Heat transfer engineering an international journal, tập 31, số 4, 2010

Heat Transfer Engineering, 31(4):255–256, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903311652 editorial Recent Developments in Flow Boiling and Two-Phase Flow in Small Channels and Microchannels JOHN R THOME and ANDREA CIONCOLINI ´ Heat and Mass Transfer Laboratory, Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland Microscale two-phase flow is at present one of the hottest topics of heat transfer research, both in academia and in the industry The miniaturization of two-phase flow systems, which has led to numerous experimental and theoretical challenges not yet completely resolved, is primarily related to the dissipation of high heat duties typical of compact systems such as CPU (central processing unit) chips, electronic devices, micro chemical reactors, and micro fuel cell combustors Among the areas concerned with CPU (central processing units) chips cooling [1], in particular, data centers have become common and are found in nearly every sector of the economy, such as manufacturing, universities, financial services, government institutions, etc The increasing demand during the past 10 years for computer resources has led to a considerable increase in the number of data centers and their corresponding energy consumption Energy considerations are becoming essential, as the International Panel on Climate Change (IPPC) and the Kyoto treaty show that drastic reductions of CO2 emissions are urgently needed In this context, information technology has a key role to play as the energy consumed in data centers represents almost 2% of the world electricity consumption and is growing by 15% annually, while the current efficiency of such systems is usually less than 20% In addition to environmental considerations, the rise in energy costs is a key motivator of technological change, as the cooling process becomes the major part of the data center operating costs Address correspondence to Professor John R Thome, Heat and Mass Trans´ fer Laboratory, Ecole Polytechnique F´ed´erale de Lausanne, EPFL-STI-IGMLTCM, Station 9, 1015 Lausanne, Switzerland E-mail: john.thome@epfl.ch The market for cooling of personal computers (PCs), data centers, and telecom equipment is at a crossroads between old air-cooling technology and more effective solutions, mainly liquid and two-phase cooling It appears that liquid cooling is the preferred near-term solution because of its higher ease of implementation, but two-phase microscale cooling is of particular interest due to evident performance advantages For instance, the latent heat allows operation at a lower mass flow rate than singlephase cooling, and thus can reduce pumping power requirements, resulting in a more energy-efficient system The boiling process takes place at an almost constant temperature, leading to a small temperature gradient along the chip surface, which is advantageous for thermal interface durability Finally, primary trends in boiling in multi-microchannels [2–4] show that the boiling heat transfer coefficient increases with heat flux and decreases slightly with increasing vapor quality Consequently, two-phase cooling is intrinsically well adapted to hot-spot management, which is a critical point for the electronics industry and for obtaining a uniform operating temperature along the chip This issue collects seven papers originally presented at the 5th International Conference on Transport Phenomena in Multiphase Systems, HEAT 2008, June 30–July 3, 2008, Bialystok, Poland These studies address several aspects of flow boiling 255 256 J R THOME AND A CIONCOLINI and two-phase flow in small channels and microchannels, both experimentally and theoretically REFERENCES [1] Thome, J R., and Bruch, A., Refrigerated Cooling of Microprocessors With Micro-Evaporation Heat Sinks: New Developments and Energy Conservation Prospects for Green Datacenters, Proc Institute of Refrigeration 2008–2009, 2–1 [2] Agostini, B., Thome, J R., Fabbri, M., Michel, B., Calmi, D., and Kloter, U., High Heat Flux Flow Boiling in Silicon MultiMicrochannels—Part I: Heat Transfer Characteristics of Refrigerant R236fa, International Journal of Heat and Mass Transfer, vol 51, pp 5400–5414, 2008 [3] Agostini, B., Thome, J R., Fabbri, M., Michel, B., Calmi, D., and Kloter, U., High Heat Flux Flow Boiling in Silicon MultiMicrochannels—Part II: Heat Transfer Characteristics of Refrigerant R245fa, International Journal of Heat and Mass Transfer, vol 51, pp 5415–5425, 2008 [4] Agostini, B., Revellin, R., Thome, J R., Fabbri, M., Michel, B., Calmi, D., and Kloter, U., High Heat Flux Flow Boiling in Silicon Multi-Microchannels—Part III: Saturated Critical Heat Flux of R236fa and Two-Phase Pressure Drops, International Journal of Heat and Mass Transfer, vol 51, pp 5426–5442, 2008 heat transfer engineering John R Thome is a professor of heat and mass transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland, since 1998, where he is director of the Laboratory of Heat and Mass Transfer (LTCM) in the Faculty of Engineering Science and Technology (STI) His primary interests of research are two-phase flow and heat transfer, covering boiling and condensation of internal flows, external flows, enhanced surfaces, and microchannels He received his Ph.D at Oxford University, England, in 1978 and was formerly a professor at Michigan State University He is the author of several books: Enhanced Boiling Heat Transfer (1990), Convective Boiling and Condensation (1994), and Wolverine Engineering Databook III (2004) He received the ASME Heat Transfer Division’s Best Paper Award in 1998 for a three-part paper on flow boiling heat transfer published in the Journal of Heat Transfer Andrea Cioncolini is a postdoctoral researcher in the Laboratory of Heat and Mass Transfer (LTCM) at the Swiss Federal Institute of Technology in Lausanne, Switzerland (EPFL) He received his Laurea degree and Ph.D in nuclear engineering at the Polytechnic University of Milan, Italy He joined LTCM after years as a senior engineer at Westinghouse Electric Company, Science and Technology Department, in Pittsburgh, Pennsylvania vol 31 no 2010 Heat Transfer Engineering, 31(4):257–275, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903311678 Flow Patterns and Heat Transfer for Flow Boiling in Small to Micro Diameter Tubes TASSOS G KARAYIANNIS1 , DEREJE SHIFERAW1 , DAVID B R KENNING1 , and VISHWAS V WADEKAR2 School of Engineering and Design, Brunel University, West London, United Kingdom HTFS, Aspen Technology Ltd., Reading, United Kingdom An overview of the recent developments in the study of flow patterns and boiling heat transfer in small to micro diameter tubes is presented The latest results of a long-term study of flow boiling of R134a in five vertical stainless-steel tubes of internal diameter 4.26, 2.88, 2.01, 1.1, and 0.52 mm are then discussed During these experiments, the mass flux was varied from 100 to 700 kg/m2 s and the heat flux from as low as 1.6 to 135 kW/m2 Five different pressures were studied, namely, 6, 8, 10, 12, and 14 bar The flow regimes were observed at a glass section located directly at the exit of the heated test section The range of diameters was chosen to investigate thresholds for macro, small, or micro tube characteristics The heat transfer coefficients in tubes ranging from 4.26 mm down to 1.1 mm increased with heat flux and system pressure, but did not change with vapor quality for low quality values At higher quality, the heat transfer coefficients decreased with increasing quality, indicating local transient dry-out, instead of increasing as expected in macro tubes There was no significant difference between the characteristics and magnitude of the heat transfer coefficients in the 4.26 mm and 2.88 mm tubes but the coefficients in the 2.01 and 1.1 mm tubes were higher Confined bubble flow was first observed in the 2.01 mm tube, which suggests that this size might be considered as a critical diameter to distinguish small from macro tubes Further differences have now been observed in the 0.52 mm tube: A transitional wavy