Advances in Multiphase Flow and Heat Transfer, Volume 2

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) i Preface Multiphase flow and heat transfer have been foun...

Author: Lixin Cheng and Dieter Mewes (Ed)

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

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Preface Multiphase flow and heat transfer have been found a wide range of applications in nearly all aspects of engineering and science fields such as mechanical engineering, chemical and petrochemical engineering, nuclear engineering, energy engineering, material engineering, ocean engineering, mineral engineering, electronics and microelectronics engineering, information technology, space technology, micro- and nanotechnologies, bio-medical and life science etc. With the rapid development of various relevant technologies, the research of multiphase flow and heat transfer is growing very fast nowadays than ever before. It is highly the time to provide a vehicle to present the state-of-the-art knowledge and research in this very active field. To facilitate the exchange and dissemination of original research results and stateof-the-art reviews pertaining to multiphase flow and heat transfer efficiently, we have proposed the e-book series entitled Advances in Multiphase Flow and Heat Transfer to present state-of-the-art reviews/technical research work in all aspects of multiphase flow and heat transfer fields by inviting renowned scientists and researchers to contribute chapters in their respective research interests. The e-book series have now been launched and two volumes have been planned to be published per year since 2009. The e-books provide a forum specially for publishing these important topics and the relevant interdisciplinary research topics in fundamental and applied research of multiphase flow and heat transfer. The topics include multiphase transport phenomena including gas-liquid, liquid-solid, gas-solid and gas-liquid-solid flows, phase change processes such as flow boiling, pool boiling, and condensation etc, nuclear thermal hydraulics, fluidization, mass transfer, bubble and drop dynamics, particle flow interactions, cavitation phenomena, numerical methods, experimental techniques, multiphase flow equipment such as multiphase pumps, mixers and separators etc, combustion processes, environmental protection and pollution control, phase change materials and their applications, macro-scale and micro-scale transport phenomena, micro- and nano-fluidics, micro-gravity multiphase flow and heat transfer, energy engineering, renewable energy, electronic chips cooling, data-centre cooling, fuel cell, multiphase flow and heat transfer in biological and life engineering and science etc. The e-book series do not only present advances in conventional research topics but also in new and interdisciplinary research fields. Thus, frontiers of the interesting research topics in a wide range of engineering and science areas are timely presented to readers. In volume 2, there are seven chapters on various relevant topics. Chapter 1 deals with the passive condensers. The condensation phenomenon plays an important role in the heat transfer process in the chemical and power industry, including nuclear power plants. Condensers that are based on natural forces are called passive condensers and they do not require pumps or blower to move fluid. Examples of passive condensers include passive condenser systems in nuclear reactor safety systems, closed loop heat pipes, passive condenser for harvesting dew from surrounding humid air and passive refrigeration systems. In nuclear reactors, there is a greater emphasis on replacing the active systems with passive systems in order to improve the reliability of operation and safety. Heat pipes with passive condensers have been developed to transport high heat

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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flux from electronic devices. In practical operations of the passive condensers, small amounts of non-condensable gas may exist in working vapors due to characteristics of the system or dissolution of working vapors. It is well known that the presence of noncondensable gases in a vapor can greatly reduce the performance of condensers. This is because of the fact that the presence of non-condensable gas lowers the partial pressure of the vapor, thus reducing the saturation temperature at which condensation occurs. In this chapter state-of-the art in passive condensers, topics are covered including various types of passive condensers designs and their applications. The theory of passive condensation, condensation models, and experimental work on the passive condensers are presented. Practical heat transfer relations applicable to various for passive condensers are presented and discussed. Chapter 2 presents a topic on phase inversion is the phenomenon where the continuous phase of a liquid-liquid dispersion changes to become dispersed and the dispersed becomes continuous. Phase inversion has important implications for a number of industrial applications where liquid-liquid dispersions are used, since the change in the mixture continuity affects drop size, settling characteristics, heat transfer and even the corrosion behaviour of the mixture. In pipeline flows, phase inversion is usually accompanied by a step change or a peak in pressure drop. The chapter reviews the work on phase inversion during the pipeline flow of liquid-liquid mixtures when no surfactants are present. Investigations have revealed that in pipes a transitional region occurs during inversion from one phase continuous to the other, characterized by complex flow morphologies (multiple drops, regions in the flow with different continuity) and even stratification of the two phases over a range of dispersed phase volume fractions. The observations on the phase inversion process in pipelines are discussed and the parameters which affect the phenomenon are summarized. In addition, the various models available for predicting phase inversion are analyzed, as well as the methodologies developed to account for the transitional region with the complex morphologies and the flow stratification and to predict pressure drop during inversion. Chapter 3 presents a study of heat transfer and friction in helically-finned tubes using artificial neural networks. The last few decades have seen a significant development of complex heat transfer enhancement geometries such as a helicallyfinned tube. The arising problem is that as the fins become more complex, so does the prediction of their performance. Presently, to predict heat transfer and pressure drop in helically-finned tubes, engineers rely on empirical correlations. Tubes with axial and transverse fins have been studied extensively and techniques for predicting the friction factor and heat transfer coefficient exist. However, fluid flow in helically-finned tubes is more difficult to model and few attempts have been made to obtain non-empirical solutions. Friction and heat transfer in helically-finned tubes are governed by an intricate set of coupled and non-linear physical interactions. Therefore, obtaining a single prediction formula seems to be an unattainable goal with the knowledge engineers currently possess. Regression techniques performed on experimental data require mathematical functional form assumptions, which limit their accuracy. To achieve accuracy, techniques that can effectively overcome the complexity of the problem without dubious assumptions are needed. One of these techniques is the

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artificial neural network (ANN), inspired by the biological network of neurons in the brain. This chapter presents an introduction to artificial neural networks (ANNs), and a literature review of the use of ANNs in heat transfer and fluid flow is also discussed. In addition, this chapter demonstrates the successful use of artificial neural networks as a correlating method for experimentally- measured heat transfer and friction data of helically-finned tubes. Chapter 4 presents a comprehensive review on the heat transfer characteristics of CO2 and CO2-oil mixture in tubes including convective flow boiling, gas cooling, and condensation are investigated. Two-phase flow patterns are thoroughly investigated based on physical phenomena, which show the early flow transition to intermittent or annular flow especially for small diameter tube. The physical phenomena for nucleate boiling of CO2 follow the same trends with other organic fluids under the same reduced pressure. The gas cooling heat transfer is critically dependent on the turbulent diffusivity related with buoyancy force due to the large density difference. Under the oil presence conditions, the interaction of oil rich layer and bubble formation is the physical mechanism for the CO2-oil mixture convective boiling. Besides, the gas cooling phenomena with oil should be investigated based on the flow patterns formed by CO2 and oil, and the oil rich layer, whose thickness are depends on the solubility of CO2 to oil explains the physical mechanisms of heat transfer. The thermodynamic properties of CO2-oil were estimated by the general model based on EOS, and they are utilized to estimate the properties for oil rich layer and oil droplet vapor core. Through these predicted properties, the convective boiling and gas cooling heat transfer coefficients and pressure drop theoretically estimated. Condensation of CO2 is not so different from the existing one, so the heat transfer coefficients and pressure drop are well estimated by the existing one developed for other fluids. Chapter 5 summarizes the work done by our research group in recent five years on the nonlinear analysis and prediction of time series from the system of fluidized bed evaporator with an external natural circulating flow. Besides traditional investigations on steady-state characters of flow and heat transfer, the nonlinear evolution behavior of the system was emphasized and explored in this chapter. Measured time series of wall temperature and heat transfer coefficient were taken as the time series for the nonlinear analysis, modeling and forecasting. The main analysis tools are based on the chaos theory. Meaningful results were obtained. Under certain conditions, the signals obtained from the system of vapor-liquid-solid flow boiling are chaotic, which is demonstrated by obvious wideband characteristic in power spectra, decreasing gradually of autocorrelation coefficients, non-integer fractal dimension and non-negative and limited Kolmogorov entropy etc. At least two independent variables are needed to describe the vapor-liquid-solid flow system according to the estimation of the correlation dimension in meso-scale. The shapes of correlation integral curves and their slopes change with the variations of boiling flow states. The identifications of various flow regimes and their transitions can be characterized by the shape variations. Multi-value phenomena of chaotic invariants were found including correlation dimension and Kolmogorov entropy at the same operation conditions, showing the appearance of multi-scale behavior in the vapor-liquid-solid flow. Time series of heat transfer coefficients in fluidized bed evaporators were modeled and predicted by the nonlinear tools and the comparisons

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between predicted and measured time series were carried out by estimating the statistics characteristics, power spectrum, phase map and chaotic invariants and good agreements were observed. This indicates that a simple nonlinear datum driving model can describe the average or steady heat transfer character with a reasonable accuracy and the transient heat transfer behavior with a general fluctuation tendency for the vapor-liquidsolid flow. These findings are useful for finding new design, operation and control strategies for such complex systems. Chapter 6 describes the phenomena of air-water two-phase flows with the particular application to the design of a drainage and vent system. The detailed knowledge of airwater interfacial mechanism, the propagation of transient air pressure and the flow resistance in a drainage system is essential in order to prevent the damage of trap seal, the unfavorable acoustic effect and the foul odors ingress into the habitable space through the interconnected drainage and vent network. For a drainage system with the air admittance valve at the exit vent of the vertical stack, the control of the propagation of the air pressure requires the understanding of the transient air-water two-phase flow phenomena in each component of a drainage system. This chapter starts with the background introduction for a drainage and vent system. Research works investigating the air-water two-phase flows through vertical, horizontal and curved tubes as well as through the tube junctions are subsequently reviewed. An illustrative numerical analysis that examines the transient air-water two-phase flow phenomena in a confluent vessel with multiple joints feeding the stratified air-water flows is presented to demonstrate the CFD treatment for resolving the complex transient air-water two-phase flow phenomena in the typical component of a drainage system. Chapter 7 presents a study on convective boiling heat transfer of pure and mixed refrigerants within plain horizontal tubes. An experimental study is carried out to investigate the characteristics of the evaporation heat transfer for different fluids. Namely: pure refrigerants fluids (R22 and R134a); azeotropic and quasi-azeotropic mixtures (R404A, R410A, R507). zeotropic mixtures (R407C and R417A). The test section is a smooth, horizontal, stainless steel tube (6 mm I.D., 6 m length) uniformly heated by the Joule effect. The flow boiling characteristics of the refrigerant fluids are evaluated in 250 different operating conditions. Thus, a data-base of more than 2000 data points is produced. The experimental tests are carried out varying: i) the refrigerant mass fluxes within the range 200 - 1100 kg/m2s; ii) the heat fluxes within the range 3.50 - 47.0 kW/m2; iii) the evaporating pressures within the range 3.00 - 12.0 bar. Experimental heat transfer coefficients and pressure drops are evaluated varying the influencing parameters. In this study the effect on measured heat transfer coefficient of vapour quality, mass flux, saturation temperature, imposed heat flux, thermo-physical properties are examined in detail. The effect on measured pressure drops of vapour quality, mass flux, saturation temperature and thermo-physical properties are examined. In this chapter the attention is focused also on the comparison between experimental results and theoretical results predicted with the most known correlations from literature, both for heat transfer coefficients and pressure drops. As the founding editors of the e-book series, we are very happy to see that the ebooks are now available to our readers. We are very much grateful to the authors who have contributed to the chapters. It is our great wishes if the e-book series are able to

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provide useful knowledge for our community and to facilitate the progress of the research in the field of multiphase flow and heat transfer. We would like to express our gratitude to our families for their great support to our work.

Editor-in-Chief: Dr. Lixin Cheng School of Engineering, University of Aberdeen, King’s College, Aberdeen, AB24 3UE, Scotland, the UK, Email: [email protected] Co-editor: Prof. Dieter Mewes Institute of Multiphase Process, Leibniz University of Hanover, Callinstraße 36, D-30167 Hannover, Germany, E-mail: [email protected]

20 10 2009

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Contributors Panagiota Angeli, Department of Chemical Engineering, University College London, UK Louay M. Chamra, School of Engineering and Computer Science, Oakland University, USA S.W. Chang, Thermal Fluids Laboratory, National Kaohsiung Marine University, Taiwan, R.O.C Adriana Greco, DETEC, University of Naples Federico II, Italy Mingyan Liu, School of Chemical Engineering and Technology, Tianjin University, China; State Key Laboratory of Chemical Engineering, China D.C. Lo, Research Institute of Navigation Science and Technology, National Kaohsiung Marine University, Taiwan, R.O.C. Pedro Mago, Department of Mechanical Engineering, Mississippi State University, USA Aihong Qiang, School of Chemical Engineering and Technology, Tianjin University, China Shripad T. Revankar, School of Nuclear Engineering, Purdue University, USA Juanping Xue, School of Chemical Engineering and Technology, Tianjin University, China Rin Yun, Department of Mechanical Engineering, Hanbat National University, South Korea Gregory Zdaniuk, Ramboll Whitbybird Ltd, London, United Kingdom

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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Research and Review Studies

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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Chapter 1 Passive Condensers Shripad T. Revankar∗ School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA

Abstract The condensation phenomenon plays an important role in the heat transfer process in the chemical and power industry, including nuclear power plants. Condensers that are based on natural forces are called passive condensers and they do not require pumps or blower to move fluid. Examples of passive condensers include passive condenser systems in nuclear reactor safety systems, closed loop heat pipes, passive condenser for harvesting dew from surrounding humid air and passive refrigeration systems. In nuclear reactors, there is a greater emphasis on replacing the active systems with passive systems in order to improve the reliability of operation and safety. Heat pipes with passive condensers have been developed to transport high heat flux from electronic devices. In practical operations of the passive condensers, small amounts of non-condensable gas may exist in working vapors due to characteristics of the system or dissolution of working vapors. It is well known that the presence of non-condensable gases in a vapor can greatly reduce the performance of condensers. This is because of the fact that the presence of non-condensable gas lowers the partial pressure of the vapor, thus reducing the saturation temperature at which condensation occurs. In this chapter, state-of-the art in passive condensers topics are covered including various types of passive condensers designs and their applications. The theory of passive condensation, condensation models, and experimental work on the passive condensers is presented. Practical heat transfer relations applicable to various passive condensers are presented and discussed.

Introduction Condensation is a process, where saturated vapor is converted in to liquid with transfer of latent heat from one fluid system to another. Since latent heat is large, a significant amount of heat can be transferred through condensation process. Hence, this mode of heat transfer is often used in a number of chemical and power industries including nuclear power plants because high heat transfer coefficients are achieved. In order to facilitate condensation of vapor, a cold surface is required whose temperature should be lower than the saturation temperature of the condensing vapor. For dynamic operation, the condensed liquid needs to be removed continuously from the condensing surface to make room for further condensation. The condensing surface is generally cooled by using an external coolant flow or radiation. In a condenser, the vapor, external coolant, and condensate liquid are often transferred through the aid of pumps, compressors, or blowers. However, there is a class of condensers that operate with gravitational force or surface tension force. These condensers do not need external pumps or blowers. These condensers are referred as passive condenser systems. The advantage with passive condenser system is that their reliability is high, since they do

∗

Email address: [email protected], tel:1-765-496-1782

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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not rely on external pumps or blowers and they do not require additional power to operate them. Several condenser systems use passive nature to operate. Examples of passive condensers include passive condenser for harvesting dew from surrounding humid air [1-3], closed heat pipes [4,5], passive refrigeration systems [6,7], geothermal heat exchangers [8,9], two-phase thermo siphons [10,11], and passive condenser systems in nuclear reactor safety systems [12,13]. In nuclear reactors, there is a greater emphasis on replacing the active systems with passive systems in order to improve the reliability of operation and safety. Two-phase heat pipes with passive condensers have been developed to transport high heat flux from electronic devices [14, 15]. Condensation on surface can occur as film-wise or drop-wise condensation. Dropwise condensation occurs when the condensate forms drops on surface at nucleation sites and grows until swept away by gravity. Generally, drop-wise condensation occurs on surfaces that are not easily wetted by the condensate. In film-wise condensation though initially the condensation occurs are at specific location as droplets, as the droplets grow, they wet the surface and make a continuous film. The dominant form of condensation is film condensation and most of industrial systems employ this form of condensation. The local heat transfer coefficients for drop-wise condensation are often an order of magnitude greater than those for film condensation. However, it is difficult to maintain the surface to have drop condensation. In this chapter, first various passive condensers are presented. One group of passive condensers is heat pipe that primarily work by using gravitational force and or surface tension force. The condensers that harvest closed environment moisture or atmospheric dew follow this. Then the passive condensers in nuclear reactor are presented. Detailed theoretical considerations on film condensation on which most of the passive condensations are based are presented. Correlations for condensation heat transfer coefficients and key heat transfer relations are given for various types of passive condensers.

Heat Pipes A heat pipe is a passive heat transfer device that has the ability to transport a large amount of energy over its length with a small temperature drop by means of liquid evaporation at the heat source and vapor condensation at the condenser. In figure 1, a conventional heat pipe is shown. It is an evacuated cylindrical vessel with internal walls lined with a capillary structure or wick that is saturated with a working fluid. Since the heat pipe is evacuated and then charged with the working fluid prior to being sealed, the internal pressure is set by the vapor pressure of the fluid. The working fluid is evaporated at the evaporator (heat source). This creates a pressure gradient in the pipe and the pressure gradient forces the vapor to flow along the pipe to a cooler section where it condenses, giving up its latent heat of vaporization. The wick structure in the heat pipe’s inner wall provides capillary forces that pump the condensate back to the hot end of the heat pipe and thereby complete the continuous passive evaporation/ condensation cycle.

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Condensation

Evaporation

Outer cylinder

Porous wick

Vapor flow

Liquid flow

Figure 1. Conventional heat pipe schematic.

Heat pipes are versatile in terms of range of operating temperatures. They can be designed to operate from cryogenic (< -243°C) applications by using material and fluid combination of titanium alloy-nitrogen, to high temperature applications (>2000°C) by using tungsten-silver heat pipes. In cooling applications, where it is desirable to maintain temperatures below 125-150°C, copper/water heat pipes are typically used. For application below 0°C Copper/methanol, heat pipes are used. There are several types of heat pipes designs, which are primarily based on their applications. The main heat pipe designs include miniature and micro heat pipes, loop heat pipes, vapor dynamic thermosyphon, and two-phase thermosyphons. In addition to these, there are several unique designs of heap pipes, such as pulsating heat pipe, sorption heat pipe, heat pipe panel and spaghetti heat pipe. Heat pipe thermal performance is characterized by the effective heat pipe thermal resistance or overall heat pipe temperature difference at a given design power. The heat pipe effective thermal resistance is a function of a large number of variables, such as heat pipe geometry, evaporator length, condenser length, wick structure, and working fluid. The total effective thermal resistance of a heat pipe is the sum of the resistances due to evaporation or boiling, axial vapor flow, condensation, conduction through the wall, conduction through the wick, and conduction losses back through the condenser section wick and wall. Typical value of thermal resistance for a copper/water heat pipe with a powder metal wick structure is ~0.2°C/W/cm2 at the evaporator and condenser, and 0.02°C/W/cm2 for axial resistance. Micro and Mini Heat Pipes Recently, there is a significant development of miniature heat pipes for electronics cooling and for use in refrigerating machines. Heat transfer rates close to 50 W have been achieved with copper sintered powder wick in miniature heat pipes with outer diameter of 4 mm and length of 200 mm [16, 17]. Various geometries, pipe materials, working fluids, and power transport levels have been used in the mini and micro heat pipes. These include geometry: circular tube diameter 4–25 mm, flat heat pipe thickness 2–20 mm, length 0.1–0.8 m, wall thickness 0.2–1.0 mm ; material––copper 99.95% purity, wick––copper sintered powder, wire mesh and wire bundle with thickness 0.2–

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0.8 mm; power transport capacity: 10–500W; working fluids: water, methanol and propane. Loop Heat Pipes Two-phase loop with capillary pump, called loop heat pipe (LHP) is a type of heat pipe in which the evaporator and the condenser are separated, with the working fluid being transported between the two components via tubing or pipes [18]. Given its high cooling capability, this type of flexible design renders LHP a highly promising candidate for advanced cooling systems in modern high-power electronic modules. In the loop heat pipe, the capillary pumped evaporator is used instead of a boiler as shown in Figures 2 and 3. Such an evaporator is more flexible from the view point of its orientation space and is more compact. In the LHP, there is a possibility to use an evaporator above the condenser. In the LHP, the vapor flows through the vapor channels towards the condenser and the liquid goes back to the evaporator due to the capillary pressure head of the porous wick.

Liquid flow

Vapor flow

Evaporator and condenser unit

Figure 2. Loop heat pipe with two evaporator/condensers, liquid and vapor lines.

Sintered power wick Liquid channel

Vapor outlet port Evaporation

Figure 3. Evaporator/condenser of a loop heat pipe.

LHP evaporators typically are cylindrical in shape with a 12–28 mm diameter and a length/diameter ratio ranging from 5 to 10 [18]. In many applications, especially when

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the length to diameter ratio is greater than 10, it is desirable that the thermal management system assure uniformly high rates of heat removal over a larger area. Cryogenic LHP are unique because they should be capable of cooling down from a room temperature, which is above the critical temperature of the working fluid, to the operating cryogenic temperature with only the condenser end, being cooled by a cryocooler. For a variety of reasons, LHPs with flexible transport lines are needed in some cryogenic applications as thermal links between cryocoolers and the cooled components. The flexible lines are used primarily for vibration isolation, and for increased thermal transport distance and thermal diode function. The inner part of cryogenic LHP evaporator is made of Ti or Ni sintered powder wick with a central tube for liquid flow and vapor flow channels on the inner surface of an SS tube or on outer surface of the wick. The evaporator has two separate tubes, the vapor tube, and the liquid tube. Evaporators are compatible with water, ammonia, methanol, ethanol, acetone, and methane. The LHP condenser is usually a tube-in-tube (coaxial) type, or it is made of a SS envelope with narrow passages, or with a porous structure. Typically, condensers are made of aluminum or SS shell with liquid cooling tube inside and capillary mini grooves in the vapor channels on the inner surface of the outer tube or on the surface of the aluminum body. As shown in Figure 4, capillary arteries provide passage for liquid film formed on the grooved surface of the shell metal (or sintered metal) body. The narrow passage slots connect the arteries to the surface for vapor condensation. Typical dimensions of the aluminum condenser have the following parameters: inner diameter––16 mm, outer diameter––32 mm, number of vapor channels––12 mm, diameter of capillary arteries––1 mm, width of narrow passages about 0.05 mm and width of triangular grooves about 1 mm [19].

Vapor channel Capillary grooves

Narrow passages Capillary arterios Cooling water

Figure 4. Condenser element with narrow passages and arteries and the porous body serves as liquid accumulator.

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Two-phase Thermosyphons Two-phase thermosyphons are the type of heat pipes that transfer heat with the aid of gravity. As shown in Figure 5, the thermosyphon is made of a closed container filled with a small amount of a working fluid to which heat is supplied to the evaporator wall, which causes the liquid contained in the pool to evaporate. The generated vapor then moves upward to the condenser due to buoyancy. The heat transported is then rejected into the heat sink by a condensation process. The condensate forms a liquid film, which flows downwards due to gravity. The design of the thermosyphons is simple as the body is a cylinder without any wicks and porous structures. Hence, the thermosyphon can be used in micro sizes as well as in large-scale systems. Two-phase thermosyphons have been used as PC electronics cooling in micro and mini size [20], geothermal heating [21], and to maintain foundation stability in permafrost areas in sizes of several meters [22].

Vapor Condenser section

Liquid film

Adiabatic section

Container Evaporator section Liquid pool

Figure 5. Two-phase closed thermosyphon.

As computers have advancements in speed and performance, the heat produced by the micro processing unit has increased rapidly, making heat dissipation a challenge. With notebook type personal computers, heat dissipation poses a problem due to their small packaging volume. Micro heat-pipe as passive heat exchangers are well suited as heat sinks for cooling the microprocessor. Micro heat pumps are piping of small diameter from 1 to 6 mm that permits easy bending and flattening. Typical thermal resistances for applications at six to eight watt heat loads are 4 - 6°C/watt. Often these are combined with thin metal fins and fans to comprise a variety of heat sinks of

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compact size. Fan cooled the heat pipe, heat sinks typically dissipate loads in the 75 to 100 watt range with resistances from 0.2 to 0.4°C/watt, depending on the available air flow. Typical thermal resistances for the high power heat sinks range from 0.05 to 0.1°C/watt. Again, the resistance is predominately controlled by the available fin volume and airflow. The heat pipes can be mounted vertically or inclined to take advantage of gravity. Figure 6 shows the schematic of a 1-mm thick micro heat-pipe, which is characterized by providing a return passage for working fluid at the center and two passages for vaporized working fluid at both sides.

⍺ Passage for vaporized working fluid

Wick

Figure 6. Schematic of 1mm thick micro heat pipe and possible orientation.

Two-phase thermosyphons have been used as heat exchanger that transforms solar radiation energy to internal energy of the transport medium [23]. As shown in Figure 7, the thermosyphon absorbs the incoming solar radiation, converts it into heat, and transfers this heat to a fluid to vaporize. In the heat pipe evaporating-condensing cycle, solar heat evaporates the liquid, and the vapor travels to the heat sink region where it condenses and releases its latent heat. The condensed fluid return back to the solar collector due to gravity and the process is repeated. Arrays of tubes are mounted on a heat exchanger manifold to the thermosyphon. Heat exchanger fluids water, or glycol, flows through the manifold, carried heat from the tubes and gives off its heat to a process or to water that is stored in a solar heat storage tank. The Thermosyphon offers

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Fluid Flow

Heat Pipe Condenser

Manifold Collector Plate

Evacuated Cylinder

Heat Pipe Evaporator

Figure 7. Schematic of a tube thermosyphon flat plate solar collector

Flat plate solar collector have been extensively studied [24, 25]. In the flat plate solar collectors the condenser section of the thermosyphon tubes is a separate tube in tube heat exchangers where, the water enters and exits these heat exchangers through two common headers. The major resistance to heat flow in the flat plate two-phase closed thermosyphon solar collector is in the condenser section of the collector. Integration of shell and tube heat exchanger at the condenser enables reduction of thermal resistance. Two-phase thermosyphons have been extensively used in extracting geothermal energy and to maintain foundation stability in permafrost areas. For permafrost areas, they have been placed in both a vertical orientation and in a near horizontal orientation, under buildings, roads, airfields and other structures. Thermosyphons have typically functioned passively in cold climates during the winter months, at which time the aboveground portion is subjected to cold ambient air. These two-phase thermosyphon are generally charged with low boiling point liquid such as ammonia, Freon, etc. The upside of thermosyphon (condensation part) has a radiator, and the downside (evaporation part) is embedded into a permafrost layer. The middle part is thermal insulating, with the special liquid inside as shown in Figure 8. In cold season, the working fluid absorbs heat from the permafrost and vaporize, then, the vapor rises and condenses above ground level releasing the latent heat to the cooler surrounding. The condensed fluid gravitates to belowground level to repeat the cycle. This continuous recycling is irreversible because the cycling ceases in the summer when the air temperature is above the soil temperature.

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recycling is irreversible because the cycling ceases in the summer when the air temperature is above the soil temperature.

30 m

Condenser

Embankment Surface Gravel Soil 30 m

Thermal insulation

Active Layer

60 m Permafrost

Evaporation section

Liquid

Figure 8. The two-phase closed thermosyphon for permafrost heat removal.

Moisture and Dew Harvest Closed Environment Moisture Harvest Condensing heat exchangers have been used for thermal and humidity control in every manned space flight system launched by the United States [26]. The current system for control and humidity removal for the space shuttle and the International Space Station utilizes a two- stage process. First, moisture is condensed onto the fins of a plate-fin heat exchanger, which is then forced through the "slurper bars" by the airflow. The slurper bars take in a two-phase mixture of air and water that are then separated by a rotary separator. Recently, a conceptual design for moisture removal and humidity control for the space shuttles and the International Space Station has been developed by researchers at the NASA Glenn Research Center in collaboration with the NASA Johnson Space Center [27]. This condensing heat exchanger can operate in varying gravitational conditions,including microgravity, lunar gravity, and Martian gravity. In this

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The condensing heat exchanger has a highly conductive porous substrate as the cold surface over which moisture condensation occurs. The condensed water vapor is removed through another embedded porous tube insert via a suction device. The pore size of the porous tube are small in comparison to the substrate enabling efficient removal of the water condensed on the substrate as shown in Figure 10.

Porous Substrate Porous Tube

Cooling Tube

Figure 9. NASA condensing heat exchanger design concept based on composite porous media.

Condensed Water

Moist Air

Unsaturated Pores Saturated Pores Closed Tube End

Porous Substrate Porous Tube Suction

Figure 10. Schematic Porous substrate and condensate removal tubes with smaller pore size

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Atmospheric Dew Harvest Dew and fog water collection have been considered as inexpensive, limited supplemental or alternative sources of water in arid to sub humid regions where other sources of water are scarce. The fog collecting was pioneered in Chile and promoted its application to the other developing countries with suitable fog conditions [28, 29]. Fog collection works on the principle that the fog droplets (1 µm to 40 µm) are carried by the wind. Thus, an object standing perpendicular to the wind, such as a tree, can intercept these droplets, which will eventually fall by gravity to the ground below. Within suitable geographic and wind conditions, 5–20 L/m2 per day of fog water can be collected from special mesh, held by vertical panels, to intercept fog droplets. Dew collection has been known over 140 years, where water vapor in the air is condensed on a given surface [30]. During the last decade, passive dew collection has become of increasing interest [31, 32] because of its potential to be used for drinking and domestic purposes. This is of special importance for the developing countries situated within arid to sub-tropical regions, where there is limited access to clean water. Dew collection is equally applicable to island, rural and isolated settings. The dew yield is dependent the cooling power, which lies in the range of 25–100W/m2 for clear evening skies. This limits the dew water yield to a theoretical maximum of about 0.8 l/m2 per night [33] with respect to latent heat of condensation of water (2500 kJ/kg at 20oC). However, in practice the meteorological conditions favoring dew formation on condensers will tend not to exceed 0.6 l/m2 per night. Therefore, a collecting area of 100 m2 could produce 50 liter per night, which is significant amount of water. The major requirement for the dew collection is a good passive condenser. Ideally, the condenser should be light sheet thermally isolated from massive parts and ground. The condensing surfaces should be open to let them irradiate the energy to space. The condenser should be placed far enough from ground to avoid the green house effect. The placing of the condenser should be such that it limits the strong winds. The surface material of the condenser should be well wetted by water to reduce the nucleation barrier. Pigmented polymer foils with high solar reflectance and high thermal emissivity in the infrared range (8 to 13 µm wavelength) that favor condensation of atmosphere moisture have been considered. Condensers can be made of several materials including polyethylene film, polyethylene mixed with titanium-oxide and barium-sulfate film, fiber reinforced plastic sheet and poly-carbonate sheet. Galvanized iron and aluminum sheets have also been used. Foil made of polyethylene embedded with TiO2 and BaSO4 microspheres were studied by Nilsson et al [34] and Vargas et al [35]. The design of the planar condenser is very simple as shown in Figure 11. The condenser sheet can be installed on existing roof for dew harvest. Planar condenser collector plate made with TiO2 and BaSO4 microspheres embedded foils inclined at of 300 from horizontal inclination was found to be optimal for gravity flow of the dewdrops [36].

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Condenser Panel Collection Channel

Water Tank

Figure 11. Dew harvest on inclined roof.

Passive Condensers in Nuclear Reactor PCCS in SBWR In a nuclear reactor industry during a loss of coolant accident, a large portion of the heat from the reactor core is removed by condensation of steam in the steam generators in reflux condensation mode. The presence of the noncondensable hampers the heat removal process. In the advanced light water reactors such as the Westinghouse Electric designed Advanced Passive 600 MWe [37], and General Electric designed Simplified Boiling Water Reactor (SBWR) [38], and recently introduced Westinghouse Electric AP1000 [39] and GE’s 4000MWt economic simplified boiling water reactor referred as ESBWR [40], there is a greater emphasis on replacing the active systems with passive systems in order to improve the reliability of operation and safety. For example, the ESBWR is based on natural circulation cooling. This reactor design uses the gravity driven cooling system as an emergency core cooling system following an accident in addition to the suppression pool. After the reactor is shut down, the reactor pressure vessel is depressurized with a system of valves that remain open up to containment. Thus, containment receives the steam produced in the core due to decay heat. In the ESBWR reactor, the containment steam is condensed by passive condenser system called Passive Containment Cooling System (PCCS). Initially the containment atmosphere is filled with nitrogen. The steam–nitrogen mixture from the containment flows to the PCCS condensers, which are vertically immersed in a large interconnected pool of water located outside and above the containment. Steam is condensed in the condenser tube while rejecting heat to the secondary pool of water. The PCCS condenser must be able to remove sufficient energy from the reactor containment to prevent containment from exceeding its design pressure following a design-basis accident. The efficient performance of the PCCS condenser is thus vital to the safety of the ESBWR.

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 13

SBWR consists of three PCCS condensers each made of two identical modules and each entire PCCS condenser two-module assembly is designed for 40MWt capacity nominal, at 412 kPa. The SBWR PCCS condenser diameter is 5.04 cm and the length is 1.8m. PCCS Operational Modes Three different operational modes are possible in the PCCS depending on the noncondensable (NC) gas concentration and the pressure difference between the drywell (DW) and suppression pool (SP), the pressure difference between the drywell (DW) and suppression pool (SP) (Figure 12). These are bypass mode, continuous condensation mode and cyclic venting mode [41]. Figure 13 shows the characteristics of three operation modes of PCCS. The PCCS will be in bypass mode when the DW pressure is greater than SP pressure plus the head due to the submergence of the vent line in the SP. This condition is realized during the blow down process, i.e., initial period of the accident. In this mode, uncondensed steam and NC gas pass through the PCCS condensers and are vented to the SP through the vent line. For this reason, this mode is also called as through flow mode. This mode of operation corresponds to forced convection. When the DW pressure is less than SP or equal to SP pressure then the PCCS will be in either continuous condensation mode or cyclic venting mode depending on the NC gas concentration. The PCCS will be in cyclic venting mode when small amount of the NC gas exists in the system. This condition sets in immediately after the blowdown process. Initially, the vent path is closed since submersion head is less than the pressure difference between DW and SP. The condensation performance is very high due to the low NC gas concentration. Therefore, the condensation rate is greater than the steam generation rate from RPV due to decay heat. Therefore, DW pressure decreases with time. As time passes, NC gas is accumulated in the PCCS and the performance of condenser is degraded. This results in the DW pressure increase. When DW pressure increases and reaches high enough to clear the vent lines the NC gas is vented to the SP. Due to the venting, condensation performance is recovered and the DW pressure decreases. Following this, the vent path is closed again and one cycle of venting period is terminated. This open-close cycle of the vent path is repeated as long as the NC gas is present in the system. The PCCS will be in continuous condensation mode when the NC gas is almost removed from system. This condition will be obtained in the later stage of an accidental transient after most of NC gas is vented to the SP. In this mode, all the steam entering the PCCS condensers are condensed in the tubes. Therefore, this mode is also called as complete condensation mode.

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Non-Condensable Gas and Steam

PCCS

Condensed Water GDCS

Non-Condensable Gas and Uncondensed Steam

Steam SP

RPV Condensed Water DW

Fig. 12. Passive containment cooling system (PCCS) condenser operation in the SBWR.

PCCS

Condenser

To GDCS

DW

SP Through Flow

DW

DW

SP Cyclic Venting

SP Complete Condensation

Figure 13 Three operation modes of the PCCS.

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Effect of Non -Condensable Gas The PCCS operates in film condensation mode. The performance of the condenser is strongly degraded when the NC gases are present in the condenser tube. The condensed water flows as an annular liquid film adjacent to the condenser tube wall and the steam– air mixture flows in the core region. Since the NC gases are impermeable to the liquid film, they are accumulated at the liquid-gas interface so their concentration is very high. The high NC gas concentration region is propagating to the gas core region by mass diffusion. The developing NC gas boundary layer acts as a strong resistance to the condensation. Uchida et al.’s [42] experiments on steam–gas condensation on the outside wall of vertical tube provided first practical correlation for the degradation of condensation. Recently, the relevant separate affects experiments on PCCS condensation under the presence of NC gas were conducted by many researchers [41, 43-48]. These studies have indicated that the condensation heat transfer decreases with very small amount of non-condensable gas. The pertaining correlations are given in next section.

Analysis of Film Condensation and Correlations Laminar Film Condensation Theoretical analysis of film wise condensation of a stationary pure saturated vapor was originally presented by Nusselt [49] in 1916 for vertical surface (Figure 14). Nusselt presented solution for the rate of heat transfer for film condensation as a function of difference between vapor saturation temperature and surface temperatures. As shown in Figure 1, the vapor condenses at its saturation temperature on the vertical plate, which is at cooler temperature. As the condensate flows downward due to gravity the thickness of the condensate film (δ) increases along the length due to mass transfer to the liquid–vapor interface.

y x

g TSAT

L TS

Vapor Film

Figure 14. Laminar condensation over vertical surface.

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The governing equations for the film on the surface are given as; ∂u ∂v + =0 ∂x ∂y

Continuity:

(1)

⎡ ∂u ∂v ⎤ ∂P ∂ 2u +v ⎥ = − + µl 2 + ρ l g ∂y ⎦ ∂x ∂y ⎣ ∂x

(2)

∂T ∂T ∂ 2T +v =α 2 ∂x ∂y ∂y

(3)

Momentum:

ρ L ⎢u

Energy:

u

Outside boundary layer (vapor zone) the momentum equation is ∂P = ρv g ∂x

(4)

The vertical pressure gradient in the liquid is the same as the hydrostatic pressure gradient in the outside vapor; hence, Eq. (2) is written as; ⎡ ∂u ∂v ⎤ ∂ 2u + v ⎥ = + µl 2 + ( ρl − ρ v )g ∂y ⎦ ∂y ⎣ ∂x

ρ l ⎢u

(5)

The assumption in the Nusselt analyses are as follows: (1) The flow is laminar flow, fully developed and constant properties for the liquid film. (2) A temperature across the film is linear and the heat transfer across the film to the plate is by one-dimensional conduction. (3) The gas is assumed as a pure saturated vapor at Tsat. (4) The shear stress at the liquid –vapor interface is assumed to be negligible ∂u in which case y =δ = 0 ∂y (5) Sensible cooling of the film is neglected compared to the latent heat

The film momentum equation reduces to ∂ 2u − g = ( ρl − ρ v ) ∂y 2 µl

The boundary conditions are

(6)

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 17

(1) y = 0; u = 0; T = TW ( 2) y = δ ;

∂u ∂y

δ

(7)

= 0, T = Tsat

Integrating Eq. (6) twice with respect to y and with boundary conditions, the film velocity profile in the film becomes ⎡ y 1 ⎛ y ⎞2 ⎤ u( y ) = ( ρl − ρ v )δ ⎢ − ⎜ ⎟ ⎥ µl ⎣⎢ δ 2 ⎝ δ ⎠ ⎦⎥ g

2

(8)

The local mass flow-rate through a cross-section of the film per width of the plate Γ(x) in terms of integral of velocity profile is *

δ( x ) m( x ) =∫ ρl u( y )dy ≡ Γ( x ) 0 b

(9)

Using Eq. (8) we have Γ( x ) =

ρl g ( ρl − ρ v )δ 3 3 µl

(10) ˙ (x) m

y x

dm dq

qs”(b dx)

dx

˙ +dm ˙ m δ(x) Liquid velocity boundary layer

Liquid Ts

Liquid thermal boundary layer Tsat Boundary layer

Figure 15. The energy balances in film

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Considering the control volume [δ ( x)dx] shown in Figure 15, the steady state from of the energy balance can be written as follows; h fg d Γ − qw′′ dx = 0

(11)

Since the liquid film temperature is linear, the wall heat flux can be written as; qw′′ = − k

T −T ∂T ≅ k sat w ∂y δ( x )

(12)

Combining Eq. (11) and (12), we obtain

d Γ k( Tsat − Tw ) = δ ( x )h fg dx

(13)

Differentiating eq. (6) yields ∂Γ g ρl ( ρl − ρ v )δ 2 ∂δ ( x ) = ∂x ∂x µl

(14)

Combining eq. (12) and eq. (13), it follows that

δ 3 dδ =

k µl (Tsat − Tw ) dx g ρl ( ρl − ρv )h fg

(15)

Integrating from x = 0 ( δ = 0) to any x location of interest on the surface ⎡ 4 µ k( T − T )x ⎤ δ ( x ) = ⎢ l sat w ⎥ ⎣⎢ g ρl ( ρl − ρ v )h′fg ⎦⎥

1/ 4

(16)

The film thickness grows like x1/4. The surface heat flux may be expressed as k ″ qW = h(Tsat − Tw ) = (Tsat − Tw ) δ ( x)

(17)

From Equation (16), the condensation heat transfer coefficient is given as h=

k δ ( x)

(18)

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From Equations (15) and (17) we have ⎡ g ρ ( ρ − ρ v )h fg k 3 ⎤ h=⎢ l l ⎥ ⎣⎢ 4 µl ( Tsat − Tw )x ⎦⎥

1/ 4

(19)

The average heat transfer coefficient for the plate of height L is obtained by integrating over the height of the plate, ⎡ g ρ ( ρ − ρ v )k 3 h fg ⎤ 1 L h ≡ ∫ hx dx = 0.943 ⎢ l l ⎥ L 0 ⎣⎢ µl ( Tsat − Tw )L ⎦⎥

1/ 4

(20)

The heat transfer coefficient is proportional to x-1/4 and (Tsat - Tw)-1/4. In terms of the dimensionless heat transfer coefficient, the average Nusselt number is give as,

hL ⎡ Ra ⎤ Nu ≡ = 0.943⎢ ⎥ kl ⎣ Ja ⎦

1/ 4

(21)

where, Ra is Rayleigh number and Ja is Jacob number and are defined as Ra = Gr Pr; Gr =

C p µl C (T − Tw ) ρl ( ρl − ρ v )gL3 . , Ja ≡ P sat ; Pr = 2 k h fg µl

(22)

Rohsenow [50] recommended using nonlinear temperature profile across the film and taking account of the additional energy to cool the film below the saturation temperatures from vapor-film interface to the plate. The modified latent heat of condensation h ′fg includes proper latent heat (hfg) and a contribution from cooling of the fresh condensate to temperature below Tsat and is given as

h′fg = h fg + 0.68C P ( Tsat − Tw ) = h fg ( 1 + 0.68Ja )

(23)

CP (Tsat − Tw ) h'fg In this case, the properties of the fluid in Eq. (18) or (19) should be evaluated at the film temperature defined as Tf = (Tsat -Tw)/2.

With this modification Jacob number in Eq. (20) is then defined as Ja ≡

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Wavy and Turbulent Film Condensation on Vertical Surface For sufficient long vertical surface, the condensate film may become turbulent. Typically, the flow is characterized with Reynolds number. The Reynolds number for the film is defined as; Reδ ≡

4Γ

(24)

µl

In terms of film thickness of δ, the Reynolds number is Reδ ≡

4g ρl ( ρl − ρ g )δ 3

(25)

3 µ l2

Three flow regimes can be distinguished in the film, laminar, wavy laminar and turbulent. At low Reynolds number, Reδ < 30, the flow is laminar with smooth film surface. With increase in Reynolds number, the film becomes unstable and waves appear at the liquid and vapor interface. The waves cause mixing to some extent, however the flow remains laminar until shear induced instabilities result in transition to turbulent flow in the film. This corresponds to Range of Reynolds number 30 < Reδ < 1800. At sufficiently high Reynolds number Reδ >1800, the film becomes turbulent. Using Eq. (19) for the average heat transfer coefficient and Eq. (23) we have relation

h kl

⎡ ⎤ µ l2 ⎢ ⎥ ⎣ ρ l ( ρ l − ρ v )g ⎦

1/ 3

= 1.47 Reδ1 / 3

(26)

The left hand term is a modified Nusselt number with a characteristic

⎡ ⎤ µ l2 length, ⎢ ⎥ ⎣ ρ l ( ρ l − ρ v )g ⎦

1/ 3

.

Assuming ρl >> ρv, we can write for the heat transfer relation in terms of modified Nusselt number h (ν l2 / g )1 / 3 = 1.47 Reδ1 / 3 , Reδ < 30 (27) kl For the laminar wavy region a correlation for modified Nusselt number is given by Kutateladze [51] as, h (ν l2 / g )1 / 3 Reδ1 / 3 = , kl 1.08 Reδ1.22 − 5.2

30 < Reδ < 1800

(28)

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For turbulent region correlation for modified Nusselt number is given by Labuntsov [52], as h (ν l2 / g )1 / 3 Reδ = , kl 18750 + 58 Pr −0.5 (Reδ0.75 − 253 )

Reδ >1800.

(29)

Condensation on Horizontal Systems Single Horizontal Cylinder and Sphere The heat transfer coefficient for laminar film condensation on outer surface of a horizontal cylinder or sphere of diameter D is given by [53]

⎡ gρ l ( ρ l − ρ v )k l3 h'fg ⎤ h = C⎢ ⎥ ⎢⎣ µ l ( Tsat − Tw )D ⎥⎦

1/ 4

(30)

where C= 0.729 for cylinder and 0.815 for the sphere. Bank of Horizontal Cylinders Industrial condensers with tube banks operate in film condensation mode. The condensate film on lower tubes is generally thicker as compared to the top tubes as the condensate drips or flows as a continuous sheet flowing on to lower tubes. Hence, the lower tubes have lower heat transfer coefficient. For number of rows of tubes in vertical direction N, the average heat transfer coefficient is given as;

hN = h N −1 / 4

(31)

where the top single tube heat transfer coefficient h is given by Eq. (29). Horizontal Downward Facing Plate A correlation for condensation on downward facing horizontal plate is given as [54],

h kl h kl where

σ g( ρ l − ρ v )

σ g( ρ l − ρ v )

= 0.69 Ra 0.20

for 1x106 < Ra < 1x 108

(32)

for 1x108 < Ra < 1x 1010

(33)

= 0.81Ra 0.193

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gh fg ρ l ( ρ l − ρ v ) ⎡ ⎤ σ Ra = ⎢ µl kl ( Tsat − Tw ) ⎣ g( ρ l − ρ v ) ⎥⎦

1/ 3

(34)

As the condensate accumulates on the downward facing plate, the film becomes unstable against gravity and creates waves. The waves grow with an increase in film thickness and the condensate drips as droplets. Horizontal Upward Facing Plate The heat transfer coefficient in terms of Nusselt number for condensation on an upward surface of infinite horizontal plate of width L is given as [55] as ⎡ gh fg ρ l2 L3 ⎤ hL = 0.82 ⎢ ⎥ kl ⎢⎣ µ l k l ( Tsat − Tw ) ⎥⎦

1/ 5

.

(35)

In this case, the condensate drains from the side of the plate under hydrostatic pressure gradient developed across the film as film thickness varies between center of the pate to the side. Single Horizontal Finned Tube Integral fins usually have two dimensional trapezoidal or rectangular cross-section. The fins enhance condensation heat transfer by increasing the condensing area due to the fins and the formation of a very thin condensate film on the flanks of the fin. However, flooding occurs between the fins in the bottom portion of the tube due to the retention of liquid by surface tension and this reduces the effective surface area. Thus, one has to select the fin geometry judiciously to exploit the favorable effect of surface tension in the unflooded crest region and minimize the adverse effect of surface tension in the flooded bottom portion. The correlation for film condensation on a horizontal tube with fins is given as [56] ⎡ gh fg ρ l2 k l3 ⎤ h = 0.689 ⎢ ⎥ ⎢⎣ µ l De ( Tsat − Tw ) ⎥⎦

1/ 5

(36)

where De is defines as Af Auf ⎛ De = ⎜⎜1.30η fin ~ + Ae L Ae Dr1 / 4 ⎝

⎞ ⎟ ⎟ ⎠

−4

(37)

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t..

p..

Dr Do

Figure 16. Finned tube dimensions.

where parameter L is calculated as L =

π ( D o2 − D r2 )

(38)

4Do

As shown in Figure 16, Do is the outer diameter of the fin, Dr is the root diameter of the finned tube, t is the fin thickness, p is fin pitch and ηfin is the fin efficiency. Af is the surface of a single fin and is calculated as

Af =

π 2

(D

2 o

− Dr2

) (39)

Auf is the area of the surface exposed tube between adjacent fins and is calculated as Auf = πDo ( p − t )

(40) The effective area of a fin Ae is calculated as Ae = ηfin Af + Auf .

(41)

Film Condensation Inside Horizontal Tube For film condensation inside horizontal tube the Chato [57] correlation is recommended for low vapor inlet Reynolds number (<35,000)

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⎡ gρ l ( ρ l − ρ v )k l3 h'fg ⎤ h = 0.555⎢ ⎥ ⎢⎣ µ l ( Tsat − Tw )L ⎥⎦

1/ 4

(42)

where the modified latent heat is h"fg = h fg + 0.375C p ( Tsat − Tw ) .

(43)

Film Condensation inside Vertical Tube and Thermosyphon Experimental study of laminar film condensations in a vertical tube in complete condensation mode was carried out by Revankar and Oh [58]. In these experiments, the steam was supplied from top of the tube and the condensate was collected at the bottom of the film. All steam injected into the tube was condensed so the results can apply to a closed two-phase thermosyphon and PCCS operating in complete condensation mode. Figure 17 shows experimental data on two-inch diameter vertical tube condensation heat transfer coefficient as a function of driving potential (Tsat –Tw). The Nusselt solution from Eq. (19) is also plotted in this figure. The complete condensation heat transfer rates for vertical tubes are higher by 15-20% than predicted by Nusselt analysis on vertical surfaces.

Condensaation HTC, kW/m 2 C

16

Revankar and Oh 2003 Poly. (Nusselt Solution)

12 8 4 0 0

10

20

Tsat-Tw, C Figure 17. Complete Condensation: Condensation Heat Transfer coefficients

These results agree with theoretical study by Spendel [59] on the condensation heat transfer inside vertical two-phase closed thermosyphons taking into account the effect

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of interfacial shear stress and vapor pressure variation. Spendel analysis showed that the analytical results of local and average condensation coefficients differed from those predicted by Nusselt’s theory by about 24 to 11% and about 1–4%, respectively. Based on experimental data Gross and Hahne [60] have given a correlation for condensation heat transfer inside two-phase closed thermosyphons with wickless tube. The correlation takes account of effects of geometry, angle of inclination, heat flow rate, temperature difference, type of fluid and state of the working fluid. This correlation applies to ranges of laminar, laminar-wavy and turbulent film flow are given as, Nu = [( 0.925 Reθ−1 / 3 f wave ) 2 + ( 0.021 Reθ1 / 3 ) 2 ] 1 / 2

(44)

where

h Nu = kl

⎤ ⎥ )⎦

1/ 3

(45)

h ( Tsat − Tw )L for θ = 90o h fg µ l

(46)

h ( Tsat − Tw )D for θ < 80o h fg µ l cos θ

(47)

Reθ =

Reθ = 2.869

⎡ µ l2 ⎢ ⎣ gρ l ( ρ l − ρ v

f wave =

1.15 1 − 0.63( P / Pc )

(48)

Here the angle θ is the inclination of the condenser with respect to horizontal. L is the length and D is the diameter of the thermosyphon tube. P and Pc refer to the thermosyphon operation pressure and critical pressure, respectively. A correlation given by Wang and Ma [61] for the condensation heats transfer of two-phase closed thermosyphons is based on theoretical analysis and experimental. This correlation takes into account the effect of vapor pressure, heat flux, amount of liquid filling and inclination angle are as follows. ⎡ gρ l ( ρ l − ρ v )k l3 h'fg ⎤ h = 0.943⎢ ⎥ ⎣⎢ µ l ( Tsat − Tw )L ⎦⎥

1/ 4

⎤ ⎡⎛ 2 L ⎞ 0.25 cos θ ( 0.54 + 5.86 × 10 −3 θ )⎥ ⎢⎜ ⎟ ⎦⎥ ⎣⎢⎝ D ⎠

(W/m2K)

(49)

Recently, an alternative correlation is given by Hussein et al [62] for condensation heat transfer for inclined wickless heat pipe flat-plate solar collectors based theoretical analysis and best fitted the available experimental data.

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[

h = 0.997 − 0.334 (cos θ )

0.108

]

⎡ gρ l ( ρ l − ρ v )k l3 h fg ⎤ ⎢ ⎥ ⎣⎢ µ l ( Tsat − Tw )L ⎦⎥

Revankar

1/ 4

⎡⎛ L ⎞ [0.254(cos θ ) ⎢⎜ ⎟ ⎢⎣⎝ D ⎠

0.385

]⎤ ⎥ ⎥⎦

(W/m2K)

(50)

Correlations for Condensation in the Presence of Non-Condensable Presence of even a small amount of non-condensable gas in the condensing vapor leads to a significant reduction in heat transfer during condensation. The buildup of non-condensable gases near the film vapor interface inhibits the diffusion of vapor from the bulk mixture to the liquid film. The net effect is to reduce the effective driving force for heat and mass transfer. In Figure 18 shows the temperature and non-condensable gas boundary layer nears the film and vapor interface. r

y x

u : velocity

W g : noncondensable gas mass fraction

g τI

τ

T : Temperature

liquid film

δ

δg

Noncondensable concentration boundary layer

Figure 18 Boundary layers due to the presence of non-condensable in vapor condensation on a plate or inside a tube.

Correlations for Outer Surfaces Condensation with Non-Condensable Gas For condensation of stagnant vapor and noncondensable gas mixture on the vertical surface, the following correlations are available. Uchida et al. [42] and Tagami [63] provided first practical correlations for the degradation of condensation due to non-

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condensable based experiments on steam-gas condensation on outside the wall of vertical tube. Their facility consisted of a series of metal cylinders inside 42 cubic meters chamber. Experiments by Uchida et al. [42] were under a natural convection regime and several different non-condensable gases, such as air and nitrogen were used. The empirical correlation fitted from experimental data relates the reduction of heat transfer coefficient to the gas mass fraction. A correlation based on Uchida’s data has been widely used in computer codes for light water nuclear reactor containment analysis involving condensation from steam-gas mixtures on interior containment surface. The correlation developed by Uchida et al [42] was correlated in terms of a single variable in order to obtain a total heat transfer coefficient ⎛ Wnc htot = 380⎜⎜ ⎝ 1 − Wnc

⎞ ⎟⎟ ⎠

−0.7

(W/m2K)

(51)

Here Wnc is the mass fraction of noncondensable. Uchida correlation is applicable for wall temperature of 322K and air, nitrogen and argon as non-condensable gases and for Wnc following ranges: 0.1 ≤ ≤ 13, 0.1 MPa ≤ Ptot ≤ 0.287 MPa, 0.3m ≤ L ≤ 0.9 1 − Wnc m. The Tagami correlation [63] has two time dependent components: a time-period corresponding to the initial stages of a large-brake large break scenario (including timedependent energy blow down parameters), and a second form for natural convection quiescent condition. For steady state the heat transfer coefficient is given as;

⎛ Wnc hsteady _ state = 11.4 − 284⎜⎜ ⎝ 1 − Wnc

⎞ ⎟⎟ (W/m2K) ⎠

for 0 < mv/mnc <1.4

(52)

where mv and mnc are the total mass of vapor and non-condensable gas, respectively. The total heat transfer coefficient for the transient period is given as; 0.5

htot −transient

⎛ t ⎞ = hmax −transient ⎜⎜ ⎟⎟ for t ≤ tA ⎝ tA ⎠

htot −transient = hsteady _ state + ( hmax −transient − hsteady _ state ) exp( −0.5( t − t A ))

hmax −transient

⎛ E = 426⎜⎜ A ⎝ t AVC

⎞ ⎟⎟ ⎠

(53) for t ≥ tA

(54)

0.6

,

(55)

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where EA is a dimensional grouping of energy (in Btu), tA is the total time for addition of non-condensable gas and VC is the containment volume. The Tagami experiments were conducted in a forced convection regime. The geometrical aspects and the effect of velocity field in the bulk of the mixture were ignored in these correlations. Therefore, caution should be used to extrapolate the Uchida and Tagami correlations. The experiment of Dehbi et al. [64] looked specifically at the effect of the containment variables at a small scale. In these experiments, they conducted experimental work on a 3.5 m long and 0.038 m diameter tubular geometry with different pressures, mass fraction of vapor/non condensable gases (helium as a hydrogen simulant). This experiment led to the development of correlations that relied on these variables. The Dehbi et al [64] correlation is the following: htot =

L0.05 [(3.7 + 28.7 Ptot ) − (2438 + 458.3Ptot )log 10 Wnc ]

(Tb − Tw )

0.25

(W/m2K)

(56)

where Ptot is the total pressure, Tb is the mixture (steam and helium/air) bulk temperature. This correlation is applicable for the following conditions: 0.3 m < L < 3.5 m, 1.5 atm. < Ptot < 4.5 atmosphere, and 10 oC < Tb − Tw < 50 oC The condensation heat transfer coefficient in presence of both air and helium [14] htot =

L0.05 [(3.7 + 28.7Ptot ) − (2438 + 458.3Ptot )log 10 (W He + Wair )]

(Tb − Tw )0.25

× [0.948 − 8.67WHe + 7.36WHe (W He + Wir )]

(57) where WHe and Wair are the mass fractions of helium and air respectively. Another correlation was given by Murase et al [65] that covered wider temperature range than Uchida correlation and is given by htot

⎛ Wnc = 0.47⎜⎜ ⎝ 1 − Wnc

⎞ ⎟⎟ ⎠

−1

(58)

The correlation applies for following ranges: 0.8≤

Wnc ≤30, 0.1≤ Ptot ≤ 0.35 MPa, 1 − Wnc

0.9 m ≤ L ≤ 0.4.2 m, 295K ≤ Tb ≤ 383 K

The correlation developed by Liu et al. [66] is given as 2.344 htot = 55.635 X steam Ptot0.252 ( Tb − Tw )0.307

(W/m2K)

(59)

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 29

Here Xsteam is the steam mole fraction, dimensionless; Ptot is the total pressure in Pa. This equation is valid for the following range of parameters 2.533 x 105 Pa < Ptot < 4.559 x 105 Pa; 0.873

4 oC < (Tb –Tw) < 25 oC

and 0.395 < Xsteam <

Correlations for Condensation inside Tube with Non-Condensable Gas There are two types of correlations for estimating the heat transfer coefficient for condensation inside vertical tube. In first type of correlations, the local heat transfer coefficient is expressed in the form of a degradation factor defined as the ratio of the experimental heat transfer coefficient (when noncondensable gas is present) and pure steam heat transfer coefficient. The correlations in general are the functions of local noncondensable gas mass fraction and mixture Reynolds number (or condensate Reynolds number). In the other type of correlation, the local heat transfer coefficient is expressed in the form of dimensionless numbers. In these correlations, local Nusselt number is expressed as a function of mixture Reynolds number, Jacob number, noncondensable gas mass fraction and condensate Reynolds number, etc. The degradation factor is defined as

h f = tot h

(60)

where, htot is the total heat transfer coefficient for the mixture of vapor and noncondensable and h the film condensation heat transfer coefficient for pure vapor. Here f may be the function of film Reynolds number (Ref) , vapor/noncondensable gas mixture Reynolds number (Reg), non-condensable gas mass fraction (Wnc), gas mixture Jakob number (Jag), Prandtl number (Prg). In Table 1, the degradation factors f in the correlation for condensation heat transfer in vertical tube with non-condensable gas by various investigators are presented. In Table 2, condensation correlations based on non-dimensional parameters are presented that are applicable to the vertical tube condensation with non-condensable gas and PCCS condenser. The correlations by Araki et al and Oh and Revankar provide correlations for the film condensation heat transfer coefficients. The correlation by Oh and Revankar applies for both pure steam and steam and air mixtures. This correlation also applies to all operational modes of the PCCS: complete condensation mode, through flow mode and cyclic venting mode. All other correlations in Table 1 and 2 apply to through flow operation of the PCCS.

30 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

Revankar

Table 1. Degradation factor for condensation correlations in vertical tube with non-condensable gas and vapor mixture Correlations Based on Degradation Factor f Authors Empirical Correlations Vierow & Schrock f = f1 ⋅ f 2 = 1 + 2.88 ⋅ 10 −5 ⋅ Re1g.18 ⋅ 1 − c ⋅ Wncb [67] where, c=10, b=1.0 for Wnc<0.063 c=0.938, b=0.13 for 0.063<Wnc <0.6 c=1.0, b=0.22 for 0.6<Wnc. Kuhn et al. [68] For Air:

(

)(

)

f = f1 f 2

-4 δ ⎛ ⎞ f 1 = f l_shear ⎜ 1 + 7.32 × 10 Re f ⎟ , f l _ shear = Nu δ shear ⎝ ⎠ 0.708 for Wair < 0.1 f 2 = (1 − 2.601W air )

(

0.292

f 2 = 1 − Wair

)

for Wair > 0.1

For Helium:

f = f1 f 2

-4 δ ⎛ ⎞ f 1 = f l_shear ⎜ 1 + 7.32 × 10 Re f ⎟ , f l _ shear = Nu δ shear ⎝ ⎠ 1.04 for 0.003<WHe<0.01 f 2 = (1 − 35.81W He )

( ) ) = (1 − 2.09W 0.292

f 2 = 1 − Wair f2

0.457

He

f 2 = ( 1 − WHe

f 1_shear

0.137

)

for Wair > 0.1 for 0.01<WHe <0.1 for WHe >0.1

- ratio of liquid film thickness with interfacial shear to film thickness without

interfacial shear, Ref -film Reynolds number, Wair -air mass fraction, WHe- helium mass fraction Park and No [46]

f = 0.0012Wnc-1.4 Ja -0.63 Re 0.24 f for 1715 < Reg < 21670, 12.4 < Ref < 633.6, 0.83 < Prg < 1.04, 0.111<Wnc<0.836, 0.01654< Ja <0.07351

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 31

Table 2. Condensation correlations in vertical tube with non-condensable gas and vapor mixture Siddique et al [45]

For Air:

Nu( x ) ≡

htot ( x )D = 1.137 ⋅ Re g0.404 Wair−1.105 Ja −0.741 kg

This relation applies for following range: 0.1 < Wair < 0.95, 445 < Reg < 22700, 0.004 < Ja < 0.07 For Helium:

Nu(x) = 0.537 Reg0.433WHe-1.249 Ja -0.624 The above correlation is applicable within the following range,

0.02 < WHe < 0.52, 300 < Araki et al [69]

hcond

Hassanein [70]

Re g < 11400,

− 0.67 ⎧ ⎪ 0.33⎛⎜ Pair ⎞⎟ ⎜ P ⎟ ⎪ ⎝ t ⎠ =⎨ ⎪ − 4 Re 0.8 ⎛⎜ Pair ⎪2.11 × 10 g ⎜ ⎝ Pt ⎩

0.004 < Ja < 0.07

for 650 < Re g < 2300 ⎞ ⎟⎟ ⎠

− 0.99 for 2300 < Re g < 21000

hcond (kW/m2K), Pair – air partial pressure, Pt -total pressure For air:

Nu(x) = 1.279 Re 0.256 Wair-0.741 Ja -0.952 g For helium:

Nu(x) = 2.244 Re0.161 Sc -1.652 Ja -1.038 g For mixture air and helium:

Nu( x ) = 1.279 Reg0.256 ( 1 − 1.681Wair )WHe0.741 Ja −0.952 . Maheshwari [71] Revankar et al. [72]

.15 Nu( x ) = 0.15 Re 0film Wair−0.85 Ja −0.8 Re g0.5

0.1 < Wair < 0.6, 8000 < Reg < 22700, 0.005 < Ja < 0.07 For turbulent flow: For laminar flow:

Nu cond = 0.08 ⋅ Wnc−0.9 ⋅ Re1g.1 ⋅ exp( −42.5 ⋅ Ja g )

Nu cond = 160 ⋅ Wnc−0.9 ⋅ exp( −42.5 ⋅ Ja g )

for 0≤ Wnc ≤0.5, 0 < Reg < 4x104, 0.002 < Ja g< 0.05.

Nomenclature A Cp D f

Area Specific heat Diameter Friction coefficient

32 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

g Gr h hfg Ja k L m N Nu P Pr q” r R Ra Re t T u V v W X x y z

Gravitational constant Grashoff number Heat transfer coefficient Latent heat of vaporization Jacob number Thermal conductivity Length, height Mass flow rate Number Nusselt number Pressure Prandtl number Heat flux Radial coordinate Radius or gas constant for a specific gas Rayleigh number Reynolds number Time Temperature Axial velocity Volume Radial velocity or specific volume Noncondensable gas mass fraction Mole fraction Independent variable Wall coordinate or dependent variable Axial or streamwise coordinate

Greek Symbols Γ Mass flow rate per unit length α Thermal diffusivity δ Film thickness

δH δM

Boundary layer thickness for temperature Boundary layer thickness for velocity

δW

Boundary layer thickness for noncondensable gas mass fraction Angle Dynamic viscosity Kinematic viscosity Density Surface tension Shear stress

θ µ ν ρ σ τ

Revankar

Passive Condensers

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 33

Subscripts b Bulk c Condensation cond Gas region condensation f Film Gas g He Helium l Liquid nc Noncondensable sat Saturation tot Total v Vapor w Wall Superscript Average value

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

V. S. Nikolayev, D. Beysens, A. Gioda, I. Milimouka, E. Katiushin and J. -P. Morel, “Water recovery from dew”, Journal of Hydrology vol. 182 (1996) pp. 19-35, 1996. G. Sharan, Dew harvest to supplement drinking water sources in arid coastal belt of Kutch, New Delhi: Cambridge University Press, 2006. O. Clus, P. Ortega, M. Muselli, I. Milimouk and D. Beysens, “Study of dew water collection in humid tropical Islands”, Journal of Hydrology vol. 361, pp. 159– 171, 2008. R.K. Shah and A.D. Giovannelli, Heat pipe heat exchanger design theory heat transfer equipment design, Washington DC: Hemisphere pp. 609–653, 1988. L. L. Vasiliev, “Heat pipes in modern heat exchangers”, Applied Thermal Engineering, vol. 25 pp.1–19, 2005. H.F. Smirnov, and B.V. Kosoy, “Refrigerating heat pipes”, Applied Thermal Engineering vol. 21 pp. 631-641, 2001. General Electric Company, “Refrigeration passive defrost system”, US Pat. 5669222 - Filed Jun 6, 1996. D. N. Anderson and J. W. Lund, Direct Utilisation of Geothermal Energy: A Technical Handbook. Geothermal Resources Council Special Report No. 7. 1979. R. Harrison, “The design and economics of European geothermal heating installations”, Geothermics, vol. 23, No. 1, pp. 61-71, 1994 M. Shiraishi, K. Kikuchi, and T. Yamanishi, “Investigation of heat transfer characteristics of a two-phase closed thermosyphon”, Proc. 4th Int. Heat Pipe Conf., 1981, pp. 95–104.

