play a minor role while the riming process might be the major process to incorporate these trace elements into the ice phase. Those experiments are currently being performed at the Mainz vertical wind tunnel.

2.3.1.3. Aerosol-Cloud Interactions Aerosol-cloud interactions were investigated in the mixed phase and in liquid clouds; these were the heterogeneous freezing of supercooled drops, the formation of aerosol particles by evaporation of drops, and the influence of aerosol particles on the radiative properties of cloud droplets. Heterogeneous Drop Freezing in the Immersion and Contact Mode In mid-latitudes, the major fraction of precipitation is initiated via the ice phase. An important process to form ice in clouds is the freezing of supercooled drops in clouds which reach altitudes where the temperature decreases below the freezing point. Homogeneous

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freezing, i.e. formation of ice without the participation of aerosol particles becomes efficient at temperatures below -35°C. Thus, at higher temperatures and lower altitudes freezing will proceed heterogeneously when suitable aerosol particles, the so-called ice nuclei, are available. The influence of these ice nuclei enhances the freezing temperatures of supercooled drops up to values not far below the freezing point. The most efficient ice nuclei are biological particles, followed by mineral dust, while soot particles are less efficient ice nuclei. Two processes are known to freeze supercooled drops: immersion freezing and contact freezing. In immersion freezing, the ice nuclei are taken up by the drop (by nucleation or by scavenging) and initiate freezing of the drop when it is supercooled below a critical temperature. In case of the contact mode, the ice nuclei collide with a supercooled drop and affect freezing of the drop if is supercooled below a critical temperature (Pruppacher and Klett, 1997). In general, contact freezing takes place at higher temperatures as immersion freezing (see Figure 6).

Fraction of frozen drops (%)

100 90 80 70 60 50 40 30 20 10 0 -24

-22

-20

-18

-16

Temperature (°C) Figure 6. Temperature dependence of the fraction of drops frozen due to contact freezing (filled symbols) and immersion freezing (open symbols) for redtop grass pollen.

In the Mainz vertical wind tunnel, these processes can be simulated similar to the atmosphere as the drops are freely suspended at their terminal velocities in the air stream of the tunnel when they freeze. Furthermore, the experimental procedure allows to clearly distinguishing between the two processes. During experiments in the immersion mode, the drops are generated from distilled water containing the immersed particles. They are freely floated in the wind tunnel while supercooled and observed if they freeze. In contact freezing experiments, pure water drops are suspended in the wind tunnel, supercooled, and afterwards particles are added to the wind tunnel air downstream of the experimental section so that they pass the floating drop. Contact freezing takes place when a drop freezes immediately after collision.

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These experiments were performed with drops of 150 to 400 µm radius at different temperatures down to -30°C. Ice nuclei which were investigated so far were soot particles from a kerosene burner to study the influence of jet traffics on ice formation, and several pollen types as representatives of biological particles. It was found that combustion particles act as ice nuclei at temperatures much warmer than the temperatures prevailing at the altitude where the jet plane cruises. This implied that drops formed at the exit of the jet plane freeze immediately not by homogenous but by heterogeneous nucleation and do not need to be supercooled to the ambient temperatures at the cruising altitude. Thus, ice formation takes place earlier than predicted according to homogeneous nucleation which agreed better with field observations (Diehl and Mitra, 1998). Regarding pollen, the experiments showed that they initiate freezing at temperatures up to -6°C. This is lower than other very efficient biological ice nuclei such as bacteria, but definitely higher than mineral dust or soot. The investigation of a wide range of pollen types indicated that the ice nucleation ability seems to be a general pollen property (Diehl et al., 2002; v. Blohn et al., 2005), but the freezing temperatures are different for the different types of pollens (as an example the fractions of frozen drops due contact and immersion freezing temperatures measured for redtop grass pollen are plotted in Figure 6). The freezing temperatures served as base for parameterizations describing immersion and contact freezing in cloud models (Diehl and Wurzler, 2004; Diehl et al., 2006) which are applicable in global models also (e.g., Lohmann and Diehl, 2006; Storelvmo et al., 2008; and Hoose et al., 2008).

Drop-to-Particle Conversion Many cloud droplets do not reach the ground as precipitation but evaporate before. Reasons may be the absence of active ice nuclei to form ice particles and the absence of larger drops or of dynamic forces to initiate collisional drop growth. Trace gases dissolved in the drops may be converted into compounds which will not desorb from the drops. If those drops evaporate they will act as a source of aerosol particles affecting the size distribution and chemical composition of atmospheric aerosol particles. During wind tunnel experiments, the dynamics in atmospheric clouds were simulated by freely floating evaporating droplets. These droplets consisted of aqueous solutions of salts which were most frequently found in atmospheric cloud water: NaCl, (NH4)2SO4, mixtures of these two salts, and salts of artificial and natural ocean water. Other droplets contained insoluble particles typically found in cloud water such as clay, soot, iron oxide, zinc oxide, manganese oxide, and calcium sulfate. The relative humidity of the wind tunnel air had values between 5 and 60%. The whole evaporation process was recorded using a 16-mm film camera. As long as the droplet was evaporating, its terminal velocity decreased requiring a continuous adjustment of the tunnel vertical air speed in order to keep the droplet stable in observation section. When crystallization started the fall mode changed abruptly into an unsteady motion with erratic sailing and spinning caused by asymmetric drag forces on the rough underside of the drop where crystallization invariably began to take place. After complete evaporation of all water, the remaining particle fell straight without sideways deflection but with axial rotation and helical motion. The concentrations of the salts were selected such that after evaporation particles with diameters between 40 and 300 µm formed. The resulting salt particles were removed from the wind tunnel and the samples were studied with a normal light microscope or a scanning electron microscope.

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It was found that the aerosol particles formed during the evaporation of cloud droplets did not break up or splinter. Thus, it was concluded that an evaporating cloud droplet produces one aerosol particle whose mass and chemistry are dependent on the salts and insoluble compounds contained in the droplet. Since most cloud drops contain a mixture of various salts it can be expected that most particles formed by drop-to-particle conversion will have a tendency to be rounded while drops containing NaCl only generated cubic shaped particles (Mitra et al., 1992).

Radiation Properties of Polluted Droplets The earth’s radiative balance and the global climate are affected by the radiative properties of clouds which are dependent on the liquid water content and the cloud droplet effective size. An instrument frequently used to determine microphysical characteristics of clouds is the Forward Scattering Spectrometer Probe (FSSP) which uses the scattering intensity in the near forward scattering range to derive droplet sizes. However, in the data analysis pure water droplets are assumed although pollutants in the water droplets might influence the droplet size analysis. To estimate these effects an FSSP was adapted and mounted to the wind tunnel. Droplets with diameters around 30 µm containing soluble ammonium sulfate or suspended absorbing graphite particles as pollutions were freely floated in the wind tunnel. The intensity of the FSSP laser radiation scattered by the drops was measured and Mie simulations were performed for pure and polluted droplets by modifying the refractive indices of the droplets. The results indicated that for high pollution concentrations in cloud droplets the FSSP detection signal significantly depends on the refractive index of the droplet, i.e. on the concentration of soluble or insoluble pollutants, respectively. However, for common atmospheric concentrations of soluble or insoluble material in droplets, a correction of the droplet size distributions measured with an FSSP can be neglected, at least for droplets in the investigated size range (Diehl et al., 2008). 2.3.2. Experiments in Turbulent Air Stream Some of the processes investigated in the laminar air stream of the wind tunnel were subsequently performed in a turbulent environment to determine the influence of atmospheric turbulence on these processes. In and below clouds, the air motions are always more or less turbulent depending on the cloud type. This is characterized by the dissipation rate of kinetic energy per unit mass ε which is varying from 0.0002 m2s-3 in thin cirrus clouds to 0.1 m2s-3 in deep convective clouds. Below clouds ε =0.0009 m2s-3 was measured (Pruppacher and Klett, 1997). Inertial particles deviate in a turbulent flow from air trajectories which is followed by the formation of turbulence induced relative velocities between particles. This leads to effects such as an increase in swept volume, formation of particle concentration non-uniformity (clustering) and an increase in the collision efficiency. Thus, the collisional growth of cloud droplets maybe enhanced by turbulence as well as impaction scavenging of aerosol particles or even the scavenging of trace gases. These processes were investigated in wind tunnel experiments where the air stream of the wind tunnel was modified by obstructing objects positioned upstream of the freely floating objects, i.e. between the contraction section and the observation section of the wind tunnel. The energy dissipation rate in the wind tunnel air stream was obtained from hot wire anemometer data for different velocity settings at various points in the zone where the objects were floating.

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2.3.2.1. Basic Cloud Physical Processes Collisional Drop Growth The experiments were performed in the same way as in the laminar air stream (described in section 2.3.1.1) but in a turbulent environment. A flat ring of 4 cm diameter was mounted just below the observation section so that it can be moved in and out and the collector drops grew by collision and coalescence with small droplets in a turbulent air stream. As before, the growth rate was determined from the change in terminal velocity. The turbulent spectral energy dissipation rate ε was measured with various settings of the wind speed at the locations where the collector drop floated. It was in the range of 1 × 10-2 m2 s-3 for mean velocities of 1.05 m s-1 and 7 × 10-2 m2 s-3 for mean velocities of 1.77 m s-1 and, thus, covered the lower end of the inertial and the viscous subrange of atmospheric values. A comparison of the experimental turbulent growth data (solid line in Figure 7 represents a linear fit to the measured data points) with laminar continuous growth results under identical environmental condition (dotted line in Figure 7) shows an increase of the collisional drop growth rates in a turbulent air stream. Numerical sensitivity studies indicated that the laminar collection kernel in the cloud model had to be enhanced by 10 to 20% to obtain good agreement with the experimental data measured under turbulent conditions. Further model simulations with detailed microphysics showed that this enhancement of the collision kernel affected a noticeably faster development of precipitation sized drops. Thus, a small increase of the collection kernel due to turbulence could have a significant effect on cloud microphysics and, in particular, on precipitation formation (Vohl et al., 1999). The turbulent collisional drop growth measured in the Mainz vertical wind tunnel was successfully modeled by Riemer et al. (2007). 240 220 200 180

Radius (μm)

160 140 120 100 80 60 40 20 0 0

200

400

600

800

1000

1200

Time (s) Figure 7. Drop growth in laminar and turbulent flow (linear fit plots). Solid line: experimental turbulent growth; dotted line: laminar continuous growth under identical environmental condition.

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2.3.2.2. Cloud Chemistry Processes Sulfur Dioxide The scavenging experiments were performed the same as the ones in a laminar air stream, see section 2.3.1.2. Drops of 360 µm radius containing 1× 10-3 M H2O2 as oxidant for sulfur dioxide were freely suspended in the wind tunnel air with a concentration of 100 ppbv SO2 gas. Turbulence was created again by a removable, flat ring construction of 4 cm inside diameter. At wind speeds between 2 and 3 m s-1 which were required to suspend drops of the desired size range the energy dissipation rate ε of the turbulent air flow was in the order of 0.06 to 0.08 m2s-3. The experimental results were compared to the results of model computations without turbulence for the experimental conditions. The comparison did not show any increased gas uptake under turbulent conditions. This can be explained because the very small eddies which are comparable in size to the thickness of the ventilated boundary layer lie at the low end of the viscous subrange of the power spectrum of turbulence and, therefore, are too weak to affect the gas transport through the boundary layer (Diehl et al., 2000). 2.3.2.3. Aerosol Cloud Interactions Impaction scavenging by water drops Similar to atmospheric trace gases, aerosol particles can be scavenged by cloud droplets and either removed by precipitation or released, during cloud evaporation, in a modified form back into the atmosphere. One possibility is impaction scavenging, the collision between aerosol particles and drops. It plays an important role in below-cloud scavenging as well as in the scavenging of inactivated or even not-wettable aerosol particles inside the clouds. Earlier experiments had been performed under laminar conditions; however, the investigation in a turbulent air stream would represent the realistic atmospheric case. This was performed at the Mainz vertical wind tunnel and the results were compared to earlier laminar studies. The freely floating collector drops had sizes of 360 µm, 1.7 mm, and 2.9 mm. The aerosol particles were produced from indium acetylacetonate, a non-hygroscopic organo-metal, and had mean radii of 0.16 to 0.24 µm. Turbulence in the wind tunnel air stream was produced by a needle of 2 cm diameter and 8 cm length. The energy dissipation rates were in the order of 0.03 m2 s-3 for lower wind speeds (2.4 to 3.2 m s-1) and in the order of 0.5 m2 s-3 for higher wind speeds (8.4 and 9.2 m s-1). After exposure, the drops were removed from the wind tunnel and analyzed for the aerosol content by neutron activation analysis, which quantifies the amount of indium in the samples. To estimate the effect of turbulence on the scavenging of submicron aerosol particles, the results were compared to those obtained under laminar conditions by Wang and Pruppacher (1977) which were performed in a fall shaft using the same kind of aerosol particles and also to a theoretical model (Grover and Pruppacher, 1985). Both comparisons did not show a significant enhancement of the collision efficiency under turbulent conditions (Vohl et al., 2001).

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SUMMARY The investigations of basic cloud processes at the Mainz vertical wind tunnel provided observations, data tables, and parameterizations of raindrop deformation and oscillation, collisional drop growth, growth of ice particles by riming, and melting of snow flakes which are applicable in cloud and precipitation models. Data from heterogeneous drop freezing serve as base for parameterizations usable in cloud and global models. Models describing the scavenging of trace gases were verified by laboratory results. Summarizing the experiments in a turbulent air stream of the wind tunnel, it is obvious that these represent the more realistic atmospheric conditions. However, not all cloud and precipitation processes seem to be affected by turbulence. One has the impression that effects are to be expected only in cases where larger objects such as cloud droplets are involved but negligible when smaller objects such as aerosol particles or gas molecules are involved. In the last 25 years the Mainz vertical wind tunnel has become a world-wide acknowledged research and educational facility in different fields of cloud physics and chemistry. The experimental and modeling works carried out at the Mainz vertical wind tunnel provided many scientific publications (listed in the References), as well as numerous PhD and Diplom (Master-equivalent degree in Germany) theses.

ACKNOWLEDGMENTS Funding for the original construction and initial instrumentation of the Mainz vertical wind tunnel was provided by the German Federal Ministry of Science and Technology (BMBF). The modification of the tunnel in such a way that the air flow could be cooled down to temperatures as low as -30 °C over the whole range of tunnel speeds, was provided by a grant under the University Development Act (“Hochschulbau-Förderungsgesetz”). Many of the scientific projects carried out at the wind tunnel have been supported by the German Science Foundation (DFG) in particular through the Collaborative Research Centers (SFB 233 and SFB 641), and by DFG projects falling under the category of “Normal Individual Applications”, which also supported Doctoral works at the facility. The authors very gratefully acknowledge the contributions of many graduate and PhD students who performed their experiments at the wind tunnel facility.

REFERENCES Barthazy, E., W. Heinrich, and A. Waldvogel, 1998: Size distribution of hydrometeors through the melting layer. Atm. Res., 47-48, 193-208. Beard, K., Pruppacher, H., 1969. A determination of the terminal velocity and drag of small water drops by means of a wind tunnel. J. Atmos. Sci., 26, 1066-1072. Beard, K. V., and C. Chuang, 1987: A new model for the equilibrium shape of raindrops. J. Atmos. Sci., 44, 1509–1524. Beard, K.V., R.J. Kubesh, and H.T. Ochs, 1991: Laboratory measurements of small raindrop distortion. Part I: Axis ratios and fall behavior. J. Atmos. Sci., 48, 698-710.

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Bertram, A.K., D.D. Patterson, and J.J. Sloan, 1996: Mechanisms and temperatures for the freezing of sulfuric acid aerosols measured by FTIR extinction spectroscopy. J. Phys. Chem., 100, 2376-2383. Blanchard, D. C., 1950: The behavior of water drops at terminal velocity in air. Trans. Amer. Geophys. Union, 31, 836 - 842. Carleton K.L., D.M. Sonnenfroh, W.T. Rawlins, B.E. Wyslouzil, and S. Arnold, 1997: Freezing behavior of single sulfuric acid aerosols suspended in a quadrupole trap. J. Geophys. Res., 102, 6025-6033. Chuang, C. H., and K. V. Beard, 1990: A numerical model for the equilibrium shape of electrified raindrops. J. Atmos. Sci., 47, 1374–1389. DeMott, P.J., and D.C. Rogers, 1990: Freezing nucleation rates of dilute solution droplets measured between -30 and -40°C in laboratory simulations of natural clouds. J. Atmos. Sci., 47, 1056-1064. Diehl, K., S.K. Mitra, and H.R. Pruppacher, 1995: A laboratory study of the uptake of HNO3 and HCl vapor by snow crystals and ice spheres at temperatures between 0 and -40° C. Atmos. Environ., 29, No.9, 975-981 Diehl, K., and S.K. Mitra, 1998: A laboratory study of the effects of a kerosene burner exhaust on ice nucleation and the evaporation of ice crystals. Atmos. Environ., 32, No.18, 3145-3151. Diehl, K., S.K. Mitra, and H.R. Pruppacher, 1998: A laboratory study on the uptake of HCl, HNO3, and SO2 gas by ice crystals and the effect of these gases on the evaporation rate of the crystals. Atmos. Res., 47-48, 235-244. Diehl, K., O. Vohl, S.K. Mitra, and H.R. Pruppacher, 2000: A laboratory and theoretical study on the uptake of sulfur dioxide gas by small water drops containing hydrogen peroxide under laminar and turbulent conditions. Atmos. Environ., 34, 2865-2871 Diehl, K., S. Matthias-Maser, S.K. Mitra, and R Jaenicke, 2002: The ice nucleating ability of pollen. Part II: Laboratory studies in immersion and contact freezing modes. Atmos. Res., 61, 125-133 Diehl, K., and S. Wurzler, 2004: Heterogeneous drop freezing in the immersion mode: Model calculations considering soluble and insoluble particles in the drops. J. Atmos. Sci., 61, 2063-2072 Diehl, K., M. Simmel, and S. Wurzler, 2006: Numerical simulations of the impact of aerosol properties and drop freezing modes on the glaciation, microphysics, and dynamics of clouds. J. Geophys. Res. 111, D07202, doi:10.1029/2005JD005884 Diehl, K., G. Huber, S.K. Mitra, and M. Wendisch, 2008: Laboratory studies of scattering properties of polluted cloud droplets: Implications for FSSP measurements. J. Atmos. Ocean. Technol., 25, 1894-1898. Diehl, K., M. Ettner-Mahl, A. Hannemann, S.K. Mitra, 2009: Homogeneous freezing of single sulfuric and nitric acid solution drops levitated in an acoustic trap. Atmos. Res., 94, 356-361. Ettner, M., S.K. Mitra, and S. Borrmann, 2004: Heterogeneous freezing of single sulfuric acid solution droplets: laboratory experiments utilizing an acoustic levitator. Atmos. Chem. Phys., 4, 1925-1932. Feng, J.Q., and K. V. Beard, 1991: A perturbation model of raindrop oscillation characteristics with aerodynamic effects. J. Atmos. Sci., 48, 1856–1868.

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Grover, S. N., and H. R. Pruppacher, 1985: The effect of vertical turbulent fluctuations in the atmosphere on the collection of aerosol particles by cloud drops. J. Atmos. Sci., 42, 2305– 2318. Green, A. W., 1975: An approximation for the shapes of large raindrops. J. Appl. Meteor., 14 (8), 1578-1583. Hannemann, A., S.K. Mitra, and H.R. Pruppacher, 1995: On the scavenging of gaseous nitrogen compounds by large and small rain drops: Part I: A wind tunnel and theoretical study of the uptake and desorption of NH3 in the presence of CO2. J. Atm. Chem., 21, 293-307 Hannemann, A., S.K. Mitra, and H.R. Pruppacher, 1996: On the scavenging of gaseous nitrogen compounds by large and small rain drops: Part II: A wind tunnel and theoretical study of the simultaneous uptake of NH3, SO2, and CO2 in water drops. J. Atm. Chem., 24, 271-284 Heusel-Waltrop, A., K. Diehl, S. K. Mitra, and H.R. Pruppacher, 2003: A laboratory and theoretical study on the uptake of SO2 gas by large and small water drops containing heavy metal ions. J. Atm. Chem., 44, 211-223 Hoog, I., S. K. Mitra, K. Diehl, and S. Borrmann, 2007: Laboratory studies about the interaction of ammonia with ice crystals at temperatures between 0 and -20°C. J. Atm. Chem., 57, 73-84 Hoose, C., U. Lohmann, R. Erdin, and I. Tegen, 2008: The global influence of dust mineralogical composition on heterogeneous ice nucleation in mixed-phase clouds. Environ. Res. Lett., 3, 025003. Kamra, A., and D. Ahire, 1989: Wind-tunnel studies of the shape of charged and uncharged water drops in the absence or presence of an electric field. Atmos. Res., 23, 117-134. LeClair, B. P., A. E. Hamielec, H. R. Pruppacher, and W. D. Hall, 1972: A theoretical and experimental study of the internal circulation in water drops falling at terminal velocity in air. J. Atmos. Sci., 29, 728–740. List, R., 1966: A hail tunnel with pressure control. J. Atmos. Sci., 23, 61-66. Lohmann, U., and K. Diehl, 2006: Sensitivity studies of the importance of dust nuclei for the indirect aerosol effect on stratiform mixed-phase clouds. J. Atmos. Sci., 63, 968-982. Mitra, S. K., O. Vohl, M. Ahr, and H.R. Pruppacher, 1990a: A wind tunnel and theoretical study of the melting behavior of atmospheric ice particles. IV: Experiment and theory for snow flakes. J. Atm. Sci., 47, No.5, 584-591 Mitra, S.K., S. Barth, and H.R. Pruppacher, 1990b: A laboratory study on the scavenging of SO2 by snow crystals. Atmos. Environ., 24a, No.9, 2307-2312 Mitra, S.K., J. Brinkmann, and H.R. Pruppacher, 1992: A wind tunnel study on the drop-toparticle conversion. J. Aerosol Sci., 23, 245-256 Mitra, S.K., and A. Hannemann, 1993: On the scavenging of by large and small rain drops: 5. A wind tunnel and theoretical study of the desorption of SO2 from water drops containing S(IV). J. Atm. Chem., 16, 201-218. Möhler, O., O. Stetzer, S. Schäfers, C. Linke, M. Schnaiter, R. Tiede, H. Saathoff, M. Krämer, A. Mangold, P. Budz, P. Zink, J. Schreiner, K. Mauersberger, W. Haag, B. Kärcher, and U. Schurath, 2003: Experimental investigation of homogeneous freezing of sulphuric acid particles in the aerosol chamber AIDA. Atmos. Chem. Phys., 3, 211–223. Pflaum, J.C., and H.R. Pruppacher, 1979: A wind tunnel investigation of the growth of graupel initiated from frozen drops. J. Atmos. Sci., 36, 680-689.

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Phillips, V.T., A. Pokrovsky, and A. Khain, 2006: The influence of time-dependant melting on the dynamics and precipitation production in maritime and continental storm clouds. J. Atmos. Sci., 64, 338-359. Pruppacher, H.R., and J.D. Klett, 1997: Microphysics of Clouds and Precipitation, 2nd ed., Kluwer Academic Publishers. Riemer, N., A.S. Wexler, and K. Diehl, 2007: Droplet growth by turbulent coagulation – Comparison of theory and measurements. J. Geophys. Res., 112, D07204, doi:10.1029/2006JD007702. Russchenberg, H.W.J., and L.P. Lighthart, 1996: Backscattering by and propagation through the melting layer of precipitation: A new polarimetric model. IEEE Trans. Geosci. Remote Sensing, 34, 3-14. Saylor, J.R., and B.K. Jones, 2005: The existence of vortices in the wakes of simulated raindrops. Phys. Fluids, 17, 031706-4. Schlesinger, W.H., and A.E. Hartley, 1992: A global budget for atmospheric NH3. Biogeochem., 15, 191-211. Storelvmo, T., J. E. Kristjansson, and U. Lohmann, 2008: Aerosol Influence on Mixed-Phase Clouds in CAM-Oslo. J. Atmos. Sci., 60, 3214-3230. Stratmann, F., A. Kiselev, S. Wurzler, M. Wendisch, J. Heintzenberg, K. Diehl, H. Wex, and S. Schmidt, 2004: Laboratory studies and numerical simulations of cloud droplet formation under realistic super-saturation conditions. J. Atmos. Ocean. Technol., 21, 876887 Szakáll, M., K. Diehl, S.K. Mitra, and S. Borrmann, 2009: A wind tunnel study on the shape, oscillation and internal circulation of large raindrops with sizes between 2.5 and 7.5 mm. J. Atmos. Sci., 66, 755-765. Szakáll, M., S.K. Mitra, K. Diehl, and S. Borrmann, 2010: Shapes and oscillations of falling raindrops – A review. Atm. Res., 97, 416-425. Szyrmer, W., and I. Zawadzki, 1999: Modeling of the melting layer. Part I: Dynamics and Microphysics. J. Atmos. Sci., 56, 3573-3592. Thurai, M., Szakáll, M., Bringi, V.N., Beard, K.V., Mitra, S.K., Borrmann, S., 2009: Drop shapes and axis ratio distributions: comparison between 2d video disdrometer and windtunnel measurements. J. Atmos. Oceanic Technol., 26, 1427–1432. Vohl, O., S. K. Mitra, S.C. Wurzler, and H.R. Pruppacher, 1999: A wind tunnel study on the effects of turbulence on the growth of cloud drops by collision and coalescence. J. Atmos. Sci., 56, 4088-4099 Vohl, O., S. K. Mitra, K. Diehl, G. Huber, S.C. Wurzler, K.-L. Kratz, and H.R. Pruppacher, 2001: A wind tunnel study of turbulence effects on the scavenging of aerosol particles by water drops. J. Atmos. Sci., 58, 3064-3072 Vohl, O., S. Wurzler, K. Diehl, M. Pinsky, A. Khain, and S.K. Mitra, 2007: Empirically determined collision efficiencies from laboratory investigations of laminar collisional growth of small raindrops. Atmos. Environ., 85, 120-125. Von Blohn, N., S.K. Mitra, K. Diehl, and S. Borrmann, 2005: The ice nucleating ability of pollen. Part III: New laboratory studies in immersion and contact freezing modes including more pollen types. Atm. Res., 78, 182-189. Von Blohn, N., K. Diehl, S.K. Mitra, and S. Borrmann, 2009: Wind tunnel investigations on the growth rates and regimes, and the collection kernels during riming. J. Atmos. Sci., 66, 2359-2366.

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Wang, P. K., and H. R. Pruppacher, 1977: An experimental determination of the efficiency with which aerosol particles are collected by water drops in subsaturated air. J. Atmos. Sci., 34, 1664–1669. Waltrop, A., S.K. Mitra, A.I. Flossmann, and H.R. Pruppacher, 1991: On the scavenging of SO2 by cloud and rain drops: 4. A wind tunnel and theoretical study of the adsorption of SO2 in the ppb(v) range by water drops containing H2O2. J. Atm. Chem., 12, 1-17 Warneck, P., 2000: Chemistry of the Natural Atmosphere, 2nd edn. Academic, New York. Wood, S.E., M.B. Baker, and B.D. Swanson, 2002: Instrument for studies of homogeneous and heterogeneous ice nucleation in free-falling supercooled water droplets. Rev. Sci. Instrum., 73, 3988-3996.

In: Wind Tunnels: Aerodynamics, Models and Experiments ISBN: 978-1-61209-204-1 Editors: Justin D. Pereira ©2011 Nova Science Publishers, inc.

Chapter 3

MODELING AND EXPERIMENTAL STUDY OF VARIATION OF DROPLET CLOUD CHARACTERISTICS IN A LOW-SPEED HORIZONTAL ICING WIND TUNNEL László E. Kollár* and Masoud Farzaneh‡ University of Québec at Chicoutimi (UQAC), Chicoutimi, QC, Canada

ABSTRACT Variation of the characteristics of aerosol clouds created in icing wind tunnels is studied theoretically and experimentally. The characteristics of interest are the droplet size distribution, liquid water content, temperature, velocity, and air humidity, which are among the most important factors affecting atmospheric icing. Several processes influence the trajectory, velocity, size and temperature of the droplets, such as collision, evaporation and cooling, gravitational settling, and turbulent dispersion. The authors have developed a two-dimensional theoretical model that takes these processes into account, and predicts how they influence the changes in the characteristics of the droplet cloud during its movement in the tunnel. The most recent development pays special attention to two of the possible collision outcomes, i.e. coalescence after minor deformation and bounce, together with the transition between them. Indeed, these outcomes are frequent when the relative velocity of the droplets is small, as is the case for a cloud formed after the injection of water droplets in the direction of air flow. An experimental study is also carried out with different thermodynamic parameters at different positions in the test section of the tunnel, which makes it possible to observe the evolution of cloud characteristics under different ambient conditions. The droplet size distribution and liquid * NSERC/Hydro-Québec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and Canada Research Chair on Atmospheric Icing Engineering of Power Networks (INGIVRE) www.cigele.ca, University of Québec at Chicoutimi (UQAC), Chicoutimi, QC, Canada, Tel.: +1 418 545 5011 / 5606, fax: +1 418 545 5012, e-mail: [email protected] ‡ NSERC/Hydro-Québec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and Canada Research Chair on Atmospheric Icing Engineering of Power Networks (INGIVRE) www.cigele.ca, University of Québec at Chicoutimi (UQAC), Chicoutimi, QC, Canada, Tel.: +1 418 545 5044, fax: +1 418 545 5032, e-mail: [email protected]

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water content of the aerosol clouds were measured using an integrated system for icing studies, which comprises two probes for droplet size measurements and a hotwire liquid water content sensor. Droplet trajectories were observed using particle image velocimetry. The experimental results are also used to validate the model by comparing them to model predictions. Satisfactory agreement between the experimental and calculated results establishes the applicability of the model to determine the evolution of droplet size distribution and liquid water content in an aerosol cloud in the streamwise direction, together with their vertical variation.

