R., Fabbri, M., Michel, B., Calmi, D., and Kloter, U., High Heat Flux Flow Boiling in Silicon Multi-Microchannels—Part I: Heat Transfer Characteristics of Refriger-ant R236fa, Internatio
Trang 2CopyrightC Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903311652
e d i t o r i a l
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,
govern-ment 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
Ky-oto 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
rep-resents 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-IGM-LTCM, Station 9, 1015 Lausanne, Switzerland E-mail: john.thome@epfl.ch
The market for cooling of personal computers (PCs), datacenters, and telecom equipment is at a crossroads between oldair-cooling technology and more effective solutions, mainly liq-uid and two-phase cooling It appears that liquid cooling is thepreferred near-term solution because of its higher ease of im-plementation, but two-phase microscale cooling is of particularinterest due to evident performance advantages For instance, thelatent heat allows operation at a lower mass flow rate than single-phase cooling, and thus can reduce pumping power require-ments, resulting in a more energy-efficient system The boilingprocess takes place at an almost constant temperature, leading
to a small temperature gradient along the chip surface, which isadvantageous for thermal interface durability Finally, primarytrends in boiling in multi-microchannels [2–4] show that theboiling heat transfer coefficient increases with heat flux anddecreases slightly with increasing vapor quality Consequently,two-phase cooling is intrinsically well adapted to hot-spot man-agement, which is a critical point for the electronics industry andfor obtaining a uniform operating temperature along the chip.This issue collects seven papers originally presented at the5th International Conference on Transport Phenomena in Mul-tiphase Systems, HEAT 2008, June 30–July 3, 2008, Bialystok,Poland These studies address several aspects of flow boiling
255
Trang 3256 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
Micropro-cessors 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
Multi-Microchannels—Part I: Heat Transfer Characteristics of
Refriger-ant 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
Multi-Microchannels—Part II: Heat Transfer Characteristics of
Refriger-ant 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
Sili-con 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.
John R Thome is a professor of heat and mass
trans-fer at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland, since 1998, where he
is director of the Laboratory of Heat and Mass fer (LTCM) in the Faculty of Engineering Science and Technology (STI) His primary interests of re- search are two-phase flow and heat transfer, covering boiling and condensation of internal flows, external flows, enhanced surfaces, and microchannels He re- ceived his Ph.D at Oxford University, England, in
Trans-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 2 years as a senior engineer at Westinghouse Electric Company, Science and Technology Department, in Pittsburgh, Pennsylvania.
heat transfer engineering vol 31 no 4 2010
Trang 4CopyrightC 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
1School of Engineering and Design, Brunel University, West London, United Kingdom
2HTFS, 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/m 2 s and the heat flux from as low as 1.6 to 135 kW/m 2 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 1 mm for R134a.
INTRODUCTION
Modeling and design of micro devices of high thermal
perfor-mance, including electronic chips and other systems containing
compact and ultra-compact heat exchangers, require a
funda-mental 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
required to understand the mechanisms of flow boiling in
small-to micro-diameter passages
Channel Size Classification
Identifying the channel diameter threshold below which themacro-scale heat transfer phenomena do not fully apply is im-portant in validating and developing predictive criteria for thethermal-hydraulic performance of small- to micro-scale chan-nels However, there is no clear and common agreement onthe definition and classification criteria for the size ranges insmall/mini/microchannel two-phase flow studies One reasoncould be the lack of comprehensive heat transfer data cover-ing a wide range of channel diameters Mehandale et al [1]defined channel size ranges as follows: microchannel (1–100257
Trang 5258 T G KARAYIANNIS ET AL.
µm), mesochannel (100 µm–1 mm), macrochannel (1–6 mm),
and conventional (dh > 6 mm) Kandlikar and Grande [2]
sug-gested the classification of microscale by hydraulic diameter,
given as conventional channels (dh ≥ 3 mm), minichannels
(200µm ≤ dh < 3 mm), and microchannels (10µm ≤ dh <
200µm) These methods based only on size do not consider the
physical mechanisms and the variation of fluid properties with
pressure The absence of stratified flow in horizontal
microchan-nels, and hence the fact that the orientation of the channel has
virtually no effect on two phase flow patterns, indicates the
pre-dominance 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 E¨otv¨os number (E¨o> 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
consid-ering 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
de-parture 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
system-atic 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 Patterns
Flow pattern studies in small/micro tubes have clearly shown
that there is a considerable difference in the flow pattern
char-acteristics 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
intermit-tent 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
de-fined the flow patterns as isolated bubble flow, conde-fined bubble
flow, and annular-slug flow Identification of flow patterns issubject to uncertainty, which is not straightforward to quantifyand can also be significantly influenced by the experimentaltechnique used Besides, the transition from one flow pattern
to another may be a gradual rather an abrupt transition, as isoften reported Hence, flow patterns may possess characteris-tics of more than one flow pattern during transition Chen et
al [9] reported the results of a detailed study of flow ization experiments with R134a for a pressure range of 6–14bar and tube diameter from 1.1, 2.01, 2.88, and 4.26 mm withthe same test rig as the present one The typical flow patternsobserved in the four tubes are presented in Figure 1 They in-cluded dispersed flow, bubbly flow, confined flow, slug flow,churn flow, annular flow, and mist flow The flow patterns inthe 2.88 and 4.26 mm tubes exhibit characteristics found inlarge tubes The flow patterns in the 2.01 mm tube demonstratesome “small tube characteristics,” e.g., the appearance of con-fined bubble flow at the lowest pressure of 6 bar, and slimmervapor slug, thinner liquid film, and a less chaotic vapor–liquidinterface in churn flow Confined flow was observed at all pres-sures when the diameter was reduced to 1.1 mm, indicating
visual-Figure 1 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]).
heat transfer engineering vol 31 no 4 2010
Trang 6T G KARAYIANNIS ET AL 259
a potential transition range for heat transfer between 2 and 1
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 100µm and 50 µm internal
diameter, respectively They found several additional features
to those observed in small-diameter tubes For air–water
two-phase flow in a 25µm silica tube the special flow pattern features
found included liquid ring flow and liquid lump flow The
liq-uid 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
consecu-tive 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
liq-uid lumps are sliding on the wall.” Experiments using the same
fluid but in a 100µm quartz tube gave similar results as for the
25µm 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 100µm tube Flow patterns similar to those of air–water
flow in the 25µm silica tube were observed in the case of steam–
water flow in a 50µm 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
ex-perimentally adiabatic gas–liquid flow patterns using nitrogen
and water in rectangular microchannels with hydraulic
diame-ter of 0.209, 0.412, and 0.622 mm They observed four
differ-ent 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
Effect of Diameter on Transition Boundaries
The effect of tube diameter on flow pattern transition
bound-aries was also studied by various researchers Damianides and
Westwater [13] studied the flow regimes in horizontal tubes
of 1 to 5 mm inside diameters using air–water They reported
that reducing the tube diameter shifted the transition boundariesbetween intermittent-dispersed bubbly and intermittent-annularflow toward lower liquid velocity and higher gas velocity, re-spectively Also, they did not observe stratified flow regimeinside the 1 mm diameter tube In the study of air–water flowpatterns in tubes of 0.5 to 4.0 mm inside diameter, for verticalflow, Lin et al [14] observed that decreasing the tube diametershifted the slug-churn and churn-annular transition boundariestoward lower vapor velocity
Recently, Chen et al [9] noted that the diameter influencesthe transition boundaries of dispersed bubble-bubbly, slug-churnand churn-annular flow Also, the slug-churn and churn-annularboundaries are weakly dependent on superficial liquid veloc-ity and strongly dependent on superficial vapor velocity Thereseems to be no effect of diameter at the boundaries of dispersedbubble-churn and bubbly-slug flow The flow pattern transitiondata of Chen et al are plotted on a mass flux versus qualitygraph in Figure 2 for pressures of 6 and 8 bar As shown in thefigure, when the diameter is reduced, the slug-churn and churn-annular 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 flowregime boundaries are shifted to significantly lower qualities asthe mass flux increases At higher quality, the transition linesfor different tubes merge into a single line Chen et al reportedthat the Weber number may be the appropriate parameter todeduce general correlations to predict the transition boundariesthat include the effect of diameter
Recently, new correlations for transition of non-adiabaticflow 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 tion from coalescing bubble to annular flow, and it is considered
transi-an indication of the end of coalescing bubble flow The flowpattern maps were plotted as mass flux versus quality graphs.Revellin and Thome proposed flow pattern transition correla-tions, which give the quality at which the transition occurs Forthe transition from the isolated bubble to the coalescing bub-ble regime, their correlation contained the Reynolds, Boiling,and Weber numbers, as in Eq (1) A similar correlation for thetransition from the coalescing bubble to the annular regime con-tained only the Reynolds number and the Weber number, as in
Trang 7260 T G KARAYIANNIS ET AL.
Figure 2 Flow pattern transition boundary lines for the four tubes (Chen
et al [9] data): (a) 6 bar and (b) 8 bar pressure.
transition from coalescing bubble to annular flow regime, which
is equivalent to churn to annular transition, shifts to lower
qual-ity 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 8 bar, the transition qualities for the
2.01 and 1.10 mm tubes arex = 0.38 and x = 0.32, respectively.
From the experimental results of Chen et al [9], shown in
Fig-ure 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
for large diameter tubes, e.g., the appearance of confined flow
at about 2 mm for R134a, which may indicate a threshold forchange from large to small diameter For the same fluid theCornwell and Kew [4] criterion gives a critical diameter of 1.7
mm for P= 6 bar pressure Flow pattern studies for even smallertubes (near or less than 1 mm) revealed the existence of a number
of different flow pattern types, e.g., ring flow and lump liquidflow, which have not been found in larger diameter tubes This
is indicative of a possible further change in flow patterns andhence in thermal characteristics at these even smaller diameters.This is discussed later in the article in light of the recent resultsfrom our own investigations
Heat Transfer
Nucleate boiling, forced convection, and a combination ofthe two are the main mechanisms often reported in the litera-ture for flow boiling heat transfer in large-diameter tubes, e.g.,Kenning and Cooper [16] These have also been adopted inidentifying the heat transfer mechanism in small-diameter tubesand microchannels, although different conclusions have beendrawn by researchers as to their prevalence Some researchersconcluded that nucleate boiling is the dominant heat transfermechanism when it was observed that the heat transfer coef-ficient is more or less independent of vapor quality and massflux, while it is strongly dependent on heat flux—e.g., Lazarekand 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 otherhand, 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 transfermechanism—e.g., Carey et al [23], Oh et al [24], Lee and Lee[25], and Qu and Mudawar [26] Some researchers reported acombined effect of both mechanisms, i.e., nucleate boiling atlow 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 thatmacroscale boiling heat transfer correlations and models did notpredict well the heat transfer coefficient in small-diameter tubes,
as noted by Qu and Mudawar [26], Owhaib and Palm [31], andHuo et al [32]
More complex behavior and differences dependent on thefluid tested were reported by other researchers For example,Dı’az and Schmidt [33] investigated transient boiling heat trans-fer in 0.3× 12.7 mm microchannels using infrared thermogra-phy to measure the wall temperature For water, the heat transfercoefficient decreased with quality near the zero quality region,followed by a uniform heat transfer coefficient However, forethanol at high quality, an increase in heat transfer coefficientwith quality was found to be independent of applied heat flux
A similar behavior, i.e., an increase in the heat transfer cient with quality, was observed by Xu et al [34] and Lie et al.heat transfer engineering vol 31 no 4 2010
Trang 8coeffi-T G KARAYIANNIS ET AL 261[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
co-efficient 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 5 to 39 kW/m2, mass
flux from 150 to 450 kg/m2s, saturation pressure from 3.5 to 4.7
bar, and inlet vapor quality from 0 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
trans-fer 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) the heat
transfer coefficient increases with heat flux and decreases or is
relatively constant with vapor quality, and at high vapor quality
it decreases sharply with vapor quality and is independent of
heat flux or mass flux
Initiation of Boiling
Flow boiling in very-small-diameter tubes is usually
associ-ated with high initial liquid superheat required to initiate boiling
Yen et al [37] conducted flow boiling experiments in 0.19, 0.3,
and 0.51 mm inside diameter tubes using R123 and FC-72 They
observed a high liquid superheat that reached up to 70 K in their
experiments In the low quality region, the heat transfer
coeffi-cient was observed to decrease with quality up to approximately
x= 0.25 and then became almost constant with further increase
in quality Hapke et al [38] investigated boiling in a 1.5 mm
internal diameter tube and reported that the onset of boiling
oc-curred at higher liquid superheat than required for conventional
tubes Peng and Wang [39] and Peng et al [40], based on their
observations of boiling in microchannels of hydraulic diameter
200–600µm, argued that nucleation can hardly be seen in
mi-crochannels They proposed a hypothesis of “evaporating space”
to explain the phenomenon They also suggested a theoretical
model to predict the superheat temperature The unusually highsuperheat in micro tubes was also reported to be related to thereduction of active nucleation sites and vapor nucleation insidevery small channels, by Zhang et al [41] and Brereton et al.[42]
Temperature and Pressure Fluctuations
Microchannel flow boiling studies have demonstrated a crease in heat transfer coefficient with increasing quality, oftenaccompanied by fluctuating wall temperatures—e.g., Lin et al.[28], Yan and Lin [43], Wen et al [44], and Huo et al [32].These have been attributed to transient dry-out, particularly atlow mass flux, and relatively high heat flux Kenning et al [45]suggested that there are two different mechanisms of dry-outaround individual bubbles in microchannels These are dry-out
de-as a result of depletion of the film thickness below a certainminimum by complete evaporation of the liquid film beneaththe confined bubble and dry-out due to surface-tension-driven
“capillary roll-up” on partially wetted surfaces with finite tact angles Experimental studies also indicated fluctuations inpressure and wall temperature Yan and Kenning [46] inves-tigated water boiling at atmospheric pressure in a 2 × 1 mmchannel They showed that the pressure fluctuations were caused
con-by the acceleration of liquid slugs con-by expanding confined bles, confirming a model of Kew and Cornwell [47], and thatthe corresponding fluctuations in saturation temperature were ofmagnitude similar to the mean superheat causing evaporation,
bub-so they could not be neglected
Effect of Decreasing Diameter
There are a limited number of experiments that have tested awide range of tube diameter to investigate the heat transfer trendwith channel size Studies that have considered the effect of di-ameter are reviewed briefly here Yan and Lin [43] conductedexperiments with R134a using a single tube of internal diame-ter 2.0 mm and heated length 100 mm They claimed that theevaporation heat transfer coefficient increased by 30% to 80%compared with conventional diameter tubes Oh et al [24] ex-perimentally investigated the evaporation heat transfer for threedifferent copper tubes of diameter 0.75, 1.0, and 2.0 mm usingR134a For vapor quality less than 0.6, they found the heat trans-fer coefficient for the 1.0 mm tube to be higher than that of the2.0 mm tube by approximately 45% However, decreasing thetube diameter shifted to a lower quality the point at which theheat transfer coefficient started to decrease axially, presumablydue to dry-out Owhaib et al [48] studied experimentally evap-orative heat transfer using R134a in vertical circular tubes ofinternal diameter 1.7, 1.22, and 0.83 mm, and a uniform heatedlength of 220 mm Other parameter ranges are: mass flux 50–
400 kg/m2-s, heat flux 3–34 kW/m2, and pressure 6.5–8.6 bar.They concluded that the heat transfer coefficient increased withdecreasing tube diameter
heat transfer engineering vol 31 no 4 2010
Trang 9262 T G KARAYIANNIS ET AL.