34 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

[11] [12] [13] [14] [15] [16]

[17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

Revankar

H. Farsi, “Experimental and theoretical analysis of the behavior of a two-phase closed thermosyphon in transient regimes. Response to requests of a chemical reactor”, Ph.D. Thesis, Paul Sabatier University, Toulouse, France, 2002. M. Gavrilas, N. E. Todreas, and M. J. Driscoll, “Containment passive-cooling design concepts”, Progress in Nuclear Energy, vol. 32, no. 3-4, pp. 647-655, 1998 S. Oh and S. T. Revankar, “Complete condensation in a vertical tube passive condenser”, Int. Comm. Heat Mass Transfer, vol. 32, pp. 593-602, 2005. G. D. Spacecraft, Thermal Control Handbook: Fundamental Technologies, El Segundo, CA: The Aerospace Press, 2002. G. P. Peterson, An Introduction to Heat Pipes Modeling, Testing, and Applications, New York: John Wiley and Sons, Inc., 1994. L.L. Vasiliev, A. Antukh, V. Maziuk, A. Kulakov, M. Rabetsky, L. Vasiliev Jr., and S. M. Oh, “Miniature heat pipes experimental analysis and software development”, in: Proceedings of the 12th International Heat Pipe Conference ‘‘Heat Pipes Science, Technology, Application’’, Moscow–Kostroma–Moscow, Russia, 19–24 May 2002, pp. 329–335. V. Maziuk, A. Kulakov, M. Rabetsky, L. Vasiliev and M. Vukovic, “Miniature heat––pipe thermal performance prediction tool––software development”, Appl. Thermal Eng. vol. 21 pp. 559–571, 2001. Y. F. Maydanic, “Loop heat pipes”, Appl. Thermal. Eng., vol. 25, pp. 635–657, 2005. L.L. Vasiliev, D.A. Mishkinis, A.A. Anukh and L.L. Vasiliev Jr., “Solar–gas solid sorption refrigerator”, J. Adsorp., Vol. 7 pp. 149–161, 2001. M. Oomi , T. Fukumoto, M. Sugiura , K. Nakayama and K. Namba and T. Kobayashi “State-of-the-art technologies of micro heat-pipe heat-sinks for notebook PCs”, Furukawa Review, No. 21 pp. 1-18, 2002. R. Harrison, “Design and performance of direct heat exchange geothermal district heating schemes”, Geothermics, vol. 16, no. 2, pp. 197-211, 1987. F. D. Haynes, J. P. Zarling, and G. E. Gooch, “Performance of a thermosyphon with a 37-meter-long, horizontal evaporator”, Cold Regions Science and Technology, vol. 20, pp. 261-269, 1992. S. A. Kalogirou, “Solar thermal collectors and applications”, Progress in Energy and Combustion Science, vol. 30, pp. 231-295, 2004. S.A. Nada, H.H. El-Ghetany and H.M.S. Hussain, “Performance of two-phase closed thermosyphon solar collector with shell and tube heat exchanger”, J. Appl. Therm. Eng. vol. 24, pp. 1959–1968, 2004. T.Y. Bong, K.C. Ng and H. Bao, “Thermal performance of a flat-plate heat pipe collector array”, J. Solar Energy vol. 50, pp. 491–498, 1993. T. A. Ozbolt, US Lab Architecture Control Document, Volume 7: Temperature and Humidity Control, Revision New, D683-14719-1-7, Huntsville, Alabama: Boeing Defense and Space Group, Missile & Space Division, December 20, 1996.

Passive Condensers

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 35

[27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]

[42]

[43]

M. M. Hasan, Lutful I. Khan, V. Nayagam and R. Balasubramaniam, Conceptual Design of a Condensing Heat Exchanger for Space Systems Using Porous Media, NASA Report NASA/TM—2006-214130, May 2006. P. Cereceda, R. Schemenauer and M. Suit, “An alternative water supply for Chilean coastal desert villages”, Int. J Water Resour. Dev., vol. 8, pp. 53–59, 1992. R. Schemenauer and P. Cereceda, “Fog collection role in water planning for developing countries”, Natural Resources Forum vol. 18, pp. 91–100, 1994. W. C. Wells, An essay on dew, and several appearances connected with it, 2nd ed. London: Taylor and Hessey, 1815. M. Muselli, D. Beysens and I. Milimouk, “A comparative study of two large radiative dew water condensers”, J. Arid Environ., vol. 64, pp. 54–76, 2006.. T. Nilsson, “Initial experiments on dew collection in Sweden and Tanzania”, Sol. Energy Mater. Sol. Cells, vol. 40, pp. 23–32, 1996. J. L. Monteith, “Dew”, Quart. J. Royal Meteorol. Soc. vol. 83, pp. 322–341, 1957. T. Nilsson, W. E. Vargas, G. A. Niklasson and C.G. Granqvist, “Condensation of water by radiative cooling”, Sol Energy, vol. 5(f), pp.310–7, 1994. W. E. Vargas, E. M. Lushiku, G. A. Niklasson and T. M. J. Nilsson, “Light scattering coatings: theory and solar applications”, Sol Energy Mater. Sol. Cells, vol. 54, pp. 343–50, 1998. D. Beysensa,_ M. Musellic, I. Milimoukd, C. Ohayone, S. M. Berkowiczf, E. Soyeuxg, M. Mileta and P. Ortega, “Application of passive radiative cooling for dew condensation”, Energy, vol. 31, pp. 2303–2315, 2006. H. J. Bruschi, “AP600-safety through simplicity”, in Proceedings of the International Topical Meeting on Advanced Reactors Safety. ANS. Part vol.1, La Grange Park, IL, USA, 1997, pp.3-8. GE Nuclear Energy, SBWR Standard Safety Analysis Report, Report No. 25A5113 Rev. A, August,1992. US NRC website: http://www.nrc.gov/reactors/new-licensing/licensereviews/ap1000.html#reviews 2002, [accessed July 12, 2008]. US NRC website: http://www.nrc.gov/reactors/new-licensing/licensereviews/esbwr.html#reviews 2002, [accessed July 12, 2008] S. T. Revankar and S. Oh, Analytical And Experimental Study Of The Effects Of Non-Condensable In A Passive Condenser System For The Advanced Boiling Water Reactor, Department of Energy, Technical report: DE-FG07-00ID13928, September 2003. H. Uchida, A. Oyama and Y. Togo, “Evaluation of post-incident cooling systems of light-water power reactors”, in Proceedings of the Third International Conference on the Peaceful Uses of Atomic Energy, Geneva, August 31September 9, 1964, Vol. 13, United Nations, New York, 1965, pp. 93-104. K.M. Vierow, “Behavior of steam-air systems condensing in concurrent vertical downflow”, M.S. thesis, University of California at Berkeley, 1990

36 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

[44] [45] [46]

[47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60]

Revankar

S. Z. Kuhn, “Investigation of heat transfer from condensing steam-gas mixtures and turbulent films flowing downward inside a vertical tube’, PhD thesis, University of California at Berkeley, 1995. M. Siddique, “The effects of noncondensable gases on steam condensation under forced convection conditions”, PhD thesis, Massachusetts Institute of Technology, 1992. H.S. Park and H.C. No, “A condensation experiment in the presence of noncondensables in a vertical tube of passive containment cooling system and its assessment with RELAP5/MOD3.2”, Nuclear Technology, vol. 127, pp. 160 -169, 1999. S. Oh and S. T. Revankar, “Effect of noncondensable gas in a vertical tube condenser”, Nuclear Eng. Design, vol. 235 pp. 1699 – 1712, 2005. S.Oh and S. T. Revankar, “Experimental and theoretical investigation of film condensation with noncondensable gas”, Intern. J. Heat Mass Transfer, vol. 49, pp. 2523-2534, 2006. W. Nusselt, “Die oberflachenkoondensation des wasserdampfes”, Z. Ver. Deut.Ing., vol. Vol. 60, pp. 541-546, 1916. W. M. Rohsenow, “Heat transfer and temperature distribution in laminar film condensation”, Trans ASME, vol. 78, pp. 1645-1654, 1956. S. S. Kutateladze, Fundamentals of heat transfer, New York: Academic Press, 1963. D. A. Labuntsov, “Heat transfer in film condensation of pure steam on vertical surfaces and horizontal tubes, Tefloenergetika, vol. 4, pp. 72-84, 1957. V.K. Dhir and J.H. Leinhard, “Laminar film condensation on plane and axisymmetric bodies in non-uniform gravity, J. Heat Transfer, vol. 93, pp. 97103, 1971. J. Gerstmann and P. Griffith, “Laminar film condensation on underside of horizontal and inclined surfaces”, Int. J. Heat Mass Transfer, vol. 10, pp. 567580, 1967. B. G. Nimmo and G. Leppert, “Laminar film condensation on a finite horizontal surfaces”, in Proc. 4th Int. Heat Transfer Conf., Paris, Vol. 6, Cs2.2 , 1970. K. O. Beatty and D.L. Katz, “Condensation of vapors on outside of finned tubes”, Chem. Eng. Prog., vol. 44, pp. 55-70, 1948. J. C. Chato, Laminar Condensation Inside Horizontal and Inclined Tubes, ASHRAE J., 4, 52-60, 1962. S. T. Revankar and S. Oh, Analytical And Experimental Study Of The Effects Of Non-Condensable In A Passive Condenser System For The Advanced Boiling Water Reactor-Third Year Report, PU/NE-03-12, September 2003. T. Spendel, “Laminar film condensation heat transfer in closed two-phase thermosyphons”, In:. Advances in heat pipe technology. Reay DA, editor, Oxford: Pergamon Press, pp. 163–73, 1981. U. Gross and E. Hahne, “Condensation heat transfer inside a closed thermosyphon-generalized correlation of experimental data”, in: Proceedings of the 6th IHPC, Grenoble, France, 1987, pp.618–23.

Passive Condensers

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 37

[61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72]

J. C. Y. Wang and Y. Ma, “Condensation heat transfer inside vertical and inclined thermosyphons”, ASME Trans J Heat Transfer, vol. 113, pp. 777-780, 1991 H.M.S. Hussein, M.A. Mohamad and A.S. El-Asfouri, “Theoretical analysis of laminar-film condensation heat transfer inside inclined wickless heat pipes flatplate solar collector”, Renewable Energy, vol. 23, pp. 525–535, 2001 T. Tagami, Interim Report on Safety Assessment and Facilities, Etablishment Project for National Japanese Atomic Energy Research Agency, Report No. 1, June 1965, A. A. Dehbi, “The effect of noncondensable gases on steam condensation under turbulent natural convection conditions”, Ph.D. thesis, Massachusetts Institute of Technology, 1991. M. Murase, Y. Kataoka and T Fujii, “Evaporation and condensation heat transfer with noncondensable gas present”, Nuclear Eng. Design, Vol. 141, pp. 135-143, 1993. H. Liu, N. E. Todreas and M. J. Driscoll, An experimental investigation of a passive cooling unit for nuclear plant containment, Nuclear Eng. Design, vol. 199, pp. 243-255, 2000. K. Vierow and V. E. Schrock, “condensation in a natural circulation loop with noncondensable gas present: Part I - Heat transfer”, Japan - U. S. Seminar on Two-Phase Flow Dynamics, Berkeley, CA, (14 pp.) 1992. S. Z. Kuhn, V.E. Schrock and P.F. Peterson, “An investigation of condensation from steam–gas mixtures flowing downward inside a vertical tube”, Nuclear Eng. Design, vol. 177, pp. 53–69, 1997. H. Araki, Y. Kataoka and M. Murase, "Measurement of condensation heat transfer coefficient inside a vertical tube in the presence of noncondensable gas", J. Nuclear Science and Technology, Vol. 32, pp. 78-91, 1995. H. A. Hassanein, M.S. Kazimi and M. W. Golay, "Forced Convection In-Tube Steam Condensation in Presence of Noncondensable Gases”, Int. J. Heat Mass Transfer, vol. 39, pp. 2625-2639, 1996. N.K. Maheshwari, “Studies on passive containment cooling system of Indian advanced heavy water reactor”, Ph. D. thesis, Tokyo Institute of Technology, Tokyo, Japan, 2006. S. T. Revankar, S. Oh, W. Zhou and G. Henderson, “Condensation correlation for a vertical passive condenser system”, in Proc. 2008 International Congress on Advances in Nuclear Power Plants (ICAPP '08), American Nuclear Society, ANS Annual Meeting, Anaheim, California, USA, June 8-12, 2008.

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38

Chapter 2 Phase Inversion in Liquid-Liquid Pipe Flows Panagiota Angeli∗ Department of Chemical Engineering, University College London Torrington Place, London WC1E 7JE, UK.

Abstract Phase inversion is the phenomenon where the continuous phase of a liquid-liquid dispersion changes to become dispersed and the dispersed becomes continuous. Phase inversion has important implications for a number of industrial applications where liquid-liquid dispersions are used, since the change in the mixture continuity affects drop size, settling characteristics, heat transfer and even the corrosion behaviour of the mixture. In pipeline flows, phase inversion is usually accompanied by a step change or a peak in pressure drop. The chapter reviews the work on phase inversion during the pipeline flow of liquid-liquid mixtures when no surfactants are present. Investigations have revealed that in pipes a transitional region occurs during inversion from one phase continuous to the other, characterized by complex flow morphologies (multiple drops, regions in the flow with different continuity) and even stratification of the two phases over a range of dispersed phase volume fractions. The observations on the phase inversion process in pipelines are discussed and the parameters which affect the phenomenon are summarized. In addition, the various models available for predicting phase inversion are analyzed, as well as the methodologies developed to account for the transitional region with the complex morphologies and the flow stratification and to predict pressure drop during inversion.

Introduction Immiscible liquid-liquid dispersions with one phase usually aqueous (e.g. water) and the other organic (e.g. oil) are widely employed in the oil, chemical, pharmaceutical and food industries. Potentially two types of dispersions can be obtained, namely oil-inwater (O/W) and water-in-oil (W/O). Phase inversion is then defined as the phenomenon whereby the phases of a liquid-liquid dispersion interchange such that the dispersed phase inverts to become the continuous one and vice versa. Liquid-liquid dispersions have wide applications in industries and a well controlled phase inversion is essential. For example in solvent extraction in mixer-settlers, it is extremely undesirable to have phase inversion to occur because it can delay the settling process by changing the properties of the continuous phase and the drop size. On the other hand, phase inversion is desirable in some operations, such as the preparation of waterborne dispersions of polymer resin. In the petroleum industry where water and oil are often transported together in pipelines, the change in the phase continuity will modify the rheology of the mixture and will affect the corrosion and injection of inhibiting agents as well as the heat transfer rates which depend on the nature of the continuous phase. In addition, an increase in pressure gradient during inversion has also ∗

Email address: [email protected]

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

Phase Inversion in Liquid-Liquid Pipe Flows

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 39

been reported which can result in substantial decrease in oil productivity and pipeline capacity. Phase inversion has been found to occur at a certain critical volume fraction of the dispersed phase (phase inversion point). The mechanism of inversion is still not well understood. In general it is accepted that at low volume fractions of the dispersed phase, stable dispersions form where the drop break up and coalescence processes are in equilibrium. As the dispersed phase fraction increases the drops grow in size and their concentration increases until a critical phase fraction where inversion happens. The transition, however, seems to be a gradual rather than a catastrophic phenomenon. Secondary (droplets of continuous phase inside the dispersed phase drops) and multiple dispersions can start forming at fractions below the phase inversion point while inversion can appear initially locally and regions of different continuity can establish before the new continuous phase spreads in the whole mixture. Previous experimental results have also revealed the existence of a hysteresis effect between inversion from an organic and from an aqueous continuous solution, which manifests itself by the formation of a so-called ambivalent region, i.e. the range of organic (or dispersed) phase volume fraction wherein either the organic or the aqueous phase can be continuous. The importance of predicting the occurrence of phase inversion has led (since the first report of phase inversion by Rodger et al. [1]) to a large number of experimental and modelling work particularly in stirred vessels. The experiments have indicated that the phase inversion point is system-specific and can be affected by a number of physical and physicochemical parameters, such as liquid properties, container geometry and initial conditions.

Phase Inversion in Stirred Vessels Liquid-liquid dispersions in stirred vessels are very frequently used in the chemical industry. Phase inversion mostly occurs when the dispersed phase holdup is increased in order to obtain higher interfacial areas. There is a large amount of work on the parameters that affect inversion in stirred vessels with no surfactants present, because they are industrially important while at the same time they are easier to study compared to pipeline flows; comprehensive reviews have been given in a number of publications (e.g. [2]). The experimental work in liquid-liquid dispersions revealed the existence of the ambivalent region over which either liquid phase can be the stable dispersed phase [39]. The ambivalent region is usually presented as a plot of the holdup of either the organic or sometimes the dispersed phase at inversion against agitation speed. An example of the former representation is given in Fig. 1a where the ambivalent region is the area between the two inversion curves. The upper curve is obtained by increasing the fraction of the dispersed organic phase at a certain agitator speed until phase inversion occurs. The lower curve is obtained through a similar procedure by changing the continuous phase to the organic one and increasing the fraction of the aqueous phase dispersed in it. An intermediate inversion curve, in between the other two, can also be found by monitoring the continuity of liquid-liquid mixtures resulting from the direct mixing of the required volumes of the liquids at different phase fractions. The

40 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

Angeli

dispersion can only exist as benzene-in-water below the lower curve and as water-inbenzene above the upper curve. In between the two curves, in the ambivalent region, depending on initial conditions and dispersion history either the aqueous or the organic phase can be continuous. The alternative way of representing the ambivalent region is given in Fig. 1b where the volume fraction of the initial dispersed phase at inversion is plotted against the agitation speed, regardless of which phase was the dispersed one. This method clearly indicates the hysteresis effect.

a) Phase inversion in a benzene-water system

b) Phase inversion in a nitrobenzene–water system

Figure 1. Ambivalent region represented in terms of (a) organic phase volume fraction (from [7]) and (b) dispersed phase volume fraction (from [9]).

In stirred vessels phase inversion and the ambivalent region can be affected by various factors. Viscosity is considered to be important and Selker & Sleicher [3] have found that as the viscosity of one phase increases, its tendency to be dispersed also increases and both the minimum fraction that the phase can be continuous as well as the maximum fraction that it can be dispersed both increase. A decrease of the interfacial tension can also lead to a widening of the ambivalent region [10,11]. Low density contrast between liquid pairs seems to show little effect on inversion [3,11], while systems in which there are large density differences between the phases were found to show an increased tendency to invert [1,8]. However, it is not only the fluid properties but also the stirred vessel geometric configuration (e.g. type of impeller), the vessel and impeller material wettability and the experimental set up (e.g. the phase that the impeller is in at the beginning of the experiment) that have been found to affect phase inversion and the limits of the ambivalent region [7-9,11,12]. At high impeller speeds the inversion holdup becomes independent of any operational and geometric parameters and is only affected by the physical properties of the liquid pair [6,9]. At high dispersed phase fractions and before inversion appears secondary dispersions (continuous phase trapped as droplets within the dispersed drops) have been observed [7,13]. Interestingly, O/W/O dispersions are much more likely to occur than

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W/O/W. The different morphology and lack of symmetry between water and oil continuous dispersions is generally considered the reason for the appearance of the ambivalent region [7]. Secondary dispersions increase the effective dispersed phase hold up, since part of the continuous phase is trapped within the dispersed, and can cause inversion at lower dispersed phase fractions than when they are not present. Kumar [14] attributed the formation of secondary dispersions to the differences of dielectric constants of the two immiscible phases. Oil drops experience repulsive forces due to the overlapping of the electrical double layers that form around the drops in the water phase and have low coalescence efficiency. In contrast, water drops in oil, of low dialectric constant, do not experience such repulsion and have high coalescence efficiencies; at high dispersed phase fractions many water drops will therefore coalesce and trap some oil continuous phase within them, forming secondary O/W/O dispersions.

Phase Inversion during Pipeline Flow The investigations on phase inversion in pipelines have been significantly fewer compared to those in stirred vessels and have generally been carried out for fluid pairs with no surfactants added. Two main categories of phase inversion experiments can be defined (the terminology is based on Piela et al. [15]). • Direct experiments where a certain volume fraction of the phases is introduced in the pipeline and the continuity of the mixture and the flow morphology are observed. In most cases during these experiments the mixture velocity is kept constant (i.e. flowrates of both phases are varied) but there is also some work where the continuous phase flowrate is kept constant while that of the dispersed phase is increased, increasing the overall mixture velocity. • Continuous experiments where the mixture starts from one phase as continuous and the fraction of the dispersed phase is gradually increased until phase inversion is obtained. Since inversion during pipeline flow is accompanied by abrupt changes (quite often a peak) in pressure drop, measurements of this parameter, rather than the conductivity of the mixture, have often been used to identify the phase inversion point. However, as will be discussed below, recent work suggests that pressure drop tends to change and even fluctuate over a region of volume fractions between the two types of dispersions (oil and water continuous) and not at just one fraction (phase inversion point). Identifying therefore the inversion point only from pressure drop measurements can be misleading. Direct experiments In these experiments the two fluids enter the test section together at high velocities to create dispersions while usually phase continuity and pressure drop are monitored at different phase fractions. The fluids usually join at the inlet at the required flowrates to achieve a certain volume fraction which makes these experiments similar to those in

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stirred vessels that yield the intermediate inversion curve; no ambivalent region is expected in this case. In a variation of this approach, Ioannou et al. [16] and Ngan et al. [17,18] started with one phase at high volume fraction which made it continuous and a small fraction of the other phase (dispersed). Without stopping the experiment the flowrates of the two phases were gradually adjusted so that the dispersed phase fraction increased in small steps, for the same mixture velocity, until change in the mixture continuity was observed and beyond. This approach sets the initial continuous phase and makes it possible to start from oil continuous and from water continuous mixtures; as a result ambivalent regions were found. Standard inlets such as T- [15] and Y- junctions [16,19] have been used. Ioannou et al. [16] and Ngan et al. [17,18] fitted their Y-inlets with plates to ensure that the fluids joined in a stratified manner and all the mixing occured downstream of the inlet due to flow turbulence. When the dispersion is not formed at the inlet then a certain development length is required. However, the work by Ioannou et al. [16], where conductivity probes were used at different locations along the pipe, demonstrated that the dispersion had similar characteristics in all locations studied and at the high flowrates needed to sustain dispersed flow the development length was very short [24]. Hu and Angeli [19] used a perforated plate after a Y-inlet to mix the fluids and thus reduce the length required to create the dispersion. In the case of Arirachakaran et al. [20] and Pal [21] the dispersion was created in a stirred vessel before it was introduced in the test section. In their majority the above studies reveal that between the two fully dispersed flows, oil continuous and water continuous at low and high water fractions respectively, there is a transitional region where different areas of continuity and complex two-phase structures are present [15,19,22-24] used a conductivity probe in the middle of the pipe and a hot film probe on the pipe wall to monitor inversion during vertical flow. They found that as the dispersed phase fraction increased, inversion started in the middle of the pipe with the formation of complex structures and large continuous regions of the one or the other phase and was completed when the continuity of the phase next to the wall had changed. The large structures in the middle of the pipe, however, existed for slightly larger dispersed phase fractions even after inversion was complete. Such structures were also observed by Liu et al. [22] in vertical flow experiments using Laser Induced Fluorescence (LIF) (see Fig. 2). To observe the morphology of the mixture Piela et al. [15,24] used sampling. Depending on their size, the complex structures were divided to: multiple drops (droplets of the continuous phases within the dispersed drops); pockets, which are areas of continuity of one fluid, that can contain several drops of the other phase and are not necessarily spherical; regions, which are areas of continuity larger than the pockets and enclose pockets and drops of the other phase. Interestingly, only O/W/O multiple drops were seen during inversion from oil to water continuous mixtures while multiple drops did not form in the water to oil continuous inversion, similar to what was found in stirred vessels [7].

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Figure 2. Time series of the transitional region starting from an oil continuous flow at mixture velocity 2.1 m/s and input oil fraction 49% (from [22]).

Figure 3. Pressure gradient and normalised conductivity from a ring and a local probe against input water fraction for oil-water flow at 4 m/s mixture velocity. The ring probe is located at the perimeter of the pipe while the local conductivity probe is located in the middle of the pipe. The arrow indicates the direction of the experiment from water to oil continuous.

Tyrode et al. [25] had shown that the formation of multiple drops depends on the value of the HLD-factor (Hydrophylic-Lipophilic Deviation from an optimum formulation) of the mixture. For HLD<0 only O/W/O and O/W dispersions are possible. In horizontal flow experiments because of the effect of gravity some stratification of the flow is expected in the transitional region where large areas of different continuity are present. Ngan et al. [17,18] investigated the configuration of the flow in a horizontal pipe using a local and a ring conductivity probes. The local probe was located in the middle of the pipe and indicated the continuity in that region while the ring probe, placed at the pipe perimeter, would give a non-zero signal when there was a water continuous phase in contact with the pipe wall. In Fig. 3 it can be seen that starting from a low input oil fraction a water continuous dispersion is formed (signals

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from both probes are high). At an oil fraction of about 46%, inversion appears at the upper part of the pipe (the signal of the local probe acquires the oil continuous zero value but the non-zero signal of the ring probe indicates that there is still a water layer in contact with the pipe wall) and the mixture obtains a dual continuous configuration, i.e. oil continuous at the top of the pipe and water continuous at the bottom of the pipe. The water continuous layer is thin and could contain a small amount of oil drops. The water layer persists until about 72% oil fraction after which the signal of the ring probe also reaches a zero value and the mixture becomes oil continuous throughout the pipe cross section. The variations in the flow configuration and the formations of zones with fluid with different continuity in the transitional region result in fluctuations in the flow properties. Ioannou et al. [16] used conductivity ring probes to monitor the continuity of the mixture in horizontal pipes. They found that while the indications of the probes where constant and fluctuated very little when the mixture was fully dispersed as soon as the phase fraction reached the value where inversion finally occurred the signals started to fluctuate significantly. 3

0.7

Pressure drop [kPa]

Impedance signal [-]

0.8

0.6 IP3

0.5 0.4 0.3 0.2

IP1

0.1

2.5 2 1.5 1 0.5 0

0 0

100

200

300

400

500

600

0

100

(a) Conductivity probe values

200

300

400

500

Time [s]

Time [s]

(b) Pressure drop

Figure 4. Time series at the phase inversion point (65% input oil fraction) of (a) the dimensionless signals of two conductivity ring probes located at 5 m (IP1) and 10 m (IP3) from the test section inlet and (b) the pressure drop. Experiments at a 60mm ID acrylic pipe (from [16]).

This can be seen in Fig. 4a for a transition from an oil continuous to a water continuous dispersion. These fluctuations lasted for about 350 s and during this time the average value of the signal changed from low (indicating oil continuous phase) to high (indicating water continuous phase). After this time the fluctuations reduced significantly and the conductivity value settled to that of a water continuous mixture. Similar behaviour can be seen in Fig. 4b for the pressure drop. Again pressure drop fluctuated significantly for about 350 s before settling to a new, lower, value where the fluctuations were very small. Hu and Angeli [19] using a conductivity wire probe in the middle of the pipe, also found fluctuations in conductivity in the transitional region. Piela et al. [15] found oscillations in pressure drop in the transitional region that corresponded to changes in the mixture conductivity measured with two conductors mounted in the pipe in the vertical and horizontal directions. They argued that the variations in the oil and water

600

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continuous regions caused the fluctuations in the pressure drop which, with a feedback effect, influenced the inlet flowrates that in turn caused further variations in the regions of continuity. Continuous experiments Piela et al. [15, 24] introduced the initial dispersed phase in the form of drops in the continuous one through holes at the periphery of the test section at the inlet. The same amount of the two-phase dispersion was removed downstream in order to keep the mixture flowrate constant. These experiments are similar to the ones that give the upper and lower inversion curves in stirred vessels. An ambivalent region can, therefore, be obtained when starting from oil and from water continuous dispersions. Photographs of samples indicated that, similar to the direct experiments, at low volume fractions of the dispersed phase, individual single drops were present. As the dispersed phase fraction increased the mixture entered a transitional region where drops, pockets and regions of different continuity appeared until eventually the other phase became the continuous one. Conductivity values in the transitional region were between the high ones of the water continuous dispersions and the low ones of the oil continuous dispersions, indicating that water and oil continuous regions alternated through the conductivity probe. The dispersed phase volume fraction, where inversion appeared, increased with decreasing injection phase volume fraction, χ (ratio of the injected dispersed phase flowrate to that of the continuous phase). The direct experiments can, therefore, be considered as a limiting case of the continuous ones for very high χ, where inversion takes place before one cycle in the pipe loop is completed (see Fig. 5). This is consistent with the low dispersed phase fractions at inversion obtained with the direct experiments (between 50-60%).

Figure 5. Variation of upper and lower phase inversion curves with injection phase volume fraction, χ. The phase inversion point from a direct experiment is also indicated (from [15]).

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Piela et al. [24] also carried out experiments where the injection of the dispersed phase was interrupted just before inversion occurred. In that case, certain time elapsed before inversion which decreased when the amount of the dispersed phase at which injection stopped increased. According to the authors, the results indicate that there are two mechanisms that increase the dispersed phase volume fraction and eventually lead to phase inversion; one is the growth of multiple drops by the entrainment of the continuous phase and the other is the injection of the dispersed phase. The former is very slow and usually not significant. Only at very low injection rates will both mechanisms become important in which case the length of the test section may influence the phase inversion point.

Pressure gradient [kPa/m]

Pressure drop Many investigators have observed an increase in pressure gradient [15,16,20,24] or viscosity [21] as the system approaches phase inversion, which then decreases as the new continuous phase is established (see Fig. 6). In Fig. 6 the maximum value of pressure drop represents the time average of the fluctuating values seen in Fig. 4. Piela et al. [15] argued that in the transitional region the areas of different continuity that form in the mixture (multiple drops, pockets, regions) interact, entrap parts of the other continuous phase, coalesce and break up causing an increase in the average effective viscosity and the pressure drop. In contrast, no peak in pressure gradient was seen by Ngan et al. [18] (see Fig. 3) and Hu and Angeli [19], but only a step change in pressure gradient when the continuous phase changed from oil to water. 1.6 1.4 1.2 1 0.8 0.6

Oil Water

0.4 0.2 0 0

20

40

60

80

100

Oil fraction [%] Figure 6. Pressure gradient when the experiment starts from oil continuous and from water continuous flows at 4 m/s in acrylic pipe with 60 mm ID (from [16]).

Parameters affecting phase inversion In contrast to stirred vessels, there is very little reported on the effect of various parameters on phase inversion in pipeline flows. Piela et al. [15] found that the phase inversion point did not depend on Reynolds, Weber or Froude numbers or the injection velocity of the dispersed phase when the mixture velocity was sufficiently large (above 2m/s in their system). It did, however, depend on the injection phase volume fraction, χ.

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This seems to suggest that phase inversion depends on the morphology/size of the dispersed phase; a lower addition rate of the dispersed phase allows the drops to break up and perhaps makes them more stable against coalescence that would lead to the larger region structures and to phase inversion. Little effect on the inversion point of the mixture velocity was also found by Ioannou et al. [16]. Interestingly, these investigators found that the pipe material could affect phase inversion, while the pressure gradient peak around phase inversion was sharper in an acrylic pipe compared to a steel one with the same diameter. Between large and small pipes of the same material, inversion appeared at similar phase fractions but the volume fraction range over which the peak in pressure gradient occurred was wider in the small pipe. Ambivalent region It should be made clear that the ambivalent region is not the same as the transitional region. Ambivalent region is the difference between the inversion points obtained when starting the inversion process from an aqueous continuous and from an organic continuous mixture. The transitional region, on the other hand, signifies that inversion does not happen at one particular phase fraction but over a range of phase fractions and has mainly been observed in pipeline flows. Ambivalent region is not always observed in pipelines. Ioannou et al. [16] in direct experiments in large pipes (see Fig. 6) and Piela et al. [15] in continuous experiments found an ambivalent region. However, no ambivalent region was seen by Ioannou et al. [16] in experiments carried out in a small acrylic pipe. In addition, no ambivalent region was seen by Hu and Angeli [19] in vertical flow studies, both upward and downward, and by Ngan et al. [18]. In these studies the changes in the mixture continuity over the inversion transitional region occurred at the same fractions when starting either from an oil continuous or from a water continuous dispersion. Piela et al. [15] found that the width of the ambivalent region reduced with increasing injection phase volume fraction but the mixture velocity or the dispersed phase injection velocity did not affect it. The pipe material and the mixture velocity have also been found to have some effect on the width of the ambivalent region [16]. A slightly different type of experiment was carried out by Hu and Angeli [19] in vertical pipes where the initial continuous phase flowrate was kept constant while that of the dispersed was increased until phase inversion appeared. In upward flow the critical oil fraction for inversion decreased with mixture velocity while in downward flow it increased which was attributed to the different in-situ phase fractions in the two cases caused by gravity induced slip between the phases. The critical fractions however, became almost constant at high mixture velocities.

Phase Inversion Mechanisms and Proposed Models Several physical mechanisms have been postulated to explain phase inversion and the existence of the ambivalent region and a number of predictive models have been suggested. The different approaches followed are detailed below.

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Empirical correlations Quinn & Sigloh [26] found the organic phase holdup at inversion, ϕ IO , obtained in oil-in-water dispersions, decreases with the increase in agitation speed before reaching a constant value at high agitation speeds, according to: ϕ IO = ϕ 0 +

c P

(1)

where φ0 is the asymptotic phase inversion holdup at high agitation speed, P is the 3 power input ( ∝ ρ m N I where ρm is mixture density and NI is the agitation speed) and c is a constant determined by the physical properties of the system which could be approximately related to the Weber number. Arirachakaran et al. [20] based on a number of experimental data in pipe flows from various investigators suggested the following equation for the critical input water fraction, ϕ IW , at inversion: ϕ IW =

µ U SW = 0.5 − 0.1108 log O U SW + U SO µW

(2)

where µO and µW are the oil and water viscosities, and USO and USW are the oil and water superficial velocities, respectively. Models based on drop breakage and coalescence rates It has been found that factors which affect drop coalescence and break up , such as agitation speed, wettability, impeller type, liquid properties and electrostatic interactions, also affect the phase inversion point and the width of the ambivalent range ( [2]). This has led investigators to consider phase inversion as an imbalance between break up and coalescence of the dispersed drops [5, 27]. In a dilute O/W dispersion, for example, a dynamic balance will exist between drop break up and coalescence. An increase of the oil phase volume fraction will lead to an increase of the coalescence rate due to an increase in the collision frequency, and also to an increase of drop break up rate because larger drops are present and in a stirred vessel more drops pass through the high shear impeller region. Up to a certain volume fraction which depends on the system properties, coalescence and break up can still reach a dynamic equilibrium forming a new dispersion with larger oil drops at each increased oil fraction. Near the phase inversion point, however, this balance can no longer be sustained following a further increase in the oil volume fraction; this will cause the coalescence rate to accelerate leading to the formation of larger drops. During this period, the time required for the breakup of these large drops is too long even in the highly turbulent impeller region. The shape of these large drops then changes from spherical to cylindrical to lamellae and ultimately to some complex structures accompanied by a viscosity maximum [28]. With a further increase in the dispersed phase fraction, oil becomes continuous and the water film trapped into the oil forms dispersed drops, which

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ultimately leads to another dynamic balance between the rate of break up and coalescence of water drops. During their experimental investigation Guilinger et al. [12] noticed that the dispersion becomes less efficiently agitated and less turbulent near the inversion point, which is consistent with the findings of viscosity maximum. As was also discussed above, multiple drops and complex structures have been seen by a number of investigators near the inversion point in both pipelines and stirred vessels [7,13,15,22]. According to Arashmid & Jeffreys [5] when the dispersion is agitated, the drops will collide and some will coalesce. As the dispersed phase holdup increases, at constant agitation speed, the proportion of the pairs of drops coalescing at each collision will increase until, at phase inversion coalescence will occur for every collision. Phase inversion will therefore occur when the frequencies of drop collision and coalescence become equal. Using the collision frequency model by Levich [29] and the coalescence frequency model by Howarth [30], the authors derived the following equation for dispersed phase holdup, ϕ dI , at inversion,

Ka =1 ϕ D 2I N 0I.48

(3)

I d

where DI is the impeller diameter, and Ka is a constant that was found to depend on the system and physical properties, varying from 10-3 to 107. Both coalescence and break up phenomena were considered by Vaessen et al. [31] who used expressions of drop coalescence and breakage frequency to estimate at each phase fraction the “stationary” drop size where coalescence and break up are balanced. Phase inversion would then occur at the dispersed phase volume fraction where the stationary drop size diverges. For the calculation of the breakage rate the following equation was used [32]:

G (d) = 1.37

σ 2 1 / 3 −2 / 3 ε d exp( ) n (d ) π 1.88ε 2 / 3 d 5 / 3

(4)

The coalescence rate was taken as [33]: Λ (d ) = 6.87ε1 / 3 d 7 / 3 n (d ) 2 exp(−

αt d ) ti

(5)

where G(d)is the breakage rate and Λ (d ) the coalescence rate of drops with mean diameter d, ε is the average energy dissipation rate per unit mass, σ is the interfacial tension, n(d) represents the number density of droplets of diameter d, td and ti are the film drainage time and drop interacting time, respectively. To account for the presence of surfactants the constant α was used and two types of inversion were considered. Easy inversion occurs when the surfactant is present in the dispersed phase and the drops are less stable because of rapid (continuous phase) film drainage; in this case α=0. In the

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difficult inversion, the surfactant is in the continuous phase and the film drainage between the dispersed drops is slow; in this case coalescence efficiency has to be taken into account and α=1. The authors suggested that these two types of inversion may be responsible for the ambivalent region. However the results from this model underestimated the phase inversion point obtained experimentally in a water - n-hexane dispersion. Population Balance Equations (PBE) modelling was used to predict the drop breakage and coalescence rates by Hu et al. [34]. Phase inversion was assumed to occur when the total volumetric breakage rate equals the total volumetric coalescence rate. With this approach an ambivalent range could be found. The agreement with literature data was reasonable apart from high dispersed phase fractions, which was attributed to the correlations for coalescence efficiency used which have not been validated in dense dispersions. Models based on zero interfacial shear Yeh et al. [35] suggested that since dispersions form by mixing, dynamic forces should play a role in determining the type of dispersion. They assumed that close to the interface the dispersion resembles a three layer system, namely dispersed phase, interfacial phase and continuous phase, parallel to each other in laminar flow. Inversion was suggested to occur when the shear at the interface becomes zero, because at this condition there is no tendency for the phases to mix or create new surfaces. The following equation was derived for the water fraction at inversion from the momentum balances of the two phases:

ϕ IW =

1 ⎛µ 1 + ⎜⎜ O ⎝ µW

⎞ ⎟⎟ ⎠

0.5

(6)

The predictions were in good agreement with the experimental results obtained in a hand shaken flask; this criterion cannot predict ambivalent region. Nädler & Mewes [36] applied the same approach to the pipe flow of two immiscible liquids. Starting from the momentum equations of the two fluids in stratified flow and assuming a negligible interfacial shear and no-slip between the two fluids at phase inversion, they obtained the following correlation:

ϕ IW =

1 ⎛ C ρ1−n O µ n O n −n 1 + k 1 ⎜ O 1O−n W On W (DU m ) W O ⎜ CW ρ µ W W ⎝

1/ k2

⎞ ⎟ ⎟ ⎠

(7)

where D is the pipe diameter; Um is the mixture velocity; ρ is density, µ is viscosity; C and n are the parameters of the Blasius equation for the friction factor, C Re − n ; k1 and k2 are empirical constants. The subscripts O and W refer to the oil and water phases

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respectively. They suggested that k1 reflects the contact perimeter of the wall with the liquids and k2 accounts for the flow regime in each phase. For laminar flow in both phases k1 = 1 and k2 = 2 and Equation (7) is identical to Equation (6) by Yeh et al. [35]. Models based on energy requirements A number of investigators have suggested that in order for phase inversion to occur, it must be accompanied by a decrease in the total energy content of the system [6, 10]. Luhning & Sawistowski [10] suggested that the energy change must come from the system itself since the measured impeller power input in a stirred vessel remained constant during inversion. The total system energy, including kinetic and interfacial energy, should then reach a minimum value at the phase inversion point. Given the spontaneous nature of the phenomenon some investigators have proposed that at the phase inversion point the surface energies of the two possible dispersions O/W and W/O, which include the interfacial energy and the surface energy from the contact of the continuous phase with the wall, should be equal [6,37-40]. An estimate is needed for the interfacial area and investigators have used either average sizes or drop size distributions calculated from Monte Carlo or population balance models. By expressing the interfacial area in terms of Sauter mean diameter, d32, Brauner and Ulmann [40] derived the following equation for the oil volume fraction at inversion: ⎛ σ ⎞ s ⎜⎜ ⎟⎟ + σ cos θ d 6 ⎝ 32 ⎠ W / O ϕ OI = ⎛ σ ⎞ ⎛ σ ⎞ ⎜⎜ ⎟⎟ ⎟⎟ + ⎜⎜ ⎝ d 32 ⎠ W / O ⎝ d 32 ⎠ O / W

(8)

where σ is the oil-water interfacial tension; s is the solid surface area per unit volume, where s = 4/D for flow in a smooth pipe of diameter D; (d 32 ) O / W and (d 32 ) W / O represent the Sauter mean diameter in a dispersion of oil-in-water and water-in-oil, respectively; θ is the liquid-solid wall contact angle, where 0 ≤ θ < 90 o corresponds to a surface which is preferentially wetted by water (hydrophilic surface) and 90 o < θ ≤ 180 o corresponds to a surface which is preferentially wetted by oil (hydrophobic surface). When the wall surface energy is small (for equipment with large volume to surface ratio) the equation is simplified to:

(d 32 ϕ OI = I (d 32 1 − ϕO

)O / W )W / O

(9)

It is often considered that in concentrated dispersed flow the Sauter mean diameter, d32, is proportional to the maximum drop diameter, dmax. Using this proportionality the above equation can be written as:

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(d max ϕ OI = I (d max 1 − ϕO

Angeli

)O / W )W / O

(10)

where (d max )O / W and (d max )W / O are the maximum drop sizes in oil-in-water and waterin-oil dispersions, respectively. This model requires the prediction of the characteristic drop size in dense dispersions. Brauner & Ullmann [40] evaluated the maximum drop size based on a local energy balance in dense dispersions, which yields the following expression for d max :

(d max )d / c D

⎛ σ = 7.61C H ⎜⎜ 2 ⎝ ρ c DU m

⎞ ⎟⎟ ⎠

0.6

⎛ ρ c DU m ⎜⎜ ⎝ µc

⎞ ⎟⎟ ⎠

0.08

⎛ ρc ⎜⎜ ⎝ ρm

⎞ ⎟⎟ ⎠

0.4

ϕ 0d.6 (1 − ϕ d ) 0.2

(11)

where subscripts d, c, m refer to the dispersed, continuous, and mixed phase and C H = O(1) is a tunable constant. The criterion of equal surface energy can also not account for the existence of the ambivalent region. Brauner & Ullmann [40] suggested that changes in the interfacial tension in the presence of contaminants could result in an ambivalent region. When contaminants or surfactants are present surface tension, σ, would be reduced. After phase inversion, where new fresh interfaces have been created, the surface tension will be different and equal to that of a pure system. Using Equation (8) with different surface tensions for an O/W and a W/O system would give different inversion points for the water and oil continuous dispersions and therefore an ambivalent region. In addition, the different wettability of the pipe wall by the oil and water phases will affect the angle θ in Equation (8) and result in different inversion points for an oil continuous and a water continuous mixture. Yeo et al. [39] were able to obtain ambivalent region with the equal surface energy criterion by calculating the drop Sauter mean diameter (d32) in the O/W and W/O dispersions from different correlations depending on the dispersed phase fraction. In their approach Poesio and Beretta [41] and Ngan et al. [42] considered that phase inversion results from the tendency of the system to minimise pressure gradient or mixture viscosity, rather than surface or interfacial energy. Poesio and Beretta [41] suggested that the dispersion will choose the continuous phase (oil or water) which provides the minimum energy dissipation (pressure gradient). Ngan et al. [42] argued that the mixture viscosity will determine phase continuity. This is exemplified in Fig. 7 where the mixture viscosities for the two possible dispersions, oil continuous and water continuous have been plotted against the water volume fraction. Starting from an oil continuous dispersion the mixture viscosity increases with the water fraction. If the mixture were to remain oil continuous for water fractions above 33.6% then its viscosity (and in effect the pressure drop) would be higher than if it inverted to water continuous. The dispersion will adopt the continuous phase that results in the lower viscosity for a given phase fraction which suggests that with inversion the mixture follows an energetically favourable route. The inversion point is therefore given by the interception of the two possible viscosity curves of an O/W and a W/O dispersion. The results can

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vary depending on the viscosity model used. Ngan et al. [42] tested a very large number of literature viscosity correlations and found that those by Brinkman /Roscoe [43,44], Furuse [45] and Pal [46] always predicted phase inversion in close agreement to the experimental data. Interestingly, very good agreement was also found with Yeh’s [35] Equation (6).

Figure 7. Prediction of phase inversion point in a water-oil dispersion. Phase inversion occurs at the phase fraction where the oil continuous and water continuous viscosity curves intercept. The Brinkman/Roscoe [43,44] model has been used to calculate the viscosities of the dispersions.

Although this criterion does not give ambivalent range either, Poesio and Beretta [41] argued that this could be included by using different viscosity correlations for the oil and the water continuous mixtures which take into account drop size, nonNewtonian behaviour and wall wettability.

Prediction of the width of the ambivalent range Luhning & Sawistowski [10] experimentally investigated the effect on ambivalent region of various parameters, such as interfacial tension and agitation speed. The results showed that the upper and lower inversion curves tend asymptotically to a constant value with increasing agitation speed, while the organic phase holdup, ϕoI, at phase inversion was found to be a linear function of the Weber number. The experimental data were fitted to the following correlations: ϕ OI = 0.16 + 6.0 × 10 −5 We

upper inversion curve

(12)

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ϕ OI = 0.47 + 2.0 × 10 −5 We

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lower inversion curve

(13)

Here, We = ρ c N 2I D 3I / σ . In addition, they found that interfacial tension is one of the principal factors affecting the width of the ambivalent region, WA , which was correlated to their experimental data as follows:

WA = (5.64 N I − 64)(1.0 × 10 −3 σ) − ( 0.82+3.96×10

−2

NI )

(14)

In later work, Fakhr-Din [47], by taking into account that phase inversion is a spontaneous process, suggested that the total system energy would be at its lowest level at the phase inversion point. Using this criterion he correlated the ambivalent region curves as follows: ⎛µ ϕ = 1.32 × 10 ⎜⎜ d ⎝ µc I O

6

⎛µ ϕ = 12.2 × ⎜⎜ d ⎝ µc I O

⎞ ⎟⎟ ⎠

⎞ ⎟⎟ ⎠

0.31

0.32

⎛ ∆ρ ⎞ ⎟⎟ ⎜⎜ ⎝ ρc ⎠

⎛ ∆ρ ⎞ ⎜⎜ ⎟⎟ ⎝ ρc ⎠

−0.11

Fr 0.71 Re 1.06 We −0.

upper inversion curve

(15)

lower inversion curve

(16)

0.04

Fr 0.13 Re 0.22 We −0.03

where ∆ρ is the density differences between the two phases; Fr is the Froude number (defined as Fr=NI2DI/g, where g is the gravitational acceleration), Re is the impeller Reynolds number (defined as Re= ρmNIDI2/ µc) and We is the Weber number.

Modelling the phase inversion process in pipelines The above models for predicting phase inversion assume a well mixed dispersion and do not take into account flow configuration, variations in drop size or the complex structures of different continuity which appear close to inversion. In reality, however, inhomogeneities exist, and inversion may initially occur at certain places in the dispersion container and not throughout. Some models have been developed which attempt to use the above correlations in order to predict phase inversion and in some cases pressure drop in pipelines for real flow configurations. For phase inversion occurring in stirred vessels Hu et al. [48] applied a two-region model to allow for the fact that break up mainly happens at the impeller vicinity while coalescence is predominant away from that region. Phase inversion was considered to occur when the coalescence frequency exceeded that of break up. To account for drop coalescence in concentrated dispersions the concept of a radial distribution function was adopted in the model. Starting both from oil and from water continuous dispersions an ambivalent region was obtained. The predictions of the model agreed well with experimental data on the effects of interfacial tension, viscosity, density and impeller size on the width of the ambivalent range. The agreement was particularly good for the

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upper curve of the ambivalent region; however, the organic phase fraction of the lower inversion curve was in some cases underestimated. The criterion of equal surface energy was used to predict the phase inversion point during pipeline flow of an oil-water dispersion (Hu et al. [49]). However, instead of using average drop sizes a population balance model was developed to predict the drop size distribution and its evolution along the pipe. Although the equal surface energy model could not give an ambivalent region, it predicted that phase inversion for the oil and water continuous dispersions appeared at different axial locations along the pipe, because of the different way the drop sizes develop in each dispersion. These results suggest that in pipes an ambivalent region may arise when measurements are carried out at an axial location where the dispersion with one phase as continuous has inverted while the dispersion with the other phase as continuous has not yet inverted.

Figure 8. Experimental and predicted pressure gradient during oil-water dispersed flow against input water fraction as the mixture changes from water to oil continuous. The oil has 5.5 mPa s viscosity and 828 kg/m3 density and the test section is an acrylic pipe with 38 mm ID. The arrow indicates the direction of the experiment. The vertical lines indicate the boundaries of the transitional region: ( ) from the experiment and ( ) from the model.

A methodology was developed by Ngan et al. [18] to predict phase inversion and pressure drop during pipeline flow that took into account the pattern changes from fully dispersed, at low dispersed phase fractions, to layered in the transitional region and again dispersed at high phase fractions of the original dispersed phase (see Fig. 3). The methodology was based on a two-layer flow configuration where the upper layer was initially assumed to be oil continuous and the lower layer water continuous. Entrainment fractions of one phase into the other were calculated from Al-Wahaibi & Angeli [50] while the phase inversion criterion by Ngan et al. [42] was used to determine the continuity in each layer after the entrainment fraction had been estimated. When both layers were found to have the same continuity then the flow was fully dispersed and a homogeneous model was used to calculate pressure drop. When the two layers had different continuity then a two-fluid model was used to predict pressure drop.

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As can be seen in Fig. 8, the model was able to predict satisfactorily the boundaries of the transitional region as well as the pressure drop.

Conclusions Phase inversion during dispersed liquid-liquid pipeline flows is an important phenomenon which affects not only the continuity of the mixture but also its rheological behaviour. It is often accompanied by an increase in pressure gradient which will change pipeline capacity during the transportation of liquid-liquid mixtures. The investigations have revealed that during the transition from one phase continuous to the other complex flow morphologies (multiple drops, regions in the flow with different continuity) and even stratification of the two phases appear over a range of dispersed phase volume fractions. The way that the dispersion is initialised and the rate that the volume fraction of the dispersed phase is increased towards phase inversion, also affect the phase fraction where inversion appears. The models that have been proposed for predicting phase inversion consider the inversion as a change of the mixture continuity at one particular phase fraction (phase inversion point) that occurs throughout the mixture and cannot therefore be applied to inversion in pipe flow. They need to be combined with models of flow pattern development, while phenomena such as secondary and multiple dispersions should also be properly modelled. Further detailed studies of the mixture morphology as it approaches phase inversion will be needed to assist the development of such models, under well defined conditions for initiating the mixture that cover a large range of fluid properties and pipe wettability characteristics.

Nomenclature c

constant in Equation (1)

C

parameter of the Blasius equation for the friction factor, C Re − n

CH

constant in Equation (11)

d

drop diameter, m

dmax

maximum drop diameter, m

d32

Sauter mean drop diameter, m

D

pipe diameter, m

DI

impeller diameter, m

Fr

Froude number -

G(d)

drop breakage rate, s-1

k1, k2

empirical constants in Equation (7)

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Ka

constant in Equation (3)

n(d)

number density of drops with diameter d, -

n

power of the Reynolds number in Blasius equation for the friction factor, C Re − n

NI

impeller agitation speed, s-1

P

power input, kg m-2 s-3

Re

Reynolds number, -

s

solid surface area per unit volume, m-1

td

drainage time of film between coalescing drops, s

ti

interaction time between coalescing drops, s

U

velocity, m s-1

WA

width of the ambivalent region, -

We

Weber number, -

Greek Symbols

α

constant in Equation (5)

ε

average energy dissipation rate per unit mass, m2 s-3

θ

liquid – solid wall contact angle, o

Λ(d)

coalescence rate of drops with mean diameter d, s-1

µ

viscosity, Pa s

ρ

density, kg m-3

∆ρ

density difference between the two liquid phases, kg m-3

σ

liquid-liquid interfacial tension, kg s-1

ϕ

volume fraction, -

ϕ dI

volume fraction of the dispersed phase at inversion, -

ϕ IO

volume fraction of the organic (oil) phase at inversion, -

ϕIW

volume fraction of the water phase at inversion, -

φ0

asymptotic phase inversion holdup at high agitation speed in Eq. (1), -

χ

injection phase volume faction, defined as the ration of the injected initial dispersed phase flow rate to that of the continuous phase, -

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Subscripts c

continuous

d

dispersed

m

mixture

o

oil

s

superficial

w

water

References [1] W.A. Rodger, V.G. Trice, Jr., and J.H.Rushton, (1956), “The effect of fluid motion on interfacial area of dispersions”, Chem. Eng. Prog., vol. 52, pp. 515–520, 1956. [2] Yeo, L. Y., Matar, O. K., Perez de Ortiz, E. S., Hewitt, G. F. (2000). Phase inversion and associated phenomena. Multiphase Science and Technology, 12(1), 51–116. [3] A. H. Selker, and C.A. Sleicher, Jr., “Factors affecting which phase will disperse when immiscible liquids are stirred together”, Can. J. Chem. Eng., vol. 43, pp. 298–301, 1965. [4] M. J. McClarey, and G. A. Mansoori, “Factors affecting the phase inversion of dispersed immiscible liquid-liquid mixtures”, AIChE Symposium Series, vol. 74, pp. 134–139, 1978. [5] M. Arashmid, and G.V. Jeffreys, “Analysis of the phase inversion characteristics of liquid-liquid dispersions”, AIChE J., vol. 26, pp. 51–55, 1980. [6] M. Tidhar, J. C. Merchuk, A. N.Sembira, and D. Wolf, “Characteristics of a motionless mixer for dispersion of immiscible fluids- Phase inversion of liquidliquid systems”, Chem. Eng. Sci., vol. 41, pp. 457–462, 1986. [7] A. W. Pacek, A. W. Nienow, and I. P. T. Moore, “On the structure of turbulent liquid-liquid dispersed flows in an agitated vessel”, Chem. Eng. Sci., vol. 49, pp. 3485–3498, 1994. [8] S. Kumar, R. Kumar, and K.S. Gandhi, “Influence of the wetting characteristics of the impeller on phase inversion”, Chem. Eng. Sci., vol. 46, pp. 2365–2367, 1991. [9] K.B. Deshpande, and S. Kumar, “A new characteristic of liquid-liquid systems– inversion holdup of intensely agitated dispersions”, Chem. Eng. Sci., vol. 58, pp. 3829–3825, 2003. [10] R.W. Luhning, and H. Sawistowski, “Phase inversion in stirred liquid-liquid systems”, Proc. Int. Solvent Extraction Conference, The Hague, pp. 873–887, Society of Chemical Industry, London, 1971. [11] M. A. Norato, C. Tsouris, and L.L. Tavlarides, “Phase inversion studies in liquidliquid dispersions”, Can. J. Chem. Eng., vol. 76, pp. 486–494, 1998. [12] T. R.Guilinger, A. K. Grislingas, and O. Erga, “Phase inversion behaviour of water-kerosene dispersions” Ind. Eng. Chem. Res., vol. 27, pp. 978–982, 1988.

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[13] L. Liu, O.K. Matar, E.S. Perez de Ortiz, and G.F. Hewitt, “Experimental investigation of phase inversion in a stirred vessel using LIF”, Chem. Eng. Sci., vol. 60, pp. 85-94, 2005. [14] S. Kumar, “On phase inversion characteristics of stirred dispersions”, Chem. Eng. Sci., vol. 51, pp. 831–834, 1996. [15] K. Piela, R. Delfos, G. Ooms, J. Westerweel, R.V.A. Oliemans, “On the phase inversion process in an oil-water pipe flow”, Int. J. Multiphase Flow, vol. 34, pp. 665-677, 2008 [16] K.K.I. Ioannou, O.J. Nydal, and P. Angeli, “Phase inversion in dispersed liquid– liquid flows”, Exp. Thermal Fluid Sci., vol. 29, pp. 331-339, 2005. [17] K.H. Ngan, M. Simeoni, K. Ioannou, L.D. Rhyne, and P. Angeli, “Phase inversion in oil-water pipe flows”, Proc. 11th Int. Conf. Multiphase Flow in Industrial Plants, Palermo, Italy, pp. 329-336, 2008. [18] K.H. Ngan, K. Ioannou, L.D. Rhyne, and P. Angeli, “Prediction of pressure gradient in dispersed liquid-liquid flows during phase inversion”, Proc. 14th Int. Conf. Multiphase Production Technology, Cannes, France, pp. 131-139, 2009. [19] B. Hu, and P. Angeli, “Phase inversion and associated phenomena in oil-water vertical pipeline flow”, Can. J. Chem. Eng., vol. 84, pp. 94-107, 2006. [20] S. Arirachakaran, K.D. Oglesby, M. S. Malinowsky, O. Shoham, and J.P. Brill, “An analysis of oil/water flow phenomena in horizontal pipes”, Society of Petroleum Engineers, Paper SPE 18836, Oklahoma, 1989. [21] R. Pal, “Pipeline flow of unstable and surfactant-stabilised emulsions”, AIChE J., vol. 39, pp. 1754-1764, 1993. [22] L. Liu, O. K. Matar, C. J. Lawrence, and G. F. Hewitt, “Laser-induced fluorescence (LIF) studies of liquid–liquid flows. Part I: Flow structures and phase inversion”, Chem. Eng. Sci., vol. 61, pp. 4007-4021, 2006. [23] D.P. Chakrabarti, G. Das, and P.K. Das, “The transition from water continuous to oil continuous flow pattern”, AIChE J., vol. 52, pp. 3668-3678, 2006. [24] K. Piela, R. Delfos, G. Ooms, J. Westerweel, R.V.A. Oliemans, and R.F. Mudde, “Experimental investigation of phase inversion in an oil-water flow through a horizontal pipe loop”, Int. J. Multiphase Flow, vol. 32, pp. 1087-1099, 2006. [25] E. Tyrode, J.Allouche, L. Choplin, and J.-L. Salager, “Emulsion catastrophic inversion from abnormal to normal morphology. 4. Following the emulsion viscosity during three inversion protocols and extending the critical dispersed-phase concept”, Ind. Eng. Chem. Res, 2005, vol. 44, pp. 67-74, 2005. [26] J. A. Quinn, and D.B. Sigloh, “Phase inversion in the mixing of immiscible liquids” Can. J. Chem. Eng., vol. 41, pp. 15–18, 1963. [27] F. Groeneweg, W. G. M. Agterof, P.Jaeger, J. J. M. Janssen, J. A.Wieringa, and J. K. Klahn, “On the mechanism of the inversion of emulsions”, Chem. Eng. Res. Des., Transaction IChemE (Part A), vol. 76, pp. 55–63, 1998. [28] J.W.Falco, R.D.Walker, D.O. Shah, “Effect of phase-volume ratio and phaseinversion on viscosity of microemulsions and liquid crystals”, AIChE J., vol. 20, pp. 510–514, 1974. [29] V. G. Levich, Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, New Jersey, 1962

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[30] W. J. Howarth, “Coalescence of drops in turbulent flow field”, Chem. Eng. Sci., vol. 19, pp. 33–38, 1967. [31] G.E.J. Vaessen, M. Visschers, and H.N. Stein, “Predicting catastrophic phase inversion on the basis of droplet coalescence kinetics” Langmuir, vol. 12, pp. 875– 882, 1996. [32] M. A. Delichatsios, R. F. Prosbstein, “The effect of coalescence on the average drop size in liquid-liquid dispersions”, Ind. Eng. Chemistry Fundamentals, vol. 15, pp. 134–138, 1976. [33] P.G. Saffman, J.S. Turner, “On the collision of drops in turbulent clouds”, J. Fluid Mech., vol. 1, pp. 16–30, 1956. [34] B. Hu, K. Ioannou, O.K. Matar G.F. Hewitt, and P. Angeli, “Theoretical prediction with PBE of phase inversion in disprsed two-phase liquid systems”, 3rd Int. Symp. Two-Phase Flow Modelling and Experimentation, Pisa, 22-24 September 2004 [35] G. C. Yeh, F. H. Haynie, Jr., and R.A. Moses, “Phase-volume relationship at the point of phase inversion in liquid dispersions” AIChE J., vol. 10, pp. 260–265, 1964. [36] M. Nädler, and D. Mewes, “Flow induced emulsification in the flow of two immiscible liquids in horizontal pipes”, Int. J. Multiphase Flow, vol. 23, pp. 55–68, 1997. [37] S. Decarre, and J. Fabre, “Phase inversion behavior for liquid-liquid dispersions”, Revue de l Institute Francais du Petrole, vol. 52, pp. 415-424, 1997 [38] Yeo, L. Y., Matar, O. K., Perez de Ortiz, E. S., Hewitt, G. F. (2002). Simulation studies of phase inversion in agitated vessels using a Monte-Carlo technique. Journal of Colloid and Interface Science, 248, 443–454. [39] Yeo LY, Matar OK, de Ortiz ESP, Hewitt G.F. (2002) A simple predictive tool for modelling phase inversion in liquid-liquid dispersions. Chemical Engineering Science, 57, 1069-1072. [40] N. Brauner, and A. Ullmann, “Modeling of phase inversion phenomenon in twophase pipe flows”, Int. J. Multiphase Flow, vol. 28, pp. 1177-1204, 2002. [41] P. Poesio, and G.P. Beretta, “Minimal dissipation rate approach to correlate phase inversion data”, Int. J. Multiphase Flow, vol. 34, pp. 684-689, 2008. [42] K.H. Ngan, K. Ioannou, L.D. Rhyne, and W. Wang, “A methodology for predicting phase inversion during liquid-liquid dispersed pipeline flow”, Chem. Eng. Res. Des., vol. 87, pp. 318-324, 2009. [43] H. C. Brinkman, “The viscosity of concentrated suspensions and solutions”, J. of Chem. Phy., vol. 20, p. 571, 1952 [44] R. Roscoe, “The viscosity of suspensions of rigid spheres”, British J. Applied Physics, pp. 267-269, 1952 [45] H. Furuse, “Viscosity of concentrated solution”, Jap. J. of Applied Physics, vol. 11, p. 1537-1541, 1972 [46] R. Pal, “Single-parameter and two-parameter rheological equations of state for nondilute emulsions”, Ind. Eng. Chem. Res., vol. 40, pp. 5666-5674, 2001 [47] S. M. Fakhr-Din, “Phase inversion and drop size measurements in agitated liquidliquid systems”, Ph.D. Thesis, University of Manchester, 1973.

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[48] B. Hu, P. Angeli, O.K. Matar, and G.F. Hewitt, “Prediction of phase inversion in agitated vessels using a two-region model”, Chem. Eng. Sci., vol. 60, pp. 34873495, 2005. [49] B. Hu B, O.K. Matar, G.F. Hewitt, and P. Angeli, “Population balance modelling of phase inversion in liquid–liquid pipeline flows”, Chem. Eng. Sci., vol. 61. 49944997, 2006. [50] T. Al-Wahaibi, and P. Angeli, “Predictive model of the entrained fraction in horizontal oil–water flows”, Chem. Eng. Sci., vol. 64, pp. 2817-282, 2009.

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Chapter 3 Heat Transfer and Friction in Helically-Finned Tubes Using Artificial Neural Networks Louay M. Chamra1, Pedro Mago2 and Gregory Zdaniuk3 1 School of Engineering and Computer Science Oakland University, 248 Dodge Hall, Rochester, MI 48309, USA 2

Department of Mechanical Engineering, Mississippi State University 210 Carpenter Engineering Building, P.O. Box ME, Mississippi State, MS 39762-5925 3

Ramboll Whitbybird Ltd 60 Newman Street, London W1T 3DA, United Kingdom

Abstract The last few decades have seen a significant development of complex heat transfer enhancement geometries such as a helically-finned tube. The arising problem is that as the fins become more complex, so does the prediction of their performance. Presently, to predict heat transfer and pressure drop in helically-finned tubes, engineers rely on empirical correlations. Tubes with axial and transverse fins have been studied extensively and techniques for predicting the friction factor and heat transfer coefficient exist. However, fluid flow in helically-finned tubes is more difficult to model and few attempts have been made to obtain non-empirical solutions. Friction and heat transfer in helically-finned tubes are governed by an intricate set of coupled and non-linear physical interactions. Therefore, obtaining a single prediction formula seems to be an unattainable goal with the knowledge engineers currently possess. Regression techniques performed on experimental data require mathematical functional form assumptions, which limit their accuracy. To achieve accuracy, techniques that can effectively overcome the complexity of the problem without dubious assumptions are needed. One of these techniques is the artificial neural network (ANN), inspired by the biological network of neurons in the brain. This chapter presents an introduction to artificial neural networks (ANNs), and a literature review of the use of ANNs in heat transfer and fluid flow is also discussed. In addition, this chapter demonstrates the successful use of artificial neural networks as a correlating method for experimentally- measured heat transfer and friction data of helicallyfinned tubes.

Introduction The use of heat transfer enhancement has become widespread during the last 50 years. The goal of heat transfer enhancement is to reduce the size and cost of heat exchanger equipment. This goal can be achieved in two ways: active and passive enhancement. Of the two, active enhancement is less common because it requires the addition of external power (e.g., an electromagnetic field) to cause a desired flow modification. On the other hand, passive enhancement consists of alteration to the heat 

Email address: [email protected]

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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transfer surface or incorporation of a device whose presence results in a flow field modification. The most popular surface enhancement is the fin. Friction and heat transfer in helically-finned tubes are governed by an intricate set of coupled and non-linear physical interactions. Therefore, obtaining a single prediction formula seems to be an unattainable goal with the knowledge engineers currently possess. Regression techniques performed on experimental data require mathematical functional form assumptions, which limit their accuracy. To achieve accuracy, techniques that can effectively overcome the complexity of the problem without dubious assumptions are needed. One of these techniques is the artificial neural network (ANN), inspired by the biological network of neurons in the brain. Despite the complexity of the natural environment, living creatures are able to perform involved activities within their ecosystems. Animals can rapidly process vast amounts of data and make “calculated” decisions. This capability, attributed to the nervous system, is partly acquired and partly enhanced through a process called learning. Last century’s advancements in bio-medical sciences have shed some light on the functioning of the nervous system. Studies in bio-medicine and psychology have always attempted to understand the brain and its elementary component - the neuron. Knowledgegained in this topic encouraged scientists to apply the concept of a neuron to mathematics and logic, giving birth to artificial neural networks (ANNs). The purpose of ANNs is to provide solution algorithms to complex problems such as classification, clustering, data compression, pattern association, function approximation, forecasting, control applications, or optimization†. To many researchers dealing with these topics, ANNs are a subject of study in themselves. The purpose of this chapter is to briefly introduce the concept of ANNs and how ANNs can be used in heat transfer and fluid problems. Readers who are interested in learning more about ANNs are encouraged to explore some of the many texts on this subject (e.g., Haykin [2] or Mehrotra et al. [3]). Biological and artificial neurons Figure 1 shows a biological (real) neuron. A real neuron is composed of a cell body, dendrites, and a tubular axon, which terminates with end bulbs called synapses. The axon of a neuron makes synaptic connections with dendrites of many other neurons. The number of connections ranges from 100 to 100 000. A neuron receives signals from other neurons at the dendrites and transmits them down the axon to the synapses. The magnitude of the signal received by a neuron depends on the efficiency, or strength, of the synaptic connection. An electrostatic potential difference is always maintained across the cell membrane. The cell membrane becomes electrically active when sufficiently excited by signals from other neurons. The neuron fires, or sends a 100 mV signal down its axon, if its net excitation during a certain period of time (period of latent summation) exceeds a threshold value. Firing is followed by a brief refractory period during which a neuron is inactive. The whole process can occur at frequencies of up to †

Heat transfer applications mostly deal with function approximation, control, and optimization. However, pattern recognition capabilities of ANNs have also been used in conjunction with flow visualization techniques to assist in unsupervised learning algorithms that develop friction, mass, and heat transfer correlations [1].