flow appeared over a significant range of quality/heat flux and dispersed flow was not observed The heat transfer characteristics were also different from those in the larger tubes The data fell into two groups that exhibited different influences of heat flux below and above a heat flux threshold These differences, in both flow patterns and heat transfer, indicate a possible second change from small to micro behavior at diameters less than mm for R134a INTRODUCTION required to understand the mechanisms of flow boiling in smallto micro-diameter passages Modeling and design of micro devices of high thermal performance, including electronic chips and other systems containing compact and ultra-compact heat exchangers, require a fundamental understanding of thermal transport phenomena for the ultra-compact systems In this emerging area of great practical interest, systematically measured boiling heat transfer data are The authors thank Professor Andrea Luke of Hannover University and her team, who carried out the surface roughness measurements for the 0.52 mm tube, and acknowledge the contributions of Drs Y S Tian, L Chen, and X Huo to the earlier part of this long-term study Address correspondence to Prof Tassos G Karayiannis, Brunel University, School of Engineering and Design, West London, Uxbridge, Middlesex, UB8 3PH, United Kingdom E-mail: tassos.karayiannis@brunel.ac.uk Channel Size Classification Identifying the channel diameter threshold below which the macro-scale heat transfer phenomena not fully apply is important in validating and developing predictive criteria for the thermal-hydraulic performance of small- to micro-scale channels However, there is no clear and common agreement on the definition and classification criteria for the size ranges in small/mini/microchannel two-phase flow studies One reason could be the lack of comprehensive heat transfer data covering a wide range of channel diameters Mehandale et al [1] defined channel size ranges as follows: microchannel (1–100 257 258 T G KARAYIANNIS ET AL µm), mesochannel (100 µm–1 mm), macrochannel (1–6 mm), and conventional (dh > mm) Kandlikar and Grande [2] suggested the classification of microscale by hydraulic diameter, given as conventional channels (dh ≥ mm), minichannels (200 µm ≤ dh < mm), and microchannels (10 µm ≤ dh < 200 µm) These methods based only on size not consider the physical mechanisms and the variation of fluid properties with pressure The absence of stratified flow in horizontal microchannels, and hence the fact that the orientation of the channel has virtually no effect on two phase flow patterns, indicates the predominance of surface tension force over gravity Consequently, a number of attempts to define macro–micro transition have used surface tension force as a base to formulate a nondimensional criterion These include Eăotvăos number (Eăo > 1) recommended by Brauner and Moalem-Maron [3] and confinement number (Co = 0.5) by Cornwell and Kew [4] Thome [5] in his review of boiling in microchannels indicated the importance of considering the effect of channel size on the physical mechanisms and discussed the use of bubble departure diameter as a preliminary criterion He also mentioned the effects of shear on bubble departure diameter and the effect of reduced pressure on bubble size that should be considered in addition to surface tension forces A comprehensive definition for normal and small size tubes is required that considers all the fundamental phenomena, based on experimental data for a wide range of conditions The research presented here addressed this requirement by systematic measurements of flow boiling of R134a over wide ranges of pressures, flow rates, and heat fluxes in five tubes with diameters ranging from 4.26 to 0.52 mm This choice of size range was based on an initial assessment using the confinement number proposed by Cornwell and Kew [4] flow, and annular-slug flow Identification of flow patterns is subject to uncertainty, which is not straightforward to quantify and can also be significantly influenced by the experimental technique used Besides, the transition from one flow pattern to another may be a gradual rather an abrupt transition, as is often reported Hence, flow patterns may possess characteristics of more than one flow pattern during transition Chen et al [9] reported the results of a detailed study of flow visualization experiments with R134a for a pressure range of 6–14 bar and tube diameter from 1.1, 2.01, 2.88, and 4.26 mm with the same test rig as the present one The typical flow patterns observed in the four tubes are presented in Figure They included dispersed flow, bubbly flow, confined flow, slug flow, churn flow, annular flow, and mist flow The flow patterns in the 2.88 and 4.26 mm tubes exhibit characteristics found in large tubes The flow patterns in the 2.01 mm tube demonstrate some “small tube characteristics,” e.g., the appearance of confined bubble flow at the lowest pressure of bar, and slimmer vapor slug, thinner liquid film, and a less chaotic vapor–liquid interface in churn flow Confined flow was observed at all pressures when the diameter was reduced to 1.1 mm, indicating Flow Patterns Flow pattern studies in small/micro tubes have clearly shown that there is a considerable difference in the flow pattern characteristics compared with conventional size channels These include the predominance of surface tension force over gravity, the absence of stratified flow pattern in horizontal channels, and the appearance of additional flow patterns that are not common in normal-diameter tubes In the past some researchers have proposed several flow pattern classes, probably more than is necessary for modeling Although there are arguments on the classification of flow patterns, the most commonly identified flow patterns so far are bubbly flow, slug flow, churn flow, and annular flow Barnea et al [6] classified the flow patterns as dispersed bubble, elongated bubble, slug, churn, and annular Elongated bubble, slug, and churn were considered as intermittent flow Dispersed flow and elongated bubble were replaced by bubbly flow in the Mishima and Hibiki [7] classification Kew and Cornwell [8] experimentally observed flow regimes during their flow boiling tests in small-diameter channels using R141b, and proposed only three distinct flow regimes They defined the flow patterns as isolated bubble flow, confined bubble heat transfer engineering Figure Flow patterns for R134a at 10 bar pressure: (a) d = 1.10 mm, (b) d = 2.01 mm, (c) d = 2.88 mm, and (d) d = 4.26 mm (Chen et al [9]) vol 31 no 2010 T G KARAYIANNIS ET AL a potential transition range for heat transfer between and mm Studies of even smaller diameter tubes are described next Serizawa et al [10] studied two phase flow in microchannels and reported the visualization results for air–water and steam–water flows in circular tube of 20, 25, and 100 µm and 50 µm internal diameter, respectively They found several additional features to those observed in small-diameter tubes For air–water twophase flow in a 25 µm silica tube the special flow pattern features found included liquid ring flow and liquid lump flow The liquid ring flow was described as the appearance of a symmetrical liquid ring with long gas slugs passing in the middle Serizawa et al hypothesized that the liquid ring flow could develop from slug flow when the gas slug velocity is too high and the liquid slug is too short to form a stable liquid bridge between consecutive gas slugs At this condition, liquid lump flow appeared with further increases in the gas flow rate According to Serizawa et al., “the high-speed core gas entrains the liquid phase and liquid lumps are sliding on the wall.” Experiments using the same fluid but in a 100 µm quartz tube gave similar results as for the 25 µm silicon tubes except that small liquid droplets in gas slug flow were sticking on the tube wall, indicating the absence of a liquid film at these locations between the slug and the wall Stable liquid ring flow and liquid lump flows were also reported for the 100 µm tube Flow patterns similar