Keywords: aerosol cloud, binary droplet collision, droplet size distribution, low-speed wind tunnel, two-phase flow

NOMENCLATURE b B

Bcr

dimensional impact parameter impact parameter critical impact parameter

CD

drag coefficient

cw

specific heat of water

Cμ

constant in the expression for characteristic size of turbulent eddy

d

droplet diameter diffusivity of water vapor

Dw ew

pressure of saturated water vapor

f g h

Stokes drag gravitational acceleration thickness of gas film between two droplets critical film thickness at rupture

hr H k l

le

Hamaker constant turbulent kinetic energy horizontal length of the computational domain characteristic size of turbulent eddy

Lev

latent heat of vaporization of water

md

droplet mass

Nu

Nusselt number static pressure of air

pst Pr r

Rw Re RH Sc Sh t

Prandtl number disc radius on the edge of droplet gas constant for water vapor Reynolds number relative humidity Schmidt number Sherwood number time

Modeling and Experimental Study … T

temperature non-dimensional time

Tu

level of turbulence eddy lifetime

T

te tr

transit time

ts

time the two droplets need to slide near each other

u u

transverse (or escaping) velocity of gas in the gap between two droplets gas (air) velocity gas (air) mean velocity fluctuating component of gas (air) velocity non-dimensional gas (air) velocity

u u′  U Ur

relative velocity of colliding droplets

v V

droplet velocity velocity of post-collision droplet non-dimensional droplet velocity

We x

Weber number streamwise position in the test section non-dimensional droplet position

y Z

α γ δ ε

ϕ′

vertical position in the test section parameter in stretching separation criterion heat transfer coefficient droplet size ratio (larger to smaller) droplet size ratio (smaller to larger) turbulent dissipation shape factor

κ λ μa

parameter in bounce criterion thermal conductivity dynamic viscosity of air

η1

parameter in reflexive separation criterion

η2

parameter in reflexive separation criterion

σ

density surface tension of liquid (water) characteristic time of film-thinning process

τr

characteristic time in the expression for transit time

 V  X

ρ

τf

ξ χ

parameter in reflexive separation criterion parameter in bounce criterion Subscripts a air d droplet f film formation L larger droplet S smaller droplet

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1. INTRODUCTION Aerosol clouds are characterized by several parameters such as temperature, velocity, air humidity, liquid water content (LWC) and droplet size distribution (DSD). These are among the most important factors affecting atmospheric icing processes; therefore, it is essential to determine them correctly when modeling atmospheric icing. A typical way to simulate natural aerosol clouds under icing conditions is to inject water spray into the cold airstream in a lowspeed horizontal icing wind tunnel, thereby creating a two-phase air/dispersed water flow. This artificial aerosol cloud undergoes significant changes in the settling chamber and test section of the wind tunnel before reaching the icing object. Several factors are responsible for this modification. The thermodynamic interactions between the dispersed and carrying phases result in evaporation and cooling, thereby lowering droplet temperature and reducing droplet size. The mutual interactions within the dispersed phase are known as binary droplet collisions that modify droplet velocity and droplet size when the collision outcome is coalescence. The effect of external forces leads to gravitational settling of droplets, which becomes considerable for low air speeds. The extent to which these processes affect the characteristics of the aerosol cloud depends on the level of turbulence in the airflow. The turbulence level is usually kept low in the test section, to better simulate natural thermodynamic processes and conditions for ice accretion; however, a certain level of turbulence is essential, particularly in the settling chamber, to ensure mixing and homogeneity in the cloud. Among the parameters characterizing droplet clouds in low-speed wind tunnels, the air temperature does not change significantly, although it may be a few degrees higher in the test section due to heat transfer from the test chamber. The temperature of injected droplets decreases until reaching a temperature close to that of the air, and then it remains approximately constant. The airstream is accelerated in the settling chamber, and ideally the flow should be steady in the test section, although some fluctuation is unavoidable. The droplet velocities quickly approach the free stream velocity, and their mean velocities remain nearly constant, but the speed of individual droplets varies due to droplet collision and turbulence. The air relative humidity is between 0.7 and 0.95 in the test section in most of the experiments under icing conditions, and it does not very considerably during an experiment. The DSD and LWC are the cloud properties that are modified the most significantly between different points of the tunnel. They vary vertically due to gravity, which causes separation of droplets of different sizes; and they also change in the streamwise direction due to cloud deformation, droplet collision and evaporation. Much effort has been made to study the factors influencing droplet cloud characteristics and the resulting modification in two-phase flows. A widely used method to analyze fluidparticle flows is the Eulerian-Lagrangian approach, which treats the fluid phase as a continuum and considers the dispersed particles as a discrete phase (Creismeas, 1995; Crowe et al., 1977; Edson et al., 1996). These authors considered the heat and mass exchange between the phases, which results in droplet evaporation and cooling. The droplet equation of motion includes the gravity term, which may be negligible for high velocities, e.g. when studying flow around aircraft, but it is important for low velocities. Droplet trajectories for different velocities of the ambient air was examined in Gates et al., 1988. Dukowicz, 1980, proposed a stochastic approach for modeling turbulent dispersion of droplets, and this idea was applied in several later studies after some modifications (Gosman and Ioannides, 1981;

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Marek and Olsen Jr., 1986; O'Rourke and Bracco, 1980). O'Rourke and Bracco, 1980, also considered droplet collision and coalescence in their model by a stochastic approach that was subsequently applied in Gavaises et al., 1996. Post and Abraham, 2002, constructed a composite collision outcome model that included the different outcomes of binary droplet collisions, but not the outcome of the lowest-kinetic-energy collisions since they studied Diesel spray with high velocities. More recent developments proposed improvements on collision models, particularly for high-kinetic-energy collisions (Kim et al., 2009; Ko and Ryou, 2005; Munnannur and Reitz, 2007). The relative velocity of colliding droplets is usually low in low-speed wind tunnels where droplets are injected in the direction of the airflow; therefore the authors herein improved the collision model in the range of the lowestkinetic-energy collisions and disregarded the formation of satellite droplets (Kollár et al., 2005a). This two-phase flow model considered droplet collision and gravitational settling, whereas evaporation and cooling were added later (Kollár et al., 2005b). This study also discussed the range of thermodynamic parameters where the three processes considered are dominant with regard to the evolution of the DSD. The turbulent dispersion of droplets was included in the model of Kollár and Farzaneh, 2007b, and time scales of the three processes involved together with that of turbulent dispersion were determined in Kollár and Farzaneh, 2007a. This study improves on the collision outcome model by replacing the transition curve between the domains of coalescence after minor deformation and bounce recommended in Kollár et al., 2005a. That boundary was based on the experimental observations of Qian and Law, 1997, whereas the boundary proposed here will be explained by the film-thinning process. The former model was applied to determine how the DSD and LWC vary vertically in the middle of test section under different ambient conditions. In this research, further droplet size and LWC measurements were carried out in different positions of the test section, which provides both the streamwise evolution and vertical variation of the characteristics of clouds produced in low-speed wind tunnels. Model predictions for two typical conditions representing in-cloud icing (CI) and freezing drizzle (ZL) are verified by comparing them to measured data.

2. BINARY DROPLET COLLISION The phenomenon of binary droplet collision is controlled by several physical parameters. The most important ones are the droplet velocities, droplet diameters, dimensional impact parameter, surface tension of the liquid, and the densities and viscosity coefficients of the liquid and surrounding gas. Further components may also be significant, such as the pressure, molecular weight, and molecular structure of the gas. From these physical parameters several dimensionless quantities can be formed, namely, the Weber number, Reynolds number, impact parameter, droplet size ratio, ratio of densities, and ratio of viscosity coefficients. For a fixed liquid-gas system, the outcome of collision is usually described by the following three non-dimensional parameters: Weber number, impact parameter, and droplet size ratio. The Weber number is the ratio of the inertial force to the surface force:

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We = where

ρd

ρ dU r2 d S σ

(1)

is the droplet density, U r is the relative velocity of the interacting droplets, d S is

the diameter of the smaller droplet, and σ is the surface tension. The impact parameter is defined as the distance, b, from the center of one droplet to the relative velocity vector passing through the center of the other droplet, divided by the sum of the radii of the colliding droplets:

B=

2b dL + dS

(2)

where d L is the diameter of the larger droplet. The droplet size ratio is given by

δ=

dS dL

although the reciprocal,

(3)

γ = 1/ δ , is also used.

When two droplets interact during flight, different events may occur depending on the parameters listed in the previous paragraph. Comprehensive experimental studies on the possible outcomes of binary droplet collisions and the transition between their regimes were provided in Orme, 1997; Qian and Law, 1997. The evolution of the pressure and velocity fields during central binary collisions together with droplet deformation in the different regimes were studied numerically in Nikolopoulos et al., 2009. The droplets may experience bounce or coalescence. Coalescence may be stable or temporary, followed by separation which may result in either disruption or fragmentation. In disruption, the number of postcollision droplets is the same as that prior to collision. In fragmentation, numerous satellite droplets are also formed (Orme, 1997). Qian and Law, 1997 distinguish two regimes of separation according to the trajectories of colliding droplets and the subsequent separation process: separation for near head-on collisions or reflexive separation, and separation for offcenter collisions or stretching separation. They also distinguish two regimes of stable coalescence that may be conjunct: coalescence after minor deformation and coalescence after substantial deformation. Thus, the binary droplet collision may result in five regimes of outcome described briefly as follows. Prior to collision a gas layer between the droplets is trapped and the pressure rises in the gap between the approaching droplets. If the drops approach each other slowly enough, or more precisely, the Weber number is low enough, then the gas has time to escape, so that coalescence occurs after minor deformation (regime I). If the Weber number is higher, then the surfaces of the droplets do not make contact due to the trapped gas layer, so the droplets become deformed and bounce apart (regime II). Further increasing the Weber number, when the kinetic energy of collision is sufficient to expel the intervening layer of gas, the droplets will coalesce after substantial deformation. The coalesced droplet deforms into a disk and oscillates until being stabilized in spherical form

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due to surface tension (regime III). For the highest Weber numbers, the kinetic energy of collision overcomes the surface energy, and the temporarily coalesced droplet is separated into two or more droplets during oscillation. The temporary coalescence is followed by reflexive separation for low impact parameters (regime IV), while the collision process ends up in stretching separation for high impact parameters (regime V).

2.1. Coalescence after Minor Deformation The droplet clouds under investigation are those produced in a horizontal wind tunnel by injection of water droplets in the direction of airflow. The simulation of the resulting twophase flow begins a short distance downstream of the nozzles, where the disintegration of the liquid jet created by the nozzles is assumed to be completed. On the other hand, aerosol clouds are examined, in which the size of largest droplets rarely exceeds 200 μm. In such flows the relative velocity of the colliding droplets, and consequently the Weber number, are small in most cases of collision. Therefore, coalescence followed by separation (regimes IV and V) is practically non-existent; and even if it did occur, disruption may be assumed, when satellite droplets are not formed. On the other hand, bounce and stable coalescence either after minor deformation or after substantial deformation appear frequently. Hence, the transitions between regimes I and II as well as between regimes II and III have particular importance. Most of the transition curves applied in the authors’ previous studies (Kollár and Farzaneh, 2007b; Kollár et al., 2005a) were determined by formerly proposed criteria based on the physics of the collision phenomenon, except the boundary between regimes I and II. This boundary was a line joining two given points on the B-We plane as follows (Kollár et al., 2005a). One of these points separates the regime of bounce from that of coalescence after substantial deformation for head-on collisions, while the other point is the one where the Weber number is zero and the impact parameter is unity. This condition provides a close approximation of the experimental observations of Qian and Law, 1997, but lacks physical explanation. The model herein applies an alternative boundary whose physical basis is explained in this section. The boundary between coalescence after minor deformation and bounce is determined by two conditions. First, the thickness of the gas film trapped between the droplets has to be reduced to a critical thickness for breaking up the gas film and resulting in the coalescence of droplets. Second, during the sliding interaction of droplets (i.e. when B ≠ 0 ), coalescence takes place only if the droplets do not pass near each other due to the sliding motion before the film thickness reduces to its critical value. When the collision model verifies these conditions, the governing equations of motion of the film-thinning process are not solved for each collision case, although approaches are available in the literature (Jeelani and Hartland, 1998; Nguyen and Schulze, 2004), because the calculation would be computationally costly. Instead, estimations based on the underlying physics are provided to obtain these conditions. The minimum film thickness that the gas layer may reach is estimated using characteristic values of the involved quantities, whereas the time required for the gas layer to be reduced to the critical thickness at rupture is estimated using time-scale analysis. Then, the two-phase flow model verifies only the two conditions in each collision case.

László E. Kollár and Masoud Farzaneh

100

Figure 1. Two approaching droplets with relative velocity of

Ur

and the gas layer trapped between

them.

To express the first condition mathematically, the minimum thickness that the gas layer can reach as well as the critical thickness at rupture have to be determined. The minor deformation of each droplet takes place where the other droplet approaches and pushes the spherical surface by forming a disc of radii rS and rL on the smaller and larger droplets, respectively (see Fig. 1). These radii are obtained from the balance of capillary and drag forces acting on the droplet. The drag force may be modeled as the viscous drag on a sphere (Steinhaus et al., 2006) so that the force balance takes the form

rS2π

4σ = 3π d S μ aU r dS

(4)

3μaU r 4σ

(5)

rS = d S

for the smaller droplet, where

μa

is dynamic viscosity of the gas which is air in this model.

Here, the velocity U r is the approach velocity of the droplets, which is equal to the relative velocity when B = 0. The pressure difference between the two sides of the droplet, which is balanced by surface tension, is smaller for the larger droplet, 4σ / d L , but the drag force is the same because it is determined by the area of the smaller droplet. Thus, the force balance for the larger droplet is written in the form

Modeling and Experimental Study …

rL = d S d L

101

3μaU r 4σ

(6)

The transverse velocity of the gas, u, is derived from a continuity condition, considering that a disc of surface rS2π approaches the other disc with velocity U r , and the gas escapes with velocity u via a surface 2rS π h , where h is the gap thickness:

u=

rSU r 2h

(7)

The radius rS is used here, because the volume intercepted between the two droplets depends on the size of smaller droplet. The dynamic pressure inside the gap, ρ a u / 2 , causes the 2

deformation of droplet surface and is balanced by surface tension, 4σ / d S , where

ρa

is the

air density (Qian and Law, 1997). This balance provides the maximum escaping velocity of the gas, u, and the minimum thickness that the gas layer can reach is obtained after the substitution of Eq. (7):

h=

ρa d S rSU r 2σ 4

(8)

Equation (8) was derived using the interaction of the film with the smaller droplet. The same thickness could be obtained, however, after considering the interaction with the larger droplet and also using Eqs. (5) and (6). The film thickness at rupture, hr , is estimated by the following formula (Chen et al., 1984; Steinhaus et al., 2006): 1/4

⎛ Hr 2 ⎞ hr = 0.802 ⎜ S ⎟ ⎝ σ ⎠

(9)

where H is the Hamaker constant (Nguyen and Schulze, 2004). Again, rS is used, because the intercepted volume depends on the size of the smaller droplet. MacKay and Mason, 1963, D

observed experimentally that the film thickness at rupture was less than 500 A for droplet diameters up to 2500 μm. According to Chen et al., 1984, Eq. (9) is valid with a Hamaker D

constant,

H = 10−21 J, if the film thickness, hr , is less than 120 A . The above calculation

for a liquid-gas system, which is the subject of this study, yields that this condition holds for droplets with diameter up to about 200 μm. Most of the droplets produced by the nozzles described in Section 5.1 are smaller than this limit, and although the diameter of largest droplets may exceed 200 μm in some cases, their numbers are so low that Eq. (9) was

László E. Kollár and Masoud Farzaneh

102

accepted for all the cases considered in these simulations. Then, the first condition of coalescence after minor deformation may be written in a simple form as:

h < hr

(10)

which may be expressed after some algebraic manipulations using Eqs. (5), (8) and (9) as follows:

WeRed3 < 564.85

where Red =

H σρ a ρ d

(11)

μ a4

ρ aU r d S denotes droplet Reynolds number. More precisely, the above μa

calculation should consider the approach velocity of the droplets, which is the component of relative velocity in the direction of the line connecting the centers of the two droplets, i.e.

U r 1 − B 2 for sliding interactions of droplets. Thus, Eq. (11) is modified as follows:

WeRed3 (1 − B 2 )

5/2

< 564.85

H σρ a ρ d

μa4

(12)

The right-hand side includes constants and fluid properties only; thus, it is constant for a fixed liquid-gas system. Equation (12) is only a sufficient condition for coalescence after minor deformation if B = 0 . If the impact parameter increases, this condition is satisfied for greater Weber numbers, which contradicts the experimental results of Qian and Law, 1997. However, the sliding velocity or the component of relative velocity perpendicular to the approach velocity increases with the impact parameter; hence, the droplets may slide near each other before the thickness of the gas film between them could be reduced to its critical value. In this case coalescence does not take place, and this is what the second condition should consider. Since the sliding velocity is U r B , the time the two droplets need to slide near each other is expressed in the form

ts =

d S + d L d S (δ + 1) = Ur B δU r B

(13)

The time for reducing the thickness h to hr is obtained as follows. The relative velocity of the approaching droplets is reduced due to the force of fluid dynamic resistance, which may be described by the following equation (Nguyen and Schulze, 2004):

Modeling and Experimental Study …

6πμaU r dU r =− md dt h where md = ρ d

⎛ dS dL ⎞ ⎜⎜ ⎟⎟ ⎝ 2 ( dS + dL ) ⎠

103

2

(14)

d S3π is the droplet mass. Equation (14) may also be written as 6

dU r 1 = − Ur τf dt

(15)

where τ f denotes the characteristic time of the process and is defined by

ρ d (δ + 1) h τf = d S 9 μa 2

(16)

An estimate of Steinhaus et al., 2006, will be applied for the initial film thickness when the droplets are close enough to each other for causing surface deformation. They chose the initial film thickness as 1/10 of the droplet radius. Thus, the characteristic time may be written as follows:

ρ d d S2 ( δ + 1) τf = 180 μa

2

(17)

Since the critical thickness, hr , is at least two orders of magnitude less than the initial thickness, it may be assumed that the film thickness should be reduced by 1/10 of the droplet radius for coalescence, and the time scale of this process is given by Eq. (17). The second condition for coalescence after minor deformation is that this time scale should be less than the time scale of sliding expressed by Eq. (13):

τ f < ts

(18)

or, after some algebraic manipulations

Red Bδ (δ + 1) < 180

ρa ρd

(19)

Again, the right-hand side is constant for a fixed liquid-gas system. Thus, if conditions (12) and (19) are satisfied, then the collision outcome is coalescence after minor deformation. It should be noted that former collision models used three parameters (We, B and δ) to determine the transition between outcome regimes; while the left-hand sides of Eqs. (12) and

László E. Kollár and Masoud Farzaneh

104

(19) include a fourth parameter, the droplet Reynolds number, Red . Furthermore, the righthand sides depend on fluid parameters; however, they are constant for a fixed liquid-gas system.

2.2. Further Regimes of Collision Outcome The transition between bounce and coalescence after minor deformation was determined in Section 2.1. The other boundaries are the same as those applied in the collision outcome model of Kollár et al., 2005a. The criterion for transition between bounce and coalescence after substantial deformation (regimes II and III) was proposed by Estrade et al., 1999. They assume that if the initial kinetic energy of deformation does not exceed the energy required to produce a limit deformation, then droplets will not coalesce, but bounce. Their condition for coalescence after substantial deformation was formulated as follows:

We >

δ (1 + δ 2 ) ( 4ϕ ′ − 12 ) χ (1 − B 2 )

(20)

where

⎧1 − (2 − κ )2 (1 + κ ) / 4 if

χ =⎨ ⎩

with

κ 2 (3 − κ ) / 4

κ > 1 .0 if κ ≤ 1.0

(21)

κ = (1 − B )(1 + Δ ) and ϕ′ denoting shape factor which measures the deformation of

the droplets from their initial spherical shape and whose proposed value is 3.351. The reflexive separation criterion (transition between regimes III and IV) was provided by Ashgriz and Poo, 1990. They consider that once the coalesced droplets have stretched far enough for a thin ligament to form, the surface energy will promote the separation rather than prevent it. Therefore, the reflexive kinetic energy need not be as high as the nominal surface energy for separation to occur. They postulate that if the reflexive kinetic energy exceeds 75% of the nominal surface energy, then separation occurs. They derived the following expression for this condition:

δ (1 + δ 3 ) 3 2/3 2 ⎤ ⎡ We > 3 ⎢ 7 (1 + δ ) − 4 (1 + δ ) ⎥ 6 ⎣ ⎦ δ η1 + η 2

2

(

where η1 = 2(1 − ξ )2 1 − ξ 2

)

1/ 2

− 1 , η2 = 2 ( δ − ξ )

2

(22)

(δ

2

− ξ 2 ) − δ 3 and ξ = B (1 + δ ) / 2 . 1/2

Modeling and Experimental Study …

105

Brazier-Smith et al., 1972, proposed the stretching separation criterion (transition between regimes III and V). The collision outcome is stretching separation if the rotational energy of the coalesced droplet exceeds the surface energy required to re-form the original two droplets from the coalesced pair, which is expressed as follows:

[

(

) ](

4.8 1 + γ 2 − 1 + γ 3 1+ γ 3 We > 2 B γ 6 (1 + γ )2 2/3

)

11 / 3

(23)

Ashgriz and Poo, 1990, derived an alternative criterion; however, they evaluated that condition (23) also provides a satisfactory prediction. The velocity of the larger post-collision droplet was determined by Gavaises et al., 1996, as follows:

VLnew =

VL d L3 + VS d S3 + d S3 (VL − VS ) Z d L3 + d S3

(24)

where VL and VS are the velocities of the larger and smaller pre-collision droplets, respectively, and Z = ( B − Bcr ) / (1 − Bcr ) in which Bcr is the critical impact parameter above which the collision results in stretching separation. This parameter is calculated from the following formula:

⎛ 2 3 2/3 ⎤ 3 11/3 ⎡ ⎜ 4.8 ⎢⎣1 + γ − (1 + γ ) ⎥⎦ (1 + γ ) Bcr = min ⎜1.0, 2 We γ 6 (1 + γ ) ⎜⎜ ⎝ new

The velocity of the smaller post-collision droplet, VS

⎞ ⎟ ⎟ ⎟⎟ ⎠

(25)

is calculated similarly, with the

quantities designating the larger and the smaller droplets interchanged in Eq. (24).

2.3. Composite Collision Outcome Model The composite collision outcome model takes into account the five regimes defined earlier in this section. A typical outcome map in the B-We plane is shown in Fig. 2 for the water-air system. When two droplets collide, the outcome model is applied to determine the collision outcome and properties of the post-collision droplet(s), as follows. The Weber number, droplet Reynolds number, impact parameter, and droplet size ratio are calculated during simulation of the droplet motion. Firstly, it is ascertained whether coalescence after minor deformation occurs using conditions (12) and (19). If these conditions are not satisfied, then criterion (20) is used to determine whether or not bounce has occurred. If bounce has not occurred, then criteria (22) and (23) are applied to determine if the collision outcome is coalescence after substantial deformation, reflexive separation, or stretching separation. After

106

László E. Kollár and Masoud Farzaneh

obtaining the collision outcome, the sizes, velocities, and temperatures of the post-collision droplets need to be determined. In case of coalescence, the size, velocity, and temperature are calculated in such a way as to conserve mass, momentum and to satisfy heat balance. When droplets bounce, their sizes and temperatures do not change and their velocities are modified according to the conservation of momentum. If separation occurs, it is assumed that satellite droplets are not formed, as discussed in Section 2.1, and that the sizes and temperatures of post-collision droplets are equal to those of the pre-collision droplets. Although Ashgriz and Poo, 1990, found that there was some minor mass transfer from the larger to the smaller droplet, they did not publish any quantitative analysis at that time. The velocities of postcollision droplets in the case of stretching separation are calculated according to the relation given by (24), while in the case of reflexive separation they are approximated by the velocities of the pre-collision droplets.

Figure 2. Collision outcome map on the B – We plane for δ = 1 and

d S = 10 μm; I: coalescence after

minor deformation; II: bounce; III: coalescence after substantial deformation; IV: reflexive separation; V: stretching separation.

3. PROCESSES INFLUENCING CLOUD CHARACTERISTICS This section discusses the processes which greatly influence cloud characteristics, and whose effects are considered in the model. Droplet collision and coalescence were discussed in detail in Section 2; therefore, this section will focus on evaporation and cooling, gravitational settling, and turbulent dispersion of droplets. The effects of these processes on droplet size were studied in former publications by the current authors. Since many of the collisions result in coalescence, the median volume diameter (MVD) increases due to droplet collision. More precisely, the number of small droplets decreases, the number of middle-size droplets does not change significantly, while the number of large droplets increases (Kollár et al., 2005a). Evaporation and cooling reduce droplet size and temperature; however, once a

Modeling and Experimental Study …

107

droplet approaches its equilibrium temperature those effects are significant only in a limiting D

case of icing conditions: when air temperature is close to 0 C and air relative humidity drops below 0.75 (Kollár et al., 2005b). Gravity causes separation of droplets of different sizes, which leads to vertical variation in DSD and LWC (Kollár et al., 2005a). Turbulent dispersion modifies droplet trajectories, and consequently the spatial variation in DSD and LWC (Kollár and Farzaneh, 2007b). The model herein involves these processes as they were presented in Kollár and Farzaneh, 2007b.

3.1. Evaporation and Cooling The method that the model applies to calculate the decrease of droplet mass and temperature due to evaporation and cooling is based on the developments of Beard and Pruppacher, 1971; Pruppacher and Klett, 1978. This section recalls the formulae, but the reader is advised to see the above references for details. The rate of droplet mass, Δmd , which is evaporated during the time interval, Δt, is obtained as follows:

π dD f ( ew (Td ) − RH a ew ( Ta ) ) Δmd =− Sh ef ⎞ Δt ⎛ RwT f ⎜ 1 − ⎟ pst ⎠ ⎝

(26)

where ew (Td ) and ew (Ta ) are the pressures of saturated water vapor at droplet temperature,

Td , and air temperature, Ta , respectively, RH a , the relative humidity of air, Sh, the Sherwood number, R w , the gas constant for water vapor, p st , the static pressure of air, and the subscript f refers to film formation on the evaporation surface involving droplet temperature and air temperature. The corresponding quantities T f = (Td + Ta ) / 2 ,

e f = (ew (Td ) + ew (Ta )) / 2 and D f = Dw (T f

) are, respectively, the mean values over the

transfer path of the temperature, the pressure of saturated water vapor, and the diffusivity of water vapor, Dw . The Sherwood number is defined by the Reynolds number based on air velocity, i.e. Rea = d u ρ a / μ a where u stands for air velocity, and the Schmidt number, Sc, as follows:

(

Sh = 2 0.78 + 0.308 Re a Sc 0.33 0 .5

)

(27)

The change in droplet temperature, ΔTd , during the time interval, Δt, is obtained from the heat balance:

László E. Kollár and Masoud Farzaneh

108

cw md

ΔTd Δmd = α d 2π (Ta − Td ) + Lev Δt Δt

(28)

where cw is the specific heat of water, Lev , the latent heat of vaporization of water, and the heat transfer coefficient, α, is determined by the following expression:

α= where

λa

Nuλa d

(29)

is the thermal conductivity of air at the temperature of the droplet surface, and the

Nusselt number, Nu, is defined by Whitaker, 1972:

(

Nu = 2 + 0.4 Rea

0.5

+ 0.06 Rea

0.67

⎛ μ (T ) ⎞ Pr ⎜⎜ a a ⎟⎟ ⎝ μ a (Td ) ⎠

)

0.4

0.25

(30)

with Pr denoting Prandtl number. The Td is the droplet temperature at the beginning of the time step, and Δmd / Δt is obtained from Eq. (26).

3.2. Gravitational Settling Gravity is an important factor affecting droplet trajectories in atmospheric icing processes with moderate wind speeds (below 20 m/s) and in low-speed wind tunnels when modeling these processes. When the air speed increases the drag forces will dominate and the gravity effect becomes negligible. The influence of gravity on droplet motion is reduced even at lower velocities for small droplets. The effect of gravity was examined in Kollár et al., 2005a, and this study revealed that the vertical deflection of droplet trajectories as well as the vertical component of droplet velocities decreased with air velocity and increased with droplet size. A term considering gravity is included in the droplet equation, which will be presented in Section 4.2.

3.3. Turbulent Dispersion The effect of turbulence on droplet motion is considered by a stochastic approach introduced by Dukowicz, 1980. The instantaneous gas velocity, u, is determined by adding a fluctuating component, u ′ , to the gas mean velocity, u , in the droplet equation (see Section 4.2). The fluctuating component, u ′ , is chosen from a Gaussian probability distribution with a standard deviation of (2k / 3)

0. 5

, where k denotes turbulent kinetic energy. The value of the

fluctuating component is changed at the beginning of each droplet – turbulent eddy interaction. The time interval of this interaction is determined by the minimum of the eddy

Modeling and Experimental Study …

109

lifetime, t e , and the transit time, t r , over which the droplet traverses the eddy (Gosman and Ioannides, 1981). The eddy lifetime is provided by the form:

te =

le u′

(31)

In this equation, le is the characteristic size of the turbulent eddy given by the following formula:

le =

Cμ

0.75 1.5

k

(32)

ε

where C μ = 0.09, and ε is the turbulent dissipation. The estimation for transit time takes the form:

⎛ le tr = −τ r ln ⎜ 1 − ⎜ τ u−v ⎝

(

⎞ ⎟⎟ ⎠

(33)

)

where τ r = 4 ρ d d / 3 ρ a C D u − v , C D is the drag coefficient, and v is the droplet

(

velocity. When le / τ r u − v

) > 1, Eq. (33) does not have a solution, therefore it is assumed

that the time of droplet – eddy interaction is equal to the eddy lifetime, t e .

4. TWO-DIMENSIONAL MODEL OF TWO-PHASE FLOW The two-dimensional model of two-phase air/dispersed water flows of Kollár and Farzaneh, 2007b, will be described in this section. The air velocity field together with turbulent parameters are determined first in a three-dimensional space, which is defined according to the tunnel geometry and is symmetric to the middle vertical plane. The data obtained in that vertical plane serve as input for the model, which solves the droplet equation, tracks droplet trajectories, and calculates droplet parameters such as size, velocity and temperature, which are modified by the processes described in Section 3. Thus, this model considers the influence of the carrier phase on particle motion, but it assumes that the dispersed phase does not change the continuous fluid phase. Some of the numerous criteria proposed in the literature have been verified in Kollár and Farzaneh, 2007b, to confirm that the two-way exchange of mass, momentum and thermal energy between the phases is negligible. Gore and Crowe, 1989, found that if the ratio of particle diameter to turbulent length scale, d / le , was less than 0.1, then particles did not increase turbulence intensity. Hetsroni, 1989, reported that the dispersed phase did not enhance turbulence in the gas phase,

László E. Kollár and Masoud Farzaneh

110

if Re ≤ 110, where Re is Reynolds number based on the gas-droplet relative velocity. Gates et al., 1988, examined if the air stream temperature and velocity changed due to heat exchange between the phases; and assumed that these changes were negligible when the liquid to air mass ratio was less than 1%. Wang et al., 2005 reported that the droplets had little effect on air turbulence in typical clouds where the droplet mass loading was on the −3

order of 10 . The inlet of the simulation domain in this model is defined as being 50 cm downstream of the nozzle outlet, where the break-up of the liquid jet may be assumed to be completed. The above conditions are satisfied in the simulation domain, as discussed in Kollár and Farzaneh, 2007b; therefore, the one-way coupled model was accepted for the cases simulated in this study.

4.1. Air Velocity Field The air velocity field is determined by the commercial software CFX, which solves the Navier-Stokes equations iteratively by using the finite volume technique. A default tetrahedral element discretization is used for meshing. Boundary conditions assume no slip at the tunnel walls and zero velocity perpendicular to the wall. Velocities at the inlet and outlet and the geometry of the computational domain are defined as input data for this computation. This software is also capable of computing turbulent kinetic energy and turbulent dissipation once the user defines what turbulence model should be applied. More realistic turbulence data were obtained, however, when the level of turbulence and the size of turbulent eddy at the inlet and outlet were defined as inputs in the droplet trajectory code, and their variations through the computational domain were approximated by a simple function which may be chosen according to the modeled process. Then, the turbulent kinetic energy, k, may be obtained from the level of turbulence, Tu, as follows:

1 k = u 2Tu 2 2

(34)

and Eq. (32) yields turbulent dissipation, ε.

4.2. Droplet Motion The droplet trajectory code is based on the particle-source-in-cell model constructed by Crowe et al., 1977, and the droplet equation derived by Maxey and Riley, 1983:

π

6

d 3 ( ρ d + 0 .5 ρ a )

dv π 3 π Du = d (ρ d − ρ a )g + 3πdμ a f (u − v ) + d 3 ρ a dt 6 4 Dt

(35)

where g is the gravity vector, f considers Stokes drag, the derivative d/dt denotes time derivative following the moving droplet, and the D/Dt stands for time derivative following a fluid element. The last term in Eq. (35) may be neglected, because this term is at least one to two orders of magnitude less than the other ones for all the cases examined. Thus, the droplet

Modeling and Experimental Study …

111

equation is simplified to the same form as was used in Kollár et al., 2005a. The parameter f, and the drag coefficient, C D , are defined by the following expressions, respectively (Crowe et al., 1977):

f = 1 + 0.15Re0.687 and C D =

24 f Re

(36)

where the Reynolds number, Re, is based on the gas-droplet relative velocity:

Re =

ρa u − v d μa

Then, assuming that

(37)

ρ d >> ρ a ,

 =u/ u , V  =v/ u U

and defining the following non-dimensional parameters:

 = t u / l , where l is the horizontal length of the and T

computational domain, the non-dimensional droplet equation is obtained after some algebraic operations:

 18μa l dV l  −V  f U = 2 g+  dT u ρd d 2 u

(

)

(38)

Since f varies with time, Eq. (38) is integrated numerically by using the Euler scheme in a predictor-corrector mode:

  =V  + dV ΔT , V * j dT j

(39)

⎛   ⎞   =V  + ⎜ dV + dV ⎟ ΔT , V j +1 j ⎜ dT dT * ⎟ 2 j ⎝ ⎠

(40)

 is the non-dimensional time interval, the subscripts j and j+1 refer to quantities at where ΔT the beginning and at the end of the time increment, respectively, while the subscript * refers  , at the end of the time increment, to an intermediate value. After the droplet velocity, V j+1  , is obtained by applying the ΔT , is determined, the corresponding droplet position, X j +1 trapezoidal scheme:

ΔT  =X  + V  +V  X j +1 j j j +1 2

(

)

(41)

112

László E. Kollár and Masoud Farzaneh

4.3. Computation The computation procedure was described in Kollár and Farzaneh, 2007b. This section recalls this procedure while keeping the following difference in mind, i.e. when the collision outcome is determined, conditions (12) and (19) are used to decide whether coalescence after minor deformation or bounce occurs. Input data for the calculation of the air velocity field (i.e. air velocities at the inlet and outlet of the simulated domain) are obtained from measurements, and then velocities are computed at many points in between by the commercial software CFX. The airflow field is subdivided into a series of cells, which are regarded as control volumes in the two-phase flow model, which is implemented in FORTRAN. The air velocity associated with each control volume is the velocity calculated closest to the midpoint of that control volume. The air velocity field obtained is used as input in the two-phase flow model, which follows the motion of droplets in the control volumes. The area of control volumes in the simulations discussed in Section 6 was chosen to be 25 x 25 mm. This satisfies two conditions: that the difference between the velocities of two neighboring control volumes be, at maximum, a few percent of the absolute value of the velocity, and that their size be at least an order of magnitude greater than the size of the largest parcel. This model considers the droplets collected into parcels, since there are too many droplets to examine individually. The method is based on the concept of the discrete parcel approach (O'Rourke and Bracco, 1980). The number of parcels has to be at least in the range of thousands to obtain reliable statistics; however, increasing the number of parcels increases computational costs significantly. As a compromise, 3000 parcels were injected in these simulations, each of which included 3000 droplets. The number of droplets per parcel was chosen so that the total volume of emanating droplets in unit time provides the required flow rate of injected water. A sufficient number of these parcels should reach the neighborhood of the icing object to form a distribution, i.e. at least 1000, before the simulation is terminated. Each parcel contains the same number of drops of identical size, velocity and temperature. These droplet parameters are also required as input data at the beginning of the computational domain. In order to introduce a DSD into the model, the droplet spectrum is first discretized into 5-μm-wide bins and the diameter of each droplet is replaced by the arithmetic mean of the corresponding bin. The relative frequencies of the appearance of droplets in each bin are then used to obtain the discrete droplet spectrum. The size of droplets in each parcel is randomly chosen from this distribution, as explained in Kollár and Farzaneh, 2007b; Kollár et al., 2005a. The water flow may also be manipulated in the model by changing the time step or the number of time steps between the injection of two parcels. The range of available time steps is limited, however, by the time scales of the processes modeled. Of these, droplet collision was found to be the decisive factor. The time step needs to be small enough to avoid one parcel “jumping” another during the simulation; nevertheless it should be large enough to avoid collisions occuring immediately at the inlet. Accordingly, the time steps were 25 µs and 50 µs in modeling CI and ZL, respectively. Further inputs are the ambient conditions, which are assumed to be constant over the computational domain, and turbulence data, i.e. the level of turbulence and size of the turbulent eddies. The parameters considering ambient conditions and turbulence data may be prescribed according to the conditions prevailing under the modeled process or may be provided by experiments. Input data for the particular cases presented in this paper are given in Section 6.

