a review of two-phase gas–liquid adiabatic flow

Renewable and Sustainable Energy Reviews

12 (2008) 824838

article. Researches on the micro-hydrodynamics concerned with two-phase gasliquid adiabatic ow

characteristics in both circular and non-circular micro-channels are discussed. This review aims to

ARTICLE IN PRESS

www.elsevier.com/locate/rser

1364-0321/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.rser.2006.10.012

Corresponding author. Tel.: +66 2 470 9115; fax: +66 2 470 9111.

E-mail address: [email protected] (S. Wongwises).survey and identify new ndings obtained from this attractive area, which may contribute to

optimum design and process control of high performance miniature devices comprising extremely

small channels. The results obtained from a number of previous studies show that the ow behaviors

in the micro-channels deviate signicantly from those in ordinarily sized channels. A clear

understanding of the ow behaviors encountered is necessary to answer the fundamental questions

related to the two-phase ow phenomena. Similar to the ordinarily sized channels, it is expected that

the ow pattern, pressure drop and void fraction will inuence the two-phase pressure drop, holdup,

system stability, exchange rates of momentum, heat and mass during the phase-change heat transfer

processes. It is obvious that publications available on micro-channels are relatively small compared

to those for ordinarily sized channels and further systematic studies of two-phase gasliquid

adiabatic ow in micro-channels are required.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Two-phase ow; Micro-channel; Flow characteristicA review of two-phase gasliquid adiabatic owcharacteristics in micro-channels

Sira Saisorna, Somchai Wongwisesb,

aEnergy Division, The Joint Graduate School of Energy and Environment,

King Mongkuts University of Technology Thonburi, Bangmod, Bangkok 10140, ThailandbFluid Mechanics, Thermal Engineering and Multiphase Flow Research Laboratory (FUTURE),

Department of Mechanical Engineering, King Mongkuts University of Technology Thonburi,

Bangmod, Bangkok 10140, Thailand

Received 7 July 2006; accepted 13 October 2006

Abstract

A literature review of recent research on two-phase ow in micro-channels is provided in this

Serizawa et al. [1] described the criterion for classication of micro-channel proposed by

ARTICLE IN PRESSSuo and Grifth [2] as follows:

lDX3:3, (1)

where l is the Laplace constant dened by

l

sgrL rG

r. (2)

Brauner and Moalem-Maron [3] proposed the different criterion as follows:Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825

2. Two-phase Gasliquid adiabatic ow characteristics in micro-channels . . . . . . . . . . . . . 828

2.1. Circular micro-channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828

2.2. Non-circular micro-channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833

3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 838

1. Introduction

In the past years, studies on two-phase ow and heat transfer characteristics inmicro-channel ow passages have become more necessary due to the rapid development ofmicro-scale devices used for several engineering applications including medical devices, highheat-ux compact heat exchangers, and cooling systems of various types of equipment suchas high performance micro-electronics, supercomputers, high-powered lasers, and so on.In addition to the attractive phenomena caused by the signicant role of the surface

effects, this emerging eld enables us to develop powerful miniature devices for operationin a domain which seemed to be unfeasible in the past. However, it is obvious that acomprehensive understanding is still lacking on the trends and parameters dominating theow behavior in mini- and micro-channels. Thus, fundamental heat transfer and owcharacteristics problems encountered in the development and processing of micro-electronic-mechanical systems (MEMS) have become a signicant challenge for the designand control of these micro-systems. According to the requirement of new solutions fordissipating heat and keeping uniform temperature distributions in modern devices, a clearunderstanding of the major mechanisms affecting micro-scale heat transfer is essential foroptimum design and process control of micro-systems.The two-phase ow and heat transfer characteristics in small channels such as micro-

channels and mini channels are likely to be strongly dependent on the surface tensioneffects in addition to viscosity and inertia forces resulting in signicant differences in thetwo-phase ow phenomena between ordinarily sized channels and small channels. Severalinvestigators have proposed the criterion for a small channel based on differentdimensionless parameters.