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several hundred Hertz. It is the neuron’s firing frequency that is referred to as the output of a neuron. Dendrites

Axon

Body Nucleus

Synapses (to other neurons)

Synapses (from other neurons)

Dendrites (of other neurons)

Figure 1. Biological neuron [3].

The picture presented so far is possibly oversimplified. Axons may form synapses with other axons. A neuron may have no axon, but only “processes” that receive and transmit signals. Dendrites may form synapses with other dendrites. A neuron may have synapses with its own dendrites. Nevertheless, the above description presents the characteristics of a neuron that are relevant to ANNs. Introduction to the artificial neuron model requires the discussion of terminology that is used in this chapter. The equivalents between biological and artificial terms are as follows:      

neuron = node synapse = connection received signal = input synaptic efficiency = weight firing frequency = node output threshold = bias

The easiest way to describe an artificial neuron model is graphically. Figure 2 shows a schematic of an artificial neuron. The similarity between an artificial neuron and a real one is in the operation. Each input (x1, x2, …, xn) is multiplied by a weight and is fed into the node. The node sends an output based on some function of the weighted inputs. The differences between an artificial neuron and a real one come from the simplifying assumptions:

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1) The position of the incoming connection is irrelevant. 2) Each node outputs a single value to other nodes via outgoing connections, irrespective of their positions. 3) All inputs come in at the same time or remain activated long enough for the computation of function F to take place. A further simplification is to postulate that: F ( w1 x1 ,...., wn x n )  F ( w1 x1  ....  wn x n )  F (net) .

This assumption is supported by the fact that voltages are added across a circuit, which is what approximately happens in a brain. In order to facilitate the learning process of an artificial neuron, a bias is often added to the sum of weighted inputs. In such case, the node function really computes F(net + bias), where bias (like w) is a node variable rather than an input. Throughout the rest of this chapter, the terms F(net) and F(net + bias) are equivalent. Although applying the node function to the sum of the weighted inputs is the most common practice, there exist networks (e.g., “sigma-pi” networks) that take the product of the weighted inputs. Nevertheless, the F(net) approach is the most widely used and will be employed herein. The next section discusses the types of functions used within the nodes.

X1

W1

X2

W

X3

W3

Xn

Wn

2

Figure 2. An Artificial neuron.

F

F( W1X1,

, WnX n )

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Node functions There are no legitimate limitations as to the type of node function F(net) one can use. Obviously, the best function to use is the one that performs the job best. Experience has shown that certain function types perform well in ANNs. Step function Figure 3 shows an arbitrary step function. This function simply outputs a value a if net is less than a threshold value c and a value b if net is greater than the threshold value:

a F (net)   b

if net  c if net  c

The output at net = c is sometimes a, sometimes b, or the average of the two. The step function is suitable for binary applications. For example, digital processes need inputs and outputs that can be represented with only two numbers, 0 and 1.

F(net)

c b a net

Figure 3. An arbitrary step function.

Although the idea of threshold is biologically plausible, the fact that the magnitude of the input has little relevance (except for whether or not it is above the threshold) seems to be against logic. On the other hand, the output of the step function saturates, meaning that it cannot go infinitely high or low, following the idea that an infinitely high neuron firing rate is biologically impossible. A potential disadvantage of the step function is that it is discontinuous, making it sensitive to noise. Moreover, nondifferentiability of this function constrains the number of learning algorithms that can be applied to the network.

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Ramp function The ramp function is an evolution of the step function that overcomes the discontinuity problem by introducing a linear “ramp” between the high and low output values. The ramp function is illustrated in Figure 4 and is defined by the following set of equations:

a  F (net)  b a  (net  c)(b  a) /(d  c) 

if net  c if net  d otherwise

F(net)

d

c

b

a net

Figure 4. An arbitrary ramp function.

By virtue of continuity, the ramp function has no binary attribute, but still saturates at a high and low output value. Even though the ramp function is continuous, it is nondifferentiable at net = c and net = d. The ramp function is an example of a simple piecewise linear function. More elaborate functions can be created by combining even more linear functions. Sigmoid functions Sigmoid functions are S-shaped functions that are smooth (continuous and differentiable), symmetric about a point, and asymptotically approach a low and high value. Because of these characteristics, effective learning algorithms are easier to apply and, as a result, sigmoid functions are the most common functions in neural network applications. In addition, experimental observation suggests that the firing rate of a biological neuron is approximately a sigmoidal function of the net input [3]. An arbitrary sigmoid function is depicted in figure 5. This function’s limits are:

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lim F (net)  b

net 

lim F (net)  a

net  

Common choices are a = -1 or a = 0, b = 1, and c = 0. Two examples of sigmoid functions are: 1 (1) F (net)  1  exp( net) and (2) F (net)  tanh( net) These two example functions can be scaled, translated, and rotated according to the application without losing the characteristics of a sigmoid function.

b

F(net)

a

0 net

Figure 5. An arbitrary sigmoid function.

Gaussian functions Bell-shaped curves such as the one illustrated in figure 6 are known as Gaussian or radial-basis functions. Gaussian functions are also continuous, differentiable, and have asymptotes but they are not monotonic. Gaussian functions are used in radial-basis function networks. Algebraically, a Gaussian function may be described with the following expression:

F (net) 

 1  net    2  exp     2   2     1

(3)

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where μ and σ are the mean and standard deviation, respectively. Network architecture The power of an artificial neuron is fully realized when nodes are combined into an interactive network. The way that nodes are connected influences the performance of an ANN, so network architecture must be considered at an early stage of the design process.

F(net)

net

Figure 6. An arbitrary Gaussian function.

Biological networks in the central nervous system are complex, but a general schematic emerges from observations. The cerebral cortex, where most processing is believed to occur, is composed of five to seven layers of neurons with each layer supplying inputs into the next. However, layer boundaries are not strict. Feedback connections, connections within layers, and crossing layers are known to exist. To simulate this, each node of the general artificial network would have to communicate with itself and all of the remaining nodes. An example of such a network is shown in Figure 7, where the network has two input and two output nodes at arbitrary locations, one hidden node (a hidden node is a neither an input or an output node). Even though a fully-connected network is most general, its use is limited due to large number of parameters. Training such a network would, therefore, be very involved. Every other type of network can be considered a special case of the fully-connected network. Simplification is achieved by dividing the network into layers and setting some weights to zero. Many variations of such networks exist, but the simplest one presented here is the feed-forward network shown in Figure 8. Feed-forward networks are the most common among ANNs. A feed-forward network allows connections from layer i to layer i + 1 only (no intra-layer connections) and can be easily described by a

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set of numbers that represent the number of nodes in each layer. E.g. the network in Figure 8 is a 3-2-3-2 network. Output Input

Output

Input

Figure 7. A fully-connected network.

Layer 0

(Input layer)

Layer 1

Layer 2

Hidden layers

Figure 8. A feed-forward network [3].

Layer 3

(Output layer)

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Networks are not limited to the above-described categories. Small networks can be treated as modules, which in turn can be combined into larger systems. These systems can be organized in different ways depending on whether modular emphasis is placed on inputs, successive refinement, etc…. ANN learning Previous sections have shown that ANNs are made up of inputs, outputs, weights, and nodes, and have elaborated on node functions and network architectures. However, the most difficult part of obtaining an effective ANN is the selection of appropriate weights and biases. The process in which weights and biases are adjusted to achieve the best performance of an ANN is called training (or learning). Mehrotra et al. [3] described three types of neural learning: 1) Correlation learning. Correlation learning is based on Hebb’s theory, which states that if the output from neuron A repeatedly or persistently takes place in firing neuron B, then the synaptic efficiency between neuron A and B is increased. For ANNs, this means that the weight between node A and B is proportional to the outputs of both nodes. 2) Competitive learning. In competitive learning, different nodes compete to become “winners” for a certain type of input parameters, weights are adjusted to promote “winners” and demote “losers” for each type of input pattern. This leads to the development of networks in which each node specializes in the given type of input parameters. One can postulate that the competitive learning technique draws its principles from the fact that in biological systems, limited resources are economically distributed to the organs that are needed the most at a given instant in time. 3) Feedback-based learning. Weights in ANNs can be adapted based on a measure associated with how close the output is to the desired value. This measure is usually quantified as error, and the weights and biases are adjusted until the error is minimized. This method , and particularly the backpropagation algorithm, is very common in ANN training. Because the backpropagation algorithm is so common, elaborating on this technique is worthwhile. The backpropagation algorithm is a supervised feedback-based learning method. The procedure consists of iteratively presenting the network with a training set of inputs and outputs, these are data from which the network can make proper pattern associations. Weights and biases are first initialized with random values, and then the training inputs are fed into the network. The output is then compared with the desired value to determine the magnitude of the error. The error gradient† is

†

Computation of error gradients requires that the node functions be differentiable.

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computed, and the weights and biases are updated in the direction of most rapidly decreasing error. The whole process is repeated until the minimum error is found. The exact number of data sets (points) needed to train the network is not known a priori, but there exist different heuristic approximations [3]. The more elaborate the ANN, the more data sets are needed to train the weights and biases. Simpler networks are, therefore, preferred to limit the number of required experiments. Moreover, the supervised training process can only utilize about 50-80% of the data sets available. The remaining data sets are used to test (or to validate) the performance of the ANN. Sometimes, the training process monitors the performance of both the training set and the test set and stops when the global error is smallest. There are some indications as to which data sets should be put in the training basket and which ones kept for testing. The idea behind this decision is that when a test sample is submitted for evaluation, the ANN “interpolates” between the training points that are close to the test sample presented. Intuitively, the training batch should include the extreme available points so that the predictions are within the same range. PachecoVega et al. [4] applied a neural network analysis to a fin-tube heat exchanger with limited experimental heat transfer data. The authors presented a cross-validation technique to identify regions where not enough training data were available to construct a reliable neural network. This technique was described as follows: “From the M available sets of experimental data, (M - 1) are used to train the ANN. After the training is finished, the data set left out is predicted and the result is compared to the experimental value. The percentage error (…) is a measure of the importance of that particular set of data with respect to all the measurements.” The work of Pacheco-Vega et al. [4] helps to determine which data points are crucial for training and where additional experimental data may be needed. ANNs in fluid flow and heat transfer literature Now that the principles of ANNs have been discussed, attention is shifted to the use of ANNs in heat transfer and fluid mechanics. Because ANNs have emerged relatively recently, their presence in the thermal science literature is limited. The following section describes several articles that can assist in getting started with a more thorough literature survey. By listing actual examples, this section can also help to understand how ANNs can be implemented successfully in heat transfer and fluid flow problems. Kalogirou [5] presented a review of various applications of ANNs in energy problems. The problems were classified into six thematic categories, and each category had subsections with specific examples as well as references. The categories described by Kalogirou [5] were as follows: 1) Modeling various aspects of a solar steam generator. 2) HVAC systems: estimation of building heating loads, prediction of energy use in commercial buildings, optimization of energy consumption by HVAC systems, or controlling a bus air conditioning system. 3) Solar radiation.

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4) Modeling and control in power generation systems: combustion modeling, control of a thermal plant, or analysis of harmonic power distortion. 5) Forecasting and prediction of power consumption and cost. 6) Refrigeration: frost prediction on evaporator coils. Sen and Yang [6] described the scope of ANNs and genetic algorithm† techniques in thermal science applications including an exhaustive bibliography. Sen and Yang [6] presented two interesting examples that use ANNs to predict the performance of compact heat exchangers. The first heat exchanger was a single-row, fin-tube, crossflow air-to-water type, and the second one was similar but with more tube rows. The second heat exchanger was more complex than the first one due to its geometry, the presence of air-side condensation, and fin spacing being a variable. The authors’ purpose was to compare the mathematical correlations for heat transfer with an ANN approach. Both techniques were compared against experimental data. Sen and Yang [6] proved that in both cases the ANN approach yields more accurate results (most errors within 0.7% for the first heat exchanger). The explanation is worth citing: “results suggest that the ANNs have the ability of recognizing all the consistent patterns in the training data including the relevant physics as well as random and biased measurement errors. (…) However, the ANN does not know and does not have to know what the physics is. It completely bypasses simplifying assumptions such as the use of coefficient of heat transfer. On the other hand, any unintended and biased errors in the training data set are also picked up by the ANN. The trained ANN, therefore, is not better than the training data, but not worse either.” Another application of ANNs that Sen and Yang [6] described is in thermal systems dynamics and control. Control of dynamic thermal systems ideally requires dynamic systems models, which relate the outputs to the inputs. Such models are usually impossible to obtain due to the complexity of practical thermal systems. This is understandable since modeling is difficult even in the static cases. Sen and Yang [6] used ANNs to perform control experiments with the first heat exchanger. Results were again excellent showing that ANNs are able to easily overcome complexities of the problems they solve. Ashforth-Frost et al. [1] described a multitude of uses of ANNs in heat transfer and fluid mechanics with emphasis on visualization processing techniques such as particle image velocimetry (see also Jambunathan et al. [7]). The authors reported several references that used ANNs to recognize different geometric patterns in multiphase flows. In these cases, ANNs have replaced methods which had been performed manually. ANN modeling of physiological flows was also mentioned as a solution to very complex medical analyses. Furthermore, the authors mentioned inverse problems as being good candidates for ANN treatment due to their sensitivity to noise and reported several successful examples reported in the literature. †

Genetic algorithms are another type of artificial intelligence techniques. Their description here is omitted for the sake of brevity.

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Thibault and Grandjean [8] were one of the early authors to show the use of ANNs in heat transfer data analysis. Thibault and Grandjean [8] solved three different heat transfer problems using three-layered, feed-forward ANNs: a thermocouple lookup table, a series of correlations between Nusselt and Rayleigh numbers for the free convection around horizontal smooth cylinders, and the problem of natural convection along slender vertical cylinders with variable surface heat flux. The backpropagation method and the quasi-Newton methods were used in the training procedure. The quasiNewton method showed faster and more robust convergence than the backpropagation technique and was, therefore, preferred by the authors. Thibault and Grandjean [8] concluded that neural networks can be used efficiently to model and correlate heat transfer data. In their opinion, the main advantage of ANNs is to remove the burden of finding appropriate model structures to fit experimental data and the disadvantage is the impossibility, simply by inspection, of determining the influence that one variable has on an output variable. ANNs, therefore, lack the transparency of most standard mathematical expressions. ANNs were also used to correlate two-phase flow data. Kelleher et al. [9] investigated data from a series of experiments on R-114 and R-113 pool boiling heat transfer from a vertical bank of tubes with variable amounts of oil present in the refrigerant. Their objective was to employ the neural network technique as a method of using experimental data to predict heat transfer behavior and to make the heat transfer predictions more accurate (than regular mathematical correlations), less reliant on assumptions, and easier to use. The ANN used by Kelleher et al. [9] had four inputs and one output. The inputs were: the temperature above saturation (superheat), the percent oil in the refrigerant, the number of active tubes, and whether the tubes were finned or staggered. The output was the heat flux. In order to graphically correlate the output for every input situation, over 60 plots would be needed. Due to this complexity, there was no attempt to correlate the data mathematically, but rather the neural network approach was used. Kelleher et al.’s [9] neural network had one hidden layer with log-sigmoid node functions and an output layer with linear node functions. The network was trained using the LevenbergMarquardt (Levenberg [10] and Marquardt [11]) accelerated backpropagation algorithm and a set of example data. The results were very good. After training, the network was able to accurately predict the heat flux for 72 different tube correlations and varying superheat. The average percent errors were well under 10%. The advantage of the neural network technique in this situation was that complex data were correlated accurately without any assumptions that would limit the neural network’s use. Heat transfer literature is most abundant in examples of ANNs used for performance prediction and control of heat exchangers. Research around the world has been fueled by the industry’s interest in being able to control heat exchangers and to provide the design engineers with simple yet effective prediction algorithms. A number of publications in this topic originated at the University of Notre Dame include Pacheco-Vega et al. [12, 13] and [4], Diaz et al. [14-17] and Sen and Yang [6]. In order to demonstrate how ANNs can be used to analyze heat exchangers a fairly simple example by Islamoglu [18] is described here. Islamoglu [18] used a feed-forward backpropagation ANN to predict heat transfer rates of a wire-on-tube type heat

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exchanger widely used in small refrigeration systems. Nineteen experiments were conducted in three air flow modes: all cross-, wire cross-, and tube cross-flow. Islamoglu’s [18] network had twelve input nodes (describing heat exchanger geometry and fluid flow rates), one output node corresponding to the heat flux, and one hidden layer with five nodes. The data were successfully correlated with a mean relative error of 4% (7.94% maximum relative error). Islamoglu’s [18] example shows how powerful ANNs are in correlating data governed by complex physics. ANNs have also been used to characterize various flows inside tubes and channels, a topic of particular interest in this dissertation. Ghajar et al. [19] used ANNs to significantly improve heat transfer correlations in the transition region for a circular tube with three different inlet configurations. The network Ghajar et al. [19] used had five input nodes, one hidden layer with eleven nodes, and one output node. A separate training process was used for each tube inlet configuration. Islamoglu and Kurt [20] trained an ANN to predict heat transfer from a channel with triangular corrugations. The input parameters were: corrugation pitch, corrugation angle, the Re number, and the hydraulic diameter. The output was the Nu number. The network had a 4-5-1 feedforward architecture and correlated Nu numbers with an average relative error <4%. Scalabrin and Piazza [21] applied neural networks to analyze heat transfer from tubes with supercritical carbon dioxide. This problem was particularly challenging due to thermophysical properties having very strong gradients in the near-critical zone. Scalabrin and Piazza [21] demonstrated the importance of selecting the proper input variables (i.e., those that account for the property gradients in the radial direction of flow) to obtain a universal ANN. In their particular case, failure to identify the correct input variables resulted in an ANN that was only able to “memorize” the training data set but was not general enough to correlate data from other sources. Chen et al. [22] is the only source known to the author that dealt with spirally corrugated tubes in terms of ANNs. However, the focus was only on the shape of the corrugation and not the helix angle. Chen et al. [22] tested tubes with four starts, a similar pitch (~9mm), diameter (~18.9mm), ridge height (~2.2mm), and helix angle (~61°) but different corrugation shapes. The shape of the corrugation was quantified in terms of angles α’ and α’’ as shown on Figure 9. The authors devised a radial-basis function ANN that correlated the angles of the triangular groove, α’ and α’’, with the inside heat transfer coefficient. Next, they used the ANN to determine the optimal corrugation shape. The highest value for the heat transfer coefficient occurred at α’’ ≈ 90° and α’ ≈ 62°. This result was outside of the range of tested tubes.

a

a FLOW DIRECTION

Figure 9. Corrugation angles investigated by Chen et al. [22].

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Albeit small, the number of publications described here indicates that ANNs can be used for a wide range of heat transfer and fluid problems. The literature review also shows that ANNs have not been applied to correlate heat transfer and friction with all of the necessary geometric parameters of a helically-finned tube. Such attempt is made in the following chapters of this dissertation.

Experimental Program An experimental program devised to measure turbulent pressure drop and heat transfer in helically-finned tubes was conducted at Mississippi State University. The experimental results were needed to train various artificial neural networks and to develop algebraic correlations for prediction purposes. Tube Geometries Tested Eight enhanced tubes and one plain tube were tested. The tubes were manufactured by Wieland-Werke AG of Ulm (Germany) for condenser applications. The geometric parameters of each tube are delineated in Table 1. The external geometry and the length were the same for each tube. The length was 10 ft; however, for installation purposes, only 9 ft of length were “finned” on both the outside and the inside of the tube. The tube material was copper-nickel. The internal fins were 0.48-mm thick at the base and 0.2mm thick at the tip. Thus, the included angle β was 41°. Tubes 5, 6, and 7 were matched to test the effect of the fin height. Tubes 2 and 3, and 4, 6, and 8 were used to analyze the influence of the helix angle. Finally, tubes 3 and 8 and 1, 2, and 4 were tested to investigate the effect of the number of starts. Table 1. Tube geometries. Tube #

Copper Wall

External Structure

Internal Structure

Outside Diameter

Fin pitch

Fin Height

Thickness

Fin Height

Number of Starts

Helix Angle

Internal Diameter

(mm)

(fins/inch)

(mm)

(mm)

(mm)

-

(°)

(mm)

1

18.82

40

0.945

0.645

0.38

10

25

15.64

2

18.82

40

0.925

0.68

0.375

30

25

15.61

3

18.86

40

0.94

0.68

0.38

30

48

15.62

4

18.79

40

0.925

0.685

0.38

45

25

15.57

5

18.82

40

0.90

0.71

0.31

45

35

15.6

6

18.79

40

0.93

0.68

0.38

45

35

15.57

7

18.82

40

0.935

0.68

0.51

45

35

15.59

8

18.77

40

0.925

0.67

0.38

45

48

15.58

9

18.85

40

0.93

0.67

0

-

-

15.65

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Experimental Apparatus A schematic of the experimental apparatus is shown in Figure 10. The helicallyfinned test tube was the inside of a double-pipe counterflow heat exchanger. Heat was transferred from the hot water flowing inside the test tube to the cold water flowing in the annulus. The cold water was provided by the city at approximately 20°C. The hot water loop consisted of a large water tank with a 15-kW variable-output heater, a 1-hp pump, the test tube, and a set of ball valves used to adjust the velocity of the water in the test tube. The cold water side consisted of a 9-ft long, 1¼-in I.D. annulus and a set of ball valves used to adjust the cold water flow rate. The water tank and all the piping were insulated. Figure 11 shows a detailed schematic of the test section. Two pressure taps were attached to the test tube. The pressure taps were connected to a Sensotec model TJE differential pressure transducer with a 0.1% accuracy. The temperatures were measured with 3-in-long type-T thermocouples mounted inside tees. The hot water line thermocouples were installed inside 1¼-in I.D. expansions in order to promote mixing of the water coming out of the test tube (and, thus, to measure the “mixing-cup” temperature). The test tube velocity was obtained by measuring the hot water line flow rate with an Omega FP-5300 flow meter accurate to 0.2 ft/s. The chilled water flow rate was measured with a Hersey 1006 flow meter accurate to 1%. Every transducer, after being carefully calibrated, was connected to an SCXI data acquisition system from National Instruments. The data acquisition system was composed of an SCXI-1102C module with an SCXI-1303 terminal block that measured temperatures and an SCXI-1100 module with an SCXI-1303 terminal block that measured flow rates and pressure drop. Both modules were installed in an SCXI-1000 chassis connected to a desktop computer via a PCI-MIO-16XE-50 data acquisition card. The hardware was controlled through a program written in LabVIEW 6.1.

hot water tank 15 kW

cold water in

+

heater _

test tube

pump cold

water out

Figure 10. Experimental apparatus schematic.

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Data reduction The Fanning friction factor was calculated according to the following data reduction equation:

f 

P  D 2  L   V 2

(4)

where L is the distance between pressure taps, ΔP is the pressure drop between pressure taps, D is the nominal inside diameter, ρ is the density at the mean bulk temperature, and V is the average velocity based on the nominal diameter. The inside heat transfer coefficient required a more complex approach because information about heat transfer in the annulus had to be obtained first. The heat transfer in the double-pipe, counterflow heat exchanger is governed by the total thermal resistance equation: lnDo Di  1 1 1 1 1      U o Ao U i Ai UA hi Ai 2k wall L ho Ao

(5)

where the areas are based on the nominal outside or inside tube diameters. Solving for the inside heat transfer coefficient yields the data reduction equation for the heat transfer coefficient measurement:

hi 

1  1 1 D lnDo Di   Ai     o U h 2 k o wall  o  Ao

(6)

cold water in hot water in

mixing cup

calming section

hot water out

anulus

test tube cold

water out

Legend pressure tap flow meter thermocouple

Figure 11. Detailed test section schematic

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In order to find hi, Uo and ho had to be known. Uo was calculated using an energy balance and the logarithmic mean temperature difference method. The mean heat transfer rate was used to find the overall heat transfer coefficient Uo:

 o c p o (To,out  To,in ) Q o  m

(7)

 i c p i (Ti ,in  Ti ,out ) Q i  m

(8)

Q  Q out Q mean  in 2

(9)

From the definition of the overall heat transfer coefficient:

Uo 

Q mean Ao LMTD

(10)

where LMTD is the logarithmic mean temperature difference. The outside heat transfer coefficient, ho, was obtained by means of the Wilson plot technique described in detail by Briggs and Young [23]. Basically, the heat transfer coefficient of the annulus is assumed to be represented by an equation of the following form (that is the same form as the Dittus-Boelter equation):

ho Dh,o ko

 C Re o Pro n

0.4

(11)

where Dh,o is the annulus hydraulic diameter, C and n are arbitrary constants, and the properties are evaluated at the mean bulk temperature. The 0.4 exponential coefficient was chosen because the water in the annulus was being heated. Based on the above analysis, Equation (5) can be represented in the following fashion:

1 n  C1 Re o  C 2 UA  k 0.4  where C1   o CAo Pro   Dh , o 

1

and C 2 

(12)

lnDo Di  1 .  2k wall L hi Ai

Constants C1 and n were found graphically, as described in section 0. With C and n known, ho was determined from Equation (11) and hi from Equation (6).

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Uncertainty analysis An uncertainty analysis was performed according to the guidelines outlined in Coleman and Steele [24]. The uncertainties of the calculated variables were found with the propagation technique, which quantifies how the uncertainties in the measured variables propagate through the data reduction equation. In general, the uncertainties of the measured variables arise from the use of calibration data fits and finite accuracy of standards and equipment used during the calibration process. Table 2 lists the uncertainties of the measured variables and calculated variables. Table 2. Uncertainties in experimental data. Measured Variables Variable Uncertainty T 0.23 K

Calculated Variables Variable Uncertainty f 15%

m i

7%

Q

8%

m o

3%

ho

10%

ΔP L D properties

150 Pa 1/16 in 0.01 mm negligible

hi Nui

10% 10%

The propagation of uncertainties associated with water and copper properties was neglected. The hot water flow meter was the largest contributor of uncertainty in the calculated variables. Therefore, the 15% uncertainty in the Fanning friction factor was largely due to the 7% uncertainty in the test water mass flow rate. The Nui had an uncertainty of only 10% because the heat flux used to compute hi was an average of Q i and Q , reducing the overall error. A physical manifestation of uncertainty in the o

measured variables was the discrepancy between Q i and Q o at steady-state conditions. These two values were measured within 10% of each other. Experimental procedure and results The objective of the first stage of the experiment was to obtain a correlation for the outside heat transfer coefficient, ho. To achieve this objective, the Wilson plot technique was utilized. The plain tube was inserted into the apparatus, and the hot water line valves were opened to full speed (Rei ≈ 56 000) and held constant. The heater setting remained at approximately 7 kW throughout the entire experiment. The cold water line (annulus) flow rate was varied and the overall heat transfer coefficient was recorded for each flow rate after steady-state conditions were reached. The data points acquired during this process were used to generate a plot of 1/UA values versus Reo-n. The value of n was varied until the data points fell on a straight line. Once the correct n value was found, C1 was the slope of this straight line and C was obtained via



C1  ko Dh , o CAo Pro



0.4 1

. The plot generated by the Wilson Plot procedure is shown in Figure 12. The values of C and n were found to be 1.302x10-3 and 1.234, respectively.

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The second stage consisted of validating the experimental apparatus. Isothermal friction factors and heat transfer coefficients were measured for the plain tube at Rei ranging from 12 000 to 50 000. During the heat transfer test, the water heater was set at 7 kW, and the annulus flow rate was maintained constant at Reo = 15 000. For consistency, these settings were used for all of the nine tubes tested. The plain tube results were compared with the Blasius and the Dittus-Boelter equations readily available in the heat transfer literature. The maximum percent difference between the measured and the theoretical values were 11% for the friction factor and 8% for the heat transfer coefficient. Once the experimental apparatus was validated, the helically-finned tubes were tested. The experimental results were cast in terms of the Fanning friction factor, f, and the Nusselt number, Nui (plotted, respectively, in Figure 13 and Figure 14). Heat transfer results were also cast in terms of the Colburn j-factor, for which the assumed dependence between Nui and Pri is j  Sti  Pri

2/3



Nu i Nu i Pri2 / 3  1/ 3 Re i  Pri Re i  Pri

(13)

The Colburn j-factor results are plotted in Figure 15. Wilson Plot 0.0018 0.0016

1/UA

0.0014 0.0012 0.0010 0.0008 0.0006 0.0004 2.0e-6

6.0e-6

1.0e-5 Reo-n

Figure 12. Wilson plot.

1.4e-5

1.8e-5

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Fanning Friction Factor Comparison 0.025

Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 Tube 6 Tube 7 Tube 8 Tube 9 Blasius

f Fanning

0.020

0.015

0.010

0.005

0.000 0

10000

20000

30000

40000

50000

60000

Re

Figure 13. Current study Fanning friction factor comparison.

Nusselt Number Comparison 500 Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 Tube 6 Tube 7 Tube 8 Tube 9 Dittus-Boulter

400

Nu

300

200

100

0 0

10000

20000

30000

Re Figure 14. Current study Nusselt number comparison.

40000

50000

60000

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Colburn j Factor Comparison 0.009 0.008 0.007 0.006

j

0.005 0.004 Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 Tube 6 Tube 7 Tube 8 Tube 9 Dittus-Boulter

0.003 0.002 0.001 0.000 0

10000

20000

30000

40000

50000

60000

Re Figure 15. Current study Colburn j- factor comparison.

Discussion of results The first topic of concern is the comparison of the plain tube performance with commonly available prediction equations. As stated in section 0, the plain tube measured friction factor was at most 11% higher than the Blasius solution, and the Nusselt number was at most 8% off from the Dittus-Boelter equation. The magnitudes of these errors are within the range obtained from the uncertainty analysis. Therefore, the plain tube results were considered acceptable, thus validating the experimental apparatus. Before discussing the enhanced-tube results presented in Figures 13 and 14, it is practical to convert the internal geometry of the tubes in Table 1 into dimensionless parameters. Table 3 was obtained by introducing the axial fin pitch, p = πD/(Ns tan α) and calculating the dimensionless factors e/D, p/e, and p/D. These dimensionless parameters allow a more direct comparison between the tubes and provide more physical insight into the results (e.g., for a transverse fin reattachment occurs at 6 < p/e < 8). Table 3 does not explicitly indicate that the helix angle and the number of starts are dimensionless parameters. However, since these parameters are unitless, they can be treated as such. Therefore, α and Ns can be used as direct parameters in any correlation. The friction results shown in Figure 13 follow a rather predictable trend. The same can be said about the Nui results from Figure 14. The friction factor decreases and the Nusselt number increases with increasing Reynolds number. In order to study the influence of geometric parameters, tubes that vary in only one of the independent variables must be identified and compared. This task is achieved qualitatively in Table 4, where each geometric parameter is listed and its influence on f and Nui is identified.

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For the most part, the results are consistent with rational expectations; that is, both f and Nui increase with increasing e/D, Ns, and α. The only exception occurs in the comparison of the friction factor in tubes 3 and 8. This exception could be caused by the high helix angle (48°) and the consequent development of skimming flow (tubes 8 and 3 have a p/e ratio of 2.577 and 3.876, respectively) with a lower friction factor for tube 8 than for tube 3. Among the helically-finned tubes, the highest friction factor was displayed by tube 3 and the lowest by tube 1. In terms of the Nusselt number, the best performance was achieved by tube 8 and the worst by tube 1. Tube 1 has the smallest helix angle and the smallest number of starts (Ns = 10; p/e = 27.729). Tubes 3 and 8 have the highest helix angle (α = 48°). Tube 7 is also worthy of note because of its highest e/D ratio (0.0327) with α = 35°. Except at Rei = 12 000, tube 7 displayed the second highest friction factor and Nusselt number. At a Reynolds number of 12 000, tube 7 had the highest Nui and a friction factor nearly equal to that of tube 3. The information presented so far would seem to confirm the theory that the helix angle is one of the most important parameters in determining the characteristics of flow in helically-finned tubes. Table 3. Test tube dimensionless parameters. Internal Structure

Dimensionless Factors

Tube D

e

p

Ns

[mm]

[mm]

[mm]

1

15.64

0.38

10.54

10

2

15.61

0.375

3.51

3

15.62

0.38

4

15.57

5

α

e/D

p/e

p/D

25

0.0243

27.729

0.674

30

25

0.0240

9.348

0.225

1.47

30

48

0.0243

3.876

0.0941

0.38

2.33

45

25

0.0244

6.134

0.150

15.6

0.31

1.56

45

35

0.0199

5.017

0.100

6

15.57

0.38

1.55

45

35

0.0244

4.085

0.100

7

15.59

0.51

1.55

45

35

0.0327

3.048

0.100

8

15.58

0.38

0.98

45

48

0.0244

2.577

0.0629

9

15.65

#

[°]

plain

Table 4. Qualitative analysis of the influence of geometric parameters on friction and heat transfer results. Parameter under study Ns or p/e Ns or p/e e/D α

Tubes used for parameter study (in order of increasing parameter) 124 38 567 468

Tube numbers in order of increasing experimental f

Tube numbers in order of increasing experimental Nui

124 83 567 468

124 38 567 468

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Empirical correlation development The purpose of the current section is to obtain least-squares empirical correlations for prediction of f- and j-factors in helically-ribbed tubes. The reason for producing algebraic least-squares correlations is to have an ANN assessment criterion (or a benchmark). The ANN performance must be better than a least-squares correlation or the extra effort of developing the ANN is of no value. A common and reasonable approach in correlating several variables is to use a power-law approach. Such an approach was utilized by Webb et al. [25], as presented in Equations (14) and (15): f  0.108Re 0.283 N s0.221 (e / D) 0.785  0.78

(14)

j  St Pr 2 / 3  0.00933Re 0.181 N s0.285 (e / D) 0.323 0.505

(15)

The process of least-squares regression consists of finding the power coefficients that make the prediction error minimal. Some preliminary algebraic manipulation can make this task a linear algebra problem. Equations (14) and (15) can be represented by the following general form: f  1 Re  2 N s 3 (e / D)  4   5

(16)

where χ1 through χ5 are constants to be determined, and the left-hand side could very well be replaced by j. Taking the natural logarithm of both sides yields: ln f  ln 1  ln Re  2  ln N s 3  ln(e / D)  4  ln  5

(17)

ln f  ln  1   2 ln Re   3 ln N s   4 ln(e / D)   2 ln 

(18)

or

The above equation can be formulated for each data point collected. When dealing with multiple equations, a matrix notation is preferred:

ln f  1 ln Re ln N s          

ln  1     2  ln(e / D) ln     3        4    5 

(19)

where the dots represent the repeating equations. There are as many equations as there are data points, so the linear algebra problem has the form:

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  

(20)

where Χ is the vector of unknown constants to be determined, Θ is the equation matrix, and Ψ is the vector of natural logarithms of experimentally determined friction factors or j factors. The key point of the correlation development is to minimize the prediction error. The easiest error to monitor is the sum of the squared errors; hence, the name leastsquares regression. Using matrix algebra formulation, the sum of the squared errors associated with any given vector Χ is

 error



2

      T

(21)

In the current study, Mathcad software was used to minimize the error function introduced in the equation above. Mathcad analysis yielded the following equations: f  0.128Re 0.305 N s0.235 (e / D) 0.319  0.397

(22)

j  0.029 Re 0.347 N s0.253 (e / D) 0.0877  0.362

(23)

Fanning Friction Factor Prediction Evaluation 1.3 Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 Tube 6 Tube 7 Tube 8

1.2

fpre/fexp

1.1

1.0

0.9

0.8

0.7 0

10000

20000

30000

40000

50000

60000

Re Figure 16. Evaluation of friction results with equation (22).

The best way to verify the performance of Equations (22) and (23) is to plot the percent error between the predicted and experimental values. The error for the friction factor is

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plotted in Figure 16 (mean squared error: MSE = 1.070x10-6) and the one for the j factor is depicted in Figure 17 (MSE = 6.945x10-8). Both figures include the vast majority of the predicted data within 10% of the experimental results. Tube 3 shows the highest under-prediction for the friction factor case and the highest over-prediction of the j factor. Tube 8 has the highest over-prediction of the friction factor, and tube 7 exhibits the highest under-prediction of the j factor. Moreover, Figure 17 demonstrates waveshaped variations of the error with respect to the Reynolds number. The mathematical form of the j factor correlation [Equation (16)] proposed a priori is unable to represent such variation; a limitation that an artificial neural network does not possess.

Artificial Neural Network Development Notation Figure 18 shows a general three-layer ANN and the notation employed. Due to the large number of parameters involved, developing an unambiguous way of presenting the constants and functions that describe a neural network is important. In this study, the software employed for ANN development is MATLAB, so the notation presented here is almost identical to that used by MATLAB. The only difference is that MATLAB indexing must start at 1 and not 0; so in MATLAB, all the 0-indexed variables are essentially replaced by a different variable. The consistency of the notation presented herein allows MATLAB to execute computations at each layer rapidly because of its matrix algebra capability [26]. The index-0 layer represents inputs (see Figure 18). x0 is a column vector of inputs of size S0; whereas, S1, S2, and S3 are the number of nodes in layer 1, 2, and 3, respectively. W1,0 is a weight matrix feeding the inputs to layer 1. The weight matrix is constructed such that entry W1,0j,k multiplies input k and feeds it into node j in layer 1. In general, Wl,mj,k multiplies output k from layer m and feeds it into node j in layer l. b is the bias column vector. Its size corresponds to the number of nodes in a given layer. F is a vector of node functions (MATLAB feed-forward backpropagation networks utilize either linear, log-sigmoid, or tan-sigmoid functions) and generally, the same function is used for the entire layer. Weights and biases are reported as matrices and vectors, respectively, in the notation presented above. Furthermore, the name of the ANN also contains the description of the network’s architecture. For example, “f_ANN_4LS_3LS_1LIN” stands for a friction factor network with 4 nodes in layer 1 using log-sigmoid functions [in MATLAB: logsig(x) = 1 / (1 + exp(-x)) ], 3 nodes in layer 2 using log-sigmoid functions, and 1 node in layer 3 using a linear function [in MATLAB: purelin(x) = x ].

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Colburn j Factor Prediction Evaluation 1.3 Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 Tube 6 Tube 7 Tube 8

1.2

jpre/jexp

1.1

1.0

0.9

0.8

0.7 0

10000

20000

30000

40000

50000

60000

Re Figure 17. Evaluation of heat transfer results with equation (23).

Layer 1

Input x0

s0 x1 1

s0

W 1.0 s 1x s b1 s 1x 1

Layer 2

+s

x1

W 2.1 s 2x s 1

1

b2 s 2x s 1

s 1x 1

x0

1x

1

F

s1

x1 = F 1( W 1,0 x0 + b1)

+

s 2x 1

Layer 3

F2

s2

s 2x 1

x2

W 3.2 s 3x s 2

1

b3 s3x 1

x2 = F 2( W 2,1 x1 + b2)

x3

+

s3x 1

F3

s3x 1

s3

x3 = F 3( W 3,2 x2 + b3)

Figure 18. Neural network notation.

Normalization of experimental data When training ANNs, normalizing the inputs and targets to ensure that all the weights are within the same order of magnitude is advantageous. The normalized data will be denoted with the symbol “*.” The data from the current study have been normalized in the following fashion:

 Re  1800  Re *     Re  1800 

2

(24)

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Ns* 

Ns 100

(25)

e / D*  10  e / D

(26)

*  sin( )

(27)

f *  10  f

(28)

j*  100  j

(29)

The significance of Equation (24) is that it forces Re* to go to zero if Re = 1 800 (critical Reynolds number for transition) and to one if Re is large. The other normalizing equations have been chosen for their simplicity. Moreover, the inputs to every neural network in this study have been organized in the following manner:

 Ns *   *    0 x   e / D *  Re* 

(30)

Determination of optimal network architecture The performance of an ANN depends on its architecture. Large networks can learn complex functions, but require more effort to train and to report. Hence, the network selection process is a compromise between a small network size and a minimal prediction error. The architecture of the optimal network to be used for prediction of friction and j-factors in helically-ribbed tubes was determined for this study by training different networks and evaluating their performance with the mean squared error (MSE) criterion. Half of the experimental data (every other Reynolds number) from each tube was put into a training basket, while the entire data set was used for validation. The Levenberg-Marquardt algorithm (Levenberg [10] and Marquardt [11]) was used for the training process. Training was stopped when the MSE of the entire data set reached a minimum. The training results were compiled in Table 5, which lists the MSEs of all networks trained with 50% of experimental data. Additional information about each network (i.e., weights, biases, training curves, and performance plots) is included in APPENDIX A. The idea behind the selection of the various networks in Table 5 was to start out with an arbitrary 4-3-1 network and to remove nodes and layers to see what happens to the network’s performance. Initially, one node was removed from each of the first two layers to yield a 3-2-1 network. Next, the second layer was removed to yield a 4-1 network. Then, a 2-1 network was constructed. For the 2-1 case, a logsigmoid output node function was also tested, but showed no improvement in performance.

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Table 5. Mean squared errors of ANNs trained with 50% of data. f Network f_4LS_3LS_1LIN f_3LS_2LS_1LIN f_4LS_1LIN f_2LS_1LIN f_2LS_1LS

j MSE 7.7760x10-9 1.6848x10-8 8.3616x10-9 1.0061x10-7 1.1755x10-7

Network j_4LS_3LS_1LIN j_3LS_2LS_1LIN j_4LS_1LIN j_2LS_1LIN j_2LS_1LS

MSE 1.0062x10-9 2.2488x10-9 1.9653x10-9 6.3833x10-9 6.5631x10-9

Table 5 reveals that even the worst performing networks, f_2LS_1LS and j_2LS_1LS, have a smaller mean squared error than the power-law regression presented in the previous section [Equations (22) and (23) showed, respectively, a MSE of 1.070x10-6 for f and a MSE of 6.945x10-8 for j]. The 4-3-1 architecture exhibited the smallest MSE. Removing one node from the first two layers deteriorated the networks’ performance more than removing the second layer. For this reason, the 4-1 network appears to be more suitable for prediction of f and j in helically-ribbed tubes. The use of the MSE is an excellent numerical criterion for evaluating the performance of a prediction tool. Nevertheless, a visual inspection of the error behavior is also very important. Figure 16 and Figure 17 visualized the performance of the power-law regressions developed in the previous chapter. For comparison purposes, these visualizations are redrawn in Figure 19 and Figure 20 in a slightly different manner, which will be employed throughout the rest of the chapter. Now, consider the performance of the f_4LS_1LIN network depicted in Figure 21 and the j_4LS_1LIN network in Figure 22. Both networks were trained with 50% of experimental data as described earlier. Both figures clearly show that the 4-1 network geometry works very well, and, more importantly, that the neural network performance is superior to the power-law regression performance. Based on this visual inspection and the MSE values of Table 5, the prediction (or “regression”) error associated with the 4-1 ANNs trained with 50% of data can be taken as negligible. Thus, the only error associated with the use of these networks is the experimental uncertainty. The information presented so far reinforces the statement that the ANN does not know and does not have to know what the physics of the problem are. The ANN completely bypasses simplifying assumptions such as the use of a power-law equation. On the other hand, any unintended and biased errors in the training data set are also picked up by the ANN. The trained ANN, therefore, is not better than the training data, but not worse either.

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Figure 19. Performance of equation (22).

Assessment of the networks’ ability to generalize The ANNs developed so far were trained with 50% of data from all tubes. One can postulate that such networks only learn to “interpolate” between the Re numbers they were trained with and are unable to predict the performance of unknown geometries. The current section attempts to prove that the 4-1 networks are indeed able to generalize. Table 6 delineates the mean squared errors (MSE) of f_4LS_1LIN and j_4LS_1LIN networks trained with data from 2, 3, 4, 5, and 6 tubes and evaluated with all of the experimental data (8 tubes). Table 6 implies that the ANNs trained with selected tube data performed worse than the networks trained with 50% of data from all 8 tubes (see Table 5). However, if enough tubes were provided for training, the ANNs performed better than correlations (22) and (23). As expected, the network performance generally improved as additional tubes were put in the training basket. In the case of the f_4LS_1LIN network, 6 training tubes were needed to obtain satisfactory performance. The j_4LS_1LIN network was more perceptive and showed outstanding results with 4 training tubes. The networks’ performance was sensitive to the randomly-generated initial guess, so the training procedure was repeated 10 to 20 times for each case, and only the best results were considered. The results summarized in Table 6 prove that the 4LS-1LIN networks recommended in the previous section are able to generalize and correctly predict the performance of unknown geometries.

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Table 6. MSE's of networks trained with selected tube data. Training Tubes 1 and 5 1, 3, and 5 1, 3, 5, and 7 1, 3, 4, 5, and 7 1, 3, 4, 5, 7, and 8

MSE f_4LS_1LIN j_4LS_1LIN 1.321x10-5 3.329x10-7 -7 9.290x10 2.324x10-7 -7 6.438x10 8.794x10-9 7.060x10-7 1.668x10-8 -8 4.713x10 6.442x10-9

Evaluation of f- and j- networks with experimental data of Webb et al. [25] In this section, the Webb et al. [25] experimental data are used to evaluate the performance of two f_4LS_1LIN and j_4LS_1LIN networks. Because of their superior performance on the current data set, ANNs trained with 50% of experimental data from all tubes and ANNs trained with 6 out of 8 tubes were chosen for evaluation. The evaluation results are summarized in Table 7.

0.009

0.008

jprediction

0.007

0.006

0.005

0.004

0.003

0.002 0.002

0.003

0.004

0.005

0.006

jexperiment Figure 20. Performance of equation (23).

0.007

0.008

0.009

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f 4LS 1LIN (Trained w/ 50% Data) 0.026 0.024 0.022

f prediction f prediction

0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.008

0.01

0.012

0.014

0.016 0.018 f experiment

0.02

0.022

0.024

0.026

Figure 21. Performance of the f_4LS_1LIN ANN trained with 50% data.

-3

j 4LS 1LIN (Trained w/ 50% Data)

x 10

8

j prediction j prediction

7

6

5

4

3

2

2

3

4

5 6 j experiment

7

8

9 -3

x 10

Figure 22. Performance of the j_4LS_1LIN ANN trained with 50% data.

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Table 7. Evaluation of f- and j- networks with data of Webb et al. (2000). f ANN f_4LS_1LIN (trained w/ 50% of data from all tubes) f_4LS_1LIN (trained w/ tubes 1, 3, 4, 5, 7, and 8)

j

MSE

Performance shown on

1.216x10-5

Figure 23

2.756x10-5

Figure 24

ANN j_4LS_1LIN (trained w/ 50% of data from all tubes) j_4LS_1LIN (trained w/ tubes 1, 3, 4, 5, 7, and 8)

MSE

Performance shown on

4.600x10-6

Figure 25

4.198x10-6

Figure 26

The first conclusion drawn from the inspection of the figures listed in Table 7 is that the neural networks do not predict the data of Webb et al. [25] very well. In fact, the mean squared errors (MSE) associated with the neural networks are in most cases higher than the ones associated with using Equations (22) and (23) [MSE = 1.345x10-5 using Equation (22) and MSE = 3.886x10-6 using Equation (23)]. Furthermore, as was the case with the power-law correlations, Webb et al.’s [25] friction data are overpredicted and heat transfer data under-predicted by the neural networks. Basically, there seems to be a difference in the experimental results between the current study and that of Webb et al. [25]. Finally, Table 7 reveals that there is no clear advantage of using networks trained with all of the tubes or with data from selected tubes. with Data of Webb et al (2000) 0.03

f prediction f predicted

0.025

0.02

0.015

0.01

0.005 0.005

0.01

0.015 0.02 f experiment

0.025

0.03

Figure 23. Evaluation of the f_4LS_1LIN ANN (trained w/ 50% Data) with data of Webb et al. [25].

Evaluation of f- and j- networks with experimental data of Jensen and Vlakancic [27] In this section, the Jensen and Vlakancic [27] experimental data are used to evaluate the performance of the f_4LS_1LIN and j_4LS_1LIN networks. As in the previous section, ANNs trained with 50% of experimental data from all tubes and

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ANNs trained with 6 out of 8 tubes were chosen for evaluation. The evaluation results are summarized inEvaluation Table 8.of f 4LS 1LIN (Trained w/ Tubes 1, 3, 4, 5, 7, and 8) with Data of W ebb et al (2000)

0.025

f prediction f prediction

0.02

0.015

0.01

0.005 0.005

0.01

0.015 f experiment

0.02

0.025

Figure 24. Evaluation of the f_4LS_1LIN ANN (trained w/ tubes 1, 3, 4, 6, 7, and 8) with data of Webb et al. [25].

x 10

-3

8

j prediction

7

6

5

4

3 3

4

5

j experiment

6

7

8

-3

x 10

Figure 25. Evaluation of the j_4LS_1LIN ANN (trained w/ 50% Data) with data of Webb et al. [25].

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-3

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Evaluation of j 4LS 1LIN (Trained w/ Tubes 1, 3, 4, 5, 7, and 8) with Data of W ebb et al (2000)

8

j prediction j prediction

7

6

5

4

3 3

4

5 6 j experiment

7

8 x 10

-3

Figure 26. Evaluation of the j_4LS_1LIN ANN (trained w/ tubes 1, 3, 4, 6, 7, and 8) with fata of Webb et al. [25]. Evaluation of f 4LS 1LIN (Trained w/ 50% of Data) with Data of Jensen and Vlakancic (1999) 0.05

0.04

f prediction

0.03

0.02

0.01

0

-0.01

-0.02 -0.02

-0.01

0

0.01 0.02 f experiment

0.03

0.04

0.05

Figure 27. Evaluation of the f_4LS_1LIN ANN (trained w/ 50% data) with data of Jensen and Vlakancic [27].

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Evaluation of f 4LS 1LIN (Trained w/ Tubes 1, 3, 4, 5, 7, and 8) with Data of Jensen and Vlakancic (1999) 0.025

f prediction

0.02

0.015

0.01

0.005 0.005

0.01

0.015 f experiment

0.02

0.025

Figure 28. Evaluation of the f_4LS_1LIN ANN (trained w/ tubes 1, 3, 4, 6, 7, and 8) with data of Jensen and Vlakancic [27].

x 10

-3

10 9

j prediction

8 7 6 5 4 3 2

2

3

4

5

6

7

j experiment

8

9

10

11 x 10

-3

Figure 29. Evaluation of the j_4LS_1LIN ANN (trained w/ 50% Data) with data of Jensen and Vlakancic [27].

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Evaluation of j 4LS 1LIN (Trained w/ Tubes 1, 3, 4, 5, 7, and 8) -3 with Data of Jensen and Vlakancic (1999) x 10

10 9

j prediction

8 7 6 5 4 3 2

2

3

4

5

6 7 j experiment

8

9

10

11 x 10

-3

Figure 30. Evaluation of the j_4LS_1LIN ANN (trained w/ tubes 1, 3, 4, 6, 7, and 8) with data of Jensen and Vlakancic [27]. Table 8. Evaluation of f- and j- networks with data of Jensen and Vlakanic [27]. f ANN f_4LS_1LIN (trained w/ 50% of data from all tubes) f_4LS_1LIN (trained w/ tubes 1, 3, 4, 5, 7, and 8)

j

MSE

Performance shown on

2.798x10-4

Figure 27

1.995x10-5

Figure 28

ANN j_4LS_1LIN (trained w/ 50% of data from all tubes) j_4LS_1LIN (trained w/ tubes 1, 3, 4, 5, 7, and 8)

MSE

Performance shown on

5.389x10-6

Figure 29

4.709x10-6

Figure 30

Table 8 implies that the ANNs trained with data of tubes 1, 3, 4, 5, 7, and 8 predict Jensen and Vlakancic’s [27] data slightly better than Equations (22) and (23) in terms of the mean squared errors [MSE = 2.666x10-5 using Equation (22) and MSE = 5.355x10-6 using Equation (23)]. Generally though, the performance of the ANNs on the Jensen and Vlakancic [27] data was poor. The f_4LS_1LIN network trained with 50% of data from all tubes predicted negative friction factors for tube JV3 and over-predicted tube JV4’s friction by as much as 400% (see Figure ). Finally, the errors associated with the f- and j-networks suggest that the results of Jensen and Vlakancic [27] demonstrate a different Reynolds number dependence than the current study results. ANNs trained with a combined database A common engineering practice is to average multiple measurements to obtain the “best” value. Therefore, a network trained with a database combining the results of

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Jensen and Vlakancic [27], Webb et al. [25], and the current study would be a useful prediction tool. To create such a tool, an f_4LS_1LIN and a j_4LS_1LIN network were trained with 50% of data points (every other Reynolds number) from a database combining the experimental results of Webb et al. [25], Jensen and Vlakancic [27], and the current study. The performance of these two networks is depicted respectively on Figure 31 and Figure 32. The mean squared errors (MSE) of the f_4LS_1LIN and j_4LS_1LIN networks are 4.553x10-7 and 7.671x10-8, respectively, and are lower than the ones associated with Equations (22) and (23) applied to any of the data sets. The network prediction errors were also plotted as a function of Re* on Figure 33 for the friction factor and on Figure 34 for the Colburn j-factor. Both figures show that the majority of data points from the combined set are predicted within plus or minus 10%. Based on the information presented so far, the f_4LS_1LIN and j_4LS_1LIN networks trained with 50% of data points from the combined database appear to be the best prediction tool friction and heat transfer in helically-ribbed tubes. The current chapter showed that ANNs perform extremely well on the data sets that they are trained with, but poorly on independent data, with experimental discrepancies being a probable reason for disagreement. Several ANNs were capable of outperforming algebraic correlations, but the key aspect (other than the network’s geometry and node functions) affecting the network performance was the selection of the training data set. This selection must be carried out carefully, so that there is enough variation in the inputs for the network to establish trends. The more data is used in training process the better the network performance. However, using too many data points during the training process can affect the network’s ability to generalize.

0.024 0.022

f prediction f prediction

0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.006 0.008

0.01

0.012 0.014 0.016 0.018 f experiment

0.02

0.022 0.024

Figure 31. Performance of f_4LS_1LIN ANN trained with 50% combined data.

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j 4LS 1LIN (Trained w/ 50% Combined Data)

x 10

11 10

j prediction j prediction

9 8 7 6 5 4 3 2

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7 8 j experiment

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Figure 32. Performance of j_4LS_1LIN ANN trained with 50% combined data. f 4LS 1LIN (Trained w/ 50% Combined Data) Errors 1.25 1.2

f prediction / f experiment

1.15 1.1 1.05 1 0.95 0.9 0.85 0.8 0.75 0.4

0.5

0.6

0.7 Re*

0.8

0.9

Figure 33. f_4LS_1LIN (trained with 50% combined data) prediction errors.

1

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j 4LS 1LIN (Trained w/ 50% Combined Data) Errors 1.3 1.25 1.2

j prediction / j experiment

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0.65

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0.75 Re*

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0.85

0.9

0.95

Figure 34. j_4LS_1LIN (trained with 50% combined data) prediction errors.

Conclusions This chapter first introduced heat transfer enhancements techniques. A literature review of heat transfer and friction in tubes with helical enhancements (indentations, ribs, fins, wire inserts, or spiral tapes) was performed, and available prediction methods were reported. The current understanding of complex secondary flows in the interfin region was discussed. An introduction to artificial neural networks (ANNs) was presented, and a literature review of the use of ANNs in heat transfer and fluid flow was conducted. Next, heat transfer coefficients and friction factors were determined experimentally for eight helically-finned tubes and one smooth tube using liquid water at 12 000 < Rei < 60 000. An uncertainty analysis was completed and plain-tube results were compared to the Blasius and Dittus-Boelter equations with satisfactory agreement. The highest jfactor was achieved by tube 8 (Ns = 45, α = 48°, e/D = 0.0244) and the lowest f-factor by tube 1 (Ns = 10, α = 48°, e/D = 0.0244). Power-law correlations for f and j-factors were developed using a least-squares regression. The performance of the correlations was evaluated with independent data of Webb et al. [25] and Jensen and Vlakancic [27]. Several ANNs were trained with 50% of friction and heat transfer data points from all tubes to determine the optimal network architecture. The best architecture was a twolayer network with four log-sigmoid nodes in the first layer and one linear node in the output layer (networks f_4LS_1LIN and j_4LS_1LIN). Then, this architecture was trained with friction and heat transfer data of 2, 3, 4, 5, then 6 tubes to check whether or

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not the ANN had the ability to generalize. Networks trained with 50% of data points from all tubes and networks trained with data of 6 tubes were evaluated with independent data of Webb et al. [25] and Jensen and Vlakancic [27]. Finally, a friction network and a heat transfer network were trained with 50% of combined experimental data of Webb et al. [25], Jensen and Vlakancic [27], and the current study. The performance of these two networks was reported graphically and in terms of the mean squared error.

Nomenclature A b cp C D Dh e e+ f F G h H HR j k lc lcsw L LMTD  m

Surface area (m2) Node bias Specific heat at constant pressure (J/kg-K) Constant used in Nusselt number correlation Diameter (m) Hydraulic diameter (m) Fin height (m) Roughness Reynolds number Fanning friction factor Node function Heat transfer roughness function Convective heat transfer coefficient (W/m2-K) Pitch for 180° rotation of twisted tape (m) Helix ratio Colburn j-factor (=StPr2/3) Thermal conductivity (W/m-K) Characteristic length (m) Modified characteristic length for swirling flows (m) Length of the tube (m) Log Mean Temperature Difference (K) Mass flow rate (kg/s)

MSE Ns Nu P p Pr q Q r R Ra Re

Mean squared error Number of fin starts Nusselt number Pressure (Pa) Axial fin pitch (m) Prandtl number Heat flux (W/m2) Heat transfer rate (W) Radial direction in cylindrical coordinates (m) Momentum transfer roughness function Rayleigh number Reynolds number

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S St t T

Number of nodes in a layer Stanton number Average rib width (m) Temperature (K)

u* V w W x z

Friction (or shear) velocity (m/s) Velocity (m/s) Weight Weight matrix Node input/output Axial direction in cylindrical coordinates (m)

Greek Letters α Helix angle (°) α’ and α’’ Corrugation shape angles (°) β Included angle (°) Γ Diffusivity (m2/N-s) Δ Difference θ Circumferential direction in cylindrical coordinates (rad) 1 ln Re ln N s ln(e / D) ln  Θ Equation matrix          μ Dynamic viscosity (N s/m2) ν Kinematic viscosity (m2/s) ρ Density (kg/m3) τ Shear stress (Pa) Φ Tube severity factor χ Constant ln  1  Χ Vector of constants     2     Ψ Subscripts eff eq i in o out p r turb z

ln f  Experimental data vector, e.g.        Effective Equivalent Inside At inlet Outside (annulus side) At outlet Plain (or smooth) tube Radial direction in cylindrical coordinates Turbulent Axial direction in cylindrical coordinates

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Angular direction in cylindrical coordinates Component parallel to the fin Component perpendicular to the fin

Superscripts * With the exception of u*, refers to normalized network inputs and outputs

References [1]

[2] [3]

[4]

[5] [6]

[7]

[8]

[9]

[10] [11] [12]

Ashforth-Frost, S., Fontama, V.N., Jambunathan, K., and Hartle, S.L., “The role of neural networks in fluid mechanics and heat Transfer”, Proceedings of the 1995 IEEE Instrumentation and Measurement Technology Conference, Vol. 1, April 1995, pp. 6-9. Haykin, S., Neural Networks: A comprehensive foundation, Macmillan, New York, 1994. Mehrotra, K., Mohan, C.M., and Ranka, S., Elements of artificial neural networks (Complex adaptive systems), The MIT Press, Cambridge, Mass., 1996. Pacheco-Vega, A., Sen, M., Yang, K.T., and McClain, R.L., “Neural network analysis of fin-tube refrigerating heat exchanger with limited experimental data”, International Journal of Heat and Mass Transfer, vol. 44, pp. 763-770, 2001. Kalogirou, S.A., “Applications of artificial neural networks in energy systems. A review”, Energy Conversion & Management, vol. 40, pp. 1073-1087, 1999. Sen, M., and Yang, K.T., “Applications of artificial neural networks and genetic algorithms in thermal engineering”, in The CRC Handbook of Thermal Engineering, 2000, pp. 620-661. Jambunathan, K., Hartle, S.L., Ashforth-Frost, S., and Fontama, V.N., “Evaluating convective heat transfer coefficients using neural networks”, International Journal of Heat and Mass Transfer, vol. 39, No. 11, pp. 23292332, 1996. Thibault, J., and Grandjean, B.P.A., “A neural network methodology for heat transfer data analysis”, International Journal of Heat and Mass Transfer, vol. 34, No. 8, pp. 2063-2070, 1991. Kelleher, M.D., Cronley, T.J., Yang, K.T., and Sen, M., “Using artificial neural networks to develop a predictive method from complex experimental heat transfer data”, American Society of Mechanical Engineers Heat Transfer Division (HTD), vol. 369, No. 5, pp. 11-34, 2001. Levenberg, K., “A method for the solution of certain problems in least squares”, Quarterly of Applied Mathematics, vol. 2, pp. 164-168, 1944. Marquardt, D., “An algorithm for least-squares estimation of nonlinear parameters”, SIAM Journal on Applied Mathematics, Vol. 11, pp 431-441, 1963. Pacheco-Vega, A., Sen, M., Yang, K.T., and McClain, R.L., “Prediction of humid air heat exchanger performance using artificial neural networks”,

Heat and Friction in Helically-Finned Tubes Using…

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24] [25]

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 105

American Society of Mechanical Engineers Heat Transfer Division (HTD), vol. 364-3, pp 307-314, 1999. Pacheco-Vega, A., Sen, M., Yang, K.T., and McClain, R.L., “Heat rate predictions in humid air-water heat exchangers using correlations and neural networks”, Transactions of the ASME: Journal of Heat Transfer, vol. 123, No. 3, pp 348-354, 2001. Diaz, G., Sen, M., McClain, R.L., and Yang, K.T., “On-line training of artificial neural networks for control of a heat exchanger test facility”, Proceedings of the National Heat Transfer Conference, vol. 1, pp. 359-365, 2001. Diaz, G., Sen, M., Yang, K.T., and McClain, R.L., “Dynamic prediction and control of heat exchangers using artificial neural networks”, International Journal of Heat and Mass Transfer, vol. 44, pp. 1671-1679, 2001. Diaz, G., Sen, M., Yang, K.T., and McClain, R.L., “Simulation of heat exchanger performance by artificial neural networks”, HVAC&R Research, vol. 5, No. 3, pp. 195-208, 1999. Diaz, G., Yanes, J., Sen, M., Yang, K.T., and McClain, R.L., “Analysis of data from single-row heat exchanger experiments using an artificial neural network”, American Society of Mechanical Engineers Fluids Engineering Division (FED), vol. 242, pp. 45-52, 1996. Islamoglu, Y., “A new approach for the prediction of the heat transfer rate of the wire-on-tube type heat exchanger - use of an artificial neural network model”, Applied Thermal Engineering, vol. 23, pp. 243-249, 2003. Ghajar, A.J., Tam, L.M., and Tam, S.C., “Improved heat transfer correlation in the transition region for a circular tube with three inlet configurations using artificial neural networks”, Heat Transfer Engineering, vol. 25, No. 2, pp. 3040, 2004. Islamoglu, Y., and Kurt, A., “Heat transfer analysis using anns with experimental data for air flowing in corrugated channels”, International Journal of Heat and Mass Transfer, vol. 47, pp. 1361-1365, 2004. Scalabrin, G., and Piazza, L., “Analysis of forced convection heat transfer to supercritical carbon dioxide inside tubes using neural networks,” International Journal of Heat and Mass Transfer, vol. 46, pp. 1139-1154, 2003. Chen, X.D., Xu, X.Y., Nguang, S.K., and Bergles, A.E., “Characterization of the effect of corrugation angles on hydrodynamic and heat transfer performance of four-start spiral tubes”, Transactions of the ASME: Journal of Heat Transfer, vol. 123, pp. 1149-1158, 2001. Briggs, D.E., and Young, E.H., “Modified wilson plot techniques for obtaining heat transfer correlation for shell-and-tube heat exchangers”, Presented at the 10th National Heat Transfer Conference in Philadelphia, Pennsylvania, American Institute of Chemical Engineers, August 11-14, 1968, pp. 2-25. Coleman, H.W., and Steele, W.G., Experimentation and uncertainty analysis for engineers, John Wiley & Sons, New York, 1999. Webb, R.L., Narayanamurthy R., and Thors, P., “Heat transfer and friction characteristics of internal helical-rib roughness”, Transactions of the ASME: Journal of Heat Transfer, vol. 122, pp. 134-142, February 2000.

106 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

[26] [27]

Chamra et al.

Hagan, M., Demuth, H., and Beale M., Neural Network Design, Martin/Hagan (Distributed by the University of Colorado), 1996. Jensen M.K., and Vlakancic, A., “Experimental investigation of turbulent heat transfer and fluid flow in internally finned tubes”, International Journal of Heat and Mass Transfer, Vol. 42, pp. 1343-1351, 1999.

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Chapter 4 The Heat Transfer Characteristics of CO2 and CO2-Oil Mixture in Tubes Rin Yun∗ Department of Mechanical Engineering, Hanbat National University Daejeon 305-719, South Korea

Abstract The heat transfer characteristics of CO2 and CO2-oil mixture in tubes including convective flow boiling, gas cooling, and condensation are investigated. Two-phase flow patterns are thoroughly investigated based on physical phenomena, which show the early flow transition to intermittent or annular flow especially for small diameter tube. The physical phenomena for nucleate boiling of CO2 follow the same trends with other organic fluids under the same reduced pressure. The gas cooling heat transfer is critically dependent on the turbulent diffusivity related with buoyancy force due to the large density difference. Under the oil presence conditions, the interaction of oil rich layer and bubble formation is the physical mechanism for the CO2-oil mixture convective boiling. Besides, the gas cooling phenomena with oil should be investigated based on the flow patterns formed by CO2 and oil, and the oil rich layer, whose thickness are depends on the solubility of CO2 to oil explains the physical mechanisms of heat transfer. The thermodynamic properties of CO2-oil were estimated by the general model based on EOS, and they are utilized to estimate the properties for oil rich layer and oil droplet vapor core. Through these predicted properties, the convective boiling and gas cooling heat transfer coefficients and pressure drop theoretically estimated. Condensation of CO2 is not so different from the existing one, so the heat transfer coefficients and pressure drop are well estimated by the existing one developed for other fluids.