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The simulation of the two-phase flow proceeds as follows. The parcels are tracked in space and time as if they were single droplets with the size, mass, velocity and temperature of one droplet from that parcel. The fluctuating component of air velocity is modified after each time interval describing the droplet – turbulent eddy interaction (see Section 3.3). The actual fluctuating velocity is added to the air velocity at the beginning of each time step, and is considered in the droplet equation. Then the position and velocity of droplets are determined by applying Eqs. (39)-(41), and the droplet size is reduced according to the loss of mass and the droplet temperature is modified according to evaporation and cooling (Eqs. (26) and (28)). If the lost mass is greater than or equal to the mass of the droplet itself, then the droplet is evaporated and the parcel is withdrawn from further computation. Afterwards, a search is made for colliding droplets. From the collisional point of view, the parcel diameter is considered so great as that of one sphere whose mass is equal to the sum of masses of each droplet carried in the parcel. If the distance between two parcels is less than the sum of their radii, then each droplet in either parcel will collide with one droplet from the other parcel. The outcome of collisions and the sizes, velocities and temperatures of post-collision droplets are determined by utilizing the composite collision outcome model (see Section 2). If coalescence occurs, then the two parcels are replaced by one parcel with the post-collision droplets. This process is continued in the next time steps until the termination condition of the simulation is satisfied.

5. EXPERIMENTAL 5.1. CIGELE Atmospheric Icing Research Wind Tunnel (CAIRWT) Experiments were carried out at the CIGELE atmospheric icing research wind tunnel (CAIRWT). The CAIRWT is a closed-loop, low-speed icing wind tunnel with a total length of about 30 m, including a 3-metre-long test section with a rectangular cross-section 45.7 cm high and 91.4 cm wide. The cross-section of the tunnel at the spray bar is also rectangular with a height of 1.7 m and width of 1.14 m. The tunnel becomes circular 1.5 m downstream from the spray bar with a diameter of 1 m. The cross-section contracts further in the next 1.1 m, and reaches the final rectangular cross-section with the size of the test section in the following 30 cm. The distance between the spray-bar and the middle of the test section where the icing object is usually placed is 4.4 m. A part of the wind tunnel including the settling chamber, contraction section and test section is shown in Fig. 3. The temperature and velocity of the circulating cold air stream is controlled by the tunnel operator. The temperature in the D

test section may be cooled down to –30 C . The velocity of circulating air in the test section may reach a maximum of 30 m/s. Water is injected into the air stream through three airassisted nozzles located on a horizontal spray bar with distances of 20 cm between them. The nozzles are manufactured by Spraying Systems Co. and incorporate a model 2050 stainless steel fluid cap and a model 67147 stainless steel air cap. This system can create an aerosol cloud with a MVD of 10 to 100 μm along the test section centerline in the middle of test section; however, the MVD may exceed the upper limit in other positions of the test section. The LWC of the produced cloud may be varied from 0.2 to 12 g/m3 in the middle of test section. Variations in both of these parameters are accomplished through variations in the

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pressures and thus the flow rates of the water and air lines. These parameters together with the nozzle characteristics have an influence on the liquid jet break-up, and they determine the resulting DSD at the nozzle outlet. This initial DSD is one of the several parameters influencing the DSD and LWC of the aerosol cloud, together with their evolution as the cloud approaches the icing object. A detailed discussion of the influencing parameters is provided in Kollár and Farzaneh, 2009.

Figure 3. Settling chamber, contraction section and test section of CAIRWT.

5.2. Velocity Measurements The air velocities and turbulence data at the spray bar and in the middle of test section where the icing object is usually placed were measured by a Pitot tube connected to an Omega differential pressure transducer. Transverse turbulent characteristics were not measured; the longitudinal ones were assumed to describe turbulence satisfactorily in both sections. Measured velocity data served as input for the CFX calculations which provided the air velocity field in the tunnel. Droplet velocities were also measured in some positions of the test section by a non-intrusive laser optical measurement technique, the particle image velocimetry (PIV). This technique measures the instantaneous velocity components of small particles following the flow. A high-intensity and high-frequency laser is used to produce a light sheet which illuminates the flow in the target area. A CCD (charge-coupled device) camera captures images, and commercial software is applied to analyze and visualize the flow. The system used for PIV in CAIRWT is provided by Dantec Dynamics.

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5.3. DSD and LWC Measurements The DSD was measured in the settling chamber using the collargol slide impact method (Godard, 1960), and its dependence on nozzle-dynamic parameters (NDPs) was scrutinized in detail in Kollár et al., 2006. Additional droplet size measurements were performed in Kollár and Farzaneh, 2007b, at different heights in the middle of the test section. The LWC was measured along the test section centerline in the middle of the test section by the rotating cylinder method (Stallabrass, 1978) for varying air velocities and NDPs in Kollár and Farzaneh, 2009. The DSDs obtained close to the nozzles serve as input for the two-phase flow model, while further DSD and LWC measurements in different vertical and streamwise positions in the test section were carried out to study the variation of cloud characteristics in the tunnel and validate the output of the model. The methods mentioned in the previous paragraph provide reliable DSD and LWC results; however, they are time consuming, especially the method to obtain a DSD with a sufficient number of droplets. These methods have been replaced by applying an integrated system for icing studies, which is manufactured by Droplet Measurement Technologies (DMT). This system includes two probes for droplet size measurements, the Cloud Droplet Probe (CDP) and Cloud Imaging Probe (CIP). These probes operate based on optical imaging techniques. The CDP is designed to measure particles with diameters between 3 μm and 50 μm, whereas the CIP measures particles ranging in size from 25 μm to 1550 μm. The CIP is a combination probe, also including a heated-element LWC sensor, air temperature sensor, and Pitot tube air speed sensor. The measured data are displayed by the Particle Analysis and Display System (PADS), which is a software package designed to interface with the instruments produced by DMT. The air temperature and air speed may also be entered manually in the PADS. This is recommended for low air speeds because the probe is designed for aircraft, thus providing reliable velocity and temperature measurements at air speeds in the range of 50-150 m/s.

6. RESULTS AND DISCUSSION The two-phase flow model was applied to simulate the evolution of aerosol clouds in the CAIRWT under two specific conditions representing CI and ZL. Table 1 summarizes the parameters adjusted in the experiments (air temperature, air velocity, nozzle pressures in the water line and in the air line) in order to reproduce CI and ZL conditions together with some measured parameters which were input for the two-phase flow model. The MVDs given in the table were obtained at the nozzle outlet for the two particular combinations of the NDPs,

p L and p A , (Kollár et al., 2006) and the corresponding measured DSDs are introduced as inputs in the simulations. The initial droplet temperature and horizontal component of droplet D

C and 20 m/s, respectively. The vertical component of droplet velocity D D was determined so that the angle of velocity vector varied in the interval of (– 7.5 , + 7.5 ) D where 7.5 is half of the spray angle for the nozzles used in the experiments. This interval velocity were 20

was divided into 59 sub-intervals; thus the vertical component of droplet velocity might take 60 different values (i.e. the limiting values of the sub-intervals). These 60 different values

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were varied so that the vertical velocity components of 60 consecutive droplets (or, more precisely, parcels) were different. Turbulence data were measured at the spray bar and in the middle of test section from wall to wall both horizontally and vertically. The turbulence data in Table 1 are approximately the averages of measured data outside the boundary layer. The decay of turbulence along the tunnel is assumed according to a decreasing power function based on the suggestion of Snyder and Lumley, 1971. Further parameters, which were kept constant or were calculated relative to temperature, are provided in the Appendix. Table 1. Parameters adjusted in the experiments and some measured parameters which serve as input for the two-phase flow model Parameter D

Air temperature ( C ) Air velocity in test section (m/s) Pressure in nozzle water line (kPa) Pressure in nozzle air line (kPa) Relative humidity of air (–) Median volume diameter in settling chamber (μm) Level of turbulence in settling chamber (%) Level of turbulence in test section (%)

In-cloud icing (CI) Freezing drizzle (ZL) –10 –5 20 450 480 0.95 27 2 0.25

10 450 180 0.8 62 3.5 0.45

6.1. Droplet Velocity in the CAIRWT The effects of gravity on droplet trajectory and droplet velocity were discussed in Kollár et al., 2005a. Gravity deflects the droplet trajectories to a greater extent for larger droplets and for lower air velocities. The vertical component of droplet velocity is greater in those cases, as it follows from the droplet equation (38). Figure 4 shows the droplet velocity as determined experimentally by PIV for two different droplet clouds in about a 4.5 cm by 4.5 cm domain located at mid-height (y = 0 cm) and 0.5 m downstream the middle of test section (x = 0.5 m) of the CAIRWT. The symbols x and y are used to denote streamwise and vertical positions, respectively. The position x = 0 means the middle of test section where the icing object is usually placed, whereas the position y = 0 refers to mid-height of the test section, which is at the same level as the spray bar and nozzles. The air velocity is 10 m/s in both cases shown in Figs. 4a and 4b, but the DSDs are different. The NDPs were p L = 400 kPa, p A = 540 kPa and

p L = 450 kPa, p A = 180 kPa, which correspond to MVDs of 10 μm and 74 μm, respectively. The conditions in Fig. 4b are those representing ZL, whereas the droplet size was chosen as small as possible in Fig. 4a for the difference between the vertical components of droplet velocity to be more visible. According to Eq. (38) the vertical component of droplet velocity increases in absolute value as the droplet moves downstream and approaches a limit when t → ∞ . In reality, however, this velocity component may oscillate significantly due to turbulence in the carrying phase and to droplet collision. The averages of these measured vertical components shown in Figs. 4a and 4b are -0.019 m/s and -0.274 m/s, respectively. These velocity components were also determined by computation at the same position for many droplets of different sizes in an aerosol cloud. Fig. 5 shows that the vertical velocity

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component for droplets with diameter of 10 μm occurs between +0.2 and –0.1 m/s. This range includes the average value measured for an aerosol cloud with this MVD. The vertical velocity component for droplets with diameter of 74 μm varies between 0 and –0.3 m/s. This range also includes the measured average value for the corresponding aerosol cloud; thus the model provides a realistic prediction for the deflection of droplet trajectory.

(a)

(b)

Figure 4. Measured droplet velocities in a 4.5 cm by 4.5 cm domain located at mid-height and 0.5 m downstream of the middle of the test section in CAIRWT with a reference velocity on the bottom showing the average values of streamwise components and vertical downward components, (a)

Vert. comp. droplet velocity (m/s)

m/s, MVD = 10 μm, (b)

Va = 10

Va = 10 m/s, MVD = 74 μm.

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0

50

100

150

200

Droplet diameter (μ m) Figure 5. Vertical components of droplet velocity as calculated for droplets of an aerosol cloud at 0.5 m downstream of the middle of the test section.

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6.2. Streamwise and Vertical Variations of DSD The influence of droplet collision on the DSD was studied in Kollár et al., 2005a. The authors demonstrated that the number of small droplets decreased due to collisions, whereas the number of large droplets increased. The number of droplets with diameter close to the MVD did not change significantly. This result was explained by the fact that the number of droplets of this diameter that coalesced and formed larger droplets was offset by the number of coalescences that resulted in droplets of this diameter. It was also observed that the changes in the number of droplets was more significant at the beginning of the simulation, because the droplets were closer together after the injection, therefore the number of collisions and coalescences were higher there. Kollár and Farzaneh, 2007b demonstrated that the effects of droplet collision on the DSD increased in turbulent flow. In this latter study, a process which may reduce droplet size, droplet evaporation, was also considered. However, the size decrease of large droplets is negligible, while the smallest droplets may be evaporated completely; therefore, this phenomenon usually results in increasing MVD for the DSDs that are produced in the CAIRWT. More detailed discussion on the effect of evaporation and cooling is provided in Kollár et al., 2005b. Moreover, it was found that the change in DSD due to collision was greater than that due to evaporation for temperatures below the freezing point of water. Therefore, the DSD of the aerosol cloud in the entire section increases as it moves downstream from the settling chamber to the test section. Nevertheless, some local DSDs may have smaller MVDs than some other ones further upstream. This result may be obtained in flows where the effects of gravity, and consequently the deflection of droplet trajectories, are considerable. In such flows, large droplets will move toward the bottom of the tunnel; hence, the MVD may become smaller downstream at the same height, even if some collisions and coalescences take place. Simulation results and experimental findings are compared in Fig. 6 and Table 2. Figure 6 evaluates model predictions when the cloud moves between two streamwise positions: from the spray bar to the middle of test section (x = 0 m); whereas Table 2 validates the model when the cloud moves downstream inside the test section (from x = –1 m to x = +0.5 m). Figure 6 compares computed results to experimental ones presented in Kollár and Farzaneh, 2007b. The conditions are those representing CI and ZL, except that the air temperature is 5 D

C that was the condition during droplet size measurements with the collargol slide impact

method. DSDs measured near the spray bar were used as input for the model, whereas DSDs measured in the middle of test section were compared to simulation results. The error bars correspond to the measurement error which was evaluated to be ±4.5 μm ±5 % in Kollár et al., 2006. Results in Fig. 6 show that the MVD increases toward the bottom of the tunnel in both simulated cases, and this increase is more significant under ZL conditions where the number of big droplets is greater. These tendencies are estimated closely by the model; however, a shortcoming may also be observed: the underestimation of droplet size in the top half of the vertical section. Table 2 compares computed results to experimental ones obtained in the present study using the CDP and CIP. Several series of experiments were carried out

C to 25 D C ). Comparisons have D been made under conditions representing CI and ZL, except that the air temperature is 20 C D and 15 C , respectively. The probe cannot be fixed in the settling chamber; therefore the

under room temperature (more precisely, in the range of 15

D

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initial DSDs were estimated by modified Rosin-Rammler distributions, because this distribution was found to be the closest estimation of measured DSDs in Kollár et al., 2006. The probe was placed at the heights of y = 0 cm and y = –7 cm in different streamwise positions in the test section. In fact, each height means a vertical interval of 5 to 10 cm, which is the distance between the arms of the CDP and CIP. Accordingly, similar intervals around the same heights were also used in the simulations. When determining the initial DSD in the model, experimental results at the first measurement point, i.e. at x = –1 m, were also considered. The calculated and measured MVD should be approximately the same at y = 0 cm for CI conditions and at y = –7 cm for ZL conditions; however, the calculated MVD at y = 0 cm for ZL conditions may be 10-20% lower than the measured one. These conditions correspond to the observations made in Fig. 6. The results presented in Table 2 confirm that droplet size increases toward the bottom for ZL conditions. They also demonstrate that droplet size decreases at the same height in the streamwise direction for ZL conditions, whereas for CI conditions most of the droplets appear in the proximity of mid-height, and the variation in the streamwise direction in the test section is negligible. Model predictions are satisfactory at y = 0 cm for CI conditions and at y = –7 cm for ZL conditions. The MVD is underestimated at y = 0 cm for ZL conditions; however, this underestimation is usually not more than the 10-20% difference which existed already at x = –1 m and which is the consequence of the underestimation of droplet size in the top half of the vertical section during the passage of the aerosol cloud from the spray bar to the test section. The greatest difference appears at x = 0 m, but it should be noted that this measured MVD is out of the decreasing tendency; thus the increased difference may be devoted to measurement error.

(a)

(b)

Figure 6. Calculated and measured MVDs at different vertical positions, (a) CI conditions, (b) ZL conditions (Kollár and Farzaneh, 2007b).

Table 2. Comparison of calculated and measured MVDs (μm) Streamwise position CI, 0 cm – simulation CI, 0 cm – experiment ZL, 0 cm – simulation ZL, 0 cm – experiment ZL, –7 cm – simulation ZL, –7 cm – experiment

–1m 27 28 78 90 118 121

– 0.5 m 28 29 75 81 111 114

0m 28 26 63 88 103 95

+ 0.5 m 29 28 62 74 95 82

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The MVDs calculated at different streamwise and vertical positions are shown in Fig. 7 for CI and ZL conditions with the temperatures given in Table 1 and with measured DSDs whose MVDs are also provided in Table 1. The same tendencies may be observed as in Table 2. Clearly, the droplet size increases toward the bottom of the tunnel at the same section; whereas the MVDs at the same height are approximately constant in the streamwise direction for CI conditions, and they decrease for ZL conditions. This result is explained by the vertical component of droplet velocity; the large droplets move closer and closer to the bottom of the tunnel so that the MVD is greater at a lower height in the same section, and it decreases at the same height as the droplet cloud moves downstream. Farther downstream, the largest droplets will occupy the bottommost part of the tunnel where the cloud was not extended upstream (see the domain below the height of –15 cm in Fig. 7b); and finally they reach the bottom when they are withdrawn from further calculation. The comparison of Figs. 7a and 7b reveals that the droplet size varies in the vertical direction to a significantly lower degree for CI conditions, and that the variation in the streamwise direction is negligible. In this case the droplets are smaller and the air velocity is higher; consequently, the vertical separation of droplets according to their size is less noticeable. The droplet cloud expands vertically to a lower degree and it remains more uniform.

(a)

(b)

Figure 7. MVDs calculated at different streamwise (x) and vertical positions; (a) CI conditions, (b) ZL conditions.

DSDs averaged over all heights in vertical sections of the cloud are calculated at three different streamwise positions as shown in Fig. 8: (i) 0.5 m downstream from the spray bar (initial DSD based on measurement), (ii) x = –1 m (or 3.4 m downstream from the spray bar), and (iii) x = +0.5 m (or 4.9 m downstream from the spray bar). The increase in MVD in the test section, compared to that in the settling chamber, may clearly be observed for both CI and ZL conditions. Then, MVDs change to a much lesser extent as the droplet cloud moves downstream in the test section. This result is due to the high droplet concentration of the cloud in the settling chamber, and a consequent high number of collisions and coalescences. The collision frequency is significantly reduced 1 m downstream from the spray bar (Kollár and Farzaneh, 2007a); hence, the change in MVD is far less considerable.

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(a)

(b)

Figure 8. DSDs averaged over all heights in vertical sections of the cloud as calculated at three different streamwise positions (x); (a) CI conditions, (b) ZL conditions; SC: settling chamber, TS: test section.

Typical DSDs are illustrated visually in Fig. 9, where images captured during droplet size measurements in the middle of the test section (x = 0 m) are presented. Figures 9a and 9b shows droplets observed at mid-height of the test section (y = 0 cm) in the cloud simulating CI and ZL conditions, respectively. Figure 9c shows droplets at y = –7 cm for ZL conditions. Some of the results discussed earlier can also be seen in these images, i.e. droplet size is greater under ZL conditions than under CI conditions; furthermore, the droplet size increases toward the bottom of the tunnel when large droplets are present.

(a)

(b)

(c)

Figure 9. Images captured during droplet size measurements; (a) CI conditions, y = 0 cm, (b) ZL conditions, y = 0 cm, (c) ZL conditions, y = –7 cm.

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6.3. Vertical Distribution of LWC and its Streamwise Variation The two-phase flow model is two dimensional; therefore, it cannot determine the mass of liquid water in a real three-dimensional unit volume. However, the ratio of masses of all the droplets in different computational domains of the same size may be obtained. Thus, the model is applicable to calculate the ratio of LWCs at different positions in the same cross section, and thereby a vertical distribution of LWC may be determined. Measured and calculated vertical distributions of LWC were compared in Kollár et al., 2005a, for different air velocities; while the vertical distributions at different streamwise positions (x = –1 m, x = –0.5 m, x = 0 m and x = +0.5 m) are determined here for the two conditions considered. The cross section in these streamwise positions is divided vertically into domains with constant size. The values of relative LWC in each domain is determined so that the relative LWC equals 1 in the domain including the position y = 0 cm. Figures 10a and 10b show these calculated values for CI and ZL conditions, respectively. The ratio of LWCs measured at two different vertical positions, y = –7 cm and y = 0 cm, are listed in Table 3, in the examined four streamwise positions listed above. According to measured results, the LWC at y = –7 cm is 0.4-0.7 times that measured at y = 0 cm for CI conditions, and this ratio increases in streamwise position. The same ratio is 1.6-2.1 for ZL conditions, and again, this ratio increases as the cloud moves downstream in the test section. The difficulty in comparing the measured and calculated results is that, in both cases, the change near the cloud boundaries is abrupt (see the steeply increasing or decreasing curves at the edges of the cloud, i.e. in the domains including the vertical positions y = +3 cm and y = –3 cm in Fig. 10a and y = 0 cm in Fig. 10b). Thus, the LWC is significantly different in the top and in the bottom of the same domain near the edges of the cloud. However, it may be observed in Fig. 10a that the relative LWC is in the range of 0.4-0.7 at y = –4 cm for CI conditions. According to Fig. 10b, the relative LWC is in the range of 2-3 and 2.5-6 at y = –2 cm and y = –7 cm, respectively, for ZL conditions; i.e. their ratio is approximately 1.6-2.1, and this ratio increases with streamwise position. Consequently, the model predicts that a 7-cm-long vertical domain of the cloud is extended to about 4-5 cm only. Therefore, it may be concluded from this comparison that the model provides a qualitatively correct prediction of the streamwise and vertical variations of LWC; however, it underestimates the vertical extent of the cloud where small droplets prevail. It should be noted that the model predicts greater vertical extension with increasing levels of turbulence, as was discussed in Kollár and Farzaneh, 2007b.

Figure 10. Relative LWC calculated at different streamwise (x) and vertical positions (its value is 1 at y = 0 cm); (a) CI conditions, (b) ZL conditions.

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Table 3. The ratio of LWCs measured at y = –7 cm and at y = 0 cm ( LWC−7 / LWC0 ) in four streamwise positions

Streamwise position

LWC−7 / LWC0

LWC−7 / LWC0

–1m – 0.5 m 0m + 0.5 m

CI conditions 0.44 0.42 0.59 0.71

ZL conditions 1.91 1.57 1.86 2.12

Figure 10 also shows clearly that the droplet cloud is significantly more extended vertically for ZL than CI conditions, because droplets are larger and air velocity is lower. Consequently, more and more droplets approach the bottom of the tunnel leading to increasing LWC in the bottom half as the cloud moves downstream in the test section. The largest droplets reach the bottom of the tunnel in the middle of the test section and farther downstream, as may also be observed in Fig. 7b.

7. CONCLUSION The collision outcome model in the authors’ previously developed theoretical model for two-phase air/dispersed water flows has been improved. The former condition for transition between two collision outcomes, coalescence after minor deformation and bounce, is replaced by another one which is supported by the underlying physics. Besides droplet collision, the two-phase flow model considers further processes in the dispersed phase: evaporation and cooling, gravitational settling, and turbulent dispersion. This model has been applied to simulate the evolution of the aerosol cloud as it moves from the settling chamber to the test section, and farther downstream inside the test section in a low-speed horizontal icing wind tunnel, and model predictions have been compared to experimental observations. The authors’ former studies in the field discussed in details the effects of the considered processes on the vertical variation of DSD and LWC in the middle of the test section. The present study completes those results by providing both the streamwise and vertical variations of these parameters in the test section. Flows were simulated under two particular icing conditions representing in-cloud icing and freezing drizzle. Observations show that the vertical component of droplet velocity and the resulting vertical separation of droplets of different sizes are almost negligible under incloud icing conditions, where droplets are small and air velocity is relatively higher. However, droplet size increases significantly towards the bottom of the tunnel under freezing drizzle conditions, where droplets are larger and the air velocity is relatively lower. On the other hand, droplet size at the same vertical level decreases downstream in the test section, because large droplets move toward the bottom of the tunnel. The MVD averaged over all heights in a vertical section is always greater in the test section than in the settling chamber, which results mainly from the coalescences following droplet collisions. The frequency of collisions is significantly greater in the settling chamber, where the cloud has not dispersed much yet, as compared to the test section; therefore, the increase of droplet size occurs mainly

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in the settling chamber. Turbulent dispersion amplifies the effect of droplet collision and causes the occurrence of droplets in a wider vertical domain, whereas the influence of evaporation becomes more significant when air temperature increases or relative humidity of air decreases. The computed streamwise and vertical variations in DSD and LWC show coincidence with measured tendencies; although the model underestimates the extension of the aerosol cloud when droplets are small, as they are in the top half of the vertical sections of the tunnel. These tendencies were observed in one wind tunnel only, but they are representative of aerosol clouds produced in low-speed horizontal icing wind tunnels, and the model is, in principle, applicable for other wind tunnels after appropriate modifications.

ACKNOWLEDGMENTS This work was carried out within the framework of the NSERC/Hydro-Québec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and the Canada Research Chair on Atmospheric Icing Engineering of Power Networks (INGIVRE) at the University of Québec at Chicoutimi. The authors would like to thank the CIGELE partners (Hydro-Québec, Hydro One, Réseau Transport d’Électricité (RTE) and Électricité de France (EDF), Alcan Cable, K-Line Insulators, Tyco Electronics, CQRDA and FUQAC) whose financial support made this research possible. The authors are grateful to H. Banitalebi Dehkordi for his valuable help in the experiments and to P. Camirand for his technical support.

REVIEWED BY Edward P. Lozowski, Department of Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB, Canada and Myron M. Oleskiw, Institute for Aerospace Research, National Research Council Canada, Ottawa, ON, Canada

APPENDIX Parameters which are constant throughout the simulation:

cw

specific heat of water

4.27 ×103 J/ ( kg × K )

Lev

latent heat of water vaporization

2.5 × 10 6 J/kg

M a molecular mass of air

28.964 g/mol

M w molecular mass of water

18.016 g/mol

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p st

static pressure of air

101325 Pa

Pr

Prandtl number

0.72

R

universal gas constant

8.3144 J/ ( mol × K )

Rw

gas constant for water vapour

R/Mw

Sc

Schmidt number

0.63

ρd

density of water droplet

1000 kg/m 3

Parameters calculated as functions of temperature (Pruppacher and Klett, 1978):

Dw diffusion coefficient of water vapor

2.11 × 10 −5 (Ta / 273.16 )

ew

6.1368 × 10 −9 Ta + 2.0341× 10 −6 Ta + 6

pressure of saturated water vapor

Ta ( K )

1.94

5

3.0312 ×10 −4 Ta + 2.6506 ×10 −2 Ta + 1.4289Ta + 4.4365 ×101 Ta + 6.1078 ×10 2 Ta ( D C ) 4

3

2

λa

thermal conductivity of air

2.384 × 10 −2 + 7.123 × 10 −5 Ta

μa

dynamic viscosity of air

(1.718 + 4.9 ×10

−3

( )

Ta D C

)

Ta − 1.2 × 10 −5 Ta ×10 −5 2

( )

Ta D C

ρa

p st M a / (RTa )

density of air The parameters Dw , ew and

μa

Ta ( K )

at droplet temperature are calculated using the

corresponding formulae given above obtained after replacing Ta by Td .

REFERENCES Ashgriz, N., Poo, J.Y., Coalescence and separation in binary collisions of liquid drops. Journal of Fluid Mechanics, 1990, 221, 183-204. Beard, K.V., Pruppacher, H.R., A wind tunnel investigation of the rate of evaporation of small water drops falling at terminal velocity in air. Journal of Atmospheric Sciences, 1971, 28, 1455-1464. Brazier-Smith, P.R., Jennings, S.G., Latham, J., The interaction of falling water droplets: coalescence. Proc. Royal. Soc. London A, 1972, 326, 393-408.

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Chen, J.-D., Hahn, P.S., Slattery, J.C., Coalescence Time for a Small Drop or Bubble at a Fluid-Fluid Interface. AIChE Journal, 1984, 30(4), 622-630. Creismeas, P., A Eulerian/Lagrangian model to calculate the evolution of a water droplet spray. International Journal for Numerical Methods in Fluids, 1995, 20(2), 135-155. Crowe, C.T., Sharma, M.P., Stock, D.E., The particle-source-in cell (PSI-CELL) model for gas-droplet flows. Journal of Fluids Engineering, 1977, 325-332. Dukowicz, J.K., A Particle-Fluid Numerical Model for Liquid Sprays. Journal of Computational Physics, 1980, 35, 229-253. Edson, J.B., Anquetin, S., Mestayer, P.G., Sini, J.F., Spray droplet modeling 2. An interactive Eulerian-Lagrangian model of evaporating spray droplets. Journal of Geophysical Research, 1996, 101(C1), 1279-1293. Estrade, J.-P., Carentz, H., Lavergne, G., Biscos, Y., Experimental investigation of dynamic binary collision of ethanol droplets - a model for droplet coalescence and bouncing. International Journal of Heat and Fluid Flow, 1999, 20, 486-491. Gates, E.M., Lam, W., Lozowski, E.P., Spray Evolution in Icing Wind Tunnels. Cold Regions Science and Technology, 1988, 15, 65-74. Gavaises, M., Theodorakakos, A., Bergeles, G., Brenn, G., Evaluation of the effect of droplet collisions on spray mixing. Proc. Inst. Mech. Eng., 1996, 210, 465-475. Godard, S., 1960. Mesure de gouttelettes de nuage avec un film de collargol. Bulletin de l'Observatoire du Puy de Dome, 41-46. Gore, R.A., Crowe, C.T., Effect of particle size on modulating turbulent intensity. International Journal of Multiphase Flow, 1989, 15, 279-285. Gosman, A.D., Ioannides, E., Aspects of Computer Simulation of Liquid-Fuelled Combustors. AIAA Paper, 1981, 1981-323. Hetsroni, G., Particles-turbulence interaction. International Journal of Multiphase Flow, 1989, 15, 735-746. Jeelani, S.A.K., Hartland, S., Effect of Surface Mobility on Collision of Spherical Drops. Journal of Colloid and Interface Science, 1998, 206, 83-93. Kim, S., Lee, D.J., Lee, C.S., Modeling of binary droplet collisions for application to interimpingement sprays. International Journal of Multiphase Flow, 2009, 35, 533-549. Ko, G.H., Ryou, H.S., Droplet collision processes in an inter-spray impingement system. Aerosol Science, 2005, 36, 1300-1321. Kollár, L.E., Farzaneh, M., 2007a. The Effects of Droplet Collision, Evaporation, Gravity and Turbulent Dispersion on the Droplet Size Distribution of an Aerosol Cloud under Icing Conditions. Proceedings of 12th International Workshop on Atmospheric Icing of Structures, Yokohama, Japan, Paper 2-3. Kollár, L.E., Farzaneh, M., Modeling the evolution of droplet size distribution in two-phase flows. International Journal of Multiphase Flow, 2007b, 33, 1255-1270. Kollár, L.E., Farzaneh, M., Spray Characteristics of Artificial Aerosol Clouds in a Low-Speed Icing Wind Tunnel. Atomization and Sprays, 2009, 19 (4), 389-407. Kollár, L.E., Farzaneh, M., Karev, A.R., Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution. International Journal of Multiphase Flow, 2005a, 31, 69-92. Kollár, L.E., Farzaneh, M., Karev, A.R., 2005b. The Role of Droplet Collision, Evaporation and Gravitational Settling in the Modeling of Two-Phase Flows under Icing Conditions.