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838 825Eop2p2, (3)

ARTICLE IN PRESS

Nomenclature

C parameter dependent on Reynolds numberC0 distribution parameterD channel diameter, mDB bubble diameter, mDe equi-periphery diameter, mDh hydraulic diameter, mdP pressure drop, Padz unit length, mEo Etovos numberF time fractionf friction factorG mass ux, kg/sm2

g gravitational acceleration, m/s2

j supercial velocity, m/sKEavg two-phase mixtures average kinetic energy, kg/m s

2

L length, mn1 1 for laminar ow; 0.25 for turbulent own2 1 for laminar ow; 0.25 for turbulent owRe Reynolds numbers channel gap, mU average velocity, m/sV rising bubble velocity relative to the liquid phase, m/sWev Weber number for vaporw channel width, mX parameter dened by Eq. (30)Xann parameter dened by Eq. (37)x ow qualitya void fractionam mean void fractionw LockhartMartinelli parameterf two-phase multiplierl Laplace constantm dynamic viscosity, kg/m sn kinematic viscosity, m2/sr density, kg/m3

s surface tension, N/m

Subscripts

ann annular ow regimeB bubble; slug bubblec contractionG gas phase, vapor phaseGS gas slug

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838826

stension, g is gravitational accelergas densities, respectively.insufcient to identify the distin

ARTICLE IN PRESSchannels and ordinarily sized channels by these equations. Some arbitrary channelclassications based on the hydraulic diameter Dh have been proposed. Recently,Mehendale et al. [4] employed the hydraulic diameter as an important parameter fordening the heat exchangers as follows:

Micro-heat exchanger: 1 mmpDhp100 mm Meso-heat exchanger: 100 mmpDhp1mm Compact heat exchanger: 1mmpDhp6mm Conventional heat exchanger: Dh46mm

Based on the evolution of small ow channels used in engineering applications, however,Kandlikar [5] proposed the channel classication as follows: Conventional channels: Mini-channels: Micro-channels:

Although there have been a number of criteria based on the hydchannel classications available cannot relate the channel diametemechanisms. Further investigations should be conducted to meet a modealing with the channel classication.To obtain an appropriate design and process control of the various

employing these small channels, the two-phase ow characteristics asmechanisms in various small channels, especially for micro-channels, shthe past decade, there has been a relatively small amount of publicmicro-channels compared to those for ordinarily sized channels.Unfortunately, it is likely to be ction between small

diameter, rL and rG are liquid and

From Eqs. (1)(4), s is surface ation, D is channelwhere Eo is the Etovos number dened by

Eo grL rGD2

. (4)vap vapor ow regime

VO all-vaporI gasliquid interfaceint intermittent ow regimeL liquid phaseLO all-liquidLS liquid slugliq liquid ow regimes smaller channelT two-phase mixtureUC unit cell

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838 827Dh43mm200 mmpDhp3mm10 mmpDhp200 mm

raulic diameter, ther to the uid owre general denition

engineering systemswell as heat transferould be claried. Inations available for

o

cir

2.1

ARTICLE IN PRESSAdiabatic two-phase airwater ow characteristics, including the two-phase ow patternas well as the void fraction and two-phase frictional pressure drop, in circular micro-channels were experimentally studied by Triplett et al. [6,7]. For ow visualization resultscorresponding to their rst paper, the ow patterns observed were bubbly, slug, churn,slug-annular and annular. These experimental results were compared with otherexperimental data obtained from previous investigators. The two-phase ow patterntransitions generally disagreed with the lines calculated from the existing models andcorrelations.According to their second paper, the measured values of void fraction and two-phase

pressure drop in bubbly and slug ow regimes were found to be best predicted by themodels based on the homogeneous mixture assumption. In the annular ow regime,however, the experimental void fractions and pressure drops were compared with themodels as well as the available correlations, with poor agreement.Kawahara et al. [8] used a circular fused silica micro-channel with a diameter of 100 mm

to investigate two-phase ow characteristics. They observed many different ow patternssimultaneously in the circular channel under any given ow condition tested. Due to suchsimultaneous appearances, they used the probability of appearance of each ow patternalong with the time-averaged void fraction obtained from each ow condition to dene theow regimes as shown below.

Slug-ring ow was dened when the probability of thin liquid lm was greater thanthat of ring liquid lm and the time-averaged void fraction was less than 0.8.

Ring-slug ow corresponded to when the probability of ring liquid lm was largerthan that of thin liquid lm and the time-averaged void fraction was less than 0.8.

