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