In general, experimental results indicate an increase in the
heat transfer coefficient as the diameter decreases However,
some contradictory results are also available For example,
Kuwahara et al [49] experimentally studied the flow boiling
heat transfer characteristic and flow pattern inside 0.84 and
2.0-mm diameter tubes using R134a and found no difference in the
heat transfer characteristics between the two tubes Baird et al
[50] conducted boiling experiments on tubes of 0.92 and 1.95
mm diameter and found no significant effect of diameter on the
heat transfer coefficient Khodabandeh [51] studied boiling in
a two-phase thermosyphon loop with iso-butene as a working
fluid with tubes ranging from 1.1 to 6 mm in diameter He also
concluded that the effect of diameter was small and not clear
In the work of Saitoh et al described earlier, there was no
obvi-ous effect of diameter on heat transfer coefficient or it was not
straightforward to deduce the influence
A theoretical three-zone model for predicting the local
dy-namic and local time-averaged heat transfer coefficient was
pre-sented by Thome et al [52] and Dupont et al [53] The model is
based on convective heat transfer in the confined bubble regime
without a contribution from nucleate boiling The model
pre-dictions indicate that the heat transfer coefficient increases with
diameter for quality greater than 0.18, while it decreases with
diameter for quality less than 0.04 Dupont and Thome [54]
compared the model results with the experiments of Owhaib
et al [48] The model did not predict the trend of increasing
heat transfer coefficient with decreasing diameter Instead an
opposite prediction was observed in the quality range covered
Dupont and Thome [54] noted the lack of adequate
experimen-tal data covering a wide range of tube diameter for boiling heat
transfer The model predictions were also compared with
ex-perimental data for R134a and tubes of 2.01 and 4.26 mm in
diameter by Shiferaw et al [55]; they reported that the model
predicts that the diameter has an opposite effect on the heat
transfer coefficient compared to the measured data
The preceding brief overview indicates that a lot of work
is still necessary to elucidate the effect of diameter on the rate
and mechanism of heat transfer, including the possible diameter
thresholds for distinguishing macro, small and microscale
char-acteristics Although more than two tubes were used in some
of the past studies, it was not possible to identify the influence
of diameter because different conditions were used for different
diameter tubes Therefore the experimental facility described in
the next section was used to determine the heat transfer
coeffi-cients for R134a in five tubes of different diameter for similar
wide ranges of heat and mass fluxes and pressure, combined
with flow visualization at the exit from the test section
EXPERIMENTAL FACILITY AND PROCEDURE
The experimental facility consists of three main systems,
which are the R134a main circuit, data acquisition and control,
and the R22 cooling system The main facility, which is shown
in Figure 3, was designed to allow testing of different fluids and
Figure 3 Schematic diagram of the experimental system.
a wide range of flow conditions Details of the experimental tem were given in Huo et al [32] The test sections were made
sys-of stainless-steel cold-drawn tubes The dimensions sys-of the fivetest tubes are given in Table 1 They were heated by the directpassage of alternating electric current The outer wall temper-atures for the 4.26 mm to 1.1 mm tubes were measured using
15 K-type thermocouples that were spot-welded to the outside
of the tube at a uniform spacing The first and last ple readings were not used in the analysis so as to avoid errorsdue to thermal conduction to the electrodes Ten thermocoupleswere spot-welded on the 0.52 mm tube; the two at each endwere located sufficiently far from the electrodes to be used inthe data analysis The pressures and temperatures at the inletand outlet were measured using pressure transducers and T-typethermocouples A differential pressure transducer was installedacross the test section to provide the pressure drop measure-ment At the exit from the heating section, a borosilicate glasstube for flow pattern observation was located A digital high-speed camera (Phantom V4 B/W, 512× 512 pixels resolution,
thermocou-1000 pictures/s with full resolution and maximum 32,000 tures/s with reduced resolution, 10 ms exposure time) was used
pic-to observe the flow patterns
A series of flow boiling tests was then performed at differentmass flux and heat flux During these tests, the inlet temperaturewas controlled at a subcooling of 1–5 K by adjusting the capacity
of the chiller and heating power to the preheater The flow rate
Table 1 Range of experiment parameters Parameters Range Diameter 4.26, 2.88, 2.01, 1.10, and 0.52 mm Wall thickness 0.245, 0.15, 0.19, 0.247, and 0.15 mm Heated length 500, 300, 211, 150, and 100 mm Roughness 1.75, 1.54, 1.82, 1.28, and 1.15 µm Mass flux 100–700 kg/m 2 -s
Heat flux 1.6–150 kW/m 2
Vapor quality 0–0.9 Pressure 6, 8, 10, 12, and 14 bar
heat transfer engineering vol 31 no 4 2010
Trang 10Heat transfer coefficient 6–12.5%
was set to the required value and the heat flux was increased in
small steps until the exit quality reached about 90% The data
were recorded after the system was steady at each heat flux,
which normally took about 15 min but sometimes longer Each
recording was the average of 20 measurements The next test
was then performed at a different flow rate All the instruments
used were carefully calibrated Tables 1 and 2 summarize the
range and uncertainties of the important parameters
DATA REDUCTION
The local heat transfer coefficientα(z) at each thermocouple
position was calculated using local values of the inside wall
temperature and the saturation temperature and is given by:
(T wi)z − (T s)z (3)whereq is the inner wall heat flux to the fluid determined from
the electric power supply to the test section and the heat loss
T wiis the local inner wall temperature, which can be determined
using the internal heat generation and radial heat conduction
across the tube wall as given by:
T wi = T wo−q · d i
4
(d i /d o)2− 2 ln(d i /d o)− 1
1− (d i /d o)2
(4)
T sis the local saturation temperature, deduced from the local
fluid pressure assuming a linear pressure drop across the test
section The local specific enthalpy,h i, at each thermocouple
position was determined from the energy balance in each heated
section considering the losses:
h i = h i−1+ L i
˙
where the heat transfer (Q) is the total electric heat input, which
is equal to the product of the voltage and the current applied
di-rectly to the test section (Q) is the heat loss determined using
the loss coefficient obtained from single-phase test before each
series of boiling tests Therefore, the local vapor quality can be
calculated from the local specific enthalpy at each thermocouple
position and is given as:
con-in Figure 4b agree very well with Dittus and Boelter [57] and
Figure 4 Single-phase results ford= 4.26 mm at 7.5 bar: (a) friction factor
vs Re, (b) Nusselt number vs Re.
heat transfer engineering vol 31 no 4 2010
Trang 11264 T G KARAYIANNIS ET AL.
Petukhov [58] correlation—again, below the uncertainty limit
The preceding results verified the overall accuracy of the
exper-imental system Experexper-imental accuracy becomes an increasing
difficult challenge as the size of the passages decreases and
ei-ther laminar or turbulent flow may exist, depending on the mass
flow rate Therefore, additional single-phase experiments were
performed with the 0.52 mm tube to assess the ability of the
test rig to produce accurate results at this small diameter The
comparisons of the experimental results with past results and
known correlations were presented in Shiferaw et al [59] The
results agreed fairly well with the modified Gnielinski [60] and
Adams et al [61] for the turbulent regime and Choi et al [62]
in the laminar regime The reproducibility of the boiling tests
was also verified The test results (4.26–1.1 mm tubes) were
mostly within the range of uncertainty of the data; see Shiferaw
et al [63] for the 1.1 mm tube The reproducibility of the
0.52 mm tube tests was acceptable in the lower range of heat flux,
had differences in the intermediate range, and was acceptable
again at high heat fluxes [64] This could be due to the sparse
and/or unstable nucleation sites at this small size and will be
examined further The preceding set of experiments confirmed
the adequate accuracy and validity of the present results
EXPERIMENTAL RESULTS AND DISCUSSION
Flow Pattern Results
Figure 5a and b, presents the flow patterns observed during
the boiling test at a mass flux of 400 kg/m2-s and pressure
8 bar for the 0.52 mm tube and should be compared with the
results of Chen et al [9], obtained with the same test facility and
procedure depicted in Figure 1 These flow patterns were taken
simultaneously with the heat transfer tests presented hereinafter
Figure 5 (a) Flow patterns in 0.52 mm tube at 400 kg/m 2 s and 8 bar; (b)
sequence of flow patterns showing coalescence.
at each value of heat flux They represent the more frequentlyobserved flow pattern for the particular heat flux However,more than one type of flow pattern occurred intermittently insome cases Image 1 shows bubbly flow Confined bubble flow(images 2 and 3) was observed at low heat flux or exit quality Asthe heat flux increased, the bubbles grew in length and becameelongated Further increase in heat flux resulted in the liquidslug between the bubbles being “pushed” onto the downstreambubble, creating coalescence of the bubbles and a wavy film
A similar phenomenon was observed by Revellin et al [65].Figure 5b shows a sequence of how three relatively short bubblescoalesce in the adiabatic viewing section to form an elongatedbubble, leaving the liquid film interface wavy Note that theseobservations were carried out at the exit of the test section andcoalescence may be different in the heated section As shownagain in Figure 5a, when increasing the heat flux even further,
a type of wavy film flow, similar in appearance to what wasdescribed earlier as liquid ring flow (Serizawa et al [10]), isobtained for a relatively wide range of quality (images 4–6) Inthis case, the film interface is highly nonuniform and can lead
to a transition to annular flow (image 7), since further increase
in heat flux reduces the wave irregularity and distributes thewaves almost uniformly: annular flow (images 8–10) At highheat flux, the annular flow patterns have small-scale roughness
of very short amplitude and wavelength
Overall, the flow patterns observed in the smaller tube ofinternal diameter 0.52 mm were different from those observed
in the larger tubes by Chen et al [9] As mentioned earlier,these differences include the absence of dispersed flow and theappearance of a transitional wavy film flow In this tube, liquidlump flow (see Serizawa et al [10]) was not observed
Heat Transfer Results
Typical experimental data for the five tubes are plotted asgraphs of heat transfer coefficient vs quality, the presentationconventionally used for large tubes This implies that heat trans-fer depends only on local flow conditions and not on how theflow is developed, so that the convective component depends
on the local flow pattern The relationship between flow patternobservations in an adiabatic section at the exit from the tube andthe flow pattern within the heated section at the same qualitymay require examination for the particular conditions in smalltubes, in which the growth of an individual bubble may influence
a considerable length of the tube
Data at a pressure of 8 bar and a mass flux of 400 kg/m2s
in the tubes with diameters 4.26–0.52 mm are plotted in Figure6a–e As seen in, for example, Figure 6a for the 4.26 mm tube,
at a qualityx < 0.5 approximately and moderate heat flux, the
heat transfer coefficient is constant within±10% at a value thatincreases with heat flux and pressure, but that is independent ofquality Huo et al [32] and Shiferaw et al [55] reported similartrends at 8 bar and a mass flux of 300 kg/m2-s in the 4.26 and2.01 mm tubes Within this range, the local variations appear toheat transfer engineering vol 31 no 4 2010
Trang 12T G KARAYIANNIS ET AL 265
Figure 6 Local heat transfer coefficient as a function of vapor quality at mass flux 400 kg/m 2 -s and pressure 8 bar: (a) 4.26 mm; (b) 2.88 mm; (c) 2.01 mm; (d) 1.10 mm; (e) 0.52 mm.
follow a pattern associated with the axial positions of the
mea-suring stations As the variations do not appear in single-phase
flow experiments, they are not associated with individual
ther-mocouples or wall roughness that would affect the liquid flow
They may indicate variations in wall characteristics that affectbubble nucleation or the stability of thin liquid films round con-fined bubbles At higher quality and/or heat flux, these patternschange to a general tendency for the heat transfer coefficientheat transfer engineering vol 31 no 4 2010
Trang 13266 T G KARAYIANNIS ET AL.
to decrease with increasing quality and to converge on a single
line that is independent of heat flux This trend cannot be fully
confirmed in these experiments with a fixed heated length for a
given diameter of tube, since high quality cannot be achieved at
low heat flux However, one can also observe that the quality at
which the heat transfer coefficient becomes independent of heat
flux and decreases with quality moves to lower values of quality
as the diameter is reduced (e.g., at approximatelyx = 0.5 for
d = 4.26 mm and x = 0.3 for d = 2.01 mm).
At very high heat flux, the heat transfer coefficient may
de-crease with heat flux The effect is particularly marked in the
2.01 mm tube, Figure 6c forq= 95–134 kW/m2 The heat flux
and quality at which this occurs both decrease with decreasing
tube diameter Shiferaw et al [55] and Huo et al [32] reported
that the tube wall temperature was highly unstable in this
par-ticular region, which could indicate the occurrence of partial
(intermittent) dry-out with a long time scale Lin et al [28] and
Sumith et al [29] observed wall temperature fluctuations that
increased as the heat flux increased This was assumed to be
related to time varying local heat transfer coefficient and local
pressure; see Lin et al [28] and Wen et al [44]
The behavior in the 0.52 mm tube at the same pressure and
mass flux is significantly different, as in Figure 6e For this
tube, the liquid-only Reynolds number is 1100, which should
correspond to laminar flow at the inlet, unlike the liquid-only Re
numbers in the 4.26, 2.88, 2.01, and 1.1 mm tubes which were
9500, 6400, 4500, and 2500, respectively There is a different
dependence of the heat transfer coefficient on heat flux and
vapor quality below and above a heat flux of 17.9 kW/m2 This
heat flux threshold coincides with the appearance of the wavy
film flow—see image 4 in Figure 5a—and the disappearance
of the small superheat that is recorded by the thermocouple in
the exit flow At the low heat fluxes, the heat transfer coefficient
does not depend on heat flux and decreases slightly with quality
However, it must be noted that the data here are limited tox <
0.15 At these low heat flux values a longer tube would be
required to reach high exit quality There is an abrupt increase
in the heat transfer coefficient and a change in its trend with
quality and heat flux at heat fluxes of 17.9 kW/m2and above At
these heat fluxes, the heat transfer coefficient initially increases
rapidly with quality, as in Figure 6e The data points for all
heat fluxes converge on approximately the same line as far as
the third thermocouple in zone I The initial variations may be
influenced by the small differences in the low inlet subcooling
In zone II, between the third and fourth thermocouples, the
heat transfer coefficient levels off at a maximum value that
depends on the heat flux This is followed by a large reduction
in heat transfer coefficient in zone III between the fourth and
fifth thermocouples After that, the data fall on another line
of increasing heat transfer coefficient that, within experimental
error, is almost independent of heat flux in zone IV At the
highest heat flux only, there is a large fall in the heat transfer
coefficient at the last measuring point at a qualityx = 0.71 This
is not reproduced in other runs at nearly the same conditions,
so it may indicate that the system is on the threshold of the
Figure 7 Heat transfer coefficient vs axial distance at mass flux 400 kg/m 2 -s and pressure 8 bar for 0.52 mm tube Heat flux values as in Figure 6e.
transient dry-out that is thought to cause the reduction in heattransfer coefficient with increasing quality in the larger tubes.When plotted againstz/L, Figure 7, the pattern of variation of
the heat transfer coefficient appears to be related to the axialpositions of the measuring stations more strongly than for thelarger tubes
Figure 8 is a plot similar to Figure 6e for the same 0.52
mm tube at a lower mass flux of 300 kg/m2-s (liquid-only Renumber 720) and a lower pressure of 6 bar, reported in Shiferaw
et al [59] It confirms that the heat transfer characteristics ofthis tube are indeed different from the larger tubes There areagain two groups of data, this time separated by a threshold heatflux of 12.5–14.8 kW/m2, which also appears to coincide withthe change of slug or confined flow to the wavy film type flowmentioned earlier at the exit from the heated section At thelow heat fluxes, the heat transfer coefficient is approximatelyindependent of heat flux although, in contrast to Figure 6e,
it initially falls significantly with quality and then exhibits aweak increase At values higher than 14.8 kW/m2, theα versus
x plot follows the same general pattern of axial development
through zones I–IV seen in Figure 6e, except that the values ofaxially increasing heat transfer coefficient in zone I depend on
Figure 8 Heat transfer coefficient vs quality at mass flux 300 kg/m 2 -s, sure 6 bar in the 0.52 mm tube.
pres-heat transfer engineering vol 31 no 4 2010
Trang 14T G KARAYIANNIS ET AL 267
Figure 9 Heat transfer coefficient vs axial distance at mass flux 300 kg/m 2 -s,
pressure 6 bar in 0.52 mm tube (The markerx= 0 indicates the position where
saturation is achieved for q = 1.6 kW/m 2 For the rest, this happens at/before
the first thermocouple position.) The symbols and colors are the same as for
Figure 8.
heat flux and the influence of heat flux extends into zone IV,
where the heat transfer coefficient again increases axially The
test section is not long enough at low heat fluxes to show for
certain whether the data converge on a line independent of heat
flux at high quality For heat fluxes above the threshold value,
the pattern of variations inα again appears to depend on the
fraction of heated lengthz/L, as in Figure 9, but the pattern is
not exactly the same as in Figure 7 The maximum heat transfer
coefficient now occurs at thermocouple 3 instead of 4 The
subsequent reduction in zone III is less abrupt, still continuing
to thermocouple 5 There are also differences in the detail of the
pattern in zone IV If the pattern depends on the effect of local
roughness on local nucleation of bubbles, the effect appears to
be moderated by the changes in flow conditions and system
pressure
Yet another way of plotting the same data in Figures 8 and
9 is as boiling curves at measuring points 3–8, as in Figure 10;
see Shiferaw et al [59] The plots look like pool boiling curves
for increasing heat flux in a system with nucleation hysteresis
at 12.5 kW/m2 If the nucleation characteristics vary axially, it
Figure 10 Wall superheat vs heat flux at each measuring station,D= 0.52
mm, mass flux 300 kg/m 2 -s, pressure 6 bar.