Introduction Carbon dioxide refrigeration systems have been reintroduced since 1990s. Lorentzen [1] gave us a great promising of using natural refrigerants in his paper. Since then, many researchers have investigated the CO2 systems, and achieved great advances in technologies for developing CO2 systems. The applications of the CO2 systems are heat pump, water heater, space heating heat distribution systems, combined space heating and hot water heating, drying, automobile air conditioner, residential air conditioning, and micro-electric cooling system. For the low temperature applications, bending machine and supermarket applications can be considered. The CO2-NH3 cascade system was commercialized for supermarket application. Besides, CO2 has been investigated as a secondary fluid because mass flow rate can be reduced by 1/6 and there are significant savings in pumping power. The CO2 system has the following two important characteristics, which come from the thermodynamic properties of CO2. One of them is that the CO2 refrigeration cycle undergoes the transcritical process. The critical temperature of CO2 is 31.1°C. In summer, the ambient temperature is larger or close to that temperature. For the heat rejection process of the cycle, the working temperature ∗

Email address: [email protected]

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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should be higher than the ambient temperature. The other is that the working pressure is very high. The critical pressure of CO2 is 7.38 MPa, so the system is operating over that critical pressure due to the transcritical cycle. The CO2 system should be designed to ensure this high working pressure. The CO2 system has large volumetric capacity due to high vapor density, which is 3 – 10 times larger than CFC, HCFC, HFC and HC. It means that a small sized design is possible. Besides, it has low pressure ratio and high pressure differences. The former means that iso-entropy efficiency is high for compressor, the latter means that it suffers a great loss in the expansion process. It has the optimum discharge pressure for the maximum COP due to the characteristics for the P-T relations under the transcritical process. The thermal conductivities of saturated liquid and vapor at 0oC for CO2 are 20% and 60% higher than of the liquid and vapor phase for R-134a, respectively. Viscosity of liquid phase CO2 is only 40% of R134a liquid viscosity, for vapors are comparable with that of R134a. Because the influences of pressure on the enthalpy and entropy are small below the critical temperature, the pressure drop may be allowed to be higher. The temperature change associated with pressure drop in the evaporator will become smaller. In this chapter, many aspects of heat transfer characteristics of CO2 in tubes are explained, which include convective boiling heat transfer, gas cooling heat transfer, and condensation. The oil effects on the heat transfer characteristics and mixture properties are also explained. The prediction methods for the gas cooling heat transfer coefficient for CO2-oil mixture are suggested too. When the heat transfer characteristics of CO2 are explained, the physical phenomenon is sought in this research, and author tries to show that CO2 is not a peculiar working fluid, simply the physical properties under the normal working conditions for a refrigeration cycle are different from the other working fluids.

Convective Boiling Heat Transfer Flow pattern in tubes Flow patterns observation Two-phase flow patterns are the most important tools for explaining the heat transfer and pressure drop characteristics in convective boiling heat transfer. The accurate models for them are developed based on the flow patterns. Compared to the conventional working fluids, the experimental visualizations of CO2 in tubes are very limited due to its high saturation pressure. Table 1 summarized the available studies of the two-phase flow patterns for CO2 from the open literatures. Pettersen [2] investigated the two-phase flow patterns for CO2 at a temperature of 20oC and mass flux ranging from 100 to 580 kg/m2s. Test tube diameter ID is 0.98 mm and vapor quality was varied from 0.12 to 0.99. Flow was mainly in the wavy annular regime, with considerable entrainment of liquid drops in the core flow. From the x/G diagram as shown in Fig. 1, the dominance of intermittent flow at low G and the dominance of annular flow at higher G can be observed. Intermittent flow includes slug, bubble, and elongated bubble flow regimes. The droplet flow regime becomes more important at higher G, a fact that may help explaining the observed dryout in heat transfer at higher G. Compared to small-diameter observations with air/water at low pressure, the transition into annular flow occurred at much lower superficial vapor

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velocity. Yun and Kim [3] studied the CO2 flow patterns with flow channel having a width of 16 mm and a height of 2 mm, and the glass is covered on that channel. Mass flux changed from 217 to 1100 kg/m2s under the heating condition. The observed flow patterns are depicted in Fig. 2. As the mass flux increases, the flow transitions of bubbly-slug and slug-annular flow occur at a lower vapor quality. These early transitions are closely related with the active bubble formation and larger liquid droplet entrainment due to a lower surface tension as shown in Table 2. For mass flux greater than 868 kg/m2s, the flow regime directly transits from bubbly to annular flow without having intermittent flow. This flow pattern is different from that with the air-water even though the similar hydraulic diameter. This is from the differences in heating conditions and the boiling characteristics of CO2. When Hosler’s data [4] were compared with those for air-water mixture test under adiabatic conditions, the flow regime transitions occurred at a lower superficial vapor velocity, which were relatively close to those of CO2. As shown in Table 2, the steam-water properties under the Hosler’s test condition are similar to those for CO2. Table 1 Flow pattern observations

Pettersen [2 ] Yun and Kim [3] Gasche [5 ] Schael and Kind [7 ] Park and Hrnjak [8] Ozawa et al. [11]

Channel configurations

Tube dia. (ID) (mm)

Mass velocity (kg/m2s)

Heat flux (kW/m2)

Single tube Horizontal Rectangular channel, horizontal Rectangular channel, horizontal Smooth glass tube + micro fin tube, horizontal Glass tube, horizontal

0.98

100 – 580

13

Saturation temperature (oC) 0, 20

16 × 2.0

217-1736

-

5

Subcooled – 0.8

0.794 × 0.685

58 - 235

Max: 1.8

23.3

0.005 – 0.88

Microfin tube: 8.62

50 - 500

-

5 and -5

0.1 – 0.9

6

100-400

-

-15, -30

0.1-0.9

1 2 3

200-700 200-500 100-300

10-50 5-35 5-25

5.3-26.8 22.0-26.8 4.5-6.5

-

Small-bore tubes

Vapor quality 0.12-0.99

Gasche [5] investigated the flow patterns for CO2 with rectangular microchannel milled into an aluminum substrate whose sizes are 0.794mm × 0.6858mm × 50.8 mm microchannel with heating blanket. Three types of flow patterns were observed, namely plug, slug, and annular flow. When mass flux is less than 149 kg/m2s plug flow is predominant for low qualities up to about 0.25, and the slug flow was predominant for intermediate qualities from 0.25 to 0.50. Annular flow was observed for high qualities above 0.5. For mass flux of 188 and 235 kg/m2s, only two flow patterns of slug and annular flow were observed. Slug flow was predominant for low qualities up to 0.25 and annular flow was observed for high vapor qualities. Gasche shows that the transition between intermittent flow and annular flow seems to be over-predicted on the Thome- El Hajal map [6].

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Table 2 Properties of CO2, steam-water, and air-water. Fluids CO2 at 5oC Steam-water at 13.8MPa Air-water at 20oC and 1 atm

pr 0.54 0.63 -

ρl - ρv 783 540 997

ρl/ ρv 7.85 7.32 864

σ(N/m) 0.0036 0.0065 0.072

µ(Pas) 9.6 × 10-5 7.23 × 10-5 1.0 × 10-3

Schael and Kind [7] investigated the flow patterns during flow boiling of CO2 in a horizontal microfin tube. The microfin tube was a Wieland Cuprofin EDX tube with 60 fins, height of 0.25 mm and a helix angle of 18o. The tube diameter is 9.52 mm. The flow patterns, observed with sight glass under the pressure conditions of 39.7 bar and 26.4 bar, show a wide range of the annular flow region. Due to the spiral fins of the microfin tube the transition flow patterns from slug to annular and wavy to annular flow respectively occupy large areas of the flow pattern map. The transition from stratified to non-stratified flows is in general accordance with the predicted curve of Thome and El Hajal [6]. However, larger deviations were observed for the transition from slug-annular to annular flow. Park and Hrnjak [8] studied the flow patterns for CO2 and R410a. Temperature conditions were –15oC and –30oC, they used a 6.0 mm glass tube. They suggested that the Weisman et al.'s flow pattern map [9] gave a good agreement with the visualized flow patterns for CO2 and R410a. Wojtan et al's flow pattern map [10] showed relatively good agreement with the flow patterns for stratified wavy, slug, and slug stratified wavy, however, intermittent to annular flow’s vapor quality is overpredicted by the model. Fig. 3 shows the comparison of the observed flow pattern by Park and Hrnjak with the Weisman et al. flow pattern map. According to Ozawa et al.’s results [11] the observed flow pattern suggests that the slug-annular flow occupies rather wide region penetrating into the annular flow region predicted by so far proposed criteria. They also observed that the slug and slug-annular flows together with the effect of phase stratification leads to the intermittent dryout at the upper wall, while the bottom wall remains still a nucleate boiling state. Test tube diameter is 1.0 to 3.0 mm, and saturation temperatures are 14.3 oC and 25.4 oC. Fig. 4 shows the observed flow patterns with the existing models. Flow pattern map of CO2 As proved by many researches, the existing flow pattern maps fail to predict the flow pattern transition from intermittent to annular for CO2. This is because most tests for the flow pattern of CO2 were conducted with micro- or mini- channels, and the thermodynamic properties under the high reduced pressure are different from the existing fluids. The new flow pattern maps for CO2 are developed by Yun and Kim [3], and Cheng et al [12]. Yun and Kim developed the flow transition criteria for CO2 of bubbly –slug, slug- annular, and bubbly – annular. Bubbly –slug model comes from the drift-flux model as eq. (1). Fig. 5 shows the flow pattern transition model with Petterson’s flow pattern data [2], which was drawn by Thome and Ribatski [13]. jg/ε = COj (Co = 1.11, ε = 0.2)

(1)

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Fig. 1. Flow pattern observation plotted against vapor quality. Conditions: D=0.98 mm, T=20oC, q = 13 kW/m2 (Reprinted from [2] with permission from Elsevier.).

Fig. 2 Flow regime map with respect to mass flux and vapor quality. (Reprinted from [3] with permission from Elsevier.).

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Fig. 3 Comparison of the flow pattern with the Weisman et al. flow pattern map. (Reprinted from [8] with permission from Elsevier.).

Fig. 4 Flow pattern map of CO2 in 2-mm tube. Solid lines: Cheng et al. and dashed lines: Revellin and Thome, IB: isolated bubble, CB: coalescing bubble, A: annular flow. (Reprinted from [11] with permission from Elsevier.).

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Slug – annular transition model comes from that for micro-gravity condition. Surface tension, which maintains the interface between froth and slug is important parameter and gravity force related with the buoyancy force can be negligible from small gap size. These conditions are well reflected by using the Weber number as shown in eq. (2). Wegs = ρjg2dh/σ =20

(2)

Bubbly – annular flow transition criteria is as follows. Wefs = ρjf2d/σ > 100, Wegs = ρjg2d/σ =20, jg/ε = COj (Co = 1.05, ε=0.35)

(3)

Cheng et al. [12] developed the flow pattern map for CO2 by modifying the Wojtan et al. model [10] with the existing experimental flow pattern data for CO2. The stratified-wavy to intermittent and annular flow (SW-I/A) transition boundary is calculated with the Kattan-Thome-Favrat criterion [14] as eq. (4).

G wavy

⎧⎪ 16 AVD 3 gDeq ρ L ρ V =⎨ 2 2 2 1/ 2 ⎪⎩ x π [1 − (2hLD − 1) ]

⎡ π2 ⎢ 2 ⎣ 25hLD

⎛ FrL ⎜⎜ ⎝ We L

⎞ ⎤ ⎫⎪ ⎟⎟ + 1⎥ ⎬ ⎠ ⎦ ⎪⎭

1/ 2

+ 50

(4)

The annular flow to dryout region (A-D) transition boundary of eq. (5) was further modified. It is calculated with the new modified criterion of Wojtan et al.

Gdryout

⎧ 1 ⎡ 0.58 ⎤⎛ Deq ⎪ ⎛ ⎞ =⎨ ln⎜ ⎟ + 0.52⎥⎜⎜ ⎢ ⎦⎝ ρV σ ⎪⎩ 0.236 ⎣ ⎝ x ⎠

⎞ ⎟⎟ ⎠

− 0.17

⎡ ⎤ 1 ⎢ ⎥ ⎣⎢ gDeq ρV ( ρ L − ρV ) ⎦⎥

− 0.17

⎛ ρV ⎜⎜ ⎝ ρL

⎞ ⎟⎟ ⎠

− 0.25

⎛ q ⎜⎜ ⎝ qcrit

⎞ ⎟⎟ ⎠

− 0.27

1.417

⎫ ⎪ ⎬ ⎪⎭

(5) A new criterion for the dryout region to mist flow(D-M) transition was proposed as eq. (6).

G mist

− 0.15 − 0.16 ⎧ 1 ⎡ 0.61 ⎡ ⎤ ⎛ ρV ⎤⎛ D eq ⎞ 1 ⎪ ⎛ ⎞ ⎟⎟ ⎜⎜ =⎨ ln⎜ ⎟ + 0.57⎥⎜⎜ ⎢ ⎥ ⎢ gD ( ) 0 . 502 x ρ σ ρ ρ − ρ ⎝ ⎠ ⎣ ⎦ ⎢ ⎥ V ⎦ ⎝ ρL ⎝ V ⎠ ⎪⎩ ⎣ eq V L

⎞ ⎟⎟ ⎠

− 0.09

⎛ q ⎜⎜ ⎝ q crit

⎞ ⎟⎟ ⎠

− 0.72

(6) The big differences between the Cheng et al. model and others, which were developed for large diameter and other refrigerants, are found at the transition vapor quality for intermittent and annular flow. This transition vapor quality for CO2 is significantly advanced to lower vapor quality. The dispersed flow for the Cheng et al. model occupies the large area when it is compared to the Wojtan et al. map. Fig. 6 shows one example of comparison between the Gashe’s observed flow pattern and the Cheng et al. model.

1.613

⎫ ⎪ ⎬ ⎪⎭

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Fig. 5 Comparison between the flow pattern map proposed by Yun and Kim [3] and the diabatic observations by Pettersen for Tsat = 20oC and a tube diameter of 0.98 mm. (Reprinted from [13] with permission from Elsevier.).

Fig. 6 The experimental data of the observed flow patterns by Gashe [5] in the updated CO2 flow pattern map. Tsat = 23.3 oC, Deq = 0.833 mm, q = 1.86 kW/m2 (Reprinted from [12] with permission from Elsevier.).

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General observation The flow pattern of CO2 should be considered from the high reduced pressure point of view. This is analogous to the steam-water flow pattern under the high pressure. There is similarity between them in terms of density ratio, viscosity, and surface tension, though the surface tension of steam-water is higher than that of CO2. With increase of saturation pressure the transition from slug to annular flow occurs at low superficial gas velocity. With increase of saturation pressure, nucleate boiling is very active, and the gas and liquid density ratio is large. It makes the gas and liquid easily changeable, and the region of the intermittent flow is getting smaller with an increase in saturation pressure. Therefore, the vapor quality at which the flow transition from intermittent flow to annular flow is lower than the existing flow pattern map. Comparing the Wojtan et al. model [10] and the Cheng et al. [12] model, the boundary for the transition from the intermittent flow to annular flow occurs at low vapor quality for the Cheng et al. model. For example, the transition boundaries are 0.68 and 0.24 at the saturation temperature of 25oC, respectively. These early transitions are closely related with the active bubble formation and larger liquid droplet entrainment due to a lower surface tension. The other observation is that the transition from the intermittent to annular is advanced with a decrease in the tube diameter as shown in Fig. 7. According to Garimella [15], liquid film easily formed with decrease of tube diameter because surface tension effects are dominant than the gravitation effects. For the dryout phenomena, it occurs earlier due to the instability of the liquid film from the lower surface tension and the similar density between liquid and vapor under the high reduced pressure, which increase of liquid droplet. When the flow patterns for CO2 are compared to other refrigerant, intermittent- annular flow transition vapor quality is higher. In other words, transition occurs at higher superficial vapor velocity for the same mass flux condition due to the high density ratio between vapor and liquid.

Convective boiling heat transfer characteristics The convective boiling heat transfer of CO2 can be characterized by the higher heat transfer coefficients compared to other refrigerant before dryout. The other is that the dryout is observed at moderate vapor quality. There are a lot of investigations for flow boiling of pure carbon dioxide, which are well summarized by Thome and Ribatski [16]. Table 3 shows the latest published experimental studies on flow boiling of CO2, which were not summarized in their review paper. Park and Hrajak [17] compared the flow boiling heat transfer characteristics of CO2 with R410a and R22 at very low temperature of -15oC and -30 oC. The heat transfer coefficient for CO2 is nearly independent of vapor quality except the condition of mass flux of 100 kg/m2s. The Wattelet et al. correlation and the Gungor and Winterton correlation give the best agreement with the measured heat transfer coefficients for CO2. Zhao and Bansal [18] showed that the boiling heat transfer coefficients increased with vapor quality prior to dryout at -30oC, and the Liu and Winterton model showed the best fit with the experimental data. Choi et al. [19] tested the boiling heat transfer of CO2, R22, and R134a with minitubes of 1.5 and 3.0 mm. The mean heat transfer coefficient ratio of R-22, R134a and CO2 was approximately 1.0:0.8:2.0. Oh et al. [20] observed a decreasing trend of heat transfer coefficients with respect to vapor quality, which is explained by the dryout at the top side of the tube. From their experimental results, the

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Jung et al. model shows the best fit. The average deviation and the mean deviation are 14.26 and 21.64%, respectively. Mastrullo et al. [21] interpreted the experimental results based on the local circumferential distribution of heat transfer coefficients, the flow regimes and the thermo-physical properties. They inferred the flow patterns of slug flow for low vapor quality, and the stratified-wavy or annular flow for high vapor quality based on the local circumferential distribution of heat transfer coefficients. The statistical analysis showed that the Cheng et al. correlation provided the best results. The suggested models by above researchers are summarized in Table 4.

800 700

2 mm 3 mm

2

Mass flux (kg/m s)

600 500 400

1 mm

300 200 100 0.0

0.2

0.4

0.6

0.8

1.0

Quality

Fig. 7 Effect of Dh on annular flow regime [15].

Table 3 Experimental studies on flow boiling for CO2

Park and Hrnjak [17 ] Zhao and Bansal [18] Choi et al. [19] Oh et al. [20 ] Mastrullo al. [21]

et

Mass velocity (kg/m2s) 100 – 400

Heat flux (kW/m2)

Vapor quality

5 – 15

Saturation temperature (oC) -15, -30

0.1 – 0.8

12.6 – 19.3

-30

0.1 -0.9

1.5, 3.0

139.5 – 230.9 200 – 600

20 – 40

-10 – 10

- 1.0

7.75

200 - 500

10 – 40

-5, 0, 5

0 -0.8

6.0

200 – 349

10 – 20.6

-7.8 – 5.8

0.02 -0.98

Channel configuration

Tube dia. (ID),(mm)

Single circular tube, horizontal Single circular tube, horizontal Single circular tubes, horizontal Single circular tube, horizontal Single circular tube, horizontal

6.1 4.57

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Table 4 Suggested convective boiling heat transfer coefficient models for CO2 in literature. Park and Hrnjak [17 ] Zhao and Bansal [18 ] Choi et al. [19] Oh et al. [20 ] Mastrullo et al. [21]

Suggested heat transfer coefficient model Gungor and Winterton Wattelet et al. Liu and winterton

Mean dev. (%) 14.4 18.3 9.2

Average Dev. (%) 1.74 -6.16 0.4

Developed model Wattelet et al. Jung et al. Whole database: Cheng et al. Intermittent flow regime: Annular flow regime: Cheng et al.

8.41 10.06 21.64 22.6 3.2 10.3

0.37 -3.03 -14.26 4.7 3.2 8.6

General observations Effects of heat flux The heat transfer coefficients increased with an increase in heat flux over the most ranges of vapor quality in the researches in the Table 3. It is well established theory that the nucleate boiling is directly dependent on the amount of heat flux. Important factors of the thermal properties for nucleate boiling are the surface tension and density ratio between the liquid and vapor, which are also related to the nucleate boiling suppression. Table 5 shows the comparison of the surface tension, density ration, reduced pressure, and vapor quality for nucleate boiling suppression of CO2 with other fluids. Because bubble formations are most effective when the surface tension is low and the density ratio is large, CO2 shows the higher heat transfer coefficients at low vapor quality compared to conventional refrigerants. In other words, the convective boiling at low vapor quality is dominated by the nucleate boiling heat transfer. Gorenflo and Kotthoff [22] investigated the nucleate pool boiling heat transfer of CO2 with a horizontal 8 mm O.D. copper tube. They concluded that the high heat transfer coefficients measured for CO2 in comparison to hydrocarbon or halocarbon refrigerants are mainly due to the fact that the application of CO2 is mostly envisaged for conditions where reduced saturation pressure pr is higher than for common refrigerants [22]. They concluded that the general trends of nucleate boiling observed with CO2 are not different from other organic fluids when they are compared at the same reduced pressure conditions as shown in Fig. 8. Eq. (7) shows the dot-dashed line in Fig. 8.

h / h 0.1 = 1.2p r

0.27

+ (2.5 + 1 /(1 − p r )) × p r

(7)

Table 5 Comparison of thermodynamic properties between CO2 and the existing refrigerants at the saturation temperature of 5oC, q=10kW/m2, ID=6mm, and G=300 kg/m2s. Fluids CO2 R22 R134a

Surface tension (N/m) 0.003489 0.011 0.01084

Density ratio (ρv/ρl) 0.1279 0.01962 0.01341

Reduced pressure 0.5381 0.1171 0.0862

Vapor quality for suppression of nucleate boiling 0.99 0.85 0.77

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Fig. 8 Comparison of the pool boiling results of CO2 with 20 other organic fluids and the seven other refrigerants. (Reprinted from [22] with permission from Elsevier.).

Effects of Mass Flux After suppression of the nucleate boiling heat transfer, the convective boiling heat transfer is dominated by the convective heat transfer between liquid film on tube wall and vapor core. Considering these physical phenomena, the convective boiling heat transfer is significantly affected by the mass flux. Under these circumstances, the flow pattern is generally annular flow. However, we can observe that the convective boiling heat transfer is not dominated by the mass flux for CO2. These characteristics can be explained by the following combined reasons. One is that the effect of nucleate boiling on the convective boiling heat transfer for CO2 is greater than that for other fluids. The other is that the flow instability increases with an increase in mass flux. As shown in Table 5, the surface tension is lower and the density ratio is larger than other conventional fluids. When the difference of densities between liquid film and vapor core is small, the probability of the detachment from the liquid film in the form of liquid drop increases, and these phenomena is favorable when the surface tension is lower. Under these conditions, the liquid film can be easily unstable and liquid droplets are dominant in the vapor core. It can be easily imagined that the positive effects from the increased mass flow rate diminished from these flow instability. Besides, the possibilities of dryout for liquid film increase with increase of mass flux. Influence of saturation temperature It is generally observed that the heat transfer coefficient of CO2 increases with increase in saturation temperature, which comes from the enhancement of nucleate boiling heat transfer at higher saturation temperature. The properties of the density ratio and surface tension significantly depend on the saturation temperature, and the heat

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transfer characteristics are varied with the saturation temperature. The most noticeable figure is that the variation trend of heat transfer coefficients with vapor quality at different saturation temperatures. When the saturation temperatures are higher than 5oC, decreasing heat transfer coefficient was dominantly observed. However, when the saturation temperatures were around -20oC, this decreasing trend with vapor quality was not observed. Although the thermo-physical properties of CO2 are still quietly different from the conventional ones at even a low saturation temperature of -20oC, the convective flow boiling heat transfer for lower saturation temperature condition is much more stable than that for higher saturation temperature. Effects of Tube Diameter In contrast to boiling in conventional tubes, the flow boiling heat transfer coefficients in microchannels are significantly dependent on heat flux and saturation pressure while only slightly dependent on flow velocity and vapor quality. Many experimental studies have concluded that the nucleate boiling is a dominant mechanism for evaporation in minichannels with a small convective evaporation contribution. Although the hydraulic diameter of multichannel is close to the minichannles, some studies concluded that for their tests with multichannel arrangement the nucleation is not an important mechanism [23]. Dryout Phenomena The rapid reduction of the heat transfer coefficient of CO2 at moderate vapor can be easily observed in many studies of the convective boiling heat transfer of CO2. This early dryout is closely related with the micro- and mini-channels and the thermophysical properties of CO2. As shown in Fig. 7, the transition to annular flow advanced to the lower vapor quality with decrease of tube diameter, and CO2 has the favorable properties for the large liquid droplet entrainments. Both of them increase the liquid film dryout at low vapor quality. Revellin et al. [24] investigated the trends for dryout vapor quality with mass flux by using the liquid film Reynolds number. There are three representative models for estimating the dryout vapor quality for CO2 in open literatures. Cheng et al. [12] suggested the dryout inception and dryout completion vapor quality by modifying criterion of the Wojtan et al.’s [10] as Eqs. (8) and (9), respectively.

[0.52 − 0.236WeV 0.17 Frv, Mori 0.17 ( ρV / ρ L ) 0.25 (q / q crit ) 0.27 ]

(8)

[0.57 − 0.502WeV 0.16 Frv, Mori 0.15 ( ρV / ρ L ) −0.09 (q / qcrit ) 0.72 ] xde = 0.61e

(9)

x di = 0.58e

Petterson [2] suggested that onset of dryout for CO2 could be estimated by the Ahmad method [25]. The basic concept of the Ahmad method is that the dryout inception of the interesting fluid can be estimated by using water dryout data, which is scaled to the fluid by eqs. (10) and (11).

120 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

⎡ GD ⎤ ⎡ µ l 2 ⎤ ψ =⎢ ⎥ ⎥⎢ ⎣ µ l ⎦ ⎣⎢σDρ l ⎦⎥

γ =

Yun

2/3

⎡ µl ⎤ ⎢ ⎥ ⎣ µv ⎦

−1 / 5

∂ ( ρ l / ρ v ) sat ∂p

(10)

(11)

Yun and Kim [26] suggested the critical liquid film thickness to predict the dryout vapor quality for CO2. The estimation procedure for dryout vapor quality of CO2 as follows. Eqs. (12) and (13) are for calculation of critical liquid film thickness utilized in the third steps; (1) Convert operating conditions for CO2 to equivalent steam-water conditions using similarity factors. (2) Apply the annular flow model with the converted conditions such as heat flux, mass flux, and saturation pressure (3) Determine the critical quality by comparing the calculated liquid film thickness of the model with the critical liquid film thickness. ⎛ 3ν 2 ⎞ δ = ⎜⎜ Re ⎟⎟ ⎝4 g ⎠

1/ 3

Re = 4Γ f ,out / µ

Prediction models for CO2 boiling heat transfer coefficients

(12) (13)

It is general to develop the heat transfer models for the prior to dryout and post-dryout separately for CO2. However, conveniently for the moderate degradation of heat transfer coefficient, which is found under the moderate mass flux, heat flux, and evaporation temperature, and a large diameter tube, it was known that the heat transfer coefficients are well estimated by using the existing models as shown in Table 4. However, when a significant drop of heat transfer coefficient occurs under the high saturation temperature or high mass flux with micro- or mini- tube, it is impossible to fit the whole data with only one model. As mentioned, the most common method is to develop the separate models for prior to dryout and post-dryout. As the latest developed model, Cheng et al. [27] divided the post-dryout region into two regions, one is transition region (inception of dryout and completion of dryout) and the other is fully dryout region (the mist flow region). As noted, it is appropriate to relate the heat transfer coefficient models to flow pattern of CO2. Concerning micro- and mini- size effects, the effects of surface tension are inevitably considered in the model. Petterson [2] suggested the model for the boiling heat transfer coefficient as shown in Table 6. Asymptotic model of eq. (14) is for the prior-dryout region. Eqs. (15) and (16) are the Cooper model [28] and the Kattan et al. model [14], respectively. The dryout inception was estimated by the Ahmad method [25] as explained in the previous

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section. Eqs. (17), (18), (19), and (20) are the Shah and Siddiqui model [29] for the post-dryout region. Because the Petterson model is verified with his own data set obtained with microchannels whose hydraulic diameter is 0.98 mm, the applicable tube diameter is limited to less than 1.0 mm. Table 6 Summary of the heat transfer coefficient model by Petterson [2] Mechanism Nucleate boiling Convective evaporation Model for combining nucleate and convective heat transfer Dryout inception Post-dryout heat transfer Applicable tube diameter

h nb = 55p r

Model Cooper Kattan et al. Asymptotic model The Ahamd method Shah and Siddiqui Less than 1.0 mm

0.12− 0.4343 ln( R P )

h ce = 0.0133 Re l

0.69

[

h = ( h nb ) 3 + (h ce ) 3

Prl

(−0.4343 ln p r ) −0.55 M −0.5 q 0.67

0.4

kl δ

(15)

]

1/ 3

Nu = 0.023 Re 0.8 Prv

0.4

(16) for Re > 104

Nu = 0.00834 Re 0.8774 Prv Re =

0.6112

(17)

for Re < 104

(18)

GDx A µvα

(19) 3

3

x A = (−0.0347 + 0.9335 x E − 0.2875 x E + 0.035 x E ) Frl

h pre = 16.26q 0.72 p r

h post

(14)

0.064

(20)

0.88

⎡⎛ GD ⎞⎛ ⎞⎤ ρ ⎟⎟⎜⎜ x + v (1 − x ) ⎟⎟⎥ = 0.00327 ⎢⎜⎜ ρl ⎠⎦ ⎣⎝ µ v ⎠⎝

(21) 0.901

Prv ,w

1.32

Y −1.5 ×

kv D

(22)

0.4

⎞ ⎛ρ Y = 1 − 0.1⎜⎜ l − 1⎟⎟ (1 − x ) 0.4 ⎠ ⎝ ρv

(23)

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Table 7 Summary of the heat transfer coefficient model by Yun and Kim [30] Mechanism Pre-dryout heat transfer Dryout inception Post-dryout heat transfer Applicable tube diameter

Model The heat flux model The critical liquid film thickness model The Groeneveld Less than 2.0 mm

Table 7 shows the summary of Yun and Kim’s model [30]. They suggested the model for the condition of the steep variation of heat transfer coefficients. Prior to the inception of dryout the heat flux model of eq. (21) was suggested. The dryout inception was predicted by the critical liquid film thickness model [26], and the Groeneveld model [31] (eqs (22) and (23)) was utilized for the post-dryout region. The applicable tube diameter is limited to less than 2.0 mm. For the large diameter tubes including multi-channel and low mass flux condition, there is a high probability of stratified flow and partial dryout, which shows the moderate variation of heat transfer coefficients with vapor quality. These moderate changes of the heat transfer coefficients are well estimated by the existing models shown in Table 4. Table 8 Summary of the heat transfer coefficient model by Cheng et al. [27] Mechanism Pre-dryout heat transfer Dryout inception Post-dryout heat transfer Applicable tube diameter

Model The modified kattan-thome-favrat The modified criterion of wojtan et al. The wojtan et al., and the modified Groeneveld Less than 7.5 mm

The Cheng et al. model [27] is summarized in Table 8. This model is based on the Wojtan et al.’s model [10], and is modified to correlate the existing CO2 data set. It should be noted that the Wojtan et al. model has different correlations for each flow patterns. Important characteristic of the Cheng et al. model is the post-dryout region divided into transition and mist flow region. The vapor quality for the completion of dryout and for the inception of mist flow can be calculated by eq. (9). Eqs. (24), (25), and (26) are for the pre-dryout region, and hV , hnb , and hcb are modified from the original Kattan-Thome-Favrat model [14]. Eq. (27) and eq. (28) are for the transition region and mist flow region, respectively. htp =

θ dry hV + (2π − θ dry )hwet 2π

hV = 0.023 ReV

[

0.8

PrV

hwet = ( Shnb ) 3 + hcb

0.4

kV Deq

]

3 1/ 3

The heat transfer coefficient in the dryout region is as follow:

(24)

(25)

(26)

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hdryout = htp ( x di ) −

x − x di htp ( x di ) − hM ( x de ) x de − x di

[

]

(27)

For mist flow, the correlation by Groeneveld is modified. hM = 2 × 10 −8 Re H

1.97

PrV

1.06

Y −1.83

kV Deq

(28)

Pressure drop Pressure drop of CO2 is smaller than that of the conventional refrigerants. This is from both the relatively small viscosity and density differences between liquid and vapor under the application conditions. Due to this small density difference the velocity difference between two-phase is less than that of the conventional refrigerants, which results into less two-phase flow interfacial shear stress. Table 9 shows the comparison of the pressure drop of CO2 with the existing models. Park and Hrnjak [17] suggested the Müller-Steihagen and Heck[32] and the Friedel model [33]. Oh et al. [20] show that most of the correlations over-predict their results about 40%, except the Choi et al.'s model [34]. As explained, the flow conditions for mini- and micro- channels are strongly affected by the thermo-physical properties of surface tension and gap size. Therefore, most pressure drop correlations for micro- and mini-channels modified the Chisholm parameters by including the tube diameter, the Laplace number (eq. (29)), and the Weber number [35]. Eq. (30) shows the Yun and Kim model [36], which considers the effects of tube diameter on the two-phase effects. The two phase effects decreased with decrease of the tube diameter. The pressure drop characteristics for multi-channel are different from those for single channel having the same hydraulic diameter with the multi-channel. We cannot neglect the flow distribution effects on the pressure drop for multi-channel. According to the Pettersen [2], the pressure drop model for the mini-single tubes shows poor prediction results for the multi-channel. Yun and Kim’s results [36] show different trends between the single mini-channels and multi-channel having the same hydraulic diameter too. Table 9 Suggested pressure drop model by authors. References Park and Hrnjak [17] Oh et al. [20]

Tube diameter 6.1 mm 7.75 mm

Suggested Pressure drop model Muller-steinhagen and Heck [32] Choi et al. [34]

⎛ ⎞ σ ⎜ ⎟ ⎜ g(ρ − ρ ) ⎟ l g ⎠ ⎝ La = d

Mean dev. (%) 19.2

Average Dev. (%) -5.29

19.5

13.9

0. 5

(29)

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C = 21 × (1 − e ( −0.085 D ) )

(30)

Because the two-phase flow pattern of mini- or micro-channels is different from the large diameter tube, it makes differences of the pressure drop characteristics for mini tubes from the large diameter tubes. For example, the dryout of liquid film occurs at low vapor quality for the small diameter tube. When the pressure drop is considered across the whole vapor quality the two-phase effects are weaker for mini tubes than the conventional sized tube from this early dryout. Considering these facts, the type of the Cheng et al model [12], which was developed for each flow pattern, is suitable. Table 10 shows the brief summary of the model. The Cheng et al. model estimated the total 387 database from 5 independent sources, and it shows mean error is 28.6%, standard deviation is 44.3%. It shows the best performance among the tested models. Eq. (31) is for the flow pattern of intermittent-slug flow, eq. (32) and eq. (33) are for annular flow and dryout region, respectively. Table 10. The Cheng et al. model [12] Flow patterns

Model descriptions

I-SLUG

∆p SLUG+ I

⎛ ε = ∆p LO ⎜⎜1 − ⎝ ε IA

Annular

∆p A = 4f A

L ρ V u 2V D eq 2

Dryout

∆p dryout = ∆p tp ( x di ) −

⎛ ε ⎞ ⎟⎟ + ∆p A ⎜⎜ ⎝ ε IA ⎠

⎞ ⎟⎟ (31) ⎠

(32)

x − x di ∆p tp ( x di ) − ∆p M ( x de ) (33) x de − x di

[

]

Comparison with other refrigerants Oh et al. [20] showed that the convective boiling heat transfer coefficient of CO2 is about 87.2 and 93% higher than that of R-22 and R-134a, which are explained by the high thermal conductivity of CO2 compared with that of R22 and R134a. The pressure drop of CO2 is about 10 - 15% of R-22. Choi et al. [19] compared the boiling heat transfer of CO2 with R-22 and R-134a. The mean heat transfer coefficient ratio of R22:R-134a:CO2 was approximately 1.0:0.8.2.0. Yun et al. [37] compared the heat transfer coefficients for CO2 with those for R134a as shown in Fig. 10. For qualities less than 0.5, the heat transfer coefficient of CO2 is on average 56% higher than that of R134a, while for all qualities tested, it is higher by 47% on average. Park and Hrnjak [17] compared the heat transfer coefficients and pressure drop for CO2 with those for R410a and R22 at low evaporation temperatures. As shown in Fig. 9 and referring to the Park and Hrnjak’s results [17], most increase of heat transfer coefficient can be attributed to the increase of nucleate boiling dominant part. However, we should note that the trends and values will be similar for all fluids at the same reduced pressure as suggested by Gorenflo and Kotthoff [22].

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Fig. 9 Comparison of the heat transfer coefficients for CO2 with those for R134a. (Reprinted from [37] with permission from Elsevier.)

Heat transfer of CO2 at supercritical condition Heat transfer characteristics Under the normal working condition of the CO2 system, the thermodynamic state of CO2 after compressor is in the supercritical region. Before entering to the expansion device, CO2 is undergoing the gas cooling process. This process is different from the conventional refrigeration cycle, which is the condensation process. Besides, there is a steep variation of the thermo-physical properties of CO2 for cp, µ , ρ , and k as shown in Fig. 10 [38]. The change of cp for the condensation process is much smaller when it is compared to the variation of cp under gas cooling process. Table 11 summarizes the recent studies for the gas cooling heat transfer for CO2, which are related with the designing of the gas cooler for CO2 refrigeration system. Studies shown in Table 11 and the earlier studies for the supercritical fluid heat transfer characteristics give the following general observations. The observed gas cooling heat transfer coefficient shows its highest value at the pseudo-critical temperature under the specific pressure condition, and it decreases prior to and subsequent of the pseudo-critical temperature. This highest heat transfer coefficient at the pseudo-critical temperature can be explained by the variation of cp under the cooling process. The specific heat means the required energy for the unit temperature change with unit mass. Therefore, during the gas cooling process around the pseudo-critical temperature the heat transfer rate shows maximum for the unit change of temperature, which makes the heat transfer coefficient to be the largest. The deterioration of heat transfer coefficient of CO2 under the cooling conditions was not observed, and the gas cooling heat transfer coefficient increased with an increase in mass flux. With the effects of heat flux being considered, the maximum heat transfer

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coefficient at Tpc decreases with the increase of heat flux. At Tb > Tpc, heat transfer coefficient increased significantly with increasing qw (both k and cp in the near-wall region increased with increasing of qw), whereas at Tb < Tpc, heat transfer coefficient was relatively unaffected by changes of qw. Such results can be understood by accounting for the changes in thermal conductivity k and cp in the near-wall region with changes in qw [38]. Concerning the effects of tube diameter [42] buoyancy effects are important parameters for explaining the heat transfer trends. Buoyancy effect is available when the mass velocity is low, which means the Gr/Re is an important parameter. Under the cooling condition, the effects of buoyancy on the heat transfer coefficients can be positive or negative with the condition of Tb/Tpc. Bae et al.’s results [46] suggested that turbulence has an important role in determining the heat transfer coefficient by interaction with a buoyancy effect. It was proved by comparing the heat transfer characteristics between the upward and downward flow.

Fig. 10 Thermophysical properties of supercritical carbon dioxide near the pseudocritical point at 8MPa. (Reprinted from [38] with permission from Elsevier.)

Contrary to the cooling process for the supercritical condition of CO2, both enhancement and deterioration of heat transfer with an increase in heat flux are found under the heating condition. The impairment of enhanced heat transfer from the increased heat flux can be explained (Fig. 15(a), (b) and (c)). Where at a low heat flux the large value of specific heat of CO2 has a capacity to deal the input heat flux across most of the boundary layer, however an increase in heat flux will produce enough energy input to overcome the large values of specific heat, resulting in an increase in temperature gradient across the boundary layer. Thus the large value of specific heat will become more localized within the boundary layer, impairing the enhanced heat transfer by reducing the integrated effect of the specific heat [47]. In the case where the mass velocity is low, it is possible that buoyancy effects can dominate and cause a deterioration and recovery of the heat transfer in upward flow (Fig. 15 (d) and (e)), which are related with the turbulent diffusivity [46].

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Table 11 Experimental studies of gas cooling heat transfer for CO2 Authors

Tube geometry

Olson and Allen [39]

Smooth tube, ID: 10.9 mm

Yoon et al. [40 ]

Smooth tube, ID: 7.75 mm, copper

Son and Park [41]

Smooth tube, ID: 7.75 mm, stainless steel

Dang and Hihara [38]

Smooth tube, ID: 1, 2, 4, 6 mm, copper

Liao and Zhao [42]

Smooth tube, ID: 0.5, 0.7, 1.1, 1.4, 1.55, 2.16 mm, stainless steel

Petterson et al. [43]

Multichannel, port ID: 0.79 mm, Aluminum

Kuang et al [44]

Multichannel, port ID: 0.79 mm, Aluminum

Huai et al. [45]

Mutichannel, Port ID: 1.31mm, Aluminum

Experimental conditions T: 20 – 126oC P: 7.8 – 13.1 MPa G: 200 – 900 kg/m2s Tavg: 50 – 80 oC P: 7.5 – 8.8 MPa G: 225, 337, 450 kg/m2s T: 25 – 90 oC P: 7.5 – 10 MPa G: 200 – 400 kg/m2s Tin: 30 – 70 oC P: 8 – 10 MPa G: 200 – 1200 kg/m2s T: 20 – 110 oC P: 7.4 – 12.0 MPa G: 136 – 4244 kg/m2s Tavg: 20 – 60 oC P: 8.1 – 10.1 MPa G: 600 – 1200 kg/m2s Tin: 22 – 55 oC P: 8 – 10 MPa G: 300 – 1200 kg/m2s Tin: 20 - 53 oC P: 7.4 – 8.5 MPa G: 22 – 53 kg/m2s

Fig. 11 Heat transfer description under supercritical condition (Reprinted from [47] with permission from Elsevier).

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Prediction models for the gas cooling heat transfer The variation of heat transfer coefficient for pure CO2 during the gas cooling process has been investigated for a long time, and it was precisely estimated by the existing models. Recently, Cheng et al. [48] summarized the heat transfer coefficient model for super-critical CO2 cooling. The following two models are the latest models, which consider the heat flux effects on the heat transfer coefficient and the buoyancy effects with increasing of tube diameter, respectively. The representative equations of the models are presented here from eq. (34) to eq. (42). Eq. (42) is the range for the application of the Liao and Zhao model. (1) Dang and Hihara model [38] Tf = (Tb + Tw ) / 2 h=

(34)

(f f / 8)(Re b − 1000) Pr 1.07 + 12.7 f f / 8 (Pr

2/3

− 1)

×

kf d

(35)

Pr = c Pb µ b / k b , for c pb ≥ c p = c p µ b / k b , for c pb < c p and µ b / k b ≥ µ f / k f = c p µ f / k f , for c pb < c p and µ b / k b < µ f / k f

(36)

f f = [1.82 log 10 (Re f ) − 1.64] −2

(37)

Re f = Gd / µ f

(38)

(2) Liao and Zhao model [42] Nu = 0.128 Re w

0.8

Prw

Gr =

cp =

0.3

⎛ Gr ⎜ ⎜ Re 2 ⎝ b

⎞ ⎟ ⎟ ⎠

0.205

⎛ ρb ⎜⎜ ⎝ ρw

⎞ ⎟⎟ ⎠

0.437

(ρ w − ρ b )ρ b gd 3 µb

2

ib − iw Tb − Tw

10-5 ≤ Gr/Reb2 ≤ 10-2, 0.5mm ≤ d ≤ 2.16mm

⎛ cp ⎜ ⎜ cp ⎝ w

⎞ ⎟ ⎟ ⎠

(39)

(40)

(41) (42)

74bar ≤ p ≤ 120bar, 20 oC ≤ Tb ≤ 110 oC, 2 oC ≤ Tb-Tw ≤ 30 oC, 0.02 kg/min<m<0.2 kg/min,

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Pressure drop Similar to the heat transfer characteristics, the effects of the steep variation of thermophysical properties near the pseudo-critical temperature are effective on the characteristics of pressure drop too. Fig. 12 shows the pressure drop with bulk temperature of Tb by Dang and Hihara [38]. When Tb < Tpc, just a slight variation of ∆P with mass flux or working pressure, and then sharply increase when Tb is close to Tpc. These characteristics are also found in the Huai et al.’s study [45]. At a given pressure and mass flux, ∆P increased with increasing Tb, due to an increased average velocity of the cross section with deceasing of density. However, the increasing rate of pressure drop around Tpc is not significant at the low mass flux.

Fig. 12 Effects of (a) mass flux and (b) pressure on pressure drop (Reprinted from [38] with permission from Elsevier.)

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The CO2-Oil Mixture Heat Transfer Characteristics CO2-oil thermodynamics properties

It is well known that the understanding of the thermodynamic properties of CO2-oil mixture is inevitable to design a compressor and a heat exchanger. For a compressor design, the solubility of refrigerant to oil and mixture viscosity are important thermodynamic properties. The heat transfer coefficient and pressure drop for the CO2oil mixture are required to design a heat exchanger. The phenomena of heat transfer and pressure drop can be correctly understood by knowing the mixture properties. Table 12 shows the comparison of four lubricants utilized for the CO2 systems [49]. They have challenging points for each lubricant. Until now, PAG and POE oil are known as the most suitable. For decision of the suitability of the oil to the specific system, miscibility between oil and refrigerant is the most important property. Hauk and Weidner [50] investigated the solubility of CO2 into three oils of PAG, POE, and PAO. Fig. 13 shows the visualization of the phase-behavior for PAG-CO2 mixture at 5oC under various pressure conditions. At the pressure of 40 bar, the three phases of CO2-oil mixture, liquid CO2, and gaseous CO2 were observed. Over the 50 bar, only two phases of CO2oil mixture and liquid CO2 were found. At the bottom CO2 solutes into oil, and this can be said as miscible between them. As shown in Fig. 14, the solubility of CO2 into oil decreases with increase of pressure at constant temperature, and the solubility of CO2 into oil increase with increase of temperature at constant pressure. However, as can be seen in Fig. 13 and Fig. 14 the PAG is only partially miscible with liquid CO2 up to 150 bar of pressure [50]. Yokozeki [51] successfully correlated experimental solubility data of PAG and POE with CO2 by using the equation of state (EOS) model. Their EOS model is based on the Redlich-Kwong type of Cubic equation of state, and suggested the optimal binary interaction parameters for the CO2-oil mixture by comparing the experimental solubility data. Table 12 Comparison of four synthetic lubricants for CO2 systems [49] Oil type Alkyl naphthalene/alkylbenz ne (AN/AB) Polyalphaolefin (PAO) Polyalkylene glycol (PAG) Polyol ester (POE)

Miscibility/Solubili ty Completely immiscible

Lubricity

Completely immiscible Partially miscible

Normal

Miscible

Good

Good

Good

Suitable system -

Challenges of CO2 systems

Cascade systems Transcritical system Transcritical system

Large oil separator on the compressor discharge is needed Oil separation and return systems are needed to avoid long term oil accumulation Mixture viscosity reduces significantly with temperature increase

-

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Fig. 13 Phase behavior of the system PAG-CO2 (T = 5oC) (Reprinted with permission from [50]. Copyright 2000 American Chemical Society)

Fig. 14 Pressure-composition diagram of the system PAG-CO2. (Reprinted with permission from [50]. Copyright 2000 American Chemical Society).

As explained, the thermo-physical properties of CO2-oil mixture are the crucial factors for designing the CO2 system. Many researchers suggested the calculation methods for estimating the mixture properties of refrigerant-lubricant and pure oils. Zhao and Bansal [49] summarized the method as shown in Table 13. Table 13 also includes the suggested model by Bandarra Filho et al. [52]. The nominal and the local oil concentrations are defined as eq. (43) and eq. (44), respectively. Two different sources for viscosity (eq. (45), eq. (46)), density (eq. (47), eq. (48)), specific heat (eq. (49), eq. (50)), and surface tension (eq. (52), eq. (53)) are given too. Mixture conductivity and bubble point temperature are eq. (51) and eq. (54), respectively. Although the estimation methods shown in Table 13 give a good predictability for the conventional refrigerants-oil mixture, it is hard to apply these equations to estimate the properties of CO2-oil mixture under the working conditions for CO2. The CO2

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systems work at high pressure and supercritical conditions. Because these equations were experimentally developed, they have the limits of application for the estimation. Yun [53] suggested the estimation methods for CO2-oil mixture properties based on the EOS (equation of state) and the TRAPP model. It should be noted that the application of the EOS model is valid for miscible range as shown in Fig. 13 and 14. For the other region, for example, mist oil with CO2, further investigation is necessary for getting the assurance of accuracy of them. The validity of the study was done in comparison with the experimental results from Pendado et al. [54]. Following equations are detailed descriptions of the model. The mixture density can be calculated by solving eq. (57) in terms of V, which was utilized to estimate the solubility of CO2-oil mixtures by Yokozeki [51]. The parameters of a and b in eq. (57) are given as eqs. (58) and (59) by the Redlich-Kwong type of cubic EOS for pure fluids, and the binary interaction parameters for a and b can be found in two different sources [51] and [55]. Table 13 Refrigerant-lubricant mixture properties calculation methods ([49], [52])

ω=

Nominal oil concentration Local oil concentration Mixture dynamic viscosity

moil moil + mref

ωlocal =

specific heat of refrigerant-oil mixture Mixture conductivity Mixture surface tension

(44)

1− x

ln µ m = (1 − ω ) ln µ ref + ω ln µ oil

(45) [52]

(46)

ρ oil

⎡⎛ ⎞⎤ ρ ⎢⎜1 + (1 − ωlocal )( oil − 1⎟⎥ ⎟⎥ ρ ref ⎢⎣⎜⎝ ⎠⎦ ωlocal 1 − ω local 1 = + ρm ρ oil ρ ref , l

c pm = (1 − ωlocal )c p, ref + ωlocal c p, oil c pm, l = ωc p, oil + (1 − ω )c p, ref

(47) [52]

(48) (49) (50)

k m = k ref (1 − ωlocal ) + k oil ωlocal − 0.72ωlocal (1 − ωlocal )(k oil − k ref ) (51)

σ m = σ ref + (σ oil + σ ref )ωlocal 1 / 2 σ m = σ ref , l + (σ oil − ω ) ω local Tbub =

Mixture bubble point temperature

ωo

µ m = µ ref (1− ω local ) µ oil ω local

ρm = Mixture density

(43)

A ln( p sat ) − B

(52) [52] (53)

(54) [52]

A = a 0 + 182.5ω local − 724.2ω local 2 + 3868ω local 5 − 5269ω local 7 (55)

B = b0 − 0.722ω local + 2.39ω local 2 − 13.78ω local 5 + 17.07ω local 7

(56)

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p=

RT a (T ) − V − b V (V + b)

(57)

N

a = ∑ a i a j f ij (T)(1 − k ij ) x i x j

(58)

i , j=1

b=

1 N ∑ (b i + b j )(1 − k ij )(1 − m ij )x i x j 2 i , j=1

(59)

The dynamic viscosity of CO2-oil mixture was predicted by the TRAPP (transport property prediction) method [56]. This method is proper to estimate the viscosity of both polar and nonpolar dense gas mixture at high pressures and can be extended into the liquid region. Because this method requires temperature and density as the input variables, eq. (57) should be coupled with the following eqs (60) – (63). The residual viscosity of mixture fluid is related to the residual viscosity of the reference fluid, propane as eq. (60). The term, ∆η ENSKOG accounts for size differences [57], which is based on a hard sphere assumption.

η m − η m 0 = Fηm [η R − η R 0 ] + ∆η ENSKOG

(60)

Fηm = ( 44.094) −1 / 2 ( h m ) −2 ∑∑ y i y j (f ij M ij )1 / 2 (h ij ) 4 / 3 i

∆η ENSKOG = η m ηm

ENSKOG

ENSKOG

−η x

(61)

j

ENSKOG

(62)

= ∑ β i Yi + αρ 2 ∑∑ y i y j σ ij ηij g ij 6

i

o

(63)

j

The mixture heat capacity of the CO2-oil mixture is calculated by following eqs. (64) – (67) [58]. The molar-based mixing rule can be applied for the heat capacity of the mixture. The residual enthalpy in eq. (67) is obtained by using eq. (66). The parameter of V was estimated by the PR EOS.

⎛ ∂h ⎞ * C pr = C p − C p = ⎜ r ⎟ ⎝ ∂T ⎠ p

(64)

hr = a r + Ts r + pV * − pV

(65)

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a r = a * − a = RT ln

V −b V

s r = s * − s = R ln

−

Yun

a (T ) 2 2b

V −b V

ln

V − 0.414b V + 2.414b

− R ln

+ RT ln

V V*

V V*

(66)

(67)

Eucken proposed the separate terms of the translation and internal energy contributions in calculation of the thermal conductivity of Polyatomic gases [56]. Most estimation models for the thermal conductivity are based on the Eucken suggestions. In the present study, the thermal conductivity of the mixture under high pressure condition was calculated by the Ely and Hanley model [59], which shows quite encouraging results for wide range of density. In their model, the thermal conductivity of mixture was calculated by a corresponding states method using methane as the reference component. The Ely and Hanley model [59] contained the terms of density correction and high density contribution. The equations of (68), (69), and (70) and calculation procedures are similar to the TRAPP method for estimating the dynamic viscosity of mixture.

λm − λm 0 = Fλm X λm (λR − λ R 0 )

(68)

Fλm = ( 44.094) −1 / 2 ( hm ) −2 ∑∑ y i y j ( f ij / M ij )1 / 2 (hij ) 4 / 3 i

X λm

(69)

j

⎡ 2.1866(ω m − ω R ) ⎤ = ⎢1 + R ⎥ ⎣ 1 − 0.505(ω m − ω ) ⎦

1/ 2

Convective boiling heat transfer characteristics for CO2-oil mixture

(70)

Bansal et al. [49] reviewed the flow boiling heat transfer of CO2-oil mixtures, which includes the studies shown in Table 14. Most researchers show that a certain oil concentration (the critical oil concentration), at which the effects of oil are insignificant. Oil may solute into CO2 at low vapor quality. In contrast, CO2 resolves into the oil layer at high vapor quality. It is hard to form an oil rich layer at low oil concentration, and oil (PAG, POE) and CO2 will exist separately when the solubility between them is considered. With an increase in oil concentration, oil film is formed and CO2 dissolves into that film. They form an oil rich layer as shown in Fig. 15 [69]. Fig. 15 shows the structure of the refrigerant vapor, refrigerant liquid, and oil excess layer under the pool boiling. The effects of oil excess layer on the average departure bubble diameters result in either an enhancement or degradation of heat transfer. It should be noted that the nucleate boiling suppression vapor quality is higher for CO2 when it is compared to that for the existing refrigerants. Because the CO2-oil solubility is determined by the pressure and temperature, the composition of the oil rich layer does not change during the evaporation process (vapor quality 0 to 1.0). The liquid state of CO2 will be

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remained in forming CO2 layer or in mixing with oil (immiscible state) at low vapor quality. However, at high vapor quality, most liquid state CO2 is evaporated; finally oil rich layer only remained. That is why the decrease of heat transfer coefficient at high vapor quality for CO2-oil mixture is significant. If the oil rich layer is saturated with CO2, the physical properties of the oil rich layer does not change with an increase in oil concentration. The dominant convective boiling heat transfer mechanism is the evaporation at the boundary of liquid film and vapor. Due to the oil-refrigerant layer (miscible or immiscible) the effective evaporation surface is blocked and the heat transfer coefficient decreased significantly. These blockage effects will be irrespective with the amount of oil concentration due to the constant composition of CO2-oil layer. If the heat transfer coefficients are dependent on the physical properties of CO2-oil layer, the concentration of the oil does not affect on the heat transfer coefficient too. Table 14 Studies of flow boiling heat transfer for CO2-oil mixture ([49], [68]) References

Channel configuration

Tube diameter (mm)

Dang et al. [60]

S.S. Smooth tube

2, 4, 6

Gao et al.[61]

Smooth steel Micro-fin copper

3 3.04

Gao and Honda [62]

S.S. Smooth tube

3

Tanaka et al. [63]

S.S. Smooth tube

1

Katsuta et al. [64]

S.S. Smooth tube

4.59

Hassan [65 ]

S.S. Smooth tube

10.06

Zhao et al. [66]

Micro-channel

0.86

Koyama et al.[ 67]

Smooth Copper tube Micro-fin Copper tube

4.42 4.90

Gau et al. [68]

Micro-fin Copper tube

1.95

Experimental conditions Tsat: 15oC G: 170 -320 kg/m2s Q: 4.6 -36 kW/m2 Tsat: 10 oC G: 190 -1300 kg/m2s Q: 5 -30 kW/m2 Tsat: 10 oC G: 200 -1300 kg/m2s Q: 10 -30 kW/m2 Tsat: 15 oC G: 360 -1440 kg/m2s Q: 36 kW/m2 Tsat: 10 oC G: 400 -800 kg/m2s Q: 5 -15 kW/m2 Tsat: -30 to -10 oC G: 90 -125 kg/m2s Q: 5.0 -16.5 kW/m2 Tsat: 0 - 15 oC G: 100 -700 kg/m2s Q: 11 kW/m2 Tsat: 5.3 oC G: 360 -650 kg/m2s Tsat: 15 oC G: 380 -1500 kg/m2s Q: 10 -40 kW/m2

Oil type and concentrations PAG: 0 – 5 wt.% PAG: 0.01 – 0.72 wt.% PAG: 0.01 – 0.57 wt.%

Gas cooling heat transfer characteristics for CO2-oil mixture

PAG PAG: 1 – 5 wt.% 0 – 7 wt.% 0 – 7 wt.%

0 – 0.4 wt.%

Table 15 shows the existing studies for the gas cooling heat transfer for CO2-oil mixture. Heat transfer coefficients are significantly affected by the oil concentration and the deterioration is largest at the pseudo-critical region. These effects depend on the operation conditions of the oil concentration, tube diameter, pressure, temperature, and mass flux, which make a different flow patterns for supercritical CO2 and oil by changing the solubility between them. The flow patterns for supercritical CO2 and oil are investigated by Dang et al [75]. Through the investigation of the flow patterns with

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the change of the thermo-physical properties, we can understand the gas cooling heat transfer characteristics for CO2-oil mixture. According to their observation the flow pattern changes with the temperature, pressure and oil concentration, as well as with the tube diameter as shown in Fig. 16. Under the test condition of 25oC, 1.0 wt.% of oil with 2.0 mm ID tube, the mist flow was observed. With an increase in temperature oil rich layer formed on the tube wall by decreasing the solubility of CO2 into oil. With further increase of temperature oil rich layer is getting thicker and the possible movement of oil droplets in the bulk region cannot be observed, which forms the annular flow. With increase of oil concentration from 1.0 wt.% to 5.0 wt.% even at 25 o C, oil rich layer can be clearly found. At 40 oC under the different pressure conditions of 8 MPa and 10 MPa, density difference between oil and CO2 is large and oil tend to separate from the bulk flow for 8 MPa. However, density difference between oil and CO2 is small for 10MPa, oil rich layer is easily transformed into oil droplets.

Fig. 15 Schematic of the average departure bubble for three R123/lubricant mixtures with corresponding excess layers (Reprinted from [69] with permission from Elsevier.)

Prediction models for the CO2-oil mixture gas cooling heat transfer in tubes Similar to the development of the convective boiling heat transfer coefficient model for pure CO2, which is based on the flow patterns, the gas cooling heat transfer model for supercritical CO2-oil mixture should be based on the flow patterns made by CO2 and oil. The gas cooling heat transfer coefficients for annular flow pattern can be estimated by the existing model, which are developed for the two-phase flow under non-boiling or non-condensation condition, but under the heating or cooling conditions with air-water. However, there exist big differences for the physical properties between them. Oil rich layer at wall is not pure oil and the vapor core is not pure CO2. CO2 solutes into oil rich layer, which are dependent on the working pressure and temperature and CO2 vapor core is mixed with oil droplet. Therefore, when we apply the existing model to estimate the gas cooling heat transfer coefficients for CO2-oil mixture the thermo-physical properties for oil rich layer and CO2 core with oil droplet should be correctly estimated.

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The Kim and Ghajar model [77] of eq. (71) is the general heat transfer correlation for non-boiling gas-liquid flow in horizontal pipes. In order to reflect the realistic shape of the gas-liquid interface, the flow pattern factor FP , is proposed by them. Eq. (72) for h L is liquid phase heat transfer coefficient correlation for turbulent flow. The mixture properties for oil rich layer can be estimated by the methods suggested in section 4.1, and the oil concentration can be estimated by the solubility model suggested by the Yokozeki [51]. As the same way, the mixture properties for oil droplet-CO2 core can be estimated and the prediction of the amount of oil droplet is possible from the liquid droplet entrainment model. However, it should be noted that we cannot assume an ideal mixture for the CO2 and oil droplet in vapor core. The application of the EOS model for them needs to be further investigated. Table 15 studies of the gas cooling heat transfer for CO2-oil mixture [76] Authors

Fluids

Tube geometry

Dang et al. [70]

CO2/PAG

Smooth tube, ID: 1 – 6 mm

Gao and Honda [71]

CO2/Oil

Smooth tube, ID: 5 mm

Mori et al. [72]

CO2/PAG

Smooth tube, ID: 4, 6, 8 mm

Zingerli and Groll [73]

CO2/POE

Smooth tube, ID: 2.75 mm

Kuang et al. [74]

CO2/Oils(PAG/A N, PAG, POE)

Microchannel, Port ID: 0.79 mm

Dang et al. [75]

CO2/PAG

Smooth tube, ID: 2, 6 mm

Yun et al [76]

CO2/PAG

Multichannel, Port ID: 1.0 mm

Experimental conditions T: 100 – 125 oC P: 8 – 10 MPa G: 200 – 1200 kg/m2s Oil concentration: 0 – 5 wt.% T: 30 – 100 oC P: 7.6 – 9.6 MPa G: 330 – 680 kg/m2s Oil concentration: 0, 1 wt.% T: 20 – 70 oC P: 9.5 MPa G: 100 – 500 kg/m2s Tin: 100 – 125 oC P: 8 – 12 MPa G: 1700 – 5100 kg/m2s Oil concentration: 0, 2, 5 wt.% T: 30 – 50 oC P: 9 MPa G: 890 kg/m2s Oil concentration: 0 – 5 wt.% T: 20 – 60 oC P: 8 – 10 MPa G: 200 – 1200 kg/m2s Oil concentration: 1 – 5 wt.% Tin: 40 – 80 oC P: 8.4 – 10.4 MPa G: 200 – 400 kg/m2s Oil concentration: 1 – 5 wt.%

Fig. 16 Classification of flow patterns for supercritical CO2 and oil. M: mist flow; AD: annulardispersed flow; A: annular flow; W: wavy flow; WD: wavy-dispersed flow. (Reprinted from [75] with permission from Elsevier.)

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When the Kim and Ghajar model is applied, the thickness of oil rich layer is necessary. To get the film thickness, the annular flow model [78] can be used as eqs. (73) and (74). For mist flow, the existing supercritical heat transfer model for CO2 can be used by applying the CO2-oil mixture properties instead of pure CO2 properties. Furthermore, this method can be extended to the estimating the boiling and condensation heat transfer coefficient for oil and refrigerant mixture. It can be assumed that the liquid film composed of liquid refrigerant and liquid oil, and vapor core composed of vapor refrigerant, liquid droplet of oil, and liquid droplet of refrigerant form the tube inside flow for annular flow. However, the calculation is much complicating than that of the gas cooling process.

h TP

⎧⎪ ⎡⎛ x ⎞ 0.08 ⎛ 1 − F P = FP h L ⎨1 + 0.7 ⎢⎜ ⎟ ⎜⎜ 1 x F − ⎠ ⎝ P ⎢⎣⎝ ⎪⎩

h L = 0.027 Re L

WLF =

2πρ l µl

4/5

PrL

1/ 3

⎛ kL ⎜ ⎝D

⎞⎛ µ B ⎟⎜⎜ ⎠⎝ µ W

⎞ ⎟⎟ ⎠

0.06

⎛ PrG ⎜⎜ ⎝ PrL

⎞ ⎟⎟ ⎠

0.03

⎛ µG ⎜⎜ ⎝ µL

⎞ 0.14 ⎟⎟ ⎠L

⎞ ⎟⎟ ⎠

−0.14

⎤ ⎫⎪ ⎥⎬ ⎥⎦ ⎪⎭

(71)

(72)

⎛ (R − δ) 2 dP ⎞ ⎛ R 2 − (R − δ) 2 (R − δ) 2 R ⎞ πρ l dP 2 ⎜⎜ τ i (R − δ) + ⎟⎟ × ⎜⎜ ⎟− − ln ( R − ( R − δ) 2 ) 2 2 dz ⎠ ⎝ 4 2 R − δ ⎟⎠ 8µ l dz ⎝

(73) 4τ i dP + =0 dz D α

(74)

Condensation Heat Transfer Characteristics Studies for the condensation heat transfer of CO2 are very limited because its application to the actual system is rare. Recently, the CO2-NH3 cascade system has been commercialized and investigated as a low temperature storage and showcase application [79], [80]. The performance of the system is better than that CO2-CO2 and it will replace other refrigerants, which are used for low temperature applications. The normal boiling point for NH3 is -33.33oC and for CO2 boiling point is -57 oC. Therefore, as a natural refrigerant we can get much lower temperature by using CO2. For the CO2-NH3 cascade system, CO2 cycle works at low temperature range, and NH3 works at high temperature range. The CO2 and NH3 cycles are cascaded by condensation of CO2 and boiling of NH3. For these low temperature applications, it is important to investigate the condensation characteristics of CO2. Park and Hanjak [81] investigated the flow condensation heat transfer coefficients and pressure drop with CO2 for 0.89 mm microchannels at horizontal flow conditions at -15 and -25oC, mass fluxes from 200 to

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800 kg/m2s. They concluded that the flow condensation mechanism for 0.89 mm tubes should not be significantly different from that in large diameter tube. The existing models for heat transfer coefficient and pressure drop well predicted the experimental data of them. It should be noted that condensation is less dynamic than evaporation, which is contrary to a flow boiling where bubble generation and growth are affected by a microchannel size. The condensation heat transfer coefficients for CO2 inside microfin tubes were predicted within +-20% by the Cavallini et al. model [82].

Conclusions The flow boiling heat transfer characteristics for CO2 can be correctly explained through the observation of the two-phase flow patterns, which shows the early flow transition to intermittent or annular flow. Nucleate boiling mechanism is dominated for the convective flow boiling of CO2, and the physical phenomenon for the nucleate boiling follows the same trends with other organic fluids under the same reduced pressure. The gas cooling heat transfer should be explained with the turbulent diffusivity related with buoyancy force, which comes from the large density difference across the tube. Under the oil presence condition, the oil rich layer explains the physical mechanisms of heat transfer for both convective boiling and gas cooling. Condensation of CO2 is not so different from those for the other conventional refrigerants.