Semi-annular ow was associated with ow in which the ow alternated mostly betweenliquid alone and ring liquid lm. The time-averaged void fraction was greater than0.8.

Multiple ow included liquid alone, thin liquid lm, ring liquid lm, thickliquid lm and deformed interface, and the time-averaged void fraction was lessthan 0.8.The ow patterns dened were used to develop a ow pattern map which was

subsequently compared to other ow regime maps existing for two-phase ow of airwaterin 1mm diameter channels. It was noted that bubbly and churn ow patterns were

ab. Circular micro-channelstwo most common types of such congurations employed by previous researchers arecular and non-circular micro-channels.theUp to now, there have been publications dealing with two-phase gasliquid adiabaticw characteristics in micro-channels with various geometrical congurations. However,done on two-phase gasliquid adiabatic ow characteristics in micro-channels, and topropose the areas available for further investigations.

2. Two-phase Gasliquid adiabatic ow characteristics in micro-channelsThe aim of this paper is to present a review of the most common types of research works

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838828sent in the experimental results due to the laminar nature of liquid owing through the

ARTICLE IN PRESSmicro-channel. The low value of the time-averaged void fraction, even at high gas owrates, indicated the large slip ratios and weak momentum coupling between the phases.The friction factor in single-phase liquid ow and two-phase friction multiplier were alsoanalyzed. The single-phase friction factor was found in reasonable agreement with theconventional correlation. The two-phase friction multiplier data correlated well with theLockhartMartinelli correlation based on a separated ow assumption, but the agreementbetween the data and homogeneous ow model was generally poor.Chen et al. [9] experimentally studied the characteristics of adiabatic two-phase ow of

nitrogenwater in glass tubes with two different diameters, 1.0 and 1.5mm. Four commonow patterns including bubbly ow, slug ow, churn ow and annular ow were observedand a so-called bubble-train slug ow previously reported in a large channel under micro-gravity effects [10] was also observed and discussed in this work. The random manner ofthe number of bubbles counted in the bubble-train slug ow pattern was attributed to theturbulent nature. Moreover, increasing liquid supercial velocity tended to lower thenumber of bubbles. A modied drift ux model was found to be an appropriate approachto correlate bubble velocity for the three different ow patterns covering slug ow, bubble-train slug ow and churn ow. The correlation is expressed as

UB 0:932j1:11T , (5)

where UB is bubble velocity and jT is supercial velocity of the two-phase mixture.Furthermore, the experimental void fractions were well predicted by the use of this

modied drift ux model in conjunction with the following fundamental equation:

a jGUB

, (6)

where a is void fraction and jG is gas supercial velocity.Serizawa et al. [1] investigated the visualization of the two-phase ow pattern in circular

micro-channels. The owing mixture of air and water in channels of 20, 25 and 100 mm indiameter and that of steam and water in a channel of 50 mm in diameter were conductedexperimentally. Two-phase ow patterns obtained from both airwater and steamwaterows were quite similar and their detailed structures were described. The study conrmedthat the surface wettability had a signicant effect on the two-phase ow patterns in verysmall channels. It was also found that the airwater two-phase ow pattern transitionsgenerally agreed with the lines predicted by the Mandhanes correlation and the cross-sectional average void fraction concerned with bubbly and slug ows followed the valuesobtained from the Armand correlation [11] for an airwater system.Chung and Kawaji [12] performed an experiment in order to distinguish two-phase ow

characteristics in micro-channels from those in mini-channels. Four different circulardiameters ranging from 50 to 526 mm were employed to examine a scaling effect onnitrogenwater two-phase ow. The results including the ow patterns, void fraction andtwo-phase pressure drop were analyzed.For larger tubes tested (250 and 526 mm), they observed ow patterns consistent with

those obtained from mini-channels having diameters of around 1mm. The correspondingow patterns were bubbly, slug, churn, slug-annular and annular ow. The time-averagedvoid fraction agreed reasonably with the Armand-type correlation available for mini-

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838 829channels. In the case of two-phase pressure drop, it was found that at a given