is unlikely that the same threshold would apply at all stations.Alternatively, nucleation may occur at upstream sites, and down-stream positions are influenced by the growth of individual con-fined bubbles that may cover a long axial length It is impossible
to observe local nucleation in a metal tube and the observations
of flow patterns are restricted to the tube exit Confined bubbleflow with smooth liquid films round long bubbles, as assumed
in the Thome et al [52] convective model, is observed with lowheat transfer coefficients just below the threshold heat flux, as
in Figure 5a, image 3, at 400 kg/m2-s, and wavy film flow justabove the threshold The large increase in heat transfer coeffi-cient above the threshold occurs throughout the length of thetube and particularly near the inlet in zones I and II, so it cannot
be caused by a gradual progression from the exit toward theinlet of a flow regime transition at a particular quality Furtherinvestigation is required of whether nucleation is triggered at asingle site, which could exert downstream influence through thebubble frequency that is an important parameter in the Thome
et al model for convective evaporation, or at more widely tributed sites The availability of sites may become subject tolarge statistical variability as the surface area decreases withdecreasing tube diameter, as in Zhang et al [41] and Brereton
dis-et al [42]
A further special feature of the 0.52 mm tube is the decrease
in the heat transfer coefficient in zone III, commencing at aquality that increases with increasing heat flux, followed byconstant or increasing heat transfer coefficient in zone IV, with
a fall very close to the tube exit in some runs It is therefore likely
to have a different mechanism from the axial decrease in heattransfer coefficient observed in the larger tubes of this study,which commences at a quality that decreases with increasingheat flux and is then maintained to the end of the tube Because
of its association with a particular axial length of the tube,the heat transfer in zone III of the 0.52 mm tube may depend
on interactions between nucleation sites and the changing flowregime From the observations of the exit flow, as in Figure5a, the flow in zone IV is annular, with intensive disturbances
to the liquid film that decrease in scale with increasing heatflux and quality It is not possible to determine directly whethernucleation occurs in the film
Conventionally, the relative importance of nucleate boilingand convective evaporation are deduced from the dependence ofthe heat transfer coefficient on heat flux or mass flux and quality.Thome et al [52] showed that this could be misleading in smallchannels Shiferaw et al [55] found that the Thome convectivemodel, which includes cyclic dry-out of the thin films round con-fined bubbles, provided satisfactory estimates for heat transfer
in the 4.26 and 2.01 mm tubes of this study under conditions parently dominated by nucleate boiling, possibly because bothmechanisms involve the cyclic creation and evaporation to dry-ness of thin liquid films It must be noted from the flow vi-sualization by Chen et al [9], Figure 2, and for the 0.52 mmtube in this article, that the regime for which the Thome model
ap-is valid (thin, undap-isturbed films around dap-iscrete confined bles) is restricted to low qualities Convective models for highheat transfer engineering vol 31 no 4 2010
Trang 15The experimental heat transfer coefficients in the 4.26–1.10
mm tubes all exhibit at low quality “apparently nucleate
boil-ing” characteristics, being nearly independent of quality and
mass flux, if the region of heat transfer coefficient decreasing
with quality, indicative of transient dry-out, is excluded For the
0.52 mm tube, the heat transfer coefficient is nearly independent
of quality and mass flux in zone II All these data are shown
in Figure 11 on a plot of heat transfer coefficient vs heat flux
for a mass flux of 400 kg/m2s at 8 bar pressure The data were
fitted by a power-law equation of the formα = Cq n, as is
con-ventional for nucleate boiling As mentioned earlier, this could
be due to the fact that both mechanisms (pool and transient
film evaporation) involve the cyclic creation and evaporation of
thin liquid films The exponentn is kept constant at 0.62 and
the values of the constantC for the 4.26, 2.88, 2.01, 1.10, and
0.52 mm diameter tubes are 14.3, 14.5, 16.6, 19.5, and 33.7,
respectively The heat transfer coefficients for the 4.26 and
2.88 mm diameter tubes are almost the same; the increases for
the 2.01, 1.10, and 0.52 mm tubes are 15, 35, and 134%,
respec-tively This last figure exaggerates the benefit from decreasing
diameter, because it is based on the peak values in zone I and
the improvement averaged over zones I plus II is about 90%
This approach may be useful for the design of cooling systems
for minimum temperature difference, achieved by operating at
low exit quality to avoid dry-out
The dependence of the heat transfer coefficient on mass
flux and local quality is shown in Figure 12 for a heat
flux of 54 (4.26 to 1.1 mm tubes) and 58 kW/m2
(0.52-mm tube) and 8 bar pressure At low qualities, the
ap-proximately constant values of the heat transfer coefficient
are almost independent of mass flux within the
experimen-tal uncertainty for the four larger diameter tubes For the
4.26 mm tube, afterx = 0.15, the heat transfer coefficient
de-creases slightly with mass flux, which could be related to an
influence on film thickness However, this is not repeated in the
2.88 to 1.1 mm tubes As also noted earlier, further experiments
are required to resolve the issue, using longer heated lengths toachieve larger exit qualities, subject to any limitations imposed
by pressure drop The results for the smallest diameter tube inFigure 12e are clearly different There is a significant effect ofmass flux in zone IV (increasing trend of heat transfer coeffi-cient with quality) In this region, the heat transfer coefficientincreases with increasing mass flux and, as seen in Figure 6e,there is no obvious effect of heat flux especially at high quality.This, with the observations at the visualization section, appar-ently supports the previous speculation that convective evapora-tion of the annular flow dominates the heat transfer mechanism
at high quality (Lin et al [28], Sumith et al [29], and Saitoh et
al [30]) However, when plotted against axial distancez/L in
Figure 13, the data for the 0.52 mm tube collapse onto a gle line independent of mass flux but with large axial variations,suggesting that time-averaged quality is not the controlling vari-able By contrast, the data for the 1.1 mm tube follow a line ofnearly constantα at high mass flux, with lines of decreasing αbranching off at points that move toward the tube inlet as themass flux is reduced It appears that quality is the relevant vari-able for the assumed process of transient dry-out in the largertubes of this study
sin-The influence of system pressure is illustrated in Figure 14
by plots of heat transfer coefficient vs quality for all the tubes
at the same mass flux of 400 kg/m2-s and heat flux of 54 kW/m2(4.26, 2.88, 2.01, and 1.10 mm tubes) and 58 kW/m2 (0.52
mm tube) (These are almost the same as plots ofα vs z/L.)
For qualityx < 0.3, the heat transfer coefficient increases with
system pressure for the 4.26 to 1.10 mm tubes The effects ofpressure at higher qualities at various values of heat flux andmass flux were reported in Shiferaw et al [55] For the 4.26
mm diameter tube, the effect of pressure was less significant
at higher qualities (x > 0.5), while for the 2.01 mm diameter
tube there was a rather uniform increase in the coefficient withpressure throughout the experimental range of quality (x < 0.7).
Again, the 0.52 mm tube behaves differently, as in Figure14e Increasing pressure causes a much larger increase in theheat transfer coefficient at smallx in zones I and II, compared to
zone IV at higherx, and the decrease in heat transfer coefficient
in zone III becomes sharper There is a drop in heat transfercoefficient at the last measuring point for 8 and 10 bar pressure,which might indicate the onset of thin film dry-out
DISCUSSION
This article is based on flow visualization studies and heattransfer measurements obtained over a period of 6 years for fivetubes of different diameters Some of the data are new and somehave been published previously When some data sets were ex-tended in range, the heat transfer coefficients were found to bereproducible within±5%, even after intervals of 3 years Thedata for the 4.26 to 1.1 mm tubes have some features that areconventionally and appropriately presented as functions of localquality, combined with a weak dependence on the axial positionheat transfer engineering vol 31 no 4 2010
Trang 16T G KARAYIANNIS ET AL 269
Figure 12 Effect of mass flux on heat transfer coefficient versus quality at heat flux (q= 54 and 58 kW/m 2 ) and pressure (P= 8 bar): (a) 4.26 mm; (b) 2.88 mm; (c) 2.01 mm; (d) 1.1 mm; (e) 0.52 mm.
within a particular test section This axial dependence was much
stronger in the data for the 0.52 mm tube These axial patterns
are not present in single-phase tests, so they are consequences
of boiling Very recent tests on this tube have shown that the
patterns tend to be stable during a series of tests on a particular
day but there may be a different pattern on other days In the
parametric studies of heat flux, mass flux, and pressure reported
in this article, examples have been chosen from tests performed
at similar times Similar variability on different days was
ob-served in the “apparently nucleate” regime during flow boiling
of water in a large (9.6 mm) tube but not in the “apparentlyconvective” regime of Kenning and Cooper [16] In that study,polishing the tube surface also modified the nucleate but not theconvective boiling regime Surface roughness has a large influ-ence on bubble nucleation in pool boiling, so axial variations insurface roughness may influence local nucleation The influence
of surface conditions on boiling in small metal tubes has as yetreceived little attention Surface roughness may also affect aparameter in the convective boiling model of Thome et al [52]for microchannels, namely, the minimum stable thickness of theheat transfer engineering vol 31 no 4 2010
Trang 17270 T G KARAYIANNIS ET AL.
Figure 13 Effect of mass flux on the heat transfer coefficient versus axial
distance at 8 bar: (a) 0.52 mm tube at 58 kW/m 2 and (b) 1.1 mm tube at 54
kW/m 2
evaporating liquid film round confined bubbles Shiferaw et al
[55] showed that the predictions of the Thome et al model were
improved if the experimental measurements of roughness were
used instead of the recommended film thickness The surface
roughness of samples from the four larger tubes used in this
study was measured after sectioning by scanning in an axial
direction with a conventional contact stylus; values are given in
Table 1 The surface roughness of the 0.52 mm tube was
ob-tained from a three-dimensional (3-D) sample, captured using a
high-resolution non-contact probe
In the experiments described here, and in those performed
earlier by Chen et al [9], flow patterns were observed at the
exit of the test section Observations within a tube are possible
for transparent tubes with transparent thin-film heaters, as in the
experiments of Owhaib et al [48], but the nucleation
charac-teristics are different and it is difficult to obtain simultaneous
accurate measurements of the wall temperature The flow
pat-terns observed at the exit from the 0.52 mm tube were certainly
different from those observed earlier in the relatively larger
di-ameter tubes (4.26–1.1 mm) by Chen et al [9] These differences
include the absence of dispersed bubble flow and the
appear-ance of a transitional wavy film flow Thus, there were further
differences between the flow patterns leaving the 2.88 and4.26 mm diameter tubes and those from the 2.01 and 1.1 mmtubes, which exhibited confined flow, slimmer vapor slugs, thin-ner liquid films, and smoother vapor–liquid interfaces Thesedifferences coincided with the progressive transition to higherheat transfer coefficients in the 2.01 and 1.10 mm tubes Usingthe confinement number (Cornwell and Kew [4]), the deviationfrom large-tube characteristics should be observed at diame-ters of 1.4 to 1.7 mm at 6–14 bar pressure for R134a, which isroughly in agreement with the present heat transfer results andflow visualization observations “Small-tube characteristics” in1.1 mm tubes were reported in the previous studies of Damian-ides and Westwater [13] and Mishima and Hibiki [7]
Flow maps such as Figure 2, based on observations at theexit from the 4.26 to 1.10 mm tubes, show that, at the lowmass fluxes covered in the present heat transfer tests, the tran-sition to annular flow shifts to higher qualities approaching
x ≈ 0.5 While the information on flow regimes cannot betransferred with certainty to upstream locations, it is likelythat slug/churn flow is the typical flow pattern in the region
of near-uniform high heat transfer coefficient dependent marily on heat flux This could be at least one of the rea-sons for the increase in the heat transfer coefficient with areduction in the channel size The relative importance of nu-cleate and convective boiling in this region is still unclear.However, there are claims that suggest that, for small pas-sages, the same behavior, i.e., uniform heat transfer coeffi-cient dependent on heat flux and independent of quality, can
pri-be explained if transient evaporation of the thin liquid filmsurrounding elongated bubbles, without nucleate boiling con-tribution, is the dominant heat transfer mechanism (Thome et
al [52]) One may argue that the variations in heat transfercoefficient with axial position, evident in Figure 6, especiallyfor the larger tubes, may indicate some dependence on nucle-ate boiling Kenning and Yan [66] observed cyclic triggering
of nucleate boiling in smooth films around confined bubbles inwater associated with pressure fluctuations This needs furtherinvestigation
The heat transfer results of the smallest diameter tube (0.52mm) demonstrated different characteristics than the rest of thetubes, particularly at the high quality region It is the only tubefor which the incoming liquid flow is laminar, and this mayinfluence the initiation of confined bubble (slug) flow Unlikethe larger tubes that were examined in this study, which exhibitdry-out phenomena at high quality as the heat flux increaseswith a drop of the heat transfer coefficient with quality, a mono-tonic increase in heat transfer coefficient was observed near theexit for the smallest diameter tube This could be related tolaminar flow and domination of surface tension force over mo-mentum, providing more uniform liquid film thickness alongthe circumference, with less interfacial waves and disturbances,which improves wetting of the wall (Shiferaw et al [59]) Inaddition, the dependence of the heat transfer coefficient on axialposition is much stronger in the 0.52 mm tube, as in Figure
13, extending to high quality in the annular flow regime Theheat transfer engineering vol 31 no 4 2010
Trang 18T G KARAYIANNIS ET AL 271
Figure 14 Effect of pressure on heat transfer coefficient vs quality,G= 400 kg/m 2 s,q= 54 and 58 kW/m 2 : (a) 4.26 mm; (b) 2.88 mm; (c) 2.01 mm; (d) 1.1 mm; (e) 0.52 mm.
experiments in this tube are currently being repeated for the
complete range of variables and further confirmation of these
characteristics
These observations indicate additional changes as the size
diminishes further into microscales In general, the complex
de-pendence of the heat transfer rate on various parameters suggests
the difficulty of interpreting the heat transfer mechanisms using
simple conventional terms and the challenge of heat transfermodeling
CONCLUSIONS
Flow boiling patterns and heat transfer results with R134aand five tubes of diameter 4.26, 2.88, 2.01, 1.10, and 0.52 mmheat transfer engineering vol 31 no 4 2010
Trang 19272 T G KARAYIANNIS ET AL.