Nomenclature A VD a ar b C CO cp

Dimentionless cross-sectional area occupied by liquid-phase Helmholtz free energy, Parameters in the EOS for pure compounds, kJmol-1 Residual function of the Helmholtz free energy, kJmol-1 Parameters in the EOS for pure compounds Chisholm parameter Distribution parameter Specific heat, Jkg-1K-1

cp

Integrated specific heat, ((h b / h w ) /(Tb / Tw ))

d, D

Inside-diameters of the test tube (hydraulic), m

D eq

Equivalent diameter, m ( D eq =

dh

Hydraulic diameter, m

4A ) π

FrV , Mori Vapor Froude number defined by Mori et al. ( [G 2 /( ρV ( ρ L − ρV ) gDeq )])

FrL f fi Frl

Liquid Froude number Friction factor, scaling parameter Interfacial friction factor Liquid Froude number

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FP Fs

Flow pattern factor Shape factor

Gr G g h h LD hr i j

Grashof number, Gr = (ρ w − ρ b )ρ b gd 3 / µ b Mass velocity, kgm-2s-1 Gravitational acceleration, 9.81 ms-2 Heat transfer coefficient, Wm-2K-1, scaling parameter Dimensionless vertical height of liquid Residual function of enthalpy, kJmol-1 Enthalpy, J/kg Mixture volumetric flux (= jf + jg )

jf jg k k , l, m La M pr Pr P q Re Rp

Superficial liquid velocity, ms-1 Superficial gas velocity, ms-1 Thermal conductivity, Wm-1K-1 Binary interaction factor Laplace number Molecular mass, kgkmol-1 Reduced pressure Prandtl number Pressure, MPa Heat flux, Wm-2 Reynolds number Surface roughness parameter, µm

Re H

Homogeneous Reynolds number, {(GD eq / µ V )[ x + ρ V / ρ L (1 − x )]}

Re V

Vapor phase Reynolds number [GxD eq /(µ V ε)]

R S sr T u uV V We We L WLF x xE yi Z

Gas constant, 8.31447 Jmol-1K-1, radius of tube Nucleate boiling suppression factor Residual function of entropy, Jmol-1K-1 Temperature, K; Tr , reduced temperature, T / Tc ; T0 , equivalent temperature Gas core velocity Mean velocity of vapor phase, ms-1 Volume, m3 Weber number Liquid Weber number Total film flow rate Mass vapor quality (-) Equilibrium vapor quality Mole fraction of component i in a vapor mixture Compressibility factor;

2

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Zc

critical compressibility factor

Greek α Γ δ δ ij

Void fraction Mass flow rate per unit periphery of tube, kgm-1s-1 liquid film thickness, m Kronecker delta function

∆

ε

ε IA η θ dry λ µ

ν ρ

σ τi ψ

ω

Difference, correction term Void fraction Vapor void fraction at x=xIA Viscosity, Nsm-2, η o low-pressure gas viscosity Dry angle of tube perimeter, rad Thermal conductivity, Wm-1K-1 Dynamic viscosity Nsm-2 Kinematic viscosity, m2s-1 Molar density, molcm-3 or molm-3, ρ 0 , density parameter °

Surface tension, Nm-1, molecular diameter, A Interfacial shear stress Barnett number Oil mass fraction, acentric factor

Subscript A Annular flow B Bulk b Bulk fluid bub Bubble point ce Convective evaporation crit Critical di Dryout inception de Dryout completion dryout Dryout region f Film temperature, liquid phase G , g Gas Radial distribution function g ij I IA L LO l local m

Intermittent flow Intermittent flow to annular flow transition Liquid Considering the total vapor-liquid flow as liquid flow Liquid Local mass concentration Mixture

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Mist flow M mist Mist flow nb Nucleate boiling Outlet out Pseudo-critical pc Two-phase flow tp sat Saturation s Superficial SLUG Slug flow Saturation sat Two-phase tp V , v Vapor w Wall, wall temperature wet On the wet perimeter wavy Wavy flow x A pure hypothetical fluid with the same density as the mixture 0.1 Value at p r =0.1 Supersripts o ideal gas value R property of reference fluid, propane * Properties of the ideal state

References [1] Lorentzen G. The use of natural refrigerant: a complete solution to the CFC/HCFC predicament. Int. J. Refrigeration 1995; 18: 190-97. [2] Pettersen J. Flow vaporization of CO2 in microchannel tubes. Exp. Thermal and Fluid Science 2004; 28: 111- 21. [3] Yun R, Kim YC. Flow regimes for horizontal two-phase flow of CO2 in heated narrow rectangular channel. Int. J. of Multiphase Flow 2004; 30: 1259 – 70. [4] Holser ER. Flow patterns in high pressure two-phase (steam-water) flow with heat addition. Chemical Engineering Progress Symposium Series 1968; 64: 54-66. [5] Gasche JL. Carbon Dioxide Evaporator in a Single Microchannel. J. of the Braz. Soc. of Mech. Sci. & Eng 2006; 28: 69 – 83. [6] Thome JR, El Hajal J. Two-phase flow pattern map for evaporation in horizontal tubes, HEFAT 2002, Kruger Park, South Africa 2002; pp. 182- 7. [7] Schael AE, Kind M. Flow pattern and heat transfer characteristics during flow boiling of CO2 in a horizontal micro fin tube and comparison with smooth tube data. Int. J. Refrigeration 2005; 28: 1186 – 95. [8] Park CY, Hrnjak PS. CO2 and R410A flow boiling heat transfer, pressure drop, and flow pattern at low temperatures in a horizontal smooth tube. Int. J. Refrigeration 2007; 30: 166-78.

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[9] Weisman J, Duncan D, Gibson J. Crawford T. Effects of fluid properties and pipe diameter on two-phase flow patterns in horizontal lines. Int. J. Multiphase Flow 1979; 5: 437-62 [10] Wojtan L, Ursenbacher T, Thome JR. Investigation of flow boiling in horizontal tubes: Part 1 – A new diabatic two-phase flow pattern map. Int. J. Heat Mass 2005; 48: 2955-69. [11] Ozawa M, Ami T, Ishihara I, Umekawa H, Matsumoto R, Tanaka Y, Yamamoto T, Ueda Y. Flow pattern and boiling heat transfer of CO2 in horizontal small-bore tubes. Int. J. of Multiphase Flow 2009; 35: 699 – 709. [12] Cheng L, Ribatski G, Quibén JM, Thome JR. New prediction methods for CO2 evaporation inside tubes: Part I – A two-phase flow pattern map and a flow pattern based phenomenological model for two-phase flow frictional pressure drops. Int. J. Heat Mass 2008; 51: 111 – 24. [13] Thome JR, Ribatski G. State-of-the-art of two-phase flow and flow boiling heat transfer and pressure drop of CO2 in macro- and micro-channels. Int. J. Refrigeration 2005;28: 1149-68. [14] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes: Part 3Development of a new heat transfer model based on flow pattern. Trans. ASME J. Heat Transfer 1998; 120: 156-65. [15] Garimella S. Condensation flow mechanisms in microchannels: Basis for pressure drop and heat transfer models. Heat transfer Engineering 2004; 25: 104 – 16. [16] Thome JR, Ribatski G. State-of-the-art of two-phase flow and flow boiling heat transfer and pressure drop of CO2 in macro- and micro-channels. Int. J. Refrig. 2005:28;1149-68. [17] Park CY, Hrnjak PS. Flow boiling heat transfer of CO2 at low temperatures in a horizontal smooth tube. Journal of heat transfer 2005; 127: 1305-12 [18] Zhao X, Bansal PK. Flow boiling heat transfer characteristics of CO2 at low temperature. Int. J. Refrigeration 2007; 30: 937 – 45. [19] Choi KI, Pamitran AS, Oh CY, Oh JT. Boiling heat transfer of R-22, R-134a, and CO2 in horizontal smooth minichannels. Int. J. Refrigeration 2007; 30: 1336-46. [20] Oh HK, Ku HG, Roh GS, Son CH, Pakr SJ. Flow boiling heat transfer characteristics of carbon dioxide in a horizontal tube. App. Thermal Eng. 2008; 28: 1022-30. [21] Mastrullo R, Mauro AW, Rosato A, Vanoli GP. Carbon dioxide local heat transfer coefficients during flow boiling in a horizontal circular smooth tube. Int. J. Heat Mass Transfer 2009; doi:10.1016/j.ijheatmasstransfer.2009.04.004. [22] Gorenflo D, Kotthoff S. Review on pool boiling heat transfer of carbon dioxide. Int. J. Refrigeration 2005; 28: 1169-85. [23] Kuznetsov MV, Vitovsky OV, Shamirazev AS. Boiling heat transfer in minichannels. Microscale heat transfer fundamentals and applications: NATO Science series 2005; pp. 255-272. [24] Revellin R, Haberschill P, Bonjour J, Thome JR. Conditions of liquid film dryout during stratified flow boiling in microchannels. Chem. Eng. Sci. 2008; 63: 5795801.

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[25] Ahmad SY. Fluid to fluid modeling of critical heat flux: a compensated distortion model. Int. J. Heat Mass Transfer 1973; 16: 641-662. [26] Yun R, Kim Y. Critical quality prediction for saturated flow boiling of CO2 in horizontal small diameter tubes. Int. J. Heat Mass Transfer 2003; 46: 2527-35. [27] Cheng L, Ribatski G, Thome JR. New prediction methods for CO2 evaporation inside tubes: Part II-An updated general flow boiling heat transfer model based on flow patterns. Int. J. Heat Mass Transfer 2008; 51: 125-35. [28] Cooper MG. Heat flow rates in saturated nucleate pool boiling- a wide-ranging examination using reduced properties. Adv. Heat Transfer 1984; 16: 157-239. [29] Shah MM, Siddiqui MA. A general correlation for heat transfer during dispersedflow film boiling in tubes. Heat Transfer Eng. 2000; 21: 18-32. [30] Yun R, Kim Y. Post-dryout heat transfer characteristics in horizontal mini-tubes and a prediction method for flow boiling of CO2. Int. J. Refrigeration 2009; 32: 1085-91. [31] Groeneveld DC. Post-dryout heat transfer at reactor operating conditions. Report AECL-4513; 1973. [32] Müller-Steinhagen H, Heck K. A simple friction pressure drop correlation for twophase flow in pipes. Chem. Eng. Process 1986:20; 29-308. [33] Friedel L. Improved friction pressure drop correlations for horizontal and vertical two phase pipe flow, paper E2, European Two Phase Flow Group Meeting, Ispra, Italy, 1979. [34] Choi JY, Kedzierski AM, Domanski PA. A generalized pressure drop correlation for boiling and condensation of alternative refrigerants in smooth tube and microfin tube. NISTIR 6333 1999: 7-15. [35] Sun L, Mishima K. Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels. Int. J. Multiphase Flow 2009; 35: 47-54 [36] Yun R, Kim Y. Two-phase pressure drop of CO2 in mini tubes and microchannels. Microscale Thermophysical Engineering 2004; 8: 259-270. [37] Yun R, Kim YC, Kim MS, Choi Y. Boiling heat transfer and dryout phenomenon of CO2 in a horizontal smooth tube. Int. J. Heat Mass Transfer 2003; 46: 2353-61. [38] Dang C, Hihara E. In-tube cooling heat transfer of supercritical carbon dioxide. Part 1. Experimental measurement. Int. J. Refrig. 2004; 27: 736-47. [39] Olson DA, Allen D, Heat transfer in turbulent supercritical carbon dioxide flowing in a heated horizontal tube. NISTIR 6234 1998. [40] Yoon S, Kim J, Hwang Y, Kim M, Min K, Kim Y. Heat transfer and pressure drop characteristics during the in-tube cooling process of carbon dioxide in the supercritical region. Int. J. Refrig. 2003; 26: 857-64. [41] Son C, Park S, An experimental study on heat transfer and pressure drop characteristics of carbon dioxide during gas cooling process in horizontal tube. Int. J. Refrig. 2006; 29: 539-46. [42] Liao SM, Zhao TS. Measurements of heat transfer coefficients from supercritical carbon dioxide flowing in horizontal mini/micro channels. J. of Heat Transfer 2002; 124: 413-20.

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[43] Pettersen J, Rieberer R, Munkejord ST. Heat transfer and pressure drop for flow of supercritical and subcritical CO2 in microchannel tubes. Technical Report, SINTEF Energy Research, Trondheim 2000. [44] Kuang G, Ohadi M, Zaho Y. Experimental study on gas cooling heat transfer for supercritical CO2 in microchannel. in: Proceedings of the Second International Conference on Microchannels and Minichannels, Rochester, NY: 2004; pp. 325332. [45] Haui XL, Koyama S, Zhao TS, An experimental study of flow and heat transfer of supercritical carbon dioxide in multi-port mini channels under cooling conditions. Chemical Engineering Science 2005; 60: 3337-45. [46] Bae JH, Yoo JY, Choi H. Direct numerical simulation of turbulent supercritical flows with heat transfer. PHYSICS OF FLUIDS 2005; 17: 105104. [47] Licht J, Anderson M, Corradini M. Heat transfer to water at supercritical pressures in a circular and square annular flow geometry. Int. J. Heat Fluid Flow 2008; 29: 156-66. [48] Cheng L, Ribatski G, Thome JR. Analysis of supercritical CO2 cooling in macroand micro-channels, Int. J. Refrigeration 2008;31:1301-16. [49] Zhao X, Bansal P. Critical review of flow boiling heat transfer of CO2-lubricant mixtures. Int. J. Heat Mass Transfer 2009; 52: 870-79. [50] Hauk A, Weidner E. Thermodynamic and Fluid-Dynamic Properties of Carbon Dioxide with Different Lubricants in Cooling Circuits for Automobile Application. Ind. Eng. Chem. Res. 2000; 39: 4646-51. [51] Yokozeki A. Solubility correlation and phase behaviors of carbon dioxide and lubricant oil mixtures. Applied Energy 2007; 84: 159-75. [52] Bandarra Filho EP, Cheng L, Thome JR. Flow boiling characteristics and flow pattern visualization of refrigerant/lubricant oil mixtures. Int. J. Refrig. 2009; 32: 185-202. [53] Yun R. Prediction of thermo-physical properties for CO2-oil mixtures at low oil concentration. 7th JSME-KSME Thermal and Fluids Engineering conference, Sapporo, Japan, 2008; B311. [54] Pensado AS, Pádua AAH, Comuñas MJP, Fernández. Viscosity and density measurements for carbon dioxide + pentaerythritol ester lubricant mixtures at low lubricant concentration. J. of Supercritical Fluids 2008: 44; 172-185. [55] Fandino O, Lopez ER, Lugo L, Teodorescu M, Mainar AM, Fernandez J. Solubility of Carbon Dioxide in Two Pentaerythritol Ester Oils between (283 and 333) K. J. Chem. Eng. Data 2008; 53: 1854-61. [56] Reid RC, Prausnitz JM, Poiling BE. The properties of gases and liquids, Mcgrawhill, 1988; pp. 388-473. [57]Ely JF, Hanley JM. Prediction of transport properties. 1. Viscosity of Fluids and Mixtures. Ind. Eng. Chem. Fundam 1981; 20: 323-32. [58] Dalin Z, Suizheng Q, Guanghui SU, Dounan J. Estimation of thermodynamic properties of the ternary molten salt system, LiF-NaF-BeF2, by the modified PengRobinson equation. Front. Energy Power Eng. China 2007; 1: 174-80. [59] Ely JF, Hanley JM. Prediction of transport properties. 2. Thermal Conductivity of Pure Fluids and Mixtures. Ind. Eng. Chem. Fundam 1983; 22: 90-7.

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[60] Dang C, Haraguchi N, Yamada HE. Effect of lubricant oil on boiling heat transfer of carbon dioxide. Proceedings of 7th IIR-Gustav Lorentzen Conference, Trondheim, Norway, 2006; pp. 495-98. [61] Gao L, Honda T, Koyama S. Experiments on flow boiling heat transfer of almost pure CO2 and CO2-oil mixtures in horizontal smooth and microfin tubes. HVAC&R Res 2007; 13: 415-25. [62] Gao L, Honda T. Flow and heat transfer characteristics of refrigerant and PAG oil in the evaporator of a CO2 heat pump system. Proceedings of 7th IIR-Gustav Lorentzen Conference, Trondheim, Norway, 2006; pp. 491-94. [63] Tanaka S, Daiguji H, Takemura F, Hihara E. Boiling heat transfer of carbon dioxide in horizontal tubes. 38th National heat transfer symposium of Japan, Saitama, Japan, 2001; pp. 899-900. [64] Katsuta M, Takeo N, Kamimura I, Mukaiyama H, A study on the evaporator of CO2 refrigerant cycle: characteristics of heat transfer coefficient and pressure drop on mixing CO2 and oil(PAG). ACRA 2000 Lecture dissertation selected work 2002; 20: 67-74. [65] Hassan M. Flow boiling of pure and oil contaminated carbon dioxide as refrigerant, Ph.D. Thesis, Technical University of Denmark, 2004. [66] Zhao Y. Molki M, Ohadi MM, Franca FHR, Radermacher R. Flow boiling of CO2 with miscible oil in microchannel. ASHRAE Trans 2002; 108 (Part 1):135-44. [67] Koyama S. Lee SM, Ito D, Kuwahara K, Ogawa H, Experimental study on flow boiling of pure CO2 and CO2-oil mixtures inside horizontal smooth and microfin cooper tubes, Proceedings of 6th IIR-Gustav Lorentzen Conference, Glasgow, UK, 2004. [68] Gao L, Matsusaka Y, Sato M, Ono T, Honda T, Flow boiling heat transfer of CO2 and oil mixtures in a horizontal thin inner grooved micro-fin tube. 7th JSME-KSME Thermal and Fluids Engineering conference, Sapporo, Japan, 2008; A222.. [69] Kedzierski MA. A semi-theoretical model for predicting refrigerant/lubricant mixture pool boiling heat transfer, Int. J. Refrig. 2003; 26: 337- 48. [70] Dang C, Iino K, Fukuoka K, Hihara E. Effect of lubricating oil on cooling heat transfer of supercritical carbon dioxide. Int. J. Refrig. 2007; 724-31. [71] Gao L, Honda T. Experiments on heat transfer characteristics of heat exchanger for CO2 heat pump system. Proceedings of the Asian Conference on Refrigeration and Air conditioning, Kobe, Japan 2002; pp.75-80. [72] Mori K, Onishi J, Shimaoka H, Nakanishi S, Kimoto H. Cooling heat transfer characteristics of CO2 and CO2-oil mixture at supercritical pressure conditions, Proceedings of the Asian Conference on Refrigeration and Air conditioning, Kobe, Japan 2002; pp.81-86. [73] Zingerli A. Groll EA. Influence of refrigeration oil on the heat transfer and pressure drop of supercritical CO2 during in-tube cooling, Proceedings of the 4th IIRGustave Lorentzen Conference, Purdue, IN, 2000; pp.269-78. [74] Kuang G, Ohadi M, Zhao Y. Experimental study of miscible and immiscible oil effects on heat transfer coefficients and pressure drop in microchannel gas cooling of supercritical CO2. Proceedings of 2003 ASME Summer Heat Transfer Conference, Las Vegas, NV, 2003; HT2003-47473.

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[75] Dang C, Iino K, Hihara E, Study on two-phase flow pattern of supercritical carbon dioxide with entrained PAG-type lubricating oil in a gas cooler. Int. J. Refrig. 2008;31: 1265-72. [76] Yun R, Hwang Y, Radermacher R, Convective gas cooling heat transfer and pressure drop characteristics of supercritical CO2/oil mixture in minichannel tube. Int. J. Heat Mass Transfer 2007; 50: 4796-4804. [77] Kim J, Ghajar AJ. A general heat transfer correlation for non-boiling gas-liquid flow with different flow patterns in horizontal pipes. Int. J. Multiphase Flow 2006; 32: 447-65. [78] Hewitt GF, Hall-taylor NS. Annular two-phase flow. Pergamon press1970. [79] Lee TS, Liu CH, Chen TW. Thermodynamic analysis of optimal condensing temperature of cascade -condenser in CO2/NH3 cascade refrigeration systems. Int. J. Refrig. 2006; 29: 1100 - 1108. [80] Dopazo JA, Fernández-Seara J, Sieres J, Uhia FJ. Theoretical analysis of a CO2– NH3 cascade refrigeration system for cooling applications at low temperatures. Applied Thermal Engineering 2009; 29: 1577-83. [81] Park CY, Hrnjak P. CO2 flow condensation heat transfer and pressure drop in multi-port microchannels at low temperatures. Int. J. Refrig. 2009;32:1129-39. [82] Cavallini A, Col DD, Mancin S, Rossetto L. Condensation of pure and nearazeotropic refrigerants in microfin tubes: A new computational procedure. Int. J. Refrig. 2009; 32: 162-74.

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Chapter 5 Nonlinear Analysis and Prediction of Time Series from Fluidized Bed Evaporator Mingyan Liu 1,2, Aihong Qiang 1 and Juanping Xue 1 1 School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China 2

State Key Laboratory of Chemical Engineering, Tianjin 300072, China

Abstract This chapter summarizes the work done by our research group in recent five years on the nonlinear analysis and prediction of time series from the system of fluidized bed evaporator with an external natural circulating flow. Besides traditional investigations on steady-state characters of flow and heat transfer, the nonlinear evolution behavior of the system was emphasized and explored in this chapter. Measured time series of wall temperature and heat transfer coefficient were taken as the time series for the nonlinear analysis, modeling and forecasting. The main analysis tools are based on the chaos theory. Meaningful results were obtained. Under certain conditions, the signals obtained from the system of vapor-liquid-solid flow boiling are chaotic, which is demonstrated by obvious wideband characteristic in power spectra, decreasing gradually of autocorrelation coefficients, non-integer fractal dimension and non-negative and limited Kolmogorov entropy etc. At least two independent variables are needed to describe the vapor-liquid-solid flow system according to the estimation of the correlation dimension in meso-scale. The shapes of correlation integral curves and their slopes change with the variations of boiling flow states. The identifications of various flow regimes and their transitions can be characterized by the shape variations. Multi-value phenomena of chaotic invariants were found including correlation dimension and Kolmogorov entropy at the same operation conditions, showing the appearance of multi-scale behavior in the vapor-liquid-solid flow. Time series of heat transfer coefficients in fluidized bed evaporators were modeled and predicted by the nonlinear tools and the comparisons between predicted and measured time series were carried out by estimating the statistics characteristics, power spectrum, phase map and chaotic invariants and good agreements were observed. This indicates that a simple nonlinear datum driving model can describe the average or steady heat transfer character with a reasonable accuracy and the transient heat transfer behavior with a general fluctuation tendency for the vapor-liquidsolid flow. These findings are useful for finding new design, operation and control strategies for such complex systems.

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Email address: [email protected]

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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Introduction A fluidized bed evaporator as a novel and powerful heat exchanger can be used in chemical, pharmaceutical, power, energy and other industry processes since it is able to solve severe fouling problem and to enhance heat transfer due to the circulation of fluidized solid particles through the surfaces of heated tubes in the shell and tube exchangers [1-6]. However, the quantitative description of flow and heat transfer features both steady-state and transient in such a system is still a difficult task due to the system complexity. Only several semi-empirical correlations were proposed to forecast the steady-state characters such as average pressure drop and heat transfer coefficients. No proper mathematical models that can describe the evolution or transient behavior of the system have been suggested in the open literature even though the evolution behavior reveals richer information on the system process mechanism. Accurately modeling the transient behavior of such a system is a crucial step to find proper design, operation and control strategies [4-5]. Generally there are three modeling methods for a system: physical modeling, datum modeling and the combination of them. Understanding well the interactions between all kinds of factors and the relationship between system and environment are the prerequisites for successfully physical modeling. For the datum modeling, when a lot of experimental data, such as time series data, of the key parameters of the system are obtained, one can develop a good model that can reflect the inherent evolutional features by using traditional statistics analysis or modern datum analysis tools. During the datum modeling, it is not necessary to understand the interior dynamic mechanisms of the system well and a mathematic model from which the calculation value is closer to the experimental datum is considered to be the proper one. For the complex systems, such as the multi-phase flow systems, the datum modeling is one of the effective methods. On the other hand, modeling can also be divided into two types: steady-state modeling and dynamic modeling. Time series datum modeling belongs to the latter, and the developed model can predict the dynamic evolution behavior of the system. There are several time series datum modeling methods, such as linear and nonlinear, explicit and implicit, single variable and multi-variable and local (for given training experimental data, only part datum points are used during searching or fitting the proper model function) and global (all the given training experimental data will be used during searching or fitting the proper model function) etc. time series modeling techniques. The key step of time series modeling is to find an approximating model function by using certain effective searching and fitting tool in order to build a model that can forecast the future characteristics of the system. The explicit nonlinear time series modeling tools include the orthogonal polynomial [7], genetic programming [8-9] and inversion theory etc. global modeling methods. There are a certain number of implicit nonlinear modeling methods, such as the chaos and neural network modeling etc. Each method has its own advantages and disadvantages. Recently, the nonlinear analysis methods including chaos and fractal analysis tools were introduced to the system of boiling heat transfer to unravel the mechanism and to

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suggest some potential reasons why only limited success was achieved in vapor-liquidsolid (V-L-S) the mechanistic modeling. Several nonlinear studies reported in open literature focused on pool nucleate boiling system due to its simple configuration from which it was easy to address fundamental issues and was reviewed recently by Mosdorf and Shoji [10]. From the point of view of practice, nonlinear investigations on the flow boiling system is more urgent because the accuracy design, optimum operation and effective control of flow boiling in heat exchangers such as the evaporator and nuclear reactor are still quite difficult due to the complexity of flow boiling phenomena. Nonlinear points were also applied to study the instabilities and oscillations appeared in the two-phase flow boiling systems [11-23]. Rizwan-uddin and Dorning [11] reconstructed a chaotic attractor in a periodically forced boiling two-phase flow with single channel system. Clausse and Lahey [12] unraveled the nonlinear characters from the density wave signals in flow boiling system. Delmastro and Clausse [13] measured experimentally nonlinear dynamical attractors of a natural circulating boiling flow and found that the complex phenomena of the system exhibit nonlinear features. Kozma, Kok, Sakuma et al [14] used the fractal technique to characterize the two-phase boiling flow loop in order to develop objective flow regime indicators. It was found that the error of the linear fit of the fractal dimension is a sensitive indicator of the changes in the flow regime, while the fractal dimension value itself is less suitable for flow regime identification and a bi-fractal behavior was found in the measurement temperature signals. Narayanan, Srinivas and Pushpavanam [15] studied the phenomena of density wave oscillations in a vertical heated channel by numerical simulation and the complex hydrodynamic behavior like relaxation oscillations, quasi-periodic behavior and chaotic solutions of the two phase flow system in an evaporator by incorporating the effect of a periodic variation in the imposed pressure drop were obtained. Lee and Pan [16] investigated the dynamics of multiple parallel boiling channel systems with forced flows by numerical simulation. The bifurcations from limit cycle, quasi-periodic to chaotic oscillation were demonstrated for a 3-channel system. Cammarata, Fichera and Pagano [17] carried out the nonlinear analysis of a rectangular natural circulation loop. The reconstructed phase maps from the time series of temperature were investigated and the fractal dimensions of attractors were estimated. Robert, Wilhemus, Tim et al. [18] investigated experimentally the nonlinear dynamics of natural-circulation, boiling two-phase flows and found that the boiling two-phase flow undergoes the well-known Feigenbaum scenario, the period-doubling route toward chaotic behavior. Their results pointed out the possible existence of chaotic behaviors in the system. These nonlinear analyses are valuable for enhancing the physical understanding of such systems. The general nonlinear analysis tools such as phase map analysis and chaotic invariant estimates were applied most often in these studies. However, as another powerful datum excavating tool, chaotic modeling and prediction was not well utilized [4]. The chaotic prediction is taken as an effective diagnostic tool to identify chaos from random, and much interesting work on chaotic prediction for some complex systems has been reported in open literature [19-22].

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It is considered that the transient behavior of flow and heat transfer in the flow boiling system manifests nonlinear and non-equilibrium characteristics. And the linear dynamic models can’t describe the system characteristics no matter how high the model order is. It may be possible to develop some effective, simple but nonlinear dynamic models from the point of view of nonlinear dynamics. In this chapter, the behavior of time series of physical parameters in fluidized bed evaporators with a natural circulating flow were investigated from the point of view of nonlinear hydrodynamics. The chaotic characters of the systems were analyzed to unravel the motion mechanism and implicit nonlinear datum modeling was done to find a simple nonlinear model to forecast the flow and heat transfer behavior.

Chaotic Characters Chaotic features of wall temperature fluctuations in the fluidized bed evaporator with V-L-S-flow were investigated by means of deterministic chaos analysis techniques. Experimental Setup In order to investigate the complex behavior often observed in industrial facilities, an experimental multiple-tube evaporator was built, consisting of 4 heated vertical stainless steel tubes. The outer diameter of each heated tube is 38 mm with the inner diameter of 32 mm. Liquid phase was tap water, and solid phase was Teflon cylindrical particles. The experimental setup is illuminated in Fig.1.

Fig.1. Experimental apparatus and flow diagram [5]. 1. Heat exchanger; 2. Separator; 3.Circulating tube; 4. Electromagnetic flow-meter; 5.Vapor condenser; 6. Vapor condensate gauge bank; 7.Valve; 8.Liquid pump; 9.Condensate gauge bank; 10. Boiler; 11. Thermocouple probe; 12.Ample plate; 11.A/D plate; 12. PC. (a) Inlet of cooling water; (b) Outlet of cooling water.

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In an ordinary evaporating operation with a vapor-liquid (Vs. V-L) flow, no solid particles were added into the evaporator. At the beginning of an experiment with V-L-S flow, the liquid and solid particles were added into the evaporation system. During evaporating, the condensation latent heat of the boiler steam in shell-side space was used to heat the mixture in tube-side space or in heated tubes in a shell-and-tube heat exchanger. The boiler steam was condensed from vapor phase to liquid phase and was collected in a condensate gauge bank. Then, the steam condensate was pumped back to the boiler by water pump after its volume flow rate was gauged. The V-L-S mixture in the upper part of the heated tubes got into the separator in which the vapor and liquidsolid (Vs. L-S) mixture separated. The produced vapor was condensed in a shell-andtube vapor condenser by cooling water in shell-side space. Then the vapor condensate was collected in a vapor condensate gauge bank, where the volume flow rate was measured to get the heat-transfer rate or the heat flux. The L-S mixture in separator circulated back to the bottom of the heat exchanger through the circulating tube and electromagnetic flow meter. And the L-S mixture was heated by boiler steam again. The liquid levels in separator were kept the same for different runs and no additional liquid phase was supplied during the datum samplings and measurements. The whole system was operated in a model of an external natural circulating flow and at an atmospheric pressure. The control parameter of the system is the pressure of boiler steam or the steam temperature. Thus, for each run, the temperature was constant. The properties of solid particles and operation conditions are shown in Table 1. Table 1 Properties of solid particles and liquid and operation conditions. Particle parameters Diameter×length/m×m 0.003×0.003

Density /kg/m3 2190

Operation conditions Steam gauge pressure /MPa

Volume holdup /%

0-0.15

0-10

When the boiler steam pressure and thus the rate of heat transfer was very low, no V-L circulating flow was formed because the boiling phenomenon didn’t appear in the heated tube. With the increase of steam pressure, the circulating flow was gradually established by the density difference between the V-L mixture in heated tube and the liquid in circulating tube. However, no V-L-S circulation flows were obtained when the steam pressures were relatively low because in this operation condition, the circulating velocity of V-L mixture was lower than the terminal velocity of added solid particles as well. When the heat-transfer rate or the heat flux reached a certain high value, a typical V-L-S circulation flow could be obtained. The experimental data were recorded when the three-phase circulating flow was established. A precise parameter measuring system aided by a personal computer for on-line automatic measuring and sampling was developed to obtain the data of wall and fluid temperatures. Wall temperatures of heated tubes were measured by means of copperconstantan thermocouples with the wire diameter of 210-4m, and fluid temperatures of the system were measured using the armored copper-constantan thermocouples with the diameter of 1.510-3m. The profile of the 4 heated tubes in heat exchanger and the distribution of the thermocouples in each heated tube when measuring the wall and fluid temperatures were shown in Fig.2. The system uncertainties are mainly associated to the

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calibration of the thermocouples, the amplifier, data acquisition and reduction systems besides the thermal resistances between thermocouples and tube walls. The dynamic error of the temperature measurements is negligible for the response time of the thermocouples is at least three orders of magnitude lower than the studied fluctuations of temperatures. The overall uncertainty of the temperature measurement is 1C, with 95% confidence level. The measured signals obtained from the probes were amplified, digitalized and stored in a PC for further processing. The sample frequency is 125Hz, and the sample time is 80s. It is well known that the measured original signals often contaminated by low amplitude and high frequency noise. Hence, measures were taken to reduce the noise. For most wall temperature signals, the main frequency and most meaningful frequencies are less than 15Hz. This can be got from the power spectrum of original wall temperature signal in linear coordinates (not given here). In order to reduce the noise and at the same time to ensure that the spectra of interest of the signal were still captured, the signals were filtered with a frequency of 31.25 (≥2×15) Hz using a lowpass algorithm (the input parameter is 125/4) before executing the datum treatment. This treatment of noise reduction is similar to that of most studies on the chaos analysis of signals [23]. The total pressure drops between the inlet and the outlet of the heated tubes and circulating flow rates of the mixture in heat exchanger were also measured by differential pressure transducer and electromagnetic flow meter, respectively. In the following investigations, the time series of wall temperature measured at the top of the left heated tube is used to judge the system either chaotic or not, and to explore the variations of chaos invariants with the operating conditions. The holdup of solid particle, ε=1% is taken as an example. The solid holdup is the ratio of the volume of solid particles to the total volume of the three-phase mixture. The height of the threephase mixture in this evaporator is kept along the horizontal centerline of the inlet of the separator, namely the horizontal centerline of outlet of the connection tube of heated tubes. Thus, the total volume of the three-phase mixture is the volume of this circulating system and it is measured at the beginning of the experiments by using the water. Nonlinear Analysis Methods The analysis methods used here include traditional tools such as time series, power spectrum and autocorrelation coefficient analyses and the deterministic chaotic analysis methods as correlation dimension (including correlation integral curves) and Kolmogorov entropy (including the slope curves) estimations. In the analyses, the signals of wall temperature measured at upper part of left heated tube are used. The deterministic chaotic analysis tools are available in literature [4-5, 21-24], and only a brief description is given here.

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(b)

2

1 100mm

4

150mm

5 3

(c) Fig. 2. The arrangements of the 4 heated tubes and the measuring details of the temperatures. (a) The distribution of the thermocouples along the axis of the middle heated tube to measure the wall and fluid temperatures. 1- thermocouples for wall temperature measurements; 2thermocouples for fluid temperature measurements. (b) Detail diagram of I in Fig.2 (a) for wall temperature measurment. 1-copper-constantan thermocouple with wire diameter of 0.2mm; 2-glue; 3-thermocouple tip; 4-wall of heated tube. (c) The arrangements of the 4 heated tubes. 1-right heated tube; 2-left heated tube; 3-front heated tube; 4-middle heated tube; 5-inlet of steam.

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Attractor is the final place where the system evolution trajectories are attracted in reconstructed phase space and the formatted structure is the attractor phase map. The geometry shape of phase map can give some qualitative complexity information of the evolution system. For example, a periodic signal shows up as a limit cycle on the phase map, meaning that the system evolution behavior is simple and is totally predictable, whereas a chaotic system exhibits a very complex and rich attractor structure, indicating that the system has mediate prediction ability. Correlation dimension of the attractor is a measure for the fractal dimension of the system, which can be used to identify the number of the system freedom degrees. The number of independent variables controlling the system behavior is a lowest integer number greater than correlation dimension. Kolmogorov entropy of the attractor is a quantitative measure of the rate of information loss of the system dynamics. For a periodic system, its value is zero and the system is totally predictable. For a random system, its value is infinite, making it impossible to predict the state of the system even after a differential time step. For the case of a chaotic system, it is finite and positive and the system holds the limited forecasting ability. The first step of deterministic chaotic analysis is to reconstruct the data of a time series into an attractor in m-dimensional phase space according to the embedding theorem. The time-delay embedding is used in the phase space reconstruction because it is perhaps the only systematic method for going from scalar data to multi-dimensional phase space. Although any value of time delay will be acceptable according to the embedding theorem, some choice rule should be observed from the practical point of view. In this work, it is chosen according to the calculations of the nonlinear invariants. When the results including the plots of correlation integral versus radius of hypersphere in phase space don’t vary obviously with the choices of time-delay, this timedelay value is considered to be a proper one. In this work, it is about 0.25s. The values of nonlinear parameters are estimated by using a software tool. It was developed and verified by the authors, and more details on the software can be found in the papers [2123, 25]. Chaotic analysis results and discussion Traditional analyses of time series The time series of wall temperature in V-L-S flow measured at upper part of left heated tube under different steam pressures are shown in Fig.3. The power spectrum in half-log coordinate and autocorrelation coefficient plots are shown in Figs.4-5. Fig.6 gives the time series under same steam pressures for V-L flow system for comparison. It can be seen from Fig.3 that the patterns of time series under different steam pressures are quite distinct and the V-L-S flows are complex or stochastic. For each signal, the periodic components are superimposed by stochastic components. The periodic fluctuations are considered to represent the large-scale motions of large vapor bubbles in measurement point, and the superimposed small fluctuations represent the disturbances of the motions of solid particles and small vapor bubbles.

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Fig.3. Time series of wall temperatures for V-L-S flows.

Fig.4 shows that all the power spectra exhibit a continuous spectrum with many spikes and fall exponentially at the high energy frequency range of 0-5 Hz. This implies that the fluctuation behavior of wall temperature signals in V-L-S flow system is chaotic. It is considered that the higher frequency peak with lower energy is relevant to the formation and departure of small bubbles, and the lower frequency peak with higher energy corresponds to the formation and departure of large bubbles. Fig.5 shows that the autocorrelation coefficients of the signals decrease gradually with the increase of time delay. This indicates that prediction ability of the system is finite, which is also the feature of the chaotic motion. In V-L flow system, the motions of large bubbles are obvious, which can be found from the time series of wall temperatures, as shown in Fig.6. However, in the V-L-S system, small bubbles are more often found. Solid particles reduce the periodicity or the instability caused by large vapor bubbles, which is often found in the V-L flow. These traditional analyses indicate that the fluctuations of V-L-S flows are nonperiodic and chaotic motions may occur in such systems. In order to confirm this, nonlinear analyses are needed. Nonlinear Analyses of Time Series Correlation Dimension Fig.7 shows the relationship between the correlation integral and radius of hypersphere or the scale in phase space. The correlation integral curves are not sensitive to the value of time delay. It can be found in Fig.7 that the curve shapes vary with different steam pressures and there are a few linear segments in the curves at a given steam pressure. When the steam pressure is low, the vapor bubbles are very small and the V-L-S flow is in the bubbling state. In this starting nucleate boiling regime, the linear sections of the curves are not obvious (see scale 2 in Fig.7(a)). With the increase of steam pressure, the large vapor bubbles can be formed and a clear platform in the middle scale (scale 2) of the horizontal ordinate is found as shown in Figs.7(b)-(c). In these conditions, the V-L-S flow is in the developed nucleate boiling regime or the slug bubble flow regime. The

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results indicate that the curve shape variation could be used as an effective tool to identify the existence of the boiling state in evaporator. Basically, there are three linear sections in the curves and three correlation dimensions can be obtained, even though in some cases the linear sections are not obvious. From left to right along the abscissa axis, the correlation dimension value of the first one (see scale 1 in Fig.7) is highest (typically 6.8) and may reflect the behavior of small scale fluctuation with high frequency resulted from the small bubbles and particles; the value of the second one (see scale 2 in Fig.7) is lowest (typically 1.6) and reflects the meso-scale periodic behavior with low frequency caused by large bubbles; the value of the third one (see scale 3 in Fig.7) is in the middle (typical 6.5) and may represent the lower frequency motion of the larger scale caused by the system boundary or installation boundary. Certainly, the definitive physical interpretation on the middle value of correlation dimension with large scale 3 remains to be studied. In most published papers on nonlinear researches, the value of fractal dimension corresponding to the meso-scale is often considered to be the correlation dimension. In this work, its value is about 1.5~2.0. This indicates that the system is chaotic and two independent variables are needed at least to describe the complex behavior of V-L-S flow, especially to describe the motion of the large bubble.

Fig.4 Power spectra of wall temperature signals with V-L-S flows.

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Fig.5 Autocorrelation coefficients of wall temperature signals for V-L-S flows.

Fig.6. Time series of wall temperatures for V-L flows.

Liu et al.

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Fig.7 Correlation integral versus radius of hyper-sphere in phase space.

Kolmogorov Entropy The relation between the slope or Kolmogorov entropy and radius of hyper-sphere or the scale in phase space with different steam pressures for V-L-S flows is given in Fig.8. Similar to the situations of correlation dimension, a few platforms and thus multiple values of Kolmogorov entropy can be obtained in different scales at the same operation condition. The range of values of Kolmogorov entropy is 0-3.5 bits/s. The Kolmogorov entropy of meso-scale (scale 2 in Fig.8) is about 1.0 bit/s for the pressure of 0.07MPa and 0.4 bit/s for the pressure of 0.15MPa. Hence, each value is finite and

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positive. The results show that the ability to predict the behavior of V-L-S flow is limited. The results give further quantitative evidence that the system is chaotic.

Fig.8. Kolmogorov entropy versus radius of hyper-sphere in phase space with V-L-S flows.

The estimations of correlation dimension and Kolmogorov entropy with meso-scale (scale 2) find that the values for V-L-S flows are higher than those for V-L flows[4] at given operation condition. This indicates that the chaos level of V-L-S flow is higher than that of V-L flow due to the addition of solid particles.

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Chaotic Modeling and Prediction [26] It has been shown that the system of V-L-S flow exhibits chaotic behavior. Hence, the technique of nonlinear modeling and prediction can be applied to describe the steady and transient behavior of heat transfer in such a system. It can be considered that if the phase maps, chaotic invariants of reconstructed attractors of the experimentally obtained and predicted signals in systems are generally equal, the nonlinear modeling and prediction is successful. Time series of heat transfer coefficients of V-L-S flow evaporator were used as the processing signals since they are more direct for the design, operation and control of the evaporator than the temperature time series. The coefficients were calculated on the temperature difference between wall temperature (transient value at measurement location) and fluid temperature (transient value at measurement location) and the heat flux (average value of whole system obtained by measuring the vapor and steam condensate volume rate). The oscillations of heat transfer coefficient actually result from the fluctuations of the wall temperature since the temperatures of fluid and heating steam are near constants during flow boiling. Method of chaotic modeling and forecast Time series nonlinear modeling is generally based on the phase space reconstruction of the system evolution with embedding theorem. The chaotic datum modeling method is something like that of the artificial neural network and the model built is a kind of history datum driving one, not an explicit mathematical expression. The historical data used in the nonlinear modeling and forecasting are the heat transfer coefficient signals derived by measured temperature signals of inner surface and boiling fluid and mean heat flux. The prediction can’t be performed without historical experimental data. The derivations from the historical data to the predicted data using the theory of nonlinear prediction has well developed and verified with a few multi-phase flow systems such as gas-liquid bubble column and V-L flow boiling systems [4,19-22]. The method of neighbor point similarity is adopted to model the fluctuations, and it is a method of local non-linear short-term prediction. In chaos prediction, a time series of single variable is transformed into a prediction of the state in m-dimensional phase space. The prediction steps are as follows: first, reconstruct the time series data into an attractor in m-dimensional phase space according to the embedding theorem and determine the prediction time, T  ; second, find a functional relationship, g , between the current m-dimensional state, X (t ) , and the future m-dimensional state, X (t T ) ; third, translate the m-dimensional state vector X (t T ) to the scalar and to get the prediction value; finally, repeat the previous steps till all the points has been predicted. In the prediction, g is approximated by a predictor G and there are two approaches to find a predictor G , local approximation and global approximation. The former is used most often, and only uses nearby states to establish a functional G . The simplest method to build a local predictor is approximation by nearest neighbor, i.e., zero-order approximation. The future of the nearest state is considered to be similar to the future of the state to be predicted. In this case, the number of the nearby states k equals to one. A

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superior one is the first-order approximation, with taking k greater than embedding dimension m and using k nearby states to make predictions. The prediction method is tested by a typical chaotic series of Lorenz. Prediction and statistics parameters are shown in Table 2, and comparisons between predicted and simulated time series of x variable is shown in Fig.9. Table 2 Prediction parameters of Lorenz chaotic time series Number neighbor points, k 4

of

Time delay, τ, s 0.03

Number known points 4600

of

Number prediction points, N 300

of

Average relative errors for first 50 points 0.67%

Average relative errors for 300 points 7.23%

Fig.9 Comparisons between predicted and simulated chaotic time series of x variable in Lorenz system.

Forecasting results and discussion The prediction parameters for V-L-S flow data are shown in Table 3. It is well known that the prediction accuracy reducing fast with the increase of the time step is a potential argument of the chaos presence. For a chaotic time series, the number of reasonable prediction points is much smaller than the number of a few thousands. However, the number of predicted points is 4096 here in order to have a whole look on the prediction results. Table 3 Prediction parameters of time series of heat transfer coefficients. Number points 4096

of

known

Number points, N 4096

of

prediction

Number points, k 6

of

neighbor

Time delay, τ, s 0.4

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Time series at top of left tube of the evaporator Time series comparison The predicted and measured time series of heat transfer coefficients obtained from top of left tube under different conditions are shown in Fig.10, in which only the first predicted 500 points are shown.

Fig.10 Predicted and measured time series of heat transfer coefficients obtained from top of left tube in V-L-S evaporator with solid holdup of 6% under different saturated steam temperatures. (a) T s =120.9C; (b) T s =123.3C; (c) T s =126.2C.

Fig.10 indicates that the agreement between predicted and measured value is acceptable in the general variation tendency. However, the agreement is not as satisfactory as that of the V-L flow system in time trajectory because only a few predicted values (less than 100 points) at the beginning of the signals approach the measured values. And with increase of the prediction time, the divergence between the measurement and the prediction increases. The limited prediction ability with high accuracy is a feature of chaotic system. Comparison of average relative error The average relative errors for the first 500 points of prediction at different saturated steam temperatures are shown in Table 4.

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Table 4 Average relative errors between predicted and calculated time series. Saturated steam temperature

Average relative errors for first 500 points

T s =120.9C

1.14%

T s =123.3C

1.31%

T s =126.2C

2.06%

Table 4 claims an average relative error of 1% to 3%, which sounds quite good on the first sight, especially when considering the error for the Lorenz time series shown in Table 2. However, the range of the Lorenz time series is from -30 to +20, so it changes very drastically, and reported average relative error is of about 1% to 7% in this dynamic range. On the other hand, the time series for heat transfer coefficients has an average value of about 2.0, with a dynamic range of about 0.1. Hence, the nonlinear prediction on average heat transfer coefficients is not quite good. For V-L-S flow, the average relative error is somewhat higher than that of V-L flow system and increases with increase of prediction points [4]. The result that the general fluctuation behavior including the fluctuation frequency and amplitude of the heat transfer coefficient is similar between the predicted and estimated signals for V-L-S system, which is similar to that of the V-L system, indicates that the prediction model generally describes the dynamic feature of the investigated system. The detail will be illuminated in the comparisons of power spectra and chaotic invariants. Comparison of statistics characters Besides the average relative error, time-averaged statistics characteristics, such as the average value, average deviation and standard deviation are also estimated, as shown in Table 5. It can be seen that the statistics parameters, especially the average heat transfer coefficients are close between estimates and predictions. Table 5 Statistical parameters of predicted and measured time series of the coefficients. T s =120.9C T s =123.3C T s =126.2C Measurement

Prediction

Measurement

Prediction

Measurement

Prediction

Average

1.874

1.874

1.994

1.996

2.044

2.046

Average

1.86E-02

1.35E-02

3.75E-02

4.04E-02

4.05E-02

3.57E-02

2.26E-02

1.67E-02

4.36E-02

4.49E-02

4.53E-02

4.06E-02

deviation Standard deviation

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Comparison of power spectra Fig.11 is the power spectra of measured and predicted time series at top of left tube under different saturated steam temperatures. The agreements between measurement and prediction are generally acceptable, and when saturated steam temperature is 126.2C, the prediction result is best with regard to the fluctuation frequency, as shown in Fig.11(c). Fig.11 indicates that the main frequencies in V-L-S system are less than 3Hz. With increment of saturated steam temperature, the dominant frequency decreases, which is the same as that of V-L flow system but is different from the gas-liquid bubble column system.

Fig.11 Power spectra of measured and predicted time series at top of left tube under different saturated steam temperatures with average solid holdup of 6%. (a) T s =120.9C; (b) T s =123.3C; (c) T s =126.2C.

Comparison of attractor phase maps Fig.12 shows the three-dimensional phase maps of predicted and measured signals of heat transfer coefficients. It can be said that from the point of view of attractor size and three-dimensional shapes, they are generally similar but not as good as those of V-L flow system. The shapes in the phase maps (Fig.12(c1)) are not simple limit cycles but rich structures, which indicates that the systems are chaotic and hold limited prediction ability.

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(c1)

(b1)

(a1)

Liu et al.

(c 2)

(b 2)

(a 2)

Fig.12 Phase maps of predicted and measured signals of heat transfer coefficients at top of left tube with average solid holdup of 6%. (a1), (a2) T s =120.9C (b1), (b2) T s =123.3C (c1), (c2) T s =126.2C. (a1), (b1),(c1) : measured; (a2), (b2), (c2): predicted.

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Comparison of correlation dimension The correlation dimensions for two different scales are given in Table 6. The average relative error for scale 1 is about 30%, which is higher than that of V-L flow (about 15%). The values of correlation dimension in V-L-S flow system are larger than those in V-L flow. These indicate that the complexity of V-L-S flow is higher than that of V-L flow due to the addition of solid particles. However, the prediction is acceptable from the point of view of statistics since the forecast on the transient behavior is more difficult than that on the steady behavior. Table 6 Correlation dimension of predicted and measured signals of heat transfer coefficients at top of left tube under different saturated steam temperatures. Correlation T s =120.9C T s =123.3C T s =126.2C dimension, D2

Measurement

Prediction

Measurement

Prediction

Measurement

Prediction

Scale 1

2.056

1.448

1.951

1.350

1.863

1.267

Scale 2

6.791

6.078

5.227

4.578

7.040

6.492

Comparison of Kolmogorov entropy Estimated values of Kolmogorov entropy using predicted and measured signals of heat transfer coefficients at top of left tube in V-L-S evaporator with average solid holdup of 6% are listed in Table 7. The average relative error for scale 1 is about 23%. The values of Kolmogorov entropy in V-L-S flow system are also larger than those in V-L flow system. The values of Kolmogorov entropy are finite and positive, which means that the system has limited forecasting ability. Table 7 Kolmogorov entropy calculated by predicted and measured signals of heat transfer coefficients at top of left tube in V-L-S evaporator with average solid holdup of 6%. Kolmogorov T s =120.9C T s =123.3C T s =126.2C entropy,

K,

bit s

Measurement

Prediction

Measurement

Prediction

Measurement

Prediction

Scale 1

0.864

0.682

0.353

0.257

0.406

0.334

Scale 2

1.526

1.301

1.028

0.886

1.308

1.241

-1

Time Series at Center Tube in the V-L-S Evaporator Three groups of time series obtained from the center tube are predicted, time series at top of center tube in the evaporator with three saturated steam temperatures (Group A), time series at three axial locations along the center tube in the evaporator under the given saturated steam temperature (Group B) and time series at top of center tube in the evaporator with three average solid holdups under given saturated steam temperature

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(Group C). The qualitative and quantitative analysis tools are the same as those mentioned above. Here, only the comparisons of statistical parameters, time series and power spectrum are illuminated. Figs.13-15 illuminate the time series and power spectra comparisons between predicted and measured heat transfer coefficients in V-L-S evaporator under different operation conditions for Group A, Group B and Group C, respectively. The comparison results of both time series and power spectrum are good. Fig.14(ii) shows that for the same heated tube, the power spectra at different axial positions are similar except at bottom where no obvious vapor bubbles appear, which indicates that the fluctuation behavior is near the same. Figs.13-14 also declare that with the increase of saturated steam temperature or the height of the heated tube, the peak number of the main fluctuation frequencies also climbs, which mainly results from the births and motions of more vapor bubbles. Fig.15(ii) indicates that under approximate saturated steam temperatures, the power spectra at different average solid holdups are similar except that the peak number of important frequencies is slightly larger for the higher average solid holdup due to the stronger disturbance of more solid particles for the V-L-S flow. The average relative errors for the first 500 points between predicted and measured time series of the three groups are all less than 2.0%. Table 8 is the statistical parameters both predicted and measured time series of heat transfer coefficients of the three groups, and the agreements of the average, average deviation and standard deviation are acceptable. For other three heated tubes, similar results can be obtained. These studies indicate that a simple nonlinear model can describe the average and temporal behavior of heat transfer coefficient in certain degree of accuracy, which may be valuable for finding new design, operation and control strategies for the system of VL-S flow. However, the forecast accuracy is not much high from the point of view of time trajectory and changes with heating steam temperature, axial height, average solid holdup, flow regime and noise. It is noteworthy that the prediction for the V-L-S flow is not as good as that for the V-L flow from the point of view of the time trajectory, even though the prediction for V-L flow is not as good as that of gas-liquid bubble column system. This can be seen from Fig.16 (drawn from Fig.10(c)), in which only about 100 points at the beginning of the time series are shown. In Fig.16, there is no datum point whose predicted value equals exactly to the measured value at the beginning of the signal for V-L-S flow boiling. However, for V-L flow, there are a few datum points whose prediction values are the same as the measurement ones in time trajectory even though this number is much lower than that of the gas-liquid bubbling system. This indicates that system of VL-S flow is more complex than those of V-L flow and of gas-liquid flow, and this manifests the differences in dynamic mechanism between these systems.

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(i) Time series

(ii) Power spectra Fig.13 Predicted and measured time series of heat transfer coefficients obtained at top of center tube in V-L-S evaporator with solid holdup of 6% under different saturated steam temperatures. (a) T s =120.9C; (b) T s =123.3C; (c) T s =126.2C.

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(i) Time series

(ii) Power spectra Fig.14 Predicted and measured time series of heat transfer coefficients obtained from center tube at different axial locations in V-L-S evaporator with solid holdup of 6% and saturated steam temperature of 126.2C. (a) Bottom (Z=0.02m); (b)Middle(Z=0.50m); (c)Top(Z=0.98m).

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(i) Time series

(ii) Power spectra Fig.15 Predicted and measured time series of heat transfer coefficients obtained from the top of center tube in V-L-S evaporator with approximate saturated steam temperatures and different average solid holdups. (a) T s =128.1C,ε=2%；(b) T s =126.6C,ε=4%；(c) T s =126.2C,ε=6%.

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Table 8 Statistical parameters of the predicted and measured time series of the three groups. Runs

Measured or

(a)

ε=6%

(c)

(a)

-2

-1

Average

Standard

deviation

deviation

Predicted

kW·m ·K

Measured

4.24

2.2E-02

2.8E-02

Predicted

4.23

1.0E-02

1.3E-02

Measured

4.65

2.4E-02

3.2E-02

Predicted

4.67

2.0E-02

2.6E-02

Measured

4.46

5.6E-02

7.1E-02

Predicted

4.47

4.3E-02

5.8E-02

Measured

8.62

20.8E-02

24.7E-02

Predicted

8.62

17.3E-02

20.6E-02

Measured

3.08

0.9E-02

1.2E-02

Predicted

3.07

0.5E-02

0.6E-02

Measured

4.46

5.6E-02

7.1E-02

Predicted

4.47

4.3E-02

5.8E-02

ε=2%;

Measured

4.76

6.0E-02

7.8E-02

T s =128.1C

Predicted

4.75

3.4E-02

4.6E-02

ε=4%;

Measured

5.11

6.2E-02

7.9E-02

T s =126.6C

Predicted

5.12

5.3E-02

6.7E-02

ε=6%;

Measured

4.46

5.6E-02

7.1E-02

T s =126.2C

Predicted

4.47

4.3E-02

5.8E-02

T s =120.9C

Group A (b)

Average of h,

T s =123.3C

T s =126.2C

Tube bottom

Group B

T s =126.2℃;

(b)

Tube middle

ε=6% (c)

Tube top

(a)

Group C (b) Tube top

(c)

It has to be pointed out that this work mainly tests the ability of local nonlinear forecast method to model the evolution behaviors of heat transfer characteristics in V-LS flow systems on the basis of identification of nonlinear features of the systems and under the present ranges of experimental parameters and operation conditions, the mathematical relations between the chaotic behavior of transient and time-averaged heat transfer coefficients were not obtained due to the limited experimental data, let alone the mathematical relations between the chaotic behavior and the transient heat transfer coefficients. And the analyses on the physical essence of the studied system are also

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limited partly due to the complexity of the engineering problems and the limitation of the nonlinear theory. All these issues need further deeper researches.

Fig.16 Comparisons between predicted and measured time series of heat transfer coefficients obtained from top of left tube in V-L-S evaporator with average solid holdup of 6% and saturated steam temperature of 126.2C for the first 100 points.

Concluding Remarks 1) Under certain operation range, the unstable or the fluctuation phenomena occurred in boiling system with V-L-S flow is chaotic. This is demonstrated by the results of traditional linear analysis and modern nonlinear analysis, such as obvious wideband characteristic in power spectra, decreasing gradually of autocorrelation coefficients, non-integer fractal dimension and non-negative and limited Kolmogorov entropy. This finding is important for the design, operation and control of such complex system. 2) According to the estimation of the correlation dimension in meso-scale (scale 2), at least two independent variables are needed to describe the V-L-S flow system. 3) The curve shapes of correlation integral and slope change with the state variations of the V-L-S flows. The identifications of the boiling flow states may be achieved by this phenomenon. 4) The multi-value phenomena are found in the estimations of chaotic invariants including correlation dimension and Kolmogorov entropy at the same operation condition. These results disclose in some degree the multi-scale behavior occurred in the V-L-S flow system. 5) Time series of heat transfer coefficients obtained at different spatial locations in a fluidized bed evaporator with V-L-S external natural circulation flow boiling were modeled by the nonlinear forecast tools. The comparisons between predicted and measured time series in such multi-phase flow systems were investigated by statistics characteristics, power spectrum, phase map and chaotic invariants. The results indicate

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that a simple nonlinear datum driving model can describe the average or steady heat transfer character with a reasonable accuracy and the transient heat transfer behavior with a general fluctuation tendency for the V-L-S flow system, which could be useful for finding new possible design, operation and control strategies for such systems. 6) The predictions for the V-L-S flow system are not as good as those for the systems of V-L flow and gas-liquid flow from the point of view of the time trajectory. This may indicate certain important differences between these systems in fluctuation mechanism and nonlinear complexity. 7) Further work is to explore the physical mechanism, mathematical relations between the chaotic behavior and heat transfer coefficients and possible thermaldynamic control methods of V-L-S fluidized bed evaporator.

Acknowledgments The authors are grateful to the National Natural Science Foundation of China (No. 20106012) and the Cheung Kong Scholar Program for Innovative Teams of the Ministry of Education (No.IRT0641) for the financial support of this work. The authors also wish to thank Profs. Hu ZD, Li JH, Li XL and Lin RT for their valuable suggestions and who had supported the projects.

Nomenclature Ac

autocorrelation coefficients, dimensionless

C (r )

correlation integral

D2

correlation dimension, dimensionless

f

frequency, Hz

g

a prediction function

G

predictor

h

heat transfer coefficient, Wm-2K-1

k

number of neighbor point

K

Kolmogorov entropy, bit/s

m

embedding dimension of phase space

N

number of prediction point

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P

steam pressure, MPa

r

radius of hypersphere, dimensionless

t

time, s

T Ts

T

X

temperature, C saturated temperature of steam, C prediction time, s restructured vector

Greek Letters ε

average solid holdup, dimensionless



time delay, s

ρ(f)

function of power spectrum density

References [1] [2]

[3] [4]

[5] [6]

[7]

Klaren DG. Revamping heat exchanger, Int. J. of Hydrocarbon Eng., 2002, 7(3): 97-102. Liu MY, Tang XP, Jiang F. Studies on the hydrodynamic and heat transfer in a vapor-liquid-solid flow boiling system with a CCD measuring technique. Chem. Eng. Sci., 2004, 59(4): 889-899. Liu MY, Nie WD, Yang Y, et al. Concentration of Gengnian’an extract with a vapor-liquid-solid evaporator. AIChE J., 2005, 51(3):759-765 Liu MY, Xue JP, Qiang AH. Chaotic forecasting of time series of heat-transfer coefficient for an evaporator with a two-phase flow, Chem. Eng. Sci., 2005, 60(3): 883-895. Liu MY, Qiang AH, Sun BF. Chaotic characteristics in an evaporator with a VL-S boiling flow, Chemical Engineering and Processing, 2006, 45(1):73-78 [6] Liu MY, Wang H, Lin RT. Visual investigations on radial solid holdup in vapor-liquid-solid fluidized bed evaporator with a CCD measuring system. Chemical Engineering Science, 2006,61(2): 802-813 Letellier C, Sceller LL, Gouesbet G et al. Topological characterization and global vector field reconstruction of and experimental electrochemical system. Phys. Chem. 1995, 99(18), 7016.

176 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

[8] [9] [10] [11] [12]

[13] [14]

[15]

[16] [17] [18]

[19] [20] [21] [22] [23] [24] [25]

[26]

Liu et al.

Kim BY, Park KS. Modeling of the Nonlinear sequences based on the genetic programming. Nonlinear Anal.1999, 36(6), 707. Lobo FG, Goldberg DE. The parameter-less genetic algorithm in practice. Information Sci. 2004, 167(1), 217. Mosdorf R, Shoji M. Chaos in nucleate boiling nonlinear analysis and modeling, Int. J. Heat Mass Transf., 2004, 47 (6/7): 1515-1524. Rizwan-unddin, Dorning JJ. A chaotic attractor in a periodically forced 2-phase flow system, Nucl. Sci. Eng., 1988, 100(2):393-404. Clausse A, Lahey RT. The analysis of periodic and strange attractors during density-wave oscillations in boiling flows, Chaos, Solition, Fractals, 1991, 1(2): 167-178. Delmastro D, Clausse A. Experimental phase trajectories in boiling flow oscillations, Exp. Therm. Fluid Sci., 1994, 9(1): 47-52. Kozma R, Kok H, Sakuma M., et al. Characterization of two-phase flows using fractal analysis of local temperature fluctuations, Int. J. Multiph. Flow, 1996, 22(5): 953-968. Narayanan S, Srinivas B, Pushpavanam S, et al. Non-linear dynamics of a two phase flow system in an evaporator: The effects of (i) a time varying pressure drop (ii) an axially varying heat flux, Nucl. Eng. Des., 1997, 178(3): 279-294. Lee JD, Pan CC. Dynamics of multiple parallel boiling channel systems with forced flows, Nucl. Eng. Des., 1999, 192(1): 31-44. Cammarata G, Fichera A, Pagano A, Nonlinear analysis of a rectangular national circulation loop, Int. Commun. Heat Mass Transf., 2000, 27(8): 1077~1089. Robert Z, Wilhemus JM, Tim DK, et al. Investigating the nonlinear dynamics of natural-circulation, boiling two-phase flows, Nucl. Technol., 2004, 146(3):244256 Farmer JD, Sidorwich JJ. Predicting chaotic time series. Phys. Rev. Lett., 1987, 59(8): 845-848 George S, Robert MM. Non-linear forecasting as a way of distinguishing chaos from measurement error in time series. Nature, 1990, 344(19): 734-741. Liu MY. PhD Thesis. Studies on the chaos hydrodynamic characteristics of multiphase reactors, Tianjin University, 1998. Liu MY, Hu ZD. Nonlinear bubbling hydrodynamics in a gas-liquid bubble column with a single nozzle. Chem. Eng. Technol., 2004, 27 (5): 537-547. Liu MY, Li JH, Hu ZD. Multi-Scale characteristics of chaos behavior in gasliquid bubble columns. Chem. Eng. Commun., 2004, 191(8): 1003-1016. Hilborn RC. Chaos and non-linear dynamics: An introduction for scientists and engineers, Oxford University Press, New York,1994. Liu MY, Yang Y. Time series modeling of two- and three-phase flow boiling systems with genetic programming. Chem. Eng and Tech., 2007, 30(11):15371545. Liu MY, Xue J, Qiang AH. Nonlinear forecast of heat transfer coefficient signal in fluidized bed evaporator, Chemical Engineering Research and Design, 2008, 86(1): 55-64

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Chapter 6 Air-Water Two-Phase Flows with Applications to Drainage System S.W. Chang1 and D.C. Lo2 Thermal Fluids Laboratory, National Kaohsiung Marine University. No. 142 Haijhuan Rd., Nanzih District, Kaohsiung City 81143, Taiwan, R.O.C. 1

2

Research Institute of Navigation Science and Technology, National Kaohsiung Marine University. No. 142 Haijhuan Rd., Nanzih District, Kaohsiung City 81143, Taiwan, R.O.C.

Abstract This chapter describes the phenomena of air-water two-phase flows with the particular application to the design of a drainage and vent system. The detailed knowledge of air-water interfacial mechanism, the propagation of transient air pressure and the flow resistance in a drainage system is essential in order to prevent the damage of trap seal, the unfavorable acoustic effect and the foul odors ingress into the habitable space through the interconnected drainage and vent network. For a drainage system with the air admittance valve at the exit vent of the vertical stack, the control of the propagation of the air pressure requires the understanding of the transient air-water twophase flow phenomena in each component of a drainage system. This chapter starts with the background introduction for a drainage and vent system. Research works investigating the air-water two-phase flows through vertical, horizontal and curved tubes as well as through the tube junctions are subsequently reviewed. An illustrative numerical analysis that examines the transient air-water two-phase flow phenomena in a confluent vessel with multiple joints feeding the stratified air-water flows is presented to demonstrate the CFD treatment for resolving the complex transient air-water twophase flow phenomena in the typical component of a drainage system.

Drainage System in Building Fundamental backgrounds A multi-storey drainage network for a building is normally constructed by a vertical stack connected with several inclined horizontal branches with a variety of terminal appliances such as bathtub and basin trap. A final bend attached at the end of the 

Email address: [email protected], [email protected].

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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vertical stack to channel the flow into the sewage. Fig. 1 depicts the air-water two-phase flow in a typical drainage network for a multi-storey building, reconstructing from the conceptual descriptions in [1]. As a primary function, a building drainage and vent system carries away the discharge from the appliance with the capability of preventing the foul odors ingress into the habitable space through the interconnected drainage/vent network. Therefore the water seal retained in the typical U bend becomes a common measure to prevent the ingress of odors by providing the regional isolation between the appliance and its downstream drainage network as seen in Fig. 1. Nevertheless, following the transient entrainment with falling water annulus in the vertical stack as indicated in Fig. 1, the water discharge from each terminal appliance often entrains airflow into the branch and forms the air-water two-phase flow with a free surface in the inclined branch. When this branch discharge reaches the stack junction, it can impinge on the opposite stack wall where the discharge separates and flows round the vertical stack with a high degree of swirl. Driven by gravity, the downward annular water flow is established in the vertical stack within about 1 meter. Prior to the established annular flow in the stack, the elliptical air spaces are intermittently formed below and on either side of the branch discharge. The structures of these regional two-phase flows are determined by the geometry of branch junction, the flow rate and the nature of the appliance discharge. The terminal water velocity of the annular flow in the stack (Vw), which is attached within a few meters from the stack entry [2-3], is correlated as Q  Vw  K w   D 

0.4

where D, Qw and K are stack diameter, volumetric water flow rate and

the empirical constant in the range of 12-15 respectively [1]. Justified by the range of superficial water and air velocity under a normal operating condition, the patterns of two-phase flow in a branch and the stack are often the stratified/wavy and the annular flows. It is also interesting to note that, due to the different physical properties such as density and viscosity between water and air, the Reynolds numbers for water and air flows are different at each channel section. While the stratified, wavy or annular water flow reaches the turbulent condition, the airflow at the same sectional location may remain as laminar. Moreover, as the branch discharge is a random and intermittent process, the stratified/wavy flow in the inclined branches and the annular flow in the vertical stack are transient phenomena. The presence of an air-water interface either in the branch or in the stack embodies a physical constraint of equal air and water velocity at the air-water interface. In these wetted conduits, air movements are induced by the interfacial shear force. Once the water velocity is established, the air velocity at the water-air interface is accordingly induced to entrain airflow. Locally positive or negative transient air pressures are accordingly generated with the pressure surge propagating through the stack and branches of the entire drainage system, as indicated in Fig. 1. In order to prevent the foul odors ingress into the habitable space through the interconnected drainage/vent network, the study of pressure surge propagation in a drainage system along with the suppression and control of such pressure surge propagation is focused on keeping the accepted trap seal. As the trap seal in the common use for a drainage system is about 50 mm, the pressure excursions within a drainage system is generally determined as + 375 Nm-2. A catastrophic failure for a

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drainage and vent system arises when the air pressure transients with a magnitude out with + 375 Nm-2 are propagating through the drainage system.

Fig. 1. Air-water two-phase flow in a typical drainage network system of a multi-storey building.