to those of air–water flow in the 25 µm silica tube were observed in the case of steam– water flow in a 50 µm silica tube, with the only difference being the absence of liquid lump flow, which, according to Serizawa et al., was not a main flow but transition type flow However, liquid ring flow was still found, which may indicate that the difference in the method of forming the two-phase flow, i.e., boiling or adiabatic mixing of air–water, seems to have no considerable effect, at least for these sizes Kawahara et al [11] studied two-phase flow characteristics of nitrogen and deionized water in a 100 µm diameter tube made of fused silica, and noted the absence of bubbly and churn flow as one of the differences between their results and results for larger diameter tubes They reported mainly intermittent and semi-annular flows Recently, Xiong and Chung [12] studied experimentally adiabatic gas–liquid flow patterns using nitrogen and water in rectangular microchannels with hydraulic diameter of 0.209, 0.412, and 0.622 mm They observed four different flow patterns: bubbly-slug flow, slug-ring flow (liquid-ring flow), dispersed-churn flow, and annular flow in the 0.412 and 0.622 mm microchannels The bubbly-slug flow developed to fully slug flow They reported that dispersed and churn flows were absent in the 0.209 mm channel 259 that reducing the tube diameter shifted the transition boundaries between intermittent-dispersed bubbly and intermittent-annular flow toward lower liquid velocity and higher gas velocity, respectively Also, they did not observe stratified flow regime inside the mm diameter tube In the study of air–water flow patterns in tubes of 0.5 to 4.0 mm inside diameter, for vertical flow, Lin et al [14] observed that decreasing the tube diameter shifted the slug-churn and churn-annular transition boundaries toward lower vapor velocity Recently, Chen et al [9] noted that the diameter influences the transition boundaries of dispersed bubble-bubbly, slug-churn and churn-annular flow Also, the slug-churn and churn-annular boundaries are weakly dependent on superficial liquid velocity and strongly dependent on superficial vapor velocity There seems to be no effect of diameter at the boundaries of dispersed bubble-churn and bubbly-slug flow The flow pattern transition data of Chen et al are plotted on a mass flux versus quality graph in Figure for pressures of and bar As shown in the figure, when the diameter is reduced, the slug-churn and churnannular transition lines shift toward higher quality The change is more pronounced for moderate and low mass fluxes There is no obvious effect on the bubbly/slug transition line The flow regime boundaries are shifted to significantly lower qualities as the mass flux increases At higher quality, the transition lines for different tubes merge into a single line Chen et al reported that the Weber number may be the appropriate parameter to deduce general correlations to predict the transition boundaries that include the effect of diameter Recently, new correlations for transition of non-adiabatic flow patterns were introduced by Revellin and Thome [15] They identified three main flow patterns, named (a) the isolated bubble regime, which includes bubbly flow and short slugs—in this regime coalescence is not significant; (b) the coalescing bubble regime, where slug flow is the main flow with some of the bubbles coalescing to form a longer slug; and (c) the annular regime According to their observations, churn flow is a transition from coalescing bubble to annular flow, and it is considered an indication of the end of coalescing bubble flow The flow pattern maps were plotted as mass flux versus quality graphs Revellin and Thome proposed flow pattern transition correlations, which give the quality at which the transition occurs For the transition from the isolated bubble to the coalescing bubble regime, their correlation contained the Reynolds, Boiling, and Weber numbers, as in Eq (1) A similar correlation for the transition from the coalescing bubble to the annular regime contained only the Reynolds number and the Weber number, as in Eq (2) x = 0.763 · Relo Bo Wego Effect of Diameter on Transition Boundaries The effect of tube diameter on flow pattern transition boundaries was also studied by various researchers Damianides and Westwater [13] studied the flow regimes in horizontal tubes of to mm inside diameters using air–water They reported heat transfer engineering 0.41 x = 0.00014 · (Relo )1.47 · Welo −1.23 (1) (2) According to Eq (1), the transition from isolated bubble to slug is independent of tube diameter, which is confirmed by the present results of Figure (bubbly to slug flow) However, the vol 31 no 2010 260 T G KARAYIANNIS ET AL for large diameter tubes, e.g., the appearance of confined flow at about mm for R134a, which may indicate a threshold for change from large to small diameter For the same fluid the Cornwell and Kew [4] criterion gives a critical diameter of 1.7 mm for P = bar pressure Flow pattern studies for even smaller tubes (near or less than mm) revealed the existence of a number of different flow pattern types, e.g., ring flow and lump liquid flow, which have not been found in larger diameter tubes This is indicative of a possible further change in flow patterns and hence in thermal characteristics at these even smaller diameters This is discussed later in the article in light of the recent results from our own investigations Heat Transfer Figure Flow pattern transition boundary lines for the four tubes (Chen et al [9] data): (a) bar and (b) bar pressure transition from coalescing bubble to annular flow regime, which is equivalent to churn to annular transition, shifts to lower quality with decreasing diameter This is contrary to the results of Chen et al [9] and could be due to the fact that the correlation was developed using tests with a single tube diameter rather than a range of tube diameters For instance, at a mass flux of 400 kg/m2 -s and pressure of bar, the transition qualities for the 2.01 and 1.10 mm tubes are x = 0.38 and x = 0.32, respectively From the experimental results of Chen et al [9], shown in Figure 2b, the corresponding values are 0.22 and 0.24, respectively From the preceding review, it appears that small-diameter tubes exhibit flow pattern characteristics different from those heat transfer engineering Nucleate boiling, forced convection, and a combination of the two are the main mechanisms often reported in the literature for flow boiling heat transfer in large-diameter tubes, e.g., Kenning and Cooper [16] These have also been adopted in identifying the heat transfer mechanism in small-diameter tubes and microchannels, although different conclusions have been drawn by researchers as to their prevalence Some researchers concluded that nucleate boiling is the dominant heat transfer mechanism when it was observed that the heat transfer coefficient is more or less independent of vapor quality and mass flux, while it is strongly dependent on heat flux—e.g., Lazarek and Black [17], Wambsganss et al [18], Tran et al [19], Bao et al [20], Yu et al [21], and Fujita et al [22] On the other hand, some experimental studies have also reported an effect of the mass velocity and vapor quality but not of the heat flux on the heat transfer coefficient The interpretation given to this is that forced convective boiling is the dominant heat transfer mechanism—e.g., Carey et al [23], Oh et al [24], Lee and Lee [25], and Qu and Mudawar [26] Some researchers reported a combined effect of both mechanisms, i.e., nucleate boiling at low quality and forced convective boiling at high quality region, in a way similar to that observed in large-diameter tubes—e.g., Kuznestov and Shamirzaev [27], Lin et al [28], Sumith et al [29], and Saitoh et al [30] However, it is worth noting here that macroscale boiling heat transfer correlations and models did not predict well the heat transfer coefficient in small-diameter tubes, as noted by Qu and Mudawar [26], Owhaib and Palm [31], and Huo et al [32] More complex behavior and differences dependent