were presented in this article It was anticipated that the wide
range of data at different diameters could be used to identify
the threshold(s) where the small or micro diameter effects
be-come significant The major conclusions that can be drawn from
the current part of this long-term study are as follows:
1 In the 4.26 and 2.88 mm diameter tubes, the heat transfer
coefficient increases with heat flux and system pressure, but
does not change with vapor quality when the quality is less
than about 40% to 50%, for low heat flux The boundary
moves to 20–30% for the 2.01 and 1.10 mm diameter tubes
The actual quality values depend also on the heat flux In this
region, there is no significant difference in the magnitude of
the heat transfer coefficient of the 4.26 and 2.88 mm tubes
However, there is an increase of 15% and 35% when the tube
diameter is reduced to 2.01 and 1.10 mm, respectively
2 The heat transfer coefficient behavior of the tubes (4.26–
1.1 mm) at low quality could be interpreted as the evidence
that nucleate boiling is the dominant heat transfer
mecha-nism However, transient evaporation of the thin liquid film
surrounding elongated bubbles, which is a dominant flow
pattern in small passages, without a nucleate boiling
con-tribution, may also result in similar heat transfer coefficient
dependence and magnitude For higher vapor qualities, the
heat transfer coefficient becomes independent of heat flux
and decreases with vapor quality This could be caused by
partial (intermittent) dry-out in the convection-dominated
region This leads to the design recommendation that exit
qualities be kept low (Zhang et al [67, 68])
3 Chen et al [9] concluded that flow patterns for the 4.26 and
2.88 mm diameter tubes exhibit flow pattern characteristics
similar to those of “normal” diameter tubes, while “small
tube characteristics,” e.g., the appearance of confined flow,
were observed when the tube diameter was reduced to 2.01
mm and further to 1.10 mm This is consistent with a
crite-rion based on the ratio of surface tension and gravitational
forces The change in behavior may be progressive, rather
than occurring at a sharp threshold
4 The heat transfer data suggest that there is some deviation
from “normal” behavior even for the 4.26 mm tube, because
the expected increase in heat transfer coefficient with
in-creasing high quality was replaced by a decrease attributed
to intermittent dry-out This may indicate that film stability
in the heated zone depends on the ratio of surface tension to
other forces This cannot be detected by flow visualization at
the exit from the test section
5 As the tube diameter decreased further down to 0.52 mm,
different flow and heat transfer characteristics were
ob-served, indicating a possible further change as the size
dimin-ished These include: (a) The flow patterns observed in the
0.52 mm tube are different, i.e., absence of dispersed bubble
flow, and the appearance of a wavy film type flow that leads
into annular flow (b) The dependence of the heat transfer
co-efficient on quality, heat flux, and mass flux changes sharply
in character at a threshold value of heat flux In the low heatflux region, there is no significant effect of heat flux but theheat transfer coefficient decreases (at low mass flux and pres-sure) or remains constant (at higher mass flux and pressure),then increases gradually with quality At moderate and highheat flux, in the front part of the channel, the heat transfercoefficient increases with increasing heat flux and also de-pends in a complex way on quality It reaches a maximum at
an intermediate quality, which might be caused by transientpartial dry-out or dry patches in the confined bubble regime
At higher quality, toward the test section exit, the heat transfercoefficient gradually increases again with quality but there
is no clear effect of heat flux The heat transfer coefficientalso increases with mass flux in this region According to theconventional interpretation, this is evidence for a convectiveboiling dominant heat transfer mechanism in annular flow
An alternative plotting of heat transfer coefficient suggeststhat it is more dependent on the surface conditions associ-ated with particular axial positions than on quality Thesemight influence bubble nucleation or the stability of thin liq-uid films The slender evidence as yet available may indicatesome variability in the activation of the small population ofnucleation sites available in a channel of small surface area.The results of the 0.52 mm tube are currently being repeated
The complexity of interpreting heat transfer tics and understanding the prevailing mechanisms and, con-sequently, the difficulty of developing generalized models areverified by the work presented in this article Phenomenologicalmodels that are based on the local flow structure may be de-veloped for clearly specified ranges Therefore, it is important
characteris-to identify the range of applicability of dominant flow regimes.Current results also indicate that much more research is needed
to understand the different characteristics associated with crotubes and channels
Trang 20T G KARAYIANNIS ET AL 273
T temperature, K
t time (s)
U gs superficial gas velocity, m/s
U ls superficila liquid velocity, m/s
[1] Mehendale, S S., Jacobi, A M., and Shah, R K., Fluid Flow
and Heat Transfer at Micro- and Meso-Scales with Application to
Heat Exchanger Design, Applied Mechanics Reviews, vol 53, no.
7, pp 175–193, 2000
[2] Kandlikar, S G., and Grande, W J., Evolution of Microchannel
Flow Passages—Thermohydraulic Performance and Fabrication
Technology, Heat Transfer Engineering, vol 25, no 1, pp 3–17,
2003
[3] Brauner, N., and Moalem-Maron, D., Identification of the Range
of Small Diameter Conduits, Regarding Two-Phase Flow
Pat-tern Transitions, InPat-ternational Communications in Heat and Mass
Transfer, vol 19, pp 29–39, 1992.
[4] Cornwell, P A K., and Kew, P A., Boiling in Small Parallel
Channels, in Energy Efficiency in Process Technology, ed P A.
Pilavachi, Elsevier Applied Science, London, pp 624–638, 1993
[5] Thome, J R., Boiling in Microchannels: A Review of Experiment
and Theory, International Journal of Heat and Fluid Flow, vol.
25, pp 128–139, 2004
[6] Barnea, D., Luninski, Y., and Taitel, Y., Flow Pattern in Horizontal
and Vertical Two Phase Flow in Small Diameter Pipes, Canadian Journal of Chemical Engineering, vol 61, no 5, pp 617–620,
1983
[7] Mishima, K., and Hibiki, T., Some Characteristics of Air-Water
Two-Phase Flow in Small Diameter Vertical Tubes, tional Journal of Multiphase Flow, vol 22, no 4, pp 703–712,
Interna-1996
[8] Kew, P A., and Cornwell, K., Correlations for the Prediction
of Boiling Heat Transfer in Small Diameter Channels, plied Thermal Engineering, vol 17, no 8–10, pp 705–715,
[10] Serizawa, A., Feng, Z., and Kawara, Z., Two Phase Flow in
Mi-crochannels, Experimental Thermal Fluid Sciences, vol 26, pp.
[13] Damianides, D A., and Westwater, J W., Two-Phase Flow
Pat-terns in a Compact Heat Exchanger and in Small Tubes, Second
UK National Conference on Heat Transfer, vol 11, Sessions 4A–
6C, pp 1257–1268, 1988
[14] Lin, S., Kew, P A., and Cornwell, K., Two-Phase Flow Regimes
and Heat Transfer in Small Tubes and Channels, Heat Transfer
1998, Proceedings of 11th IHTC, vol 2, August 23–28, Kyongju,
Korea, pp 45–50, 1998
[15] Revellin, R., and Thome, J R., A New Type of Diabatic Flow
Pattern Map for Boiling Heat Transfer in Microchannels, Journal
of Micromechanics and Microengineering, vol 17, pp 788–796,
2007
[16] Kenning, D B R., and Cooper, M G., Saturated Flow Boiling of
Water in Vertical Tubes, International Journal of Heat and Mass Transfer, vol 32, pp 445–458, 1989.
[17] Lazarek, G M., and Black, S H., Evaporative Heat Transfer,Pressure Drop and Critical Heat Flux in a Small Vertical Tube
With R-113, International Journal of Heat and Mass Transfer,
[20] Bao, Z Y., Fletcher, D F., and Haynes, B S., Flow Boiling Heat
Transfer of Freon R11 and HCFC123 in Narrow Passages, national Journal of Heat and Mass Transfer, vol 43, pp 3347–
Inter-3358, 2000
[21] Yu, W., France, D M., Wambsganss, M W., and Hull, J R., Phase Pressure Drop, Boiling Heat Transfer, and Critical Heatheat transfer engineering vol 31 no 4 2010
Trang 21Two-274 T G KARAYIANNIS ET AL.
Flux to Water in a Small Diameter Horizontal Tube, International
Journal of Multiphase Flow, vol 28, pp 927–941, 2002.
[22] Fujita, Y., Yang, Y., and Nami, F., Flow Boiling Heat Transfer and
Pressure Drop in Uniformly Heated Small Tubes, in Proc 12th
International Heat Transfer Conf., Grenoble, vol 3, pp 743–748,
2002
[23] Carey V P., Tervo, P., and Shullenberger, K., Partial Dryout in
Enhanced Evaporator Tubes and Its Impact On Heat Transfer
Per-formance, SAE Technical Paper 920551, 1992 Available online
at http://www.SAE.org
[24] Oh, H K., Katsuta, M., and Shibata, K., Heat Transfer
Character-istics of R134a in a Capillary Tube Heat Exchanger, in Proc 11th
IHTC, vol 6, pp 131–136, 1998.
[25] Lee, H J., and Lee, S Y., Heat Transfer Correlation for Boiling
Flows in Small Rectangular Horizontal Channels With Low
As-pect Ratios, International Journal of Multiphase Flow, vol 27,
pp 2043–2062, 2001
[26] Qu, W., and Mudawar, I., Flow Boiling Heat Transfer in Two
Phase Microchannel Heat Sinks I Experimental Investigation
and Assessment of Correlation Methods, International Journal of
Heat and Mass Transfer, vol 46, pp 2755–2771, 2003.
[27] Kuznetsov, V V., and Shamirzaev, A S., Two Phase Flow Pattern
and Flow Boiling Heat Transfer in Non-Circular Channel With
a Small Gap, Two-Phase Flow Modeling and Experimentation,
Pisa, Italy, vol 1, pp 249–253, 1999.
[28] Lin, S., Kew, P A., and Cornwell, K., Two-Phase Heat Transfer
to a Refrigerant in a 1 mm Diameter Tube, International Journal
of Refrigeration, vol 24, pp 51–56, 2001.
[29] Sumith, B., Kaminaga, F., and Matsumura, K., Saturated Flow
Boiling of Water in a Vertical Small Diameter Tube, Experimental
Thermal Fluid Sciences, vol 27, pp 789–801, 2003.
[30] Saitoh, S., Daiguji, H., and Hihara, E., Effect of Tube Diameter
on Boiling Heat Transfer of R134a in Horizontal Small Diameter
Tubes, International Journal of Heat and Mass Transfer, vol 48,
pp 4973–4984, 2005
[31] Owhaib, W., and Palm, B., Flow Boiling Heat Transfer in a
Ver-tical Circular Microchannel Tube, Eurotherm Seminar, no 72,
Valencia, Spain, 2003
[32] Huo, X., Tian, Y S., and Karayiannis, T G., R134a Flow
Boil-ing Heat Transfer in Small Diameter Tubes, Advances in
Com-pact Heat Exchangers, R T Edwards, Philadelphia, pp 95–111,
2007
[33] D´ıaz, M C., and Schmidt, J., Experimental investigation of
tran-sient boiling heat transfer in microchannels, Int Journal of Heat
and Fluid Flow, vol 28, pp 95–102, 2007
[34] Xu, J., Shen, S., Gan, Y., Li, Y., Zhang, W., Su, Q., Transient
flow pattern based microscale boiling heat transfer mechanisms,
Journal of Micromechanics and Microengineering, vol 15, pp
1344-1361, 2005
[35] Lie, Y M., Su, F Q., Lai, R.L., Lin, T F., Experimental
Study of Evaporation Heat Transfer Characteristics of
Refrig-erants R-134a and R-407C in Horizontal Small Tubes,
Interna-tional Journal of Heat and Mass Transfer, vol 49, pp 207–218,
2006
[36] Agostini, B., and Thome, J R., Comparison of an Extended
Database of Flow Boiling Heat Transfer Coefficient in
Multi-Microchannel Elements With the Three-Zone Model, in ECI
In-ternational Conference on Heat Transfer and Fluid Flow in
Mi-croscale, Castelvecchio Pascoli, Italy, 2005.
[37] Yen, T., Kasagi, N., and Suzuki, Y., Forced Convective Boiling
Heat Transfer in Microtubes at Low Mass and Heat Fluxes, ternational Journal of Multiphase Flow, vol 29, pp 1771–1792,
In-2003
[38] Hapke, I., Boye, H., and Schmidt, J., Onset of Nucleate Boiling
in Minichannels, International Journal of Thermal Sciences, vol.
[40] Peng, X F., Hu, H Y., and Wang, B X., Boiling Nucleation
During Liquid Flow in Microchannels, International Journal of Heat and Mass Transfer, vol 41, pp 101–106, 1998.
[41] Zhang, L., Koo, J., Jiang, L., Goodson, K E., Santiago, J G.,and Kenny, T W., Study of Boiling Regimes and Transient Signal
Measurements in Microchannels, Proc Transducers ’01, Munich,
Germany, pp 1514–1517, 2001
[42] Brereton, G J., Crilly, R J., and Spears, J R., Nucleation in
Small Capillary Tubes, Chemical Physics, vol 230, pp 253–265,
1998
[43] Yan, Y Y., and Lin, T F, Evaporation Heat Transfer and
Pres-sure Drop of Refrigerant R-134a in a Small Pipe, International Journal of Heat and Mass Transfer, vol 41, pp 4183–4194,
[46] Yan, Y., and Kenning, D B R., Pressure and Temperature
Fluc-tuations During Boiling in Narrow Channel, Eurotherm 62: Heat Transfer in Condensation and Evaporation, Grenoble, pp 107–
1223, 1998
[47] Kew, P A., and Cornwell, K., On Pressure Fluctuations During
Boiling in Narrow Channels, 2nd European Thermal-Science and 14th UIT National Heat Transfer Conference, Rome, pp 1323–
1327, 1996
[48] Owhaib, W., Martin-Callizo, C., and Palm, B., Evaporative Heat
Transfer in Vertical Circular Microchannels, Applied Thermal gineering, vol 24, pp 1241–1253, 2004.
En-[49] Kuwahara, K., Koyama, S., and Hashimoto, Y., Characteristics ofEvaporation Heat Transfer and Flow Pattern of Pure Refrigerant
HFC134a in a Horizontal Capillary Tube, in Proc 4th KSME Thermal Engineering Conference, pp 385–390, 2000.
JSME-[50] Baird, J R., Bao, Z Y., Fletcher, D F., and Haynes, B S., LocalFlow Boiling Heat Transfer Coefficients in Narrow Conduits, in
Boiling: Phenomena and Engineering Applications, Multiphase
Science and Technology, vol 12, no 3–4, pp 129–144, 2000.[51] Khodabandeh, R., Influence of Channel Diameter on Boiling HeatTransfer in a Closed Advanced Two-Phase Thermosiphon Loop,
Proc 5th International Boiling Conference, Montego Bay,
Ja-maica, 2003
[52] Thome, J R., Dupont, V., and Jacobi, A M, Heat Transfer Modelfor Evaporation in Microchannels, Part I: Presentation of theheat transfer engineering vol 31 no 4 2010
Trang 22T G KARAYIANNIS ET AL 275
Model, International Journal of Heat and Mass Transfer, vol.
47, pp 3375–3385, 2004
[53] Dupont, V., Thome, J R., and Jacobi, A M., Heat Transfer Model
for Evaporation in Microchannels, Part II: Comparison With the
Database, International Journal of Heat and Mass Transfer, vol.
47, pp 3387–3401, 2004
[54] Dupont, D., and Thorne, J R., Evaporation in Microchannels:
Influence of the Channel Diameter on Heat Transfer, Journal of
Microfluidics and Nanofluidics, vol 1, no 2, pp 119–125, 2005.
[55] Shiferaw, D., Huo, X., Karayiannis, T G., and Kenning, D B
R., Examination of Heat Transfer Correlations and a Model for
Flow Boiling of R134a in Small Diameter Tubes, International
Journal of Heat and Mass Transfer, vol 50, pp 5177–5193,
2007
[56] Blasius, H., Das Ahnlichkeitsgesetz bei Reibungsvorgangen in
Flussigkeiten, Forschungs-Arbeit des lgenieur-wesens, vol 131,
no 1, 1913
[57] Dittus, F W., and Boelter L M K., Heat Transfer in Automobile
Radiators of Tubular Type, University California, Berkeley, Publ.
Eng 2/13, pp 443–461, 1930
[58] Petukhov, B S., Heat Transfer and Friction in Turbulent Pipe Flow
With Variable Physical Properties, in Advances in Heat Transfer,
vol 6, Academic Press, New York, pp 503–564, 1970
[59] Shiferaw, D., Mahmoud, M M., Karayiannis, T G., and Kenning,
D B R., Experimental Flow Boiling Study in a 0.52 mm
Diam-eter Vertical Tube Using R134a, 5th European Thermal-Sciences
Conference, Eindhoven, the Netherlands, 2008.
[60] Gnielinski, V., VDI-W¨armeatlas, Springer-Verlag, Berlin, 1997.
[61] Adams, T M., Abdel-khalik S I., Jeter S M., and Qureshi Z H.,
An Experimental Investigation of Single-Phase Forced
Convec-tion in Micro-Channels, InternaConvec-tional Journal of Heat and Mass
Transfer, vol 41, no 6–7, pp 851–857, 1998.
[62] Choi, S B Barron, R F., and Warrington, R O., Fluid Flow and
Heat Transfer in Microtubes, Micromechanical Sensors,
Actua-tors and Systems, ASME DSC, vol 32, pp 123–128, 1991.
[63] Shiferaw, D., Karayiannis, T G., and Kenning, D B R., Flow
Boiling in a 1.1 mm Vertical Tube With R134a: Experimental
Results and Comparison With Model, International Journal of
Thermal Sciences, doi:10.1016/j.ijthermalsci.2008.02.009, 2008.
[64] Shiferaw, D., Two-Phase Flow Boiling in Small- to
Micro-Diameter Tubes, Ph.D Thesis, Brunel University, 2008
[65] Revellin, R., Dupont, V., Ursenbacher, T Thome, J R., and Zun,
I., Characterization of Diabatic Two-Phase Flows in
Microchan-nels: Flow Parameter Results for R-134a in a 0.5 mm Channel,
International Journal of Multiphase Flow, vol 32, pp 755–774,
2006
[66] Kenning, D B R., and Yan, Y., Saturated Flow Boiling of Water
in a Narrow Channel: Experimental Investigation of Local
Phe-nomena, IChemE Trans A, Chemical Engineering Research and
Design, vol 79, pp 425–436, 2001.