The transient propagation of air pressure at the appropriate acoustic velocity, affecting by the local interfacial structure as well as the reflection and transmission at the flow boundaries, incurs complicate two-phase phenomena to signify the characteristics of a particular drainage network. In this respect, the air-water interfacial mechanism taking place in the stack plays a crucial role in determining the transient propagation of air pressure in a drainage network. Such air-water interfacial mechanism is unsteady as the water flow is itself inherently unstable due to the random system usage. In particular, the stoppage of a moving airflow possessing a high velocity can diminish a trap seal by the water hammer effect. Therefore the propagation of positive

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or negative transient pressures, which consequently alter the interfacial structure and the airflow velocity, can possibly damage the trap seal, cause unfavorable acoustic effect and limit the maximum capacity of air-water flow in a drainage network. Due to such propagation of pressure transients in the entire drainage network, the appropriate designs for channel configurations, terminal appliances, trap seals and the associated venting devices are necessary. As described previously, the water velocity induced by gravity drives the entrained airflow via the air-water interfacial action, following the transient discharges from several branches. While the airflow causes local pressure reduction in the vertical stack by converting its pressure potential into kinetic energy, the blockage of stack by branch discharge from the highest level at the branch junction results in positive pressure transient in the dry stack above this branch. Negative transient air pressures are induced in the downstream branches and stack, as in Fig. 1. However, when air is drawn down the dry upper stack above any active discharging branches to feed the airflow, a pressure drop occurs because this drawn airflow encounters entry and frictional losses. At the end of the final bend where the intermittent water curtain is formed, the back transient pressure propagates upstream in the stack, leading to a pressure recovery between the lowest branch and the final bend as seen in Fig. 1. With the local void fraction approaching zero at the water curtain in the final bend, the downward airflow is blocked with the positive transient air pressure generated which subsequently overcomes the water blockage in an intermittent manner. As a result, the pulsate pressure waves are generated over the region forming the intermittent water curtain in the final bend. Due to the propagation of air pressure transients within the entire drainage network, the degrees of sub-atmospheric pressure in the network are locally varied following the typical pattern of pressure variation along the stack as displayed in Fig. 1. However, air pressure transients will also arise due to the sudden stoppage of airflow. Such airflow stoppages can arise due to the occlusion of the stack by a discharging branch inlet. Under these circumstances, high negative air pressures will suddenly developed below the branch inlet with the positive pressures of similar magnitude developing above [1]. This mechanism leads to sever pressure excursions (Δp) which can be determined by the Joukowsky relationship [4] as p  cVair where Vair is the air velocity destroyed and c is the acoustic air velocity at density ρ. Figure 2 depicts the typical varying manner of the sub-atmospheric pressure (Psub) above the point of stack-entry against the entrained airflow rate (Qa) caused by the falling annulus water flow in a vertical stack at fixed water flow rates (Qw) [1, 5]. As shown as Fig. 2, the greatest negative pressure at each fixed Qw emerges at the limiting condition of Qa →0. Such sub-atmospheric pressure at the limiting condition of zero air entry flow is further reduced increases as Qw increases. At each fixed Qw, the increase of Qa by increasing the entrained airflow from the stack vent causes Psub to be recovered from the zero-Qa condition toward the atmospheric level. At each fixed Qa, the increase of Qw generally increases the interfacial velocity, which increases the interfacial velocity and promotes the energy conversion in the entrained airflow from pressure potential to kinetic energy. As a result, the sub-atmospheric pressure in the stack is

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further reduced if Qw is increased at a fixed Qa. These typical data trends collected in Fig. 2 clearly illustrate how the air and water flow rates are interdependently affecting the sub-atmospheric pressure above the point of the stack-entry due to the falling water annulus in the stack.

Fig. 2. Typical variations of sub-atmospheric pressure above stack top-entry against entrained airflow rate at fixed water flow rate [1].

The general impacts of Qa and Qw on the back pressure (Pb) at the stack base where the end bend is installed are illustrated by Fig. 3. Similar to Fig. 2, each data point simulates a system load. As seen in Fig. 3 for any fixed Qw, the positive back pressure due to the blockage of water curtain at the location upstream the end bend is increased by increasing Qa. With any fixed Qa, the increase of Qw reduces the void fraction and in turn increases the interfacial air velocity to enhance the blockage effect on the positive pressure transient when sudden stoppage of the airflow occurs. As a result, Pb increases with the increase of Qw at each fixed Qa as seen in Fig. 3. The experimental measurements collected in Figs. 2 and 3 were normalized by Q w2 as an attempt to correlate Psub and Pb into functions of Qa/Qw by Swaffield and Campbell [1]. As depicted by Fig. 4 where the normalized Psub/Qw2 and Pb/Qw2 are plotted against Qa/Qw, the experimental data collected in Figs. 2 and 3 converge into the tight data bands to feature the characteristics of Psub and Pb in the vertical tack for a typical drainage system. As seen in Fig. 4, both Psub/Qw2 and Pb/Qw2 increase with the increase of Qa/Qw. While Qa is increased at a fixed Qw for a particular system load, the condition of sub-atmospheric pressure is improved but the back pressure due to the blockage of the water curtain at the stack base is getting worse. Inversely, the reduction of Qa at fixed Qw that decreases Qa/Qw causes the further reduction in the subatmospheric pressure Psub but moderates the surge of back pressure Pb. As the trap

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displacement is caused by the differential pressure between two ends of the water seal, either the decreased negative pressure transient or the increased positive pressure transient can lead to the damaged trap seal or the lost trap at extreme conditions. The transient pressures in the drainage system during the propagation of the air pressure need to be controlled in the appropriate range in order to maintain all the trap seals in the terminal appliances connecting with the drainage system.

Fig. 3. Typical back pressure (Pb) developed at upstream of water curtain at stack base [1].

Fig. 4. Typical variations of Psub/Qw2 and Pb/Qw2 against Qa/Qw [1].

Another worth noting feature in Fig. 1 is the installation of Air Admittance Valve (AAV) which excludes the need for another vertical venting stack in a drainage system. Introducing AAVs to the stack or branches in a drainage system provides alternative air paths for feeding air into the stack. As the amount of accumulated air at any point in the stack generally increases with the increase of the number of AAV-vented branches, the degree of sub-atmospheric pressure along the stack is reduced by installing AAV properly. This, in turn, greatly moderates the generation of positive pressure transients

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following an airflow blockage by adding alternative and restricted air paths to reduce the gradient of volumetric airflow along the stack. As a result, the degrees of positive and negative pressure transients at all points in the stack above the lowest vented branch are moderated by fitting negative relief AAVs to branches and the stack [1]. The amplitudes of trap-seal displacements and pressure fluctuations responding to a sudden blockage or pressure pulse in the drainage network with AAVs are reduced from the conditions with the twin-stack drainage system [1]. Relative to the condition with the twin-stack drainage system, AAV at the top entry-end of the stack as seen in Fig. 1 can also restrict the airflow into the stack. By reducing the total airflow down the upper levels of the stack, the frictional pressure drop and the suction pressures can also be reduced from those in a twin-stack drainage network. Clearly, the pressure transients and air/water velocities in each section of a drainage system are interdependent and affected by the interfacial two-phase structures in a drainage system. When the water flow rate responds to a random discharge form the terminal appliance, the corresponding changes in airflows are induced via the propagation of air pressure transients that can be locally positive or negative in the drainage system. Such transient propagation of air pressure proceeds into all the elements of a drainage network after transmission or reflection by the interfacial boundaries; such as the solid component walls, the surfaces of water traps, the water curtains falling through branch junctions and the AAV diaphragms. As the transient flows in the branches and the stack are interdependent, the pressure transients affected by the two-phase flow phenomena in each component can modify the pressure distribution along the stack in addition to the separation loss, the friction and form drags and the pressure drop through each branch junction. Therefore the air-water two-phase flow characteristics of the terminal appliances, branch junctions as well as in the inclined branch, end bend and the vertical stack are the long term research subjects. Suppression of positive and negative air pressure transients The surge of airflow pressure due to the random discharge from the terminal appliance(s) generates negative and positive pressure transients at different locations in a drainage system as a result of air pressure propagation. The negative pressure transient may induce siphonage effect to deplete the trap seals attached with the appliances and open an air path into the habitable space. At the base of the stack or the branch junction, the annular water downflow may generate the water curtain to block the airflow. With extreme condition, the water curtain at the base of the stack can completely cut off the airflow and induce the severe positive pressure transient that propagates upstream and drives the airflow through the trap seal or pushes the trap seal water into the appliance leaving the trap completely or partially depleted. These unfavorable transient effects due to the propagation of air pressure within the entire drainage network require appropriate surge suppression and control in the design stage. To suppress the negative pressure transients in a drainage network, the air admittance valve (AAV) is installed at the highest venting location of the vertical stack as seen in Fig. 1 or at the appropriate location in a drainage system. The general configuration and operation of a typical AAV is depicted by Fig. 5(a). The diaphragm in the AAV is sensitive to the sub-atmospheric pressure and free to rise when the negative

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pressure wave reaches AAV. Upon the instant that AAV is opened, the airflow entering the vertical stack through the AAV suppresses the negative pressure transient. Once the local pressure at the AAV has reached the pre-defined positive level, the AAV shuts immediately. The performance of an AAV is generally characterized by correlating the pressure drop (ΔPAAV) and the accompanying airflow rate (QAAV) through the AAV; hence acquiring its pressure loss coefficient (KAAV) as K AAV  PAAV QAAV 2 . Fig. 5(b) depicts the typical performance curve of an AAV. In general, the increase of the applied sub-atmospheric pressure to AAV increases the lifts of the diaphragm, which in turn reduces the pressure loss coefficient (KAAV) as seen in Fig. 5-b. When the applied subatmospheric pressure to AAV exceeds the limit for fully open, the pressure loss coefficient (KAAV) remains rather constant after the diaphragm becomes fully opened. Several standards [6-7] were relevant for AAV applications in order to ensure its quality for engineering applications. A high admitted airflow rate at the small pressure loss coefficient is a favorable AAV performance. Therefore the better performance zone for an AAV is indicated at the bottom right corner in Fig. 5(b). As an attempt for control and suppression of the pressure surge in a drainage system, Swaffield et al [8] simulated the propagation of air pressure transients in the drainage system by solving the St. Venant equations numerically. With the air pressure wave conveys at the speed of sound, the modified laminar forms of continuity and momentum equations for the airflow in the stack were solved using the finite difference scheme developed in [8]. Having acquired the temporal streamwise airflow velocities, local pressures transients were converted via the Joukowsky relationship [4] as p  cVair . In [8], the interfacial velocity at the air-water interface was defined as 1/ 3

Q  Vw  K w   D 

; while the positive or negative pressure reflections at the interfacial

boundaries were embodied in the airflow momentum equation via the friction coefficient which quantified the manifesting shearing drag in the airflow. Fig. 6 summarizes the simulating results of transient pressure propagation and trap seal responses with and without the control and suppression measures reported by Swaffield et al [8]. Three flow scenarios corresponding to the test conditions A, B, C shared the identical model but with different applied conditions itemized in the table of Fig. 6. The test condition A simulated a failure case where the upper termination of the drainage system was completely blocked prior to the appliance discharge through pipe 4. Due to the blockage of upper termination that prohibited airflow down pipe 7, the negative pressure transient immediately developed in pipe 7 and destroyed the trap seals on two branches, pipes 4 and 6, as seen in Fig. 6(a). In this respect, the falling water annular film causes negative pressure transient in the network for the first 1.8 seconds during which the instant pressure at the stack base reaches -120 mm water gauge. The severe pressure oscillations and the loss of trap seals are then followed at test condition A. By 1.5 seconds, the trap seals in traps 4 and 6 indicated by Fig. 6(a) were lost, hence allowing the entrained airflows into the drainage network to moderate the effect due to the blockage of upper termination. As a result, the oscillations of pressure transients and trap seal displacements depicted in Fig 6-a for test condition A were eventually damped out. Clearly, without the appropriate measures for suppression the pressure surge in a

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drainage system at test condition A, the system failure due to the loss of two trap seals was observed.

Fig. 5 (a) General configuration and operation of a typical AAV; (b) typical AAV performances (reconstructed from [8]).

The results obtained from the remedial condition B by installing an AAV at pipe 4 where the appliance discharge flows through is depicted in Fig. 6(b). As the AAV opens in response to the local suction pressure in the downstream branch, the relief airflow enters the system to suppress the negative pressure surge. Relative to the results acquired at test condition A in Fig. 6(a), negative pressure transients and trap seal displacements at test condition B are immediately damped at 1.5 seconds after opening the AAV. As a result, the trap seals on pipe 2 and 6 in Fig. 6(b) are not lost but with about -20 mm displacements due to such transient action. Residual oscillations in pressures and trap seal displacements decay slowly after the AAV is closed. The comparative results obtained from test conditions A and B demonstrate the feasibility of controlling the negative air pressure transients by installing AAV at the appropriate locations in a drainage system.

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Fig. 6 Air pressure and trap seal water levels in the single stack building drainage system following the appliance discharge at various tested conditions [8].

Fig. 6(c) depicts the trap seal displacement and the airflow rate in the drainage system with the positive pressure surge at the base of the stack responding to the test condition C for which an air pressure attenuator can be connected with the branch 9. As seen in Fig. 6(c), the positive pressure transient initiated from the stack base propagates throughout the drainage network and leads to the depletion of the trap seal at pipe 8 and a reduction of seal water at trap 4 where an airflow path is developed. Cross examining the transient airflows and trap-seal displacements developed in the drainage network,

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the open period of AAV on branch 6 has a phase leading to the stack surcharge and the diaphragm in AAV flutters to cause the high frequency oscillations on the inflow from branch 6. During the period of 4-4.55 seconds immediately followed by the positive pressure surcharge, the AAV at branch 6 is fully opened to allow the airflow into the network. An inward airflow emerges in Fig. 6(c) through the depleted trap seal on pipe 8 after the positive pressure surge, indicating the blown status of the trap seal on pipe 8. Instead of the downward airflow in the upper stack termination, the positive pressure surge from the stack base drives the upward airflow out of the network as indicated by Fig. 6(c) where the exhaust airflow from upper termination remains negative after the surcharge. Nevertheless, this vented upper termination can suppress the positive pressure surge from the stack base but cannot protect the trap seals at the lower levels of the drainage system. Justified by the surged trap-seal displacements and airflow rates at about 4 seconds in Fig. 6(c), the AAV cannot suppress the positive surge transmission. By way of installing an inflatable positive air pressure attenuator at the lower level of the stack to attenuate the positive pressure transient before it affects the lower trap seals, the airflow from upper stack is diverted into the flexible bag before it reaches the stack base. Swaffield et al [8] has demonstrated the trap seal retention for both traps on pipe 4 and 8 after connecting a positive air pressure attenuator to branch 9 for the test condition C. It is clearly demonstrated by Fig. 6 that the positive and negative pressure transients can damage or destroy the trap seals. The suppression of these undesirable pressure transients propagating within the drainage network is a formidable task due to the interdependent and complicate two-phase phenomena generated in each appliance, branch, junction and the stack of a drainage system. Although the transient pressure propagation in a drainage network plays the crucial role for implementing the control and suppression of the air pressure transients in a building drainage system, the twophase phenomena generated in each component and appliance of a drainage system also constitute the overall performance of a drainage system, which require design precautions for achieving optimal performances. In what follows, the air-water two phase phenomena in vertical, horizontal and inclined tubes, through bends, expansions and contractions as well as in tube junctions are reviewed in sequence.

Air-Water Flows through Vertical and Horizontal Tubes Two predominant forces, namely the surface tension and gravity, affect the flow pattern in a tube with multi-phase flows. By flow pattern, it is referred to as the distribution of each phase relative to the others. The surface tension keeps tube walls wet and makes small liquid drops and gas bubbles spherical. The differences in the volumetric gravitational forces between the fluids with different phases can create various interfacial patterns in horizontal, vertical and bent pipes. The pre-definition of flow pattern is often essential in order to predict the flow structures and their accompanying pressure-drop and heat transfer properties. Although the complexities of two-phase flow have prohibited standardizing the procedure for identification of twophase flow pattern, it is a general practice to specify the two-phase flow pattern using the interfacial gas and liquid velocities as the controlling parameters. In this respect, the

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flow pattern map was experimentally generated for a set of pre-defined test conditions such as the shape and diameter of the tubes and the vertical, horizontal or inclined tubes with the countercurrent or concurrent two-phase flows. In a vertical tube with air-water two-phase flow, the flow patterns generally evolve from bubbly flow → slug flow → Churn flow → annular flow as the quality is gradually increased. In a horizontal tube with air-water two-phase flow, the phases with different fluid densities are separated by gravity, which commonly causes the stratified flow with the liquid phase accumulating at the bottom of tube. As the quality is gradually increased from zero, the flow patterns in a horizontal tube generally yield from plug flow → stratified flow → wavy flow → slug flow → dispersed bubble flow → annular flow. A detailed tutorial description for the flow-pattern of non-boiling two phase flow was reported by Ghajar [9]. With application to drainage system, the annular flow in a vertical tube and the stratified or wavy flows in a horizontal or slightly inclined horizontal tube are the most common two-phase flow patterns. As depicted by Fig. 1, the flow in the vertical stack of a drainage system is the downward air-water two-phase annular co-current flow. There have been many studies of vertically upward two-phase flow at the co-current or countercurrent conditions, but only few studies have examined the detailed flow structure and the entrained airflow pressure for the downward cocurrent annular twophase flow; although the downward annular cocurrent air-water flow is the predominant flow feature in the vertical stack of a drainage system. In the early study of Bergelin et al. [10], the waves of annular liquid film in a vertical tube with downward cocurrent gas liquid flow was treated as the surface roughness for the airflow, which increased the pressure drop through the tube due to the increased form drag. Consequently, the wave height to tube diameter ratio of the annular water film was considered as an important dimensionless parameter that affected the pressure drop characteristics. With research focus on the pressure drop or the skin friction coefficients for the vertical tube with downward cocurrent air-water flow, Chien and Ibele [11] measured pressure drop and mean film thickness for both the annular and annular-mist flow regimes with liquid (ReL) and gas (ReG) Reynolds number ranges of 1250-22000 and 28000-350000 respectively. For the annular flow regime, the skin friction coefficient (f) is correlated as f  0.92 107 Re G0.582 Re L0.705

(1)

where f   i 0.5G U G 2 , Re G  GU G D G , Re L   LU L D  L and the velocities are

 P  D  2  G g  in  L  4

superficial values. The interfacial shear stress (τi) is evaluated as 

which P is the pressured drop over a tube length L and δ is the mean water film thickness. The superficial gas (UG) and liquid (UL) velocities are respectively evaluated as QG D 2 4 and QL D 2 4 , where QG and QL are the volume flow rates of gas and liquid; and D is the tube diameter. As an attempt to examine the effect of tube diameter on f, Hajiloo et al [12] measured the pressure drop for downward cocurrent annular air-water flow, with water and air flow Reynolds numbers in the ranges 510027200 and 3400-21600, respectively. To determine the interfacial shear stress (τi), the mean film thickness (δ) was obtained from the correlation of Henstock and Hanratty

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[13]



as

 0.707 Re 0.5 L 

 D



6.59F

where

1  1400F 0.5

  0.0379Re 

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0.4 0.9 2.5 

2.5

L



F   (L G )( L G )0.5 ReG 0.9

and

γ

=

in which the kinetic liquid and gas viscosities are

defined as  L   L  L ,G  G G . Fig. 7 depicts the f results collected in [12]. After combining the f data reported by various research groups [10-12] to extend the parametric range, there is the characteristic S-shaped variation of f with ReG as seen in Fig. 7. At the lower ends of ReG and ReL in Fig. 7, f decreases with ReG and approaches toward the smooth wall single-phase behavior as ReL → 0. With the higher ReG and ReL, f increases rapidly with ReG, primarily due to the form drag induced by the water wave. For each ReL controlled data trend in Fig. 7, a maximum of friction factor (f) can be reached with a subsequent gradual decrease by way of increasing ReG. Such f maximum is attributed to the on-set of liquid entrainment by Chen and Ibele [11]. In general, f increases with ReG and ReL, which also increases as the tube diameter (D) is reduced.

Fig. 7 Variations of skin friction coefficient (f) against ReG at predefined ReL for cocurrent airwater downward flow in vertical tubes [12].

Based on the experimental data obtained by Hajiloo et al [12], the empirical f equation which correlated well all the f results depicted by Fig. 7 was reported as

f f s  125.2mG where f s  0.046 Re G defined as

0.2

1.51

Re G

1.05

(2)

and the dimensionless film thickness (mG) in equation (2) is

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mG  0.19Re L

0.7

Chang and Lo

L  L  i    G   G  c 

0.5

The characteristics shear stress (τc) in equation 3 is defined as

(3)

2 1  w   i , where the 3 3

shear stress at wall (τw) is evaluated as

w  

2 2 P D D   D  2   D  D  2    L g 1     g     G L 4 4   D   4 D 

(4)

The cocurrent gas-liquid flow in horizontal and slightly inclined pipes is another dominant flow feature in a drainage system. Unlike the single-phase pipe flow, a small departure from horizontal geometry can considerably affect the characteristics of the two-phase flow. Generally, the hydrostatic component of pressure drop cannot be recovered in the uphill and downhill inclined horizontal pipes with two-phase flow. For the two-phase flow in a horizontal pipe, the interfacial segregation is caused by gravity with the liquid to flow preferentially along the bottom portion of the tube. In general, the following flow regimes in a horizontal pipe with two-phase flow are identified: bubbly flow, plug flow, stratified flow with smooth or wavy interface, slug flow, pseudo-slug flow and annular flow. As the airflow in a drainage system is entrained rather than supplied, the stratified flow with smooth or wavy interface is the most common two-phase pattern in the horizontal or the slightly inclined pipes for a drainage system. With stratified flow, the liquid flows along the bottom portion of the horizontal pipe. At low superficial gas and liquid velocities, the smooth gas-liquid interfacial surface is remained. The pressure drop for this two-phase flow regime is small. By increasing the gas velocity, the interfacial smooth surface transits into continuous waves. Further increase of the gas velocity generates liquid droplets which are torn from the surface wave, causing liquid entrainment in the gas. When the liquid flow pattern has the appearance of slug form, the pseudo-slug flow emerges. Although the liquid in pseudo-slug flow can occasionally touch the top of the tube, but the liquid flow does not block the entire cross-section of the pipe. For the various two-phase flow regimes, the pressure drop and the hold-up criteria are the two most predominant factors for engineering applications. A number of correlations and models that determine the pressure drop and/or hold-up for gas-liquid two-phase flows in the horizontal pipelines have been developed [13-21]. Tribbe and Müller-Sreinhagen [18] have reviewed a large number of these pressure-drop models with their performances examined and compared. For the co-current air-water flow in the horizontal or inclined tubes, the pressure drop data, as typified by Fig. 8, exhibit the similar trend for each tube but with increasing pressure drop as the superficial liquid velocity increases. For the stratified smooth flow with low gas velocity (VG), the pressure drops fall away towards the open channel solutions. Further increase of gas velocity to the condition where the flow transits from Annular Roll (AR) wave to Annular Droplet (AD) flow, the slope of each

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VL controlled data trend in Fig. 8-a for the horizontal tube is increased. Such increased pressure drop at the AR-to-AD transit is caused by the increased energy conversion from pressure potential to form the liquid droplets. For the flow in the tube with uphill inclination of 5, the pattern of pressure-drop variation against VG as seen in Fig. 8(b) is further complicated. As VL increases at each fixed VG, the pressure drop in Fig. 8(b) generally increases. However, at the test conditions of VL=0.0176 ms-1 with inclination of 2.75 and VL=0.0247 and 0.0411 ms-1 with inclination of 5, the pressure drops decrease with increasing VG until at about VG=10 ms-1. With VG>10 ms-1, the pressure drop data obtained at different VL in Fig. 8(b) increase with the increase of VG. The general data trend for the pressure drop with increasing VG in an uphill inclined tube is the initial high pressure drop followed by a decline to a minimum value after which the pressure drop yields to be linearly increased as VG increases. The pressure-drop versus VG for the tube with downhill inclination of 5 is depicted by Fig. 8(c). For the stratified flow regime with low VG, the pressure drops are not considerably affected by changing VG. With VG>10 ms-1, the pressure drop at each fixed VSL in Fig. 8(b) increases linearly with the increase of VG. Clearly, the tube inclination has profound influences on the pressure drop performances for co-current horizontal air-water flow. Cross examination of the pressure data collected in Figs. 8(a), (b) and(c) indicates that the lowest and highest pressure drops can develop in the horizontal or inclined tubes, depending on the operating range of VG.

Fig. 8 Typical pressure drop against superficial gas velocity in (a) horizontal (b) uphill inclined (c) downhill inclined tubes with co-current air-water flow [19].

By considering the pressure drop of a stratified air-water flow in a horizontal tube due to the flow resistances from tube wall and gas-liquid interface, the empirical method permitting the evaluation of pressured drop coefficient has been proposed by Spedding and Hand [20] based on the one-dimensional momentum balances over each phase. Following the definitions of geometrical parameters and shear stresses in Fig. 9 for a stratified gas-liquid flow, the accountancy of one-dimensional momentum balance

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across each phase give rise the force balance equations for liquid and gas phases as equations 5 and 6:

 i .Si  AL (dP dX ) L   WL.S L   L AL g sin

(Liquid phase)

 i .Si  AG (dP dX )G   WG .SG  G AG g sin (Gas phase)

(5)

(6)

where dP dx is the streamwise pressure gradient and sG  h   cos 1  2 L  1 D  D 

Si  h   1   2 L  1 D  D 

2

SL  h     cos1  2 L  1 D  D 

AC D

2

(7)

2   h   h   h   0.25 cos 1  2 L  1   2 L  1 1   2 L  1    D   D   D    

2  AL hL   hL   hL   1    0 . 25   cos 2  1  2  1 1  2  1       D2   D   D   D   

(8)

(9)

(10)

(11)

The controlling flow parameters used by Spedding and Hand [20] in their model are defined as: VL,G 

U L,G R L,G

(12)

ReL 

 L D L VL L

(13)

ReG 

 G D G VG G

(14)

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where DL 

4A L SL

(15)

DG 

4A G S G  Si

(16)

The shear stresses in equations 5 and 6 are defined as:

 i  f i G

VG  VL 2

(17)

2

 W G  fG

ρ G VG 2

WL  f L

ρ G VG 2

2

(18)

2

(19)

Fig. 9 Shearing forces acting on smooth stratified gas-liquid flow in tube [20].

In equations 6 and 18, fG can be accurately predicted by the Blasius equation; while the friction coefficients fL is evaluated by equations 20 and 21 with the suffix S standing for the superficial values.

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f L  24 Re L

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1

f L  0.0262( RL Re SL )0.139

(ReL < 2100)

(20)

(ReL > 2100)

(21)

where ReL, ReSL, RL are the liquid Reynolds number, superficial liquid Reynolds number and liquid hold-up respectively. The liquid hold-up (RL) can be accurately calculated using the following equations [21].

RL  (0.205Ku 0.12  0.06Ku 1.6 )  X (0.87log Ku 0.725)

(22)

In equation 22, Ku and X are the Kutadelaze number and Lockhart-Martinelli parameter, which are respectively defined as:



Ku  U L ρ L σg ρ L  ρ G 0.25

 dP  X    dx SL



1

 dP     dx SG

(23)

(24)

dP dP in which   and   are the streamwise liquid-phase and gas-phase pressure  dx SL

 dx SG

gradients evaluated from the superficial values; while is the surface tension. Nevertheless, the gas hold-up (RG) and liquid hold-up (RL) are approximated in [20] as: (25)

The interfacial friction factor ( fi) is calculated as:    UL  U    7.8035 f i  f SG 1.76 G   2.7847 log10   6   UL  6   

(26)

In order to determine fG, fL and fi, the liquid and gas flow rates, the fluid properties and the pipe diameter are pre-defined as the boundary conditions; along with a initial guess value of hL/D in the range of 0< hL/D <1. Based on the initial assumption of hL/D, the geometrical parameters, namely AG, AL, SG, Si, SL as labeled in Fig. 9, are determined using equations 7-11. The phase Reynolds numbers, ReL and ReG, are

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accordingly defined through equations 12-16 so that the laminar-laminar or turbulentturbulent air-water flow conditions can be revealed. With ReL lesser or larger than 2100, fL is calculated using equations 20 and 21 respectively. To calculate fG, equations 27 and 28 are respectively used.

fG,SG  16 ReG,SG 1

(ReL < 2100)

(27)

fG ,SG  0.046 ReG ,SG 0.2

(ReL > 2100)

(28)

The interfacial friction factor ( fi) is then determined using equation 26. Having obtained fG, fL and fi for the pre-assumed film thickness (hL/D), the shear stresses τWG, τWL and τi are defined using equations 17-19. By substituting τWG, τWL and τi into equations 5 and 6, the calculated pressure drops (dP/dx)SL and (dP/dx) SG are acquired and compared with the experimental measurements in order to verify the assumer hL/D. The aforementioned iteration scheme is repeated until the pre-defined convergence criterion is satisfied and the film thickness hL/D can be determined. In addition to the aforementioned complex two-phase flow features for the airwater flow in a horizontal pipe, the transient flow phenomena resulting from the random discharge of an appliance in a drainage system and the presence of interfacial surface waves introduce the additional difficulties for engineering applications. As described previously, the interfacial wavy surface has caused a noticeable increase in the pressure drop due to the increased interfacial form drag. The type of waves in such a horizontal or inclined channel with air-water two-phase flow is mainly controlled by the superficial gas velocity. As the superficial gas velocity increases at constant superficial liquid velocity, the following transition of wavy pattern is observed [22]: smooth→ two dimensional or three dimensional wave → three dimensional to solitary wave → solitary wave → atomization wave. For such two-phase flow configuration, Bertola [23] measured the local time-averaged void fraction and the cross-sectional averaged void fraction for air-water flow in a horizontal tube with and without sudden area contraction. Without the abrupt area contraction at the entry of a horizontal tube, the distribution of local void fraction (α) along the vertically diametrical axis of the tube follows the hyperbolic profile and increases as the gas fraction of volume flow (Q G*) increases; as typified by Fig. 10 [22]. The phase segregation by gravity has caused the maximum void fraction at location of dver = 0 as seen in Fig. 10. As dver increases in the downward direction, α is monotonically decreased until reaching the wet region that is fully occupied by liquid. Based on the experimental results reported in [22], α correlation for the air-water flow in a horizontal tube without the abrupt entrance effect is derived as equation 29. α

  d 0.472  0.55Q G *      1  tanh 5.077  1.53 ln Q G *   2  ver  0.572QG * 0.254  1  2       D 

(29)

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Fig. 10 Typical variations of time-averaged void fraction (α) along the vertically diametrical axis of a horizontal tube at fixed gas fraction of volume flow (QG*).

Air-Water Flows through Curved Tube and T-Junction When flow through a curved channel, the centrifugal force is induced as an additional body force to affect the flow structure. The flow mechanism in association with the centrifugal force for the air-water flow through a small-diameter curved tube at the water trap or through the vertical to horizontal elbow with a large diameter at the bottom of the vertical stack can modify the interfacial structures. In this respect, Kirpalani et al [22] reported the flow regime maps and the flow morphology for airwater flows through the 1 and 3 mm diameter tubes connected by a single curved “C” tube and the serpentine tubes. The Eotvos numbers (Eo) for their 1 and 3 mm diameter test tubes were 0.134 and 1.2 respectively [22]. With Eo<<1, the surface forces strongly affect the flow patterns developed in the 1 mm tube; while the dominant effects on twophase flow phenomena at Eo ~ 1 are caused by viscous and inertial forces [22]. The flow patterns and flow regime map observed by Kirpalani et al [22] for their straight test tubes of 3 mm diameter with Eo ~ 1 agreed favorably with the results reported by Taitel and Dukler [23] for pipes with the larger diameters. When the inertial forces and viscous forces become dominant, the liquid-phase tends to move towards the tube wall and agitates the onset of intermittent flow that enhances the phase interaction. The transition of flow patterns from annular to intermittent flows becomes increasingly prominent in the tubes connected by the single or multiple “C” curved tubes. When the large gas bubbles or slugs travel through the bends, these large air bubbles tend to break-up forming the disperse bubbles. Such break-up of large air bubbles through the curved tube is more predominant in the serpentine channels. The process showing the break-up of the large air bubble through the C-curved bend in a serpentine passage is clearly seen in Fig. 11 by the successive Frames (Frames 1→2→3). This result enlightens the distortion of the gas-liquid interface which raises the twist in the bend to

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generate strong secondary flows which cause significant stretching and eventual breakup of the large bubbles. Such break-up of gas bubbles can occur at lower gas velocities if the liquid velocities are higher, indicating a critical ratio of inertial forces between the gas and the liquid for initiating the bubble breakup for a set of specified curved geometries.

Fig. 11 Instant flow images showing break-up of large gas bubbles due to secondary vortices in bend of a serpentine channel [22].

The air-water flow through the bottom of the stack from the vertical down pipe to horizontal bend generally takes the form of annular flow in the vertical pipe and transits to the stratified- smooth or wavy flow in the horizontal pipe after flowing through the bend. Previous studies which investigated two-phase flow in curved pipe or bend with emphasis on drainage applications were very rare. It is not clear as to the transition of flow regimes and pressure-drops, while the temporal and spatial variations in air pressure from the vertical-down to horizontal pipes through an elbow bend which must be of significance for drainage applications requires elucidation. As summarized by Spedding and Benard [24], the early works on two phase flow in curved pipes have largely been confined to the horizontal plane and have taken little interest in the actual flow regimes present. In particular, previous works focused on the effect of bend orientation, such as the horizontal bend, the horizontal to vertical up bend and the vertical down to horizontal bend, on flow phenomena has often given contrary results [24]. Peshkin [25] reported that the two-phase flow in bend with horizontal to vertical down flow had about 10% more bend pressure drop than the corresponding horizontal to vertical up flow case. As the uplift or the downward forces in the inlet vertical tangent leg of an elbow bend is absent in its outlet horizontal tangent leg for the vertical to horizontal orientation; and gravity acts in different directions on the flows in the inlet and outlet tangent legs, the gas-liquid two phase flows in the inlet and outlet tangent legs of a vertical to horizontal elbow bend are different. Often the flow regimes and other flow phenomena are dramatically different between the two tangents. In general, the total bend pressure drop for a two phase flow through a vertical to horizontal bend is composed of the bend pressure loss from the inlet and outlet tangent legs and the pressure drop along the centre line of the bend length. In [26], Spedding et al. reported that the slight interfacial disturbances across the near vertical pipe generally led to an increase of pressure drop over that observed for the corresponding straight vertical pipe

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due to increased liquid holdup. Therefore, the interfacial disturbances caused by the elbow bend could affect the two phase flow in the vertical tangent leg by instituting some measure of choking and increased pressure loss [24]. In the vertical tangent leg of a vertical-to-horizontal elbow bend, the flow patterns passed successively from slug to churn to semi-annular and then annular flow as the gas rate increased for a set of liquid flow rates. Differences in pressured drops between two vertical pipes with and without the inclusion of an elbow bend are gradually developed as the liquid velocity increases. But for the flow regions where the pressure drop in the vertical pipe is larger with the inclusion of the elbow bend, the flow regimes between the two vertical pipes with and without the elbow bend exhibit subtle differences. In this respect, the slugs tend to be of shorter length in the vertical pipe with the elbow bend resulting in a narrower but increased frequency of pressure fluctuations. Liquid holdup is also higher in the vertical pipe with the elbow bend which, particularly at the higher liquid rates, elevates the pressure drop in the vertical pipe with the elbow bend from that obtained with the straight vertical pipe. Nevertheless, the effect of uplift in the vertical tangent leg of the vertical-to-horizontal elbow bend is less noticeable and its frictional loss is virtually similar to that of the straight vertical pipe [26]. Therefore, as described previously, the effect of a vertical to horizontal elbow bend on the pressure drop in the vertical tangent leg is similar to that noted by Spedding et al. [26] for the case when the pipe was slightly off the vertical. In a slightly inclined vertical pipe, the anisotropy of the liquid flow causes an increase in both liquid holdup and pressure drop over the similar vertical pipe. The elbow bend causes an increase in the absolute pressure within its inlet vertical tangent leg due to the choked flow by the elbow bend [24]. For the horizontal outlet tangent leg of a vertical 900 elbow bend, the pressure drop performance agrees favorably with the data obtained from the horizontal pipes with gas-liquid two phase flows. Typical variations of the total elbow bend pressure drop against superficial gas velocity (UG) are exemplified by Fig. 12 [24]. At low superficial liquid velocities (UL), the elbow bend pressure drop passes through a minimum from negative to positive values as UG increases. By way of increasing UL and/or UG, the pressure drop increases consistently. There is different varying pattern of the pressure drop against UG that depends on whether UL is lower or higher than the free bubble rising velocity in the inlet vertical tangent leg. As seen in Fig. 12, the elbow bend pressure drop is negative at the lower UL (and gas flow rates); while at the highest UL (and gas flow rate) the pressure drop commences to level off. These particular data trends for total elbow bend pressure drop against UG revealed by Fig. 12 are attributed to the different flow regimes present in the two tangent legs of the elbow bend. The negative elbow bend pressure drop region at the lower UL and UG is developed when the slug regime in the inlet vertical tangent passes smoothly through the elbow bend and generates the smooth stratified regime in the outlet horizontal tangent leg. At high UL and UG, the flow regime in the outlet horizontal tangent leg transits successively into the stratified plus roll wave flow with the stratified blow through slug so that the negative pressure drop region is bypassed as there is no longer a smooth regime transition within the elbow bend [24]. The total elbow bend pressure drop becomes leveling off when the flow regime in the inlet vertical tangent leg passes from churn to semi-annular flow. When

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UL in the inlet vertical tangent leg exceeds Taylor bubble rise velocity at low gas rates, the slug or blow through slug flow regimes are initially developed in the outlet tangent leg and the varying manner of the total elbow bend pressure against UG becomes rather flat. However, when the flow regime changes to stratified roll wave in the outlet horizontal tangent leg of the elbow bend due to the increase of UG, the total elbow bend pressure starts to rise. In such flow regime, the elbow bend acts as a droplet generator causing the pressure drop to increase rapidly [24].

Fig. 12 Variations of total elbow pressure drop against UG for various UL [24].

Gas-liquid flows in tube junctions, either on horizontal or horizontal-to-vertical plan, are common features in pipe lines for chemical, power, oil/gas production, oil refining plants and drainage systems. While research emphasis vary with practical applications, the research works focused on the transient air-flow pressure for air-water flows through tube junctions with applications to drainage system are not well documented. Nevertheless, relevant research works have shown that the misdistribution of the phases occurs when the gas-liquid flow passes through a T-junction. The liquid and gas flows are not equally distributed at all terminal points on branched pipelines of a T-junction. As a result, the phase split at T-junction is used for industrial plant. In this respect, a large number of studies for phase split have been comprehensively reviewed by Azzopardi [27]. The flow pattern has profound influences on phase split at Tjunctions and the diversion of fluids depends on their local momentum fluxes [28]. In general, the liquid film and gas-flow have less momentum than the liquid droplets. As a result, the liquid droplets are carried on past the junction. Therefore the information about the film flow variations is essential for modeling the phase split through a Tjunction. The counterbalancing condition between the gravity and the dynamic forces arising from the secondary flow in the gas phase, the pumping action in the disturbance waves and the entrainment/deposition determines the liquid film at the top of the pipe. For larger pipes, the liquid film is generally less symmetric with a stratified layer at the bottom and a thin film around the top; which has been referred to as the as semi-annular

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flow. Conte and Azzopardi [29] experimentally studied the division of gas-liquid flow at a 127 mm diameter T-junction on the horizontal plan. The misdistribution of the phase was quantified as semi-annular flow; and the film thickness variations about the circumference of the inlet and outlet pipes as well as the liquid depth profiles within the junction were measured [29]. Fig. 13 typifies the phase split at T-junction by plotting the split as fraction of incoming liquid emerging through the side outlet of the Tjunction, which is referred to the fraction of liquid taken off, against the fraction of gas taken off. As indicated by Fig. 13, the gas taken off is predominant for such phase split through a T-junction. Even with the gas taken off above than 80%, the liquid taken off is less than 20%. The data obtained at the fixed interfacial liquid velocity but with different interfacial gas velocity tend to merge into a converged data trend; while the increase of interfacial liquid velocity reduces the fraction of liquid taken off.

Fig. 13 Phase split at 127 mm diameter horizontal T-junction [29].

Variations of the film-thickness to pipe-diameter ratio at inlet, side-outlet and runoutlet about the horizontal T-junction [29] at different fractions of liquid and gas taken off are respectively shown in Figs. 14 (a), (b) and (c). At each particular phase split, the circumferential profiles of film thickness at inlet, side-outlet and run-outlet about the horizontal T-junction follow their characteristic patterns exemplified by Fig. 14. At the inlet upstream of the T-junction, the film thickness increases noticeably in the angular range of 1200-2400 at the bottom portion of the pipe and distributes quite symmetrically. The distribution of film thickness at the upstream inlet is insensible to the variation of fraction of gas or liquid taken off. Therefore the phase split at the T-junction cannot significantly affect the film distribution upstream the horizontal T-junction. At the side outlet as seen in Fig. 14 (b), the liquid film impinges onto the downstream corner of the junction and subsequently climbs along the pipe wall to surge a peak of thick liquid film between 1000 and 1500. At the downstream corner of the T-junction, part of liquid film in the side pipe flows as a thick rivulet, resulting in another film peak between 2000 and 2500, and moves toward the bottom of the side outlet pipe. The secondary film peak

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between 2000 and 2500 is generated by the opposing forces between gravity and the momentum of the liquid entering the side pipe in the circumferential direction. Consequently, the location of this secondary peak is closer to the pipe bottom when the fraction of liquid taken off increases as seen in Fig. 14 (b). When the liquid taken off is increased, the action of gravity to drain the larger volume of liquid on the wall of the downstream corner is stronger and the film-peak moves closer to the bottom of the side outlet pipe. Depending on the momentum of the liquid taken off, the remaining liquid film can climb up the wall of side pipe against gravity. With high liquid flow rates or large take off of liquid, the liquid film can flow around the entire circumference of the side outlet pipe. This up-surging film along the circumferential of the side pipe wall joins the liquid diverted at the upstream corner of the T-junction to form a ridge of liquid peak at the location between 1000 and 1500 from which the liquid droplets are entrained in the gas stream. As a result, there are two areas of locally thicker film in the side outlet pipe as seen in Fig. 14 (b). The variation of gas or liquid fractional taken off therefore provides noticeable influences on the film thickness on the side outlet pipe. In the section of the pipe circumference between 2000 and 2500, the liquid film is thickened as the diverted fractional taken off increases. At the bottom of the side pipe near the center of 1800, the film thickness is thinner. For the run outlet, the distribution of film thickness depicted by Fig. 14 (c) shows a small amount of asymmetry due to the pulling action from the side outlet pipe. At the bottom of the run outlet, the film thickness decreases as the diverted fraction of liquid or gas increases. Away from the bottom center of the run outlet, the varying trend of film thickness against the diverted fraction gradually yields and reverses toward the opposite downstream corner in the run outlet pipe. There is a distinct trend of liquid thickening with diverted fraction at the angular spans of 2500-3600 and 00-1000. As compared in Fig. 14 (c), the data bands driven by varying the diverted fraction at the downstream corner of the run outlet pipe between 2500 and 3600 are larger than those at the upstream corner connecting the side outlet pipe. Such difference is due to the turning of the film towards the side outlet pipe which occurs at the T-junction. For this reason, when the diverted fraction increases so that the liquid enters the run outlet pipe is lesser, the film climbing up the wall becomes thicker as the lateral velocity component of the film is of larger magnitude [29]. In the follow-up work of this research group that investigated the phase split occurring at a small diameter vertical T-junction [30], it was experimentally confirmed that the orientation of the junction had negligible influence on the phase split through comparisons with the results obtained from the horizontal T-junctions. Such similarity was attributed to the absence of flooding. Nevertheless, as indicated in Fig. 1, the air-water flow at a T-junction connecting with the main stack is directed from the horizontal or slightly inclined branch with the smaller diameter toward the vertical stack. Due to the variation in pipe diameters and the turning motion of bulk air-water flow dragged by gravity at the T-junction, the phase split as well as the interfacial structures is expected to be modified from the results reported in [27-30]. However, the insufficient research works reporting the flow structures and the two-phase mechanism at such T-junction connecting with the stack of a drainage system prevents the detailed review.

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Fig. 14 Circumferential distributions of dimensionless film thickness about horizontal T-junction at (a) inlet (b) side outlet (c) run outlet for various fractions of gas and liquid taken off. (Superficial gas and liquid velocities = 24.5 ms-1 and 0.28 ms-1 respectively) Reproduced from [29]

Numerical Analysis of Air-Water Flow in Multi-Joint Vessel In previous sections, the two phase flow phenomena encountered by the fundamental assemblies in a drainage system are briefly described. In order to comply with the various national and international standards specified for the drainage system, various research works are motivated with their particular aims at revealing the characteristics of a drainage system as well as for optimizing the performance of subassemblies in a drainage system. A variety of innovative drainage components is accordingly devised with their performances examined. In this respect, China has regulated that the water trap needs to be retained after a confluent vessel. The two-phase air-water flow for such confluent vessel with multi joints raises another research challenge and enlightens the opportunities to gain more scientific insights of complex two-phase flow phenomena. The following numerical study is motivated by the need to provide the fundamental understanding of the air-water flow structures in a confluent unit connected with multiple joints with different pipe diameters. The numerical method employed can be extended to attack the flow problems encountered by a drainage system for which the transient air pressure remains as a primary design concern. The interaction of the air-water flow in a drainage system is discussed in this section. Fig. 15 illustrates the geometry of the computational domain and the detailed parameters of a drainage system. To design an innovative drainage component, the parametric optimization plays a major role in determining the capacity of a drainage system. Due to the need to design a confluent unit for keeping the water seal that

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prohibits the odour spreading between spaces, the confluent vessel with multiple joints, showed by Fig. 15, is devised. For the present numerical analysis, the initial condition of the three inlets for this confluent vessel is assumed to have a constant volumetric water flow rate in a horizontal tube. The total computational domain is restricted within the multi-joint confluent vessel. The void air pressure in the confluent vessel is assumed at 1 atm (Pa= 1.013 105 N/m2). Simulations are conducted under the different conditions, as denoted by the Test Cases in Table 1. The flow calculation for an initial free-surface height of h0  d1 / 2  2.5 cm is performed using a total of 1,213,132 grid points for the case 1 (Qi=600 cm3s-1) and case 2 (Qi=900 cm3s-1) and case 3 (Qi=1200 cm3s-1), respectively. Table 1 Numerical test conditions for the confluent unit. Case 1:

Case 2:

Case 3:

Total volumetric water flow rate

Qi=600(cm s )

Qi=900(cm s )

Qi=1200(cm3s-1)

Number of inlet

3

3

3

Volumetric water flow rate of each inlet

3 -1

3 -1

200(cm s )

3 -1

3 -1

400(cm3s-1)

300(cm s )

d1 h3

h2 dd

h1

d2

d1=5, d2=7, h1=10.5, h2=22.95, h3=29, b1=10.5, b2=13.6, dd=0.45 (dimension: cm). b1

b2 Fig. 15 Geometrical details of the confluent unit with multiple joints.

To reveal the flow patterns associated with a constant volumetric water flow rate, the instantaneous velocity magnitude and vectors at different time lapses for the case 3 are shown in Fig. 16.

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(a) t = 2 s

(b) t = 3 s

(c) t = 4 s

(d) t = 5 s

(e) t = 10 s

(f) t = 20 s

Fig. 16 Velocity magnitude and vectors at the plane of y=0 (Case 3).

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The flow streams entering the confluent plenum gradually evolve into several clockwise and counterclockwise vortices within the main vessel. Notably, the strengths and dimensions of the primary vortices developed in the confluent plenum at the test condition case 3 of the higher entering flow rate are more stronger than those obtained at the test conditions of cases 1 and 2. It is clearly demonstrated by Fig. 16 that the gravity affects the flow pattern in a multi-joint drainage system even with the air-water two-phase complexities. The hydraulic jump was found in the upstream of the outlet for all the cases examined in the periodic manner. For the present confluent device, the maximum height of the hydraulic jump in the outlet pipe increases as the flow rate from each inlet pipe increases. At the case 3 test condition, the temporal evolution of the instantaneous water velocity magnitudes and vectors at the plane of x=0 is depicted in Fig. 17. The combined effects of gravitational, inertial and viscous forces affect the flow structures in the confluent vessel. As shown in Fig. 17. The large air bubbles tend to break-up forming the disperse bubbles in the confluent vessel. Such bubble break-up becomes a way to allow the transportation of entrained air from the inlet pipes into the exhaust pipe through the water seal developed in the confluent unit. Once again, the transportation process for the air-water two phase flow is a temporal process and highly unsteady. The water surge in the exhaust pipe, as seen Fig. 16(e), has the upstream effect that affects the two-phase flow structures in the vertical confluent plenum, which certainly limits the maximum flow capacity through this confluent unit. Figures 18 (a)-(c) shows the temporal variations of the water depth upstream and downstream the outlet of the vertical confluent plenum at each tested Qi at 600, 900 and 1200 cm3s-1, respectively. At each tested Qi, the water depth at the upstream of the exhaust pipe is higher than its downstream level. Fig. 18(a) shows that, at the upstream and downstream locations of the exhaust pipe, the water depths oscillate about two different mean levels corresponding to the upstream and downstream locations. This oscillatory behavior indicates that the air-water two-phase flow for such a confluent unit with multiple joints is predominant by the unsteady flow features. The pressure difference between the upstream and downstream sectional planes determines the flow velocity through the exhaust pipe and therefore the volume flow rate through the confluent unit. For the case with the water volumetric flow rate at 900 cm3s-1, the results presented in Fig. 18(b) indicate that the water depth tends to oscillate between 2.5 cm and 5 cm as the flow travels in the downstream direction. In view of the temporal water depth variation, it is interesting to note that the quasi-steady state appears at the upstream location after several time intervals. For the case with the higher water volumetric flow rate at 1200 cm3s-1, Fig. 18(c) indicates that the temporal variation of the water depth is the function of the streamwise location with the values of 7.1 cm and 20 cm at the upstream and downstream locations, respectively. At the downstream location, the water surface is undulating with a jump at time of approximately 14.5 second. Furthermore, it is seen that the water depth has a constant distributing pattern during an interval of approximately 15 to 20 seconds. Comparing the Figs. 18(a, b, c), it is evident that the water depth is dominated by the water volumetric low rate.

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(a) t = 2 s

(c) t = 4 s

(b) t = 3 s

(d) t = 5 s

(e) t = 10 s

Fig. 17 Velocity magnitude and vectors at the plane of x=0 (Case 3).

(f) t = 20 s

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10

10 Upstream (x=7.1 cm) Downstream (x=20 cm)

Upstream (x=7.1 cm) Downstream (x=20 cm)

8

8

6

6

Fluid depth (cm)

Fluid depth (cm)

4

4

2

2

0

0 0

4

8

12

16

20

0

4

8

t (s)

(a)

t (s)

12

16

(b)

10 Upstream (x=7.1 cm) Downstream (x=20 cm) 8

6 Fluid depth (cm)

4

2

0 0

4

8

12

16

20

t (s)

(c) Fig. 18 Temporal variations of water depth at upstream and downstream locations of the exhaust pipe with (a) Qi  600 cm3 / s (b) Qi  900 cm3 / s (c) Qi  1200 cm3 / s .

Figures 19(a), (b), (c) illustrate the temporal variation of the Froude number at the upstream and downstream locations of the exhaust pipe with the water volumetric flow rates of Qi=600 cm3s-1, 900 cm3s-1 and 1200 cm3s-1, respectively. Comparing the three plots, it is evident that the Froude number at the upstream region is less than that at the downstream region. The three figures show that the sharp fluctuations in the Froude number variations manifest the varying patterns during the initial elapsed simulation

20

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time of approximately 1 to 4 seconds. At Qi=1200 cm3s-1, this type of sharp jump is characterized by an instability with the high flow velocity flow in the water surge which oscillates in a random manner between the bottom pipe wall and the air-water interface. These oscillations introduce large surface waves that travel a considerable downstream distance. 2.5

4

2

Upstream (x=7.1 cm) Downstream (x=20 cm)

Upstream (x=7.1 cm) Downstream (x=20 cm)

3

1.5 Fr

Fr 2

1

1

0.5

0

0 0

4

8

12

16

0

20

4

8

12

16

t (s)

t (s)

(a)

(b)

6

Upstream (x=7.1 cm) Downstream (x=20 cm)

4

Fr

2

0 0

4

8

12

16

20

t (s)

(c) Fig. 19 Temporal variation of Froude number at upstream and downstream locations of the exhaust pipe at (a) Qi  600 cm3 / s (b) Qi  900 cm3 / s (c) Qi  1200 cm3 / s .

20

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When the air-water stream flows through the confluent unit with multiple joints, the air/water pressure transients are interdependent and affected by the two-phase flow phenomena in each component. Fig. 20 shows the cross-sectional view of the confluent vessel in which the randomly selected nine locations showing the temporal pressure variations are indicated. Figs. 21 and 22 illustrate the temporal pressure variations at these nine selected locations. The flow agitation by the dispersed air bubbles induces the considerable water pressure oscillations at nine locations selected. The differential phase shifts and the magnitudes for these oscillatory pressures between the nine plots indicate that the unsteadiness of the pressure field is sensitive to the location. Through this numerical analysis, the air-water two-phase flow for the confluent unit with an exhaust pipe appears to be highly unsteady. Nevertheless, the present numerical analysis, involving the turbulence accountancy for the air and water flows, has demonstrated the applicability of numerical treatment using air bubble model to attack this type of problem.

Fig. 20 Cross-sectional view showing the nine locations where the temporal pressure variations are presented.

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1.02

1.024

P4(4,0,10.5) Qi=1200 cm3/s

P1(0,0,10.5) Qi=1200 cm3/s Qi=900 cm3/s

Qi=900 cm3/s Qi=600 cm3/s

1.018

Qi=600 cm3/s

1.02

1.016 P (N/m2)105

1.016 P (N/m2)105

1.014

1.012 1.012

1.01

1.008 0

4

8

12

16

0

20

4

8

12

16

20

t(s)

t(s) 1.08

1.04

P5(4,0,5) Qi=1200 cm3/s

P2(0,0,5) Qi=1200 cm3/s

Qi=900 cm3/s Qi=600 cm3/s

Qi=900 cm3/s Qi=600 cm3/s 1.03

1.06

1.02

1.04 P (N/m2)105

P (N/m2)105

1.02

1.01

1

1 0

4

8

12

16

0

20

4

8

12

16

20

t(s)

t(s) 1.06

1.2 P3(0,0,1) Qi=1200 cm3/s

P6(4,0,1) Qi=1200 cm3/s

Qi=900 cm3/s Qi=600 cm3/s

Qi=900 cm3/s Qi=600 cm3/s

1.16

1.04

1.12

P (N/m2)105

P (N/m2)105 1.08

1.02

1.04

1

1 0

4

8

12 t(s)

16

20

0

4

8

12

16

20

t(s)

Fig. 21 Temporal pressure variations at nine selected locations on the sectional plane of the confluent vessel.

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1.03 P7(6,0,10.5) Qi=1200 cm3/s Qi=900 cm3/s Qi=600 cm3/s

1.02

P (N/m2)105 1.01

1 0

4

8

12

16

20

t(s)

1.1

1.1

P8(6,0,5) Qi=1200 cm3/s

P9(6,0,1) Qi=1200 cm3/s

Qi=900 cm3/s Qi=600 cm3/s

1.08

1.08

1.06

1.06

P (N/m2)105

P (N/m2)105

1.04

1.04

1.02

1.02

1

1

0

4

8

t(s)

12

16

Qi=900 cm3/s Qi=600 cm3/s

20

0

4

8

12

16

t(s)

Fig. 22 Temporal pressure variations at nine selected locations on the sectional plane of the confluent vessel (Continued).

20

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Nomenclature D

stack (tube) diameter (m)

dver

vertical diametrical coordinate in horizontal tube (m) g  L   G D 2

Eo

Eotvos number =

f

friction drag coefficient

hL

liquid film thickness (m)

KAAV

pressure loss coefficient of AAV

L

tube length (m)

P

pressured drop over a tube length (Nm-2)

ΔPAAV

pressure drop through AAV (Nm-2)

QAAV

volumetric air flow rate through AAV (m3s-1)

QG

volume flow rate of gas (m3s-1)

QG*

gas fraction of volume flow

QL

volume flow rate of liquid (m3s-1)

Qw

volumetric water flow rate (m3s-1)

Qi

volumetric water flow rate in the inlet of a drainage system (cm3s-1)

ReG

gas Reynolds number = ρGUGD/μG

ReL

liquid Reynolds number = ρLULD/μL

UG

superficial velocity of gas (ms-1)

UL

superficial velocity of liquid (ms-1)

Vair

airflow velocity in stack (ms-1)

Vw

water velocity of the annular flow in stack (ms-1)

X

Lockhart-Martinelli parameter = X  



 dP    dx SL

 dP     dx SG

Greek symbols α void fraction (gas flow cross sectional area to total cross sectional area) δ

mean thickness of annular water film for annular air-water cocurrent downward flow (m)

σ

surface tension (kgs-2, N/m)

Air-Water Two-Phase Flows with Applications to…

τi

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the interfacial shear stress. For annular air-water cocurrent downward flow τi  P  D  2  G g  =  L



4

μG

dynamic viscosity of gaseous fluid (kgs-1m-1)

μL

dynamic viscosity of liquid fluid (kgs-1m-1)

ρG

density of gas (kgm-3)

ρL

density of liquid (kgm-3)

References [1]

Swaffield J.A. and Campbell D.P., The simulation of air pressure propagation in building drainage and vent system, Building and Environment 30 (1995) 115-127.

[2]

Swaffield J.A. and Galowin L.S., The Engineering Design of Building Drainage Systems, Ashgate, England (1992).

[3]

A.F.E. Wise, Water, Sanitary and Waste Services for Buildings, 2nd, Mitchel, London (1986).

[4]

Swaffield J.A. and Boldy A.P., Pressure Surge in Pipe and Duct Systems, Avebury Technical Press (1993).

[5]

Swaffield J.A. and Campbell D.P., Air pressure transient propagation in building drainage vent systems, an application of unsteady flow analysis, Building and Environment 27 (1992) 357-365.

[6]

European committee for standardization, European Standard EN 12380, Air admittance valves for drainage systems – Requirements, tests methods and evaluation of conformity, 2002.

[7]

European committee for standardization, European Standard EN 12056, Gravity drainage systems inside buildings – Part 1: General and performance requirements, 2000.

[8]

Swaffield J.A., Jack L.B. and Campbell D.P., Control and suppression of air pressure transients in building drainage and vent systems, Building and Environment 39 (2004) 783-794.

[9]

Ghajar A.J., Non-boiling heat transfer in gas-liquid flow in pipes – a tutorial, J. Brazil Society of Mechanical Science and Engineering 27 (2005) 47-73.

[10] Bergelin O.P., Kegel P.K., Carpenter F.G. and Gazley C. Jr., Co-current gas liquid flow. II. Flow in vertical tubes, Heat Transfer and Fluid Mechanics Institute (1949) 19-28. [11] Chien S.F. and Ibele W., Pressure drop and liquid film thickness of two-phase annular and annular-mist flows, ASME J. Heat Transfer 86 (1964) 89-96.

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[12] Hajiloo M., Chang B.H., B.H. and Mills A.F., Interfacial shear in downward twophase annular co-current flow, Int. J. Multiphase Flow 27 (2001) 1095-1108. [13] Agrawal S.S., Gregory G.A and Govier G.W., An analysis of horizontal stratified two phase flow in pipes, The Canadian Journal of Chemical Engineering 51 (1973) 280-286. [14] Beattie D.R.H and Whalley P.B., A simple two-phase frictional pressure drop calculation method, Int. J. Multiphase Flow 8 (1982) 83-87. [15] Hart J., Hamersa P.J. and Fortuin J.M.H., Correlations predicting frictional pressure drop and liquid hold-up during horizontal gas-liquid pipe flow with a small liquid holdup, Int. J. Multiphase Flow 15 (1989) 947-964. [16] Spedding P.L. and Hand N.P., Prediction in stratified gas-liquid co-current flow in horizontal pipelines, Int. J. Heat Mass Transfer 40 (1997) 1923-1935. [17] Spedding P.L., Watterson J.K., Raghunathan S.R. and Ferguson M.E.G., Twophase co-current flow in inclined pipe, Int. J. Heat Mass Transfer 41 (1998) 42054228. [18] Tribbe C. and Müller-Sreinhagen H.M., An evaluation of the performance of phenomenological models for predicting pressure gradient during gas-liquid flow in horizontal pipeline, Int. J. Multiphase Flow 26 (2000) 1019-1036. [19] Spedding P.L., Watterson J.K., Raghunathan S.R. and Ferguson M.F.G., Twophase co-current flow in inclined pipe, Int. J. Heat Mass Transfer 41 (1998) 42054228. [20] Spedding P.L. and Hand N.P., Prediction in stratified gas-liquid co-current flow in horizontal pipelines, Int. J. Heat Mass Transfer 40 (1997) 1923-1935. [21] Spedding P.L. and Cooper R.K., A note on the prediction of liquid hold-up with the stratified roll wave regime for gas/liquid co-current flow in horizontal pipe, Int. J. Heat Mass Transfer 45 (2002) 219-222. [22] Kirpalani D.M., Patel T., Mehrani P. and Macchi A., Experimental analysis of the unit cell approach for two-phase flow dynamics in curved flow channels, Int. J. Heat Mass Transfer 51 (2008) 1095-1103. [23] Taitel Y. and Dukler A.E., A model for predicting flow regime transition in horizontal and near horizontal gas liquid flow, AIChE. J. 22 (1976) 47-55. [24] Spedding P.L. and Benard E., Gas-liquid two phase flow through a vertical 90 elbow bend, Int. J. Experimental Thermal and Fluid Science 31 (2007) 761-769. [25] Peshkin M.A., About the hydraulic resistance of pipe bends to the flow of gasliquid mixtures, Teploenergetika 8 (1961) 79-80. [26] Spedding P.L., Woods G.S., Raghunathan R.S. and Watterson J.K., Flow pattern, holdup and pressure drop in vertical and near vertical two and three-phase up flow, Trans. Inst. Chem. Eng. 78A (2000) 404-418.

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[27] Azzopardi B.J., Phase separation at T-junctions, Multiphase Science and Technology 11 (1999) 223-329. [28]

Azzopardi B.J. and Whalley P.B., The effect of flow pattern on two-phase flow in a T-junction, Int. J. Multiphase Flow 8 (1982) 481-507.

[29] Conte G. and Azzopardi B.J., Film thickness variation about a T-junction, Int. J. Multiphase Flow 29 (2003) 305-328. [30] Mak C.Y., Omebere-Iyari N.K. and Azzopardi B.J., The split of vertical twophase f low at a small diameter T-junction, Chemical Engineering Science 61 (2006) 6261-6272.

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216

Chapter 7 Convective Boiling Heat Transfer of Pure and Mixed Refrigerants within Plain Horizontal Tubes: An Experimental Study Adriana Greco DETEC, University of Naples Federico II, P.le Tecchio 80, 80125, Naples, Italy

Abstract An experimental study is carried out to investigate the characteristics of the evaporation heat transfer for different fluids. Namely: pure refrigerants fluids (R22 and R134a); azeotropic and quasi-azeotropic mixtures (R404A, R410A, R507). zeotropic mixtures (R407C and R417A). The test section is a smooth, horizontal, stainless steel tube (6 mm I.D., 6 m length) uniformly heated by the Joule effect. The flow boiling characteristics of the refrigerant fluids are evaluated in 250 different operating conditions. Thus, a data-base of more than 2000 data points is produced. The experimental tests are carried out varying: i) the refrigerant mass fluxes within the range 200 - 1100 kg/m2s; ii) the heat fluxes within the range 3.50 - 47.0 kW/m2; iii) the evaporating pressures within the range 3.00 - 12.0 bar. Experimental heat transfer coefficients and pressure drops are evaluated varying the influencing parameters. In this study the effect on measured heat transfer coefficient of vapour quality, mass flux, saturation temperature, imposed heat flux, thermo-physical properties are examined in detail. The effect on measured pressure drops of vapour quality, mass flux, saturation temperature and thermo-physical properties are examined. In this chapter the attention is focused also on the comparison between experimental results and theoretical results predicted with the most known correlations from literature, both for heat transfer coefficients and pressure drops.

Experimental Study Introduction Liquid-vapour phase-change processes play a vital role in many technological applications [1, 2]. Heat transfer associated with boiling and condensation processes is used in power and refrigeration cycles. Liquid-vapour phase change is also encountered in petroleum and chemical processing, liquefaction of nitrogen and other gases at cryogenic temperatures, and during evaporation or precipitation of water at earth’s atmosphere. Furthermore, the high heat transfer coefficients associated with boiling and condensation have made the use of these processes attractive in thermal control of compact devices with high dissipation rates. Application of this type include the use of boiling heat transfer to cool electronic components and the use of compact evaporators 

Email address: [email protected]

Lixin Cheng and Dieter Mewes (Ed) All right reserved – © Bentham Science Publishers Ltd.

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 217

and condensers for thermal control of aircraft avionics and spacecraft environments. Liquid-vapour phase-change processes are also of critical importance to nuclear power plant design. The heat transfer and fluid flow processes associated with liquid-vapour phase change are typically among the more complex transport phenomena encountered in engineering applications [3-5]. Heat transfer during convection can be described by physical properties, such as viscosity, density, thermal conductivity, thermal coefficient of expansion, as well as by geometric parameters. In two phase flow there is a multiplicity of variables connected with the heat transfer processes, that take into account not only physical properties of the boiling/condensing fluid but also the microstructure and the material of the heating/ cooling surface. Therefore it is more difficult to suggest equations for the calculation of heat transfer coefficients. Also we are far from having worked out a complete theory, because the physical phenomena are too complicated. From an engineering viewpoint, the final objective of studying two-phase flow is to determine the heat transfer and pressure drops characteristics of a given two-phase flow. One of the more important boundary condition in two phase flow is the presence or absence of heat transfer. Thus the adiabatic two phase flow is differentiated from the diabatic flow. In the latter case, the flow with heat addition is coupled thermohydrodynamic problem. On the other hand, heat transfer causes phase change and hence a change of phase distribution and flow pattern; on the other hand, it causes a change in the hydrodynamics, such as a pressure drop along the flow path that affects the heat transfer characteristics. In the present chapter attention is focused on convective flow boiling of pure and mixed refrigerant fluids used in vapour compression plants. The refrigerant fluids enters as saturated liquid-vapour mixture in the evaporator of a vapour compression plants and leaves it as a superheated vapour, changing of phase while flowing inside the tubes. The evaporating fluids analysed are the most common refrigerant used in vapour compression plants. The constant depletion of the ozone layer has determined many international agreements demanding a gradual phase-out of the halogenated fluids. As known the CFCs (chlorofluorocarbons) have been banned since 1996. Also the partially halogenated HCFCs (hydrochlorofluorocarbons) can’t be used for the manufacture of new equipment in all refrigerating and air conditioning applications from 1st January 2001; relatively to the existing equipment there will be a ban on the use of virgin HCFCs from 1st January 2010 and a ban on the use of all HCFCs, including recycled materials, from 1 January 2015. The HFCs (hydrofluorocarbons) are synthetic refrigerant fluids entirely harmless towards the ozone layer since they do not contain chlorine. For this reason actually they are the most used substitutes of HCFCs. In the present study the evaporating heat-transfer characteristics of the refrigerant fluid alternative to R22 were analyzed. R22 is a HCFC, widely used in refrigerant and air-conditioning plants. The basic requirements for possible substitutes for HCFC are: no flammability, no toxicity, similar thermophysical properties, economical and technological feasibility of the production process. Only a limited number of pure HFCs fluids comply with these requirements, e.g.: R134a, R152a, R32, R125 and R143a.