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Proceedings of 11th International Workshop on Atmospheric Icing of Structures, Montreal, QC, Canada, Paper IW38. Kollár, L.E., Farzaneh, M., Karev, A.R., Modeling Droplet Size Distribution Near a Nozzle Outlet in an Icing Wind Tunnel. Atomization and Sprays, 2006, 16 (6), 673-686. MacKay, G.D.M., Mason, S.G., The Gravity Approach and Coalescence of Fluid Drops at Liquid Interfaces. The Canadian Journal of Chemical Engineering, 1963, 41, 203-212. Marek, J., Olsen Jr., W.A., 1986. Turbulent Dispersion of the Icing Cloud from Spray Nozzles Used in Icing Tunnels. Proceedings of 3rd Int. Workshop on Atmospheric Icing of Structures, Vancouver, BC, Canada, 103-110. Maxey, M.R., Riley, J.J., Equation of motion for a small rigid sphere in a nonuniform flow. Physics of Fluids, 1983, 26, 883-889. Munnannur, A., Reitz, R.D., A new predictive model for fragmanting and non-fragmanting binary droplet collisions. International Journal of Multiphase Flow, 2007, 33, 873-896. Nguyen, A.V., Schulze, H.J., Colloidal Science of Flotation, Marcel Dekker, Inc.: New York, NY, 2004. Nikolopoulos, N., Nikas, K.-S., Bergeles, G., A numerical investigation of central binary collision of droplets. Computers & Fluids, 2009, 38, 1191-1202. O'Rourke, P.J., Bracco, F.V., Modelling of Drop Interactions in Thick Sprays and a Comparison with Experiments. Proc. Inst. Mech. Eng., 1980, 9, 101-116. Orme, M., Experiments on Droplet Collisions, Bounce, Coalescence and Disruption. Prog. Energy Combust. Sci., 1997, 23, 65-79. Post, S.L., Abraham, J., Modeling the outcome of drop-drop collisions in Diesel sprays. International Journal of Multiphase Flow, 2002, 28, 997-1019. Pruppacher, H.R., Klett, J.D., Microphysics of Clouds and Precipitation, D. Reidel Publishing Company: Dordrecht, Holland, 1978. Qian, J., Law, C.K., Regimes of coalescence and separation in droplet collision. Journal of Fluid Mechanics, 1997, 331, 59-80. Snyder, W.H., Lumley, J.L., Some measurements of particle velocity autocorrelation functions in a turbulent flow. Journal of Fluid Mechanics, 1971, 48, 41-71. Stallabrass, J.R., 1978. An Appraisal of the Single Rotating Cylinder Method of Liquid Water Content Measurement, LTR-LT-92, National Research Council of Canada, Division of Mechanical Engineering. Steinhaus, B., Spicer, P.T., Shen, A.Q., Droplet Size Effects on Film Drainage between Droplet and Substrate. Langmuir, 2006, 22, 5308-5313. Wang, L.-P., Ayala, O., Kasprzak, S.E., Theoretical formulation of collision rate and collision efficiency of hydrodynamically interacting cloud droplets in turbulent atmosphere. Journal of Atmospheric Sciences, 2005, 62, 2433-2450. Whitaker, S., Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, and for flow in packed beds and tube bundles. AIChE Journal, 1972, 18, 361-371.

In: Wind Tunnels: Aerodynamics, Models and Experiments ISBN 978-1-61209-204-1 © 2011 Nova Science Publishers, Inc. Editor: Justin D. Pereira

Chapter 4

AN AIR-CONDITIONED WIND TUNNEL ENVIRONMENT FOR THE STUDY OF MASS AND HEAT FLUX DUE TO CONDENSATION OF HUMID AIR Akhilesh Tiwari1*, Pascal Lafon1, Alain Kondjoyan2 and Jean-Pierre Fontaine1 1. Clermont Université, Université Blaise Pascal, Laboratoire de Génie Chimique et Biochimique (LGCB), BP10488, F-63000, Clermont Ferrand, France 2. Institut National de la recherché Agronomie (INRA), UR Qualité des Produits Animaux, F-63122, Saint Genès Champanelle, France

ABSTRACT The development of an artificial ecosystem inside a closed environment is one of the future challenging problems, which is mandatory for the long duration manned space missions like lunar base or mission to Mars. Plants will be essential companion life forms for such space missions, where human habitats must mimic the cycles of life on earth to generate and recycle food, oxygen and water. Thus the optimized growth of higher plants inside the closed environment is required to obtain efficient biological life support systems. The stability and success of such systems lie on the control of the hydrodynamics and on an accurate characterisation of the coupled heat and mass transfer that develop at interfaces (solids, plants,..) within the space habitat. However, very few data can be found on the precise characterization / prediction of the mass transfer at interfaces, and more particularly in space. In most studies the mass flux is deduced from the measured / calculated heat flux by a heat and mass transfer analogy. Hence, we have developed a ground based experimental set-up to measure the air flow velocities and concomitant mass transfer on specific geometries under controlled air flow conditions (flow regime, hygrometry, temperature). The final goal is to derive a theoretical model that could help for the prediction of the hydrodynamics and coupled heat/mass transfer on earth, and eventually in reduced gravity. We have used a closedcircuit wind tunnel for our experiments, which can produce very laminar to turbulent flows with controlled temperature and hygrometric parameters inside the test cell. The * E-mail : [email protected]

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initial experiments have been performed in dry air with an average velocity between 0.52.5 m.s-1. The velocity profiles near a clean aluminium flat plate in horizontal or vertical positions have been studied for low Reynolds number flows by hot wire anemometry. The measurements with the horizontal plate showed a boundary layer thickness in agreement with the Blasius’ solutions. Condensation of humid air was induced on an isothermal flat plate, which was cooled by thermoelectricity. The mass transfer on the plate was controlled and recorded with a precise balance. The obtained results are analyzed, and compared to the available data on condensation.

INTRODUCTION Human life is precious and its existence on Earth is characterised by few very important factors or parameters. The availability of these parameters on the earth is monitored and recycled by nature itself. The basic functions that sustain life on earth are breathable air, food, usable water, optimum temperature and pressure, and also recycling of waste. To maintain human life away from earth, we have to recreate a sustainable environment, with the abovementioned life supporting basic systems. Today’s technology is capable of supporting human crews in space for missions in low earth orbit (LEO) of short or indefinite duration as long as resupply is readily available, as evidenced by the International Space Station (ISS). All crewed space missions rely on resupply from Earth for some or nearly all of the required consumable resources (oxygen, water, food). The technology used on the ISS is capable of recovering water from humidity condensate, waste hygiene water, and crew urine with 80 to 90 percent efficiency [1]. The air and water treatments are performed with physico-chemical processes. However, no space-qualified technologies are capable of recycling food or oxygen from waste materials, and wastes have to be discarded or stored for return to Earth. Resupplying future missions beyond LEO, missions to Mars or to the moon for example, will be even more intricate, if not impossible. The major advantage of a bio-regenerative life support system (BLSS) is that it does not need to be resupplied with food, water, and air, nor does it require expendable water or air filtration systems as present-day mechanical spacecraft life support systems do [2-4]. Indeed, throughout the history of manned-space flight, one of the key problems has been the development of bio-regenerative life support systems (BLSS), to provide autonomy to piloted spacecraft and planetary outposts for multiyear missions [5]. The importance of recycling within the spacecraft, with crews consuming the products of autotrophic synthesis, needs recycling of materials, requires exchanges between photoautotrophic organisms, which synthesize organic substances using solar or artificial light, and heterotrophic organisms. Hence, growing plants is a vital component and its performance in BLSS for space missions will be principally dependent on the progress of plant cultivation technology for space and the achievement of associated equipment. The growth of higher plants in a green house is optimized by the environmental conditions among which the effect of ventilation, condensation and evaporation phenomena on the surfaces of leaves, plants, windows, and walls. Our study is devoted to the control of the hydrodynamics and concomitant heat and mass transfer (gas /liquid) at interfaces. Furthermore, condensation on solid walls or on plants has to be controlled to provide optimized living conditions (for astronauts or plants), although the humidity level may be

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particularly high in a greenhouse (75-80%). Air-conditioning systems have always been known as good solutions to prevent condensation while maintaining optimized conditions for life, but an adapted ventilation system (forced convection) is needed, particularly in a microgravity or reduced gravity environment. Thus, a precise control of the hydrodynamics and the concomitant heat, humidity and mass transfer developing in the space station has to be performed. Numerical simulation or theoretical models could give insights into the dynamics of transport phenomena and assist in the design of an optimized and reliable air-conditioning system. However, a precise mathematical model requires the knowledge of the local mass transfer coefficient (for condensation or evaporation) for the specific configurations, and a validated turbulent model. Such data can only be given by experimental works or by literature. We have developed an experimental set-up to measure mass flux in a closed loop wind tunnel, where temperature and humidity are regulated.

EXPERIMENTAL MATERIAL AND METHODS A wind tunnel is used to generate and control the mass flux of humid air that condenses on the active surface, which is a square flat plate. The temperature of this plate is kept constant below the dew point by an arrangement of thermoelectric cooling in order to induce a steady flow of condensation on the air/plate interface, and the produced condensate is regularly measured by weighing the whole system. The system consists of square shaped Peltier modules sandwiched between a square shaped aluminium flat plate and a heat exchanger device, and a temperature regulator which provides the power supply of the thermoelectric Peltier module. The overall arrangement is placed in the experimental cell of a wind tunnel in which the hydrodynamics, temperature and hygrometry are controlled.

Wind Tunnel The wind tunnel facility built by INRA-Theix under the direction of Dr Kondjoyan [6] aimed to generate from nearly laminar to highly turbulent flows. The detailed description of the wind tunnel is given in the literature [6-8]. The data for laminar flows were compared in these studies for turbulent flows are similar to those encountered in industrial and outdoor environments. The temperature, humidity and wind velocity can all be regulated inside the wind tunnel. The main characteristics of the wind tunnel are: • • •

The testing chamber has a cross section of 0.8 m x 0.8 m and a length of 1.6 m in the direction of the flow. It was designed to generate average air flow velocities from 0.5 m.s-1 to 5.0 m.s-1 and turbulence intensity ranging between 1% and 20%. Temperature and humidity (characterized by the dew point) are controlled with an accuracy of ±0.1°C (air temperatures and dew point are homogeneous to 0.1°C within the area where the experimental set-up is located).

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The wind tunnel is shown schematically in Figure 1. It is a closed loop of 12 m long and 4 m high. The flow is initially made as laminar as possible and to get a very little turbulence intensity in the order of 1% in the test chamber (1), the diffusers (2, 6, 8 and 10) and elbows (4 and 7) were designed to bring the air of the ventilator (5) to the damping screen (11) without generation of turbulence due to separations on the walls of ducts. The fine mesh grid located in the damping chamber dissipates turbulence by viscous effects. The contraction area (12) makes the flow more uniform at the entrance of the experimental chamber through a contraction ratio of 9. Two drawers (12, 14) located respectively upstream and downstream of the contraction area may optionally be used as generators of turbulence by adding or removing extra perforated plates, perpendicular to the direction of the flow. The use of two drawers at different distances from the experimental test chamber strongly increases the possibility of obtaining flows whose turbulence intensity is uniform around the experimental set-up.

Figure 1. Schematic of wind tunnel.

Two devices of air-conditioning assistant are associated with the wind tunnel installation to ensure the temperature and humidity control. The measurement of the dew point is carried out using a cooled mirror hygrometer with a precision of ±0.1°C (Dew 10 of National Instrument). The wind tunnel is a closed loop, sealed, strongly isolated and the devices of conditioning are located upstream of the ventilator. The hydrodynamic homogeneity of the experimental test chamber was validated by velocity measurements taken in many points of this chamber, these measurements showed that the mean velocities differ by less than 5% within the total volume, the intensity of turbulence varies by less than 3% in the area, where we should place our experimental prototype of condensation. Previous measurements showed a very good uniformity in temperature and humidity in the test area, the variations were lower than ±0.1°C for the temperature of the air and the dew point, even for a nearly laminar flow [7].

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M Measuremen nt of Wind Velocity V The characcterization of the t flow, meann flow velocitty and fluctuattions, was carrried out by coonstant temperature hot wirre anemometryy. The hot wirres are normallly 5 µm in diameter and 1..25 mm long suspended between b two needle-shaped n d prongs. Thee sensor posssesses flow seensitivity and wide frequenncy response inn turbulent floow. Miniaturee wire probes with offset prrongs and witth the sensor perpendicular p to the probe axis (DANTE EC 55P15) weere selected ass they are deesigned for measurements m within the booundary layerr. This shape of prongs alllows measureements close to t a solid walll without distturbance from m the body off the probe, w which remains beyond the boundary b layeer. The wind tunnel is equuipped with a three-axis trraversing systeem that enablles the displaccement of thee hot wire proobe in an areaa of chosen diimension and location with a selected dispplacement in the t order of abbout 0.01 mm.

D DANTEC 55P15 5. Fiigure 2. Hot wirre sensor probe.

A telescope (magnificatiion ×24) placeed at a distancce (about 3 m) m was used too locate the prrobe, with preecision (± 0.055 mm), close too the plate andd to avoid anyy contact. (See figure 2) The hot wires availaable were calibrated witth room tem mperature foor velocity m measurements averaged rannging betweenn 0.5 m.s-1 too 5 m.s-1 withh an accuracyy of 1-3%. B Below 0.4 m.s-1 hot wire measurements laack accuracy because b of therrmal exchange. The data accquisition for the localizatioon of the hot wire w probe andd the average velocity v fluctuuations was reecorded using a computer coonnected to thhe system. A photograph p off the test cham mber, where w have placedd our set-up is shown in figuure 3. we

Fiigure 3. A view w of the test cham mber with telesscope.

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Condensation Unit The whole system of cooling a square flat plate is shown in Figure 4. The temperature of the active surface is controlled by a Peltier element owing to a thermistor (1), which is itself inserted inside the square aluminium flat plate near its geometrical centre for the regulation of the input current of the Peltier element. The aluminium flat plate (2) is glued on a Peltier module (3) of the same size, with a thermal adhesive, loaded with micronized silver (Arctic Silver – Premium Silver). The preliminary tests were carried out by pasting the aluminium flat plates with a thermal paste. The other side of the Peltier module is pasted on a heat sink (4). This heat sink made up of single-piece extruded aluminium has a strong density of wings aligned with the direction of the flow to reinforce the convective exchange. To increase the effectiveness of the Peltier module, the use of a heat sink on the hot side of the Peltier plate is a key parameter. The objective is to dissipate the heat flux produced on the “hot” side of the Peltier module in order to maintain this side at a temperature as close as the ambient temperature Ta, which can be used as a reference temperature. The value of the electric current in a Peltier module theoretically makes it possible to create an absorption of heat on one side (“cold”) and an equivalent heat emission on the opposite side (“hot”). Keeping this surface at room temperature, which is the reference temperature, makes it possible to create the necessary temperature difference with the dew point Td in order to induce the desired rate of condensation on the cold surface temperature Ts. Indeed, the rate of condensation is directly related to this difference in temperature ΔT=Td- Ts.

Figure 4. Schematic of the whole condensation unit.

Air-Conditioned Wind Tunnel Environment…

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In order to control this rate of condensation, we need, on the one hand, to maintain this temperature contrast constant (ΔT=Td-Ts) throughout the experiment. For this purpose, a thermistor of small size (1) is inserted in the plate to measure the temperature in its centre under the plate/air interface. It is connected to the temperature regulation controller (7), which adjusts the electric current transmitted to the Peltier module to maintain Ts constant. In addition, to obtain a uniform mass flux on the whole surface for a precise measurement of the rate of mass flux, we must maintain the temperature of the active surface (plate/air) as isothermal as possible. Aluminium plates (strong thermal conductivity) of thickness 2, 3, 4, 5 mm were studied. The 3 mm thickness make it possible to homogenize the thermal distribution obtained directly on the cold surface, the one produced at the ceramic Peltier module side (variations of several degrees Celsius for a 50 mm x 50 mm plate) with a weak inertia. A programmable temperature regulation controller (LFI-3751 of Wavelength Electronics) for the Peltier module was chosen for its stability over time and accuracy (± 0.1°C). In addition, it is possible to add an auxiliary thermistor sensor (for the study of temperature difference inside and on the upper surface eventually). The main goal of this study is to evaluate local mass transfer coefficients. Thus, we must study acive surfaces of small sizes for the measurement to be considered local and for the surface to be nearly isothermal, but which are however sufficiently large in order to condense a quantity of water that can be recorded with a precise balance. Plates measuring 30 mm x 30 mm, 40 mm x 40 mm and 50 mm x 50 mm were considered.

Thermoelectric Cooler (TEC) – Peltier Element The idea behind the Peltier effect [9-11] is that, whenever a direct current flows through the circuit of heterogeneous conductors, heat is either released or absorbed at the conductors’ junctions, which depends on the current polarity. The amount of heat is proportional to the current that passes through the conductors. The basic TEC unit is a thermocouple, which consists of a p-type and a n-type semiconductor elements, or pellets, which are traditionally made of Bismuth Telluride (Bi2Te3)-based alloy and normally copper commutation tabs are used to interconnect these pellets. Thus, a typical TEC consists of thermocouples connected electrically in series and sandwiched between two Alumina ceramic plates. The number of thermocouples may vary greatly from several elements to hundred of units.

Specifications of Used Peltier Modules The Peltier Modules were manufactured by KRYOTHERM, Russia, the different parameters are given below.

136

Akhilesh Tiwari, Pascal Lafon, Alain Kondjoyan, et al. Table 1. Different parameters of single stage thermoelectric coolers

Snow Ball – 71-S ICE-71 HT(120) E L3 TB-127-2.0-2.5

Imax Am ps 3.6 8 7.6

36 80

Umax Volt s 16.1 16.1

76.0

16.3

Qmax Watts

ΔTm (K) 71 71

Rac Oh m 3.2 1.5

No of thermocouples 71 71

30 x 30 x 3.6 40 x 40 x 3.4

72

1.65

127

48 x 48 x 4.8

ax

Dimensions (mm x mm x m)

ΔTmax = Maximum achievable temperature difference between the hot and cold side of a thermoelectric cooler Imax = Input current through a thermoelectric cooler resulting in greatest ΔT (ΔTmax) Umax = Voltage on a thermoelectric cooler contacts at ΔTmax Qmax = Maximum cooling capacity of a thermoelectric cooler. It is determined at maximum current through a thermoelectric cooler and at zero temperature difference between hot and cold sides Rac = Electric resistance of a thermoelectric cooler measured at an alternating current with the frequency of 1 kHz.

Advantages and Disadvantages of Using a Peltier Module as CoolingDevices Advantages: • • • • • •

A Thermoelectric cooler module has no moving part, therefore, it needs virtually no maintenance; Capability of modules to operate for more than hundred thousand hours of steadystate operation; Compactness and lightness; Very fast response time; No orientation / position dependence; Reliability.

Disadvantages • • • •

Heat dissipation, which requires heat sinks and fans; Control of the reference temperature; Non-uniformity of the cold power produced at the ceramic interface; Condensation inside the Peltier elements.

To prevent condensation inside the Peltier elements the Peltier modules have been sealed with Silicon and Epoxy.

Weighing The whole experimental arrangement with the condensation unit, the temperature regulator and all the connecting wires is placed on a weighing balance (Figure 3). Also, it is maintained in the measuring chamber by a shaft (5) fixed itself at the balance pan (8). There

Air-C Conditioned Wind W Tunnel Environment… E …

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arre two horizoontal parallel plates p conneccted by four screws s and pllaced on the balance, b in beetween these two t plates thee temperature regulation coontroller (7) iss placed. The wire w of the Peeltier module and the therm mistor insertedd in the activee plate (1) wallk along the axxis and are coonnected to th he temperaturee controller. Thhe balance is put on a mobiile platform, a trolley (9) w which makes it i possible to slide the whhole system on o a rail (10)). This device allows a coontinuous sign nal acquisitionn recorded byy a precision balance b (Mettller 30, precisiion of ±0.1 g)), which is co onnected to thee computer foor monitoring the increase in i mass as thee humid air w condense on will o the active surface.

EXPERIM MENTAL RESULTS E AN ND DISCUSS SIONS V Velocity and d Turbulent Intensity Profiles P in Dry Conditioons

Fiigure 5 (a-d). Comparative surface plots above the flat plate in i horizontal poosition at 1 mm (a, c) and att 3 mm (b, d): (aa-b) velocity prrofiles in metre per second and (c-d) turbulencce intensity in per p cent.

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Preliminary experiments have been performed inside the wind tunnel for the study of velocity and turbulence intensity profiles in dry conditions at room temperature (Ta ≈ 22°C) [12-13]. The mean velocity measurements have been performed at 1 mm and 3 mm above the surface of the horizontal plate. The surface plots of the velocity profile are given in figure 5(a, b) and for the turbulence intensity in figure 5(c, d) for mean velocity of 1.5 m.s-1. The experiments were performed for a mean entrance velocity of 0.5, 1.1, 1.5, and 2.0 m.s-1 and the wind velocity as well as the turbulence intensity were measured. It is observed from figure 5(a, b) that, on moving from the surface of the flat plate to free stream velocity, the fluctuations in the velocity decrease and the shape of the velocity profile is almost conical, and centred towards the middle to back part of the flat plate. It is also observed in figure 5(c, d), that the maximum turbulence intensity at 1 mm above the surface of the plate reaches 3040%, and at 3 mm above the surface drops to 3-4%, whereas the turbulence intensity at the entrance of the tunnel was about 1.5%. Slightly above a height of 3.2 mm of the plate, the turbulence intensity suddenly reached the range of the turbulence intensity measured at the entrance of the tunnel (1.5%), which shows that the probe was outside the boundary layer. The symmetry of the measured profiles (velocity and turbulence intensity) reflects the accuracy of the experimental set-up (position, manufacturing etc.). All our results showed that we observe the development of a boundary layer on top of the aluminium plate. This boundary layer could not be considered as the classical laminar boundary layer on a flat plate. Even if the upstream edge of the plate was thin (3 mm in thickness) it generated vortices which increased turbulence near the plate wall. Actually turbulence intensities up to 30-40% were measured in the wind tunnel above the plate which revealed the development of those turbulent vortices. In this case it was shown in literature [14] that close to the wall the velocity profile was similar to that of a classical laminar boundary layer, even if the velocity gradient increased with turbulence, while the contact region between the free stream and the boundary layer became less distinct similarly to the outer region of a turbulent boundary but without any logarithmic behaviour of the velocity profile. It was also shown in literature that the global boundary layer thickness including the outer turbulent part was a little bit increased compared to thickness of a classical laminar boundary layer. This thickening of the boundary layer due to free stream turbulence was always very small (10% to 20%). Boundary layer thickness was measured in our study for different air flow velocities by considering that the end of the boundary layer was reached when the turbulence intensity was the same as in the upstream flow. Results are compared with Blasius’ solution ( δ x ≅ 4.64

υx U ) [15] in

figure 6. In agreement with previous literature boundary layer thickness was close to Blasius’ solution. Table 3. Values of parameters used in calculations and taken at the time of the experiment Parameter

Range

Atmospheric pressure, mbar Dew point temperature, °C

920-924 < 7.0 °C

Density of air, kg/m3

1.202 2

Kinematic viscosity, m /s

1.525 x 10-5

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139

Figure 6: Comparative plot of boundary layer thickness calculated by using Blasius solution (continuous line) and (observed experimentally) on a plate of surface area 5 cm x 5 cm.

Condensation Experiments in Ambient Conditions Some experiments for condensation on the surface of a flat square plate were carried out in a closed room in which the hygrometric and hydrodynamic parameters varied according to the inside ambient weather conditions, except for a fan which was used to produce the air turbulence for the heat exchanger. The condensation unit was put directly on top of a balance (Ohaus Navigator-N24120). A non laminar flow of humid air was generated on the active surface by a very small fan (same size as the heat exchanger) of 12 V power supply. The average air velocity was almost constant during all the experiments. More than 15 experiments were carried out with three different sizes of the plates. Each experiment was performed in different ambient atmospheric conditions. The measurements of the temperature distribution on the surface of the flat plate and on the surface of the Peltier element only were carried out in the ambient air and they showed that the top surface temperature was more or less homogeneous for 3 mm thick plate (variation of less than 1°C for a 3 mm thick plate of 5 cm x 5 cm): it was observed in a local temperature distribution measurement with 25 equidistant points on the surface of 5 cm x 5 cm or 4 cm x 4 cm plates, and with 17 points on the 3 cm x 3 cm that the variation in temperature on the active surface was higher for thinner plates (1 mm and 2 mm thickness). Also the similar local temperature distribution measurements directly on the ceramic surface of the Peltier element (without the aluminium plate) showed a temperature difference larger by 1.5°C for the 5 cm x 5 cm plate. In all cases the temperature was minimum at the centre and maximum at the boundaries.

Akhilesh Tiwari, Pascal Lafon, Alain Kondjoyan, et al.

1,5

18,50

1,20

15,50

0,90

12,50

0,60

9,50

0,30

6,50

0,00

Amount of condensate (g)

3,50 0,0

1,0

2,0 3,0 Time (h)

4,0

1,2

12,5

0,6

9,5

0,3

6,5

0,0

3,5 0,0

5,0

1,0

2,0

3,0

4,0

5,0

Time (h)

(B)

2,00

7,0E-05 6,0E-05 5,0E-05

1,50

4,0E-05 3,0E-05

1,00

temp diff (°C) rate of condensation (g/h)

8,0E-05

2,0E-05

2,50

8,0E-05 7,0E-05

Temp difference (°C)

temp Diff (°C) rate of condensation (g/h)

Mass flux (Kg m-2 s-1)

Temp difference (°C)

15,5

0,9

(A) 2,50

18,5

wt of condensate ambient temp (+10°C) dew point temp set on the controller

2,00

6,0E-05 5,0E-05

1,50

4,0E-05 3,0E-05

1,00

2,0E-05 1,0E-05

1,0E-05 0,50

0,0E+00 0,0

1,0

2,0 3,0 Time (h)

(C)

4,0

5,0

0,50

Mass flux (Kg m -2 s-1)

1,50

Temperature (°C)

wt of condensate dew point temp set on the controller ambient temp (+10°C)

Temperature (°C)

Amount of condensate (g)

140

0,0E+00 0,0

1,0

2,0

3,0

4,0

5,0

Time (h)

(D)

Figure 7: a-b) Amount of condensate and temperature as a function of time. The value of ambient temperature is also given in the graph after reducing 10°C to fit in scale. c-d) The temperature difference and mass flux as a function of total time.

Figure 7 (a-d) shows the plots of condensation experiments carried out on two different days with variable hygrometric and hydrodynamic atmospheric conditions. These experiments were performed on a horizontal aluminium square flat plate of 50 cm x 50 cm in open environment and for temperature differences, ΔT = Td - Ts (between the surface temperature (Ts) and the dewpoint (Td)) of approximately 1.50 °C. The variation in relative humidity was 2 to 12% and in ambient temperature less than 10% according to the local weather conditions during day time, sometimes both data increased or decreased simultaneously, other times one increased and the other decreased, which varied the dewpoint temperature by less than 1°C up or down during the experiment. However, it was important to maintain the temperature of the active surface sufficiently below the dewpoint for the condensation of water vapour in air to proceed. It is observed from figure 7(a), the mass increase versus time and that the temperature difference ΔT varies from 1.2°C to 1.8°C. The ambient temperature is increased by 8% and the relative humidity decreased by almost 15% during the 5 h experiment, which provided a decrement in the initial dewpoint value of about 0.5 °C. The amount of condensate collected during this time was 1.5 g with an average rate of condensation of 0.26 g/h. Figure 7(b) shows a similar experiment, in which the temperature difference ΔT was first decreased then went up almost 0.7°C and then was decreased by 0.8°C, because the ambient temperature

Air-Conditioned Wind Tunnel Environment…

141

went up 5%, but the relative humidity was slightly increased and then decreased with a variation of almost 5%. The dewpoint decreased for about 1 h and then increased, but the difference was less than 1°C during the 5 h experiment, which resulted in a collection of 1.4 g of condensate. Figure 7 (c, d) shows the rate of condensation and temperature difference as a function of the total time of the experiments. Figure 7(c) indicates that the rate of condensation follows the trend of the temperature difference except after 4 h, where the measured rate of condensation decreased even though the temperature difference increased. Figure 7(d) shows that the rate of condensation has more or less a similar behavior as the temperature difference ΔT. As the temperature difference starts decreasing, the condensation rate decreases significantly, because of the low temperature difference and the reduced active surface area left on the surface of the plate as the interface condensate/air may not be cold enough to induce condensation. The figures 8(a-b) shows similar plots as 7(a-b) but measured inside the wind tunnel and with slightly higher temperatures to get similar rates of condensation. The Reynolds number

Re = ( ρ ∞νL) / μ∞ was in the range of 3800 – 4000 and the Schmidt number Sc = μ ∞ /( ρ s D) was 0.6. Figure 8 (a) shows again that the mass flux of condensation varies according to the temperature difference ΔT represented on the graph by the dewpoint variation (as Ts is constant). Two main trends can be observed: (i) a mass rate of 0.36 g/h for 0 ≤ t ≤ 2.5 h (ii) a mass rate of 0.2 g/h for 5 ≤ t ≤ 8 h. The trend (i) corresponds to the early condensation period when drops grow all over the surface and coalesce according to the well known process [16-17]. The trend (ii) corresponds to a lower mass increase as the surface of the plate is covered by large mass of water leaving a much smaller active area for most of the condensation to proceed, as a much lower condensation rate develops at the condensate/ air interface. Figure 8(b) shows a more linear trend during the 8 h experiment with a mass rate of about 0.4 g/h, but a slight decrease seems to be seen at the end of the experiment. 18,5 wt of c ondens ate temp s et on c ontroller ambient temp dew point

2,5 12,5

2,0 1,5

9,5

1,0

wt of c ondens ate temp s et on c ontroller ambient temp dew point

0,5

6,5

3,5 2,0

4,0 T im e  (h)

(A)

6,0

3,0

18,5

15,5

2,5 12,5

2,0 1,5

9,5

1,0 6,5 0,5

0,0 0,0

Am ount of c ondens ate (g )

15,5 T em perature (°C )

Am ount of c ondens ate (g )

3,5

3,0

T em perature (°C )

3,5

8,0

0,0

3,5 0,0

2,0

4,0 T im e  (h)

6,0

8,0

(B)

Figure 8: a-b) Amount of condensate and temperature as a function of time inside the wind tunnel.

Figure 9(a) shows the variation of the amount of condensate versus time for several average temperature differences ΔT in an open environment. The trends are affected by the hygrometric ambient conditions, which are not completely stable as we did not perform the experiments in air-conditioned environments. The figure 9(b) indicates more regular variations inside the controlled wind tunnel for three different temperature differences, which

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indicates that on increasing the temperature difference the amount of condensate also increases accordingly. However, the main behavior indicates the sensitivity of the slope and, thus, of the mass flux to the temperature difference as expected. The evaluation in time is also influenced by the active area which decreases with time as condensation covers more and more the flat plate and after long duration we can observe some type of saturation as most of the plate surface is covered with water. It is also worth noting that the shape of the condensate is also strongly influenced by the physico-chemical properties of the aluminium plate (contact angle, etc.). Initially drop-wise condensation is induced (Figure 10(1)), but after a few hours (Figure 10 (3)), a large part of the plate is covered by mainly 4-5 big drops of water which can flow out of the plate or be thrown out by the air flow. These complex phenomena greatly affect the heat-mass transfer at the surface of the plate. In the future condensation process will be analyzed step by step trying to characterize as much as possible the formation of condensate. 4,5 (1,5±0,3) °C (2,3±0,4) °C (2,5±0,1) °C (2,6±0,3) °C (2,7±0,8) °C (3,6±0,4) °C (3,9±2,9)°C (4,2±0,7) °C

3,5 3,0 2,5

3,0

Amount of condensate (g)

Amount of condensate (g)

4,0

2,0 1,5 1,0

5.4±0.4

2,5

5.1±0.6 6.7±0.9

2,0 1,5 1,0 0,5

0,5 0,0

0,0 0,0

1,0

2,0

3,0

4,0

5,0

0,0

6,0

1,0

2,0

3,0

4,0

5,0

6,0

Time (h)

Total time (h)

(A)

(B) Rate of condensation (g/h)

0,70 0,60 0,50 0,40 0,30 Experimental (wind tunnel) Experimental (open) Theoretical (wind tunnel)

0,20 0,10 0,00 0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

Time (h)

(C) Figure 9. (a) Amount of condensate as a function of total time of experiment for 8 experiments in open environment (b) inside the wind tunnel for 3 experiments at given temperature differences (c) comparative rate of condensation as a function of time measured experimentally in open air and wind tunnel and calculated theoretically for wind tunnel.