[67] Zhang, L., Goodson, K E., and Kenny, T W., Silicon
Microchan-nel Heat Sinks, Theories and Phenomena, Springer, Berlin, chaps.
5–7, 2004
[68] Zhang, L., Wang, E N., Goodson, K E., and Kenny, T W., Phase
Change Phenomena in Silicon Microchannels, International nal of Heat and Mass Transfer, vol 48, pp 1572–1582, 2005.
Jour-Tassos G Karayiannis is a professor of thermal
en-gineering in the School of Enen-gineering and Design of Brunel University, UK, where he is co-director of the Centre for Energy and Built Environment Research.
He obtained a B.Sc in mechanical engineering from City University (UK) in 1981 and a Ph.D from the University of Western Ontario (Canada) in 1986 He has carried out research in single-phase heat transfer, enhanced heat transfer, and thermal systems He has been involved with research in two-phase flow and heat transfer for about 20 years He is a fellow of the Institution of Mechanical Engineers and the Institute of Energy.
Dereje Shiferaw received his M.Sc in sustainable
energy engineering in 2004 from the Royal Institute
of Technology (Sweden) and his Ph.D from Brunel University (UK) in 2008 He won an award for the best master’s thesis from the Swedish Center for Nu- clear Research His research interests include single- and two-phase flow heat transfer in microchannels, nanofluids, compact heat exchangers, cooling of elec- tronics, and renewable energy systems.
David Kenning graduated in mechanical sciences
from Cambridge University in 1957 and worked for the UK Atomic Energy Authority for 3 years before returning to Cambridge to start his career of research
on multiphase flows and boiling heat transfer He joined Oxford University in 1963 and was a univer- sity lecturer in engineering science and tutorial fellow
of Lincoln College from 1967 until his official ment in 2003 He then joined the research group of Professor Tassos Karayiannis as a visiting professor, first at London South Bank University and now at Brunel University.
retire-Vishwas V Wadekar is Technology Director, HTFS
Research, at AspenTech Ltd, UK In addition to aging HTFS research, he chairs the HTFS Industrial Review Panel on Compact Heat Exchangers He has authored or co-authored a number of technical and re- search papers in the area of compact heat exchangers, multiphase flow heat and mass transfer, and boiling.
man-He has held visiting faculty positions in a number of universities United Kingdom and abroad Currently
he serves as a visiting professor at the University of Hamburg in Germany and the Lund Institute of Technology in Sweden He obtained his B.Chem.Eng and Ph.D degrees from UDCT, Bombay University.
He is a member of AIChE and is actively involved in organizing technical sions at AIChE and ASME conferences He is also a member of the Eurotherm
ses-Committee and an associate editor of Heat Transfer Engineering.
heat transfer engineering vol 31 no 4 2010
Trang 23CopyrightC Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903311694
A New Method for Determination
of Flow Boiling Heat Transfer
Coefficient in Conventional-Diameter Channels and Minichannels
DARIUSZ MIKIELEWICZ
Faculty of Mechanical Engineering, Gdansk University of Technology, Gdansk, Poland
Presented in this article are considerations regarding modeling of flow boiling in conventional, small-diameter channels and
minichannels A concise survey of available methods for prediction of heat transfer coefficient in saturated boiling regime is
given and in that light a modified author’s own model is presented The presented model, contrary to other approaches, finds
application in the cases of both conventional and small-diameter channels The results of calculations are compared with
some experimental data available from literature on conventional-size tubes and also minichannels Obtained agreement is
satisfactory.
INTRODUCTION
Boiling heat transfer, as one of the most efficient techniques
for removing high heat fluxes, has been studied and applied in
practice for a very long time Nowadays, rapid development
of practical engineering applications for devices,
micro-systems, advanced material designs, manufacturing of compact
heat exchangers, high-capacity micro heat pipes for spacecraft
thermal control, and electronic microchips increases the demand
for better understanding of small and micro-scale transport
phe-nomena The last decade of the 20th century witnessed rapid
progress in the research into micro- and nano-scale transport
phenomena, which bore important applications in modern
tech-nologies such as microelectronics
Despite numerous applications, the theoretical approaches
to modeling of flow boiling still require substantial progress, as
determination of heat transfer and pressure losses is done mostly
by means of empirical correlations Their drawback is that they
feature fluid-dependent coefficients and thus are not general
Such correlations must be therefore used with special care and
precautions, only in the range of conditions that such
correla-tions have been developed for That fact also disables direct
ap-plication of correlations developed for conventional channels to
Address correspondence to Professor Dariusz Mikielewicz, Faculty of
Me-chanical Engineering, Gdañsk University of Technology, ul G Narutowicza
11/12, 80-952 Gdañsk, Poland E-mail: Dariusz.Mikielewicz@pg.gda.pl
small-diameter channels Recently there has also been progressattained using structure-dependent modeling using flow maps,which is, however, tedious and not very convenient for engi-neering applications
Following a brief presentation of available approaches tomodeling of flow boiling, a model is presented here that is de-veloped on the basis of considerations of dissipation of energy
in the flow and is deemed to be applicable to both tional and small-diameter channels, laminar and turbulent flowregimes, and flow with bubble generation and without it
conven-REVIEW OF EXISTING FLOW BOILING CORRELATIONS
The topic of flow boiling predictions has been scrutinized forover half a century, as the interest in that kind of heat transferstarted in the early 1960s In the present article it is not theintention of the author to provide a survey of all available meth-ods for that purpose, but only to indicate the major approaches
to modeling of flow boiling heat transfer in conventional andsmall diameter channels For an extensive literature survey offlow boiling in conventional-size channels the reader is referred
to Thome [1] or for small-diameter channels to Bergles et al [2],Kandlikar [3], or Thome [4] In general, all existing approachesare either the empirical fits to the experimental data, or form276
Trang 24D MIKIELEWICZ 277
an attempt to combine two major influences to heat transfer,
namely, the convective flow boiling without bubble generation
and nucleate boiling Generally that is done in a linear or
nonlin-ear manner Alternatively, there is a group of modern approaches
based on models that start from modeling a specific flow
struc-ture and in such a way postulate more accurate flow boiling
models, usually pertinent to slug and annular flows
The empirical correlations suggested to date are based on
reduction of a restricted number of authors’ own experimental
data or form a generalization of a greater number of
experimen-tal data from various authors In the latter case correlations are
usually of less accuracy in predicting the heat transfer
coeffi-cient, or the pressure drop, due to the fact that each experiment
contributes with its own systematic measurement error;
how-ever, such correlations are of more general character All such
empirical correlations, however, are the fits to experimental data,
which restricts their generality In the case of a lack of generation
of bubbles the experimental data in conventional-size tubes, i.e.,
having diameters greater than 3 mm [3], are usually modeled as
a function of the Martinelli parameter Xttin the form:
αTP
αL = a (Xtt) b
(1)
Dengler and Addoms [5] suggested values of a and b to be a=
3.5 and b= –0.5, respectively, whereas Guerrieri and Talty [6]
determined as a = 3.4 and b = –0.45 In the case when bubble
generation in the flow is present, such an approach encounters
some limitations, and in order to alleviate that an approach
based on incorporation of the Bond number, Bo= q w /(Gh lg),
into the correlation is often used A general form of heat transfer
coefficient with account of bubble generation yields:
αTP
αL = a
Schrock and Grossman [7] recommended a correlation where
coefficients a, b, and m assume values of a= 7400, b= 0.66,
and m = 0.00015 Collier and Pulling [8] suggested another
set of coefficients in Eq (2): a = 6700, b = 0.66, and m =
0.00035 On the basis of that approach several other correlations
for conventional channels have been developed, and here is just
a mention of those due to Shah [9], Kandlikar [10], and Gungor
and Winterton [11]
The most popular approach, however, to model flow boiling
is to present the resulting heat transfer coefficient in terms of
a combination of nucleate boiling heat transfer coefficient and
convective boiling heat transfer coefficient:
αTP= [(αcbF)n+ (αPBS)n]1/n (3)
where αPBis the pool boiling heat transfer coefficient, and αcb
the liquid convective heat transfer coefficient, which can be
evaluated using, for example, the Dittus–Boelter type of
corre-lation Exponent n is an experimentally fitted coefficient
with-out recourse to any theoretical foundations Function S is the
so-called suppression factor, which accounts for the fact that
to-gether with increase of vapor flow rate the effect related to forced
convection increases, which on the other hand impairs the tribution from nucleate boiling, as the thermal layer is reduced
con-The parameter F accounts for the increase of convective heat
transfer with increase of vapor quality That parameter alwaysassumes values greater than unity, as flow velocities in two-phase flow are always greater than in the case of single-phaseflow The approach represented by Eq (3) is usually dedicated
to Rohsenow [12], who suggested a linear superposition with
n= 1, which has been later modified by Chen [13], who
incor-porated the suppression and enhancement functions, S and F ,
respectively The correlation due to Chen is used up to date with
a significant appreciation in the case of flows in size tubes It was also Kutateladze [14] who recommended asuperposition approach, but combined in a geometrical rather
conventional-than linear manner with the value of exponent n = 2 A ilar summative nonlinear approach was recommended later by
sim-Steiner and Taborek [15] with n = 3 There is also an issue
of the choice of appropriate correlation selection for tion of pool boiling heat transfer coefficient, as Chen [13] usedthe model due to Forster and Zuber [16], whereas later studiestend to use rather the more general correlation due to Cooper[17], which enables calculations of pool boiling heat transfercoefficient for different modern fluids
calcula-Kattan et al [18] concluded that only the models based ondistinguishing between flow regimes should be genuinely con-sidered for a general use in prediction of heat transfer coefficient
in channels A model for flow boiling in horizontal tubes hasbeen developed by him based on a flow map It was assumed that
in the flow the upper part of the tube inside is usually contactingvapor and the remaining part is flooded with liquid The heattransfer coefficient for such case was taking that fact into ac-count and the heat transfer for these two regions was evaluated
in the following manner:
αTPB= [R · θdryαv + R(2π − θdry)αwet]/2πR (4)The heat transfer coefficient for a wetted part of the tube, αwet,
is to be obtained from the form of Eq (3) with n = 3 Thenucleate boiling heat transfer coefficient αPBis calculated fromthe Cooper’s [17] correlation, whereas αcbis from this author’sown empirical correlation Some refinement to that approachwas introduced by Wojtan et al [19] That kind of approach
to modeling seems to be promising and falls to the class ofthe regime-dependent models It requires prior knowledge ofthe particular flow regime, as well as the proportion of liquidand gaseous phase in the flow For that reason such a model isdifficult to apply in engineering practice Following that briefsurvey of superposition models, the question arises of how to
select the appropriate value of exponent n, in Eq (3) Should there be a value of n= 1 or 2 or 3 assumed? Or maybe someother value of that exponent ought to be looked for? Mikielewicz[20] provided an answer to that question, showing on the ba-sis of consideration of energy dissipation in the two-phase
flow that the exponent should be n = 2 A modified version
of that model will be examined in the course of the presentstudy
heat transfer engineering vol 31 no 4 2010
Trang 25278 D MIKIELEWICZ
A completely different kind of approach to model flow
boil-ing is presented in tacklboil-ing the problem from the principles of
conservation of mass, momentum, and energy, and subsequently
through a numerical solution to such problem An example of
such an approach is a four-field two-fluid model due to Lahey
and Drew [21] In such an approach the two phases of fluid can
exist in continuous or dispersed form, leading to the occurrence
of four fields, namely, continuous liquid–dispersed gas and
con-tinuous gas–dispersed liquid Some success has been obtained in
modeling of bubbly flows and annular flows; however, the major
challenge is to predict the flow development and transformation
through consecutively developing flow structures (Podowski
[22]) The closure models and jump conditions form a very
difficult task to be implemented into the calculation procedure,
similar to the transient conditions Apparently the research is
still being exercised in that direction but there is still some time
to go before useful results are to be obtained of simulation of
the entire transformation from subcooled liquid to superheated
vapor
For that reason most of the approaches to date use
empir-ical correlations Presented next in brief is a model due to
Mikielewicz [20], which, as mentioned earlier, has been
de-veloped on the basis of consideration of dissipation in the flow
and recently modified to its final form, in Mikielewicz et al
[23] In the present article its further extension to transitional
and laminar flows is presented Such cases are often found in
minichannels, i.e., channels with diameters ranging from 600
µm to 3 mm [3] Empirical correlations known to date
can-not distinguish between the laminar and turbulent flow regimes
They are specially tailored to either one of the flow regimes
MODEL OF FLOW BOILING
The principal idea in the development of the model by
Mikielewicz [20] was a hypothesis that evaluation of energy
dissipation of major contributions in the flow boiling process
with bubble generation will lead to determination of heat
trans-fer in such flow Energy dissipation results from the friction in
the flow, which, on the basis of thermal hydraulic analogy, is
linked to heat transfer The flow is considered as an equivalent
liquid flow with properties of a two-phase flow
A fundamental hypothesis in the original model under
scrutiny [20] here is the fact that heat transfer in flow
boil-ing with bubble generation, treated here as an equivalent flow
of liquid with properties of a two-phase flow, can be modeled as
a sum of two contributions leading to the total energy
dissipa-tion in the flow, namely, energy dissipadissipa-tion due to shearing flow
without the bubbles, ETP, and dissipation resulting from bubble
generation, EPB:
Energy dissipation under steady-state conditions in the
two-phase flow can be approximated as energy dissipation in the
laminar boundary layer, which dominates in heat and tum transfer in the considered process Expressed as a powerlost in a unit volume of a boundary layer of two-phase flow ityields [20]:
momen-ETP= τTP2
µL = ξ2TPρ2
Lw4 TP
Analogically the energy dissipation due to bubble generation
in the two-phase flow can be expressed with velocity wTPandfriction factor ξPB:
EPB=ξ2PBρ2
Lw4 TP
In the Russian literature there are a number of contributionswhere investigations into flow resistance caused merely by thegeneration of bubbles on the wall are reported [24], which con-firm that the modeling approach presented in this article is pos-sible
The final term in Eq (5), E TPB, is modeled as the total energy
dissipation in the equivalent two-phase flow with velocity wTP
and some friction factor ξTPB, which after Eq (6) can be modeledas:
Making use of the analogy between the momentum and heat
we can generalize the preceding result to extend it over to heattransfer coefficients to yield heat transfer coefficient in flowboiling with bubble generation in terms of simpler modes of heattransfer, namely, heat transfer coefficient in flow without bubblegeneration and heat transfer coefficient in nucleate boiling:
Heat Transfer in Flow Boiling Without Nucleation
Let’s focus our attention first on the case without nucleation,which will lead to determination of a problem where convectiveboiling is dominant From the definition of the two-phase flowmultiplier, the pressure drop in two-phase flow can be related to
the pressure drop of a flow where only liquid at a flow rate G is
present:
The pressure drop in the two-phase flow without bubble ation can also be considered as a pressure drop in the equivalentheat transfer engineering vol 31 no 4 2010
Trang 26The pressure drop of the liquid flowing alone can be determined
from a corresponding single-phase flow relation:
pL= l
dξLρLw
2 L
In the present article the most up-to-date relations for the friction
coefficient ξ, required for calculation of pressure drop, both in
laminar and turbulent flows will be used In case of turbulent
flow we use the Blasius equation for determination of the friction
In Eq (14) ReTP = (wTP d )/ν Land ReL = (w L d )/ν L The
defi-nition of the two-phase flow multiplier therefore leads us to the
following relation between the velocity in a two-phase flow and
Substituting relations (12) to (14) into (11), with relations
rele-vant to turbulent flow, we obtain a relation between the velocity
of two-phase flow and liquid-only:
wTP= R 1
1.75 wL ≈ R 0.571 wL (16)
An expression for the heat transfer coefficient, in the case of
tur-bulent flow, can be obtained if Eq (16) is used in determination
of the Reynolds number in expressions of the Dittus–Boelter
type, where ReLOis raised to the power 0.8, valid for turbulent
flows:
αTP
αL =
ReTPReL
0.8
=R 0.5710.8 ∼
= R 0.45 (17)where αLO is a heat transfer coefficient in the flow of only
liquid and the relation stemming from Eq (16), namely, ReTP =
R0.57ReLO, was used Use of the Dittus–Boelter equation with
properties referred to liquid is possible as the heat transfer in the