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Greco

Binary or ternary mixtures are often used instead of pure fluids, because the required overall properties could be obtained more easily by mixing two or three components. There is a continuous pressure by the market that force the manufacturer to provide refrigerators and heat pumps with higher and higher efficiencies, even with new refrigerants. The accurate knowledge heat transfer coefficients of the new-fluid and of their parametric behaviour especially in flow boiling can reduce costs by avoiding both underdesign and overdesign of evaporators, boilers, and other two-phase process equipment. The accurate prediction of heat transfer characteristics in condensers and evaporators is therefore a prerequisite to increase the cycle-performance through the correct sizing of each plant component. An experimental plant was set up at the University of Naples for evaluating the heat transfer characteristics of new refrigerant fluids in convective boiling. In the present paper, the local heat-transfer coefficients and pressure drops are evaluated for pure refrigerant fluids R22 and R134a, for azeotropic and quasi-azeotropic mixtures R507, R404A and R410A, for zeotropic mixtures R407C and R417A. R507, R404A and R410A are azeotropic and near azeotropic mixtures of R125/R143a (50/50 % by weight), R125/R143a/R134a (44/52/4 % by weight), R32/R125 (50/50 % by weight). R407C and R417A are zeotropic mixture of R32/R125/R134a (23/25/52 % by weight) and of R125/R134a/R600 (46.6/50/3.40 % by weight). R407C has a temperature glide of about 6°C, whereas R417A has a temperature glide of about 4°C. The flow boiling characteristics of the above mentioned refrigerant fluids are evaluated in 250 different operating conditions with a data-base of more than 2000 data points. The experimental tests are carried out by varying refrigerant mass fluxes within the range from 200 to 1100 kg/m2s; heat fluxes within the range from 3.50 to 47.0 kW/m2; evaporating pressures within the range from 3.00 to 12.0 bar. The objective of the present experimental study are: (i) to develop an accurate flow boiling heat transfer database for several important new fluids and to provide data to the refrigeration industry for the design of high efficiency evaporators, (ii) to investigate in depth the influence of vapour quality, evaporating pressure, heat flux, refrigerant mass flux, refrigerant fluid thermo-physical properties on the flow boiling characteristics. Experimental apparatus The experimental plant was designed to investigate two-phase-flow heat-transfer phenomena during convective boiling under uniform heat-flux conditions. A schematic view of the experimental apparatus is provided in figure 1.1. It consists in two main loops: the refrigerant loop and two secondary vapour-compression loops for refrigerant-fluid condensation operating alternatively.

Convective Boiling Heat Transfer of Pure and Mixed…

water

water

coaxial heat exchanger

coaxial heat exchanger

Oil separator

Inverter

Oil separator

Liquid receiver

Oil separator Compressor

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Liquid receiver

Oil separator Filter

Filter

Compressor

Thermostatic valves

Thermostatic valves

Inverter

Plate heat exchanger

Boiler

Main loop

Charge Gear Pump

T

T

T

T

T

P T

T T

Coriolis effect flowmeter

Test section Manifold +

-

Electric resistance

Sight Glass

P

Wattmeter

Fig. 1.1. The experimental apparatus.

The refrigerant fluid evaporates in the test section. Its condensation can be achieved in two plate type evaporators. A gear pump drives the refrigerant fluid circulating in the experimental loop. The pump is equipped with a hydrodynamic speed variator allowing experimental test at different refrigerating fluid flow-rates. In this way the mass flux can be varied within the range 200 ÷1100 kg/m2s. In the main loop, the refrigerant fluid is entirely oil–free. Usually in a typical vapour compression plant the refrigerant fluids contains approximately 2÷4% by weight of compressor lubricating oil in dependence of the layout of the plant and of the refrigerant temperature level. The evaporation of test fluid occurs in 6 meter stainless steel horizontal tube, inside diameter 6 mm, wall thickness 1 mm. The energy required for evaporation is provided by Joule effect. A direct electrical current supplied by a feed current device circulates within the wall of the tube. The heat flux can be safely assumed to be constant along the tube length. Varying the direct electrical current, it is possible to have a heat flux within the range of 8÷70 kW/m2. Obviously the tube is electrically insulated from the experimental loop using PFA connections.

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In order to insure saturated liquid conditions at the inlet of the evaporating section, the fluid temperature is regulated through a thermally-controlled electric ribbon heather wound around a tube upstream from the test section. At the outlet of the test section, to insure vapour superheating conditions, there is a similar electric heather. Two sight glasses are installed at the inlet and the outlet of the test section to observe the refrigerant flow patterns. The refrigerant condenses in a plate heat exchanger that acts as the evaporator of two different vapour compression plants working alternatively. In both, R507 is the working fluid. Each secondary vapour compression loop is composed by a semi hermetic bi-cylindrical compressor, a tap water plate condenser, two thermostatic valves, the above mentioned plate evaporator where the test refrigerant fluid works as secondary fluid. The experimental apparatus has to be able to carry out tests in which it is possible to control independently the evaporating temperature, the mass flow rate of the circuiting refrigerant and the heat flux in the test section. To this aim the components of the two auxiliary loops are sized differently, in order to work at a high range and at low range of evaporating temperatures, respectively. The compressor of each loop is connected to an inverter, which enables to vary the revolution speed. Each loop has two thermostatic expansion valves, in order to work under different operating conditions. To avoid that the lubricant oil might flows from one auxiliary loop to the other one, two oil separators in sequence have been inserted in each auxiliary loop. Measurements Location of the sensors in the experimental apparatus is shown in Figure 1.1. In order to obtain the heat transfer coefficients along the test section, the heat flux supplied to the refrigerant and temperatures of the refrigerant and of the wall should be measured. Heat-transferred to the refrigerant at the test section is evaluated measuring the values of the voltage supplied to the test section and of the consequent current. The voltage and the current are monitored by means of a voltmeter and an amperometer, respectively. The voltmeter has an accuracy of ± 0.2% in the range of 0÷30 V and the amperometer has an accuracy of ± 0.2% in the range of 0÷220 A. The tube has been divided in eight test stations. Their relative distance varies according to the qualitative diagram relating the evaporative heat transfer coefficient to vapour quality. For each station there are four-wire 100  platinum resistance thermometers. These thermometers are located on the top, bottom and both sides of the wall tube. The adhesive layer clamping the thermo-resistances to the tube wall provides electrical insulation, as well, thus preventing any interference with the direct electrical current heating the tube by Joule effect. Two four wire 100  platinum resistance thermometers are inserted in the refrigerant flow stream at the inlet and outlet of the test section. Such types of resistance thermometers are located in other key-points of the test circuit and of the secondary circuit. All the resistance thermometers are calibrated in the proper operating range and have an accuracy of ± 0.03°C. Refrigerant mass flow-rate is measured by a Coriolis effect mass flow-meter, insert after the gear pump, where sub cooled liquid conditions have been achieved. This meter

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has an accuracy of ± 0.01 % F.S. in the range 0÷2 kg/min. Since it could be affected by mechanical vibrations, it was mounted on a 5 kg steel plate separated from the plant. Two absolute piezoelectric pressure transducers measure the pressure at the inlet and outlet of the test section. They have an accuracy of 0.1% F.S. in the range 0 ÷ 14 bar. Other absolute pressure gauges are located in the focal point of the circuit. The pressure drops during the evaporation is measured with a piezoelectric difference gauge, that measures the pressure drop between the inlet and the outlet of the test evaporator, and in conjunction with a manifold measured the pressure drop in each test station. This pressure gauge has an accuracy of 0.1% F.S. within the range 0 ÷ 1 bar calibrated in laboratory before use. The test apparatus was heavily insulated with a 32 mm layer of cellular insulate for the heat exchangers and with a coaxial tube of armaflex insulate for tubes and tube fittings. Heat transfer data reduction The evaluation of local heat transfer coefficient and pressure drop is made when the steady state conditions have been achieved. A personal computer connected to a dataacquisition system, consisting in a controller, a 48-channel scanner and a multimeter, performs data collection. To control the achievement of the steady state conditions temperature and pressure value in key points of the plant are continuously monitored. Preliminarily it was fixed a deviations value and the steady state conditions are assumed to hold when the deviations of the controlled variables from their corresponding mean value are lower than the fixed deviation. If steady state conditions have been achieved, the test starts and the logging of data with 1 Hz sampling rate is performed on all channels for 1000 s. For the channels corresponding to the gauges of the test section, the 1000 samples recorded are averaged. Each sample is checked against the corresponding mean value and it is rejected if it does not lay within the fixed range. If more than 5% of the samples are rejected, the whole test is discharged. The local heat transfer coefficient was obtained by the following equations: .

Q q   hev Tw  Tsat  A .

(1)

where q is the heat flux, hev is the local heat-transfer coefficient, Tw is the inner wall temperature, and Tsat is the evaporating fluid temperature. The heat flux is supposed to be uniform along the test section. Thanks to the accurate test section insulation the heat losses (or gains) from the ambient are negligible and it is possible to calculate the heat flux knowing the total heat input to the evaporating fluid that is measured considering the values of the voltage and of the current. The inner wall temperature of the test section, Tw, is estimated from the measured outside wall temperature by applying the one-dimensional, radial, steady-state heat conduction equation for a hollow cylinder assuming uniform heat generation within the

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tube wall and an adiabatic condition on the outside of the tube. The corrections made by this procedure depend on the heat flux of the experimental tests. In the operating conditions corresponding to the tests reported in this paper, the correction is of about 1.5/-0.5 °C. The evaporating-fluid temperature Tsat is calculated rather than directly measured. Indeed, apart from the experimental difficulties arising when installing an in-stream resistance thermometer at each measuring-station, in-stream sensors considerably perturbate both fluid flow-pattern and heat-transfer process. Therefore, the pressure at each measuring section is estimated from the pressure measured at the inlet of the test section and from the pressure-drop measured in the sub-section. For pure fluids or for azeotropic mixtures, the corresponding saturation temperature is obtained from the vapour pressure curve. For a zeotropic mixture the saturation temperature is a function of quality as well as pressure. The enthalpy in each subsection is estimated from an energy balance between the inlet and the wall temperature measurement position: h  h in 

qA 

(2)

m

where hin is the enthalpy evaluated at the inlet of the test section evaluated from the 

measured temperature and pressure, m is the measured refrigerant mass flux, q is the constant heat flux and A is the local area of the tube. Therefore, knowing the enthalpy together with the measured pressure is possible to evaluate the local vapour quality. All thermodynamic and transport properties of pure and mixed fluids are evaluated using a computer program [6]. In each section, since there are four resistance thermometers to measure the tube wall, the average local two-phase flow heat-transfer coefficient is determined by: hev 

ht  hb  hls  hrs 4

(3)

The error analysis for the heat transfer coefficient is carried out by applying the uncertainty analysis suggested by Moffat [7]. In the present study, the data were classified as single sample. The uncertainty of each measured quantity consisted mainly of the uncertainty of the measurement device, of the data-acquisition system, of system-sensor interaction errors, of system disturbance errors. The experimental uncertainties evaluated with the error analysis are of ± 1.7%, as regards the heat flux, and of ± 1.6% for the refrigerant mass flux. The experimental uncertainty of the measured absolute pressure is ± 0.014 bar, of the measured pressure drop is ± 0.0001 bar. The error analysis for the heat transfer coefficient was carried out following the equation:

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2

  Tsat  h ev  Q   A   Tw                 h ev Q A T  T T  T     sat  sat   w  w 2

2

2

(4)

according to the uncertainty analysis. The error depends on the operating conditions and mainly on the accuracy of the wall temperature-difference. Therefore, it depends largely upon the accuracy of the measurements of the local pressure and of the wall temperature, and on the accuracy of the state-equation employed in evaluating the equilibrium temperature used in the computer program. In the operating condition of our tests, the errors in the heat transfer coefficients stemming from these uncertainties should range between 3.5 and 12.4 %. Data verification In the test section, the transferred heat (evaluated through the supplied voltage and the ensuing current) and those evaluated by means of an energy balance on the refrigerant fluid agree to within + 3% maximum error (less then 1 % average error). The validity of the pressure drop data was checked by measuring single phase pressure drops of pure R22 and R134a in the liquid phase varying the mass flow rate. The liquid phase pressure drops have been measured in these preliminary tests and compared with those obtained with the well known Blasius type correlation [8] which is valid for smooth tubes: 2 fl G 2  dp      di l  dz  l

(5)

where f l  M Re l

n

(6)

In the above friction factors relation, the constants can be taken to be M = 16 and n = 1 for laminar flow (Rel < 2000) or M = 0.079 and n = 0.25 for turbulent flow (Rel ≥ 2000). This correlation predicts the experimental data with a mean deviation of 7.4 %, substantiating the pressure drop measurements.

Two-Phase Flow Pattern in Horizontal and Vertical Plain Tubes in Convective Boiling Introduction The hydrodynamic behaviour of two-phase flows, such as pressure drop, void fraction, velocity distribution varies in a systematic way with the observed flow pattern. Heat transfer coefficients and pressure drops are closely related to the local two-phase flow structure of the fluid, and thus two-phase flow pattern prediction is an important aspect of modelling evaporation and condensation.

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Flow patterns in adiabatic flow Figure 2.1 and 2.2 show the flow patterns in vertical and horizontal plain tubes, respectively. Obviously, stratified flow does not exist in vertical flow, because of the relative direction of the flow and gravitational force, and a more symmetrical flow pattern is possible in vertical flow than in horizontal flow. Flow patterns identified in the figures can be described as follows.

Bubbly flow

Slug flow

Fig. 2.1. Flow patterns in a vertical tube.

Churn flow

Annular flow

Mist flow

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a

e

b

f

c

d

a = Bubbly flow b = Plug flow c = Stratified flow flow

d = Wavy flow e = Slug flow f = Annular

Direction of flow

Fig. 2.2. Flow patterns in horizontal flow.

Bubbly flow. In bubbly flow the vapour phase is uniformly dispersed as isolated bubbles in the continuous liquid phase. This flow pattern occur at low vapour qualities. Plug flow. With increasing vapour quality, the proximity of the bubbles is very close such that bubbles collide and coalescence to form larger bubbles (plugs) that fill up almost the entire tube cross section. The diameters of the elongated bubbles are smaller than the tube. Slug flow. Increasing the vapour quality the diameters of the elongated bubbles become similar in size to the channel diameter. The liquid slugs separating such elongated bubbles may include small bubbles. Intermittent flow. Plug and Slug flow are subcategories of Intermittent flow. Intermittent flow is a composite of plug and slug flow regimes. This regime is characterized by large amplitude waves intermittently washing the top of the tube with smaller amplitude waves in between. Churn flow. Increasing the vapour quality the velocity of the flow also increases and the slug flow regime begins to break down. The vapour bubbles become unstable, leading to an oscillating churning flow. Thus an alternative name for this region is unstable slug flow. Stratified flow. In horizontal tubes, at low liquid and vapour velocities, complete separation of the two phases occurs. The vapour phase goes to the top and the liquid to the bottom of the tube, separated by an undisturbed horizontal interface. Hence liquid and vapour are fully stratified in this regime. Stratified wavy flow. Increasing the vapour velocity in a stratified flow, waves are formed on the interface. The amplitude of the waves depends on the relative velocity of the two phases; however, their crest do not reach the top of the tube.

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Annular flow. Once the interfacial shear of the high velocity vapour on the liquid film becomes dominant over gravity, the liquid is expelled from the centre of the tube. Therefore in annular flow there is a continuous liquid in annulus along the tube wall and a continuous vapour phase in the core. The vapour core may contain entrained droplets. This flow pattern occurs at high flow velocities. Annular flow with partial dry out. In annular flow liquid film is thicker at the bottom than at the top. In horizontal tubes, at high vapour qualities, the top of the tube with its thinner film becomes dry first, so that the annular film covers only part of the tube perimeter. This regime can be stratified also as stratified-wavy flow. Mist flow. At very high vapour velocities, the annular film is thinned by the vapour shear on the interface until it becomes unstable and is destroyed, such that all the liquid in entrained as droplets in the continuous vapour phase. In figure 2.3 are reported typical flow patterns encountered in a horizontal tube.

x-1

x-0

Flow

Bubbly Plug Flow Flow

Slug Flow

Wavy Flow

Single-Phase Liquid Flow

Annular Flow Dispersod Mist Flow Single-Phase Vapor Flow

Fig. 2.3. Flow patterns in a horizontal evaporator tube.

Flow patterns maps Because the different flow patterns are determined by forces between the phases, above all by the inertia and gravity force, it is reasonable to use diagrams, so-called flow pattern maps, to depict the boundaries between the various flow patterns in their dependence on these forces. In these work attention is focused on the older Taitel and Dukler map and on the more recently developed Kattan-Tome-Favrat map in horizontal tubes. Taitel and Dukler map An accurate analysis of regime transitions with flows in horizontal pipes was first reported by Taitel and Dukler [9], using a physically based model for steady adiabatic flow without phase change. Their proposed map has been compared successfully with a large amount of experimental data.

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The map is reported in Figure 2.4. The map uses the Martinelli parameter X, the gas Froude number FTD and the parameters TTD and KTD. The map is reported in logarithmic scale. The Martinelli parameter is plotted on the abscissa and is defined as: 1

  dp   2   dz  l  X     dp     dz  v 

(7)

where in (dp/dz)l and (dp/dz)v are the frictional pressure gradient for the liquid and vapour phases flowing alone in the pipe, respectively. These frictional gradients can be computed as: 2 f l G 2 1  x 2 G 1  x  d i  dp  ; where f l  M Rel- n ; Rel     l di l  dz  l

(8)

2 fv G 2 x2 G x di  dp  ; where f v  M Rev- n ; Rev     v di v  dz  v

(9)

In the above fiction factors relations, for round rubes the constants can be taken to be M = 16 and n = 1, respectively, for laminar flow (Rel or Rev < 2000), or M=0.079 and n = 0.25 for turbulent flow (Rel or Rev > 2000). When both the liquid and vapour phase are in turbulent flow the Martinelli parameter can be expressed as:  X tt   v  l

  

0.5

 l   v

  

0.1

1 x     x 

0.9

(10)

In the transition between stratified smooth and stratified wavy flow the parameter KTD is defined as: K TD

  v  j v2  jl        (    )  g l v  l 

(11)

In the transition between stratified wavy and annular or intermittent flow the parameter FTD is defined as: 1

FTD

 2 ρv  jv2     ρl  ρv   g  d i 

(12)

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In the transition between intermittent and mist flow the parameter TTD is defined as: 1

 dp dz l  2     (ρl  ρv )  g 

TTD

(13)

where jv and jl are the superficial vapour and liquid fluxes, respectively defined as: jv 

Gx

v

; jl 

G 1 - x 

(14)

l

The transition between intermittent and annular flow or between mist and annular flow corresponds simply to X = 1.6 on this map.

10

Annular

Mist

1

FTD TTD

0.1

Intermittent

Stratified Wavy

0.01

KTD

Stratified Smooth 0.001 0.001

0.01

0.1

1

x

10

100

1000

Fig. 2.4. Taitel and Dukler map.

Kattan-Thome-Favrat map For small diameters in horizontal tubes, typical of heat exchangers, Kattan, Thome and Favrat [10 - 13] proposed a new map. In this map the vapour quality x is reported as abscissa and the mass flux of the evaporating fluid G is reported as ordinate.

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The void fraction is defined as.



Av A

(15)

where A is the cross section of the tube and Av is the portion of the tube filled with the vapour phase. In this map as a model of void fraction is utilized the Rouhani-Axelsson equation [14]:  x 1  x  1,18( 1  x )[ g (  l   v )] 0 ,25  x  1  0 ,12( 1  x )         0 ,5 v   G  v l   l  

Ar

Vapor

1

(16)

θstrat

Ar

Pr Ar

Liquid

Ar

Fig. 2.5. Geometrical dimensions in two phase flow.

Figure 2.5 defines the geometrical dimensions of the flow. The portion of the cross sectional area of the tube occupied with the liquid phase can be evaluated as:

d 2 2   d2 d2 strat Al   i  i sin2   strat   i 2   strat   sin2   strat  (17) 4 2 8 8 whereas the vapour phase portion can be evaluated as: Av  

d i2  Al 4

(18)

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The height of the completely stratified liquid layer can be evaluated as:

hl 

di 2

  2   strat 1  cos 2  

   

(19)

The wetted perimeter of the tube can be evaluated as:

 2   strat  Pi  d i sin  2  

(20)

Normalizing with the internal diameter of the tube four dimensionless variables can be obtained: Ald 

Al d i2

; Avd 

Av

h P ; hld  l ; Pid  i di di d i2

(21)

The stratified flow angle of tube perimeter can be calculated iteratively with the following equation:

d2 i

8

2   strat   sin2   strat   

d2 i

4

1   

(22)

The transition boundary curve between stratified wavy to annular flow is as:

Gwavy

 3  16 Avd gdi  l  v   x 2 2 1  2hld  12





0,5

 F2 ( q )  2   F1 ( q )  We       1  x  1   Fr  25hld2   l  



0,5

 50  75e



2  2  x 0,97     x  x 1   

(23)

where: We is the Weber number of liquid phase We 

Fr is the Froude number of liquid phase Fr 

G 2di

 l

;

G2 ;  l2 gdi

F1(q) and F2(q) are two parameters expressed as:

 q F1 (q)  646  qcr

2

  q   64,8   qcr

  

(24)

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 q F2 (q)  18,8  qcr

   1,023 

(25)

where qcr is the critical heat flux evacuate with the Kutateladze correlation [15]:

qcr  0,131  v1/ 2  hev g  l   v  

14

(26)

The transition between stratified wavy and fully stratified flow is given by the expression: 1

2 2   226,3 Ald Avd  v  l   v  l g  3    20x 2 3   x 1  x     

Gstrat

(27)

The transition between stratified wavy and mist flow is given by the expression:

Gmist

2   7680Avd  g  d i  l  v   x 2 2 

  Fr       We  l  

0,5

(28)

where  is the friction factor evaluated as:

     1,138  2 log   1,5 Ald

  

2

(29)

The transition between annular and intermittent flow is given by the expression:

x IA

    0,2914 v  l  

Figure 2.6 is the reported map.

  



1 1, 75 

   l   v 



1 7

      1  

1

(30)

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1200

Gwawy Gstrat Gmist

MF

1000

G [kg/sm2 ]

800 A

I

600

400

200

SW S

0 0,0

0,2

0,4

0,6

0,8

1,0

Quality

Fig. 2.6. Kattan, Thome and Favrat map.

The map is therefore specific to the fluid properties, flow conditions and tube geometrical parameters. Since the heat transfer process depends upon the flow regime, to analyse the heat transfer characteristics of the present data base, one must first estimate which flow pattern is present. In the present paper the evaluation is made with the Taitel and Dukler map and with the latest version of the flow pattern map of Kattan-Thome-Favrat. From the maps, it can be seen that the flow pattern is intermittent from the inlet section to a quality between 20 – 40 %, depending on test conditions. With increasing vapour content, an annular flow is achieved. At higher quality-values (>70 %) the liquid film in the upper portion of the tube disappears and the flow becomes annular with a partial dry-out. Only few data points corresponding to very low mass fluxes are in stratified-wavy flow regime. Few data points corresponding to very high mass fluxes and evaporating pressures are in mist flow regime. In Figure 2.7 is shown as an example the Kattan-Thome-Favrat map for R404A in a test condition corresponding to a saturation pressure of 9.9 bar, an heat flux of 12.9 kW/m2, a mass flux of 291 kg/s m2.

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1200

Gwawy Gstrat Gmist

MF

1000

G [kg/sm2]

800 I

A

600

400

200

SW S

0

0,0

0,2

0,4

0,6

0,8

1,0

Quality

Fig. 2.7. Kattan, Thome and Favrat map for R404A, with p sat = 9.9 bar, q=12.9 kW/m2, di=6.0 mm.

Experimental Local Heat Transfer Coefficients of Pure and Mixed Refrigerants during Convective Boiling in Horizontal Flow Experimental results As already stated, in this work, the experiments are performed for seven pure and mixed refrigerants (R22, R134a, R404A, R410A, R507, R407C, R417A) varying the evaporating pressure, the heat flux, the refrigerant mass flux. The experimental conditions are summarized in Table 3.1. The heat transfer coefficients are evaluated in 250 different operating conditions. The objective of the present experimental study are: (i) to develop an accurate flow boiling heat transfer database for several important new fluids and to provide data to the refrigeration industry for the design of high efficiency evaporators, (ii) to investigate in depth the influence of vapour quality, evaporating pressure, heat flux, refrigerant mass

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flux, refrigerant fluid thermo-physical properties on the flow boiling characteristics [16].

Table 3.1 The operating conditions Parameters

Range

Refrigerant fluid

R22, R134a, R404A, R507, R410A, R407C, R417A

Evaporatine pressure

2.90 - 12.4

(bar) Mass flux

200 - 1100

(kg/m2s) Heat flux

3.50 – 47.0

2

(kW/m )

Influence of different parameters on heat transfer coefficients In order to determine the characteristics and the mechanism of convective boiling, the influence of vapour quality, mass flux, heat flux, evaporating pressure, refrigerant fluid thermo-physical properties on heat transfer coefficients is investigated. Effect of vapour quality on boiling heat transfer From figure 3.1 to figure 3.3, local boiling heat transfer coefficients are reported for R404A, R507, and R410A to investigate the influence of vapour quality on heat transfer. Similar trends are observed in all the experiments with similar operating conditions. In Fig. 3.1 [17] the heat transfer coefficients of R404A are reported in two different operating conditions. Both are achieved with an almost constant refrigerant mass flux of 480 kg/m2s. The former corresponds to a heat flux of 12.0 kW/m2, with an evaporating pressure of 4.30 bar. The latter to a heat flux of 24.4 kW/m2, with an evaporating pressure of 7.40 bar. In Fig. 3.2 [18], the heat transfer coefficients of R507 are reported as a function of vapour quality corresponding to a low mass flux of 286 kg/m2s, a low evaporating pressure of 4.00 bar and a low heat flux of 11.2 kW/m 2. In Fig. 3.3 the heat transfer coefficients of R410A are reported with a refrigerant mass flux of 589 kg/m2s, a high value of evaporating pressure of 11.2 bar and a high heat flux of 29.2 kW/m2. In all the experimental tests performed, a different dependence of the heat-transfer coefficients on vapour quality is apparent. Indeed, at low values of the evaporating pressure and heat flux, the heat-transfer coefficient increases with increasing vapour quality. On the contrary, for high pressure and heat flux values, the heat-transfer coefficient initially decreases with quality and then increases, presenting a local minimum in the vapour quality range between 20 and 50%. In both cases, the heattransfer coefficients suddenly drop when the liquid film disappears (for high vapour qualities), leaving the tube-wall partially or totally dry.

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8000 7000

5000

2

hev (W/m K)

6000

pev= 7.40 bar

4000

pev= 4.30 bar 3000 2000 1000 0 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.1. Heat transfer coefficients of R404A at G=483 kg/m2s, pev = 7.40 bar, q = 24.4 kW/m2; and at G = 474 kg/m2s, pev = 4.30 bar, q =12.0 kW/m2.

3000

2

hev (W/m K)

2000

1000

0 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.2. Heat transfer coefficients of R507 at G=286 kg/m2s, pev = 3.99bar, q = 11.2 kW/m2.

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4

1.8 10

4

1.6 10

4

2

hev (W/m K)

1.4 10

4

1.2 10

4

1 10

8000

6000 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.3. Heat transfer coefficients of R410A at G=589 kg/m2s, pev = 11.6 bar, q = 29.2 kW/m2.

The heat-transfer coefficient in flow-boiling results from the interaction between nucleate boiling and liquid convection. At high heat fluxes and evaporating pressures, heat-transfer is predominantly influenced by the nucleate-boiling mechanism. The convective contribution to heat-transfer predominates at low heat-fluxes and evaporating pressures. In the experimental tests where liquid convection is the main mechanism, the heattransfer coefficient increases with quality. Indeed, as the flow proceeds downstream and vaporization takes place, the void fraction increases, thus decreasing the density of the liquid-vapour mixture. As a result, the flow accelerates enhancing convective transport from the heated wall of the tube. The ensuing increase in heat-transfer coefficient proceeds until the liquid film disappears, leaving the tube-wall partially or totally dry. In this region, the heat-transfer coefficient decreases because of the low thermal conductivity of the vapour. In the experimental tests corresponding to higher values of heat flux and of evaporating pressure, there are two distinct heat-transfer regions during evaporation. In the first one, occurring at low qualities, nucleate boiling dominates. In this region, heattransfer coefficients decrease as the effect of nucleate-boiling diminishes. Indeed, as quality increases in annular flow, the effective wall superheat decreases due to a thinner liquid film (less thermal resistance) and to an enhanced convection caused by high

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 237

vapour velocity. Thus the number of active nucleation sites decreases until a transition quality is reached. Beyond the transition quality, the effective wall superheat is below the threshold value required for bubble nucleation on the wall. The second region corresponds to convective evaporation. It is characterized by the increase of the heattransfer coefficients with quality. This increase proceeds until the liquid film disappears. Effect of mass flux on boiling heat transfer In figures 3.4 and 3.5 [19], local boiling heat transfer coefficients are reported for R407C and R410A, in order to illustrate the influence of mass flux on heat transfer. The data reported for each refrigerant fluid corresponds to experiments with an almost constant heat flux and evaporating pressure, at different refrigerant mass fluxes. Similar trends are observed for the other refrigerant fluids. The data reported in the figures correspond to a low evaporating pressure of about 4.00 bar. The experimental data clearly show that the heat transfer coefficients increase with increasing the refrigerant mass flux. Indeed, increasing the refrigerant mass flux increase the fluid velocity, thus enhancing convective boiling. In a very low quality region, corresponding to bubbly, plug and slug flow regimes, where nucleate boiling is dominant, the influence of the refrigerant mass flux became weaker and the heat transfer coefficients tend to merge together. In literature, many correlations are available for the evaluation of the heat transfer coefficient in flow boiling for pure and mixed refrigerants. In most of them, the convective contribution to the heat transfer is proportional to the power 0.80 of the mass flux, because they follow the Dittus-Boelter type correlation. The mass flux has a negligible effect on nucleate boiling. Indeed, by increasing the mass flux, the interfacial shear stress is also increased. The bubbles on the heated surface are removed from the wall under the influence of shear stress, and do not attain the larger diameters seen in pool boiling. This effect leads to slight reductions in the nucleate boiling component with increasing shear stress. In the present study, the influence of mass flux on the heat transfer coefficient in flow boiling was investigated. Figure 3.6 reports the exponent n, that describes the dependency of the heat transfer coefficient on the refrigerant mass flux G, as a function of the vapour quality, within the range 200 - 1100 kg/m2s, with an almost constant evaporating pressure of about 4.00 bar. This exponent was obtained as a result of curve fitting of our experimental data. By inspection of Figure3.6, it can be seen to vary within the range 0.52 – 0.83, except for some data points corresponding to very low vapour quality. The exponent n slightly increases with increasing vapour quality, as a consequence of the progressive increase in the relative relevance of the convective boiling contribution. Indeed, the data points reported in this figure correspond to a low evaporating pressure and therefore the influence of convective boiling is predominant. Increasing the evaporating pressure and the heat fluxes decreases the exponent n because of the increasing relative importance of nucleate boiling.

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2

G = 199 kg/m s 2

G = 344kg/m s

6000

2

G= 507kg/m s 2

G= 700kg/m s 5000

2

G= 1100kg/m s

2

hev (W/m K)

4000

3000

2000

1000

0 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.4. Heat transfer coefficients of R407C varying the refrigerant mass flux at , p ev = 3.60bar and q = 7.67 kW/ m2.

9000

8000

2

hev (W/m K)

7000

6000

5000

2

G=1068 kg/sm 2

G=784 kg/sm 4000

2

G=574 kg/sm

2

G=363 kg/sm 3000

2000 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.5. Heat transfer coefficients of R410A varying the refrigerant mass flux at , p ev = 4.90bar and q = 14.2 kW/ m2.

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1

0.8

n

0.6 R134a R404A R410A R507 R407C R22 R417A

0.4

0.2

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Quality

Fig. 3.6. Values of n(G) power exponent as a function of vapour quality at an almost constant , p ev = 4.00 bar and q = 15.0 kW/ m2.

x=0.1 x=0.2 x=0.3 x=0.4 x=0.5

7000

2

hev (W/m K)

6000

5000

4000

3000

2000 300

400

500

600

700

800

900

1000

1100

2

G (kg/m s)

Fig. 3.7. Heat transfer coefficients of R134a as a function of mass flux varying vapour quality at p ev = 3.10 bar and q= 14.0 kW/ m2.

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In figure3.7, R134a heat transfer coefficients are evaluated as a function of mass flux by varying the vapour quality at an almost constant evaporating pressure of 3.10 bar and at a heat flux of 14.0 kW/m2. In figure 3.8, R404A heat transfer coefficients are evaluated as a function of mass flux by varying the vapour quality at an almost constant evaporating pressure of 4.13 bar and at a heat flux of 11.5 kW/m2. In these two figures at any given vapour quality, the dependence of the heat transfer coefficients on mass flux it is clearly shown.

x=0.05 x=0.1 x=0.2 x=0.3 x=0.4 x=0.5 x=0.6 x=0.65

8000

7000

2

hev (W/m K)

6000

5000

4000

3000

2000 200

400

600

800

1000

1200

2

G (kg/m s)

Fig. 3.8. Heat transfer coefficients of R404A as a function of mass flux varying vapour quality at pev = 4.13 bar and q= 11.5 kW/ m2.

Effect of heat flux on boiling heat transfer The heat flux has a negligible effect on the convective contribution to heat transfer, while strongly affecting nucleate boiling. Indeed, as heat flux increases, bubble departure frequency rapidly increases, and additional cavities of smaller sizes are activated on the heated surface. As a consequence, the nucleate boiling contribution increases. Figure 3.9 shows the heat transfer coefficients of R407C as a function of vapour quality at an almost constant mass flux of 200 kg/m2s and an evaporating pressure of 3.50 bar. The heat flux remains in the range 3.98 - 7.96 kW/m2. Figure 3.10 shows the heat transfer coefficients of R407C as a function of vapour quality at an almost constant mass flux of 200 kg/m2s and an evaporating pressure of 6.00 bar. The heat flux remains in the range 4.10 - 7.96 kW/m2.

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 241

3000 2

q=7.96 kW/m

2

q=3.98 kW/m

2

q=5.97 kW/m

2

hev (W/m K)

2500

2000

1500

1000 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.9. Heat transfer coefficients of R407C as a function of vapour quality varying heat flux at p ev = 3.50 bar and G=200 kg/m2s.

2

q=7.96 kW/m

3000

2

q= 4.10 kW/m

2

q= 5.99 kW/m

2

hev (W/m K)

2500

2000

1500

1000 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.10. Heat transfer coefficients of R407C as a function of vapour quality varying heat flux at pev = 6.00 bar and G=200 kg/m2s.

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From the experimental data, it is clear that the heat transfer coefficients depend on the heat flux, increasing with the latter, only in the region where nucleate boiling is dominant. After a transition quality (in the range 0.40 - 0.50), in the convective boiling region, the heat transfer coefficients merge together and the heat flux has a negligible effect. In the nucleate boiling region the dependence of heat transfer coefficient on heat flux can be expressed as: hev   a q nq   

(31)

where a and nq are constants. The values of nq obtained from many experimental results vary from 0.5 to 0.8. Webb and Pais [20] showed that the slope of hnb vs. q curve is not the same for different refrigerants. Gorenflo [21] found that nq is not a constant but is a function of the reduced pressure, Kandlikar [22] found it to be 0.7, Gungor [23] 0.86, Lazarek [24] 0.714, Klimenko [25] 0.6, Cooper [26] 0.67. From the best exponential fit of our experimental data in the nucleate boiling region, we found that nq varies in the range 0.53 - 0.74, for heat flux varying between 4.00 and 25.0 kW/m2. From the experimental results, it is apparent that nq is not a constant. Indeed, it varies with the evaporating pressure (and therefore with the reduced pressure) in the range 3.00 – 12.0 bar. As regards the reduced pressure, for the different fluids this interval corresponds to a range of variation between 0.06 and 0.323. Indeed, the exponent nq increases with increasing reduced pressure in the nucleate boiling region. This is a consequence of the increasing importance of the nucleate boiling increasing with the pressure. The exponent nq has the following expression: nq  0.80 -  0.30 x 10-0.8pr  (32)   From the reported figures it is apparent that, in the nucleate boiling region, the heat transfer coefficients slightly depend on vapour quality and strongly on heat flux. Beyond a transition quality, the influence of heat flux becomes negligible and the heat transfer coefficient starts to increase strongly with the vapour quality. Based on experimental results, a criterion can be found to characterize the transition between nucleate and convective boiling. The transition quality can be identified from the ratio between the time characteristics of nucleate boiling and that of convective boiling. The latter can be evaluated as the ratio between the thickness of the liquid film and liquid velocity: cb 

 ul

(33)

If a simplified annular flow structure is assumed, i.e. an annular liquid ring of uniform thickness <
Convective Boiling Heat Transfer of Pure and Mixed…

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 243



di (1 -  ) 4

(34)

where  is the cross sectional void fraction of the vapour. The liquid velocity can be defined as: ul 

G (1 - x ) l 1   

(35)

Therefore, the characteristic time of convective boiling is defined as:

di (1 -  )2  l  cb  G1  x 

(36)

The time characteristic of nucleate boiling can be evaluated as the ratio between the bubble diameter and the bubble velocity: d nb  b ub

(37)

From the analyses of Fritz [27] and Wark [28] the bubble diameter just breaking off from a heated surface was found to be:   2  d b  0.0146      g    l v  

0.5

(38)

From the Rohsenow [29] analysis, the vapour superficial velocity, i.e. the velocity of a bubble leaving the heated wall, is defined as: ub 

q v h ev

(39)

Thus, the ratio between the two characteristic times can be estimated as:

 cb di 1   2  l q Bo 1 -  2   A 1  x   nb 4 G 1 - x  v hev d b

(40)

The transition quality depends on the constant A, which is a function of tube geometry, of fluid properties and of tube wall characteristics; on the boiling number, on the vapour quality, on the void fraction, that is a function of the vapour quality, as well. Therefore,

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the boiling number is the appropriate dimensionless number to account for the transition between convective and nucleate boiling. In evaluating the transition quality, the correct tool to be adopted is difficult to determine, because of the different void fraction expressions available, that depends on flow pattern and on tube and channel geometries In the experimental data–base, this transition occurs for an almost constant value of the product:

1- x  Bo    x 

2 (41)

Effect of evaporating pressure on boiling heat transfer Figures 3.11-3.13 show the influence of the evaporating pressure on the heat transfer coefficient. Figure 3.11 refers to R410A, at a fixed refrigerant mass flux of 380 kg/m2s, at a heat flux of about 17.0 kW/m2, by varying the evaporating pressure.

pev =4.83 bar pev =7.20 bar pev = 11.5 bar pev =12.0 bar

4

1 10

9000

2

hev (W/m K)

8000

7000

6000

5000

4000

3000 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.11. Heat transfer coefficients of R410A as a function of vapour quality varying evaporating pressure at q= 17.0 kW/ m2 and G=380 kg/m2s.

Figure 3.12 shows the heat transfer coefficient of R407C at a fixed refrigerant mass flux of 200 kg/m2s, at a heat flux of about 8.80 kW/m2, by varying the evaporating pressure. Figure 3.13 shows the heat transfer coefficient of R417A at a fixed refrigerant mass flux of 200 kg/m2s, at a heat flux of about 8.00 kW/m2, by varying the evaporating pressure.

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pev = 3.50 bar pev = 6.00 bar pev = 7.88 bar pev =10.0 bar

4000 3500

2500

2

hev (W/m K)

3000

2000 1500 1000 500 0 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.12. Heat transfer coefficients of R407C as a function of vapour quality varying evaporating pressure at q= 8.75 kW/ m2 and G=200 kg/m2s.

pev =3.80 bar pev=4.80 bar pev =6.30 bar pev= 9.60 bar

3500

2

hev (W/m K)

3000

2500

2000

1500 0

0.2

0.4

0.6

0.8

1

Quality

. Fig. 3.13. Heat transfer coefficients of R417A as a function of vapour quality varying evaporating pressure at q= 8.09 kW/ m2 and G=200 kg/m2s.

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The experimental results indicate that, at a given mass flux, the heat transfer coefficients increase with increasing pressure. The experimental tests reported correspond to low refrigerant mass fluxes, where the nucleate boiling contribution is always important. With increasing vapour quality, the influence of the evaporation temperature became weaker, along with the increase of the relative importance of the convective contribution to global heat transfer. With increasing pressure, the contribution of nucleate boiling to the heat transfer coefficients increases, mainly due to the corresponding decrease in the average bubble departure diameter for any given wall superheat. This effect induces the activation of additional new small cavities on the heated surface, thus increasing the number of active nucleation sites. Furthermore, under nucleate boiling, the product of bubble departure frequency and diameter is constant. At increased pressure, bubble frequency increases with decreasing bubble departure diameter, thus contributing to the increase of the heat transfer coefficient. Assuming spherical nuclei, the bubble departure diameter for a given wall superheat follows from the well-known equilibrium conditions for a small bubble (Thomson equation) and the linearized Clausius-Clapeyron equation and depends on physical properties (surface tension, enthalpy of vaporization, vapour-phase density). With increasing pressure, the vapour density strongly increased and the surface tension decreases. An increase in pressure would also cause the decrease of the ratio l/v too, with an ensuing decrease in interfacial shear stress. This leads to a larger effective film thickness on the tube wall, and the suppression effect of nucleate boiling is reduced. The effect of pressure on convective boiling contribution mainly results from changes in fluid properties. Indeed, the vapour density increases with increasing pressure. Therefore, the higher average density of the vapour-liquid mixture leads a lower velocity at any given refrigerant mass flux. The liquid conductivity decreases, but the liquid specific heat increases and the liquid viscosity decreases. Both effects lead to a negligible effect of the pressure on convective contribution. Therefore, the increase of the evaporating pressure has on opposite effect on the nucleate and on the convective contribution. Indeed, the former increases and the latter slightly decreases. For low mass fluxes, in the whole vapour quality range, the nucleate boiling contribution is important and therefore the heat transfer coefficients always increases with pressure. For higher mass fluxes, the relevance of the convective contribution increases. Therefore, in the low quality range, where nucleate boiling is dominant, the heat transfer coefficients increase with pressure; at higher vapour quality the coefficient tend to merge together because the opposite effects tend to cancel one another. In the Cooper [26] correlation for nucleate boiling, the effect of pressure is evaluated as:

- log pr 0.55 h nb  p0.12 r

(42)

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In all the other correlations, the heat transfer coefficient is proportional to the power of 0.2 - 0.4 of the reduced pressure, but in the proximity of the critical point, where the exponent is larger. In our experimental tests, in the region dominated by nucleate boiling, the exponent ranges between 0.39 - 0.52, for all the refrigerant fluids tested. Correspondingly, the reduced pressure ranges between 0.06 and 0.323. Effect of both evaporating pressure and heat flux on boiling heat transfer The effect of the evaporating pressure and of the heat flux on boiling heat transfer was investigated, as well. Figure 3.14 reports the R404A heat transfer coefficients at a mass flux of 790 kg/m2s, varying both the evaporating pressure and the heat flux. Figure 3.15 reports the R4010A heat transfer coefficients for a fixed mass flux of 1079 kg/m2s, varying both the evaporating pressure and the heat flux. The experimental results indicate that, in the nucleate boiling region (vapour qualities between 0-30%) for any given refrigerant mass flux, the heat transfer coefficients increase with increasing pressure and heat flux. Indeed, increasing either leads to a corresponding increase in the nucleate boiling contribution to the heat transfer coefficient. In the region dominated by convective boiling (vapour qualities>30%), the heat transfer coefficients merge, since heat flux and pressure both have a negligible effect on convective boiling. Increasing the mass flux reduces the region dominated by nucleate boiling dominate and the heat transfer coefficients merge at a lower vapour quality.

4

1.6 10

4

1.4 10

4

2

hev (W/m K)

1.2 10

4

1 10

8000

2

pev=4.98bar q=11.8 kW/m

2

pev=7.43bar q=27.0 kW/m 6000

2

pev=12.0bar q=34.9 kW/m

4000

2000 0

0.2

0.4

0.6

0.8

1

Quality

Fig. 3.14. Heat transfer coefficients of R404A as a function of vapour quality varying evaporating pressure and heat flux at G=790 kg/m2s.

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4

1.8 10

4

1.6 10

4

4

1.2 10

2

hev (W/m K)

1.4 10

2

pev=5.20bar q=13.4 kW/m

4

1 10

2

pev=7.10bar q=22.4 kW/m

2

pev=11.3bar q=36.4 kW/m

8000

2

pev=12.3bar q=38.5 kW/m 6000 4000 2000 0

0.2

0.4 Quality

0.6

0.8

1

Fig. 3.15 Heat transfer coefficients of R410A as a function of vapour quality varying evaporating pressure and heat flux at G=1079 kg/m2s.

Effect of fluid properties on boiling heat transfer The experimental data allow comparing the heat transfer coefficients of R134a, R507, R404A, R410A, R22, R407C and R417A at almost equal pressure, refrigerant mass-flux and heat flux [30, 31]. Figure 3.16 represents heat transfer coefficients of all the refrigerant fluids at a mass flux of 250 kg/m2s, a heat flux of about 10.8 kW/m2, and an evaporating pressure of about 4.00 bar. Figure 3.17 represents heat transfer coefficients of all the refrigerant fluids at a mass flux of 360 kg/m2s, a heat flux of about 17.5 kW/m2, and an evaporating pressure of about 7.40 bar. Table 3.2 summarizes the relevant thermo-physical properties of the refrigerants fluids in the operating conditions adopted in the experiments reported. It can be shown that (i)

in the experimental tests corresponding to the lower value of evaporating pressures and heat flux, the heat transfer coefficients of R134a are better than those pertaining to R22, by a mean factor of about +16 %. R410A heat transfer coefficients are slightly better than those of R22, by a mean factor of 11 %. R404A heat transfer coefficients are lower than those of R22, by a mean factor of -17%. R507, R407C and R417A heat transfer coefficients are consistently lower than those pertaining to R22 (with mean values of the deviations of -40%, -45% and – 46 %, respectively).

Convective Boiling Heat Transfer of Pure and Mixed…

(ii)

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 249

in the experimental tests corresponding to higher values of evaporating pressures and heat fluxes, R134a heat transfer coefficients are consistently better than those pertaining to R22, by a mean factor of about + 29 %. R410A, R507 and R404A heat transfer coefficients are similar and are lower than those pertaining to R22, with a mean value of -19 %, -20%, and -26%, respectively. R417A and R407C heat transfer coefficients are consistently lower than those of R22, with a mean value of -37% and -55 %, respectively.

Table 3.2. The thermo-physical properties affecting heat transfer. Fluid

Tubble/T (°C)

pev (bar)

v

hev 3

(kg/m )

(kJ/kg)

Cpl (kJ/kgK)

kl (mW/mK)

l (Pas)





(N/m)

m /kgK)0.4 3

(W/mK)0.6 R22

-6.56

4.00

17.19

210

1.152

97.695

232

0.01269

7455

R134a

8.93

4.00

19.53

192

1.367

88.084

238

0.01029

7424

R410A

-20.0/0.087

4.00

15.10

249

1.438

122.69

226

0.01235

9435

R404A

-12.7/0.57

4.00

20.47

175

1.339

78.939

212

0.00906

7220

R507

-13.4

4.00

20.82

173

1.328

78.388

214

0.00898

7140

R407C

-10.3/6.36

4.00

16.11

228

1.383

105.89

244

0.01229

8247

R417A

-4.61/4.05

4.00

22.00

164

1.322

84.224

247

0.01052

7025

R22

12.8

7.40

31.29

194

1.209

88.991

188

0.00981

7815

R134a

28.6

7.40

36.03

174

1.440

79.585

186

0.00760

7871

R410A

-2.45/0.100

7.40

27.72

229

1.507

111.39

176

0.00946

10026

R404A

-6.25/0.485

7.40

37.88

158

1.418

71.549

164

0.00679

7718

R507

5.50

7.40

38.53

156

1.407

71.016

165

0.00671

7640

R407C

8.41/5.91

7.40

29.78

208

1.449

95.950

190

0.009375

8753

R417A

14.9/3.52

7.40

40.43

149

1.394

75.680

188

0.007803

7506

The heat-transfer coefficient in convective boiling results from the interaction between nucleate boiling and liquid convection. According to the Dittus-Boelter, singlephase forced convection correlation, the convective contribution to heat-transfer coefficient is strongly affected by vapour density and is directly proportional to the liquid property combination :  Cp    l  l

0 .4

  k l 0.6 

(43)

Therefore, by increasing the value of , the convective contribution to the heat transfer coefficient increases, as well. Furthermore, at any given refrigerant massflux, the decrease in vapour and liquid density results in a lower velocity of the refrigerant fluid.

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R22 R507 R134a R407C R404A R417A R410A

5000

2

hev (W/m K)

4000

3000

2000

1000

0 0

0.2

0.4 Quality

0.6

0.8

1

Fig. 3.16 Heat transfer coefficients as a function of vapour quality varying the refrigerant fluid at G=250 kg/m2s, q= 10.8 kW/ m2, pev = 4.00 bar.

4

1.2 10

4

8000

2

hev (W/m K)

1 10

6000

4000

2000

0 0

0.2

0.4 Quality

0.6

0.8

1

R407C R22 R507 R410A R134a R417A R404A

Fig. 3.17 Heat transfer coefficients as a function of vapour quality varying the refrigerant fluid at G=360 kg/m2s, q= 17.5 kW/ m2, pev = 7.40 bar.

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For R134a the liquid property combination  is very close to R22, for R404A, R507 and R417A  is slightly lower, whereas for R410A and R407C is respectively about 28% and 11% greater. The vapour density of R404A, R507 and R417A are consistently greater than that pertaining to R22. The nucleate boiling contribution to the heat transfer coefficient is strongly affected by the heat flux, the vapour density, the superficial tension, the heat of vaporization. The greater vapour density of R134a, together with a lower superficial tension and a greater enthalpy of vaporization, leads to a greater contribution of nucleate boiling, as compared to that of R22. Therefore, in the experimental tests corresponding to the lower value of the evaporating pressure, R134a heat-transfer coefficients are slightly better than those pertaining to R22 because of the greater nucleate boiling contribution. The difference in the heat-transfer coefficients increases with increasing pressure, since the relative importance of the nucleate boiling contribution increases. In the experimental tests with low evaporating pressure R410A heat transfer coefficients are better than those of R22 because of the more relevant convective contribution. For higher evaporating pressures and heat fluxes, i.e. for an increasing relative effect of nucleate boiling, the heat transfer coefficients of R410A become lower than that of R22, because of the lower nucleate boiling contribution (greater superficial tension, lower vapour density) of the latter. The heat transfer coefficients of R404A and R507 are always lower than that of R22 because of the lower convective contribution than that pertaining to R22 (lower  values and higher vapour density). The thermal performance of both R404A and R507 increases with the pressure because of the greater nucleate boiling contribution. Furthermore, R404A and R410A are almost azeotrope mixtures, with a gliding temperature difference less than 0.5 and 0.1 °C, respectively. Therefore in the region dominated by nucleate boiling, a little mass transfer resistance can be observed. The heat transfer coefficients of R407C and R417A are always consistently lower than those of R22. Indeed, the convective contribution of R407C is always higher than those or R22, but the potential for higher heat transfer coefficients is cancelled because of the temperature glide. Indeed, both fluids are zeotropic mixtures with a temperature glide of about 6 and 4 °C, respectively. Therefore the nucleate boiling contribution to the global heat transfer coefficients is strongly reduced by diffusional limitation. The superposition of heat transfer and mass transfer phenomena associated with the evaporation of a zeotropic mixture decreases the heat transfer coefficient as compare to those pertaining to pure liquids. The heat transfer coefficients decreases with the difference in concentration more strongly at high pressure than at low pressures. This can be explained by the fact that the number of vapour bubbles being formed per surface unit increases with the pressure. The vapour bubbles are more densely packed, and there is less surface available for the mass flow rate in the liquid space. The delivery of low boiling components is thus more strongly impeded, this leads to a further reduction in the heat transfer. Conclusions In this study the effects of the refrigerant vapour quality, mass flux, saturation temperature, imposed heat flux and thermo-physical properties on the measured heat

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transfer coefficient were analysed in detail. The following conclusions can be drawn from the experimental evidence: 1) In the experimental tests where liquid convection is the dominating mechanism, the heat-transfer coefficient increases with quality. In the experimental tests at high evaporation pressures and heat fluxes there are two distinct heat-transfer regions during evaporation and the heat transfer coefficients initially decrease with vapour quality and then after increase. 2) The heat transfer coefficients always increase with mass flux. The exponent n that describes the influence of the refrigerant mass flux G on the heat transfer coefficients varies in the range 0.52 – 0.83, except for some data points corresponding to a very low- quality region. 3) The heat transfer coefficients depend on the heat flux only in the region where nucleate boiling dominates. In this region, the exponent nq that describes the influence of the heat flux on the heat transfer coefficients varies in the range 0.53 - 0.74. From the experimental results it is apparent that nq varies with the evaporating pressure and therefore with the reduced pressure. 4) The heat transfer coefficients increase with the evaporating pressure. For low mass fluxes, in all the vapour quality range explored, the heat transfer coefficients always increase with pressure. For higher mass fluxes, in the low quality range, the heat transfer coefficients increase with pressure; at higher vapour quality the coefficient tend to merge together. The exponent n that describes the influence of the evaporating pressure on the heat transfer coefficients in the nucleate boiling dominate region varies between 0.39 - 0.52. 5) The heat transfer coefficients of R134a are higher than those of all the other refrigerant fluids. The difference increases with increasing evaporating pressure. The heat transfer coefficients of the zeotropic mixtures R407C and R417A are always lower because of the mass transfer resistances in nucleate boiling.

An Overview of the Heat Transfer Correlations for Convective Boiling in Plain Tubes Introduction In spite of the enormous number of publications, the prediction of heat transfer coefficients remains essentially empirical due to the complex hydrodynamic and heat transfer processes. A number of correlations have been developed for predicting heat transfer coefficients in horizontal and vertical smooth tubes for pure substances and mixtures during convective boiling. To date, no analytical models have been developed for convective boiling heat transfer coefficients. All correlations contain one or more empirical constants. It was recognized since the beginning of boiling research that the flow boiling heat transfer coefficient is an interaction of nucleate boiling and evaporation at the vapour – liquid interface. All the developed correlations are based on a specific model. The term

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model describes the concept used to combine the nucleate and the convective contribution to the heat transfer coefficient. The three main models are: “superposition”, “asymptotic” and “enhancement”. Recently a new model based on two phase flow pattern has been developed. The superposition model assumes that the heat transfer coefficient is equal to the sum of a nucleate boiling coefficient and of a convective boiling coefficient: hev  hnb S  hl F

(44)

where hnb is the pool boiling heat transfer coefficient and hcb is the convective heat transfer coefficient. The latter coefficient was evaluated with the Dittus Boelter equation [32] for the liquid phase only. The factor S is a suppression factor ( ≤1 ), which takes into account, that with increasing vapour quality the forced convective effect also increases and the nucleate boiling contribution is more strongly suppressed, because of the reduction of the thermal boundary layer thickness. The parameter F takes into account the heat transfer enhancement with increasing vapour quality. The enhancement factor F is always greater than 1, because the fluid velocities are higher in two-phase flow than in single-phase liquid flow. Correlations of: Chen [33], Gungor and Winterton [23, 34], Yoshida [35], Jung - Radermacher [36] use the superposition model. The asymptotic model calculates the convective boiling heat transfer coefficient as follows:



hev  S hnb n  F hl n



1/ n

(45)

This model is best termed asymptotic as the value of the convective boiling heat transfer coefficient approaches the larger of the two components. This assures a smooth transition from the nucleate to the convective dominated flow regime. Steiner – Taborek [37] and Liu-Winterton [38] use the asymptotic model. The enhancement model is described as: h ev  E h l

(46)

where E is the enhancement factor, and hl is the single-phase heat transfer coefficient for liquid phase only. For horizontal tubes the enhancement factor E also depends on a third parameter, the Froude number Frl. Correlations of Kandlikar [22] and Shah [39] use this model. Kattan, et al. [40, 41] recently proposed a new correlation based on a flow boiling model for evaporation inside horizontal tubes. The general equation for this model for a tube of internal radius R is: R  dry h v  R 2 -  dry  h wet (47) h ev  2R

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The Chen correlation Chen [33] used the superposition model in principle. In his correlation Chen suggests to evaluate the nucleate boiling term with the Forster and Zuber correlation [42]:   k l0, 79  c 0pl, 45   l0, 49 T  Tsat 0,24  p sat Tw   p 0,75 hnb  0,00122  0,5 0, 29 0 , 24 0 , 24  w      h     l ev v

(48)

The suppression factor S was evaluated with an empirical correlation as:

S

1



1  2,56  106  Re l  F 1, 25

(49)



1,17

where the Reynold liquid phase number can be defined as:

Re l 

G 1  x d i

(50)

l

The enhancement factor F was evaluated as a function of the Martinelli parameter in turbulent flow Xtt by fitting the experimental data:  1   F  2 ,35 0 ,213  X tt  

0 ,736

(51)

This correlation was developed for vertical tubes, but it can also be used for horizontal tubes taking into account the influence of the gravitational forces by the Froude number. The single-phase heat transfer coefficient for liquid phase only can be evaluated by means of the Dittus Boelter equation:

hl 

kl 0,023 Re l0,8 Prl0, 4 di

(52)

The Gungor and Winterton correlations Gungor and Winterton [23] developed a correlation based on the same superposition model. The forced convection heat transfer enhancement factor F in this correlation depends on the boiling number Bo and on the Martinelli parameter Xtt: F  1  24000  Bo

1,1

where the Boiling number can be defined as:

 1  1,37  X tt

  

0 ,86

(53)

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 255

Bo 

q Ghev

(54)

The Forster and Zuber pool boiling correlation, used in the Chen correlation, was replaced by the Cooper correlation [26]. The suppression factor S was evaluated as a function of the liquid Reynolds number and of the enhancement factor F:

S

1 1  1,15  10

6

(55)

 F 2  Rel1,17

This correlation was obtained through a repeated regression analysis with an experimental data-base of about 4200 data points, varying all possible parameters. One year later Gungor and Winterton [34] proposed another similar correlation, that used the same enhancement factor F, but a different suppression factor S. In fact, they replace the term hnb S by the term 0.9 hl0.85. Thus, they suppose that the suppression factor S is influenced by hnb, which is contrary to Chen. 0 ,75   l  0 ,86  x   hev  hl   1  3000  Bo    1 x   v 

  

0 ,41 

  

(56)

Recently, Yu et al. [43] proposed a modification of the first Gungor and Winterton correlation. For the determination of the convective boiling heat transfer coefficient they used the average liquid film thickness as characteristic length instead of the tube diameter. The Yoshida correlation Yoshida et al. [35] used their experimental data to develop an empirical correlation. In this correlation they suggest to determine the nucleate pool boiling heat transfer coefficient with the Stephan – Abdelsalam [44] correlation:

hnb

k  207   l  db

  q  db      k l Tsat

  

0, 745

 v   l

  

0,581

Prl0,533

(57)

where db is the bubble diameter and can be evaluated as:   2  d b  0,0146    g  l   v  

where  is the contact angle and can be assumed 35°.

0,5

(58)

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The enhancement factor F is a function of the Martinelli parameter Xtt: F  1  2  X tt 0 ,88

(59)

The suppression factor S was found as a function of the two-phases Reynolds number ReTP (ReTP = F1.25 Rel) , the Boiling number Bo and the vapour quality. The Jung and Radermacher correlation Jung and Radermacher [36] proposed a correlation based on a large experimental database and on the same superposition model. In this correlation the nucleate pool boiling heat transfer coefficient was determined with the Stephan – Abdelsalam correlation [44]; the suppression factor S was expressed as a function of the Martinelli parameter Xtt and of the Boiling number Bo and can be expressed as: if Xtt  1

S  4048  X tt1,22  Bo 1,13

(60)

if 1 <Xtt < 5

S  2 ,0  0 ,1  X tt0 ,28  Bo  0 ,33

(61)

The enhancement factor F was expressed as a function of the Martinelli turbulent parameter Xtt:  1   F  2 ,37 0 ,29  X tt  

0 ,85

(62)

The Steiner and Taborek correlation Steiner and Taborek [37] proposed a correlation based on 13000 data points obtained from experiments with vertical tubes, based on the asymptotic model with the exponent n set to 3. In this correlation the convective boiling heat transfer coefficient was evaluated with the Gnielinski equation [45] based on the total flow as liquid:     Re lo  1000 Prl   k  hlo  l  8 di   2/3  Prl  1  1  12,7 8  



where  

0,3164 4

Re lo

and Re lo 

Gd i

l



(63)

.

The enhancement factor F was derived as a function of the vapour quality and of the density ratio l/v:

Convective Boiling Heat Transfer of Pure and Mixed…

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 F  1  x 1,5  1,9  x 0 ,6  

   l  v

  

0 ,35  1,1

  

(64)

The nucleate boiling term was based on the Gorenflo correlation [21]: k hnb  0 ,1   l  db

  l      v

  

0 ,156

 A0 ,674  B 0 ,371  C 0 ,35  D  0 ,16

(65)

where the parameters can be evaluate as follow: A

B

qo d b kl Tsat

hev  d b2   l2  c 2pl k l2

 kl C    l  c pl 

D

(66)

(67)

2

 l     db 

 l  c pl

(68)

(69)

kl

The bubble diameter can be evaluated with equation (58). In the equation of Steiner and Taborek no suppression factor is used, only a correction factor which compensates the differences between pool boiling and flow boiling conditions. This parameter includes the influence of the pressure, the heat flux, the tube diameter and the surface roughness and can be evaluated as:  q S  F ( M )    qo

where:

F M   0,36  M 0,27 q o = 20 kW/m2 for refrigerant fluids;

 d  Fd   i   0,01 

0, 4

;

n

   Fd  F pf 

(70)

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n  0,8  0,1  e1,75Pr ;

  1,7 F pf  2,816  Pr 0, 45   3,4   1  Pr 7  

 3,7   Pr    

The correlation of Liu and Winterton [38] used this approach with an exponent n of 2. The factors S and F were determined based on the analysis of a database containing 4183 experimental results from tests with 9 fluids. The enhancement factor F was expressed as a function of the vapour quality, the liquid Prandtl number Prl, and the vapour and liquid density. The suppression S factor was found as an inverse function of the enhancement factor F and of the liquid Reynolds number Rel. The Shah correlation Shah [39] proposed an enhancement model for flow boiling in tubes. The heat transfer coefficient can be evaluated in the form: hev  hl  ( Co , Bo , Fr )

(71)

where Co is the convective number defined as: 1 x  Co     x 

0 .8

 v   l

  

0 .5

(72)

and Fr is the liquid Froude number:

G2 Fr  2  l gdi

(73)

The single phase coefficient for the liquid phase flowing alone in the tube can be evaluated with equation (52). The Convection number Co is a replacement of the Martinelli parameter Xtt, because the viscosity effect was found to have no significant influence. The Boiling number Bo characterized the nucleate boiling term, while the convection number Co characterized the convective boiling term. The correlation in term of these variables was specified in graphical form. Later Shah has recommended the following computational representation of his correlation for horizontal tubes: Ns = Co

for Fr ≥ 0,04

(74)

Ns = 0,38 Fr-0.3 Co

for Fr < 0,04

(75)

FS = 14,7

for Bo > 11·10-4

(76)

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for Bo < 11·10-4

FS = 15,4

(77)

cb=1,8 Ns-0,8

(78) for Bo  0 ,3  10 4 for Bo  0 ,3  10 4

 nb  230Bo 0 ,5   nb  1  46 Bo 0 ,5

For N >1

For 0,1 < N  1

nb  Fs  Bo 0,5 e 2,74N

For N  0,1 nb  Fs  Bo 0,5 e 2,47 N  is the larger of cb and nb.

0 ,1

(79)

(80)

0 ,15

(81)

The Kandlikar correlation Kandlikar’s correlation [22] expands the Shah correlation. In this correlation the enhancement factor E is also a function of the Boiling number Bo, the Convection number Co, the Froude number Frl and of a fluid dependent parameter. The evaporating fluid heat transfer coefficient can be evaluated as:





hev  hl  C1  Co C 2  25Fr C5  C3  Bo C4  Fk



(82)

The constants C1 through C5 are given in Table 4.1. The factor Fk is a fluiddependent parameter, values of which are listed for various fluid in Table 4.2. Table 4.1 Constants in Kandlikar’s correlation Co < 0,65

Co ≥ 0,65

(convective region)

(nucleate boiling region)

C1

1,1360

0,6683

C2

-0,9

-0,2

C3

667,2

1058

C4

0,7

0,7

C5

0,3

0,3

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Table 4.2 Fk values for different fluids. Fluid

Fk

Fluid

Fk

R-11

1,30

R-152a

1,10

R-12

1,50

R-13BI

1,31

R-22

2,20

Water

1,00

R-113

1,30

Nitrogen

4,70

R-114

1,24

Neon

3,50

For fluid other than those listed in Table 4.2, Kandlikar recommends that Fk be estimated as the multiplier that must be applied to the Forster and Zuber correlation to correlate pool boiling data for the fluid of interest. The Kattan-Thome-Favrat correlation Kattan, et al. [40, 41] recently proposed a new correlation based on a flow boiling model for evaporation inside horizontal tubes. The authors suggest that each of the previous mentioned heat transfer models has a limited range of applicability, essentially for annular flow. Therefore they develop a flow pattern map based heat transfer model. The general equation for this model for a tube of internal radius R is:

h ev 

R  dry h v  R 2 -  dry  h wet 2R

(83)

The heat transfer coefficient on the wetted part of the tube surface (h wet) was obtained with an asymptotic equation with an exponent n of 3:



h wet  h cb   h nb  3



3 1/ 3

(84)

In this equation hnb was calculated with the Cooper correlation and hcb with an empirical correlation determined by the authors. This equation for hcb includes the liquid film Reynolds number, based on the average liquid velocity in the annular film, which is a local function of the vapour quality, the annular liquid film thickness and the void fraction . This correlation modelling the liquid flow as a film eliminates the need for an enhancement factor F, which is used in other correlations. hcb  0,0133Re0,69 PrL0, 4

where the liquid film Reynolds number is:

kl



(85)

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Re 

4  G  1  x    1      L

(86)

The void fraction can be determined with the Rouhani-Axelsson equation (16). The liquid film thickness can be evaluated as follows:



AL A  1      D  1      R  2     dry R  2     dry 2  2     dry













(87)

The dry angle dry defines the flow structure. In stratified flow equals the stratified angle strat and was calculated iteratively from equation (22). Obviously for annular and intermittent flows, where the tube perimeter is continuously wet, dry =0. A more complicated approach is used to predict dry for stratified wavy flows [13]. The heat transfer coefficient for the dry perimeter was determined with the Dittus Boelter correlation assuming tubular flow over the dry perimeter of the tube: hv  0,023Re 0v ,8 Prv0, 4

where: Rev 

kv di

G  x  di v  

(88)

(89)

In this correlation no boiling suppression factor was included. Comparison of experimental results with existing correlations The experimentally determined evaporative heat transfer coefficients have been compared with the results of theoretical correlations from literature[46]. The selected correlations were published by Chen [33], Gungor and Winterton [23, 34], Jung and Radermacher [36], Kandlikar [22], Yoshida et al. [35], Steiner and Taborek [37], Shah [39] and Kattan et al. [40, 41]. Recently, Yu et al. [43] proposed a modification of the first Gungor and Winterton correlation. In the Kandlikar correlation a fluid dependent parameter Fk is used, which enhance the nucleate boiling term. This parameter is not available for most of the refrigerant fluids. In the present study this parameter has been obtained by fitting of the experimental data. The test conditions of each experiment have been applied to the above-mentioned correlations, so the local variation of the heat transfer coefficient could be compared with the experimental data. Examples of the variation of the heat transfer coefficient along the test section for evaporation with R410A are presented in the Figures 4.1 and 4.2 calculated with different correlations. Similar trends have been obtained for different mass fluxes and with other refrigerant fluids. Figure 4.1 depicts the experimental and theoretical results of R410A for a mass flux of 381 kg/m2s , an evaporating pressure of 11.5 bar and a heat flux of 18.1 kW/m2.