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143

The figures 9(c) shows the variation of the theoretical and experimental values of the rate of condensation versus total time. The theoretical diffusion coefficients were calculated here by using the binary diffusion coefficient of water vapour in air from the kinetic theory of gases [18]. The mass flux of water vapour in air was calculated by using the formula [19]:

NWV =

Shρ s D (ω ∞ − ω s ) L(1 − ω s ) 1

1

where the average Sherwood number is computed from, Sh(1 − ω s ) = 0.664 Re 2 Sc 3 and the Reynolds number (Re) and the Schmidt number (Sc) are standard dimensionless numbers, where the Sherwood number is expressed with mass fraction and not with concentration. From the observation of plot 9(c), we can say that the rate of condensation was not constant with time. For the first hour of the experiment it went down in the open environment, and then was decreased gradually. It differs in the wind tunnel for the first 2.5 h when the rate was increased, because the temperature difference was increased by 15%, and then a similar trend is seen. It is worth noting that the rate of condensation is proportional to the active surface and that this area decreases with time as condensation develops. Moreover, some evaporation takes place at the water / air interface. The theoretical value of the mass flux is almost constant during the whole experiment because the effect of the condensate collected on the surface was not considered in the theory.

Figure 10. (1-4) Photographs of the flat plate with condensation on it at different duration of time (in hours) from starting point of condensation.

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CONCLUSION The above experimental findings show that the use of a wind tunnel is needed for the precise characterization of mass transfer by condensation of air on surfaces and that it will provide a very powerful tool to establish a theoretical model for the prediction of such phenomena. Also the concept based on thermoelectric cooling and weighing the growing mass of condensation to study mass transfer is validated. To be more accurate further experiments are being performed in the wind tunnel. Indeed, we have performed experiments in a closed wind tunnel, in which, it is possible to control the psychometric parameters (relative humidity, temperature) and to generate almost laminar to turbulent flows. The results in dry conditions determined the velocity profile above a flat horizontal plate and estimated a boundary layer thickness, which fits with Blasius’ solutions. More complete results will allow in developing a theoretical model for the mass transfer flux of condensation at interfaces.

NOMENCLATURE T L Cp h N D Tu U u Tc x

= = = = = = = = = = =

temperature, K characteristic length of the plate, m specific heat capacity, J/ kg K heat transfer coefficient, J/m2 K s mass flux, Kg/m2 s binary diffusion coefficient at interface m2/s turbulence intensity of air, % mean air velocity in the free stream, m/s velocity fluctuations around U in the main flow direction, m/s temperature constraint set on controller, °C distance from the starting edge of the plate, m

Dimensionless Quantity Sh = Re = Sc =

Sherwood number Reynolds number Schmidt number

Greek ρ μ ω Δ ν δ

= = = = = =

density, kg/m3 dynamic viscosity, Pa s mass fraction of water vapour in air difference kinematic viscosity, m2/s boundary Layer thickness, m

Air-Conditioned Wind Tunnel Environment…

145

Subscripts ∞ wv s d

= = = =

value at ambient temperature or free flow temperature water vapour surface or interface of air and flat plate dewpoint

ACKNOWLEDGMENTS The authors are grateful to the Centre National d’Etudes Spatiales (CNES), France for providing financial support. They also thank Prof. Jean Bernard Gros, LGCB for fruitful discussions.

REFERENCES [1] [2]

[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

Advanced Technology for Human Support in Space, National Academy Press, No. 9768305, 1997. Mergeay, M.; Verstraete, W.; Dubertret, G.; Lefort-tran, M.; Chipaux, C.; Binot, R. Proc. 3rd Symp. Space Thermal Control and Life Support Systems. Noordwijk, The Netherlands. pp 65-68. Gros, J. B.; Poughon, L.; Lasseur, C.; Tikhomirov, A. A. Adv. Space Res. 2003, 31(1), pp. 195-199. Bérangère F.; Poughon, L.; Creuly C.; Cornet, J-F. ; Dussap, C-G. & Lasseur, C. Appl Biochem Biotechnol 2008, 151, 686–699. Erokhin, A.N.; Berkovich, Yu A.; Smolianina, S.O.; Krivobok, N.M.; Agureev, A.N.; Kalandarov, S.K. Advances in space Research 2006, 38, 1240–1247. Kondjoyan, A. Contribution à la connaissance des coefficients de transfert de chaleur et de matière à l’interface air-solide ; Thèse de Docteur de l’E.N.S.I.A., 1993. Kondjoyan, A.; Daudin, J.D. Int. J. Heat Mass Transfer, 1995, 38(10), 1735-1749. Kondjoyan, A. L’échange de chaleur et d’eau à l’interface air/solide, Habilitation à Diriger des Recherches de l’Université Blaise Pascal, 1999. Peltier, J. C. A. Ann. Chem. Phys. 1834, 56, 371. Rowe, D.M. Handbook of thermoelectrics, CRC Press Inc., 1995. Goldsmith, H.J. Electronic refrigeneration, Pion Ltd, London, 1986. Tiwari, A.; Fontaine, J-P. Water, Air, & Soil Pollution: Focus, 2009, 9, No. 5-6, 539547. Tiwari, A.; Fontaine, J-P., Lafon, P.; Kondjoyan, A. 40th ICES -2010, Bercelona, Spain, (AIAA2010-6171). Kondjoyan, A.; Peneau, F.; Boisson, H-C. Int. J. Therm. Sci. 2002, 41, 1-16. Bird, R.B.; Stewart W.E.; Lightfoot, E.N. Transport Phenomena, John-Wiley & Sons Inc., NY, USA, 2002. Beysens, D. Atmospheric Research 1995, 39, 215-237. Beysens, D. C R Physique 2006, 7, 1082-1100.

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[18] Hirschfelder, J.O.; Curtis, C.F.; Bird, R.B. Molecular theory of gases and liquids, John Wiley and Sons, 1952, pp. 441-610. [19] Asano, K. Mass Transfer- from fundamentals to modern industrial applications, WileyVCH, Verlag GmbH & Co. KGaA, Weinheim, 2006, chapter 3.

In: Wind Tunnels: Aerodynamics, Models and Experiments ISBN 978-1-61209-204-1 © 2011 Nova Science Publishers, Inc. Editor: Justin D. Pereira

Chapter 5

IN-SITU EVALUATION FOR DRAG COEFFICIENTS OF TREE CROWNS Akio Koizumi Graduate School of Agriculture, Hokkaido University, Japan

ABSTRACT In order to make a hazard prediction of trees against wind damage, such as stem breakage or uprooting, it is essential to quantitatively estimate the wind force acting on a tree. The drag coefficient of the tree crown, which is necessary to estimate wind force, has been evaluated using wind tunnel studies. Most of the specimens used for wind tunnel studies were dwarf trees, because of the restrictions due to wind tunnel size. However, with regard to the wind-force response, the similarity rule is not applicable to the relationship between dwarf trees and actual-sized trees. In fact, the drag coefficients of small trees were found to be considerably greater than those of actual-sized trees. To estimate the drag coefficients of actual-sized trees accurately and easily, a field test method was developed. Using this method, wind speed and stem deflection were monitored simultaneously. The wind force acting on the tree crown was calculated from the stem deflection; the stem stiffness was evaluated by conducting tree-bending tests. The field tests were conducted on black poplars and a Norway maple; the results showed that the drag coefficients decreased with an increase in wind speed. This decrease can be explained mainly by the decrease in the projected area of the crown, because of the swaying movement of the leaves and branches. Although the variation in the drag coefficients was large at low wind speeds because of the swaying behavior of the stem subjected to a variable wind force, the variation at wind speeds above 10 m/s was small. The average drag coefficient for black poplars at a wind speed of 30 m/s was estimated by the curve fitting of a power function to the wind velocity-drag coefficient relationship, and this value was found to be not greater than that of actual-sized conifers previously studied in wind tunnel experiments. These results suggest that the wind permeability of poplar crowns is greater than that of conifer crowns due to the difference in leaf flexibility. Although the drag coefficients in the defoliation season were smaller than those measured in the leaved season at low wind speeds, the difference in drag coefficients became less pronounced at high wind speeds.

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INTRODUCTION Windthrow damage to trees is associated with huge economic losses in silviculture and danger to humans from park or roadside trees. To analyze this damage, trees can be assumed to be cantilevered beams supported by the root plate on the ground, which receives the load of the wind force acting on the crown and stem. The bending moment would cause bending failure of tree trunks as tapered beams (Chiba 2000). In the case of cylindrical hollow trunks with decayed heartwood, the moment may cause shell buckling or the shear force may cause splitting failure (Peters et al. 1985). If the moment resistance of the root plate is critical, the moment will cause uprooting (Peltola et al. 2000). The wind force acts mainly on the tree crown, including the stem above the crown base. Therefore, in order to predict wind damage to trees, it is essential to quantitatively estimate the wind force acting on the tree crown. The drag coefficient of tree crowns (CD), defined in Eq. 1, is necessary to estimate wind force; and has been evaluated using wind tunnel studies (Hirata 1953; Mayhead 1973; Johnson et al. 1982; Murakami et al. 1984; Ishikawa 2005).

1 PW = CD ρACU 2 2

(1)

where Pw is wind force, ρ is the air density, AC is the horizontally projected crown area, and U is the wind speed. AC may be measured by the planimetric method using photographs or calculated from geometric approximation. If the crown shape is approximated as a triangle or a diamond, the crown area can be calculated using Eq. 2.

1 AC = BC LC 2

(2)

where BC is crown breadth and LC is crown length. Johnson et al. (1982) reported that the crown area estimated from Eq. 2 overestimated the area measured from photographs by a maximum of 7% for dwarf coniferous specimens. Since AC was measured in still air conditions, CD values decreased with an increase in wind speed, because of the decrease in projected area caused by the streamlining of tree crowns. Mayhead (1973) performed a regression analysis using the quadratic function of Eq. 3 to establish the relationship between wind speed and CD; and found good agreement between the 2 variables.

C D = C + m1U + m2U 2

(3)

where C, m1, and m2 are constants. Vollsinger et al. (2005) observed that the streamlining effect reduced the crown areas at the still condition to 28% for Populus trichocarpa, 37% for Alnus rubra, and 20% for Betula papyrifera at the wind speed of 20 m/s in the wind tunnel experiment for small crowns of hardwood species.

Table 1. Summary of wind tunnel studies determining drag coefficients (CD) of tree crowns Reference

Number of specimens

Height (m)

Assumed crown shape

Average CD 10 m/s

20 m/s

Ishikawa (2005)

Cupressus macrocarpa

2

0.13–0.17

Diamond

1.00

Hirata (1953)

Picea glehnii

11

0.25–0.75

Diamond

0.77

0.68

Thuja orientalis

4

0.31–0.64

Diamond

1.08

0.76

Triangle Triangle Triangle Photographb Photographb Photographb Triangle Triangle Triangle Triangle Triangle Triangle Triangle

1.15 1.02 0.97 0.87 0.95 0.75 0.88 0.71 0.66 0.57 0.46 0.43 0.29

0.83 0.69 0.95 0.76 0.88 0.54 0.50 0.54 0.49 0.36 0.35 0.31 0.20

Johnson et al. (1982)

Murakami et al. (1984)

Mayhead (1973)

a

Species

Pinus strobus Cryptomeria japonica Picea glauca Camellia sasanqua Juniperus chinensis Lithocarpus edulis Abies grandis Picea sitchensis Pinus nigra Pinus contorta Pinus silvestris Pseudotsuga menziesii Tsuga heterophylla

2 2 1 1 1 1 1 2 4 1 4 3 2

less than 0.8 m; b measured by planimetric method using photographs

a

Dwarf tree Dwarf treea Dwarf treea 1.5 1.5 2.5 5.8–8.5 5.8–8.5 5.8–8.5 5.8–8.5 5.8–8.5 5.8–8.5 5.8–8.5

26 m/s

0.68 0.56 0.91

0.41 0.45 0.35 0.30 0.30 0.25 0.16

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Akio Koizumi

Most of the specimens used for the above-mentioned wind tunnel studies were small trees, because of the restriction in wind tunnel size (Table 1). Tests of actual-sized coniferous species used for plantations were performed in 1962 and 1967 at the Royal Aircraft Establishment at Farnborough, UK (Fraser 1962; Mayhead 1973). Mayhead (1973) determined the CD for 7 species from the data obtained in these tests. With regard to the windforce response, it is noteworthy that the similarity rule is not applicable to the relationship between dwarf trees and actual-sized trees. The CD values for small trees at a wind speed of 10 m/s were found to be 1.00 (Ishikawa 2005), 0.97–1.15 (Johnson et al. 1982), and 0.75– 0.95 (Murakami et al. 1984). These values seem to be inversely related to tree size, and were considerably greater for dwarf trees than for actual-sized trees, i.e., 0.29–0.88 (Mayhead 1973). The same trend of difference for CD values between specimen sizes was observed also at high wind speeds. The average ratio of CD at a wind speed of 20 m/s to that at 10 m/s for small trees was 0.793 (Hirata 1953), 0.792 (Johnson et al. 1982), and 0.840 (Murakami et al. 1984), while it was 0.696 for actual-sized trees (Mayhead 1973). The difference in CD associated with tree size seems to be greater at higher wind speeds. This finding suggests that the wind permeability of an actual-sized crown is greater than that of a small crown, because of the difference in streamlining behavior. The height of the wind pressure center (HW) was evaluated in several wind tunnel experiments by measuring the pitching moment evoked by wind force. Johnson et al. (1982) found that the HW was located at 37–56% of the crown length from the crown base for dwarf conifer specimens. When using geometric approximation, HW was assumed to be the height of the gravity center of the shape used. As stated above, it is difficult to test actual-sized trees in wind tunnels and the CD determined for small trees is inaccurate to predict critical wind speed in actual-sized trees. Therefore, the CD for wind damage assessment concerning coniferous plantation forests has been based on the limited data for actual-sized trees obtained by Mayhead in 1973 (Peltola et al. 1999; Gardiner et al. 2000). The drag coefficients of actual-sized broadleaf trees have not yet been determined. These CD values are necessary for wind damage assessment for park trees or roadside trees. This chapter presents details of the test method used to evaluate the CD of actual-sized trees in the field; this method was developed by Koizumi et al. (2010) and is more convenient than wind tunnel experiments. The proposed field test method consists of simultaneous monitoring of wind speed and stem deflection.

MATERIALS AND METHODS Sample Site and Trees We tested black poplar (Populus nigra var. italica) and Norway maple (Acer platanoides) planted in the Hokkaido University Campus; the dimensions of the sample trees are shown in Table 2.

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151

Table 2. Dimensions of sample trees Tree no. 1 2 3 4

Species Poplar Poplar Poplar Maple

H (m) 13.1 12.3 12.9 4.9

DB (cm) 24.2 19.3 24.1 7.8

LC (m) 9.3 7.8 8.9 3.7

BC (m) 4.4 3.6 4.1 2.9

HW (m) 8.4 8.4 8.5 3.1

H, tree height; DB, breast-height diameter; LC, crown length; BC, crown breadth (east-west direction); HW, height of wind pressure center. The dimensions of tree nos. 1 and 2 were measured in October 2007 and those of tree nos. 3 and 4 were measured in October 2008.

Three poplar trees were sampled from the east-west row planted in 2000. The south side of the row of trees was an open space without buildings and the prevailing wind direction was south. Therefore, the effect of turbulent flow was considered to be small. A small Norway maple (tree no. 4) was sampled from the planting strip next to a building in the north-south row. The prevailing wind direction at the site was north and south.

Monitoring of Wind Speed and Stem Deflection The field test consisted of monitoring wind speed and stem deflection, as shown in Figure 1. The north-south and east-west components of the wind speed were monitored using an ultrasonic anemometer (Young Company, Model 85000) by placing it near each sample tree. The height of the anemometer was adjusted to one half of the crown length from the crown base, which was considered the height of the wind pressure center.

Figure 1. Schematic diagram of the field test for monitoring wind speed and stem deflection.

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Stem deflection was measured using a self-made middle-ordinate gauge (Figure 2; Koizumi and Ueda 1986). Both ends of the 500 mm long gauge were screwed onto the stem at a height of 115–165 cm. Gauge span could be changed depending on the stiffness of the sample stem. A displacement transducer (Kyowa Dengyo, DTH-A-5) was set at the center of the gauge span. The sensitivity of the transducer was 0.1% of a 5-mm stroke. The strain on the xylem surface parallel to the grain was also measured in a preliminary test conducted on a larch tree (Larix kaempferi). Strain gauges were glued onto debarked xylem spots at opposite sides of the middle-ordinate gauge setting (Figure 3). The strain and the stem deflection measured with the middle-ordinate gauge showed high correlation and both methods were found to be able to estimate bending deformation of stems accurately. In this chapter, the stem deflection method is described, because of its non-destructive nature; unlike the stem deflection method, attaching strain gauges requires the removal of bark.

Figure 2. Dimensions of middle-ordinate gauge.

Figure 3. Attaching strain gauges on debarked xylem of a larch tree.

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153

Wind speed and stem deflection were measured along both north-south and east-west orientations and recorded in a data logger at 10-Hz intervals. The measurements were performed on windy days in both leaved and defoliation seasons for the poplar trees and in leaved season for the maple tree. The series of data were divided into 1-h segments and averaged every second. Thus, each segment consisted of 3600 data points. A total of 579 segments, which included those measured at wind speeds above 5 m/s, were analyzed. Details of the measurement times are listed in Table 3. The maximum wind speed observed in each measurement period was 10–15 m/s. Table 3. Measurement periods for wind velocity and stem deflection Tree no. 1 2 3 4 a

Leaf condition Leaved Defoliated Leaved Defoliated Leaved Defoliated Leaved

Measurement period

Measurement time (h)

Analysis time (h) Data set Aa

Data set Bb

Oct. 2007 Apr. 2008 Oct. 2007 Apr. 2008 Oct. 2008 Apr. 2008 Jul.-Sep. 2008

232 120 235 117 402 48 735

82 59 58 31 115 44 190

4 10 24 0 28 13 9

Measurement time including data for wind speeds above 5 m/s; b measurement time including data for wind speeds above 10 m/s

Determination of Stem Stiffness Factor In order to measure the stiffness of the tree stem, bending tests of the sample trees were conducted once on calm days in each measurement period. A bending moment below the elastic limit was applied by pulling the stem from north and east directions using a hand winch. The applied force was measured using a load cell that connected the sling, which was tied to the stem at a height of approximately 3 m, to the hand winch. The load and stem deflection measured with the middle ordinate gauge were recorded in a data logger at 10-Hz intervals. The test setup is shown in Figure 4. From the elastic relationship between the applied moment at the middle-ordinate gauge (M) and the stem deflection (δ), the stem stiffness factor (KS) was determined for both the north-south and the east-west orientations.

KS =

M

δ

(4)

After the stem bending test, the natural swaying period of the sample trees was determined from the free-swaying movement of the stem deflection recorded in the data logger when a tense rope was suddenly released.

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Akkio Koizumi

Fiigure 4. Tree beending test for determining d stem m stiffness.

C Calculation of o CD m dataa of wind speeed and stem deeflection, the wind force accting on the From the monitored crrown was calcculated using Eq. E 5.

PW =

K Sδ S (H W − H D )

(5)

i the wind forrce, δS is stem deflection, HW is the heiight of the winnd pressure where Pw is ceenter, and HD is the height of o the deflectioon sensor. Then, CD was calculatted every secoond from the ratio of PW too U2 using Eqq. 6, which w derived by was y substituting Eq. 5 into Eqq. 1. The consttant value of 1.20 kg/m3 waas used for thhe air density (ρ). (

CD =

2 K Sδ S ρAC ( H W − H D )U 2

(6)

The projeccted crown areea (AC) was obbtained from bitmap imagees converted from f crown phhotographs. After A correctinng the photogrraphs with reggard to trapezzoidal skew using image

In-Situ Evaluation for Drag Coefficients of Tree Crowns

155

processing software, outlines of the crowns were traced and binarized to the bitmap image. HW was assumed to be the height of the gravity center of the image. HW and AC estimated from photographs taken for leaved crowns were also used for calculating the CD for defoliated crowns. In this chapter, the CD of only the north-south component was analyzed, because the eastwest component was rather small during the measurement periods. Furthermore, the CD may have been disturbed by the adjacent trees for poplar specimens.

RESULTS AND DISCUSSION Stiffness of Tree Stems The relationship between the applied moment and stem deflection observed in the stembending test was found to be almost linear and adequate for the determination of the stiffness factor (KS). For example, the KS for tree no. 3 in the leaved season was calculated to be 15.4×106 N from the regression equation (Figure 5).

Moment (Nm)

800 700

Tree no. 3

600

Y = 15.4 X + 69.1

500 400 300 200 100 0 0

10

20

30

40

Stem deflection (μm)

Figure 5. Relationship between applied moment and stem deflection in tree bending test.

50

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Area and Height of Wind Pressure Center of the Sample Crowns Examples of the binary image processing for poplar and maple crowns are shown in Figure 6. All areas enclosed by foliage were included in the crown area. The projected crown area (AC) and the height of the wind pressure center (HW) for the sample crowns obtained by the planimetric method using the bitmap images are presented in Table 4, along with those calculated from geometric assumptions; the crown was assumed to be a triangle or a diamond, or an ellipse whose major and minor axes were the length and breadth of the crown, respectively. These values are shown as ratios to those obtained from the bitmap images. Although the crown area of the triangle and diamond shapes was the same, the height of the gravity center differed between the 2 shapes. As seen in Table 4, the actual crown area was found to be 19–30% smaller than that estimated by assuming an ellipsoidal shape and 9–27% greater than that estimated by assuming a diamond or a triangle shape, which had been previously applied to coniferous crowns (Mayhead 1973). The height of the wind pressure center (HW) was estimated to be 47–48% and 40% of the LC from the crown base for black poplars and the Norway maple, respectively. The HW was found to be 3–22% smaller than that obtained by assuming an ellipsoidal or diamond shape and 19–22% greater than that obtained by assuming a triangle shape. As a result, the assumption of an ellipsoidal shape underestimated the CD of the actual shape by 21–46%. Meanwhile, the assumption of a triangle shape overestimated the CD by 33–52%. The best agreememt was found for the assumption of a diamond shape; the CD ratio for the diamond shape to the actual shape was in the range of 0.856–1.240.

Figure 6. Examples of photographs and binarized images of black poplar (tree no. 2) and Norway maple (tree no. 4).

Table 4. Comparison of crown area (AC), height of wind pressure center (HW), and drag coefficient (CD) between crown-shape assumptions Tree no. 1 2 3 4

AC (m2) 23.73 17.82 22.45 5.86

HW (m) 8.12 8.22 8.19 2.67

R-AE 1.368 1.235 1.290 1.438

R-AC-T,D 0.871 0.786 0.821 0.915

R-HW-E,D

R-HW-T

R-CD-E

R-CD-T

R-CD-D

1.048 1.026 1.038 1.277

0.821 0.838 0.823 0.825

0.697 0.789 0.747 0.544

1.398 1.518 1.480 1.325

1.095 1.240 1.174 0.856

R- indicates AC, HW, and CD ratios for ellipsoidal (E), triangle (T), and diamond (D) shape crowns to those obtained from bitmap images

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The effect of the wind force acting on the stem below the crown was neglected, because of the small area of the stem compared to that of the crown, the low wind speed near ground level, and the short distance between the wind-pressure center of the stem below the crown base and the height of the middle-ordinate gauge.

Relationship between Wind Speed and CD Stem deflection showed a positive correlation with wind speed (U), as shown in Figure 7. The relationship between U and CD calculated by Eq. 6 using a data segment that included 3600 data points is shown in Figure 8. The average CD decreased with an increase in the wind speed. This decrease in CD can be explained by the decrease in the area of the crown, because of the streamlining of leaves and branches, as observed in wind tunnel studies.

Figure 7. An example of the time-series fluctuations of wind speed (U) and stem deflection (δS).

Figure 8. Relationship between wind speed (U) and drag coefficient (CD).

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Figure 9. Average and standard deviations of drag coefficient (CD) calculated by generating moving averages from 1–10 seconds.

At the same time, the variation in CD was found to be large at a low wind speed. This observation could be explained by the swaying movement of a stem subjected to a variable wind force, which can be seen from the fine fluctuations observed in the time-stem deflection relationship (Figure 7). The variation in CD was small at wind speeds above 10 m/s. In order to reduce the effect of vibrations at low wind speeds such as 5 m/s, the CD was calculated by generating moving averages from 1–10 s. This range includes the natural periods (swaying periods) of the sample trees; the natural period for the poplar trees ranged from 2.8–3.7 s. However, no significant change was found in the average CD or the standard deviations associated with the period of moving averages, as shown in Figure 9.

Data Necessary for Adequate Prediction of CD As mentioned above, CD calculation using data at low wind speeds may lead to considerable error due to swaying movement if the tree was subjected to strong winds immediately before the recording. To assess the effect of wind speed variation on CD calculation, measurement times were divided into 2 data sets: A and B, which included those measured at wind speeds above 5 m/s and 10 m/s, respectively. The analysis times of these 2 data sets are shown in Table 3. Average CDs were calculated for wind speeds at 0.5-m/s intervals using the 2 data sets for the leaved period of the sample trees (Figure 10). Here, the data for wind speeds less than 1.75 m/s were neglected. Naturally, the average CDs calculated for wind speeds above 10 m/s were the same for the 2 data sets. However, there appears to be a large difference between the 2 data sets at wind speeds below 5 m/s. The reduction in CD at wind speeds below 5 m/s for data set B seemed to be greater than that for data set A. Wind speeds of 30–46 m/s are assumed to be the maximum possible speed and are considered the maximum wind speed in Japanese building design codes in urban areas. Therefore, the critical wind speed could also be assumed to be 30 m/s with regard to wind resistance of roadside or park trees (Ishikawa et al. 1984). Mayhead (1973) found that the CD

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is nearly uniform at the wind speeds above 30.5 m/s, which is likely to cause windthrow damage. He determined the minimum CD values from the regression equations of the quadratic function (Eq. 3) for the prediction of critical tree heights. In order to estimate the CD at a wind speed of 30 m/s, the relationship between the average CD and U calculated for wind speed classes was curve-fitted with the power function of Eq. 7, which is a monotonic decreasing function (Figure 10).

C D = aU b

(7)

where a and b are constants. Although the quadratic function of Eq. 3 (Mayhead 1973) was curve-fitted for this relationship, the fitting was poor. An exponential function (Eq. 8) with a convergence value, which seemed to be a reasonable model, was also attempted for curve-fitting. However, the parameters could not be determined by the non-linear least square method for the data sets of tree no. 4, because the reduction rate for CD was conparatively constant for that case (see Figure 10).

C D = cd U + g

(8)

where c, d, and g are constants.

1.5 Data set A (Curve fit) Data set B (Curve fit)

1.0 0.5

Tree no.3

CD

Tree no.1 0 1.5 1.0 0.5

Tree no.4

Tree no.2 0 0

5

10

15 0

5

10

15

U (m/s)

Figure 10. Relationship between wind speed class and average drag coefficient (CD) with curve fit of power function.

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Table 5. Regression coefficients and expected drag coefficient (CD) at a wind speed of 30 m/s Tree no. 1 2 3 4

Data set A a b 2.53 -0.910 1.45 -0.824 2.40 -0.714 1.14 -0.328

CD-30 0.115 0.088 0.212 0.374

Data set B a b 2.33 -0.872 1.11 -0.724 2.64 -0.755 1.98 -0.570

CD-30 0.120 0.095 0.202 0.285

Coefficients: a and b are defined in Eq. 7.

The constants a and b in Eq. 7 determined for the 2 data sets are shown in Table 5, with the CD values expected at a wind speed of 30 m/s obtained by extrapolation using Eq. 7. The regression curves agreed well with U–CD relationships, which may justify extrapolation at high wind speeds. No significant difference was found in the estimated CD at a wind speed of 30 m/s between the 2 data sets, except for tree no. 4. Since the Norway maple (tree no. 4) was planted in a north-south row, the effect of turbulent flow on CD estimation may be considerable for the north-south component of the wind. No magnitude relation for the estimated value of CD was found between the 2 data sets. Using data set B for CD prediction may be convenient, because the measurement time of data set B was less than that of data set A. In conclusion, the CD at a wind speed of 30 m/s can be accurately predicted with the curve fit of Eq. 7 on average values calculated for wind speed intervals of 0.5 m/s using data set B.

0.3

CD

0.2

0.1 Average value Calculated using all 28-h data 0

1

2

3

4 5 6 7 Sample size

8

9

10

Figure 11. Drag coefficients (CD) estimated for a wind speed of 30 m/s using 1–10 measurement hours.

To identify the minimum measurement hours necessary for proper CD estimation, 1–10 measurement hours were sampled randomly from data set B for the leaved season of tree no. 3, for which 28 hours of data were available, and bundled. With 5 repetitions of random sampling for each sample size, 50 bundled data points were prepared for the analysis in total.

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The estimated CDs at a wind speed of 30 m/s regressed using the bundled data are shown in Figure 11. Averages of the 5 repetitions showed good agreement with the CD values of 0.202 that was estimated using all 28–hour data points (broken line in Figure 11). No relationship between the sample size and average CD values was found. The largest deviance from 0.202 was found at a sample size of 8. Although the fluctuation was large, the standard deviation of the CD calculated for 5 repetitions seemed to decrease with an increase in sample size (Figure 12). It can thus be said that the greater the sample size, the higher the accuracy of CD prediction. At least 2 measurement hours that include wind speeds above 10 m/s are necessary to predict CD. No difference was found in standard deviation between the estimated CD at various wind speeds (Figure 12). Wind speed values for both north and south directions were used in the analysis. The U– CD relationship obtained for north and south wind directions separately is shown in Figure 13. The prevailing wind direction was from the south for tree nos. 1–3 and from the north for tree no. 4. It is reasonable to combine the data for both wind directions.

Standard deviation (%)

0.1 U (m/s) 10 20 30 0.05

0

1

2

3

4 5 6 7 Sample size

8

9

10

Figure 12. Standard deviations of 5 drag coefficient (CD) values estimated for wind speed at 10, 20, and 30 m/s using 1–10 measurement hours. 1.5 South wind North wind

1.0

CD

0.5 Tree no.1

Tree no. 3

Tree no. 2

Tree no. 4

0 1.5 1.0 0.5 0 0

5

10

15 0

5

10

15

U (m/s)

Figure 13. Relationship between wind speed (U) and drag coefficient (CD) obtained for north and south wind conditions.

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Effect of Leaves on CD for Poplar Crowns The U–CD relationships obtained for poplar crowns in the defoliated season are shown in Figure 14. The CD in the defoliation season was smaller than that in the leaved season, because the same crown areas were used for the calculation. The change in the crown area with wind speed variation would be small in the defoliation season because the streamlining behavior of the defoliated branches would be small. In fact, the decrease in the CD with an increase in the wind speed was small for tree nos.1 and 2, as shown in Figure 14. Consequently, the average ratios of the estimated CD of defoliated crowns to leaved crowns at wind speeds of 10, 20, and 30 m/s determined from the curve fit of Eq. 7 were 0.563, 0.804, and 1.008, respectively (Figure 15). It is therefore recommended that the same CD value of leaved crowns without any reduction be used to predict the wind force at wind speeds above 30 m/s for winter storms.

1

CD

Tree no. 1 Tree no. 2 Tree no. 3 0.5

0 0

5

10

U (m/s)

CD ratio (defoliated / leaved)

Figure 14. Relationship between wind speed (U) and drag coefficient (CD) for defoliated crowns.

2 1.5

Average value

1 0.5 0

10

20 U (m/s)

30

Figure 15. Ratios of estimated drag coefficient (CD) for defoliated crowns to those for leaved crowns.

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Comparison between CD Values of Poplars, Maple, and Conifers Average CD values estimated for a wind speed of 30 m/s using data set B for black poplar and Norway maple are presented in Table 6. CDs for 7 coniferous species in Table 6 were calculated by regression analysis using Eq. 7 from data published by Mayhead (1973) assuming a triangular-shaped crown. Although the method of AC estimation was different, the average CD of poplar crowns was found to be smaller than that of western hemlock, which showed the smallest value among those for conifers determine d by the wind tunnel study. These results suggest that the wind permeability of poplar crowns is greater than that of conifer crowns due to differences in leaf flexibility. The average extrapolated value of the CD at wind speed of 30 m/s was 0.14; this value can be used to estimate wind speeds that induce wind damage in poplar trees. The CD for Norway maple was 0.29, which was greater than that for black poplar and corresponded to that for Scots pine (Pinus silvestris) and lodgepole pine (Pinus contorta) (Mayhead 1973). It should be noted that only one Norway maple specimen was tested in this study. Furthermore, the estimated CD for Norway maple may be affected by turbulent flow, because the direction of the prevailing wind and the planted row was similar. Table 6. Drag coefficient (CD) values for prediction of windthrow damage Species Black poplar Norway maple

CD 0.14 0.29 0.38

Grand fira Sitka sprucea Corsican pine Scots pinea

0.44 0.32

a

0.28 0.22

a

Douglas fir Lodgepole pinea Westerm hemlock a

0.29 0.15

a

calculated from data published by Mayhead (1973).