on the fluid tested were reported by other researchers For example, Dı’az and Schmidt [33] investigated transient boiling heat transfer in 0.3 × 12.7 mm microchannels using infrared thermography to measure the wall temperature For water, the heat transfer coefficient decreased with quality near the zero quality region, followed by a uniform heat transfer coefficient However, for ethanol at high quality, an increase in heat transfer coefficient with quality was found to be independent of applied heat flux A similar behavior, i.e., an increase in the heat transfer coefficient with quality, was observed by Xu et al [34] and Lie et al vol 31 no 2010 T G KARAYIANNIS ET AL [35] Lie et al [35] investigated experimentally evaporation heat transfer of R134a and R407c flow in horizontal small tubes of 0.83 and 2.0 mm internal diameter The fluid was preheated to an inlet quality that varied from 0.2 to 0.8 The heat transfer coefficient was observed to increase with quality almost linearly, except at lower mass flux and heat flux It also increased with heat flux, mass flux, and saturation pressure Saitoh et al [30] studied the effect of tube diameter on boiling heat transfer of R134a in horizontal tubes with inner diameter of 0.51, 1.12, and 3.1 mm The heated lengths were 3.24, 0.935, and 0.550 m respectively The heat flux ranged from to 39 kW/m2 , mass flux from 150 to 450 kg/m2 s, saturation pressure from 3.5 to 4.7 bar, and inlet vapor quality from to 0.2 For the 3.1 mm tube, when the quality was less than 0.6, the heat transfer coefficient was strongly affected by heat flux and was not a function of mass flux and quality For quality greater than 0.5, heat transfer coefficient increased with mass flux and quality, but was not affected by heat flux This quality limit shifted to 0.4 for the 1.12 mm tube The 0.51 mm results did not exhibit the same heat transfer characteristic as the rest of the tubes When the quality was less than 0.5, the heat transfer coefficient seemed to increase with quality and heat flux and slightly with mass flux In this region, the heat transfer coefficient was slightly higher than the 1.12 and 3.1 mm tubes There was also an early dry-out compared with the other tubes, and the region of decreasing heat transfer coefficient with quality is not such a sharp drop as the rest They observed flow instabilities in the two larger tubes (3.1 and 1.12 mm), but not in the 0.51 mm tube Agostini and Thome [36] categorized the trends in the local heat transfer coefficient versus vapor quality and its relation to heat and mass flux after reviewing 13 different studies They noted that in most of the cases reviewed that at low quality ( 0.5, channels with these diameters can be considered to be minichannels On the pipes, at distances of 150 mm from the front and 50 mm from the end of the minichannel, small cuts were made with a milling cutter The cuts were made in compliance with the remarks concerning execution of experiments in channels with diameters small than those conventional ones (Kandlikar [8]), and therefore in such a manner as to make it possible to receive the pressure impulse while heat transfer engineering not interfering with the flow inside the minichannel In this way, the whole 500 mm minichannel was divided into sections The first 150 mm section “a” stabilized the flow, the second— insulated—300 mm section “b” constituted the measurement section, and the third 50 mm section was the outlet section, “c.” In accordance with the equation x + = x/(d·Re), where x + is a dimensionless hydrodynamic length and x is length measured from the channel inlet; the flow can be considered to be fully developed when dimensionless length x + = 0.05 (Steinke and Kandlikar [12]) or x + = 0.055 (Celata et al [13]) A section of 150 mm used on the experimental setup is sufficient to state that in the measuring section flow is fully developed when the inner diameter of the minichannel is 1.05 and 1.35 mm The results of experimental investigations made by Wolf et al [14] show that rapid changes in the two-phase air–water flow parameters occur within the first 50 tube diameters Entrained fraction and the film thickness appear to be the slowest to respond, and these may take 100 to 300 tube diameters to develop fully Through the T-junction, which was fixed at the first orifice, it is possible to measure the pressure at the input to the measuring section and one of signals necessary for the measurement of the pressure drop The second impulse, through the T-junction, is received from the next orifice For the pressure measurement, a piezoelectric sensor with a transducer (Cerabar M PMP41 manufactured by Endress + Hauser) was applied This sensor has a measuring range of 0–1 MPa, and its accuracy does not exceed 0.2% of the measurement range This gives a pressure measuring error of ±2 kPa The pressure drop on the pipe length was measured with a piezoresistive pressure difference sensor with a transducer (Deltabar S PMD75 manufactured by Endress + Hauser) The factory measuring range of the device is 0–500 kPa The measuring accuracy for this device is 0.075% of the measuring range set In the measuring range of 0–500 kPa, the measuring error is ±0.375 kPa The flow meter, the pressure sensor, and the difference pressure sensor were individually calibrated by the manufacturer vol 31 no 2010 K DUTKOWSKI The temperature of the liquid flowing inside a mini-pipe on the length of the measuring section was measured with three K-type thermocouples with a thickness of 0.2 mm The thermocouples were individually calibrated in the range of 10–30◦ C with an accuracy of ±0.1◦ C, and were soldered on the length of 300 mm of the test section: right after the beginning, in the middle of the length, and right before the end The whole was separated from the environment with 10 mm thick silicone insulation The flow process was considered to be adiabatic The air–water mixture flowed from test section to the tank As the tank a narrow transparent pipe was used When the valve under pipe was closed, the liquid level increased A calibrated pressure transducer (0–10 000 Pa, with measuring accuracy 0.075% of the measuring range set) reads the hydrostatic pressure This reading was converted to the mass flow rate of water Using this technique, mass flows below the 0.2 kg/h could be measured (Shin and Kim [15]) Verification with the Coriolis mass flow meter (Promass 80A) shows accuracy of ±5% of the measured value Data from the measuring apparatus were all registered by a data acquisition system made up of a 16 bit, MHz DaqBoard 3005 measuring card working with a PC In steady-state conditions, the registration of measurement was started The measurement lasted ∼10–20 s In this time, data from the measuring devices were registered every 0.5 s The average from the individual results gave quantities corresponding to a given measurement, which was further used in the calculation procedure RESULTS AND DISCUSSION Pressure Drop Data Prior to performing the two-phase pressure drop experiments, the friction factor for single-phase flow was obtained to verify the test system The friction factor for the laminar and turbulent flow of the water and the air was obtained In the laminar and turbulent region, the experimental data of the friction factor perfectly agreed with theoretical Darcy and Blasius friction factor, respectively (Dutkowski and Charun [16], Dutkowski [17, 18, 19]) The two-phase pressure drop tests were carried out inside 1.05, 1.35, 1.68, and 2.30 mm internal diameter single minichannels with air–water mixture as a working fluid The mixture test were carried out at mass flux of 170–6240 kg/m2 -s, gas quality from 0.001 to 0.22 Superficial velocity ranges of water and air were 0.2–7.4 and 1.7–41.8 m/s, respectively The experimental pressure gradient data are plotted versus mass flux of mixture in Figure It should be noted that the scattering of the points in Figure is the result of the presence of measuring points with different values of the parameter x Therefore, the pressure drops at higher mass fluxes sometimes are lower than those at lower