LockhartMartinelli parameter the two-phase friction multiplier tended to change with thevariation of mass ux, similar to that appearing in mini-channels.For relatively small channels (49.5 and 100mm), only slug ow was observed under the

experimental conditions tested. The void fraction and pressure drop characteristics weregenerally opposite to those of larger channels previously discussed. The relationship betweenthe void fraction and volumetric quality was found to be non-linear and hence, the Armand-type correlation became unpredictable for these channel sizes. In addition, the frictionalmultiplier was independent of mass ux. Apparently, diameters between 100 and 250mmseemed to be in the range causing the notable change in two-phase ow mechanisms.Additionally, they modied Garimella et al.s [13] model to predict the two-phase pressuredrop for micro-channels having diameters of less than 100mm. In the proposed model, theyassumed that the ow consisting of unit cells (UC) was completely intermittent as shown inFig. 1. For each unit cell, there were two regions, including liquid single-phase ow region (orliquid slug), which had no entrained gas bubbles and the region occupied by the two-phaseow of liquid and gas. The latter region was formed by axially symmetrical gas slugsurrounded by an annular liquid lm with uniform thickness around the channelcircumference. Because of the viscous effect, the velocity of the liquid lm around the gasslug was assumed to be signicantly low compared to that of liquid and gas slugs.In the single-phase region, the pressure gradient in the liquid slug is evaluated from the

DarcyWeisbach equation:

dP

f rLU2LS , (7)

ARTICLE IN PRESSS. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838830dz LSLS 2DFig. 1. Schematic diagram of unit cell for model of Chung and Kawaji [12].

ARTICLE IN PRESSwhere (dP/dz)LS is the pressure gradient in the liquid slug, and fLS is the friction factor forthe liquid slug. The friction factor for uid ow in a circular channel is given by

f LS 64

ReLS;

for laminar flow ReLSp2100, 8

f LS 0:3164

Re0:25LS,

for turbulent flow ReLSo100; 000in a smooth channel. 9

Eq. (9) is known as Blasius equation. In the model, it was noted that, for the transitionfrom laminar to turbulent ow (2100oReLSo4000), the Blasius formula was alsoemployed to obtain the friction factor. The Reynolds number of the liquid slug, ReLS, isdened as

ReLS rLULSD

mL, (10)

where mL is the dynamic viscosity for liquid phase. In Eqs. (7) and (10), ULS represents theaverage velocity of the liquid slug and is expressed by

ULS jL

1 a , (11)

where jL is the supercial liquid velocity.In the two-phase region, the average velocity of the gas slug, UGS, is taken to be equal to

that of the gas phase, UG

UGS UG (12)and

UG jGa. (13)

The pressure gradient in the two-phase region, (dP/dz)T, is given by

dP

dz

T

f GSrGUGS U I2

2DB, (14)

where fGS represents the friction factor for the gas slug and the determination of fGS issimilar to that of fLS. The Reynolds number of the gas slug, ReGS, is given by

ReGS rGUGS U IDB

mG, (15)

where mG is the dynamic viscosity for gas phase. UI and DB in Eqs. (14) and (15) represent

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838 831the average velocity of the gasliquid interface and bubble diameter, respectively. UI is

ARTICLE IN PRESSdened by Chung and Kawaji [12] as follows:

U I dP=dz

T

16mLD2 D2B. (16)

The bubble diameter is assumed to be

DB 0:90D. (17)

The unknown variables including ReGS, UI, and (dP/dz)T are obtained throughEqs. (14)(16). Finally, the total frictional pressure gradient, (dP/dz)UC, across the wholeunit cell is expressed by

dP

dz

UC

dPdz

T

LGS

LUC dP

dz

LS

LLS

LUC, (18)

where the relative lengths of the gas slug (LGS/LUC) and liquid slug (LLS/LUC) areapproximated by

LGS

LUC a D

DB

2, (19)

LLS

LUC 1 LGS

LUC. (20)

Based on the micro-channels having diameters of 100 and 50 mm, the experimental two-phase pressure drop data were predicted well by this slug ow model.Coleman and Krause [14] carried out an experiment to measure R-134a two-phase

pressure drops due to contraction in circular micro-channel headers. The measured two-phase pressure drops were considerably high compared to some existing correlations.However, the authors suggested that the use of model developed by Schmidt and Friedel[15] in conjunction with the momentum density model was in reasonable agreement withthe measured data.Two-phase airwater pressure changes in the circular channel, having sudden expansion

and contraction sections, were experimentally studied by Abdelall et al. [16]. Two stainlesssteel tubes were connected to form such sections. The diameters of the larger tube andsmaller tube were 1.6 and 0.84mm, respectively. The two-phase pressure changes werefound to be considerably small when compared to those predicted by the homogeneousow model. This indicated signicant velocity slip in the neighborhood of the owdisturbance resulting from the area change. On the other hand, the pressure changedata were well predicted by a simple one-dimensional (1D) ow theory with the slip ratiomodel based on the ideal annular ow regime with minimum entropy generation. They