CONCLUSION 1) Drag coefficients of black poplar crowns were successfully evaluated using a field test method in which the wind velocity and stem deflection were monitored simultaneously. 2) Open space around the sample tree with regard to prevailing wind direction is desirable for eliminating the effect of turbulent flow. 3) Two or more measurement hours that include wind speeds above 10 m/s are necessary to predict the critical wind speed for the sample tree crown.

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4) The drag coefficient for black poplar crowns was smaller than that for conifers studied in previous wind tunnel experiments. The difference in drag coefficients suggests a difference in the wind permeability of the tree crown between species. 5) Although the drag coefficient of defoliated crowns was smaller than that of leaved crowns at low wind speeds, it is recommended that the same CD value of leaved crowns without any reduction be used to predict the wind force at wind speeds above 30 m/s.

ACKNOWLEDGEMENT The author would like to acknowledge Mr. Jun-ichi Motoyama for his kind assistance in the experimental work. This study was supported in part by JSPS KAKENHI (21580169).

REFERENCES Chiba Y (2000) Modelling stem breakage caused by typhoons in plantation Cryptomeria japonica forests. Forest Ecology and Management, 135:123-131 Fraser AI (1962) Wind tunnel studies of the forces acting on the crowns of small trees. Forestry Commission, Annual Report on Forest Research, 178-183. Gardiner B, Peltola H, Kellomäki S (2000) Comparison of two models for predicting the critical wind speeds required to damage coniferous trees. Ecological Modelling, 129:123. Hirata T (1953) Fundamental studies on the formation of cutting series (2) (in Japanese). Bull Tokyo Univ Forests, 45: 67-88. Ishikawa H (2005) Experimental study on flow characteristics of trees (In Japanese). Nagare, 24:483-490. Johnson RC, Ramey GE, O'Hagan DS (1982) Wind induced forces on trees. J Fluid Eng. 104: 25-30. Koizumi A, Ueda K (1986) Estimation of the mechanical properties of standing trees by bending test (1) (In Japanese). Mokuzai Gakkaishi, 32: 669-676. Koizumi A, Motoyama J, Sawata K, Sasaki Y, Hirai T (2010) Evaluation of drag coefficients of poplar-tree crowns by a field test method. J Wood Science, 56:189-193. Mayhead GJ (1973) Some drag coefficients for British forest trees derived from wind tunnel studies. Agr Meteorol. 12: 123-130. Murakami S, Deguchi K, Takahashi T (1984) Shelter effects of trees as wind-breaks (In Japanese). Proceedings of Symposium on Wind Engineering, Tokyo, pp 129-136. Peters M, Ossenbruggen P, Shigo A (1985) Cracking and failure behavior models of defective balsam fir trees. Holzforschung, 39:125-135. Peltola H, Kellomäki S, Valsanen H, Ikonen VP (1999) A mechanistic model for assessing the risk of wind and snow damage to single trees and stands of Scots pine, Norway spruce, and birch. Canadian J Forest Res. 29:647-659.

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Peltola H, Kellomäki S, Hassinen A, Granander M (2000) Mechanical stability of Scots pine, Norway spruce and birch: an analysis of tree-pulling experiments in Finland. Forest Ecology and Management, 135: 143-153. Vollsinger S, Mitchell SJ, Byrne KE, Novak MD (2005) Wind tunnel measurements of crown streamlining and drag relationships for several hardwood species. Canadian J Forest Res. 35:1238-1249.

In: Wind Tunnels: Aerodynamics, Models and Experiments ISBN 978-1-61209-204-1 © 2011 Nova Science Publishers, Inc. Editor: Justin D. Pereira

Chapter 6

THE PRE-X LIFTING BODY COMPUTATIONAL FLUID DYNAMICS AND WIND TUNNEL TEST CAMPAIGN Paolo Baiocco*1, Sylvain Guedron1, Jean Oswald1, Marc Dormieux2, Emmanuel Cosson2, Jean-Pierre Tribot3 and Alain Bugeau3 1

CNES Direction des Lanceurs Rond Point de l’Espace – 91023 Evry Cedex, France 2 ASTRIUM SAS Avenue du Général Niox – BP1, 33165 Saint-Médard-en-Jalles Cedex, France 3 Dassault Aviation 78, Quai Marcel Dassault – Cedex 300 92552 St Cloud Cedex, France

ABSTRACT Pre-X was the CNES proposal for demonstrating the maturity of European technology for gliding re-entry spacecraft. The program finished in year 2007 with the end of the phase B and a successful PDR. Then it was stopped with the aim of joining the ESA project IXV. The main goal of this experience is to demonstrate the implementation of reusable thermal protections, perform aero thermo dynamics experiments and efficiency of a suitable guidance navigation and control system. The attitude control is realised by elevons and reaction thrusters overall the hypersonic flight, with a functional and experimental objective. This paper presents the Pre-X aerodynamic / aerothermal characterisation through computational fluid dynamics and wind tunnels tests performed during the phases A and B of the programme. The tests permitted to cover the Mach range from 0.8 to 14 and to *

Copyright @ 2010 by P. Baiocco CNES. Released to Nova Science Publishers, Inc.to publish in all forms. Phone : +33 (0)1.60.87.72.14, Fax : +33 (0)1.60.87.72.66 Email: [email protected]; [email protected]; [email protected]

1 2

Phone : +33 (0)5.56.57.20.70, Fax : +33 (0)5.56.57.32.84 E-mail : [email protected]; [email protected] 3 Phone : +33 (0)1.47.11.37.60, Fax : +33 (0)1.47.11.57.95 E-mail : [email protected]; [email protected]

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investigate the main effects of aerodynamic and aerothermal phenomena. In the preceding phases the aerodynamic shape and centring had been defined. The logic and main results of this activity are presented in this paper.

INTRODUCTION The Pre-X baseline mission was performed by the VEGA launch vehicle in a quasi equatorial ballistic trajectory. The spacecraft makes an almost complete earth revolution before splashing down on the Pacific Ocean. The vehicle re-entry point is at 120 km and the mission objectives are fulfilled between Mach 25 and 5. Then the vehicle has to pass to subsonic speeds (either under drog chute or by controlled symmetric flight), the main chute opens and it is finally recovered in the sea. Nominal flight foresees an impact at the mean way between Galapagos and Marquise islands. There the spacecraft is recovered by boat. The hypersonic supersonic aerodynamic data base has been assessed via Euler and Navier-Stokes modelling. Euler data have been used to refine the aerodynamic data base in terms of Mach number, angle of attack, flap setting, while Navier-Stokes to consolidate the viscous effect implemented in the data base by previous phases. The aerodynamic tests have been performed in the TsAGI wind tunnels T-128, T-116 and T-117, the ONERA wind tunnel F4, the VKI longshot. The Mach range covered by these tests and CFD is from M=0.8 to M=25. The ATD tests in the TSNIIMASH facility PGU7, the DLR HEG and the ONERA R2Ch. The Computation Fluid Dynamics (CFD ) has been used to rebuilt these tests and compare numerical with experimental solutions. The equivalent actual flight conditions have also been simulated. The ATD characterisation has been used in order to size the thermal protections and find the most suitable architecture.

PRE-X REQUIREMENTS This project addresses a first generation of re-entry experimental vehicle necessary in Europe for risk mitigation before opening the way for future spacecraft applications. Due to atmospheric re-entry specificity in terms of environment and phenomena, ground based experiments are not always representatives and in flight experimentation is mandatory. The idea was to perform on Pre-X the in-flight experimentation which cannot be simulated on ground. The flight control by means of body flaps is the first time to fly in Europe, as well as a complete fully reusable TPS architecture. A procurement specification has been assessed for the Pre-X vehicle including the following constraints: • • • • •

Mission objectives are covered between Mach 25 and Mach 5. No active oxidation during nominal trajectory . Recovery of vehicle and measures is mandatory. TPS expertise and dismantling without damage is mandatory. Recovery in sea and buoyancy greater than 48h.

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Possibility to fly both on the VEGA and DNEPR launch vehicles, with VEGA as baseline. Mission reliability 0.95 after separation of launcher. Safety criteria lower than 10-7 to do a victim. Ambitious design to cost objective, excluding launch.

VEHICLE GEOMETRY AND MASS BUDGET The vehicle shape is depicted in Figure 1. The mass and centre of mass positions are given in Tables 1 and 2. Three items are defined: nominal, with margins and a maximum value. The vehicle is about 5 m long (including elevons) and 2 m wide. Table 1. Pre-X mass (kg) Minimal 1440

Maximal 1900

Table 2. Centre of mass coordinates (mm) x back 1484

y 0

z up -120

Figure 1. Pre-X geometry.

LOGIC AND TEST PLAN From the vehicle requirement it is apparent that the main domain of investigation concerning aerodynamics and ATD is the hypersonic range. The vehicle has been designed in order to have good flying qualities and ATD similarity with full scale spacecraft from Mach

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25 to 5. However, the vehicle performance for Mach numbers below 5 is important to take the vehicle in safe conditions up to parachute opening. The transonic region can be passed in two ways: • •

Supersonic scenario: A drogue chute opens at about Mach 1.5, then the main parachute is opened ones, reached suitable conditions. Subsonic scenario: A main chute opens at a descent velocity of about 65 m/s and takes the vehicle to a descent velocity of about 9 m/s.

For this reason tests and computations on fluid dynamic codes have been performed up to Mach 0.8 and an Aero Dynamic Data Base (AEDB) computed for the Mach range from 25 to 0.8. The test campaign for aerodynamic and ATD characterisation has been assessed on the base of the nominal Pre-X re-entry trajectory and main phenomena to be investigated. The main similarity parameters considered are: ρVL for viscous effects on elevons and nose μ

•

Re =

• • •

ρL (dissociation parameter) for real gas effects q for thermal flux at stagnation point Mach number.

The wind tunnel test campaign for aerodynamics and ATD has been performed in the facilities listed in Tables 3 and 4. These facilities performances are placed on the Reynolds versus Mach number re-entry trajectory profile in order to assess the aerodynamic similarity with respect to Pre-X flight conditions (Figure 2). The similarity law for ATD is given in Figure 3 and Figure 4 respectively for the dissociation parameter ρL and nose heat flux. Table 3. Aerodynamic facilities Regime Transonic-Sup. Supersonic Hypersonic Hypersonic High enthalpy

Facility T-128 T-116 T-117 Long shot F4

Company TsAGI TsAGI TsAGI VKI ONERA

Table 4. ATD facilities Regime Hypersonic High enthalpy Hypersonic

Facility R2Ch HEG PGU-7

Company ONERA DLR TSIIMASH

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171

Trajectoire Phase A2

100 000 000

10 000 000

1 000 000

100 000

10 000

Re (Lref) ONERA R2Ch ONERA - F4 Tuyère N°2 VKI Longshort DLR HEG TSAGI T128 TSAGI T116 TSAGI T117 Tuyère 1 TSAGI T117 Tuyère 3 TSNII PGU7

1 000

100

10

1 0

5

10

15

20

Mach 30

25

Figure 2. Re versus Mach along Pre-X trajectory.

Pre-X phase A2 - Dissociation Parameter 1.00E+00

1.00E-01

1.00E-02

rho L kg/m2

1.00E-03 rho L HEG - TC I

1.00E-04

HEG - TC II HEG - TC III HEG - TC IV

1.00E-05

R2Ch

1.00E-06

1.00E-07

1.00E-08 0

5

10

15

20

25

30

Mach number

Figure 3. ρL versus Mach along Pre-X trajectory.

Pre-X Phase A2 - Heat Flux 140

120

Altitude (km)

100

80

60

40

20

0 0

50

100

150

200

250

300

350

400

450

500

Stagnation point heat flux (kw/m2)

Figure 4. Nose heat flux along Pre-X trajectory.

As it is well known, the above cited similarities cannot be realised all in once or even never. For example the ground facilities of Table 3 cannot realise Mach numbers greater than

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14. For this reason most of the flight conditions above Mach 10 have been studied only with CFD. Air chemistry plays an important role above Mach 5, producing the O2 and N2 dissociations, which depend on the Mach number itself. In particular, the shape and position of the shock wave is affected by this phenomenon and consequently the aerodynamic characteristics. In particular, the pressure distribution over the body surface, and hence the centre of pressure, change. The effects of altitude plays a role on the velocity of chemical reactions occurring behind the shock: these reactions are faster at high static pressure. Hence at low altitudes there is more probability to get equilibrium conditions for dissociated molecules, while at high altitudes the non equilibrium condition is easier. At high altitudes the Reynolds number is lower and viscous effects are more important giving rise to phenomena such as elevons control efficiency reduction and increased skin friction. All the above cited phenomena have an impact on both aerodynamics and ATD and are one of the main concern of Pre-X flight experience. The other is the TPS material and architecture characterisation during the mission.

AERODYNAMICS Mach numbers 10 and 25 have been chosen for performing intensive CFD characterisation, because of the lack of data from wind tunnels and most important air chemistry and viscous effects occurring in this flight regime. For Mach number between Mach 4 and 10, the hypothesis of perfect gas for air with γ=1.4 has been considered, based on X-38 experience, where real gas effects are negligible in this range. For Mach above 10, air in chemical equilibrium or in chemical non-equilibrium have been assumed. For boundary layer regimes, the following hypotheses have been considered: • • •

4≤ M ≤ 10 turbulent boundary layer from the nose and downstream. M=17.75 laminar regime or sudden transition at elevons hinge line. M=25 laminar boundary layer for all computations.

Euler computations have been performed in the following flight conditions: • • • • •

Mach = 4, 7, 10, 14, 17.75, 25 Angle of attack α=35°, 40°, 45°, 50°, 55° Sideslip angle β=0°, 5° Elevons deflection δe=-10°, -5°, 0°, 5°, 10°, 15°, 20° Ailerons efficiency δa=0°, 5°

The nominal Pre-X flight conditions are α=45°, β=0° overall the hypersonic phase.

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Conventions about vehicle axes are given in Figure 5. Other reference parameters are given below: • • •

Moments are computed with respect to the point centre of mass. δe=(right elevon deflection + left elevon deflection) / 2, δE=>0 for pitch down. δA =(right elevon deflection - left elevon deflection) / 2, δA >0 for right wing upward.

Figure 5. Pre-X vehicle and aerodynamic axes definition.

WIND TUNNEL TESTS This section gives the description of wind tunnel tests performed during the Phase A/B of the Pre-X programme for the constitution of the aerodynamic data base. The model used for all the TsAGI wind tunnel is the same and has a scale of 1/13.75. The sting is different.

T-128 The transonic-supersonic tests have been performed in the TsAGI wind tunnel test T-128 for angle of attack range 30÷85 degrees, Mach 0.8÷4, flap-ailerons deflection -10÷10 degrees. The sting effect has been assessed by means of 3D Navier-Stokes computations, as shown in Figure 6. Figure 7 shows the Pre-X model in the test section. The result is that the longitudinal stability is assured for the angle of attack range 60÷90 degrees. The lateral stability needs to be consolidated with respect to ailerons efficiency even if it has been refined by these tests. In particular, the coefficient Cnβ, defining the yaw moment (n) due to sideslip (β), is always positive and increases for decreasing Mach number.

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Plane of symmetry

Y= 300 mm

Figure 6. Pre-X sting effect for T-128.

interim sting

AOA gage

pressure measurement device (MMD)

balance

Figure 7. Pre-X in the T-128 transonic wind tunnel.

T-116 In the supersonic regime, tests have been performed at Mach 2 and 4 in T-116. The Reynolds number is higher in the wind tunnel than during flight. This effect has been estimated by means of CFD and it is small with respect to elevons efficiency. However, at Mach 2 the Reynolds number effect is really negligible and the flow remains attached in the flap area (at least at flap deflection δE=10°). At Mach 4 a separation zone appears and it is slightly larger for the flight conditions (resulting from CFD analysis). The streamlines resulting from CFD are given in Figure 8 at Mach 4 and Re 11 106.

Figure 8. Pre-X streamline at Mach 4 in the T-116.

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T-117 The scope of T-117 tests is to validate the CFD computations in hypersonic flight and verify the lateral behaviour of the vehicle. The test campaign has been performed at Mach 7.5 and 10.5. The model scale is 1/13.5. The angle of attack range is 30°÷60°, the sideslip 10°÷10° and the flap deflection -10°÷15°. The nominal test conditions are summarised in Table 5. An interesting result of this campaign is that Cm exhibits a non linear behaviour versus angle of attack due to shock structure modification, as shown in Figure 9. This phenomenon is emphasized at δE=15°. Table 5. T-117 nominal test conditions Mach 7.5 70.5

Re (106 m-1) 3.22 2.

ReLref 1030000 704000

p0 (105 Pa) 12 43

T0 (K) 712 1100

Figure 9. T-117: Flow patterns over the windward side.

LONG SHOT The VKI wind tunnel tests have been used to identify the hypersonic aerodynamics in longitudinal, lateral directions and the flap/ailerons efficiency. The M= 14 (contour nozzle) has been selected and nitrogen gas has been used, behaving as a perfect gas at such conditions. The scale of the model is 1/22 (Figure 10). Since the standard aerodynamic balance is used, the accuracy of wind tunnel measurement for lateral aerodynamic components is less than for the longitudinal ones. A quite good agreement has resulted between CFD and WTT. Figure 11 shows the comparison of the pitching moment versus flap deflections for different angles of attack.

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Figure 10. Long shot 1/22 mock-up.

Figure 11. Pitching moment versus flap deflection for different angles of attack.

F4 The aim of F4 test campaign was to determine the real gas effects on the aerodynamic forces and moments at the re-entry velocities and to compare the results with numerical predictions. Four flap deflections have been investigated, namely 0°, 5°, 10°, 15° with angle of attack 45° and 0° sideslip. The specified test conditions were: total enthalpy of 12 MJ at stagnation pressure of 300±10 bar in air. The model scale is 1/12.5 (Figure 12). For different reasons the specified test conditions have not been reached. Instead the following values have been obtained: • •

Total pressure p0: 280 bar Total enthalpy h0: 14.5 MJ/kg

An enthalpy effect on global aerodynamic coefficient has been pointed out, but an actual real gas effect during this campaign cannot be assessed before further analysis.

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The CFD prediction of the F4 has been performed by means of Euler computations assuming thermo-chemical non equilibrium flow field for two F4 conditions, summarised in Table 6. The real gas seems poor in the stagnation region, meanwhile it remains more significant on the flap itself (Figure 13). As far as pitching moment evolution is concerned, the real gas effect induces a very smooth pitch down without flap setting. However for flap deflection of 10°, the pitch down is more significant and is equivalent to 2.5° flap setting (Figure14). Due to real gas effect the bow shock is closer to the vehicle windward than for M=10 solution in perfect gas (Figure 15, comparison of F4 and T-117 M=10 cold gas).

Figure 12. F4 test campaign: model set up.

Table 6. F4 conditions used for CFD Enthalpy 12 14

ρ (kg/m3) 0.00068 0.000536

V (m/s) 4752 5170.7

T0 (K) 742.857 1071.428

Figure 13. F4 CFD results: pressure coefficient on lower surface at section y=300 mm, AoA=45°, de=10°.

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Figure 14. Real gas effect prediction on cm.

Figure 15. CFD comparison between perfect gas and F4 conditions.

CONCLUSION ON AERODYNAMICS The core of the AEDB is constituted by Euler computations. The discrepancies on the results among codes are well below the aerodynamic uncertainties, namely one order of magnitude on global coefficients. The viscous effects are assessed by means of Navier-Stokes computations at high altitudes for Mach numbers greater than 10 (DLR and ONERA). The effect of air dissociations impacts essentially the bow shock (generating a higher drag force), the elevons efficiency, the centre of pressure position. The viscous effects on CL and CD are of the same order of magnitude than the AEBD uncertainty. These effects become significant on Cm for elevons deflections greater than 10°. The effect is increasing for increasing δE. It is important for M=25 and tends to vanish for M=17.75. A correlation to non equilibrium chemistry exists for M≥17.75. A difference in terms of pressure distribution appears on the elevons for deflections greater than 10° between the equilibrium and non equilibrium solution. The effect of

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chemistry modelling on pressure distribution is depicted in Figure 16. This translates into a change on pitching moment consistent at δE=20°.

Figure 16. Effect of chemistry modelling on cp.

The global longitudinal aerodynamic coefficients versus Mach number are given in Figure 17 for α=45°. Values for Mach number greater than 10 are taken from real gas at non equilibrium solution in laminar conditions. The aerodynamic efficiency changes slightly in the Mach range 4 to 25. The pitching moment is a negative derivative function versus angle of attack and is null for about α= 47° for zero elevon deflection and Mach=10.5. Figure 18 shows this case in comparison with the T-117 results in these conditions. The difference between CFD and WTT is always low, but becomes greater for higher α. Real gas effects are effective up to Mach 10, mainly on drag coefficient, placing the real value above the upper boundary of the uncertainty, whatever the elevon deflection (Figure 19). AERODYNAMIC GLOBAL LONGITUDINAL COEFFICIENTS AoA=45° 1

0.8

Coefficient

0.6

CL de=0°

0.4

CD de=0° Cm de=0° CL de=10°

0.2

CD de=10° Cm de=10° 0

-0.2 0

5

10

15 Mach number

Figure 17. Global longitudinal aerodynamic coefficients.

20

25

30

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Figure 18. Pitching moment coefficient, M=10°, δE=0°.

Figure 19. Drag coefficient, M=10°, δE=0°.

Derivatives of aerodynamic coefficients, such as ∂Cy/∂β, ∂Cl/∂β, ∂Cn/∂β, with respect to sideslip are weakly dependent on elevon deflections. This results from CFD and is confirmed by the T-117 outcomes. The introduction of viscous effects and air chemistry at Mach 25 induces signification variations on side force and yawing moment coefficient derivatives. A good agreement on lateral coefficients between CFD and T-117 is obtained.

Flying Qualities The main goal of the flying qualities consists in: • •

Guarantee the longitudinal and lateral stability and controllability. Estimate the maximum sideslip and elevon deflection needed for longitudinal and lateral trim.

The flight qualities have been computed with a given uncertainty on the Pre-X MCI.

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Stability • •

Longitudinal dynamic short period mode is always statically stable with worst case off nominal static margin greater than 4.5%. Lateral Dutch roll dynamic oscillation remains stable within the required margin (C*nβ>10-3).

Longitudinal and Lateral Trim • • • •

Maximum longitudinal deflection needs remain in the range of about ±7°. The Lateral Control Departure Parameter (LCDP4) remains always negative insuring lateral/directional stability. Worst off nominal sideslip needs are β<5° for Mach<2 and <6° for Mach>20. Worst off nominal asymmetric deflection are δA<17° for Mach=2 and δA<10° for Mach>8.

Almost all the available elevon deflection is used for longitudinal trim at Mach>10. This value is greater that the maximum allowable 8° due to thermal constraint. In addition, lateral trim must be achieved at the same time. These results have been obtained with the MCI uncertainties. Moving the centre of mass forward helps reducing the longitudinal trim deflection need and is also favourable for lateral/directional flight qualities. The vertical position must be kept. In this case the deflection envelope is decreased. However, also in this case the maximum deflection constraint of δ=8° is not fulfilled. A possibility to reach lateral trim satisfying the maximum allowable elevon deflection, consists in using a movable mass along the y axis together with sideslip and a centre of mass at xcm=58%. But in this case three control means are used: elevons, RCS, movable mass.

Figure 20. Global deflection needs. 4

The LCDP is the vector product

G G G G u β × uδ A , where u β = [C nβ , Clβ ]T , uδ = [Cnδ , Clδ A

A

] . When the two vectors T

A

are collinear, the lateral/directional trim is impossible. The greater the Euclidean norm, the greater the trim capability is.

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The proposed solution for vehicle trim must be confirmed by further analysis, including transients, control logic, feasibility of RCS control, updated AEDB. The global deflection need for the two possible centre of mass positions is given in Figure 20.

Aerothermics The objective the Aero Thermo Dynamic data Base (ATDB) is to provide heat fluxes for a selected control points on the vehicle along the flight path to provide input data for TPS sizing (Figure 21). With this objective, investigations have been performed in phase A/B to characterise the Pre-X aero thermal environment during re-entry.

Figure 21. ATDB control points.

CFD Euler plus boundary layer, Navier-Stokes computations and wind tunnel test in ONERA R2Ch, DLR HEG and TSIIMASH PGU7 have been performed. These tests give a contribution to investigation of laminar, turbulent and natural transition flow to give a contribution to the ATDB. An ATD plasma activity has been carried out in order to assess the radio frequency attenuation and black-out duration. In Pre-X black-out occurs between 105 and 47 km in the worst case. The atmospheric density of the reference and sizing trajectories has been assumed together with an angle of attack of 35, 45, 55 degrees. Mach 7 and 10 computations were made with perfect gas assumption (γ=1.4), while Mach 17.75 and 25 were made with air at equilibrium. Other computations have been performed to consider the sideslip and laminar or turbulent regime. The wall was assumed to be in radiating equilibrium withsurface emission of ε=0.8. Figure 22 shows the temperature mapping from a Navier-Stokes computations in laminar conditions at Mach 25 and angle of attack 45 degrees. For turbulent computations the Wilcox k-ω method has been considered to better fit the R2Ch results than the Spalard Almaras and had been used as default.

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Fiigure 22. Lamin nar flow simulaation: Navier Stookes CFD tempperature for Macch 25, AoA=455°, de=10°.

R R2Ch Ch is 1/27.5 annd the main gooal of this cam mpaign was too determine The model scale of R2C laaminar to turb bulent transitioon and SWBL LI. The tests in i the ONERA A R2Ch and HEG wind tuunnels have prrovided imporrtant informatiion on vehiclee general heatting, laminar to t turbulent trransition, SWS SWI, SWBLI and real gas effects. Figure 23 (left) shows a comparisonn between CF FD computation and R2Chh results at M Mach 7 in term ms of heat flux. fl Figure 23 2 (right) shows the shockk visualisationn. R2Ch is reepresentative of o Pre-X flighht at Mach 7 and Reynoldds number 1.44÷14·106 (Figuure 23). In paarticular, R2C Ch runs have demonstratedd a transitionaal interaction at a Mach 7, AoA=35÷45 A deegrees for flaps deflectionns 15÷20 deegrees. Viscouus effects annd laminar too turbulent trransition havee been investigated for different d sidesslips, Reynollds number, AoA, flap deeflections. Thhe extension of o boundary laayer separatioon decreases for f increasingg Reynolds. Soome critical heating h may exist on the boody flap if a conservative c m margin policy is applied. The effect of thhe angle of atttack with resppect to shock waves interacction is shownn in Figure 244.

Fiigure 23. Lamin nar flow Navierr Stokes CFD veersus R2Ch (M M=7) heat flux.

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Figure 24. Effect of angle of attack at R2Ch (M=7).

HEG The HEG test conditions are given in Table 9. The model scale is 1/13.75 and the stagnation enthalpy between 15 and 22 MJ/kg. Figure 25 gives a comparison between computation and results from HEG at Mach 8 in laminar conditions at 45 degrees of angle of attack and flap deflection at 10 degrees. A comparison of the normalised pressure by means of CFD performed at DLR and HEG measurements shows a good agreement (Figure 26). The main objectives of the campaign were the effect of angle of attack variation, the ailerons and sideslip effects, the elevon deflection effect on SWBLI. Table 9. HEG test conditions h0 (MJ/kg) 22 23 12 15

Mach 8.2 7.8 8.1 7.9

Re (105/m) 2 4.2 3.9 6.7

ρ (10-3 kg/m3) 1.7 3.5 3.3 5.3

Figure 25. Heat flux: comparison CFD, HEG results at Mach 8, AoA 45° flap deflection 10°, laminar flow.

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Figure 26. Normalised pressure from DLR HEG – CFD.

PGU7 The main goal of the tests at PGU7 (TSNIIMASH) are to cross check the CFD and contribute to the final ATDB. The ranges of Table 10 have been investigated. Ten discrete heat flux measurements have been performed by using thermocouples in order to correlate the Infra-Red thermography on the windward and flaps. The use of a “medium” Reynolds number was supposed to reproduce a transitional SWBLI on the flaps (Re~3÷5 106). The test model at 1/15 scale is depicted in Figure 27. Table 10. PGU7 test conditions AoA (degrees) Sideslip (degrees) Flap deflection (degrees) Reynolds number Mach Effective test time (ms)

Figure 27. Model for PGU7 tests, scale 1/15.

40÷50 0÷5 0÷15 106÷6 106 ~10.5 130

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STEPS AND GAPS ASSESSMENT A classical Space shuttle Reynolds type correlation is used to forecast laminar to turbulent transition along the trajectory for given protuberances due to TPS steps and gaps. A deeper analysis is ongoing in order to state the requirement in terms of maximum step and gaps compatible with maximum allowable heat fluxes, turbulence transition and vehicle assembly.

CONCLUSIONS ON AEROTHERMICS The CFD and high enthalpy wind tunnel tests permitted to determine the heat flux and temperature evolution on the control points during re-entry, as well as the associated uncertainties. In particular, the core of the ATDB is constituted by the Euler plus boundary layer computations. Navier-Stokes and WTT are used for validation and uncertainty assessment. The heat flux history for the worst case is shown in Figure 28 for some control points referenced in Figure 21. N0 is the stagnation point and F1 is the central point in the elevon. These results apply for a maximum flap deflection of 8°, constrained by the control law in order not to exceed the maximum C/SiC allowable temperature. In some specific points the temperature can slightly exceed the material allowable maximum temperature, but the time for which this occurs is usually short. In addition, this happens only in the most conservative case with phase B margins, to be reduced and refined in the successive phases. Pre-X Phase B - HEAT FLUX 600

Control Point N0 Control Point S4-1

500

Control Point S9-1 Control Point F1

Heat Flux (kw/m2)

400

300

200

100

0 0

200

400

600

800

1000

1200

Time (s)

Figure 28. Heat flux versus time.

SUMMARY AND CONCLUSION Pre-X was the re-entry experimental hypersonic glider that CNES proposed as candidate for ESA re-entry programme. It completed the phase B in 2007 and then was stopped. This vehicle was considered as the necessary step for risk mitigation of future re-entry space

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planes or lifting bodies. The main goal of Pre-X was to demonstrate that Europe has the technology to master gliding re-entry of a reusable vehicle controlled by movable surfaces and jets. For aerodynamic and ATD data base, wind tunnels tests have been performed in France, Germany, Belgium, Russia. A first assessment of the AEDB is based on CFD and WTT. In particular, most of the data are coming from Euler – boundary layer computations. Navier Stokes and wind tunnel tests have been used for a finer assessment of specific flight points and uncertainty evaluation. The results of the ATDB have been used to size the TPS of the vehicle, on the base of the heat flux computed on specific control points. The flap heating is an important system constraint and the maximum flap deflection has been reduced in order to respect the maximum C/SiC allowable temperature. The flying qualities have been studied in detail and are satisfying at least in 2 to 25 Mach range, even if lateral control is sensible because of the Pre-X vehicle configuration. Below M= 2, preliminary flight qualities analysis demonstrated promising scenario enabling to fly properly in supersonic-transonic regime.

SYMBOLS α β ε μ μi ρ δA δE Θ c cm CL CD Cm Cnβ, Ik L M Re RN T V xg yg zg

: angle of attack : sideslip : thermal emissivity : bank angle : bank angle : gas density : (right flap deflection+left flap deflection)/2 : (right flap deflection-left flap deflection)/2 : flight path angle : constant : centre of mass : Lift coefficient : Drag coefficient : moment coefficient : yaw moment (n) due to sideslip (β), : inertia about k axis : vehicle reference length (4.4 m) : Mach number : Reynolds number : nose radius : gas temperature : vehicle velocity : x coordinate of vehicle centre of mass : y coordinate of vehicle centre of mass : z coordinate of vehicle centre of mass

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GLOSSARY AEDB ATD ATDB CFD C/SiC FLPP IXV SWBLI TPS WTT

AErodynamic Data Base Aero Termo Dynamics Aero Thermodynamic Data Base Computational Fluid Dynamics Carbon / Silicon Carbide Future Launchers Preparatory Program Intermediate eXperimental Vehicle Shock Wave Boundary Layer Interaction Thermal Protection System Wind Tunnel Tests

REFERENCES [1]

[2]

J.P. Tribot, O. Lambert, O. Cantinaud, Ph. Tran, M. Prampolini, J.C Paulat, S. Guédron, Pre-X Program : Aerothermodynamic objectives and aeroshape definition for in flight experiment, IAC-02- V.5.03- October 2002. E. Cosson, F. Thivet et Al., « Pre-X aerothermodynamics implications at system level », Atmospheric re-entry Symposium, March 21-23, 2005.