flow is governed merely by the flow of liquid The bubbles are
forming only a void and hence influence only the velocity of the
flow The scaling of velocity into the two-phase flow velocity is
done by means of application of a two-phase flow multiplier to
a single flow velocity (a result of rearrangement from definition
of a two-phase flow multiplier (11)) In case of laminar flow the
friction factor can be evaluated from the expression:
ξTP= 16
ReTP ξL= 16
Reynolds numbers are defined in a same way as in Eq (14)
Substituting Eq (18) into the definition of the two-phase flow
As can be noted, a linear relation between velocities results:
Utilizing Eq (20) in a correlation for the heat transfer coefficient
in laminar flow, where the Nusselt number is a function of asquare of the Reynolds number, we obtain a relation for two-phase heat transfer coefficient without nucleation in laminarflow:
of flows in channels Therefore, a value of 0.5 was selected forthe present modeling in laminar and transitional flows in tubes.Also in laminar flows past plates there are both analytical andempirical relations incorporating the Reynolds number raised tothe power 0.5
The following final form of correlation for flow boiling insmall diameter channels can be now postulated:
In the case of flow boiling the boundary layer is thinner andhence the gradient of temperature is more pronounced, whichsuppresses generation of bubbles in flow boiling That is thereason why heat flux is included into modeling That term ismore important for conventional size tubes, but cannot be totallyneglected in small-diameter tubes in the bubbly flow regime,where it is important A postulated form of correction has a formpreventing it from assuming values greater than 1, which was
a fundamental weakness of the model in earlier modifications
In the case of turbulent flow the exponent n assumes a value of
0.9, whereas in the case of laminar flow that exponent assumes
a value of n= 2
The two-phase flow multiplier RMSdue to M¨uller-Steinhagenand Heck [27] is recommended for use in the case of refriger-ants (Ould Didi et al [28]) It should be noted, however, that theheat transfer engineering vol 31 no 4 2010
Trang 27280 D MIKIELEWICZ
choice of a two-phase flow multiplier to be used in the
postu-lated model is arbitrary In the activities presented in this article
the Muller-Steinhagen and Heck model [27] has been selected
for use as it is regarded best for refrigerants such as
hydrocar-bons; however, a different model could be selected, such as the
Lockhart–Martinelli model, where the two-phase flow
multi-plier is a direct function of the Martinelli parameter The latter
model is often found in correlations of flow boiling without
bubble generation, similar to Eq (1) Another conclusion could
be drawn from the presented model that in correlations of the
type of Eq (1) the two-phase flow multiplier could also be used
for modeling instead of the Martinelli parameter The author’s
experience to date shows that the influence of the two-phase
flow multiplier is very important and each fluid has a different
description of a two-phase resistance, which will be apparent
later when data for fluids other than hydrocarbons will be used
(Sumith et al [29]) In some of recent works by Thome [30],
there are three-zone approaches to devise a proper pressure drop
in the flow, which subsequently are used in heat transfer
calcu-lations Such an approach, in my opinion, is just confirming the
presented model, where it is stated that the flow resistance must
be incorporated directly into modeling of flow boiling heat
trans-fer The more accurate the two-phase flow multiplier, the more
accurate are the heat transfer predictions In the presented model
the RMSacts in the correction P as a sort of convective number,
known from other correlations In the form applicable to
con-ventional and small-diameter channels the Muller-Steinhagen
and Heck model [27] yields:
RMS=
1+2
1
and m = 0 for conventional channels Best consistency with
experimental data, in the case of small-diameter channels and
minichannels, is obtained for m = –1 In Eq (23) f1= (ρL/ρG)
(µL/µG)0.25 for turbulent flow and f1 = (ρL/ρG)(µL/µG) for
laminar flow Introduction of the function f1z, expressing the
ratio of heat transfer coefficient for liquid only flow to the heat
transfer coefficient for gas-only flow, is to meet the limiting
conditions; i.e., for x = 0 the correlation should reduce to a
value of heat transfer coefficient for liquid, αTPB= αL, whereas
for x= 1, approximately that for vapor, i.e., αTPB∼= αG.Hence:
f 1z= αGO
where f 1z = (µG/µL)(λL/λG)1.5(CpL/CpG) for turbulent flows
and f 1z= (λG/λL) for laminar flows When we want to consider
a limiting behavior of a correlation for vapor in a turbulent flow
regime then we consider only the abbreviated form of relation
(22), where the Dittus–Boelter relation is used for expressing
respective heat transfer coeffients:
αTPB
αL = R 0.5n
MS =
1
1.5 0.4
(26)
If we substitute Eq (26) into Eq (25) the right-hand side ofthe equation will have the exponent equal approximately 1 (as
n= 0.9 in turbulent flows) and the heat transfer coefficient will
assume a value of a vapor one for x = 1 A similar analysiscan be conducted for the case of laminar flow We should be
now convinced that introduction of the function f1zrenders that
correlation (22) obeying the limiting conditions; i.e., for x= 0,the correlation reduces to a value of heat transfer coefficient forliquid, αTPB = αL, whereas for x= 1, the correlation reduces
to approximately that for vapor, i.e., αTPB∼= αG.
It is possible to compare the proposed model (22) with themethod due to Chen [13] on the basis of comparisons of respec-
tive terms with the intensifying term F , which in the case of the model is approximately the term R 0.5n
MS, or the suppression term
S, which in the case of the present model is (1/(1+P )) 0.5 ple calculations performed for R123 are presented in Figures 1and 2 The character of changes shown by both distributions isconsistent with experimental data, which confirms a good quali-tative behavior of the model Subsequent comparisons, confirm-ing a good quantitative performance of the correlation, will beshown on the basis of comparisons of the results of calculationsagainst the experimental data
Sam-Figure 1 Correction (1+ P ) −0.5for different values of quality in comparison
with the suppression term in Chen’s correlation (term S) for R123.
heat transfer engineering vol 31 no 4 2010
Trang 28D MIKIELEWICZ 281
Figure 2 Enhancement term F in Chen’s correlation for R123 in comparison
to corresponding term R 0.5n
MS in Eq (22).
APPLICATION TO SMALL-DIAMETER CHANNELS
It is a major drawback of most correlations developed for
calculation of heat transfer in conventional-size tubes that their
accuracy significantly deteriorates when applied to small-size
tubes, regarded here as greater than 600 µm [3] In such a
situa-tion the surface tension effects become more dominant and need
to be reflected in the model Most of the experimental data
in-dicate that most important for small channels is the convective
flow boiling mode, which, as stems from Eq (22), is
depen-dent on the flow resistance In such a case a great deal of care
must be exercised in the use of an appropriate friction model
Again, available correlations of two-phase flow friction fail to
be accurate for small-diameter channels A recent study due to
Tran et al [32] recommends a modification of the Chisholm
model to be applicable to small-diameter channels A very good
consistency with experimental data is reported; however, when
applied to relation (22) an inappropriate behavior is found when
quality x approaches unity, as the heat transfer coefficient for
vapor is not retrieved For that reason the Muller-Steinhagen
and Heck two-phase multiplier correlation [27] was modified to
incorporate the function f 1z, the derivation of which has been
presented in Eq (24) In case of modeling for small-diameter
passages the additional term responsible for surface tension
ef-fects, namely, the constraint number Con, has also been applied
to the discussed method (Mikielewicz et al [23]) The version of
Eq (23) ought to be therefore used with the constraint number,
Con, where the exponent index is m= –1, if calculations are
carried out for tube diameters smaller than 3 mm, and in cases
where the diameter is greater than 3 mm, the version without it
is appropriate, i.e., m= 0
Some effort has also been exercised to extend the correlation
(22) into the subcooled flow regime In the course of activities it
has been assumed that in the case of subcooled flow boiling the
correlation (22) can be adopted to subcooling if we assume that
the two-phase flow multiplier tends to unity, R → 1, and that
the correction function P tends to zero, P → 0 The nucleateboiling heat transfer coefficient in subcooled boiling is related
to the tsat temperature drop in the channel, instead of total
tsat+ t sub , where tsat is the difference between the walltemperature and the saturation temperature (superheating), and
t subis the difference between the saturation temperature andthe mean fluid temperature along the channel (subcooling) Insuch a case the heat transfer coefficient in subcooled boiling isreduced to:
αPBsubαPB
postulated model The empirical correction P in relation (22)
is dependent upon quality, which shows up in Figures 1 and 2,
whereas the suppression factor S in the model due to Chen is
independent of quality The conclusion that can be drawn from
examination of distributions of correction P in Figure 1 is that
the suppression is smaller for higher qualities and it exhibits adecrease with increasing Reynolds number
Next, the available data bank for conventional size tubes hasbeen revisited, featuring about 2500 data points [22], and thecalculations of theoretical values were made for the amended
value of exponent n = 0.9 in (22); see Figure 3 It must benoted that data for conventional-size tubes fall to the turbu-lent flow regime The accuracy of calculations has not wors-ened and again about 65% of points were within ±30% oferror
From examination of Figure 4 we can see that the data spreadaround the expected value of unity is also uniform, and thecorrelation assumes an equal spread in error for consideredqualities
heat transfer engineering vol 31 no 4 2010
Trang 29282 D MIKIELEWICZ
Figure 3 Data bank for conventional size tubes reduced with correlation (22).
Small-Diameter Tubes and Minichannels
Having shown that correlation behaves reasonably well in the
case of conventional-size tubes, some comparisons were made
with the data for small-diameter channels In order to do that,
the only correlation adjustment, in comparison to
conventional-channels data, was that the version of Eq (23) incorporating the
constraint number Con raised to power m= –1 was used
First, attention was focused on a set of experimental points
due to Karayiannis [34] These investigations were carried out
on stainless-steel tubes with internal diameters of 2 mm and
4.26 mm using R134a as a working fluid and 996 data points
were at the disposal for comparisons The test section was 40
cm long The flow parameters were the following: x= 0.1–0.8,
mass flow rate G = 100–500 kg/m2-s, applied heat flux q =
Figure 4 Data bank for conventional size tubes versus quality reduced with
correlation (22).
Figure 5 Data due to Karayiannis [34] reduced with correlation (22).
11–100 kW/m2, saturation temperature TSAT = 30–46◦C, and
tube diameters d = 2 mm and 4.26 mm In Figures 5 and 6are presented calculations using the author’s own method, Eq.(22), of data due to Karayiannis [34] It is apparent from Fig-ure 6 that the discrepancies exceeding 30% are visible only forthe quality close to zero All other data fall into the envelope
of ±30% That result must be deemed satisfactory In Figure
7, presented for comparison are calculations obtained using theChen [13] method Notably the agreement is worse, and ac-cording to communication with the author of the experimentaldata the correlation due to Chen [13] was performing best of allothers known in literature It is important to note that the bigger
Figure 6 Data due to Karayiannis [34] versus quality reduced with correlation (22).
heat transfer engineering vol 31 no 4 2010
Trang 30Another data set that has been tested in the course of the
present study was experimental data collected for water in a
tube diameter of d = 1.45 mm due to Sumith et al [29] The
experimental parameters were as follows: quality x= 0.1–0.8,
mass flow rate G= 80–250 kg/m2-s, heat flux= 0.3–80 kW/m2,
and saturation temperature TSAT= 263◦C The results of the
cal-culations are presented in Figure 8 As can be seen, the available
database does not correlate too well The heat transfer
coeffi-cient, αTPB, calculated using Eq (22) returns somewhat lower
Figure 8 Data due to Sumith et al [29] reduced with correlation (22).
Figure 9 Data due to Summith et al [29] reduced with correlation (22) incorporating the two-phase flow multiplier due to Gronnerud [28].
values than the experimental data The first question in the ysis of these data was whether the expression for the two-phaseflow multiplier was adequate for calculations of water heat trans-fer Subsequently, calculations were performed using the Gron-nerud correlation of two-phase flow multiplier [28] rather thanthat of Muller-Steinhagen and Heck [27] In Figure 9 are pre-sented calculations obtained using the Gronnerud correlation[28] In this case the comparison is much better, as more than60% of experimental points are found in the±30% envelope oferror The conclusion that can be drawn here is that the postu-lated correlation still preserves its qualitative consistency andshows only the quantitative discrepancy, which can be reduced ifthe appropriate model for the two-phase flow multiplier is used.However, the obtained results are still acceptable, from the point
anal-of view that the suggested correlation is anal-of a general character.The data set due to Sumith et al [29] shows the necessity for veryaccurate methods of determination of two-phase flow multiplierfor different flow regimes It can also be concluded that if theexperimental data exhibits very strong dependence on the flowresistance then the bubble generation is of secondary impor-tance That finds confirmation in recent works by Thome [30],who states that in small-diameter channels and minichannels,dominant is the convective heat transfer and bubble nucleation
is negligible The models of flow boiling developed by Thomeand his coworkers are looking very detailed at the first glance,but in perspective are aimed at the development of a precisevalue of the pressure drop in the channel, which further con-verts to the two-phase flow multiplier Hence, we can regardthe model presented here as the sort of top-to-bottom approach,whereas the approach by Thome [30] is the bottom-up approach.heat transfer engineering vol 31 no 4 2010
Trang 31284 D MIKIELEWICZ
We find a necessity of obtaining very accurate models for
the two-phase flow multipliers, whereas Thome’s approaches
are forming one of the ways of postulating the appropriate
pres-sure drop in the channel However, as ought to be remembered,
none of the models presented so far in the literature incorporate
flow resistance, which is a key for success in small-diameter
channels, minichannels, and probably microchannels, which
have a dominant character in convective heat transfer
Another data set under scrutiny here is the nitrogen data due
to Qi et al [35] Nitrogen is practically an ideal wetting fluid on
most solid surfaces It features a small value of surface tension,
which may have a significant influence on the bubble
nucle-ation, growth, and detachment Moreover, liquid nitrogen also
has smaller viscosity, higher thermal conductivity, and smaller
density ratio of liquid phase to vapor phase, compared to the
nor-mal fluids (water and refrigerants) These features undoubtedly
affect the heat transfer and pressure drop characteristics of flow
boiling in both macro- and microchannels The experiments due
to Qi et al [35] have been performed in the stainless-steel
circu-lar tubes with diameters of 0.531, 0.834, 1.042, and 1.931 mm
The range of flow parameters was: x= 0.1–0.8, mass flow rate
G= 195–2000 kg/m2-s, heat flux q= 10–15 kW/m2, and
satu-ration pressure pSAT= 200–800 kPa Data have been presented
in Figure 10 We can see that 60% of results fall into the error
band of±30% That result should be regarded as quite
satisfac-tory Some of the data have been collected for the flows in tubes
with diameters smaller than 1 mm
In the case of other dimensions of the tubes we can observe
that the distribution of the ratio αth /α expis somewhat linear in
relation to quality x That is apparent for the remaining diameters
of tubes However, the slope is more or less the same in all cases
Qi et al [35] in their paper tested other empirical correlations
Figure 10 Data due to Qi et al [35] reduced with correlation (22).
Figure 11 Data due to Bohdal [33] reduced with correlation (25).
against their experimental data These were correlations due
to Klimenko, Shah, Chen, and Tran; see [35] None of thesecorrelations was found suitable to be relevant to reflect that type
of experimental data
Subcooled Boiling in Conventional Tubes
Subsequently, our attention is focused on flow boiling insubcooled channels The relation (25), describing that process,which is a reduced form of expression (22), is used in calcula-tions The technical capabilities enabled for experiments in the
following range of parameters: mass flow rate G = 100–1600kg/m2-s, saturation temperature TSAT= –30 to 20◦C, fluid sub-
cooling (TSAT – T f) = 0–10 K, and heat flux, q = 0–30,000
W/m2 In Figure 11 are presented comparisons of model dictions using Eq (25) and experimental data for subcooledflow boiling of R134a, in a vertical channels of 13 mm in in-ner diameter As can be seen, the model underpredicts the heattransfer coefficient by about 30% That is primarily due to thefact that the assumption has been made during the reduction ofthe correlation to the subcooled flow regime that the two-phaseflow multiplier assumes a value of unity, which is not true, asthe presence of bubbles leads to the increase of two-phase flowmultiplier above unity
pre-Therefore, calculations have been repeated with a value of
two-phase flow multiplier artificially set to RMS = 3 The results
of calculations have been presented in Figure 12 We can see
a much better agreement with experimental data We can alsoconclude that the correct form of two-phase flow resistance is
of paramount importance in simulations of flow boiling heattransfer, in both saturated and subcooled regimes
heat transfer engineering vol 31 no 4 2010
Trang 32D MIKIELEWICZ 285
Figure 12 Data due to Bohdal [33] reduced with correlation (25), RMS = 3.