mass fluxes for the same test tubes The same reason is the cause for the pressure drops in smaller heat transfer engineering 323 Figure Pressure gradient vs mass flux diameter tubes being sometimes lower than (or nearly the same as) those in larger diameter tubes for the same mass fluxes At the same mass flux and considering the selected pipe, the pressure gradient increases with increase of gas quality Pressure gradient data versus superficial gas velocity are presented in Figures 4–7 Figure presents the experimental results regarding the pressure gradients measured inside a pipe of 1.05 mm internal diameter, while Figures 5–7 present the experimental results regarding the inner diameter values of 1.35, 1.68, and 2.30 mm, respectively In these figures, there are only selected points (jL ≈ constant) Considering the pressure drop in Figures 5–8, it can be seen, that the pressure drop depends on superficial gas velocity (gas quality) and superficial liquid velocity (mass flux) The pressure drop increases when superficial gas velocity or superficial liquid velocity increases Similar dependences are shown by Tripplett et al [20], Lee and Lee [21], Kawahara et al [22], Kawahara et al [23], Ribeiro et al [24], and Wongwises et al [25] Two-Phase Pressure Drop Homogeneous Equilibrium Model The homogeneous equilibrium model is based on the assumption that the two-phase mixture behaves as a pseudo-single- Figure Pressure gradient vs superficial air velocity (d = 1.05 mm) vol 31 no 2010 324 K DUTKOWSKI Figure Pressure gradient vs superficial air velocity (d = 1.35 mm) phase fluid with mean properties that are weighted relative to vapor and liquid content The pressure gradient, according to the Darcy–Weisbach formula, can be expressed as p z = λHOM HOM d ρHOM wHOM (1) Figure Pressure gradient vs superficial air velocity (d = 2.30 mm) ã àM = àl ã where HOM is the homogeneous Darcy friction factor (λHOM = −0,25 64 for laminar flow; λHOM = 0, 316ReHOM for turbulent ReHOM flow), ρHOM is the density of the homogeneous mixture, ρHOM = x 1−x + ρg ρl (2) ˙g ˙l +m m ρHOM · A (3) • • wHOM · ρHOM · d µM (4) Theoretical values of the pressure gradient were calculated using seven different definitions for the two-phase mixture viscosity, proposed by: Figure Pressure gradient vs superficial air velocity (d = 1.68 mm) heat transfer engineering McAdams (Tripplett et al [20], Kawahara et al [22], Lee and Mudawar [26], Pehlivan et al [27], Wongwises and Pirompak [28]): Ackers (Lee and Mudawar [26]): µl µM = (1 − x) + x · ρl ρg (6) 0.5 • (7) Cicchitti (Kawahara et al [22], Lee and Mudawar [26]): µM = x · µg + (1 − x) · µl The Reynolds number of the mixture can be expressed as: ReHOM = (5) x 1−x = + , µM µg µl and wHOM is the velocity of the homogeneous mixture, wHOM = Owens (Kawahara et al [22]): (8) Dukler (Kawahara et al [22], Lee and Mudawar [26], Wongwises and Pirompak [28]): µM = ρHOM · [x · vg · µg + (1 + x) · vl · µl ], (9) Figure Comparison of present air–water mixture pressure gradient data with homogeneous equilibrium model prediction based on two-phase viscosity model by Owens vol 31 no 2010 K DUTKOWSKI Figure Comparison of present air–water mixture pressure gradient data with homogeneous equilibrium model prediction based on two-phase viscosity model by McAdams • 325 Figure 10 Comparison of present air–water mixture pressure gradient data with homogeneous equilibrium model prediction based on two-phase viscosity model by Ackers Beattie and Whalley (Kawahara et al [22], Lee and Mudawar [26], Wongwises and Pirompak [28]): µM = β · µg + µl · (1 − β) · (1 + 2.5 · β) (10) where β= • x · ρl x · ρl + (1 + x) · ρg (11) Lin (Lee and Mudawar [26]): µM = µg + µl · µg 1,4 x · (µl − µg ) (12) The experimental values of the pressure gradient were compared with the theoretical values obtained using the definitions just presented Figures 8–14 show the comparison of the experimental pressure gradient values with the theoretical pressure gradient calculated using Owens, McAdams, Ackers, Cicchitti, Dukler, Beattie and Whalley, and Lin definitions, respectively It can be seen that HEM models yield deviation from the data (especially the Owens and Cicchitti models) Figures 9–15 show that the two-phase pressure gradient increases with decreasing internal diameter of pipe The HEM models overpredict pressure gradient for the pipe with 1.05 mm internal diameter and underpredict for the pipe with 2.30 mm internal diameter The mean absolute error defined as ⎡ ⎤ p p − z th z exp ⎢ ⎥ ⎢ × 100⎥ (13) MAE = ⎣ ⎦ p N z Figure 11 Comparison of present air–water mixture pressure gradient data with homogeneous equilibrium model prediction based on two-phase viscosity model by Cicchitti exp was used to compare the experimental results with theory Obtained mean absolute errors of each correlation are provided in Table heat transfer engineering Figure 12 Comparison of present air–water mixture pressure gradient data with homogeneous equilibrium model prediction based on two-phase viscosity model by Dukler vol 31 no 2010 326 K DUTKOWSKI Table Comparison of mean absolute error (MAE) with homogeneous equilibrium model (HEM) Mean absolute error, MAE (%) HEM Owens McAdams Ackers Cicchitti Dukler Beattie and Whalley Lin Figure 13 Comparison of present air–water mixture pressure gradient data with homogeneous equilibrium model prediction based on two-phase viscosity model by Beattie and Whalley Two-Phase Pressure Drop Homogeneous Equilibrium Model by Chen Experimental data are compared against a model available in the literature for predicting two-phase pressure drop during flow in minichannels based on the homogeneous equilibrium model There is only one widely tested model proposed by Chen The pressure gradient, according to Chen’s model (Chen et al [29]), can be expressed as p z = HOM,MINI p z × (14) HOM where = + 0.2 − 0.9 · e−Be 0,2 + WBoe0,3 − 0.9e−Bo e ; ; Bo < 2.5 Bo ≥ 2.5 The Bond number is defined as Bo = g ρl − ρg Weber number We = d(wρ)2 ρHOM σ (15) (d/2)2 σ and Figure 14 Comparison of present air–water mixture pressure gradient data with homogeneous equilibrium model prediction based on two-phase viscosity model by Lin heat transfer engineering 1.05 mm 1.35 mm 1.68 mm 2.30 mm 114.0 60.4 81.8 106.4 18.3 49.0 76.8 39.9 12.5 18.7 34.2 34.8 17.2 10.3 60.9 10.1 28.1 52.3 30.6 14.4 13.4 39.5 32.2 27.1 35.0 50.9 37.5 22.8 Chen tested his own model using the two-phase viscosity proposed by Beattie and Whalley Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model using seven two-phase viscosities are shown in Figures 15–21 As shown in Figures 15–21 these correlations give worse agreement with experimental data It is clearly shown also in Table where the mean absolute errors of each modified correlation are provided For every case the modified HEM model underpredicts pressure-gradient data Kaminaga et al [30] measured adiabatic air–water two-phase pressure drop in a tube of 1.45 mm diameter They confirmed that the frictional pressure drop modified HEM correlation proposed by Chen give worse predictions than the traditional HEM correlation Chen et al [31] tested their own model using data points obtained by different authors and different fluids (air–water, R12, R-22, R-134a, R-404a, R-410A, R-125, R-407C) Comparisons of mean deviations with the data source presented by Chen shows, analyzing only the air–water mixture, better predictive ability only for one case This case is when the author is using his own data point Comparisons with air–water data points by other authors show bigger mean absolute errors The significant Figure 15 Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model (two-phase viscosity defined by Owens) vol 31 no 2010 K DUTKOWSKI Figure 16 Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model (two-phase viscosity defined by McAdams) Figure 17 Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model (two-phase viscosity defined by Ackers) Figure 18 Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model (two-phase viscosity defined by Cicchitti) heat transfer engineering 327 Figure 19 Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model (two-phase viscosity defined by Dukler) Figure 20 Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model (two-phase viscosity defined by Beattie and Whalley) Figure 21 Comparisons between the measured pressure gradient data and predictions by the modified homogeneous model (two-phase viscosity defined by Lin) vol 31 no 2010 328 K DUTKOWSKI Table Comparison of mean absolute error (MAE) with modified homogeneous equilibrium model (HEM) Mean Absolute Error [%] Modified HEM Owens McAdams Ackers Cicchitti Dukler Beattie and Whalley Lin 1.05 mm 1.35 mm 1.68 mm 2.30 mm 39.2 47.1 39.6 35.4 60.9 50.3 41.3 51.7 68.9 60.5 53.9 76.9 70.6 63.7 48.5 65.1 54.3 47.6 73.6 67.2 60.5 55.9 69.0 59.9 54.7 77.6 71.4 64.8 difference of the surface tension between refrigerants and the air–water mixture can explain these large deviations SUMMARY AND CONCLUSIONS An experimental study was performed for air–water twophase flow in horizontal capillary tubes with internal diameters of 1.05, 1.35, 1.68, and 2.30 mm Investigations were carried out at mass flux of 170–6240 kg/m2 -s and gas quality from 0.001 to 0.22 Superficial velocity ranges of water and air were 0.2–7.4 m/s and 1.7–41.8 m/s, respectively Detailed descriptions of the experimental setup used to determine the pressure drop as well as of the procedure for data reduction were presented A total of 163 data points of experimental pressure gradient versus mass flux was presented Comparisons between the measured pressure gradient data and predictions by the homogeneous equilibrium model and modified homogeneous equilibrium model using two-phase viscosity defined by Owens, McAdams, Ackers, Cicchitti, Dukler, Beattie and Whalley, and Lin were graphically shown Mean absolute errors of each case are presented The following concluding remarks apply to the results found: The traditional HEM with two-phase viscosity proposed by Owens and Cicchitti predicts the data poorly and produces mean absolute errors 35% up to 114% The traditional HEM with two-phase viscosity proposed by McAdams, Ackers, Dukler, Beattie and Whalley, and Lin predicts the data roughly and produces mean absolute errors between 10 and 82% The traditional HEM has enjoyed success in predicting the two-phase pressure drop in 1.35 mm internal diameter pipe (MAE = 10–40%) The traditional HEM shows that the two-phase pressure gradient increases with decreasing internal diameter of pipe The traditional HEM model overpredicts the experimental pressure gradient data for the pipe with 1.05 mm internal diameter and underpredicts for the pipe with 2.30 mm internal diameter heat transfer engineering The homogeneous equilibrium model as modified by Chen for minichannels mostly underpredicts the experimental pressure gradient data and enlarges the mean absolute errors with respect to the conventional homogeneous model The classical HEM (McAdams, Dukler, Beattie, and Whalley) serves as a primary estimation of resistances in the adiabatic two-phase flow in tubular minichannels Experiments confirmed the need for an introduction of corrections and modifications to the classical method to obtain reliable minichannel results Further investigations are necessary in order to check the proposals of other authors concerning the correct determination of two-phase pressure drop in minichannels NOMENCLATURE A Bo d Co p ˙ m MAE N Re v w We (wρ) x z cross section, m2 Bond number diameter, m Confinement number pressure, Pa mass flow rate, kg/s mean absolute error, Eq (13) number of samples, Eq (13) Reynolds number specific volume, m3 /kg mean velocity, m/s Weber number mass flux, kg/m2 -s mass fraction of gas in two-phase mixture (vapor quality) length of test section, m Greek Symbols factor, Eq (11) friction factor dynamic viscosity, N-s/m2 density, kg/m3 surface tension, N/m Chen factor, Eq (15) β λ µ ρ σ Subscripts exp g HOM l M MINI th experimental value gas phase homogeneous liquid phase mixture minichannel theoretical value vol 31 no 2010 K DUTKOWSKI REFERENCES [1] Mishima, K., and Hibiki, T., Some Characteristics of Air–Water Two-Phase Flow in Small Diameter Vertical Tubes, International Journal of Multiphase Flow, vol 22, pp 703–712, 1996 [2] Zhao, T S., and Bi, Q C., Pressure Drop Characteristics of Gas– Liquid Two-Phase Flow in Vertical Miniature Triangular Channels, International Journal of Heat and Mass Transfer, vol 44, pp 2523–2534, 2001 [3] Ribatski, G., Wojtan, L., and Thome, J., An Analysis of Experimental Data and Prediction Methods for Two-Phase Frictional Pressure Drop and Flow Boiling Heat Transfer in Micro-Scale Channels, Experimental Thermal and Fluid Science, vol 31, pp 1–19, 2006 [4] Chen, I Y., Chen, Y.-M., Liaw, J.-S., and Wang, C.-C., TwoPhase Frictional Pressure Drop in Small Rectangular Channels, Experimental Thermal and Fluid Science, vol 32, pp 60–66, 2007 [5] Hibiki, T., Hazuku, T., Takamasa, T., and Ishii, M., Some Characteristics of Developing Bubbly Flow in a Vertical Mini Pipe, International Journal of Heat and Fluid Flow, vol 28, pp 1034– 1048, 2007 [6] Ide, H., Kariyasaki, A., and Fukano, T., Fundamental Data on the Gas–Liquid Two-Phase Flow in Minichannels, International Journal of Thermal Sciences, vol 46, pp 519–530, 2007 [7] Kandlikar, S G., and Balasubramanian, P., Extending the Applicability of the Flow Boiling Correlations to Low Reynolds Number Flows in mMicrochannel, First International Conference on Microchannels and Minichannels, New York, 2003 [8] Kandlikar, S G., Microchannels and Minichannels—History, Terminology, Classification and Current Research Needs, First International Conference on Microchannels and Minichannels, New York, 2003 [9] Kandlikar, S G., Willistein, D A., and Borrelli, J., Experimental Evaluation of Pressure Drop Elements and Fabricated Nucleation Sites for Stabilizing Flow Boiling in Minichannels and Microchannels, 3rd International Conference on Microchannels and Minichannels, Toronto, Ontario, Canada, 2005 [10] Kandlikar, S G., Fundamental Issues Related to Flow Boiling in Minichannels and Micro-Channels, Experimental Thermal and Fluid Science, vol 26, pp 389–407, 2002 [11] Kew, P A., and Cornwell, K., Correlations for the Prediction of Boiling Heat Transfer in Small-Diameter Channels, Applied Thermal Engineering, vol 17, pp 705–715, 1997 [12] Steinke, M E., and Kandlikar, S G., Control and Effect of Dissolved Air in Water During Flow Boiling in Microchannels, International Journal of Heat and Mass Transfer, vol 47, pp 1925– 1935, 2004 [13] Celata, G P., Cumo, M., McPhail, S., and Zummo, G., Characterization of Fluid Dynamic Behaviour and Channel Wall Effects in Microtube, International Journal of Heat and Fluid Flow, vol 27, pp 135–143, 2006 [14] Wolf, A., Jayanti, S., and Hewitt, G F., Flow Development in Vertical Annular Flow, Chemical Engineering Science, vol 56, pp 3221–3235, 2001 [15] Shin, J S., and Kim, M H., An Experimental Study of Condensation Heat Transfer Inside a Mini-Channel With a New Measurement Technique, International Journal of Multiphase Flow, vol 30, pp 311–325, 2004 heat transfer engineering 329 [16] Dutkowski, K., and Charun, H., Badania eksperymentalne opor´ow przeplywu jednofazowego w minikanalach, Cieplownictwo, Ogrzewnictwo, Wentylacja, vol 7–8, pp 44–49, 2007 [17] Dutkowski, K., Wyznaczanie stalej Poiseuille’a dla laminarnego przeplywu wody w minikanalach, XIII Sympozjum Wymiany Ciepla I Masy, Darl´owko, pp 387–394, 2007 [18] Dutkowski, K., Experimental Investigations of Poiseuille Number Laminar Flow of Water and Air in Minichannels, International Journal of Heat and Mass Transfer, doi:101016/ j.ijhaetmasstransfer.2008.04.070, 2008 [19] Dutkowski, K., Single-Phase Pressure Drop of Laminar and Turbulent Water Flow in Minichannels, Proc 5th International Conference on Transport Phenomena in Multiphase Systems, HEAT 2008, Bialystok, Poland, pp 283–288, 2008 [20] Tripplett, K A., Ghiaasiaan, S M., Abdel-Khalik, S I., LeMouel, A., and McCord, B N., Gas–Liquid Two-Phase Flow in Microchannels Part Ii: Void Fraction and Pressure Drop, International Journal of Multiphase Flow, vol 25, pp 395–410, 1999 [21] Lee, H J., and Lee, S Y., Pressure Drop Correlations for TwoPhase Flow Within Horizontal Rectangular Channels With Small Heights, International Journal of Multiphase Flow, vol 27, pp 783–796, 2001 [22] Kawahara, A., Chung, P M.