In: Wind Tunnels: Aerodynamics, Models and Experiments ISBN: 978-1-61209-204-1 Editors: Justin D. Pereira ©2011 Nova Science Publishers, inc.

Chapter 7

LOW-SPEED WIND TUNNEL: DESIGN AND BUILD S. Brusca, R. Lanzafame and M. Messina* Department of Industrial and Mechanical Engineering – Faculty of Engineering, University of Catania, Catania – Italy

ABSTRACT In this chapter the authors deal with a procedure for the design and build of a low speed wind tunnel for airfoil aerodynamic analyses and micro wind turbine studies. The designed closed-circuit wind tunnel has a test chamber with a square cross section (500 mm x 500 mm) with a design average flow velocity of about 30 m/s along its axis. The designed wind tunnel has a square test chamber, two diffusers (one adjacent to the test section and one adjacent to the fan to slow the flow), four corners (with turning vanes) to guide the flow around the 90° corners, an axial fan to guarantee the mass flow rate and balance any pressure loss throughout the circuit, a settling chamber with a honeycomb (to eliminate any transverse flow), a series of ever-finer mesh screens (to reduce turbulence) and a nozzle to accelerate flow and provide constant velocity over the whole test chamber. The pressure losses of single components were evaluated as well as the global pressure loss (the sum of pressure losses of all the single components). Once the pressure losses were evaluated, the axial fan was chosen to guarantee the design’s volumetric flow, balance pressure losses and above all maximise its performance. The definitive dimensions of the wind tunnel are 10.49 m x 3.65 m. Once the design targets were defined, the test chamber dimensions, maximum wind speed and Reynolds numbers were calculated. At the end of the design process, the wind tunnel energy consumption was estimated and on-design and off-design performance was evaluated to obtain the wind tunnel circuit characteristics for a defined velocity range (0 – 50 m/s). The best circuit and axial fan matches were performed in both the open and closed test section configurations. Using the matching procedure between the fan and wind tunnel’s mechanical characteristics (global pressure loss as a function of wind velocity), the fan operating parameters were set up for optimum energy conservation.

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1.0. INTRODUCTION This chapter deals with the fluid-dynamics design of a closed-loop wind tunnel for airfoil aerodynamic analyses and micro wind turbine studies. Wind tunnels are measurement tools to study gas flows around a body and the forces generated by the gas-body interaction. For the most part, air is used in wind tunnels. Using such tool it is possible to measure global and local flow velocities, as well as pressure and temperature around the body. Moreover, optical tests using special insemination substances or wool wires can be performed to visualize flow motion. The components of a wind tunnel are specifically designed and built to ensure the test chamber an as near as possible uniform in space and independent of time air flow. Wind tunnels’ global dimensions depend mainly on the type of testing, so knowing the shape and dimensions of the wind tunnel test chamber as well as the in-chamber flow velocity, the Reynolds numbers can be established. Knowing the test chamber dimensions and wind tunnel test type, all the wind tunnel components can be designed. Wind tunnels can be classified into two main types: open and closed circuit. Wind tunnels can also have two basic test section configurations: open and closed. The air flowing through an open wind tunnel circuit follows essentially a straight path from the nozzle inlet to the test section outlet, prosecuting in the diffuser. The air flowing in a closed-return wind tunnel, recirculates continuously with no air leakage. There are advantages with both the open and closed circuit tunnels and with both open and closed jets. For an open-return wind tunnel the advantages are related to lower construction costs and being able to visualize the flow using smoke without needing to purge the tunnel. The disadvantages are needing to mount extensive screens to obtain high quality flow, greater energy to run the wind tunnel and high noise levels which may cause environmental problems. The closed-circuit wind tunnel has high quality flow, independent of weather conditions and other activities in the building. It requires less energy compared to the open-circuit wind tunnel and produces less noise. The disadvantages of closed-circuit wind tunnels are high construction costs, purging after flow visualization using smoke and needing to mount a heat exchanger. In conjunction with an open-circuit tunnel, the open test section will require an enclosure to prevent air leaking to the diffuser while for closed-circuit wind tunnels, the flow in the open test section tends to have a solid boundary. Hence, the open test sections is best suited to operating with closed-circuit wind tunnel. This chapter presents the criteria for wind tunnel design applying them to a specific case study.

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2.0. WIND TUNNEL DESIGN The first step in wind tunnel design is related to the shape and main dimensions of the test chamber [1] which depends on the type of intended tests. Generally, wind tunnel dimensions are directly related to the test chamber cross-section. The bigger the test chamber cross-section, the greater the overall wind tunnel dimensions. Test chamber main dimensions and air velocity, as well as wind tunnel type bring to the necessary fan power. These and the wind tunnel’s overall dimensions are key factors in its structure and running costs so the best trade-off between costs and tests is necessary. The main goal of wind tunnel design is to have uniform flow within the test chamber. It is best to have a big testing chamber with very high air velocity. The design starts by defining the test chamber dimensions and proceeds counter-stream wise to the design of other wind tunnel components. The principal components of a closed-loop wind tunnel are reported in Figure 1. Larger Corner

Second Diffuser Adapter

Smaller Corner

Fan

Contraction or nozzle First Diffuser Settling chamber

Larger Corner

Honeycomb & Screens

Test section

Smaller Corner

Figure 1. Closed circuit wind tunnel.

2.1. Test Chamber The first step in wind tunnel design is defining a priori the test chamber criteria which are dimensions, shape and desired air velocity. In this test case, a square testing chamber with a 0.5 m side was used with an air velocity of 30 m/s. From the testing section dimensions the hydraulic diameter can be calculated as in Eq. (1).

Dh = 2 A / π where A is the test chamber cross sectional area.

(1)

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The test chamber length has to be in the range of 0.5 - 3 times its hydraulic diameter [1]. This choice takes into account that the air flow exiting the nozzle needs 0.5 times the hydraulic diameter to become almost uniform. Moreover, a long test chamber (more than 3 times the equivalent hydraulic diameter) could increase boundary layer thickness causing the boundary layer to detach at the test chamber exit. So, in this case study the length of the testing chamber was set to twice the hydraulic diameter of the testing section. Moreover, to avoid air velocity reduction and an increase in boundary layer thickness at the sharp edges of the test chamber, the sharp edges should be rounded off. 45° chamfers are best. The test chamber also has flanges and windows to allow sample observations and introduce measuring tools. Figure 2 shows a test chamber coupled to a nozzle.

Figure 2. Test chamber (above) coupled to the nozzle (below).

2.2. Nozzle The contraction or "nozzle" accelerates the flow from the settling chamber to the test section, further reducing any variations in velocity. In a wind tunnel, the nozzle is the most difficult component to design. Flow velocity and its uniformity within the test chamber cross-section depend on the nozzle’s design. The nozzle exit cross-section dimensions and shape are identical to the test chamber ones since they are joined together. Consequently, the nozzle also has 45° chamfers.

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Knowing the nozzle exit cross-section dimensions and shape, those of its inlet crosssection must be determined. The nozzle area ratio should be ‘as large as possible’, to reduce the total-pressure loss through the screens mounted between the settling chamber and the nozzle (see Fig. 1). Normally, the nozzle inlet/outlet cross-section area ratio should be in the range 6 - 10 [4]. Area ratios greater than 10 lead to excessive inlet dimensions while area ratios less than 6 lead to high pressure loss through the screens. In the test case, an area ratio of 7 was chosen. With the inlet and outlet nozzle crosssections, the nozzle’s silhouette is defined by fifth order Bell-Metha polynomials [4] represented mathematically by Eq. (2).

y = a ξ 5 + b ξ 4 + cξ 3 + d ξ 2 + eξ + f

(2)

where

ξ=

X L

(3)

and (4)

y=h L is the total axial nozzle length and h is half the cross-section side-length.

0≤ X ≤L

(5)

In order to determine the Bell-Metha polynomial coefficients, the boundary conditions are imposed. Equations. (6) – (11) report boundary conditions.

ξ = 0 → y = y0

(6)

ξ = 1 → y = y1

(7)

ξ = 0→

dy =0 dξ

(8)

ξ = 1→

dy =0 dξ

(9)

ξ = 0→

d2y =0 dξ 2

(10)

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ξ = 1→

d2y =0 dξ 2

(11)

Figure 3 shows the nozzle shape.

y1 y0

Figure 3. Nozzle shape.

A nozzle should have a total length and double semi side-length of inlet cross-section about equal to 1 (see Eq. (12) and Fig. 3) [4].

L ≅1 2 y0

(12)

In fact, it was experimentally evident that a L/(2y0) ratio less than 0.667 causes the air flow to detach close to the nozzle exit, whilst a value greater than 1.79 increases boundary layer thickness. In this case study, the value of L/(2y0) was set to 0.91 obtaining a nozzle length of 1.3 m. Connecting the nozzle to the testing section requires the sharp edges of the nozzle’s outlet to be rounded off with 45° chamfers. Figure 4 shows the nozzle under construction.

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Figure 4. Nozzle under construction.

2.3. Second Diffuser In order to design the second diffuser, the inlet cross-section area must first be calculated while the exit is equal to the nozzle inlet cross-section area. The second diffuser inlet crosssection area is governed by the fan dimensions (see Figure 1). Therefore, it is essential to first design the fan. From specialist literature [4], it is known that the ratio between the fan cross-section area Af and the test chamber cross-section area Ats has to be in the range 2 - 3 (see Eq. (13)).

2≤

Af Ats

≤3

(13)

To use an Af /Ats ratio value greater than 3 is not recommended because irregular flow velocities at the fan entrance may be generated. To use a Af /Ats ratio value less than 2 is also not recommended because it may increase the overall wind tunnel dimensions (higher wind tunnel construction costs). A Af /Ats ratio equal to 2 is a good choice for maintaining low wind tunnel dimensions and costs. In the present case study an Af /Ats ratio equal to 2 was used. Taking into account the area ratios and using the mass conservation law, the air velocity at the fan exit can be calculated using Eq. (14).

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1 c f = cts 2

(14)

Eq. (20) yields 15 m/s for the case study (cf - air flow velocity at fan outlet; cts - air flow velocity in test section). Also, from the area ratios, the diameter of the fan cross-section (circular) can be calculated. In this test case it equals to 0.800 m. The usual design rule for subsonic diffusers is that the total ( 2ϑe ) included angle of a portion of a circular cone with the same length (L) and area ratio (AR) as the diffuser should not exceed a maximum value (6 ° [1]). The second diffuser inlet cross-section area is equal to the fan’s, while the second diffuser outlet cross-section area is equal to the nozzle’s inlet. So, they are known values at this stage of the design process. With the hydraulic diameters of the inlet and outlet diffuser cross-sections, the equivalent cone expansion angle can be calculated given by Eq. (15).

⎛ 1 AR − 1 ⎞ ⎟ ⎜ 2 L / Dh1 ⎟ ⎝ ⎠

ϑe = arctan ⎜

(15)

Dh1 is the inlet section’s hydraulic diameter. To avoid having a very long diffuser, 3 ° was chosen (used at the National Full-Scale Aerodynamics Complex at NASA Ames Research Center [9]). Solving Eq. (15) for L, the minimum diffuser length can be determined (6.58 m for this test case). Figure 5 shows the diffuser in 3D.

Figure 5. Second diffuser.

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In Figure 5, it is evident that the second diffuser inlet cross-section is circular like the fan’s, while the second diffuser outlet cross-section is square. Consequently, the second diffuser also acts as a shape adapter. The second diffuser also has flanges which connect with other wind tunnel parts. Another shape adapter is connected to the fan inlet section so the fan and other wind tunnel components (smaller corner) match. The shape adapter also has flanges. In this case study, the shape adapter between the fan and smaller corner has been designed. Its total length equals 0.3 m. Figure 6 shows shape adapter in 3D.

Figure 6. Shape adapter.

2.4. First Diffuser The inlet cross-section area and shape of the first diffuser are known because they equal the cross-section area and shape of the test chamber. The outlet cross-section area is also known because it equals the inlet fan cross-section area. Since the fan inlet cross-section is round and the first diffuser’s is square, the side l of the outlet cross-section can be calculated equaling the areas as in Eq. (16).

l=

φf 2

π

(16)

It equals 0.710 m for this case study. As in the case of the second diffuser, the minimum diffuser length can be calculated using Eq. (15). With a maximum total cone angle of 4 °, the first diffuser length equals 3.32 m. Figure 7 shows the first diffuser in 3D.

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Figure 7. First diffuser in 3D.

Figure 8. Turning vanes inside a corner.

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2.5. Corners This wind tunnel is a closed-loop type so flow must be deflected by 90° four times with minimum turbulence at the four corners. For this reason the corners are equipped with blades (more efficient but more costly) or bent flat plates (more economical - our case study). The corners’ dimensions match their related wind tunnel components. Thus, corners are equal in pair and than they will design in couple.

2.5.1. Smaller Corners (1 and 2) Corners 1 and 2 have a square cross-section equal to the first diffuser outlet’s. The bent flat plates’ leading edges are set to 5°, while the trailing edges are 0°. Thus, the bent flat plates’ chord is calculated for 85 ° (see Fig. 8). To determine the minimum number of bent flat plates, the chord value must first be calculated and is given by the ratio between the corner section width and the corner divisions chosen. A vane number of 25 is a good choice [3].

h1− 2 =

l 25

(17)

Using the first diffuser outlet cross-section (l=0.710 m in the case study), a vane gap (h1-2) of 2.84 10-2 m is obtained. The vane gap-chord ratio has must be less than 0.25, the minimum chord value being calculated by Eq. (18).

c1− 2 min =

h1− 2 0.25

(18)

A value of 0.1136 m was obtained. From chord value, the minimum bent flat plate radius (see Eq. (19)) is calculated.

r1− 2 min =

c1− 2 min 2

1

sin (γ / 2)

(19)

where c1-2 is the chord, r1-2 is the bent flat plate curvature radius, γ being the central angle subtended by the chord. A minimum radius of 8.4*10-2 m was obtained and 24 blades were needed. The blades could be installed on a removable frame for cleaning and maintenance. Figure 9 shows the corner in 3D, Figure 10 showing the blades.

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S. Brusca, R. Lanzafame and M. Messina

Figure 9. The corner in 3D.

Figure 10. The turning vanes in 3D.

2.5.2. Larger Corners (3 and 4) Using corners 1 and 2 design criteria, corners 3 and 4 can be designed. They have a square cross-section equal to the second diffuser outlet’s (inlet nozzle cross-section). The vane gap can be calculated using Eq. (20) with corners 3/4 side length (1.320 m in the case study). In the 3/4 corner design, a vane number of 25 is also a good choice [3].

Low-Speed Wind Tunnel: Design and Build

h3− 4 =

l 25

201

(20)

Using corners 3/4 data, a vane gap of 5.28 10-2 m is obtained for the case study. The minimum chord value and minimum blade curvature radius are obtained using Eq. (21) and Eq. (22) as per corners 1 and 2.

c3− 4 min =

h3− 4 0.25

r3− 4 min =

c3− 4 min 2

(21)

1

sin (γ / 2)

(22)

Considering the overall dimensions of corners 3 and 4 a blade curvature radius greater than the minimum was used: c3-4 = 0.211 m and r3-4 = 0.156 m.

2.6. Settling Chamber Joined to the 4th corner there is a settling chamber with a constant cross-sectional area. The aim of a settling chamber which contains honeycombs and screens is to reduce the flow turbulence before it enters the nozzle.

Figure 11. The settling chamber in 3D.

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The settling chamber cross-sectional area matches the dimensions of the other components it is joined to, while the settling chamber length is designed to fit the gap between the components close to the wind tunnel loop. In this study the total settling chamber length is 2.070 m and is able to contain one honeycomb and three screens. Figure 11 shows the settling chamber in 3D.

2.7. Honeycomb A honeycomb with its cells aligned in the flow direction is able to reduce fluctuating variations in transverse velocity [8]. The honeycomb has little effect on stream-wise velocity due to the fact that the pressure drop through a honeycomb is small [8]. In the honeycomb design procedure, its length (Lh), cell hydraulic diameter (Dh), and the porosity (βh) are key factors [2]. Honeycomb porosity is defined as the ratio of actual flow cross-section area over the total cross-section area (see Eq. (23)).

βh =

Aflow Atot

(23)

Two main criteria have to be verified in wind tunnel honeycomb design. These criteria are expressed by Eq. (24) and Eq. (25) [2].

6≤

Lh ≤8 Dh

(24)

β h ≥ 0.8

(25)

The test case main honeycomb characteristics are reported in Tab. I (see Fig. 12 and Fig. 13 for symbol notation). Table I. main honeycomb characteristics DESCRIPTION Cell diameter Sheet metal thickness Roughness Length

SYMB dhoney shoney

Δ

Lh

VAL 9 0.06 15 62

UOM mm mm μm mm

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203

Figure 12. Honeycomb structure and symbols.

In Figure 12, the honeycomb cell side (lhoney) can be evaluated with Eq. (26).

lhoney =

d honey

(26)

2 sin 60°

while the external cell side (lg honey) can be calculated with Eq. (27).

lg honey = lhoney + 2

shoney tan 60°

(27)

The metal sheet divisions (z) can be evaluated with Eq. (28).

z = 2lhoney + l g honey

(28)

To calculate the metal honeycomb’s area, a single division could be considered. The latter is composed by two twin area parallelograms and two twin area trapezes (see Fig. 12). These areas can be easily calculated with Eqs. (29) and (30).

Aparalle log ram = lhoney shoney

Atrapeze =

(l

honey

+ lg honey )shoney 2

(29)

(30)

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For honeycomb porosity, the number of divisions height-wise and width-wise must first be calculated. The former is given by the ratio of settling chamber cross-section height (L1) over honeycomb divisions (z) (see Eq. (31)).

nz =

L1 z

(31)

The latter is given by the ratio between settling chamber cross-section width (L2) and the sum of half dhoney and shoney (see Fig. 12) as in Eq. (32).

nsheet =

L2 d honey / 2 + shoney

(32)

For a square cross section L1 = L2 = L . The cross-section area of the honeycomb metal sheet can be determined with Eq. (33).

Asheet = 2 (Aparalle log ram + Atrapeze )nz nsheet

(33)

The honeycomb solidity σh is defined as the ratio between the cross-section area occupied by the metal sheet and the settling chamber cross-section area (see Eq. (34)).

σh =

Asheet Atotal

(34)

It is evident from Eqs. (23) and (34) that honeycomb solidity and porosity are complementary factors. Thus, their sum is an identity.

βh + σ h = 1

(35)

Now, honeycomb porosity can be calculated with Eq. (35). To verify the Eq. (24) criterion, the honeycomb cell hydraulic diameter must first be calculated by starting with the honeycomb cell area.

d d ⎛d 1⎞ 1 3 d 2 honey Acell = 6⎜⎜ honey lhoney ⎟⎟ = 6 honey honey = 2⎠ 2 3 2 2 3 ⎝ 2

(36)

The honeycomb cell hydraulic diameter can be evaluated by imposing the same area of the equivalent circle (see Eq. (37) and Eq. (38)). 2

D 3 d 2 honey π h = 4 2 3

(37)

Low-Speed Wind Tunnel: Design and Build

Dh = d honey

205

6

(38)

π 3 Table II. Test case honeycomb main parameters

DESCRIPTION Honeycomb cell side External cell side Divisions Divisions height-wise Divisions width-wise Honeycomb solidity Honeycomb porosity Cell hydraulic diameter Length-hydraulic diameter ratio

SYMB lhoney lg honey z nz nsheet

σh βh

Dh Lh/Dh

VAL 5.20 5.26 15.66 84.3 289.47 1.75 10-2 0.9825 9.45 6.56

UOM mm mm mm mm -

To establish if the chosen honeycomb meets the test case wind tunnel design, the two criteria expressed by Eqs. (24) and (25) have to be verified. The length/hydraulic diameter ratio is greater than 6 and less than 8. So, the Eq. (24) criterion is verified. The honeycomb porosity is greater than 0.8 so the Eq. (25) criterion is also verified. With both criteria verified, the chosen honeycomb is suitable for the designed wind tunnel.

2.8. Screens It is well known that screens mainly reduce stream-wise velocity fluctuations, with little effect on flow direction [8]. Moreover, it has been demonstrated [8] that a series of screens with different mesh qualities (coarse, medium and fine) is more efficient than only one fine mesh screen. To be effective in reducing turbulence a screen must have a porosity in the range 0.58 – 0.8 [2].

0.58 ≤ β s ≤ 0.8

(39)

Screen porosity values over 0.8 are not suitable for good turbulence control, while values below 0.58 lead to flow instability. Screens could also be installed on a removable frame for cleaning and maintenance. Since the screens are inside the settling chamber (square cross-section side l = 1320 mm in case study) and have a square mesh (commonest), the area occupied by the screen wire can be calculated with Eq. (40).

(

nwldw + nwldw − nw nwd 2 w

)

(40)

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where dw is the wire diameter, nw is the generic wire number in the mesh and l is the settling chamber cross-section side. The last term in Eq. (40) takes into account the areas where the wires cross (black areas in Fig. 13).

Figure 13. Screen sample.

As in the honeycomb case, it is possible to calculate screen porosity (see Eq. (42)).

A flow

βs =

Atotal

2 2 l 2 −2nw l d w + nw2 d w2 dw nw dw = = 1−2nw + 2 l2 l l

(41)

Simplifying Eq. (41) produces Eq. (42).

⎛ ⎝

β s = ⎜1 −

nw d w ⎞ ⎟ l ⎠

2

(42)

Screen mesh density is defined as the ratio between the mesh wire number and the crosssection side of the chamber into which the screens are inserted [1]. Eq. (43) defines mesh density .

ρm =

nw l

(43)

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The mesh density inverse represents the screen mesh divisions (wm) as shown in Figure 13 and Eq. (44).

wm =

1

(44)

ρm

Taking screen mesh density into account, porosity can be written as in Eq. (45).

β s = (1−d w ρ m )2

(45)

Tab. III shows the main screen characteristics for the case study. It also shows that the screen porosities for the three screens (M1, M2 and M3) verify the Eq. (39) criterion. Table III. main screen characteristics Description Mesh wire diameter Mesh divisions Screen porosity

SYMB dw wm

βs

UOM mm mm -

M1 0.7 3.2 0.61

M2 0.56 2.5 0.60

M3 0.15 0.7 0.61

3.0. PRESSURE LOSSES Closed-loop wind tunnel pressure is studied by considering wind tunnel sections separately. Each section is functional as described by F. L. Wattendorf in [5]. In a wind tunnel, pressure losses occur as consecutive pressure losses in the different sections. Overall pressure loss (Δpglobal) equals the pressure gain due to the fan. In a wind tunnel component, i, pressure loss (Δpi) can be written as the product of constant Ki and the dynamic pressure at the entrance of the component (see Eq. 46).

Ki =

Δpi 1 ρi c 2i 2

(46)

where ci is the mean flow velocity (in the section) at the entrance of component i.

3.1. Pressure Losses in Constant Cross-Section Area Sections Considering a constant-area section, the pressure loss (Δp) along the duct is proportional to its length (L), hydraulic diameter (Dh), fluid density (ρ), and the square of mean flow velocity (c) (see Eq. (47)). The constant of proportionality is the friction factor ( f ).

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208

Δp

ρ

=f

L c2 Dh 2

(47)

The hydraulic diameter of the duct can be calculated as in Eq. (1). Combining Eqs. (46) and (47), the loss coefficient can be related to duct geometry producing Eq. (48).

Kl = f

L Dh

(48)

For smooth pipes at high Reynolds numbers, Shames [7] uses the Prandtl universal law of friction to determine the friction factor:

[

(

)

]

f i +1 = 2 log10 Re f i − 0.8

2

(49)

where

Re =

ρ c Dh μ

(50)

Eq. (54) can easily be solved iteratively starting from a tentatively chosen friction factor value. A starting value as distant as f = 1 will lead to convergence within four to six iterations.

3.2. Pressure Losses in Diffusers To calculate pressure loss in a diffuser, the energy loss due to friction must be considered. The main parameters are the equivalent conical expansion angle (Eq. 15) and the ratio between inlet and outlet cross-section areas (AR=A2/A1). The loss coefficient is the sum of the two. The first relates to friction and the second to expansion (see Eq. (51)).

K d = K f + K exp

(51)

For one-dimensional flow, constant friction factor and constant density with the stream, Eq. (52) is produced.

⎛ 1 ⎞ f K f = ⎜⎜1 − 2 ⎟⎟ ⎝ AR ⎠ 8 sinϑe

(52)

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209

The expansion loss coefficient can be calculated with the empirical expression in Eq. (53).

⎛ A −1⎞ K exp =K e (ϑe ) ⎜⎜ R ⎟⎟ ⎝ AR ⎠

2

(53)

The term Ke( ϑe ) can be expressed as a geometrical function. W.T. Eckert [3] proposed the expressions in Eqs. (54) and (55) for circular and square cross-sections (Tab. IV). The lower the equivalent conical expansion angle, the lower the loss.

⎧ A1 + B1ϑe if 0 <ϑe < 1.5° ⎪ 2 3 4 5 6 K e(circular ) =⎨ A2 + B2ϑe +C 2ϑe + D2ϑe + E2ϑe + F2ϑe +G2ϑe ⎪ A + B ϑ if ϑ > 5° e ⎩ 3 3 e

if 1.5° ≤ ϑe ≤ 5° (54)

⎧ A1 + B1ϑe if 0 < ϑe < 1.5° ⎪ 2 3 4 5 6 K e( square ) =⎨ A2 + B2ϑe +C2ϑe + D2ϑe + E2ϑe + F2ϑe +G2ϑe if 1.5° ≤ ϑe ≤ 5° ⎪ A + B ϑ if ϑ > 5° e ⎩ 3 3 e

(55)

Table IV. Eckert’s Ke parameters for circular and square cross-sections Parameter A1 B1 A2 B2 C2 D2 E2 F2 G2 A3 B3

Circular 0.1033 -0.02389 0.1709 -0.1170 0.03260 0.001078 -0.0009076 -0.00001331 0.0001345 -0.09661 0.04672

Square 0.09623 -0.004152 0.1222 0.04590 0.02203 0.003269 -0.0006145 -0.0000280 0.00002337 -0.01322 0.05866

3.3. Pressure Losses In Corners As far as energy loss in corners is concerned, the critical corner sections are the two after the test chamber because of greater dynamic pressure and the need for uniform flow at the fan inlet section [1].

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The losses in the corner vanes can be minimised with an efficient blade cross-section, as well as an appropriate chord-to-gap ratio. Vanes with cambered airfoils and straight leading edges are less sensitive to approaching flow angularities than sharp leading edge vanes. To estimate the corner loss coefficient, Eq. (56) can be used [1], assuming that skin friction as a function of the Reynolds number is similar to that on a flat plate.

K c = 0.10 +

4.55 (log10 Re c ) 2.58

(56)

where Rec is the local Reynolds number based on the vane chord.

3.4. Pressure Losses in Screens In wind tunnels, screen is installed just before the fan section for security reasons. This kind of screen has a significant impact on pressure loss since this is a relatively high velocity section. Other screens control turbulence just before the nozzle inlet. In terms of energy loss, all screens are treated in the same manner. W. T. Eckert [3] proposes an empirical relation for the screen loss coefficient based on three main parameters: porosity or its complement solidity, the Reynolds number calculated with wire diameter Rew, and mesh factor Kmesh. The latter was studied by I. E. Idel’chik [6] who assigned it a value of 1.0 for new metallic wires, 1.3 for circular metallic wires, and 2.1 for silk fibres. An average value of 1.3 for Kmesh is a good choice in most of cases. Eckert’s empirical equation for calculating the screen loss coefficient is reported in Eq. (57).

K m =K mesh K Rn σ s +

σ s2 β s2

(57)

where:

⎧ ⎛ Re w ⎞ ⎟ 0 ≤ Re w < 400 ⎪0.785 ⎜1 − K Rn =⎨ ⎝ 354 ⎠ ⎪1.0 Re ≥ 400 w ⎩

(58)

3.5. Pressure Losses in Honeycombs To determine the pressure loss in honeycombs, the three main parameters of stream-wise length to cell hydraulic diameter ratio, porosity and Reynolds number based on cell hydraulic diameter must be accounted for. W. T. Eckert, K. W. Mort, and J. Jope [3] proposed the relation reported in Eq. (59).

Low-Speed Wind Tunnel: Design and Build 2

⎛L ⎞⎛ 1 ⎞ ⎛ 1 ⎞ K h = λh ⎜⎜ h + 3 ⎟⎟ ⎜⎜ ⎟⎟ + ⎜⎜ − 1⎟⎟ ⎝ Dh ⎠ ⎝ βh ⎠ ⎝ βh ⎠

211

2

(59)

where: 0 .4 ⎧ ⎛ Δ ⎞ ⎟⎟ Re −Δ0.1 ⎪0.375 ⎜⎜ ⎪ ⎝ Dh ⎠ λh =⎨ 0. 4 ⎛ Δ ⎞ ⎪ ⎟⎟ ⎪0.214 ⎜⎜ D ⎝ h⎠ ⎩

Re Δ ≤ 275 (60)

Re Δ > 275

In Eq. (60) ReΔ is the Reynolds number based on material roughness Δ and Dh is the cell hydraulic diameter.

3.6. Pressure Losses in Nozzle The pressure loss in a nozzle is considered only due to skin friction. Since pressure loss in the nozzle is about 3% of total loss, errors evaluating Knt are less significant than those made in the high velocity wind tunnel sections so the approximated expression proposed by F. L. Wattendorf [5] (Eq. 61) can be used.

⎛ L ⎞ K n = 0.32 f av ⎜⎜ n ⎟⎟ ⎝ Dsc ⎠

(61)

where Ln is the nozzle length, Dsc is the settling chamber hydraulic diameter, and fav is the average friction factor between nozzle inlet and outlet sections. The average friction factor fav can be evaluated by Eq. (49), with Re equal to the mean value between Re evaluated at the inlet and outlet of the nozzle.

4.0. CASE STUDY LOSSES With the above criteria, the loss coefficients for each wind tunnel component can be calculated. Tab. V shows pressure drops for each wind tunnel component. Summing all the wind tunnel section pressure drop values produces the total pressure drop (in this case total pressure drop equalled 141.50 Pa). This pressure drop has to be compensated by the wind tunnel fan.

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Table V. Component Pressure loss at cts=30 m/s (cts = test section air speed) Δp [Pa] 12.531 33.429 22.33 2.064 22.33 0.616 1 1.808 4.6 1.965 0.0215 1.965 0.2134 2.76 10.25 10.86 11.31 1.47 141.5

Components Closed Test Section First Diffuser Smaller Corner Constant-Area Section Smaller Corner Adapter Fan Screen Fan Constant-Area Section Second Diffuser Larger Corner Constant-Area Section Larger Corner Settling Chamber Honeycomb First Screen Second Screen Third Screen Nozzle Total pressure loss

Based on the loss coefficients and wind tunnel section pressure drops, and assuming a null relative pressure value in the testing section, the relative pressure values in the wind tunnel sections can be calculated (ideal, without energy loss see Eq. (62);) real, with energy loss see Eq. (63)).

(

)

(62)

(

)

(63)

pout − pin =

1 2 ρ uin2 −uout 2

pout − pin =

1 2 ρ uin2 −uout − Δploss − in − out 2

where Δploss-in– out is the pressure loss between inlet and outlet cross-sections of the component correlated to the Ki factors. Static pressure variation within the wind tunnel in ideal and real cases is reported in Figure 14, while Figure 15 shows incremental pressure loss. Figure 14 clearly shows lower pressure values in the real case compared to the ideal case up to the fan section. From the fan on, the real pressure curve is always greater than the ideal one which is due to an energy gap in the fan section which balances out the pressure losses throughout the wind tunnel. The wind tunnel sections’ contribution to pressure loss is shown in Figure 16. Clearly most occurs in the first diffuser section.

Low-Speed Wind Tunnel: Design and Build

Test Section air speed = 30 m/s

Relative Static Pressure [Pa]

600

500

400

300 Ideal Case Real Case

200

100

0

Figure 14. Relative static pressure inside the Wind Tunnel.

Test Section air speed = 30 m/s

Cumulative Pressure loss [Pa]

160 140 120 100 80 60 40 20 0

Figure 15. Cumulative static pressure inside the Wind Tunnel.