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838832also developed an empirical correlation of two-phase multiplier for the ow area

ARTICLE IN PRESScontraction, fLO,c:

fLO;cw

120wReLO;s0:7, (21)

where ReLO,s is the Reynolds number with the total ow in the liquid phase in smallerchannel and the LockhartMartinelli parameter, w, is expressed by

w mLmG

0:11 xx

0:9 rGrL

0:5, (22)

where x is quality, mL and mG represent liquid and gas viscosities, respectively. Liquid andgas densities are denoted by rL and rG, respectively. In Eq. (21), the subscript LOcorresponds to the value with the total ow in the liquid phase and the subscript c and scorrespond to contraction and the smaller channel, respectively.

2.2. Non-circular micro-channels

Triplett et al. [6,7] also conducted the same systematic experiments as discussed in theprevious section to study gasliquid two-phase ow characteristics in semi-triangular micro-channels. The results obtained were similar to those obtained from circular channels.Xu et al. [17] investigated an adiabatic co-current vertical two-phase ow of air and water in

rectangular channels (12mm 260mm) with mini-/micro-gaps of 0.3, 0.6 and 1.0mm. Forchannel gaps of 1.0 and 0.6mm, the ow patterns observed were similar to those found inordinarily sized channels but peculiar ow structures which were different from typical two-phase ow patterns were observed in the channel having a micro-gap of 0.3mm. In the 0.3mmgap, they found that bubbly ow was never observed and new ow regimes including slug-droplet ow and annular-droplet ow were addressed. For the new ow regimes, it was observedthat liquid droplets were always adhered to the wall surface and such droplets were blown by themoving gas phase. They also presented the models to predict the ow regime transitions invertical rectangular channels. The models for bubbly ow to slug ow transition and slug ow tochurn ow transition were developed based on Mishima and Ishii [18].The transition from bubbly ow to slug ow is described by

jL 1

0:3Co 1

jG

0:35gDe

p

Co, (23)

where Co is the distribution parameter and De represents the equi-periphery diameter andis given by

De 2s w

p, (24)

where s and w are the channel gap and width, respectively. In Eq. (23), the distributionparameter, Co, for rectangular channels is given by

Co 1:35 0:35rGrL

r. (25)

The slug-churn ow transition took place when

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838 833a4am. (26)

ARTICLE IN PRESSThe void fraction, a, is given by

a jGCojG jL V

, (27)

where V is the rising bubble velocity relative to the liquid phase and is expressed by

V 0:35gDe

p. (28)

The slug bubble mean void fraction am, shown in Eq. (26), is dened as

am 1 0:813X 0:75, (29)where

X

rL2gDrLB

rCo 1jG jL 0:35

gDe

ph i. (30)

LB and Dr are the slug bubble length and density difference between the two phases,respectively.Based on a void fraction of 0.75, the transition of the annular ow took place when gas

and liquid supercial velocities satised the following relationship:

1:33jG 4jL

rL rGgDh 128CL jLDhnL

n2rLj

2L

9:24CGDhnG

n1rG 1 1:5 rLrG

1=3

vuuuut jn1=2G , 31

where CL and CG are dependent on the Reynolds number.In Eq. (31), nL and nG, are kinematic liquid and gas viscosities, respectively. n1 or n2 is

equal to unity for a laminar ow and n1 or n2 is equal to 0.25 for a turbulent ow.However, the models developed were found to be predictable for gaps larger than 0.6mm.For the 0.3mm micro-gap, they suggested that an appropriate theory consistent withpeculiar ow regimes observed was needed to develop the ow regime transition models.Zhao and Bi [19,20] performed experiments to study two-phase ow patterns in vertical