-Y., and Kawaji, M., Investigation of Two-Phase Flow Pattern, Void Fraction and Pressure Drop in a Microchannel, International Journal of Multiphase Flow, vol 28, pp 1411–1435, 2002 [23] Kawahara, A., Sadatami, M., Okayama, K., and Kawaji, M., Effects of Liquid Properties on Pressure Drop of Two-Phase Gas–Liquid Flow Through a Microchannel, First International Conference on Microchannels and Minichannels, New York, 2003 [24] Ribeiro, A M., Ferreira, V., and Campos, J B L M., On the Comparison of New Pressure Drop and Hold-Up Data for Horizontal Air–Water Flow in a Square Cross-Section Channel Against Existing Correlations and Models, International Journal of Multiphase Flow, vol 32, pp 1029–1036, 2006 [25] Wongwises, S., and Pipathattakul, M., Flow Pattern, Pressure Drop and Void Fraction of Two-Phase Gas–Liquid Flow in an Inclined Narrow Annular Channel, Experimental Thermal and Fluid Science, vol 30, pp 345–354, 2006 [26] Lee, J., and Mudawar, I., Two-Phase Flow in High-Heat-Flux Micro-Channel Heat Sink for Refrigeration Cooling Applications: Part II—Heat Transfer Characteristics, International Journal of Heat and Mass Transfer, vol 48, pp 941–955, 2005 [27] Pehlivan, K., Hassan, I., and Vaillancourt, M., Experimental Study on Two-Phase Flow and Pressure Drop in Millimeter-Size Channels, Applied Thermal Engineering, vol 26, pp 1506–1514, 2006 [28] Wongwises, S., and Pirompak, W., Flow Characteristics of Pure Refrigerants and Refrigerant Mixtures in Adiabatic Capillary Tubes, Applied Thermal Engineering, vol 21, pp 845–861, 2001 [29] Chen, I Y., Yang, K.-S., Chang, Y.-J., and Wang, C.-C., TwoPhase Pressure Drop of Air–Water and R-410A in Small Horizontal Tubes, International Journal of Multiphase Flow, vol 27, pp 1293–1299, 2001 vol 31 no 2010 330 K DUTKOWSKI [30] Kaminaga, F., Sumith, B., and Matsumura, K., Pressure Drop in Capillary Tube in Boiling Two-Phase Flow, First International Conference on Microchannels and Minichannels, New York, 2003 [31] Chen, I Y., Yang, K.-S., and Wang, C.-C., An Empirical Correlation for Two-Phase Frictional Performance in Small Diameter Tubes, International Journal of Heat and Mass Transfer, vol 45, pp 3667–3671, 2002 heat transfer engineering Krzysztof Dutkowski received his Ph.D in 2001 from the Koszalin University of Technology, Koszalin, Poland Since graduation, he has become an academic researcher at the same university His main research interests are in heat transfer with phase change, especially in flow boiling of environmentally friendly refrigerants His current work involves heat transfer and fluid flow in minichannels vol 31 no 2010 Heat Transfer Engineering, 31(4):331–334, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903312098 Experimental Investigations of Two-Phase Steam Flows in Horizontal Channels of Small Diameter MICHAŁ ŁUKASZUK Mechanical Engineering Department, Bialystok Technical University, Bialystok, Poland This article describes experimental investigations of two-phase flow regimes for steam–water flowing in horizontal ducts of small diameters In this respect two-phase flow patterns are determined on a test stand based on visualization of real flows Measurements were performed for a round tube with an internal diameter of 2.8 mm under mass flux ranging from 160 kg/s-m2 to 1600 kg/s-m2 at saturation temperatures between 373 K and 403 K Registered steam quality varied from 0.02 to 0.27 Experimental setup, methodology, and recorded two-phase flow patterns referenced to annular, intermittent, and transient flows are presented The results obtained have been compared with annular to wavy transition criteria described on the flow map by Soliman INTRODUCTION Two-phase flows inside channels are encountered in an increasing amount of engineering equipment used in the power and process industries In the last couple of years such flows in channels of small diameter received significance attention due to the high heat transfer coefficients This is an area of growing importance [1] because increasing trends in miniaturization technologies applied for cooling of sophisticated electronic instruments and for air-cooled compact heat exchangers Twophase flow patterns strongly influence the heat and momentum transfer process; therefore, it is very important for designers to predict what flow pattern is expected based on the flow rate, tube diameter, fluid properties, and vapor quality There are numerous flow regime maps for predicting flow patterns Most of them are based on experimental observations and some others are theoretically based [2] One of them is a map to predicting flow regime transition developed by Soliman [3, 4] In these works he distinguished between three flow regimes: mist, The author gratefully acknowledges financial support for this work from the Ministry of Science and Higher Education of Poland under grant S/WM/3/08 of Bialystok Technical University Address correspondence to Mr Michal Łukaszuk, Mechanical Engineering Department, Bialystok Technical University, ul Wiejska 45C, 15-351 Bialystok, Poland E-mail: lukaszm@pb.edu.pl annular, and wavy flow In his approach the wavy flow regime includes commonly called stratified, intermittent (slug, plug), and wavy regimes There he developed two flow regime transition criteria: mist to annular and annular to wavy transitions Soliman postulated that the wave to annular transition can be determined based on a balance between inertia and gravitational forces for the liquid film Based on comparisons with experimental data [5–8] with fluids: • • • R-12 (D = 4.8–15.9 mm, Tsat ∼ = 303 K) R-113 (D = 4.8–15.9 mm, Tsat ∼ = 333 K) Steam (D = 13.4 mm, Tsat ∼ = 383 K) Soliman [3] concluded that wavy flows are observed for Frso < and annular flows are observed for Frso > Dobson [9] and Dobson et al [10, 11] reported that Frso = can serve as good indicator of the transition from wavy to wavy annular flow, although a symmetric annular flow was not observed until around Frso = 18 [12] Soliman’s investigations concern channels classified as conventional (D > mm) [3] However, experimental data presented in this paper are obtained for the two-phase flow in a circular channel of small diameter: minichannels (D = 2.8 mm) [3] The aim of this work is to extend Soliman’s approach for flow regime predictions under steam–water flows in minichannels 331 332 M ŁUKASZUK where the values of the enthalpies and densities of liquid and vapour were introduced in forms of the polynomials For image registration a monochromatic digital camera SONY XCD-X710 equipped with relevant software is used Flow patterns images were recorded at shutter speed of 1/100,000 s and speed frame of 1/30 s ANNULAR TO INTERMITTENT FLOW TRANSITION Soliman’s investigations [3] have led finally to a correlation determining the transition between annular flow and intermittent flow as 0.313 (φv /Xtt )−0.938 Rel = 10.18Fr0.625 so Ga Rei ≤ 1250 (2) 0.481 (φv /Xtt )−1.442 Rel = 0.79Fr0.962 so Ga Rei > 1250 (3) Figure Schematic diagram of the test facility and EXPERIMENTAL TECHNIQUES where the Galileo number is defined by the expression The experimental facility used in this study was designed for the steam–water flow in a round horizontal channel with an internal diameter of 2.8 mm A schematic diagram of test facility is presented in Figure 1, where it is shown that the stand consists of two arrangements (setup and setup 2) The auxiliary heat exchanger is a common part of both the setups The setup arrangement is used to power the auxiliary heat exchanger from an external source of the saturated steam (x = 1) In this part of the test stand the saturated steam temperature Tsat1 , condensate temperature Tc1 , and mass of condensate mc1 are ˙ c1 is measured The value of the condensate mass flow rate m determined as the ratio of condensate mass collected during the test divided by the test duration time period The setup arrangement consists of an auxiliary