CONCLUSIONS
The model of flow boiling presented in this article is a
gen-eral model, which can be advised for use in numerous
engineer-ing applications Comparisons with different experimental data
show its robustness and satisfactory accuracy The model,
con-trary to other methods of calculating heat transfer coefficients in
flow boiling, has been developed on a theoretical basis, as a result
of consideration of energy dissipation in the flow, where boiling
occurs That led, first of all, to devising a value of exponent n
in Eq (1), most often used for reduction of experimental data
The presented model gives the value of exponent n = 2 The
postulated model also incorporates another term, which proves
to be very important in case of minichannels and
microchan-nels That is the inclusion of a two-phase flow multiplier, which
models the convective flow without bubble nucleation The
se-lection of the two-phase flow multiplier is also very important
for calculations In the case of refrigerants, the most effective
is a model due to M¨uller-Steinhagen and Heck [27] In the case
of other fluids the latter model may not provide good accuracy
of calculations For example, the data set due to Sumith et al
[29] shows that the best two-phase pressure drop model is due
to Gronnerud [28] The more accurate is the selected model for
the two-phase flow multiplier, the more accurate are the results
obtained In order to get the most accurate results of calculations
we must use the models of pressure drop developed for specific
flow structures That proves that the approach to model heat
transfer in flow boiling starting from precise evaluation of
pres-sure drop is very promising [19, 30], but that is also consistent
with the general structure of the model presented here, with the
two-phase flow multiplier being an important item in it What
can be advised for prospective research into flow boiling is that
the measurements of pressure drop and quantities constituting
the heat transfer coefficient should take place simultaneously,
in order to obtain the most accurate information
The model presented here is applicable both to conventionalchannels and to small-diameter channels It has been tested forchannel diameters greater than 1 mm In the case of smallerchannel dimensions the presented model tends to overpredictthe experimental data Very useful here are the findings ofThome [30], who stipulates that in small-diameter channels,and minichannels and microchannels in particular, the bubblenucleation is not present and only the slug and annular flowstructures are dominant That observation may also be incor-porated into the postulated model (22), as in such cases it may
be recommended to drop the entire nucleate boiling term Such
an operation will lead to the dependence of the two-phase flowheat transfer coefficient merely on the two-phase flow multiplier,which would serve as useful information to other researchers as
to how continue their investigations
The model presented can also be reduced to a form cable for the analysis of subcooled flow boiling Also here wecan notice that the knowledge of precise pressure drop is veryimportant In the case of subcooled boiling there is a lack ofmodels for two-phase flow multipliers By guessing the value oftwo-phase flow multipliers we can significantly improve modelpredictions
appli-In the author’s opinion, the presented model can be suggestedfor a wider use among engineers, but further validation withexperimental data would add value to its robustness
NOMENCLATURE
Bo Boiling number, Bo= q ·l·ρL
ρG·hLG ·µ L
Cp specific heat at constant pressure, J/kg-K
d channel inner diameter, m
g gravity, m/s2
G mass flow rate, kg/m2-s
hLG latent heat of evaporation, J/kg
l bubble characteristic length, channel length, m
P correction in Eq (2)
Pr Prandtl number, Pr=µL·CL
λL
q heat flux density, W/m2
R two-phase flow multiplier
Trang 33[1] Thome, J R., Boiling of New Refrigerants: A State-of-the-Art
Review, International Journal of Refrigeration, vol 19, no 7, pp.
435–457, 1996
[2] Bergles, A E., Lienhard, V J H., Kendall, G E., and
Grif-fith, P., Boiling and Evaporation in Small Diameter
Chan-nels, Heat Transfer Engineering, vol 24, no 1, pp 18–40,
2003
[3] Kandlikar, S G., Fundamental Issues Related to Flow Boiling
in Minichannels and Microchannels, Proc Experimental Heat
Transfer, Fluid Mechanics and Thermodynamics, pp 129–146,
Thesalloniki, Greece, 2001
[4] Thome, J R., Boiling in Microchannels: A Review of Experiment
and Theory, International Journal of Heat and Fluid Flow, vol.
25, no 2, pp 128–139, 2004
[5] Dengler, C E., and Addoms, J N., Heat Transfer Mechanism for
Vaporisation of Water in Vertical Tube, Chem Eng Prog Symp.
Ser., 52, 18, 95–103, 1956.
[6] Guerrieri, S A., and Talty, R D., A Study of Heat Transfer to
Organic Liquids in Single Tube Natural Circulation Vertical Tube
Boilers, Chem Eng Prog Symp Ser., vol 52, no.18, pp 69–77,
1956
[7] Schrock, V E., and Grossman, L M., Forced Convection
Boiling Studies, University of California, Institute of
Engi-neering Research, Report 73308-UCX-2182, Berkeley, CA,
1959
[8] Collier, J G., and Pulling, D J., Heat Transfer to Two-Phase
Gas–Liquid Systems, Report AERE-R3908, Harwell, UK, 1962
[9] Shah, M M., Chart Correlation for Saturated Boiling Heat
Trans-fer: Equations and Further Study, ASHRAE Trans., vol 88, pp.
185–196, 1982
[10] Kandlikar, S G., A General Correlation for Saturated
Two-Phase Flow Boiling Heat Transfer Inside Horizontal and
Ver-tical Tubes, Journal of Heat Transfer, vol 112, pp 219–228,
1989
[11] Gungor, K E., and Winterton, R H S., A General Correlation for
Flow Boiling in Tubes and Annuli, International Journal of Heat
Mass Transfer, vol 29, pp 351–358, 1986.
[12] Rohsenow, W M., A Method of Correlating Heat Transfer Data
for Surface Boiling of Liquids, Trans ASME, vol 74, pp 969–
976, 1952
[13] Chen, J C., Correlation for Boiling Heat-Transfer to Saturated
Fluids in Convective Flow, Industrial & Chemical Engineering
Process Design and Development, vol 5, no 3, pp 322–339,
1966
[14] Kutateładze, S S., Boiling Heat Transfer, International Journal
of Heat and Mass Transfer, vol 4, pp 31–45, 1961.
[15] Steiner, D., and Taborek, J., Flow Boiling Heat Transfer in Vertical
Tubes Correlated by Asymptotic Model, Heat Transfer ing, vol 23, no 2, pp 43–68, 1992.
Engineer-[16] Forster, H K., and Zuber, N., Dynamics of Vapour Bubbles and
Boiling Heat-Transfer, AIChE J., vol 1, no 4, pp 531–535,
1955
[17] Cooper, M G., Saturation Nucleate Pool Boiling: A Simple
Cor-relation, International Chemical Engineering Symposium, ser no.
[22] Podowski, M., Understanding Multiphase Flow and Heat
Trans-fer: Perception, Reality, Future Needs, Archives of ics, vol 26, no 3, pp 3–20, 2005.
Thermodynam-[23] Mikielewicz, D., Mikielewicz, J., and Tesmar, J., Improved Empirical Method for Determination of Heat Transfer Coefficient
Semi-in Flow BoilSemi-ing Semi-in Conventional and Small Diameter Tubes, ternational Journal of Heat and Mass Transfer, vol 50, pp 3949–
In-3956, 2007
[24] Ananiev, E L., On the Mechanism of Heat Transfer in NucleateBoiling Flow of Water in a Tube Against the Reynolds Analogy,
in Convective Heat Transfer in Single and Two-Phase Flows, ed.
V W Borishansky, Energia, Leningrad, 1964 (in Russian)
[25] Shah, R K., and London, A L., Laminar Flow Forced Convection
in Ducts, Advances in Heat Transfer, Suppl 1, Academic Press,
London, 1978
[26] Park, H S., Dependency of Heat Transfer Rate on the Brinkman
Number in Microchannels, Proc Therminic 2007, Budapest,
Hun-gary, pp 61–65, 2007[27] M¨uller-Steinhagen, H., and Heck, K A., A Simple Fric-tion Pressure Drop Correlation for Two-Phase Flow in Pipes,
Chemical Engineering and Processing, vol 20, pp 297–308,
[29] Sumith, B., Kaminaga, F., and Matsumura, K., Saturated Flow
Boiling of Water in Vertical Small Diameter Tube, Experimental Thermal Fluid Sciences, vol 27, pp 789–801, 2003.
[30] Thome, J R., Wolverine Engineering Databook III, Chapter I,
2007, www.wlv.com/products/databook/db3/DataBookIII.pdf[31] Kew, P., and Cornwell, K., Correlations for the Prediction of Boil-
ing Heat Transfer in Small Diameter Channels, Applied Thermal Engineering, vol 17, nos 8–10, pp 705–715, 1997.
heat transfer engineering vol 31 no 4 2010
Trang 34D MIKIELEWICZ 287[32] Tran, T N., Chyu, M C., Wambsganss, M W., and France, D.
M., Two-Phase Pressure of Refrigerants During Flow Boiling in
Small Channels: An Experimental Investigation and Correlation
Development, International Journal of Multiphase Flow, vol 26,
pp 1739–1754, 2000
[33] Bohdal, T., Nucleate Boiling Phenomena, Koszalin University of
Technology Publishers, Koszalin, vol 76, 2001 (in Polish)
[34] Karayiannis, T., Private communication, 2004
[35] Qi, S L., Zhang, P., Wang, R Z., and Xu, L X., Flow
Boil-ing of Liquid Nitrogen in Micro-Tubes: Part II—Heat
Trans-fer Characteristic and Critical Heat Flux, International
Jour-nal of Heat and Mass Transfer, vol 50, pp 5017–5030,
2007
Dariusz Mikielewicz is a professor of thermal
sciences at the Gdansk University of Technology, Gdansk, Poland He received his M.Sc degree from the Gdansk University of Technology (1990), and his Ph.D degree from the University of Manchester (1994) In 2002 he presented his habilitational dis- sertation at the Gdansk University of Technology In 1994–1996 he worked as an engineer at the Berkeley Nuclear Laboratories, Gloucestershire, UK He has been teaching at the GUT since 1996 He has been
an elected member to the Science Council in 2004–2008 His research tributions have been in the field of modeling of mixed convection, two-phase flows, and recently renewable energy He is currently working on enhanced heat transfer and condensation in heat exchangers.
con-heat transfer engineering vol 31 no 4 2010
Trang 35CopyrightC Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903312049
Mechanisms of Boiling in
Micro-Channels: Critical Assessment
JOHN R THOME and LORENZO CONSOLINI
Laboratoire de Transfert de Chaleur et de Masse, ´Ecole Polytechnique F´ed´erale de Lausanne, Switzerland
Numerous characteristic trends and effects have been observed in published studies on two-phase micro-channel boiling heat
transfer While macro-scale flow boiling heat transfer may be decomposed into nucleate and convective boiling contributions,
at the micro-scale the extent of these two important mechanisms remains unclear Although many experimental studies have
proposed nucleate boiling as the dominant micro-scale mechanism, based on the strong dependence of the heat transfer
coefficient on the heat flux similar to nucleate pool boiling, they fall short when it comes to actual physical proof A strong
presence of nucleate boiling is reasonably associated to a flow of bubbles with sizes ranging from the microscopic scale
to the magnitude of the channel diameter The bubbly flow pattern, which adapts well to this description, is observed,
however, only over an extremely limited range of low vapor qualities (typically for quality less than 0.01–0.05) Furthermore,
at intermediate and high vapor qualities, when the flow assumes the annular configuration and a convective behavior is
expected to dominate the heat transfer process, the experimental evidence yields entirely counterintuitive results, with heat
transfer coefficients often decreasing with increasing vapor quality rather than increasing as in macro-scale channels,
and with a much diminished heat flux dependency compared with would be expected In summary, convective boiling in
micro-channels has been revealed to be much more complex than originally thought The present review aims at describing
and analyzing the boiling mechanisms that have been proposed for two-phase micro-channel flows and confronting them
with the available experimental heat transfer results, while highlighting those questions that, to date, remain unanswered.
INTRODUCTION
The initial purpose of the studies on two-phase heat transfer
in micro-channels was (and still is, to a certain extent) aimed
at understanding the mechanisms controlling the flow boiling
process The earliest results of Lazarek and Black [1] showed
values for the heat transfer coefficient that were unaffected by
vapor quality, but were a function of heat flux, leading them
to conclude that nucleate boiling was the dominant heat
trans-fer mechanism as in macro-scale flow boiling While others
confirmed this trend and adopted their explanation, new trends
arose as the amount of experimentation in the sector grew A
significant number of studies found decreasing curves in the
α–x plane rather than flat ones (with α the heat transfer
coeffi-cient and x the thermodynamic vapor quality), and even some
increasing trends in α versus x, giving rise to a rather puzzling
scenario with respect to the macro-scale knowledge base (these
were documented, for instance, in Agostini and Thome [2])
Address correspondence to Professor John R Thome, EPFL STI IGM
LTCM, ME G1 464, Station 9, 1015 Lausanne, Switzerland E-mail:
john.thome@epfl.ch
The relative importance of nucleate boiling, thin film ration, and convective boiling in the individual flow patterns thatare characteristic to a micro-channel flow is thus still unclear.The studies directed specifically to flow patterns (see, for exam-ple, Tripplett et al [3] and Serizawa et al [4]), many of whichare for air–water flows, found general agreement as to the fourmain regimes: (i) bubbly flow, at very low mass fractions of air orvapor, (ii) slug flow, describing the passage of long bubbles sep-arated by liquid slugs, (iii) churn flow, a transition mode betweenslug flow and fully annular flow, and (iv) annular flow, occurring
evapo-at the highest gas superficial velocities (see Figure 1) Recently,similar flow patterns have also been reported for the flow ofrefrigerants (cf Revellin et al [5]), confirming the absence ofany stratified regime in the micro-scale Cornwell and Kew [6]coupled flow patterns and heat transfer, by arguing that differ-ent flow regimes presented different heat transfer mechanisms,varying from essentially nucleate boiling, to confined bubbleboiling, and finally to purely convective evaporation for annularflows Jacobi and Thome [7] and Thome et al [8] postulatedthat during slug flow, nucleate boiling is completely suppressedand heat is transferred primarily by conduction through the thinevaporating film surrounding the elongated bubbles, while heat288
Trang 36J R THOME AND L CONSOLINI 289
Figure 1 From top to bottom: bubbly, slug, churn, and annular flows for
R-134a in a 510 µm tube at a mass velocity of 500 kg/m2-s Taken from Consolini
[30].
transfer to the liquid slug and any dry zone are only of second
and third importance depending on their respective residence
times
An element added to the discussion concerns the possibility
of periodic dry-out of the channel wall (see Thome et al [8],
Kew and Cornwell [9], and Kandlikar [10]) This mechanism,
however, was not entirely understood, and very few gave a clear
opinion as to how and when it occurred The work presented in
Thome et al [8] was among the few studies that attempted to
address this issue, suggesting the development of a dry zone at
the tail of an evaporating bubble
In recent years, a number of studies provided evidence of
the sensitivity of two-phase micro-channel systems to flow
in-stabilities Oscillating pressure drops and wall temperatures,
and visualizations showing cyclical backflow, were
encoun-tered in many experiments Unfortunately, many of these
data have been mingled in with stable data and thus
cre-ate a confusing situation Bergles and Kandlikar [11]
clas-sified these flows as compressible volume instabilities,
re-lating them to the presence of compressibility prior to the
heated channels Relative to a stable mode, an unstable
sys-tem presents entirely different flow features and may bring
about substantial differences in the heat transfer mechanisms
(see [12])
The discussion that follows is aimed at providing a critical
review of the main conclusions that may be drawn to date on
the mechanisms of heat transfer for boiling in micro-channels,
Figure 2 Experimental heat transfer coefficients from Lazarek and Black [1] for R-113 in a 3.1 mm tube.