upward airwater ow in equilateral triangular channels having hydraulic diameters of2.886, 1.443 and 0.866mm. The images of the ow patterns were taken by a high-speedmotion analyzer along with the transient pressure-drop measurements. The ow patterns,including dispersed bubbly ow, slug ow, churn ow and annular ow, were observed inthe two larger triangular channels. These observations were similar to those generallyencountered in the ordinarily sized tubes placed in vertical direction. However, it wasinteresting to note that a new ow pattern, namely capillary bubbly ow, was identied inthe smallest channel in addition to the typical ow patterns, excluding the dispersed bubblyow. Another interesting point to note was that the slugchurn ow and churnannularow transition lines shifted to the right as the hydraulic diameter decreased. In addition,the previous ow regime transition models being available for upward gasliquid two-phase ow in the ordinarily sized tubes could not be used to predict the ow transitions.According to their second paper, the experimental investigation for analyzing gas

velocity, void fraction, and pressure drop was carried out in the same experimental setup.They reported that, based on the distribution of the parameter suggested by Ishii [21] and

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838834based on negligible drift velocity, the drift-ux model was in reasonable agreement with the

ARTICLE IN PRESSexperimental data for gas velocity obtained from all three test sections. In addition, theyobtained a correlation for predicting the void fraction and single-phase pressure drop. Thevoid fraction correlation developed was similar to that suggested by Armand and Treschev[11]. It was found that the LockhartMartinelli correlation was in good agreement with thetwo-phase pressure drop data when the proposed new single-phase friction factorcorrelation was employed.Chung et al. [22] explored nitrogen gaswater two-phase ow characteristics in a square

channel having a hydraulic diameter of 96mm and compared the results with those for a100mm circular channel employed by Kawahara et al. [8]. Similar results including pressuredrop and void fraction data were obtained, regardless of the channel geometry. In bothchannels, the LockhartMartinelli correlation appeared to do rather well when compared withthe pressure drop data while the void fraction data were found to be in poor agreement withthe homogeneous ow model as well as the Armand-type correlation. They also discussed theeffect of channel shape on the transition boundaries for ow patterns observed.A ow visualization study to clarify the ow patterns of vertical upward gasliquid two-

phase ow in rectangular mini-channels with hydraulic diameter ranging from 1.95 to5.58mm was carried out by Satitchaicharoen and Wongwises [23]. Airwater, air20wt%glycerol solution, and air40wt% glycerol solution were used as working uids. In theexperiments, they employed various rectangular test sections: 20mm 2mm,40mm 1mm, 40mm 2mm, 40mm 3mm and 60mm 2mm at an equal length of1m. The ow phenomena, which were bubbly ow, cap-bubbly ow, slug ow, churn owand annular ow, were observed and recorded by a high-speed camera. The effects of gapsize, channel width and liquid viscosity on the ow pattern transitions were discussed.English and Kandlikar [24] carried out experiments to explore the effect of surfactants

on two-phase pressure drop of airwater adiabatic ow in a 1mm square channel. Theconditions they tested were based on the operating control in a proton exchange membrane(PEM) fuel cell. The surfactant Triton

TM

DF-12 was employed to reduce the surfacetension to 0.034N/m. The application of the surfactant solutions appeared to have noeffect on the pressure drop due to many possible reasons, such as characteristics of the owpattern affecting interaction between the two phases, insufcient surface tension for anobservable change, and temperature variation. The accuracy of existing models for two-phase pressure drop prediction was evaluated. Based on the Mishima and Hibiki model[25], English and Kandlikar [24] also developed a new model applicable to low mass uxes,high mass qualities and annular ow by applying the Chisholm value for laminarlaminarow of 5 instead of the original constant of 21.Two-phase ow characteristics including ow pattern and pressure drop of ethanolCO2

owing through a converging or diverging rectangular micro-channel were explored byHwang et al. [26]. Different from previous works associated with the ow in micro-channels, they observed stratied wavy ows at the entrance of the converging micro-channel. Peculiar ow patterns and bubble interactions, which were due to the presence ofpressure and acceleration effects in the variable cross-section channels, were also discussed.For the pressure drop, they found that the channel pressure drop in the diverging micro-channel was substantially small in comparison to that in the converging micro-channel.However, the two-phase frictional multiplier plotted against the LockhartMartinelliparameter for both channels was independent of the liquid ow rate. This result was inagreement with that observed in nitrogenwater two-phase ow in circular micro-channels

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838 835investigated by Chung and Kawaji [12].