heat exchanger, transparent test section with the image acquisition system, condenser, condensate reservoir, gear pump, and control valve In this arrangement the following values are measured: temperature of condensate flowing into the heat exchanger Tc2 , temperature of saturated steam (medium under test) Tsat2 , and volumetric flow rate of condensate V˙ c2 All measured values are displayed and recorded on the PC-based system with 34970A data acquisition switch unit (manufactured by Agilent) The two-phase flow test section was made of glass with an inner diameter of 2.8 mm Flow pattern images were recorded using an incandescent lamp Two-phase steam is generated in an auxiliary heat exchanger through partial evaporation of water flowing in Vapor quality at the inlet to the test section is determined based on an energy (heat) balance of the auxiliary heat exchanger, taking into account that this heat exchange is supplied by saturated steam, x = Hence the vapor quality at the inlet of the test channel is calculated as follows: x= ˙ c1 (h1 − h1 ) − V˙ c2 ρl2 (h2 − hc2 ) m hx − h = h −h V˙ c2 ρl2 (h2 − h2 ) (1) heat transfer engineering Ga = gD µl /ρl (4) In the approach developed by Soliman [3] the Froude number Fr = V /gL is proposed in which the appropriate velocity is the actual liquid velocity and appropriate length scale is the film thickness Soliman [3] expressed the Froude number in terms of the Reynolds number and Lockhart–Martinelli parameter accordingly as Frso = 0.25Rel ((0.15(νl D)(φv /Xtt )Rel0.9 δ+ )1.5 (gνl )0.5 (5) where Re is the liquid Reynolds number, defined as Rel = G(1 − x)D µl (6) Figure Soliman’s flows regime map [3] of horizontal two-phase steam flow with experimental data (D = 2.8 mm) vol 31 no 2010 M ŁUKASZUK 333 and the fraction multiplier φν is given by φv = + 1.09Xtt0.039 (7) The turbulent–turbulent Lockhart–Martinelli parameter is Xtt = Figure m−2 Annular flow pattern recorded at x = 0.246 and G = 510 kg.s−1 - 1−x x 0.9 δ+ = 0.0504Re0.5 l , Annular flow patterns recorded at x = 0.060 and G = 744 kg-s−1 - Figure Transient annular/intermittent flow patterns recorded at x = 0.048 and G = 770 kg-s−1 -m−2 0.1 ρv ρl 0.5 (8) and dimensionless liquid film thickness is expressed δ+ = 0.707Rel0.5 , Figure m−2 µl µv Rei ≤ 1250 Rei > 1250 (9) (10) Based on collected experimental data, the liquid Reynolds number and Lockhart–Martinelli parameter were calculated using Eqs (2), (3), and (8), respectively, for registered two-phase steam flow patterns During experiments a data set of 37 points has been collected for annular, intermittent, and transient annular/intermittent flow patterns The points obtained have been placed on Soliman map prepared with Rel –Xtt coordinates The map is presented in Figure Based on Eqs (2) and (3), two annular to intermittent flow boundary transitions are plotted in Figure for Frso = and Frso = 90, respectively One can see in Figure that the annular to intermittent flow boundary transition criterion does not respond to obtained data for Frso = However, the transition criteria based on Frso = 90 match relatively well to received experimental data In Figures to examples of the registered steam flow patterns observed in the channel with an internal diameter of 2.8 mm are presented In Figures and annular patterns are shown Figures and present the slug and plug patterns, respectively Transient annular/intermittent patterns are displayed in Figure CONCLUSIONS Figure Intermittent flow patterns (slug) recorded at x = 0.031 and G = 781 kg-s−1 -m−2 Figure Intermittent flow patterns (plug) recorded at x = 0.024 and G = 765 kg-s−1 -m−2 heat transfer engineering Based on analysis of experimental data set collected for steam–water flows in a minichannel of diameter 2.8 mm it is possible to conclude that the Soliman correlation for modified Froude number Frso = obtained for two-phase flows in a channels of diameter D > mm [3] matches only to annular patterns registered at experiments described in this paper An important observation derived based on experiments carried out for steam – water flows in minichannels is that the transition from annular to intermittent flow regime in channels of small diameters can take place for Frso ∼ = 90 The results presented allow extending Soliman’s macroscale approach to minichannels for Frso > The results described in the paper can be applied for more accurate predictions of transitions from annular to intermittent patterns Consequently, applications of these results can improve accuracy of heat transfer coefficient and pressure loss predictions for two – phase steam – water flows in minichannels vol 31 no 2010 334 M ŁUKASZUK NOMENCLATURE D Fr Frso g G Ga h ˙ m Re T V˙ x Xtt inner diameter, m Froude number, dimensionless modified Froude number, dimensionless acceleration due to gravity, m-s−2 mass flux, kg.s−1 -m−2 Galileo number, dimensionless enthalpy, J-kg−1 mass flow rate, kg-s−1 Reynolds number, dimensionless temperature, K volumetric flow rate, m3 -s−1 vapor quality, dimensionless turbulent–turbulent Lockhart–Martinelli parameter, dimensionless Greek Symbols δ+ φ µ ρ ν thickness of liquid film, dimensionless two-phase friction multiplier, dimensionless dynamic viscosity, Pa-s density, kg-m−3 kinematic viscosity, m2 -s−1 Subscripts c l v sat x setup setup condensate liquid vapor saturation steam quality [2] Kandlikar, S G., Garimella, S., Li, D., Colin, S., and King, M R., Heat Transfer and Fluid Flow in Minichannels and Microchannels, Elsevier, Oxford, 2006 [3] Soliman, H M., On the Annular to Wavy Flow Pattern Transition During Condensation Inside Horizontal Tubes, Canadian Journal of Chemical Engineering, vol 60, pp 475–481, 1982 [4] Soliman, H M., Correlation of Mist-to-Annular Transition During Condensation, Canadian Journal of Chemical Engineering, vol 61, pp 178–182, 1983 [5] Soliman, H M., and Azer, N Z., Flow Patterns During Condensation Inside Horizontal Tube, ASHRAE Trans., vol 77, pp 210–224, 1971 [6] Soliman, H M., and Azer, N Z., Visual Studies of Flow Patterns During Condensation Inside Horizontal Tubes, Proc 5th International Heat Transfer Conference, vol 3, pp 241–245, 1974 [7] Traviss, D P., and Rohsenow, W M., Flow Regimes in Horizontal Two-Phase Flow with Condensation, ASHRAE Trans., vol 79, pp 31–39, 1973 [8] Fathi, A M., Analysis of Two-Phase Flow Patterns of Condensing Steam Inside a Horizontal Tube, M.Sc Thesis, University of Manitoba, Winnipeg, Canada, 1980 [9] Dobson, M K., Heat Transfer and Flow Regimes During Condensation in Horizontal Tubes, Ph.D Thesis, Department of Mechanical and Industrial Engineering, University of Illinois at UrbanaChampaign, 1994 [10] Dobson, M K., Chato, J C., Wattelet, J P., Gaibel, J A., Ponchner, M., Kenney, P J., Shimon, R L., Villaneuva, T C., Rhines, N L., Sweeney, K A., Allen, D G., and Hershberger, T T., Heat Transfer and Flow Regimes During Condensation in Horizontal Tubes, ACRC Technical Report 57, University of Illinois at Urbana-Champaign, 1994 [11] Dobson, M K., Chato, J C., Hinde, D K., and Wang, S P., Experimental Evaluation of Internal Condensation of Refrigerants R-12 and R-134a, ASHRAE Trans., vol 100, no 1, pp 744–754, 1994 [12] Dobson, M K., and Chato, J C., Condensation in Smooth Horizontal Tubes, Journal of Heat Transfer, ASME, vol 120, pp 193o 213, 1998 Superscripts saturated liquid saturated steam REFERENCES [1] Garimella, S., Condensation in Minichannels and Microchannels, in Heat Transfer and Fluid Flow in Minichannels and Microchannels, ed S G Kandlikar, pp 227–408, Elsevier, Oxford, 2006 heat transfer engineering Michal Łukaszuk obtained his M.Sc degree in mechanical engineering at Bialystok Technical University in Bialystok, Poland, in 1999 He is now a Ph.D student at the Department of Mechanical Engineering at the same university The topic of his study is heat transfer during condensation in two-phase flows in minichannels At present he works on the project “Heat Transfer Investigations in Intermittent Steam Flow During Condensation in Minichannels” with financial support from the Ministry of Science and Higher Education of Poland vol 31 no 2010