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Experimental Chen Kandlikar Shah

Steiner Jung-Rader. Thome

4

8000

2

hev (W/m K)

1 10

Yoshida Gung-Wint.86 Gung-Wint.87 Gung-Wint. mod.

Greco

6000 4000 2000 0 0

0.2

0.4 0.6 Vapour quality

0.8

1

Fig. 4.1 Heat transfer coefficients of R410A at G = 381 kg/m2s and pev = 11.5 bar.

It is shown that the experimental heat transfer coefficients first decrease with the vapour quality and then increase, whereas the theoretical heat transfer coefficients always increase with the vapour quality. The experimental tests with higher heat fluxes and higher evaporating pressures showed two distinct heat transfer regions during evaporation. In the first region, occurring at low qualities, where nucleate boiling was the dominant the heat transfer coefficients decreased with decreasing influence of the nucleate boiling. With increasing vapour quality the annular liquid film became thinner and the wall-to-interface temperature difference needed to drive the heat flux was reduced. The smaller wall superheat reduced also the number of active nucleation sites. The second important region was the convective evaporation regime, characterized by enhanced heat transfer coefficients with increased vapour qualities. Figure 4.2 depicts the experimental and theoretical results of R410A with a mass flux of 363 kg/m2s, an evaporating pressure of 4.83 bar and a heat flux of 15.0 kW/m2. In this case both the experimental and the theoretical heat transfer coefficients increase with increasing vapour quality. Corresponding to this operating conditions (low pressure and low heat flux), convection is the dominant heat transfer mechanism. As the flow proceeds downstream and vaporization occurs, the void fraction rapidly increases, decreasing the density of the liquid-vapour mixture. For this reason the flow velocity was increased and the convective heat transfer from the heated tube wall was enhanced. Figure 4.3 shows R404A heat transfer coefficients calculated with the Jung and Radermacher correlation as a function of the vapour quality varying the evaporation pressure for an almost constant refrigerant mass flux of 293 kg/m2s.

Convective Boiling Heat Transfer of Pure and Mixed…

1 10

Experimental Chen Kandlikar Shah

4

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 263

Yoshida Gung.-Wint.86 Gung.-Wint. 87 Gung.-Wint. mod.

Steiner Jung.-Rad. Thome

2

hev (W/m K)

8000 6000 4000 2000 0 0

0.2

0.4 0.6 Vapour quality

0.8

1

Fig. 4.2 Heat transfer coefficients of R410A at G = 363 kg/m2s and pev = 4.83 bar.

7000 6000

2

hev (W/m K)

5000 4000 3000

pev= 12.1 bar pev = 9.90 bar

2000

pev = 7.20 bar pev = 5.23 bar

1000

pev = 3.75 bar

0 0

0.2

0.4 0.6 Vapour quality

0.8

1

Fig. 4.3 Heat transfer coefficients of R404A evaluated with the Jung and Radermacher correlation as a function of the vapour quality for different evaporation pressures at G=293 kg/m 2s.

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1.2 10

4

1 10

4

8000

2

hev (W/m K)

The experimental results show an increase of the heat transfer coefficients with increasing pressure and heat flux for a constant refrigerant mass flux due to an increase in the nucleate boiling contribution to the heat transfer coefficient. Whereas, the heat transfer coefficients predicted with the correlation decrease with increasing evaporating pressure. Figure 4.4 shows the heat transfer coefficients of R404A calculated with the Jung and Radermacher correlation as a function of the vapour quality varying the evaporative pressure at an almost constant refrigerant mass flux of 1074 kg/m2s.

pev = 11.7 bar

6000

pev = 6.90 bar pev = 4.30 bar

4000 2000 0 0

0.2

0.4 0.6 Vapour quality

0.8

1

Fig. 4.4 Heat transfer coefficients of R404A evaluated with the Jung and Radermacher correlation as a function of the vapour quality for different evaporation pressures at G=1074 kg/m 2s.

In this case both the experimental and the theoretical heat transfer coefficients show a similar trend. The local heat transfer coefficients increased with increasing evaporation pressure until a vapour quality of about 20 % was reached. For higher vapour qualities the influence of the evaporation temperature became weaker and the difference between the heat transfer coefficients became smaller. For higher refrigerant mass fluxes the convective contribution to the heat transfer coefficient is dominant, therefore the influence of the evaporating pressure became weaker and the heat transfer coefficients are only higher for higher pressure at low vapour qualities. For lower refrigerant mass fluxes the heat transfer coefficients are more influenced by nucleate boiling. The experimental heat transfer coefficients decreased for higher vapour qualities, whereas the theoretical results don’t show this trend. Indeed, the KattanThome-Favrat map clearly shows that starting from a vapour quality of 49% a mist flow occurs. A statistical comparison of the standard deviation, the mean deviation and the average deviation has been carried out for all experiments and for each correlation. Table 4.3 depicts the statistical comparison for each refrigerant fluid.

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Table 4.3 A statistical comparison of the experimental results with the selected correlations. Correlation

Chen

Kandlikar

Shah

Yoshida et al.

Gung.-Wint. 1986

Gung.-Wint. 1987 Yu et al.

Steiner-Taborek

Jung.- Rader.

Thome et al.

Deviation %

R22 R134a R507

R404A R410A R407C R417A Average %

Standard

78

74

63

65

57

122

89

78

Mean

56

53

46

46

35

94

68

57

Average

31.1

33

36

36

23

-80

30

16

Standard

37

32

29

38

35

70

80

46

Mean

28

24

21

28

25

55

58

34

Average

-3.3

2.3

-1.9

-5.1

13

-45

0

-5.7

Standard

45

47

49

42

38

70

70

52

Mean

34

35

37

31

28

55

51

39

Average

7.9

11

13

7.0

-4.4

-70

30

-0.79

Standard

65

55

69

50

43

80

90

65

Mean

46

39

49

30

23

60

68

45

Average

29

29

33

27

17

-83

30

12

Standard

89

70

71

46

41

60

60

62

Mean

64

51

52

36

23

43

42

44

Average

21

10

23

32

22

-50

20

11.1

Standard

53

60

58

42

36

50

50

50

Mean

38

43

42

30

28

37

35

36

Average

7.9

30

12

5.7

1.7

-80

40

2.5

Standard

59

61

55

55

47

66

69

59

Mean

44

41

39

55

38

47

50

44

Average

31

33

35

47

31

-69

-51

8.1

Standard

110

122

71

61

52

155

98

95

Mean

79

83

60

54

48

112

72

72

Average

-43

-11

-10

55

40

-88

-72

-18

Standard

49

80

55

47

39

80

70

60

Mean

37

59

40

34

29

59

51

44

Average

20

20

23

32

14

-77

30

8.9

Standard

63

65

60

58

49

39

59

56

Mean

49

55

51

46

38

29

44

44

Average

32

30

36

36

29

25

32

31

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This statistical comparison shows that the best-fitting correlation is that of Kandlikar. Acceptable results were also obtained with the second Gungor and Winteron correlation (1987) and the Shah correlation. The worst fitting correlations are those of Chen and of Steiner and Taborek, because both correlations have been developed for flow boiling in vertical tubes. Therefore the conversion of the model for the use with horizontal tubes, by adding a flow stratification criterion without any consideration of the two-phase flow structure, is not sufficient. Most of the correlations strongly overpredict the experimental data of the zeotropic mixture R407C. The reason for the observed discrepancies consists in none of the correlations taking into account: the effect of composition on nucleation, a significant change in physical properties of the mixture with composition and the retardation of vapor-liquid exchange and evaporative mechanisms. The Kandlikar correlation, that is the best-fitting of our experimental data. This correlation contains a fluid dependent parameter, Fk, which multiplies the nucleate boiling term. This parameter has no physical significance. Furthermore, the nucleate boiling term is independent of the reduced pressure (p/pc). Based on our experimental data a modification of the Kandlikar correlation is proposed. Modifications have been made to the original model to predict the local heat transfer coefficients obtained with the test facility. As a result of a curve fitting of our experimental data the empirical constant C3 has been slightly modified (Table 4.4). In our modification of the Kandlikar correlation the fluid dependent parameter has been eliminated (Fk =1). Furthermore, a pressure correction factor has been introduced, for replacing the original Fk factor. The pressure correction factor Fp multiplies the nucleate boiling term and takes into account the influence of the reduced pressure. This pressure correction factor Fp can be expressed as follow:

 p Fk  Fp  3.73    pc 

n

    8.83  5.66   p      2.53  4.26    p    pc   1 -      pc   

 p n  1.1 - 2.8    pc 

(90)

(91)

The modified correlation shows a much better agreement with the experimental results than all other correlations. A statistical comparison of the standard deviation, the mean deviation and the average deviation has been carried out for all the experiments and for the modified Kandlikar correlation. Table 4.5 shows the statistical comparison for all the working fluids.

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Table 4.4 Constants in Kandlikar’s correlation. Co<0.65

Co >0.65

(convective region)

(nucleate boiling region)

C1

1.1360

0.6683

C2

-0.9

-0.2

C3

667.2

1058

C4

0.7

0.7

C5a

0.3

0.3

Fk

0.74 Fp

0.74 Fp

Fp

 p Fp  3.73   pc

  

n

   5.66   2.53  4.26   p  1 -     pc  

 p n  1.1 - 2.8   pc

a

  

   p     pc  

8.83

 p  Fp  3.73    pc

  

n

   5.66   2.53  4.26   p  1 -     pc  

 p n  1.1 - 2.8   pc

   p     pc  

  

  

C5 = 0 for vertical tubes or horizontal tubes with Frl > 0.04

Table 4.5. A statistical comparison of the modified Kandlikar correlation with the experimental data Deviation % Average % Standard Mean Average

18.5 14 -3.84

The standard deviation has been reduced by more than 100% and the mean deviation by 60% when using the modified model instead the original one. The modified model has not the intention to replace the original model, which was developed by using results from many experiments, with many different fluids, under varied operating conditions. The modified model is valid only for the for the refrigerant fluids tested for the test conditions mentioned before.

8.83

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Conclusions The experimental results were compared with the theoretical results of several correlations selected from literature to verify their suitability to estimate the local heat transfer coefficients. The selected correlations were published by Chen, Gungor and Winterton, Jung and Radermacher, Kandlikar, Yoshida et al., Steiner and Taborek, Shah, Kattan et al. Gungor and Winterton proposed two correlations, the first in 1986 and a second in 1987. Recently, Yu et al. proposed a modification of the first Gungor and Winterton correlation. The following general conclusions can be drawn from this comparison: i)

ii)

iii) iv) v)

vi)

the low pressure heat transfer coefficients are almost overestimated by all correlations. However, it should be noted, that most experiments carried out with low pressures referred to low vapour qualities. Many correlations show a good agreement with the experimental heat transfer coefficients for the annular flow region, whereas are rather unsatisfactory for the intermittent flow regime. Many correlations make a poor prediction of the heat transfer coefficients at low refrigerant mass flux. The experimental results show that in this case the nucleate boiling regime is dominant. The influence of the pressure on the heat transfer coefficients is poorly accounted for. All correlations (except that of Thome et al.) do not accurately predict the heat transfer coefficients when the upper part of the tube wall is not wetted. If the mist-flow regime is dominant, i.e. at high pressures and high heat fluxes, the predicted heat transfer coefficients show higher deviations as compared with the experimental results. Most of the correlations strongly overpredict the experimental data of the zeotropic mixture R407C.

The comparison between the experimental results and the theoretical data obtained with the above mentioned correlations shows that the best-fitting correlation is that of Kandlikar. Acceptable results are also given by the second Gungor and Winterton correlation and the Shah correlation. A modification of the Kandlikar correlation has been proposed in the present paper to predict the local heat transfer coefficients obtained with the test facility. The modified correlation describes the experimental results much better than all other described correlations.

Experimental Local Pressure Drops of Pure and Mixed Refrigerants during Convective Boiling in Horizontal Flow Experimental results As already stated, in this work, the experiments are performed for seven pure and mixed refrigerants (R22, R134a, R404A, R410A, R507, R407C, R417A) varying the evaporating pressure, the heat flux, the refrigerant mass flux.

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The objective of the present experimental study are: (i) to develop an accurate flow boiling pressure drops database during evaporation in order to gather new design data for heat exchanger design with new fluids; (ii) to investigate in depth the influence of vapour quality, evaporating pressure, mass flux on pressure drops; (iii) to compare pressure gradients of R134a, R507, R404A, R410A and R407C to R22 (which they replace) under the same operating conditions [47]. From figure 5.1 to figure 5.7, the pressure gradients during flow boiling are reported for R22, R134a, R404A, R410A, R407C, R507, R417A as a function of vapour quality obtained by varying the refrigerant mass flux at an almost constant evaporating pressure of 7 bar. The pressure drop is evaluated as the pressure drop per unit length between the pressures taps. Similar trends are observed in all the experiments with similar operating conditions.

R22 - p = 7 bar 30 2

G = 351 kg/sm 2 G = 447 kg/sm 2 G = 476 kg/sm 2 G = 660 kg/sm 2 G = 738 kg/sm 2 G = 936 kg/sm 2 G = 1082 kg/sm

25

p/z [kPa/m]

20

15

10

5

0 0,0

0,2

0,4

0,6

Vapor quality Fig. 5.1. R22 pressure gradient data during flow boiling at pev = 7.0 bar.

0,8

1,0

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R134a - p = 7 bar 30 2

G = 290 kg/sm 2 G = 488 kg/sm 2 G = 586 kg/sm 2 G = 651 kg/sm 2 G = 780 kg/sm 2 G = 948 kg/sm 2 G = 1074 kg/sm

25

p/z [kPa/m]

20

15

10

5

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality Fig. 5.2. R134a pressure gradient data during flow boiling at pev = 7.0 bar.

R404A - p = 7 bar 30 2

G=483 kg/sm 2 G=808 kg/sm 2 G=1074 kg/sm

p/z [kPa/m]

25

20

15

10

5

0 0,0

0,2

0,4

0,6

0,8

Vapor quality

Fig. 5.3. R404A pressure gradient data during flow boiling at pev = 7.0 bar.

1,0

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R410a - p = 7 bar 30 2

G = 360 kg/sm 2 G = 573 kg/sm 2 G = 802 kg/sm 2 G = 1075 kg/sm

25

p/z [kPa/m]

20

15

10

5

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality Fig. 5.4. R410A pressure gradient data during flow boiling at pev = 7.0 bar.

R407C - p = 6 bar 30 2

G = 376 kg/sm 2 G = 593 kg/sm 2 G = 1064 kg/sm

25

p/z [kPa/m]

20

15

10

5

0 0,0

0,2

0,4

0,6

0,8

Vapor quality

Fig. 5.5. R407C pressure gradient data during flow boiling at pev = 6.0 bar.

1,0

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R507 - p = 7 bar 30 2

G = 285 kg/sm 2 G = 361 kg/sm 2 G = 489 kg/sm 2 G = 584 kg/sm 2 G = 655 kg/sm 2 G = 944 kg/sm 2 G = 1060 kg/sm

25

p/z [kPa/m]

20

15

10

5

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

Fig.5.6. R507 pressure gradient data during flow boiling at pev = 7.0 bar.

R417-p=7 bar 2

30

G =1127 kg/s m

2

G = 703 kg/s m

2

G = 527kg/s m

25

2

G = 346 kg/s m

2

G = 203 kg/s m

p/ z [kPa/m]

20

15

10

5

0 0

0,2

0,4

0,6

0,8

Vapour quality

Fig. 5.7 R417A pressure gradient data during flow boiling at p ev = 7.0 bar.

1

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As seen in the figures, the pressure drop increases with the quality. The total pressure drop is mainly caused by the frictional pressure drop. It involves not only the transfer of momentum between fluid and wall, but also the transfer of momentum between the individual phases. This contribution increases with the vapour quality to a maximum between 70-90% and then decreases to the pressure drop of the subcritical vapour flow. Indeed, as the flow proceeds downstream and vaporization takes place, the void fraction increases, thus decreasing the density of the liquid-vapour mixture. As a result, the flow accelerates increasing the pressure drop. The pressure drop depends upon the flow regime throughout the evaporation. In fact for low qualities (less than 40%) the flow regime is, in most cases, intermittent. This type of flow regime is characterised by vapour bubbles in the liquid phase, and the pressure drops are mainly influenced from the friction of the liquid along the tube walls. In this flow region the gradients are less emphasized and they often show some anomalies, caused by the distributions of liquid and vapour phase in this flow. When the quality increases the flow tends to become annular and slope of the curves representing the pressure drop varying the quality increases at fixed refrigerant mass flux. When the quality is more than 80%, the liquid’s thickness dries, the friction reduces and as a consequence pressure drop decreases.

2

R22 - G = 570 kg/s m 25 p = 5.2 bar p = 5.78 bar p = 8.20 bar p = 9.9 bar

p/z (kPa/m)

20

15

10

5

0 0

0,2

0,4 0,6 Vapour quality

0,8

1

Fig. 5.8. R22 pressure gradient data during flow boiling at G = 570 kg/s m2.

The figures clearly show that at fixed pressure, pressure drop increases significantly with the increase of the mass flux. For a given quality, the pressure gradient is approximately proportional to G 1,5 ÷ 1.8 for all refrigerant fluids. With low mass fluxes (< 400 kg/sm2), when the flow regime is annular, gradients are no greater than 5 kPa/m. While at high mass fluxes (> 1000 kg/sm2), when the flow regime is intermittent, the gradients are over 20 kPa/m.

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From figure 5.8 to figure 5.14, the pressure gradients during flow boiling are reported for R22, R134a, R404A, R410A, R407C, R507, R417A as a function of vapour quality obtained by varying the evaporating pressure at an almost mass flux. Similar trends are observed in all the experiments with similar operating conditions. Figures clearly show that the pressure drops strongly increase with the decreases of the evaporating pressure. Indeed, as the evaporating temperature decreases, the vapour density strongly decreases. Therefore, the lower average density of the vapour-liquid mixture leads a greater velocity at any given refrigerant mass flux. Furthermore, the liquid viscosity increases with the decrease of the evaporating temperature. Both effects lead to an increase of the pressure drops with the decrease of the evaporating pressure. The experimental data allow the comparison of the pressure gradients for the tested fluids at equal pressure and refrigerant mass-flux. It can be shown that the pressure drop of R22 is significantly higher as compared to all the other fluids (with mean values of +4 % with R407C, +13% with R410A, +31% with R507, +34% with R404A, +44% with R417A, +55 % with R134a). This is a direct consequence of the greater R22 liquid viscosity. Furthermore R22 shows a low vapour phase density; therefore the lower mean density of the vapour-liquid mixture of R22 leads to a higher velocity at a fixed refrigerant mass flux. The experimental data also indicate that the difference between pressure gradients decreases decreasing the refrigerant mass flux and increasing the evaporating temperature. R134a shows lower two phase pressure gradients as compared to all the other fluids. This is a consequence of the higher R134a vapour and liquid density that leads to a lower velocity at a fixed refrigerant mass flux.

2

R134a - G = 575 kg/s m 25 p = 9.82 bar p = 7.30 bar p = 5.30 bar p = 4.45 bar p = 3.11 bar p = 2.29 bar

p/z (kPa/m)

20

15

10

5

0 0

0,1

0,2 0,3 Vapour quality

0,4

0,5

0,6

Fig. 5.9. R134a pressure gradient data during flow boiling at G = 575 kg/s m2.

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2

R404A - G = 490 kg/sm 25 p = 4.30 bar p = 7.40 bar

p/z (kPa/m)

20

15

10

5

0 0

0,2

0,4 0,6 Vapour quality

0,8

1

Fig. 5.10. R404A pressure gradient data during flow boiling at G = 490 kg/s m2.

2

R410 - G= 580 kg/sm 25 p = 4.90 bar p = 7.20 bar p = 11.6 bar

p/z (kPa/m)

20

15

10

5

0 0

0,2

0,4 0,6 Vapour quality

0,8

Fig. 5.11. R410A pressure gradient data during flow boiling at G = 580 kg/s m2.

1

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2

R407C - G = 503 kg/sm 25 p = 3,59 bar p = 3,74 bar p = 4,55 bar p = 4,57 bar p = 5,65 bar p = 7,66 bar p = 10,23 bar

p/z (kPa/m)

20

15

10

5

0 0

0,2

0,4 Vapour quality

0,6

0,8

1

Fig.5.12. R407C pressure gradient data during flow boiling at G = 503 kg/s m2.

2

R507 - G = 570 kg/sm 25 p = 12.1bar p = 10.0 bar p = 7.50 bar p = 5.60 bar

p/z (kPa/m)

20

15

10

5 0 0

0,2

0,4

0,6

0,8

Vapour quality

Fig. 5.13. R507 pressure gradient data during flow boiling at G = 570 kg/s m2.

1

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2

R417a - G = 507 kg/sm 25 p = 3.96 bar p = 4.67 bar p=5.92 bar p = 7.46 bar p=9.70 bar

p/z (kPa/m)

20

15

10

5

0 0

0,2

0,4 0,6 Vapour quality

0,8

1

Fig. 5.14. R417A pressure gradient data during flow boiling at G = 507 kg/s m2.

An Overview of the Pressure Drop Correlations for Convective Boiling in Plain Tubes Introduction An accurate prediction of pressure drop during two-phase flow of pure and mixed refrigerants is essential for the design of industrial heat exchangers including evaporators, condensers and two phase refrigerant transfer lines. Many predictive methods for evaluating pressure losses for two phase flow originate from experimental tests carried out with water - air, oil - air or water - steam mixtures. These methods are originated for power plant applications. The latter is characterised by large pipe diameter heat exchangers, vertical geometry, and low quality range; whereas refrigeration and heat pump industry deals with small diameter evaporators, horizontal geometry and the quality range of interest is typically 20 - 100%. Nonetheless, the same predictive methods are currently used in refrigeration and heat pumps applications, as well. The pressure drop during convective boiling inside horizontal tubes is the sum of two contributions, frictional and momentum pressure drop:

ptot = pf + pm

(92)

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The momentum pressure drop results from the change in momentum of the two phases. This causes a change of mass and velocity in each phase caused by evaporation and, consequently, also of the momentum flux of both phases. This contribution, from the balance of momentum in each phase, can be calculated with the following equation:

 1  x 2  1  x 2 x2  x2             1     v    1     v     out  L in   L

pm  G 2 

(93)

In vertical tubes, there is also the drop in pressure based upon gravity, which is also called the geodetic pressure drop. In the thermodynamically efficient evaporators, the ratio L/di would be typically in the range of 500 - 1000. For this range the momentum pressure drop is small in comparison to the frictional pressure drop, thus frictional pressure drop alone would constitute most of the two phase pressure drop in the evaporators. The frictional pressure drop results from the shear stress between the flowing fluid and the channel wall. It involves not only the transfer of momentum between fluid and wall, but also the transfer of momentum between the individual phases. The two processes cannot be measured separately and can only be estimated for simple flows. For the calculation of the frictional pressure drop, it is advantageous to define several parameters that are suitable for the description of the two phase pressure drop as well as of the quality. The frictional pressure drop is often reduced to pressure drop of single phase flow by using the following parameters, first introduced by Lockhart and Martinelli [48]:  dp / dz  fr   lo     ( dp / dz )lo 

1/ 2

 dp / dz  fr   vo     dp / dz vo   dp / dz  fr    ( dp / dz )l 

1/ 2

1/ 2

(94)

l  

 dp / dz  fr  v     ( dp / dz )v 

1/ 2

Here (dp/dz)fr is the frictional pressure drop of the two phase flow, (dp/dz)l is the frictional pressure gradient that would result if the liquid flowed alone through the channel; (dp/dz)v is the frictional pressure gradient that would result if the vapour flowed alone through the channel; (dp/dz)lo is the frictional pressure gradient that would

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result if the liquid flowed alone through the channel at the same total mass flow rate; (dp/dz)vo is the frictional pressure gradient that would result if the vapour flowed alone through the channel at the same total mass flow rate; l, v, lo, vo are the two phase multiplier defined by equations (94). If these factors are known, then only the pressure drops of the individual phases need to be determined in order to calculate the frictional pressure drop of the two phase flow. For establishing the frictional pressure drop of the two phase flow is possible first determining the frictional pressure drop of liquid assuming that the entire mass of fluid is flowing as liquid through the channel. According to a Blasius type equation, the frictional pressure drop of liquid flow can be evaluated from: 2 f lo G 2  dp     di L  dz  lo

(95)

where the friction factor can be evaluated:

f lo  M Re lo

n

(96)

Here the two constants M and n can be evaluated as: M = 16 and n = 1 for laminar flow (Relo < 2000) and M = 0.079 and n = 0.25 turbolent flow (Relo ≥ 2000). The liquid only Reynolds number can be defined as: Relo 

Gdi

l

(97)

For establishing the frictional pressure drop of the two phase flow is possible first determining the frictional pressure drop of vapour assuming that the entire mass of fluid is flowing as vapour through the channel. According to a Blasius type equation, the frictional pressure drop of vapour flow can be evaluated from: 2 f voG 2  dp      di  v  dz  vo

(98)

where the friction factor can be evaluated: f vo  M Revo  n

(99)

Here the two constants M and n can be evaluated as: M = 16 and n = 1 for laminar flow (Revo < 2000) and M = 0.079 and n = 0.25 turbolent flow (Revo ≥ 2000). The vapour only Reynolds number can be defined as:

280 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

Revo 

Greco

G di

v

(100)

For establishing the frictional pressure drop of the two phase flow is possible first determining the frictional pressure drop of liquid assuming that the liquid phase flows alone through the channel with its mass flow rate. According to a Blasius type equation, the frictional pressure drop of liquid can be evaluated from: 2 f l G 2 ( 1  x )2  dp     di  L  dz  l

(101)

where the friction factor can be evaluated: f l  M Rel  n

(102)

Here the two constants M and n can be evaluated as: M = 16 and n = 1 for laminar flow (Rel < 2000) and M = 0.079 and n = 0.25 turbolent flow (Rel ≥ 2000). The liquid Reynolds number can be defined as: Rel 

G( 1  x ) di

l

(103)

For establishing the frictional pressure drop of the two phase flow is possible first determining the frictional pressure drop of vapour assuming that the vapour phase flows alone through the channel with its mass flow rate. According to a Blasius type equation, the frictional pressure drop of vapour can be evaluated from: 2 fvG 2 x 2  dp     di  v  dz  v

(104)

where the friction factor can be evaluated:

fv  M Re v n

(105)

Here the two constants M and n can be evaluated as: M = 16 and n = 1 for laminar flow (Rev < 2000) and M = 0.079 and n = 0.25 turbulent flow (Rev ≥ 2000). The vapour Reynolds number can be defined as: Rev 

G x di

v

(106)

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 281

The frictional pressure drops for the heterogeneous model, where the two phases are assumed to flow separately from one another and to have different velocities, can be calculated with the following correlations. Lockhart and Martinelli correlation. In this correlation [48] the frictional pressure drop can be determined by using a correction factor from the frictional pressure drop of the single phases, considering the liquid or the vapour phase flowing alone in the channel with their actual flow rates. From this, the two phase multiplier l2 and v2 for the liquid and the vapour phase, are respectively given:

p f   l2 pl

p f   v2 pv

(107)

(108)

where:

pl  4 f l 

1 1  G 2  1  x 2  di 2l

pv  4 f v 

1 1  G2  x2  di 2v

(109)

(110)

The liquid and vapour friction factor are functions of the liquid and vapour Reynolds numbers, and are given for turbulent flow with the following equations:

fl 

fv 

0.079 Rel0.25 0.079 Rev0.25

(111)

(112)

The two-phase multiplier factors are calculated as follows:

 l2  1 

C 1  X X2

 v2  1  CX  X 2 The values of the constant C is given in the following Table 6.1.

(113)

(114)

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Table 6.1 Constant C values. Vapour phase flow

Liquid phase flow

C

laminar

laminar

5

laminar

turbulent

10

turbulent

laminar

12

turbulent

turbulent

20

Laminar flow is assumed if Re <1000, and turbulent flow occurs if Re > 2000. No certain prediction can be made for transition region, to be safe, one should assume the presence of turbulent flow. Martinelli and Nelson correlation Because the Lockhart-Martinelli multipliers were determined from experiments at atmospheric pressure, Martinelli and Nelson [49] extended the region of validity of the procedure up to the critical pressure. In this correlation the frictional pressure drop is determined by using a correction factor from the frictional pressure drop of the single phases, considering the liquid and the vapour phase flowing alone in the channel with the total mass flow rate. In these correlations the following two phase multiplier Lo2 and Go2 are defined:

 dp   dp      dz  lo  dz  fr

(115)

 dp   dp      dz  vo  dz  fr

(116)

 lo2 

2  vo 

where (dp/dz)lo and (dp/dz)vo are the pressure drop of the entire mass flow rate, which is calculated with the liquid and vapour properties, respectively. Martinelli and Nelson assumed in their correlation that the relationship between lo2 and l2 was:

 lo2   l2 1  x 2  n

(117)

where l was found with the Lockhart and Martinelli results for atmospheric pressure. From experimental tests, they determined in graphical form the function between the two phase multiplier lo2and the Martinelli parameter X.

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Friedel correlation This correlation [50] utilizes the two-phase liquid multiplier considering the liquid phase flowing alone in the channel with the total mass flow rate, defined as:

 2Lo  C F 1 

3.24  C F 2 Frh0.045  We L0.035

(118)

where

   C F 1  1  x 2  x 2  L    v 

CF 2  x

0.78

0.224   L 

1  x 

0.91

   v

f vo   f Lo 

 v   L

  

0.19

(119)

   1  v L 

  

0.7

(120)

The Froude number is defined as:

G2 Frh  gd i  h2

(121)

where h is the mean liquid vapour density based on the homogeneous model:  x 1 x    h     L   G

1

(122)

The liquid Weber number is defined as:

Wel 

G 2 di

(123)

 h

The ratio between the vapour and the liquid friction factor for both phases in turbulent flow is given: f vo   v  f lo   l

  

0.25

Grønnerud correlation In this correlation [51] the two phase multiplier is given as:

(124)

284 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

 l2

   dp   1      L  dz  fr   v 

where:



 L     v 

Greco

   1    

0.25 



(125)



 dp  0.5 1.8 10    f fr  x  4  x  x f fr dz   fr The frictional factor ffr depends on the liquid Froude number:

(126)

G2 if FrL   1 then ffr = 1 di g  2L

else:

 1   f fr  FrL0.3  0.0055 ln  FrL 

2

(127)

Baroczy-Chisholm correlation Baroczy developed the correlation in graphical form [52], Chisholm [53] reproduced the values of Baroczy by a mathematical equation. In this correlation the two phase all liquid multiplier is:



 2 e  2 2  Lo  1  Y 2  1 A x 2 e  2 1  x   x 2 e



(128)

where e is the Blasius exponent (e = 0.25) and Y2 

dp dz vo dp dz lo

(129)

The A parameter depends on the mass flux and on Y parameter on the following rules: if 0 < Y < 9.5

A

55

A

2400 G

G

A = 4.8 If 9.5 < Y < 28

for G ≥ 19000 kg/sm2

(130)

for 500 < G < 19000 kg/sm2

(131)

for G ≤ 500 kg/sm2

(132)

Convective Boiling Heat Transfer of Pure and Mixed…

A

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 285

520

for G ≤ 600 kg/sm2

(133)

for G > 600 kg/sm2

(134)

Y G

A

21 Y

A

15000

Finally if Y > 28 (135)

Y2 G

The pressure drops for the only liquid and vapour phases are expressed as:

2G 2  dp     fl di l  dz  lo

(136)

2G 2  dp     fv di v  dz  vo

(137)

Chawla correlation The Chawla correlation [54] is based on the assumption that the flow is annular and determines the two-phase frictional pressure drop considering the friction between the two phases and the friction between the fluid and the wall.

0.3164 G 2 x7 8  dp      0.25  2d i  v  dz  v Revo

   1 x  1   C v  x L  

19 8

(138)

The  C parameter is calculated as follow: 1



3 C



1



3 C1



1

(139)

 C3 2

with ln  C1  0.960  ln B and ln  C 2  0.168  0.055lnk / d   ln B  0.67 . The B parameter is a function of Reynolds number and of Froude number:  1 x Rel Frl  1 6  v B x  l

  

0.9

 v   l

  

0.5

(140)

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The ratio k/d represents the relative roughness; the correlation is valid in the low range of roughness: 10-6 < k/d < 10-3. Lombardi and Pedrocchi correlation Lombardi and Pedrocchi [55] found a very simple empirical correlation based upon an investigation on the determining parameters of influence for the frictional pressure drop in vertical two phase flow: k  G q   0.4  dp      1.2 0.866  dz  fr di h

(141)

where k = 0.83, q = 1.4 Theissing correlation The procedure [56] resumes that of Lockhart and Martinelli. It contains as limiting cases the pressure drop of the single-phase flow. The increase of pressure drop by momentum exchange between the phases is allowed for by an interaction parameter . In this way Theissing obtains the following empirical correlation for frictional pressure drop:



1 n 1 n 1  1  x 1   pvo p f  plo x



n

(142)

where:  2  L v     3  2  1   L v   

0.7 n

(143)

lnpv pvo  n  n2 pv p L 0.1 lnp L p Lo  n 1 where n1  , n2  (144) ln x ln1  x  1  pv p L 0.1

Müller-Steinhagen correlation This correlation [57] is an empirical extrapolation of only liquid and only vapour flow. The frictional pressure gradient drop is expressed with the following equation:

 dp  13 3    M 1  x   plo x  dz  fr where

M  plo  2pvo  plo x

(145)

(146)

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 287

Comparison of experimental results with existing correlations The experimental results of the total pressure drops for the refrigerant fluids tested have been compared with the results of the above mentioned theoretical correlations selected from literature. The selected correlations were published by LockhartMartinelli, Martinelli-Nelson, Friedel, Grønnerud, Baroczy-Chisholm, Chawla, Lombardi-Pedrocchi, Theissing and Müller-Steinhagen. The test conditions of each experiment have been applied to the above-mentioned correlations, so the local variation of the pressure gradient could be compared with the experimental data. Figures 6.1-6.6 compare, as an example, experimental results with values predictable from correlations of the pressure gradients, at the same flow conditions (mass flux of about 500 kg/sm2 and saturation pressure of about 7 bar) for the refrigerant fluids R22, R134a, R404A, R410A, R407C, R507. In each figure the top graph reports the experimental pressure drops and the pressure drops evaluated with the above mentioned correlations as a function of vapour quality. The bottom graphs show the experimental pressure drop values normalized by the predicted values for each correlation. Similar trends are observed in all the experiments with similar operating conditions. The Chawla, Theissing, and Grønnerud correlations better describe the behaviours of all tested fluids. Whereas using the methods by Lockart-Martinelli, Martinelli-Nelson and by Chisholm the results obtained overestimate more than 100% the experimental data. For each analyzed fluid Chawla’s correlation better predicts experimental results; in fact for R410A, R404A and R407C the difference is lower that 20%. The Theissing’s correlation shows good results for R410A, R407C, R417A and R404A, acceptable for R22 and worse for R134a and R507.

288 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

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R22 - G = 447 kg/sm2 - p = 7,37 bar Experimental Chawla Baroczy-Chisholm Friedel Grønnerud Lockart and Martinelli Lombardi and Pedrocchi Martinelli and Nelson Müller-Steinhagen Theissing

20

15

p/z [kPa/m]

x

x x x

x

10 x

x

5

x

x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality 2

R22 - G = 447 kg/sm - p = 7,37 bar 18 16

p/zexp)/(p/z) %

14 x

12 10

Friedel Lockart and Martinelli Martinelli and Nelson Grønnerud Baroczy-Chisholm Müller-Steinhagen Chawla Lombardi and Pedrocchi Theissing

8 6 4

x

x

x

x x

2

x x

x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

Fig. 6.1. Experimental and predicted pressure drop value for R22 during flow boiling at p ev = 7.4 bar and G = 447 kg/sm2.

Convective Boiling Heat Transfer of Pure and Mixed…

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 289

2

R134a - G = 488 kg/sm - p = 7,56 bar 20 Experimental Chawla Baroczy-Chisholm Friedel Grønnerud Lockhart and Martinelli Lombardi and Pedrocchi Martinelli and Nelson Müller-Steinhagen Theissing

p/z [kPa/m]

15 x

10 x x x x

5 x

x x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

R134a - G = 488 kg/sm2 - p = 7,56 bar 1

x

0 x

p/zexp)/(p/z) %

x x

-1

x

x

x

x

Friedel Lockart and Martinelli Martinelli and Nelson Grønnerud Baroczy-Chisholm Müller-Steinhagen Chawla Lombardi and Pedrocchi Theissing

-2

-3

-4 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

Fig.6.2. Experimental and predicted pressure drop value for R134a during flow boiling at p ev = 7.6 bar and G = 488 kg/sm2.

290 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

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2

R404A - G = 483 kg/sm - p = 7,44 bar 20

15

p/z [kPa/m]

x

Experimental Chawla Baroczy-Chisholm Friedel Grønnerud Lockhart and Martinelli Lombardi and Pedrocchi Martinelli and Nelson Müller-Steinhagen Theissing

x x x

10 x x x

5

x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

R404A - G = 483 kg/sm2 - p = 7,44 bar 1,0

p/zexp)/(p/z) %

0,5

x x

x

0,0

x

x

x

x

Friedel Lockart and Martinelli Martinelli and Nelson Grønnerud Baroczy-Chisholm Müller-Steinhagen Chawla Lombardi and Pedrocchi Theissing

x

-0,5

-1,0

0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality Fig. 6.3. Experimental and predicted pressure drop value for R404A during flow boiling at pev = 7.4 bar and G = 483 kg/sm2.

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Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 291

2

R410a - G = 573 kg/sm - p = 7,20 bar 30

25

20

p/z [kPa/m]

x

Experimental Chawla Baroczy-Chisholm Friedel Grønnerud Lockhart and Martinelli Lombardi and Pedrocchi Martinelli and Nelson Müller-Steinhagen Theissing

x

15

x x x x

10

x x x

5 x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

R410a - G = 573 kg/sm2 - p = 7,20 bar 30

25

p/zexp)/(p/z) %

x

20

Friedel Lockart and Martinelli Martinelli and Nelson Grønnerud Baroczy-Chisholm Müller-Steinhagen Chawla Lombardi and Pedrocchi Theissing

15

10

x

5

x

x

x

x

x

x

x x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

Fig. 6.4. Experimental and predicted pressure drop value for R410A during flow boiling at p ev = 7.2 bar and G = 573 kg/sm2.

292 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

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2

R407C - G = 593 [kg/sm ] - p = 6,00 [bar] 35 Experimental Chawla Baroczy-Chisholm Friedel Grønnerud Lockart and Martinelli Lombardi and Pedrocchi Martinelli and Nelson Müller-Steinhagen Theissing

30

25

p/z [kPa/m]

x

x

x

20 x

15

x x x

10

x x

5 x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

2

R407C - G = 593 [kg/sm ] - p = 6,00 [bar]

p/zexp)/(p/z) %

30

25 x

20

Friedel Lockart and Martinelli Martinelli and Nelson Grønnerud Baroczy-Chisholm Müller-Steinhagen Chawla Lombardi and Pedrocchi Theissing

15

10 x

x

x

x

x

x

x

5

x x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality

Fig. 6.5. Experimental and predicted pressure drop value for R407C during flow boiling at pev = 6.0 bar and G = 593 kg/sm2.

Convective Boiling Heat Transfer of Pure and Mixed…

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 293

2

R507 - G = 489 kg/sm - p = 7,87 bar 16 14

p/z [kPa/m]

12 10

x

8

Experimental Chawla Baroczy-Chisholm Friedel Grønnerud Lockhart and Martinelli Lombardi and Pedrocchi Martinelli and Nelson Müller-Steinhagen Theissing

x x x

6 x x

4 x

2 x

0 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality 2

R507 - G = 489 kg/sm - p = 7,87 bar 1 0

x

p/zexp)/(p/z) %

x

x

-1

x

x x

x x

-2

Friedel Lockart and Martinelli Martinelli and Nelson Grønnerud Baroczy-Chisholm Müller-Steinhagen Chawla Lombardi and Pedrocchi Theissing

-3 -4 -5 -6 -7 0,0

0,2

0,4

0,6

0,8

1,0

Vapor quality Fig. 6.6. Experimental and predicted pressure drop value for R507 during flow boiling at p ev = 7.8 bar and G = 489 kg/sm2.

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A statistical comparison of the standard deviation, the mean deviation and the average deviation has been carried out for all experiments and for each correlation. The definition of the standard, mean and average deviation used in the statistical comparison is, respectively:

Standard deviation % =

Mean deviation % =

Average deviation % =

 N  p  p exp,i    pred ,i pexp,i i 1  

   

2

 100   N 

 N p pred ,i  pexp,i  100   pexp,i  N i1  N p pred ,i  p exp,i  100   p exp,i i 1  N

(147)

(148)

(149)

Table 6.2 depicts the statistical comparison for all refrigerant fluids. This statistical comparison shows that the best-fitting correlation is that of Chawla, with a standard deviation of 24%. Acceptable results were also obtained with the Theissing, and Grønnerud correlations with standard deviations of 31 and 39 %, respectively. The worst fitting correlations are those of Lockart-Martinelli, Martinelli-Nelson and by Chisholm standard deviations of 220 and 283 %, respectively. The results obtained have been influenced by the theoretical hypotheses and by the experimental conditions formulated for the set up of the correlations. Indeed, the hypotheses and the experimental database on which the Chawla method is based are congruent with the modalities used for the tests of the present paper. Indeed, the correlation is set up for convective boiling in horizontal tubes with diameters varying from 6 to 154 millimetres, for smalls roughness of the heating surface and assuming an annular flow. The refrigerant fluid in all the tests carried out and reported in the present paper evolves mainly with an annular flow. Therefore the two-phase frictional pressure drop is well predicted taking in consideration the contributions of the exchange of momentum between the two phases and between the fluid and the tube wall. The best results are obtained when the mass fluxes are low (< 400 g/sm2); less reliable results when the quality increases (when the dry out of the wall begins). The Lockhart and Martinelli is the worst fitting correlation because has been developed for mixtures of air-water and air-oil in horizontal tubes for low pressures. Consequently it is not suited to describe the behaviour of the refrigerant fluids at different evaporation pressures. Moreover this correlation does not consider the type of two-phase flow regime. Similar results have been obtained with the Martinelli and Nelson correlation. The latter extended the region of validity of the Lockhart and Martinelli procedure up to the critical pressure and was built for the water vapour.

Convective Boiling Heat Transfer of Pure and Mixed…

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 295

Table 6.2. A statistical description of the experimental results with the selected correlations. Correlation

Friedel

LockhartMartinelli

Martinelli-Nelson

Grønnerud

Baroczy-Chisholm

Müller-Steinhagen

Chawla

LombardiPedrocchi

Theissing

Deviation % Standard

R22

R407C

62

45

43

45

47

60

60

Average % 52

Mean

57

42

36

38

40

46

47

44

Average

-54

-37

-24

-25

-18

-45

-3.0

-29

Standard

145

171

188

162

462

164

254

220

Mean

132

126

149

146

192

199

228

167

Average

129

123

141

146

187

199

154

154

Standard

172

196

188

187

606

201

288

283

Mean

178

157

159

172

224

256

266

202

Average

175

155

157

172

219

256

266

200

Standard

49

36

41

36

13

51

46

39

Mean

48

33

31

28

29

40

38

41

Average

-44.

-30

-39

-22

-16

-38

1.0

-27

Standard

114

141

133

113

140

118

224

140

Mean

99

136

102

105

111

96

198

121

Average

95

133

101

104

106

96

198

119

Standard

55

53

58

44

37

53

90

56

Mean

59

45

49

40

55

61

82

56

Average

51

36

39

33

48

59

78

49

Standard

28

25

29

25

7.0

25

32

24

Mean

20

19

17

18

18

15

24

19

Average

-7.0

-15

-18

-17

-9.0

-2.0

10

-8.3

Standard

66

67

59

47

26

55

113

62

Mean

63

65

45

44

49

44

103

59

Average

58

61

42

40

42

42

101

55

Standard

34

29

36

22

11

31

54

31

Mean

34

25

28

17

28

34

49

31

Average

24

10

26

4

18

29

43

22

Nomenclature A = annular flow a = constant A = constant A = parameter in Chisholm’s equation 2

A = heat-transfer area of the tube (m )

R417A

R410A

R404A R507 R134a

296 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

A = parameter in Gorenflo correlation A = parameter in Baroczy-Chisholm equation Ald = dimensionless liquid area Avd = dimensionless vapour area B = parameter in Gorenflo correlation B = Parameter in Chawla’s equation C = parameter in Gorenflo correlation C = Parameter in Lockhart and Martinelli’s equation C1, C2, C3, C4, C5 = empirical constants in Kandlikar correlation CF1 = Parameter in Friedel’s equation CF2 = Parameter in Friedel’s equation Cp = specific heat capacity (J/kg K) D = parameter in Gorenflo correlation d = tube diameter (m) db = bubble diameter (m) E, F = enhancement factor e = Blasius equation exponent f = friction factor Fd = parameter in Gorenflo correlation Fpf = parameter in Gorenflo correlation F1 (q) = dimensionless parameter in Kattan-Tome-Favrat map F2 (q) = dimensionless parameter in Kattan-Tome-Favrat map Fk = fluid dependent parameter in Kandlikar correlation Fp = pressure correction factor in Kandlikar correlation Fs = parameter in Shah correlation FTD = Taitel-Dukler flow regime parameter G = mass flux (kg/ s m2) Gwavy = transition boundary curve in Kattan-Tome-Favrat map Gstrat = transition boundary curve in Kattan-Tome-Favrat map Gmist = transition boundary curve in Kattan-Tome-Favrat map g = gravitational acceleration (m/s2) h = heat transfer coefficient (W/ m2 K) h = enthalpy (kJ/kg) hl = height of stratified liquid layer (m) hld= dimesionless height of stratified liquid layer hwet = heat transfer coefficient of the wetted part of the tube (W/ m2 K) I = intermittent flow j = superficial flux k = thermal conductivity (W/mK) k = constant in Lombardi and Pedrocchi equation k/d = relative roughness KTD = Taitel-Dukler flow regime parameter M = constant in Blasius equation M = molecular weight (kg/mol)

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M = parameter in Müller-Steinhagen correlation MF = mist Flow m = mass flow rate (kg/s) n = constant in Blasius equation n = exponent in asymptotic model n = Parameter in Theissing’s equation n1 = Parameter in Theissing’s equation n2 = Parameter in Theissing’s equation nq = power exponent N = parameter in Shah correlation Ns = parameter in Shah correlation p = pressure (Pa) pr = reduced pressure Pi = wetted perimeter (m) Pid = dimensionless wetted perimeter (m) q = constant in Lombardi and Pedrocchi equation q= heat flux (W/m2) qcr = critical heat flux (W/m2) Q= heat transfer rate (W) R = inner tube radius (m) S = suppression factor SW = Stratified wavy flow T = temperature (°C, K) TTD = Taitel-Dukler flow regime parameter u = velocity (m/s) X = Martinelli parameter x= vapour quality xIA = transition boundary curve in Kattan-Tome-Favrat map Y = parameter in Chisholm’s equation z = coordinate (m) Greek symbols liquid contact angle (rad) thickness of annular liquid film (m) T = temperature glide (°C, K) p = pressure drop (bar, kPa) void fraction C = Parameter in Chawla’s equation C1 = Parameter in Chawla’s equation C2 = Parameter in Chawla’s equation = angle (rad) dry= dry angle (rad) hev= latent heat of vaporization (J/kg)

298 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

= friction factor  = dynamic viscosity (Pa s)  = kinematic viscosity (m2/s)  = density (kg/m3)  = surface tension (N/m) time characteristics (s) liquid property combination (m3/kg K)0.4 (W/mK)0.6  = Multiplier for pressure drop in two phase flow = interaction parameter in Theissing correlation parameter in Shah correlation Subscripts b = bottom b = bubble c = critical cb = convective boiling ev = evaporation exp = experimental fr = frictional h = homogeneous model i = inner in = inlet l = liquid phase ll = laminar-laminar flow lo = liquid phase flowed with the total mass flow ls = left side lt = laminar-turbulent flow m = momentum nb = nucleate boiling out = outlet pred = predicted with correlations rs = right side sat = saturation strat = stratification t = top tl = turbulent-laminar flow tot = total tt = turbulent-turbulent flow v = vapour vo = vapour phase flowed with the total mass flow w = wall wet= wetted

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Dimensionless numbers q Bo= Boiling number = G hev 0. 5

 v     l  G2 Frl = liquid phase Froude number = 2 l g D 1 x   Co= Convection number =   x 

0 .8

Frh = homogeneous model Froude number =

G2 gd i  h2

Cp l  l kl Cp v  v Prv = Prandtl number for vapour phase = kv G di Re= Reynolds number = Prl = Prandtl number for liquid phase =



4  G  1  x    1      l G1  x di Rel= Reynolds number for liquid phase =

Re = liquid film Reynolds number =

l G  di Relo = Only liquid phase Reynolds number = L 1.25 ReTP = Two phase Reynolds number = F Rel Rev= Reynolds number for vapour phase = Revo= Only vapour Reynolds number =

G x di

v

G di

v

1 x  Xtt = Martinelli parameter for turbulent-turbulent flow=    x 

Wel = liquid phase Weber number =

0. 9

 l   v

  

0.5

 l   v

  

0 .1

G 2 di

 h

References [1] Carey V.P., Liquid - vapour phase change phenomena, Taylor & Francis, (1992). [2] Stephan K., Heat transfer in condensation and boiling, Springer – Verlag, (1992).

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[3] Tong L.S., Tang Y.S., Boiling Heat Transfer and Two-Phase Flow, Taylor & Francis, (1997). [4] Kandlikar S.G., Shoji M., Dhir V.K., Handbook of Pahse Change, Taylor & Francis, (1999). [5] Collier J. G., Thome R.J., Convective Boiling and Condensation, Oxford Science Publications, (2001). [6] Mc Linden, M. et al., NIST Standard Reference Database 23: Refprop 7.0, computer software, U.S. Department of Commerce, Technology Administration, National Institute of Standard and Technology, Gaithersburg, (2002). [7] Moffat, R.J., Describing uncertainties in experimental results, Experimental Thermal and Fluid Science, vol.1, pp. 3-17. (1988). [8] Mc Adams, Heat Transmission, Mc Graw-Hill, New York (1954). [9] Taitel Y., Dukler A.E., A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow, AIChE J., vol. 22, pp.47-55, (1976). [10] Kattan N., Thome J.R., Favrat D., Flow boiling in Horizontal Tubes. Part 1: Developments of a Diabatic Two-Phase Flow Pattern Map, J. Heat Transfer, Vol. 120, n.1, pp. 140-147, (1998a). [11] Kattan N., Thome J.R., Favrat D., Flow boiling in Horizontal Tubes. Part 2: New Heat Transfer Data for Five Refrigerants, J. Heat Transfer, Vol. 120, n.1, pp. 148155, (1998b). [12] Kattan N., Thome J.R., Favrat D., Flow boiling in Horizontal Tubes. Part 3: Development of a New Heat Transfer Model Based on Flow Pattern, J. Heat Transfer, Vol. 120, n.1, pp. 156-165, (1998c). [13] Wojtan L., Ursenbacher T., Thome J. R., Investigation of flow boiling in horizontal tubes: Part I - A new diabatic two-phase flow pattern map, International Journal of Heat and Mass Transfer 48 (2005), pp. 2955–2969. [14] Rouhani Z., Axelsson E., Calculation of void volume fraction in the subcooled and boiling region”, Int. J. Heat Transfer, Vol. 13, pp. 383-393, (1970). [15] Kutateladze S.S., On the transition to Film Boiling under Natural Convection, Kotloturbostroenie, n.3, pp.10 and 152-158, (1948). [16] Greco A., Convective boiling of pure and mixed refrigerants: An experimental study of the major parameters affecting heat transfer, Int. Journal of Heat and Mass Transfer, vol. 51, pp. 896-909, (2008). [17] A. Greco, G.P. Vanoli, Flow boiling heat transfer with HFC mixtures in a smooth horizontal tube. Part I: an experimental investigation, Experimental Thermal and Fluid Science, vol. 29, Issue 2, pp.189-198, January (2005). [18] A. Greco, G.P. Vanoli, Evaporation of refrigerants in a smooth horizontal tube: prediction of R22 and R507 heat transfer coefficients and pressure drop, Applied Thermal Engineering, vol.24, Issue14-15, (2004) pp. 2189-2206. [19] A. Greco, G.P. Vanoli, Flow boiling heat transfer with HFC mixtures in a smooth horizontal tube. Part I: an experimental investigation, Experimental Thermal and Fluid Science, vol. 29, Issue 2, pp.189-198, January (2005).

Convective Boiling Heat Transfer of Pure and Mixed…

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 301

[20] R.L. Webb, C. Pais, Nucleate pool boiling data for five refrigerants on plain, integral-fin and enhanced tube geometries, Int. Journ. Heat Mass Transfer, 35 (8), (1992), pp. 1893-1904. [21] Gorenflo D., Behältersieden, Sec. Ha, VDI Wärmeatlas, VDI Verlag, Düsseldorf, (1988). [22] Kandlikar S.G., A general correlation for saturated two-phase flow boiling heattransfer inside horizontal and vertical tubes, J. Heat-Transfer , no.112, (1990) pp.219-228. [23] Gungor K.E., Winterton R.H.S., A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transfer, no. 29, (1986), pp. 351-358 . [24] Lazarek G.M., Black S.H., Evaporative heat transfer, pressure drop and critical heat flux in small vertical tube with R113, Int. J. Heat Mass Transfer, 25 (7), (1982) pp. 945-960. [25] Klimenko V.V., A generalized correlation for two-phase forced flow heat transfer, Int. J. Heat Mass Transfer 31, (3), (1998), pp. 541-552. [26] Cooper M.G., Saturation nucleate pool boiling: A simple correlation, Int. Chem. Eng. Symposium, no. 86, (1984), pp. 785-793. [27] Fritz W., Maximum volume of vapour bubbles, Phys. Z., 36, (2), (1935), pp. 379384. [28] Wark J. W., The physical chemistry of flotation, J. Phys. Chem., 37, (2), (1933), pp. 623-644. [29] Rohsenow W. M., A method of correlating heat transfer data for surface boiling of liquids, Trans. ASME, vol. 84, (1962), p. 969. [30] Greco A., Vanoli G. P., Flow - boiling of R22, R134a, R507, R404A and R410A inside a smooth horizontal tube, International Journal of Refrigeration, vol. 28, Issue 6, pp.872-880, September (2005). [31] Aprea C., Greco A., Rosato A., Vanoli G.P., Comparison of R407C and R417A heat transfer coefficients and pressure drops during flow boiling in a horizontal smooth tube, Energy Conversion and Management., Vol. 49, Issue 6, pp.16291636, June, (2008). [32] Dittus F.W., Boelter L.K.M., University of California (Berkley) publications on engineering, vol. 2, Berkley (CA): University of California, (1930), p.443. [33] Chen, J.C. Correlation for boiling heat-transfer to saturated fluids in convective flow, Ind. Chem. Eng. Proc. Design and Dev., No. 5 (3) (1966), pp. 322- 339. [34] Gungor K.E., Winterton R.H.S., Simplified general correlation for saturated flow boiling and comparison with data, Chem. Eng. Res. Dev., no. 65, (1987), pp. 148156. [35] Yoshida S., Mari H., Hong H., Matsunaga T., Prediction of binary mixture boiling heat transfer coefficient using only phase equilibrium data, Trans. JAR, no. 11, (1994), pp.67-78. [36] Jung D. S., Radermacher R., Prediction of heat transfer coefficient of various refrigerants during evaporation, Paper no. 3492, ASHRAE Annual Meeting, Indianapolis, June (1991). [37] Steiner D., Taborek J., Flow boiling heat transfer in vertical tubes correlated by asymptotic model, Heat Transfer Engineering, vol. 23, no.2, (1992), pp. 43-68.

302 Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

Greco

[38] Liu Z., Winterton R.H.S., A general correlation for saturated and subcooled flow boiling in tubes and annuli based on nucleate pool boiling equation, Int. J. Heat Mass Transfer, vol. 34, no. 11, (1991), pp.2759 – 2766. [39] Shah M., A new correlation for heat-transfer during boiling flow through pipes, ASHRAE Trans., no. 82 (2), (1976) pp.66-86. [40] Kattan N., Thome J.R., Favrat D., Flow boiling in horizontal tubes: Part 3 – Development of a new heat transfer model based on flow patter, Transaction of ASME, vol. 120, February, (1998). [41] Zürcher O., Favrat D., Thome J.R., Evaporation of refrigerants in a horizontal tube: an improved flow pattern dependent heat transfer model compared to ammonia data, Int. J. Heat and Mass Transfer, 45, (2002), pp. 303 –317. [42] Forster H.K., Zuber N., Dynamics of vapour bubbles and boiling heat-transfer, AIChE Journal, (1955), pp.531-535. [43] Yu M., Lin T., Tseng C., Heat transfer and fluid flow pattern during two-phase flow boiling of R-134a in horizontal smooth and microfin tubes, Int. J. of Refrigeration, no.25, (2002), pp. 789-798. [44] Stephan K., Abdelsalam M., Heat transfer correlations for natural convection boiling, Int. J. Heat Mass Transfer, vol. 23, (1980), pp.73 – 80. [45] Gnielinski V., Forced convection in ducts, Heat Exchanger Design Handbook (HEDH), Hemisphere, New York, (1983). [46] Greco A., Vanoli G.P., Flow boiling heat transfer with HFC mixtures in a smooth horizontal tube. Part II: assessment of predictive methods, Experimental Thermal and Fluid Science, vol. 29, Issue 2, pp.199-208, January (2005). [47] Greco A., Vanoli G.P., Prediction of two-phase pressure gradients during evaporation of pure and mixed refrigerants in a smooth horizontal tubes, Heat and Mass Transfer, vol.42, pp. 709 – 725 (2006). [48] Lockhart RW, Martinelli RC. Proposed correlation of data for isothermal twophase two-component flow in pipes, Chem Eng Progr vol. 45, pp. 39-45, (1949). [49] Martinelli R.C., Nelson D.B., Prediction of pressure drop during forced-circulation boiling of water, Transaction of ASME, vol. 70, pp 695-702, (1948). [50] Friedel L., Improved friction pressure drop correlation for horizontal and vertical two-phase pipe flow. European Two-Phase Flow Group Meeting, Paper E2; June; Ispra Italy, (1979). [51] Grønnerud R., Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type evaporators, part IV: two-phase flow resistance in boiling refrigerants. Annexe 1972-1, Bull. De l’Inst. du Froid, (1979). [52] Baroczy C. J., A systematic correlation for two-phase pressure drop, Chem. Eng. Prog. Symp. Ser. 62, pp. 232-249, (1966). [53] Chisholm D., Pressure gradients due to friction during the flow of evaporating twophase mixtures in smooth tubes and channels, Int. J. Heat Transfer, no. 16, pp. 347-358, (1973). [54] Chawla JM, Warmeübergang und Druckabfall in waagerechten Rohren bei der Stromung von verdampfenden Kältemitteln, VDI-Forschungs heft 523, (1967). [55] Lombardi C., Pedrocchi E., A pressure drop correlation in two phase flow, Energia Nucleare, vol. 19, pp 91-99, (1972).

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[56] Theissing P.A., A Generally Valid Method for Calculating Frictional Pressure Drop in Multiphase Flow, Chemic. Ing. Technik. vol.52 pp 344-355, (1980). [57] Müller-Steinhagen H, Heck K. S., A simple friction pressure drop correlation for two-phase flow in pipes, Chem. Eng. Process; 20, pp. 279-308, (1986).

Index

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009) 304-307

304

Index A Ability, 91 Abstract, 1, 38, 6, 107, 148, 177, 216 Acknowledgement, 174 Adiabatic, 224 Affecting, 46 Air, 177, 183, 187, 196, 202 Air-water, 177, 187, 196, 202 Ambivalent, 47, 53 Analysis, 15, 80, 148, 153, 155, 156, 202 ANN, 71, 72, 99 Apparatus, 77, 218 Application, 177 Architecture, 69, 89 Artificial neutral network, 62, 63, 87 Artificial, 62, 63, 87 Assessment, 91 Atmospheric, 11 Attractor, 165 Average, 163

Characteristics, 107, 115, 125, 130, 134, 135, 138 Chaotic, 151 Character, 151, 164 Closed, 9 Coalescence, 48 CO2, 107, 110, 125, 130, 134-136 Combined, 99 Comparison, 124, 163-165, 167, 287 Concluding, 173 Conclusion, 102, 251, 268 Condensation, 15, 20-24, 26, 29, 138 Condenser, 1, 12 Condition, 125 Continuous, 45 Convective, 108, 115, 130, 134-136, 138, 216, 223, 233, 52, 268, 277 Cooling, 128, 135, 136 Correlation, 15, 26, 29, 47, 85, 156, 167, 252, 254-256, 258-261, 277, 281287 Curved, 196 Cylinder, 21

B

D

Background, 177 Bank, 21 Based, 48-51 Bed, 148 Biological, 63 Boiling, 108, 115, 120, 134, 216, 223, 233, 234, 237, 240, 247, 248, 252, 268, 277 Breakage, 48 Building, 177

Data, 78, 88, 92, 94, 221, 223 Database, 99 Data reduction, 78 Determination, 89 Development, 85, 87 Dew, 9, 11 Diameter, 119 Different, 234 Direct, 41 Dimension, 156, 167 Dimensionless number, 299 Discussion, 83, 155, 162 Downward, 21 Drainage, 177 Drop, 48

C Center, 167 Chapter, 1, 38, 62, 107, 148, 177, 216

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

Dryout, 119

Index

305

Greek, 32, 57, 130, 140, 175, 212, 272, 297

E H Effect, 15, 117-119, 234, 237, 240, 247, 248 Empirical, 47, 85 Energy, 51 Entropy, 159, 167 Environment, 9 Existing, 261, 287 Experiment, 41, 45 Experimental, 76, 77, 80, 88, 92, 94, 151, 216, 218, 233, 261, 268, 287 Error, 163 Evaluation, 92, 94 Evaporating, 247 Evaporator, 148, 167

F f-, 92, 94 Facing, 21, 22 Film, 15, 20-24 Finned, 22, 62 Flow, 72, 187, 196, 202 Flow pattern map, 110, 226 Fluid, 72, 248 Fluidized, 148 Flow, 38, 41, 224, 233, 268 Flow pattern 108, 110, 223, 224 Forecast, 161, 162 Fundamental, 177 Friction, 62 Function, 66, 67, 68

G Gas, 15, 26, 29, 128, 135, 136 Gas cooling, 128, 135, 136 Gaussian, 68 General, 115, 117 Generalize, 91 Geometry, 76

Harvest, 9, 11 Heat flux, 117, 240, 247 Heat pipe, 2, 3, 4 Heat transfer, 62, 72, 107, 108, 115, 120, 125, 128, 216, 221, 234, 237, 240, 247, 248, 252 Heat transfer coefficient, 120, 233, 234 Helically, 62 Horizontal, 21-23, 187, 216, 223, 233, 268

I Influence, 118, 234 Interfacial, 50 Introduction, 1, 38, 62, 107, 149, 216, 223, 252, 277 Inversion, 38, 39, 41, 46, 47, 54 J j-, 92, 94 K Kolmogorov, 159, 167

L Laminar, 15 Learning, 71 Left, 163 Letter, 130, 175 Liquid-liquid, 38 Liquid, 38 Literature, 72 Local, 233, 268 Loop, 4

M Map, 165 Mass flux, 118, 237

306

Advances in Multiphase Flow and Heat Transfer Vol. 1 (2009)

Measurement, 220 Mechanism, 47 Method, 153, 161 Micro, 3 Mini, 3 Mixture, 107, 130, 134-136 Model, 47, 48, 50, 51, 120, 128, 136 Modeling, 54, 161 Mode, 13 Moisture, 9 Multi-joint, 202

N Negative, 183 Neuron, 63 Neutral, 62, 87 Network, 62, 87, 69, 89, 91, 92, 94 Node, 66 Nomenclature, 31, 56, 102, 139, 174, 212, 295 Non-condensable, 15, 26, 29 Nonlinear, 148, 153, 156 Normalization, 88 Notation, 87 Nuclear, 12 Numerical, 202

O Observation, 108, 115, 117 Oil, 107, 130, 134-136 Operational, 13 Optimal, 89 Other, 124 Overview, 252, 277 Outer, 26

P Parameter, 46, 234 Passive PCCS, 12, 13 Phase, 38, 39, 41, 46, 47, 54, 165

Index

Phenomena, 119 Pipe, 38 Pipeline, 41, 54 Plain, 216, 223, 52, 277 Plate, 21, 22 Positive, 193 Power, 165 Prediction, 53, 120, 128, 136, 148, 161 Presence, 26 Pressure, 183, 247 Pressure drop, 46, 123, 129, 268, 277 Procedure, 80 Process, 54 Program, 76 Property, 248 Proposed, 47 Property, 130 Pure, 216, 233, 268

R Ramp, 67 Rate, 48 Reactor, 12 Reduction, 78, 221 Reference, 33, 58, 104, 142, 175, 213, 299 Refrigerant, 124, 216, 233, 268 Region, 47 Relative, 163 Remark, 173 Requirement, 51 Result, 80, 83, 155, 162, 233, 261, 268, 287

S Saturation, 118 SBWR, 12 Series, 148, 155, 156, 163, 167 Setup, 151 Shear, 50 Sigmoid, 67 Single, 21, 22 Spectra, 165

Advances in Multiphase Flow and Heat Transfer Vol. 2 (2009)

Sphere, 21 Statistics, 164 Step, 66 Stirred, 39 Superscript, 104 Supercritical, 125 Suppression, 183 Surface, 20, 26 Symbol, 46, 109, 297 Subscript, 32, 104, 142, 157, 298 System, 21, 177

T Temperature, 118 Thermodynamics, 130 Thermosyphon, 6, 24 Time, 148, 155, 156, 163, 167 Time-series, 148, 155, 56, 163, 167 T-junction, 196 Tested, 76 Traditional, 155 Trained, 99 Transient, 183 Tube, 22-24, 29, 62, 76, 107, 108, 119, 136, 163, 167, 187, 196, 216, 223, 252, 277 Turbulent, 20 Two phase, 6 Two-phase flow 177, 223

U Upward 22

V Vapor quality, 234 Vertical, 223 Verification, 223 Vertical, 20, 24, 187 Vessel, 39, 202 V-L-S, 167

Index

W Water, 177, 187, 196, 202 Wavy, 20 Width, 53

Z Zero, 50

307