ARTICLE IN PRESSDue to different ow regimes raised in the same micro-channel under a given owcondition, Jassim and Newell [27] proposed void fraction and pressure drop models basedon the probabilistic ow regime map. This modeling technique was developed in such away that ow visualization data were incorporated into the models developed forpredicting pressure drop as well as the void fraction for airwater at 20 1C and refrigerantsincluding R410A and R134a at 10 1C with mass ux values ranging between 50 and 300 kg/m2 s. A test section with 6-port micro-channels of 1.54mm in hydraulic diameter was usedto obtain time fraction data for different ow regimes including liquid, intermittent,annular, and vapor ows. The proposed probabilistic model for predicting total pressuredrop in micro-channels can be expressed with many ow regime time fraction functionsand is given by

dP

dz

total

F liqdP

dz

liq

F intdP

dz

int

FvapdP

dz

vap

F anndP

dz

ann

, (32)

where Fliq, Fint, Fvap and Fann represent time fraction curve ts in liquid, intermittent,vapor and annular ow regimes, respectively. The pressure drop for single-phase ow,including that for liquid ow (dP/dz)liq and that for vapor ow (dP/dz)vap, is determinedfrom the conventional relation:

dP

dz

liq or vap

f G2

2r1

Dh

, (33)

where G is mass ux. The pressure drop model for intermittent ow assuming ahomogeneous density, rT, and employing the average kinetic energy, KEavg, is given by

dP

dz

int

0:045 1Dh

KEavg,

where

KEavg G2

2rT

and

rT x

rG 1 x

rL

1. (34)

The annular ow pressure drop model is evaluated as follows:

dP

dz

ann

f2vodP

dz

VO

, (35)

where f2VO is two-phase multiplier and is expressed by

f2VO exp 0:046X ann 0:22 exp 0:002X ann exp 7X ann , (36)

X ann w1

We1:3

rLr

0:9" #, (37)

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838836v G

In Eq. (35), the vapor only pressure drop is given by

a 0:833 0:167xx 1=rG , (41)

ARTICLE IN PRESSint 1 x 1=rL x 1=rG

aann 1 w1

We1:3v

rLrG

0:9" #0:06. (42)

Pressure drop and void fraction predictions based on the probabilistic ow regime mapwere found to be in accordance with the measured data obtained in micro-channels.However, care should be taken when the models are needed to be applied under conditionsand geometries other than those in which the probabilistic ow regime maps wereestablished.

3. Conclusions

As discussed above, this review reveals that there is only a small amount of publicationsavailable for the two-phase gasliquid adiabatic ow in micro-channels. The existingliterature is still lacking in various aspects, including geometry of mixing chamberconguration, uid properties, channel orientation and relevant ow models.It is obvious that the status of current researches on phase-change heat transfer and two-

phase ow phenomena in micro-channels is still in infant stage and a great deal ofsystematic investigations will become substantially more necessary to meet generalconclusions needed for the appropriate design and process control of several engineeringapplications.

Acknowledgements

The authors would like to express their appreciation to the Thailand Research Fund(TRF) and the Joint Graduate School of Energy and Environment (JGSEE) for providingdP

dz

VO

2f VO1

Dh

G2

rG. (39)

The probabilistic void fraction model proposed is also expressed with many ow regimetime fraction functions as shown by

atotal F liqaliq F intaint Fvapavap F annaann, (40)where aliq represents the void fraction for liquid only ow and is equal to 0, while avaprepresents the vapor only ow void fraction which is equal to 1. The intermittent ow voidfraction, aint, and annular ow void fraction, aann, are dened as follows: where Wev in Eq. (37) represents the Weber number for vapor and is dened as

Wev xG2rG s=Dh

. (38)

S. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838 837nancial support for this study.

ARTICLE IN PRESSS. Saisorn, S. Wongwises / Renewable and Sustainable Energy Reviews 12 (2008) 824838838References

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A review of two-phase gas-liquid adiabatic flow characteristics in micro-channelsIntroductionTwo-phase Gas-liquid adiabatic flow characteristics in micro-channelsCircular micro-channelsNon-circular micro-channels

ConclusionsAcknowledgementsReferences

a review of two-phase gas–liquid adiabatic flow

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