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S. Brusca, R. Lanzafame and M. Messina

214 40

Test Section air speed = 30 m/s

35

Pressure loss [Pa]

30 25 20 15 10 5 0

Figure 16. Wind Tunnel component pressure losses.

5.0. ENERGY RATIO OF THE WIND TUNNEL The wind tunnel energy ratio was calculated as the ratio between flow power in the testing section and the power lost along the circuit due to pressure losses in all the wind tunnel components (Eq. (64))

1

ER =

∑

i

⎡ ⎛ c ⎞2 ⎤ ⎢ K i ⎜⎜ i ⎟⎟ ⎥ ⎢⎣ ⎝ cts ⎠ ⎥⎦

(64)

where i is the i-th component of the wind tunnel. Figure (17) shows energy ratio against testing section air speed. Energy ratio measures the energy efficiency of a wind tunnel [1] and is typically in the range 3-7 for closed circuit wind tunnels. The greater the Energy Ratio the better the wind tunnel energy efficiency.

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215

5 4.5

Energy Ratio

4 3.5 3 2.5 2 1.5 1 0.5 0 0

10

20

30

40

50

60

Test section air speed [m/s] Figure 17. Wind Tunnel Energy Ratio.

6.0. AXIAL FAN CHOICE Fans generate air motion within wind tunnel circuits and generally these axial fans are installed at the exit of the second corner (see Fig. 1). 800

Closed Test Section 700

Open Test Section

Static Pressure loss [Pa]

600

500

400

300

200

100

Test Section air speed [m/s]  16.2

0 0

2

4

24.4

32.5

40.7

48.8

6

8

10

12

Fan air flow rate [m3/s]

Figure 18. Wind Tunnel mechanical characteristics.

14

S. Brusca, R. Lanzafame and M. Messina

216

The design process consists essentially of matching fan choice from the manufacturer’s catalogue to the wind tunnel circuit. The first step is determining the wind tunnel’s mechanical characteristics (overall pressure drop as a function of air velocity in the test section). The air velocity in the test section can also be expressed as a function of the fan’s air-flow rate using the Mass Conservation Equation. Two mechanical characteristics can be calculated: the cases of closed and open test sections. These curves are shown in Figure 18. Firstly, for an open testing section, a reasonable friction factor is f = 0.08 [1]. Secondly, the two curves above can be superimposed onto the mechanical characteristics (supplied by the fan manufacturer) of possible fans with matching points graphically determined. Thirdly, the best match indicates the most suitable fan. Figure 19 shows a typical axial fan’s mechanical characteristic. 600

Fan at n=1430 rpm

Static Pressure loss [Pa]

500

Fan at n=1200 rpm Fan at n=1000 rpm

400

300

200

100

0 0

2

4

6

8

10

12

14

Fan Flow Rate [m3/s]

Figure 19. Axial fan mechanical characteristic.

In that figure pressure gain as function of flow rate is reported. Moreover, different curves, each for a specific fan rotational speed, are shown in Figure 19. By combining the two mechanical characteristics on the same graph (see Fig. 20), the right fan will match the wind tunnel circuit by intersecting the curve. Choosing the most suitable fan takes into account fan efficiency and design requirements like flow rate and air velocity in the testing section and cost. Different graph intersects for different fan rotational speeds provide fan pressure gain and volumetric flow rate. The Mass Conservation Equation can help determine air velocity in the testing section for each rotational speed. Using an inverter to control the electric current frequency and thus the fan motor’s rotational speed, the desiderated air velocity in the testing section is obtained.

Low w-Speed Windd Tunnel: Desiign and Build

217

600

Closed Test Section Open Test Section Fan aat n=1430 rpm Fan aat n=1200 rpm Fan aat n=1000 rpm

Static Pressure loss [Pa]

500

400

300

D open D

200

100

0 0

2

4

6

8

10

12

14

Faan Flow Rate [m3/ss]

Fiigure 20. Wind Tunnel – Fan matching. m

By applyinng this matchinng procedure, a 5.5 kW axial fan at 14300 rpm was choosen for the caase study (see Fig. 21).

Fiigure 21. Wind Tunnel Axial Fan. F

Fig. 20 shoows the interseection points at a maximum fan f rotational speeds s (D), wiith air flow 3 raates greater th han the desiggned ones (7.5 m /s and 35 3 m/s at thee testing sectiion) which haappens in the closed testingg section and the open onee (Dopen, Fig. 20). 2 Thus, thiis axial fan m meets all the wind tunnel reqquirements witth an efficienccy greater thann 70%.

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S. Brusca, R. Lanzafame and M. Messina

From 0 - 1430 rpm, testing section air velocities from 0 – 37 m/s are achievable in the closed configuration and from 0–32 m/s in the open.

7.0. WIND TUNNEL CONSTRUCTION The present test case has been built from a mechanical construction company (SET Impianti S.r.l) in the industrial area of Augusta (Syracuse – Italy). All the designed wind tunnel components have been built and joined to obtain the closed-loop wind tunnel in the sequence shown in Figure 1. Figure 22 shows the wind tunnel under construction.

Figure 22. Wind Tunnel under construction.

CONCLUSION This chapter deals with the design procedure of a low-velocity wind tunnel for airfoil aerodynamics analyses and micro wind turbine studies. In particular, it focuses on a closedloop system with a square test section. A test-case design of a wind tunnel with a 500 x 500 mm test section of 30 m/s along the axis was used as an aid to the design procedure description. The procedure described relates to the design/choice of square testing chambers, diffusers (generally two: one adjacent to the testing section and one adjacent to the fan to slow the flow), corners (with turning vanes) to guide the flow around 90°, axial fans, a settling

Low-Speed Wind Tunnel: Design and Build

219

chamber with a honeycomb, a series of ever-finer mesh screens, and nozzles to accelerate flow and provide constant velocity throughout the testing chamber. The design procedure consists of the following main steps: 1. 2. 3. 4.

Defining the test section dimensions and desired flow velocity by test type; Wind tunnel component design by test section criteria; Wind tunnel component pressure loss calculation; Determining pressure loss throughout the wind tunnel circuit as a function of the possible flow velocity in the testing section in both open and closed configurations; 5. Matching wind tunnel components to commercial fans, and energy considerations.

From fundamental choices about wind tunnel design (defining the testing section dimensions and desired flow velocity), the design of all the wind tunnel components is described on the basis of a case study. Particular attention was paid to the nozzle design. This wind tunnel component is the most critical since it strongly affects the quality of the flow (velocity, turbulence level, velocity uniformity) in the test section. Thus, detailed design criteria using Bell-Metha polynomials are shown and specific data for the test case are provided. Following the components design, determining pressure losses in the wind tunnel circuit is described and energy considerations lead to a proper fan choice by means of a matching procedure. The matching procedure helps study wind tunnel behaviour at different flow velocities in the testing section. In this test case, a testing section flow velocity in the range from 0 m/s to 50 m/s was used to determine the wind tunnel’s internal characteristics (pressure loss as a function of testing section flow velocity or fan flow rate). The matching procedure was used to determine the possible wind tunnel running condition. The matching procedure is also useful for establishing the fan speed controller (inverter) positions for the desired flow velocity. In conclusion, the wind tunnel build data confirm the efficacy and usefulness of the design procedure.

REFERENCES [1] [2] [3]

[4]

Barlow J. B., Rae W. H. Jr.- Pope A. Low Speed Wind Tunnel Testing; 3rd Ed. WileyInterscience: New York, 1999. Metha R. D., Bradshaw P. Design Rules for Small Low Speed Wind Tunnels Journal of Royal Aeronautical Society 1979, Vol. 73. Eckert W., Mort K. W. - Pope J. - Aerodynamic Design Guidelines and Computer Program for Estimation of Subsonic Wind Tunnel Performance National Aeronautics and Space Administration NASA TN D-8243, Washington, D.C., October, 1976. Bell J. H., Metha R. D. Contraction Design for Small Low-Speed Wind Tunnels NASACR-182747, April 1988.

220 [5]

[6] [7] [8] [9]

S. Brusca, R. Lanzafame and M. Messina Wattendorf F. L. Factors Influencing the Energy Ratio of Return Flow Wind Tunnels Fifth International Congress for Applied Mechanics, Cambridge, September 12-16, 1938. Idel’chick I. E. Handbook of Hydraulic Resistance; The Israel Program for Scientific Translation, Tel Aviv, 1966, AEC-TR-6630. Shames I. H. Mechanics of Fluids; 3rd Ed. McGraw Hill, New York, 1992. Prandtl L. Attaining a Steady Stream in Wind Tunnel NACA TM 726, Oct. 1933. Zell, P. Performance and Test Section Flow Characteristics of the National Full-Scale Aerodynamics Complex 80- by 120-Foot Wind Tunnel. NASA TM 103920, 1993.

INDEX A  acid, 80, 88, 89 acidic, 70 adjustment, 83 adsorption, 91 aerodynamic, vii, x, 3, 4, 5, 67, 88, 167, 168, 170, 172, 173, 175, 176, 178, 179, 180, 187, 189, 190 aerosol, viii, 69, 70, 71, 73, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 93, 94, 96, 99, 113, 115, 116, 117, 118, 119, 123, 124 aerosol clouds, viii, 93, 96, 99, 115, 124 aerosols, 88 aerospace, 2, 3, 9 aerothermal, vii, x, 32, 167 aggregation, 79 air flow velocities, ix, 129, 131, 138 air temperature, 96, 107, 115, 118, 124, 131 aluminium, ix, 130, 131, 134, 138, 139, 140, 142 ambient air, 9, 72, 96, 139 ammonia, 79, 80, 89 ammonium, 84 amplitude, 74, 75 aqueous solutions, 83 arithmetic, 112 assessment, 150, 186, 187 atmosphere, viii, 9, 69, 70, 77, 79, 80, 82, 86, 89, 127 atmospheric icing, viii, 93, 96, 108, 113 Atmospheric processes, viii, 69 axial fan, x, xi, 189, 215, 216, 217, 218

B  bacteria, 83 base, ix, 12, 34, 36, 42, 43, 44, 80, 83, 87, 129, 148, 150, 151, 156, 158, 168, 170, 173, 187

beams, 33, 34, 148 Belgium, 187 bending, ix, 147, 148, 152, 153, 154, 155, 165 biomass, 80

C  calcium, 83 calibration, 4, 10 CAM, 90 campaigns, 55 capillary, 100 capsule, vii, 1, 6, 7, 8, 9, 10, 17, 24, 27, 29, 34, 37, 46, 47, 56, 64 carbon, 18 case study, 190, 192, 194, 195, 196, 197, 199, 200, 201, 205, 207, 217, 219 catalysis, 9, 27, 37, 38, 39, 40, 64 catalytic effect, viii, 2, 37, 52 catalytic properties, 50 catastrophic failure, 2 ceramic, 29, 31, 135, 136, 139 CFD code, vii, 1, 4, 5 chemical, 4, 8, 11, 24, 63, 70, 71, 73, 75, 80, 81, 83, 130, 142, 172, 177 chemical properties, 142 chemical reactions, 8, 172 chemistry, vii, viii, 7, 69, 70, 71, 80, 81, 84, 87, 172, 178, 179, 180 chromatography, 79 CIRA Plasma Wind Tunnel, vii, 1, 8, 9, 10, 64 circulation, 74, 76, 89, 90 classes, 160 cleaning, 199, 205 climate, 70, 84 climate change, 70 closure, 43 cloud chemistry models, viii, 69

Index

222

cloud physics, vii, viii, 69, 70, 71, 87 Cloud processes, viii, 69 clustering, 84 CO2, 80, 81, 89 collisions, 76, 78, 96, 97, 98, 99, 106, 112, 113, 118, 120, 123, 126, 127 combined effect, 50 combustion, 79, 83 commercial, 18, 27, 34, 110, 112, 114, 219 complement, 3, 210 complexity, 4, 12, 64 composition, 83, 89 compounds, 83, 84 compression, 66 computation, 37, 39, 44, 110, 112, 113, 116, 183, 184 computational fluid dynamics, vii, x, 4, 167 computational grid, 35 computer, 133, 137 computing, 8, 110 concomitant mass transfer, ix, 129 condensation, ix, 130, 131, 132, 134, 135, 136, 139, 140, 141, 142, 143, 144 conditioning, 71, 72, 131, 132 conductivity, 95, 108, 135 configuration, 3, 6, 8, 9, 16, 17, 35, 43, 187, 218 conifer, x, 147, 150, 164 conservation, xi, 106, 189, 195 construction, 3, 71, 73, 86, 87, 190, 194, 195, 218 contamination, 6, 32 contour, 47, 54, 56, 175 convergence, 42, 160, 208 cooling, viii, 15, 17, 32, 33, 41, 46, 71, 93, 96, 106, 107, 113, 118, 123, 131, 134, 136, 144 copper, 9, 10, 17, 27, 32, 33, 41, 60, 135 correlation, vii, 1, 79, 152, 178, 186 correlations, 128 cost, 2, 169, 216 covering, 18 CPU, 36 critical value, 99, 102 crown, vii, ix, 147, 148, 149, 150, 151, 154, 156, 157, 158, 163, 164, 165, 166 crowns, x, 147, 148, 149, 155, 156, 157, 163, 164, 165 crystallization, 83 crystals, viii, 69, 70, 79, 88, 89 cultivation, 130 cycles, ix, 129

D  data analysis, 84

data set, 4, 159, 160, 161, 164 decay, 116 decomposition, 34, 35 deformation, viii, 87, 93, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 112, 123, 152 degradation, 6, 26 deposition, 70, 77 derivatives, 180 desorption, 79, 80, 89 detachment, 27 detection, 84 deviation, 162 dew, 131, 132, 134 diffusers, x, 132, 189, 196, 218 diffusion, 70, 80, 143, 144 diffusivity, 94, 107 dimensionality, 47, 50 direct observation, 72 discontinuity, 39, 65 discretization, 110 dispersion, viii, 93, 96, 106, 123, 124 displacement, 133, 152 dissociation, 7, 170 distilled water, 82 distribution, viii, 9, 13, 14, 16, 24, 25, 27, 29, 37, 38, 39, 40, 41, 42, 44, 45, 46, 49, 50, 52, 55, 57, 61, 62, 63, 64, 73, 83, 87, 93, 94, 96, 112, 119, 122, 127, 135, 139, 172, 178 drag coefficient, vii, ix, 94, 109, 111, 147, 148, 149, 150, 157, 158, 159, 160, 161, 162, 163, 165, 179 drawing, 71, 72 droplet size distribution, viii, 84, 93, 94, 96, 127 Droplet trajectories, ix, 94, 96 dwarf trees, ix, 147, 150 dynamic viscosity, 95, 100, 144

E  economic losses, 148 ecosystem, ix, 129 elbows, 132 electric current, 134, 135, 216 electric field, 89 electrodes, 10 electron, 83 e-mail, 93 emission, 134, 182 energy, x, xi, 4, 5, 6, 8, 39, 54, 64, 70, 73, 84, 85, 86, 94, 97, 98, 104, 105, 108, 110, 189, 190, 208, 209, 210, 212, 214, 219 energy consumption, x, 189 energy efficiency, 214

Index environment, vii, ix, 5, 64, 71, 73, 84, 85, 129, 130, 131, 140, 141, 142, 143, 168, 182 environmental characteristics, 72 environmental conditions, 71, 130 equilibrium, 8, 10, 11, 12, 14, 15, 24, 30, 36, 37, 38, 41, 43, 46, 49, 52, 63, 74, 75, 80, 81, 87, 88, 107, 172, 177, 178, 179, 182 equipment, 9, 130 ESA EXPERT capsule, vii, 1, 6 ethanol, 126 Europe, 2, 3, 4, 65, 66, 168, 187 evaporation, viii, 81, 83, 84, 86, 88, 93, 96, 106, 107, 113, 118, 123, 124, 126, 130, 131, 143 evolution, viii, 60, 93, 97, 98, 114, 115, 123, 126, 127, 177, 186 execution, vii, 1, 15, 16, 18, 60, 63 experimental condition, 86 extraction, 46, 47, 58, 60

F  field tests, ix, 147 film formation, 95, 107 film thickness, 94, 99, 101, 103 filtration, 130 financial, 124, 145 financial support, 124, 145 Finland, 166 first generation, 2, 168 flap region, vii, 2, 6, 12, 48, 49, 57, 65 flexibility, x, 4, 147, 164 flight, vii, viii, x, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 24, 26, 34, 41, 47, 55, 56, 62, 63, 64, 98, 130, 167, 168, 170, 172, 174, 175, 180, 181, 182, 183, 187, 188 flight data, vii, 1, 4, 5, 6 floods, 70 flow field, 4, 177 fluctuations, 73, 89, 133, 138, 144, 158, 159, 205 fluid, 8, 9, 10, 32, 74, 76, 96, 102, 104, 109, 110, 113, 170, 190, 207 food, ix, 129, 130 force, ix, 75, 97, 100, 102, 147, 148, 150, 153, 154, 158, 159, 163, 165, 178, 180 forecasting, viii, 69 formation, viii, 69, 70, 76, 79, 81, 82, 83, 84, 85, 90, 97, 142, 165 formula, 76, 101, 105, 109, 143 France, 65, 66, 124, 129, 145, 167, 187 freezing, viii, 69, 70, 81, 82, 83, 87, 88, 89, 90, 97, 118, 123 friction, 16, 24, 37, 38, 40, 41, 42, 44, 46, 47, 48, 49, 172, 207, 208, 210, 211, 216

223

FTIR, 88

G  geometry, vii, 2, 6, 7, 12, 32, 36, 41, 44, 52, 75, 109, 110, 169, 208 Germany, 65, 69, 71, 87, 187 graph, 75, 140, 141, 216 graphite, 84 grass, 82, 83 graupels, viii, 69, 71 gravity, ix, 96, 108, 110, 116, 118, 129, 131, 150, 155, 156 greenhouse, 131 grid generation, 4 grids, 34 growth, viii, ix, 69, 70, 76, 77, 83, 84, 85, 87, 89, 90, 129, 130 growth rate, 77, 85, 90 guidance, x, 167 guidelines, 3

H  habitat, ix, 129 habitats, ix, 129 heat flux, vii, ix, 2, 6, 8, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 32, 33, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 65, 129, 134, 170, 171, 182, 183, 185, 186, 187 heat transfer, 13, 95, 96, 108, 128, 144 heating rate, 65 heavy metals, 80 height, 113, 116, 117, 118, 119, 120, 121, 138, 150, 151, 152, 153, 154, 155, 156, 157, 158, 204, 205 high enthalpy conditions, vii, 1, 3, 64 history, 130, 186 homogeneity, 96, 132 hot wire anemometry, ix, 130, 133 hotwire liquid, ix, 94 human, ix, 129, 130 humidity, viii, 69, 70, 71, 72, 83, 93, 94, 96, 107, 116, 124, 130, 131, 132, 140, 144 hurricanes, 70 hydrodynamics, ix, 129, 130, 131 hydrogen, 88 hydrogen peroxide, 88 Hydrometeors, viii, 69 hygiene, 130 hypersonic re-entry conditions, vii, 1 hypothesis, 11, 15, 29, 31, 43, 46, 54, 172

Index

224

I  ice crystals, viii, 69, 70, 79, 88, 89 ideal, 212 identity, 204 image, ix, 74, 75, 94, 114, 154, 156 images, 74, 75, 114, 121, 154, 156, 157 immersion, 82, 83, 88, 90 improvements, 97 incidence, 13, 25 independence, 35 indium, 86 inertia, 135, 187 insertion, 10, 58, 73 integration, 3, 8 integrity, 27 interaction effect, 5 interaction effects, 5 interface, 8, 18, 27, 28, 29, 30, 31, 34, 35, 36, 41, 46, 50, 52, 53, 54, 115, 131, 135, 136, 141, 143, 144, 145 International Space Station, 130 ionization, 80 iron, 80, 83 islands, 168 Israel, 220 issues, 5, 17 Italy, 1, 189, 218

J  Japan, 126, 147

K  kerosene, 83, 88 kinetics, 80

L  laboratory studies, 90 laminar, viii, ix, 3, 6, 10, 11, 12, 13, 52, 63, 65, 66, 69, 71, 72, 73, 84, 85, 86, 88, 90, 129, 131, 132, 138, 139, 144, 172, 179, 182, 183, 184, 186 laminarity, viii, 69 laser radiation, 84 laws, 3, 64 lead, 159, 193, 205, 208, 219 leakage, 190 life support systems, ix, 129, 130 lifetime, 95, 109

ligament, 104 light, 6, 83, 114, 130 linear function, 20, 22, 23 liquid phase, 79, 80, 81 liquid water content, viii, 77, 84, 93, 96 liquids, 146 livestock, 80 living conditions, 130 local conditions, 5

M  magnitude, 31, 103, 110, 112, 161, 178 Mainz vertical wind tunnel, vii, viii, 69, 71, 72, 73, 74, 75, 79, 80, 81, 82, 85, 86, 87 majority, 42 manganese, 80, 83 manufacturing, 138 mapping, 182 Mars, ix, 129, 130 mass, vii, ix, x, 8, 10, 54, 55, 73, 77, 84, 94, 96, 103, 106, 107, 109, 113, 122, 129, 130, 131, 135, 137, 140, 141, 142, 143, 144, 169, 173, 181, 182, 187, 189, 195 mass flux, ix, 129, 131, 135, 140, 141, 142, 143, 144 materials, viii, 2, 4, 9, 17, 34, 36, 46, 72, 130 matrix, 11, 36, 46 matter, iv, 4, 5, 61 measurement, 6, 56, 58, 59, 60, 75, 114, 118, 120, 132, 135, 139, 153, 155, 159, 161, 162, 164, 175, 190 measurements, ix, 55, 56, 58, 59, 60, 61, 65, 70, 71, 87, 88, 90, 94, 97, 112, 115, 118, 121, 127, 130, 132, 133, 138, 139, 153, 166, 184, 185 mechanical properties, 34, 165 median, 106 melting, viii, 28, 69, 78, 79, 87, 89, 90 melting temperature, 28 metal ion, 89 metal ions, 89 metals, 79 methodology, vii, viii, 2, 5, 6, 7, 8, 10, 62, 63, 64 microscope, 83 mission, ix, 2, 6, 9, 55, 129, 168, 172 missions, ix, 129, 130 mixing, 96, 126 modelling, 4, 7, 9, 64, 168, 179 models, viii, 5, 8, 15, 69, 70, 74, 75, 77, 78, 79, 80, 83, 87, 97, 103, 131, 165 modifications, 96, 124 modules, 131, 136 molecular structure, 97 molecular weight, 97

Index molecules, 7, 87, 172 momentum, 8, 77, 78, 106, 109 Moscow, 67

N  NaCl, 83, 84 National Aeronautics and Space Administration, 219 National Research Council, 124, 127 neglect, 43 Netherlands, 145 next generation, 2, 5, 64 nitrogen, 7, 39, 54, 55, 89, 175 nitrogen compounds, 89 nitrogen gas, 175 Norway, ix, 147, 150, 151, 156, 161, 164, 165, 166 Norway spruce, 165, 166 nucleation, 70, 82, 83, 88, 89, 91 nuclei, 82, 83, 89 null, 179, 212 numerical analysis, 15 numerical computations, 8, 24, 42 numerical tool, 4, 7, 63

225

pollen, 82, 83, 88, 90 pollutants, 84 pollution, 80, 84 porosity, 79, 202, 204, 205, 206, 207, 210 positive correlation, 158 precipitation, viii, 69, 70, 76, 77, 78, 81, 83, 85, 86, 87, 90 preparation, iv pressure gradient, 48, 52 principles, 73 probability, 108, 172 probability distribution, 108 probe, 10, 58, 115, 118, 133, 138 project, x, 6, 167, 168 propagation, 14, 90 proportionality, 207 protection, 3, 5, 9, 27, 49 prototype, 132 pumps, 72, 73 pure water, 79, 82, 84

Q  quantitative estimation, 44

O  operations, 111 optimization, 3 orbit, 130 oscillation, 74, 75, 76, 87, 88, 90, 99, 181 oxidation, 10, 18, 24, 47, 79, 168 oxygen, ix, 7, 39, 54, 129, 130

P  Pacific, 168 parallel, 7, 34, 137, 152 particle image velocimetry, ix, 94, 114 permeability, x, 147, 150, 164, 165 permission, iv permit, 5, 8, 32, 34 phenomenology, 5 photographs, 148, 149, 154, 156 physical features, vii, 1 physics, vii, viii, 3, 4, 69, 70, 71, 87, 99, 123 pitch, 173, 177 plants, ix, 129, 130 Plants, ix, 129 plasma wind tunnel, vii, 1, 6, 17, 56 Plasma Wind Tunnel Scirocco, viii, 2 platform, 137

R  radar, viii, 69 radiation, 56, 70 radius, vii, 2, 7, 8, 12, 15, 16, 18, 19, 32, 43, 64, 76, 77, 80, 83, 86, 94, 101, 103, 187, 199, 201 ramp, 66 reactions, 172 reality, 116 recombination, viii, 2, 9, 36, 37, 38, 39, 54, 65 recombination coefficient, viii, 2, 9, 36, 37, 38, 39, 65 recommendations, iv reconstruction, 8 recycling, 130 refractive index, 84 refractive indices, 84 regression, 148, 155, 160, 161, 164 regression analysis, 148, 164 regression equation, 155, 160 regulations, 10 reliability, 4, 63, 169 repetitions, 161 reproduction, viii, 2, 8 requirements, 3, 15, 17, 18, 24, 25, 36, 41, 63, 71, 72, 216, 217 resistance, 102, 136, 148, 159

Index

226 resources, 130 response, ix, 133, 136, 147, 150 response time, 136 restrictions, ix, 147 reusability, 3 Riemann problem, 8 risk, 165, 168, 186 robust design, 2 room temperature, 118, 133, 134, 138 Russia, 135, 187

S  safety, 34 salts, 83, 84 saturation, viii, 69, 70, 72, 90, 142 scaling, 5 scaling law, 5 scattering, 70, 84, 88 scientific publications, 87 Scots pine, 164, 165, 166 second generation, 71 security, 210 semiconductor, 135 sensitivity, 15, 46, 53, 85, 133, 142, 152 sensors, 7, 9, 10, 18, 55, 56, 57, 60, 61 services, iv shape, x, 12, 18, 32, 44, 61, 72, 73, 75, 76, 87, 88, 89, 90, 95, 104, 133, 138, 142, 148, 149, 150, 156, 157, 168, 169, 172, 190, 191, 192, 193, 194, 197 shear, 148 shock, vii, 1, 2, 3, 6, 7, 8, 13, 24, 32, 46, 47, 49, 52, 57, 59, 63, 64, 65, 172, 175, 177, 178, 183 shock wave boundary layer interaction phenomena, vii, 1 shock waves, 183 showing, viii, 2, 43, 117, 199 signals, 55 silhouette, 193 silicones, 32 silk, 210 silver, 134 simulation, viii, 5, 11, 12, 27, 34, 43, 61, 69, 70, 99, 105, 110, 112, 113, 118, 119, 124, 131, 183 simulations, 4, 5, 6, 10, 12, 34, 36, 38, 53, 63, 70, 79, 84, 85, 88, 90, 102, 112, 115, 119 skin, 16, 24, 37, 38, 40, 41, 42, 44, 46, 47, 48, 49, 172, 210, 211 smoothing, 60 snow flakes, viii, 69, 79, 87, 89 software, 34, 110, 112, 114, 115, 155

solution, 16, 25, 27, 29, 80, 88, 109, 138, 139, 177, 178, 179, 182 space missions, ix, 129, 130 space station, 131 Spain, 145 species, 8, 54, 80, 148, 150, 164, 165, 166 specific heat, 94, 108, 144 spectroscopy, 88 square test chamber, x, 189 stability, ix, 3, 71, 129, 135, 166, 173, 180, 181 standard deviation, 108, 159, 162 state, 4, 7, 8, 136, 186 states, 8 statistics, 112 steel, 18, 27, 113 stem breakage, ix, 147, 165 stem deflection, ix, 147, 150, 151, 152, 153, 154, 155, 158, 159, 164 stem stiffness, ix, 147, 153, 154 storms, 163 streamwise direction, ix, 94, 96, 119, 120 stress, 27, 29, 31, 34 stress fields, 31 stretching, 95, 98, 105, 106 stroke, 152 structure, 29, 30, 34, 36, 49, 56, 175, 191, 203 substitution, 101 sulfate, 79, 80, 83, 84 sulfur, 79, 86, 88 sulfur dioxide, 79, 86, 88 sulfuric acid, 88 supervision, 71 surface area, 139, 141 surface energy, 99, 104, 105 surface properties, 27, 56 surface tension, 95, 97, 98, 99, 100, 101 symmetry, 12, 24, 34, 35, 36, 46, 49, 50, 55, 62, 64, 138 synthesis, 130

T  target, 26, 63, 114 technical support, 124 techniques, 115 technologies, 2, 5, 130 technology, x, 130, 167, 187 temperature, vii, viii, ix, 1, 3, 5, 6, 7, 12, 14, 15, 27, 28, 29, 30, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 65, 69, 71, 77, 81, 93, 95, 96, 106, 107, 108, 109, 112, 113, 115, 116, 118, 125, 129, 130, 131, 132, 133, 134, 135,

Index 136, 138, 139, 140, 141, 142, 143, 144, 145, 182, 183, 186, 187, 190 terminal velocities, viii, 69, 70, 71, 77, 79, 82 testing, 5, 131, 190, 191, 192, 194, 212, 214, 216, 217, 218, 219 thermal analysis, 24, 29, 30 thermal energy, 109 thermal expansion, 32 thermodynamic parameters, viii, 93, 97 thermodynamics, 8 thinning, 47, 49, 52, 95, 97, 99 three-dimensional space, 109 three-dimensionality, 47, 50, 52 time increment, 111 trace gases, viii, 69, 70, 71, 79, 80, 81, 84, 86, 87 trade-off, 17, 191 trajectory, vii, viii, 1, 10, 18, 19, 20, 24, 26, 34, 46, 47, 58, 64, 76, 93, 110, 116, 168, 170, 171, 186 transducer, 60, 114, 152 transport, 8, 86, 131 transportation, 2, 3 treatment, 80, 81 turbulence, viii, x, 6, 69, 71, 73, 84, 85, 86, 87, 90, 95, 96, 108, 109, 110, 112, 114, 116, 122, 126, 131, 132, 137, 138, 139, 144, 186, 189, 199, 201, 205, 210, 219 turbulent flows, ix, 129, 131, 144

U  UK, 150 uniform, 72, 73, 120, 132, 135, 160, 190, 191, 192, 209 United, 65 United Kingdom, 65 uprooting, ix, 147, 148

V  vacuum, 10, 71, 73 validation, vii, viii, 2, 4, 5, 10, 186 variables, 4, 8, 13, 15, 19, 46, 65, 148 variations, 70, 73, 110, 113, 122, 123, 124, 132, 135, 141, 180, 192, 202 vector, 98, 110, 115, 181 vehicles, vii, 1, 2, 3, 4, 5, 9, 67, 169 velocity, viii, ix, x, xi, 71, 72, 73, 74, 76, 77, 79, 83, 84, 85, 87, 88, 89, 93, 95, 96, 97, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 120, 123, 126, 127, 130, 131, 132, 133, 137, 138, 139, 144, 147, 153, 164,

227

170, 172, 187, 189, 190, 191, 192, 195, 196, 202, 205, 207, 210, 211, 216, 218, 219 ventilation, 130, 131 vertical air stream, viii, 69 vertical variation, ix, 94, 97, 107, 122, 123, 124 viscosity, 97, 138, 144 visualization, 190

W  wall temperature, 14, 19, 20, 22, 24, 36, 38, 40, 41, 42, 44, 45, 50, 61, 62 water, viii, ix, 10, 27, 32, 33, 41, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 99, 105, 107, 108, 109, 112, 114, 115, 116, 118, 122, 123, 126, 129, 130, 135, 140, 141, 142, 143, 144, 145 water drops, viii, 69, 71, 75, 79, 80, 82, 86, 87, 88, 89, 90, 91, 126 water vapor, 70, 94, 107 wavelengths, 56 welding, 33 wind force, ix, 147, 148, 150, 154, 158, 159, 163, 165 wind speeds, x, 86, 108, 147, 150, 153, 159, 160, 161, 162, 163, 164, 165 wind tunnels, vii, viii, x, 3, 4, 5, 64, 70, 93, 96, 97, 108, 124, 150, 167, 168, 172, 183, 187, 190, 210, 214 windows, 130, 192 wires, 133, 136, 190, 206, 210 wool, 190 worldwide, viii, 69, 71

X  X-axis, 17 xylem, 152

Y  yield, 34

Z  zinc, 83 zinc oxide, 83 zone of interest, vii, 2