focusing primarily on the characteristics of stable two-phaseflows
EXPERIMENTAL HEAT TRANSFER
Among the first studies on flow boiling heat transfer in asingle channel was the one by Lazarek and Black [1], who re-ported experimental heat transfer coefficients for flow boiling
of R-113 in a vertical tube with an inner diameter of 3.1 mm(Figure 2) Their heat transfer coefficients had a strong depen-dency on the applied heat flux, but were essentially independent
of vapor quality Similar results were obtained by Tran et al.[13] and Bao et al [14] Tran and coworkers performed exper-iments on R-12 in circular and rectangular channels with sizesranging from 2.40 to 2.92 mm Their data showed that for a suffi-ciently high wall superheat (above 2.75 K) the values of the heattransfer coefficient were unaffected by vapor quality and massvelocity, but increased significantly with heat flux The flowboiling experiments of Bao et al again confirmed these trendsand presented additional data showing the improvement in heattransfer with increasing saturation pressure, further promotingthe view that nucleate boiling was dominating (no visualization
of the flow was possible in their setup) More recently, Lihong
et al [15] performed experiments on a 1.3 mm circular channelfor refrigerant R-134a, yielding similar results
Added trends in heat transfer were reported in the work byLin and coworkers [16] (Figure 3) In their study on R-141b(1.1 mm tube), they observed three distinct responses in theheat transfer coefficient to changes in heat flux and vapor qual-ity: (1) At low heat fluxes, heat transfer improved with increas-ing vapor quality, (2) for intermediate values from 30 to 53kW/m2 in Figure 3 and vapor qualities within 0.40, the heattransfer coefficient increased with heat flux, much like whatwas observed in the investigations cited previously, and (3) at
the highest heat fluxes, heat transfer gradually fell with x and
heat transfer engineering vol 31 no 4 2010
Trang 37290 J R THOME AND L CONSOLINI
Figure 3 Experimental heat transfer coefficients from Lin et al [16] for
R-141b in a 1.1 mm channel and a mass velocity of 510 kg/m 2 -s.
tended to heat-flux-independent values While further heating
increased the heat transfer coefficient for vapor fractions up
to 0.40, the correspondence was much less clear beyond this
threshold
Saitoh et al [17] obtained heat transfer data for boiling of
R-134a in a 0.51 mm tube (550 mm long) at 15 and 29 kW/m2
for qualities extending to almost unity Their heat transfer
co-efficients showed an inverted “U” shape in the α–x plane The
heat transfer data increased up to a quality of 0.60, beyond
which the coefficients declined monotonically In another study
on R-134a, Martin-Callizo et al [18] presented results for a
ver-tical 0.64 mm stainless-steel micro-channel, finding that once
again the dominant effect was that of heat flux while mass
velocity was less important They found that their heat
trans-fer coefficients were rather insensitive to vapor quality until
reaching the higher range of their heat flux test range,
where-upon the heat transfer coefficients then decreased
monoton-ically from vapor qualities of about 0.01–0.02 down to
val-ues of about 0.6–0.8 without going through any maximum or
minimum
As for the effect of mass velocity, a number of investigations
have shown heat transfer coefficients to remain unchanged when
varying the fluid flow rate, as in the data from Tran et al [13]
(see Figure 4) Tran and coworkers reported an improvement in
heat transfer with mass velocity only for wall superheats lower
than 2.75 K The experiments from Bao et al [14] on R-11 and
R-123, and from Lihong et al [15] on R-134a, also showed no
change in heat transfer with flow rate, with the latter observing
mild differences only at the lowest heat flux tested One of
the few studies on a single channel that presented a different
outcome was that of Sumith et al [19] for flow boiling of water
in a 1.45 mm vertical tube, reporting heat transfer coefficients
that often decreased when increasing the flow, even at high heat
fluxes
At present, there is general agreement among the studies that
addressed the effect of saturation conditions on heat transfer,
Figure 4 Experimental heat transfer coefficients from Tran et al [13] for R-12 in a 2.46 mm channel at different heat fluxes and mass velocities and wall superheats above 2.75 ◦C.
that a higher saturation pressure/temperature yields higher heattransfer coefficients (see for example [14, 15, 18])
Similar results have also been recently reported in flow ing heat transfer experiments on multi-micro-channel systems,
boil-as in the cboil-ase of Agostini et al [20, 21], who tested refrigerantsR-134a and R-236fa in a 67-parallel-micro-channel evaporator(rectangular channels, 0.223 mm wide, 0.680 mm high, and20.0 mm long, separated by 0.80 mm wide fins) It can be seenfrom Figure 5 that their heat transfer data at low heat fluxes tend
to increase with vapor quality until intermediate heat fluxes,where they first increase and then show nearly no influence ofvapor quality At higher heat fluxes, the heat transfer coefficientsstart to decline with increasing vapor quality While the heattransfer coefficients rise sharply with increasing heat flux, at the
Figure 5 Flow boiling data of Agostini et al [20] for R-236fa in a silicon multi-micro-channel test section at a mass velocity of 810.7 kg/m 2 -s, a nominal pressure of 2.73 bar, and saturation temperature of 25 ◦C The silicon test section
without its cover plate is shown in the inset photograph.
heat transfer engineering vol 31 no 4 2010
Trang 38J R THOME AND L CONSOLINI 291
highest values (starting at 178.4 W/cm2relative to the surface
area of the heating element) a peak is reached and the heat
trans-fer coefficients begin to decrease with increasing heat flux as
the critical heat flux is approached (but not reached) in this data
set
HEAT TRANSFER MECHANISMS
The heat transfer mechanisms that are active in boiling in
micro-channels can be summarized as follows: (i) In bubbly
flow, nucleate boiling and liquid convection would appear to be
dominant, (ii) in slug flow, the thin film evaporation of the liquid
film trapped between the bubble and the wall and convection to
the liquid and vapor slugs between two successive bubbles are
the most important heat transfer mechanisms, including in terms
of their relative residence times, (iii) in annular flow, laminar or
turbulent convective evaporation across the liquid film should be
dominant, and (iv) in mist flow, vapor-phase heat transfer with
droplet impingement will be the primary mode of heat transfer
For those interested, a large number of two-phase videos for
micro-channel flows from numerous laboratories can be seen in
the free e-book of Thome [22]
Notably, many experimental papers conclude without proof
that nucleate boiling is dominant in their data only because they
find a substantial heat flux dependency; a heat flux dependency,
however, does not prove that nucleate boiling is dominant or
even present For instance, Jacobi and Thome [7] and Thome et
al [8] have argued that the heat flux effect can be explained and
predicted by the thin-film evaporation process occurring around
elongated bubbles in the slug flow regime without any
nucle-ation sites Their model shows that the heat flux dependency
comes mainly through its effect on the bubble frequency and
the thin film evaporation process Thus, simply labeling
micro-channel flow boiling data as being nucleate boiling dominated
is misleading since this seems to only be the case for the bubbly
flow regime, which occurs at very low vapor qualities (typically
for x < 0.01–0.05 depending on the mass velocity, etc.) Some
experimental flow boiling studies that report that nucleate
boil-ing was dominant at low vapor qualities also report that the flow
regime observed at these conditions was elongated bubble flow
without any bubbly flow observed These two conclusions thus
seem to be contradictory One should further contemplate that a
nucleate boiling correlation does not actually model the
nucle-ate boiling process, but is only an empirical relationship relating
the heat transfer coefficient to the heat flux, and hence the actual
mechanism is not actually addressed in the correlation Hence,
in flow boiling in a micro-channel in elongated bubble (slug)
flows, the heat flux dependency in such a correlation most likely
is coming in through the bubble frequency and thin film effects,
not that of nucleate boiling
To date, many types of noncircular micro-channels have
been tested; for instance, results for square, rectangular,
par-allel plate, triangular, and trapezoidal geometries are currently
available in the literature Besides the problems associated withcharacterizing the channel size (e.g., a hydraulic diameter of anoncircular channel has no physical relationship to an annularfilm flow), the rectangular channels tested sometimes have veryhigh aspect ratios whose effect on heat transfer is not well un-derstood Recalling the wedge flows observed by Cubaud and
Ho [23] for air–water, a partially wetted perimeter along andaround elongated bubbles will have an influence on heat trans-fer while the wet corners may tend to better resist completedry-out
EMPIRICAL PREDICTION METHODS
The variety of trends in heat transfer data and the inherentdifficulties in performing experimental work on these small sys-tems have made it very challenging to develop a well-establishedunderstanding of boiling in micro-channels Several authorshave correlated their experimental results through different sets
of generally non-dimensional groups Others, on the other hand,have attempted to either extend methods previously developedfor conventional macro-scale systems to the micro-scale, or todefine new approaches specifically for micro-channel two-phaseflows
Lazarek and Black Correlation
From their heat transfer experiments on R-113, Lazarek andBlack [1] proposed the following nondimensional correlationfor the flow boiling Nusselt number (Nul = αD/k l):
Nul = 30Re0.857
with Relo = GD/µ l, the all-liquid Reynolds number, Bo =
q /(Gh lv ) the Boiling number, and G the mass velocity of the total
flow of liquid and vapor Equation (1) expresses no dependence
of the heat transfer process on the local vapor quality
Tran et al Correlation
As mentioned earlier, in their experiments on 12 and
R-113 Tran and coworkers [13] observed that for wall superheatsabove 2.75 K their heat transfer data expressed a strong α versus
q behavior, assigning this to the macro-scale mechanism ofnucleate boiling The authors therefore modified the correlation
of Lazarek and Black [1], Eq (1), by replacing the Reynoldsnumber with the Weber number, Welo = G2D/(ρl σ), removingviscous effects in favor of surface tension The liquid to vapordensity ratio was added to further account for variations in fluidproperties, so that
Trang 39292 J R THOME AND L CONSOLINI
The 8.4× 105factor in Eq (2) is dimensional, with units of
W/(m2-K) Equation (2) removes any dependence of the heat
transfer coefficient on mass velocity Furthermore, Eq (2) also
yields the following proportionality between the heat transfer
coefficient and the channel diameter: α∝ D 0.3, which seems to
be the opposite of experimental trends found in later studies
Kandlikar and Balasubramanian Correlation
Kandlikar and Balasubramanian [24] extended the
correla-tion proposed by Kandlikar for convencorrela-tional tubes, where the
local two-phase heat transfer coefficient was determined
accord-ing to the value of the dominant mechanism between nucleate
boiling (nb) and convective evaporation (cv):
α= larger of
αnb
The original correlations for the two coefficients in Eq (3)
were developed for all-liquid Reynolds numbers, Relo, above
3000, and presented the following functional dependencies:
The nondimensional groups in Eq (4) are respectively the
Convection number, Cv, the Boiling number, Bo, the all-liquid
Froude number, Frlo, and the vapor quality For Relo >3000,
Kandlikar suggested using transition (Gnielinski) and fully
tur-bulent (Petukhov and Popov) correlations for the single-phase
liquid heat transfer coefficient, αl, based on the all-liquid
Reynolds number However, for smaller channels the authors
argued that the value of the Reynolds number was generally
lower than 3000, making the preceding single-phase
correla-tions inconsistent Furthermore, the reduced effect of gravity
in micro-channels justified the removal of the Froude number
from Eq (4) In view of both these considerations, Kandlikar and
Balasubramanian proposed the following modified correlations
with F sf a constant that was used to fit the expressions to each
particular surface material–fluid combination For Reynolds
numbers in the range 1600≤ Relo <3000, the authors suggested
interpolating between laminar and transition correlations for αl
On the other hand, for Relo <1600 the flow was considered
laminar, and a laminar correlation of the form Nu= αl D/k l =
constant was deemed applicable Finally, for Relo≤ 100, Eq (3)
was modified to α= αnb, with αnbgiven by Eq (5) ingly, their nucleate boiling and convective boiling heat transfercorrelations in Eq (5) are identical, except for values of the twolead constants and one of the exponents Thus, it is not clearhow one represents nucleate boiling and the other convectiveboiling
Interest-Zhang et al Extension of Chen’s Correlation
Zhang and coworkers [25] analyzed 13 separate databases,confronting them with some of the most widely quoted cor-relations for two-phase heat transfer in conventional systems.Chen’s superposition model gave the best outcome However,the authors observed that for micro-channels, the values of theliquid Reynolds numbers, Rel = G(1 – x)/µ l, were mostly lowerthan 2000, i.e., lower than the laminar–transition threshold,and argued that this was inconsistent with the original form
of Chen’s model (similar to the reasoning of Kandlikar and asubramanian [24]) Chen’s superposition model for convectiveboiling states that heat is transferred by two competing mech-anisms, namely, nucleate boiling and convective vaporization.The overall heat transfer coefficient is given by an additive lawthat combines these different contributions,
The nucleate boiling term in Eq (6) is expressed as theproduct of the nucleate pool boiling value (αnpb) computed
at the corresponding wall superheat through the Forster and
Zuber [26] correlation, and a boiling suppression factor, S, that
accounts for the suppression of bubble nucleation due to theconvective nature of the two-phase system On the other hand,the convective contribution depends on the flow properties and
is given as an all liquid heat transfer coefficient multiplied by a
two-phase correction factor, F That is:
For the all liquid heat transfer coefficients in Eqs (7) and(8), Zhang et al [25] suggested using a laminar or turbulentexpression according to the value of the liquid Reynolds number,
Rel For the two-phase factor, F , they proposed using the larger value of 1 and an expression, F, based on the general form of
the Martinelli parameter, X:
where C is Chisholm’s constant For the suppression factor, S,
they presented a form similar to the one given by Chen:
Trang 40J R THOME AND L CONSOLINI 293(with a liquid Reynolds number in the place of the two-phase
Reynolds number as originally proposed by Chen), justifying
their choice by assuming the nucleate boiling suppression
mech-anism to remain the same as in the macro-scale
Further Remarks
Some further comments about the methods just described are
in order All of the preceding methods are essentially
modifica-tions of macro-scale flow boiling methods, and thus assume that
nucleate boiling is an important heat transfer mechanism
with-out proof of its existence for the two principal micro-channel
flow regimes: slug (elongated bubble) flow and annular flow
Furthermore, using a tubular single-phase flow correlation to
predict convective heat transfer in an annular flow is not
phys-ically realistic since an annular flow is a film flow and is thus
governed by its film Reynolds number rather than by a tubular
Reynolds number Similar to Nusselt’s laminar film
condensa-tion theory, as long as there are no interfacial waves, the local
laminar annular flow heat transfer coefficient is dependent on
heat conduction across the liquid film thickness, and it is thus
not appropriate to calculate its value in terms of the tubular
so-lution of Nul = 4.36 For instance, no one applies the tubular
flow solution to predict laminar falling film condensation on a
vertical plate, so it does not seem to be appropriate to apply it to
an evaporating laminar annular film flow either For that matter,
turbulent falling film condensation on a vertical plate is
corre-lated based on its local liquid film Reynolds number in which
the film thickness is the active characteristic dimension, and
hence turbulent annular film evaporation should be correlated
in the same manner, not using a tubular flow Reynolds number
Not withstanding the preceding comments, wholly empirical
methods can be fitted to experimental databases for prediction
purposes On the other hand, none of the preceding correlations
is able to predict the diverse trends in the heat transfer coefficient
versus vapor quality described earlier
MECHANISTIC PREDICTION METHOD
Thome et al Three-Zone Evaporation Model for Slug Flow
Thome and coworkers [8] developed a phenomenological
method to describe heat transfer for a purely convective
micro-channel slug flow (no nucleate boiling), based principally on the
following assumptions:
1 The vapor and liquid travel at the same velocity
2 The heat flux is uniform and constant with time along the
inner wall of the micro-channel
3 All energy entering the fluid is used to vaporize liquid Thus,
the temperatures of the liquid and vapor remain at the
satura-tion value, i.e., neither the liquid nor the vapor is superheated
Figure 6 Image of an elongated bubble (top) and a schematic diagram of the three-zone evaporation model (bottom).
4 The local saturation pressure is used for determining the localsaturation temperature
5 The liquid film remains attached to the wall The influence
of vapor shear stress on the liquid film is assumed negligible,
so that it remains smooth without ripples
6 The thickness of the film is very small with respect to theinner radius of the tube
7 The thermal inertia of the channel wall can be neglected
Slug flow was modeled as a cyclical passage of a zone” sequence, comprising a liquid slug, an elongated bubblesurrounded by an evaporating liquid film, and an all-vapor dry-zone at the bubble tail (see Figure 6), respectively referred to
“three-by subscripts L, F , and D The first assumption yields an equal velocity, W , for the vapor and liquid, given by the homogeneous
elongated bubble plus the dry zone (t V = t F + t D), and
the liquid slug, t L, were derived from the definition of vaporquality and through Eq (11) as
with t the passage period of the three-zone structure, and
having neglected the liquid mass within the film The local filmbehavior was modeled as the evaporation of a stagnant liquid
layer; from an energy balance at given axial position, z:
2π R qdz = −2π ρ l (R− δ)dδ
dt h lv dz (13)
heat transfer engineering vol 31 no 4 2010