International Journal of Heat and Mass Transfer 88 (2015) 368–378

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Experimental and theoretical studies of critical heat flux of flow boilingin microchannels with microbubble-excited high-frequency two-phaseoscillations

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.04.0610017-9310/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 803 777 7155.E-mail address: li01@cec.sc.edu (C. Li).

Wenming Li, Fanghao Yang, Tamanna Alam, Jamil Khan, Chen Li ⇑Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29210, United States

a r t i c l e i n f o

Article history:Received 9 February 2015Received in revised form 20 April 2015Accepted 21 April 2015

Keywords:Critical heat fluxFlow boilingMicrochannelsJacob numberHelmholtz instability

a b s t r a c t

Critical heat flux (CHF) during flow boiling in silicon microchannels (H = 250 lm, W = 200 lm, L = 10 mm)using self-excited and self-sustained high frequency two-phase oscillations is studied both experimentallyand theoretically. Tests are performed on deionized water over a mass flux range of 200–1350 kg/m2 s.An enhanced CHF of 1020 W/cm2 is achieved experimentally at a mass flux of 1350 kg/m2 s in the presentstudy. Since no existing CHF models and correlations on parallel mini/microchannels considered highfrequency two-phase oscillations, hence are not applicable to predict CHF in the present microchannelconfiguration. Adopting Helmholtz and Rayleigh instability theories and based on experimental studyof liquid thin film dry-out phenomena in two-phase oscillations, a semi-theoretical CHF model isproposed. The proposed theoretical predictions show satisfactory agreement with experimental data witha reasonable low mean absolute error (MAE) of 25–32%.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Critical heat flux (CHF) of flow boiling refers to the maximumheat flux just before the boiling crisis where a drastic decrease ofheat transfer rate or a sudden increase of surface temperatureoccurs. Hence, this is one of the critical thermal limits in electron-ics cooling systems, heat exchangers and thermal–hydraulicsystem of nuclear power plants. Achieving an ultra-high CHF isdesirable to increase the heat flux safety margin of thermal system.Additionally, high power electronics cooling becomes even morechallenging as the transistor size keeps shrinking with anincreasing power density. Therefore, it is of great interest toimprove CHF of these miniature electronic devices. CHF can be trig-gered by boundary layer separation [1], bubble crowding [2] andsub-layer dryout on heated surface [3]. Many flow boilingenhancement techniques have been developed to enhance CHF inlast decades. The main enhancement mechanisms are: regulatingbubble slugs, suppressing flow instability, modifying surfacecharacteristics, improving surface to volume ratio, and promotingliquid rewetting. For example, to suppress flow instability,inlet/outlet restrictors [4,5] and reentrant cavity [6,7] wereintroduced. Recently, nanofluid (e.g., Al2O3 nanoparticle inDI-water [8]) and nano/microscale coating (e.g., nanowire [9–11],

nanotube [12] and nanoporous surface [13]) were developed toimprove wettability. Meanwhile, surfactant can enhance CHF byreducing surface tension of fluids [14]. In addition, techniques,such as micro/mini-jets [15,16], tapered manifod [17], micromixer[18] and solution (e.g., aqueous n-butanol, TSP and boric acid solu-tions) [19,20] can enhance CHF as well. However, some enhance-ment techniques are at the cost of pressure drop. For example,inlet restrictors are considered as one of the most effective waysto improve CHF. However, significant additional pumping poweris required for this technique. Furthermore, nano/microscale coat-ing technique can drastically enhance CHF with penalty of pressuredrop [9,21] as well. Pros and cons of existing CHF enhancementtechniques are listed in Table 1.

Ultra high CHF (>30,000 W/cm2) was achieved at high mass fluxes(>38,111 kg/m2 s) in microchannel flow boiling [28]. However,much more pumping power was required. Most recently, in our pre-vious studies, a microbubble-excited actuation mechanism has beenestablished to create intense mixing in the microchannels [16,29].This new enhancement mechanism can effectively suppress flowboiling instabilities and significantly improve liquid rewetting with-out adding additional pressure drops [16]. In the present study, CHFof flow boiling in a multiple microchannel array with self-excitedand self-sustained high frequency two-phase oscillations is experi-mentally studied. Experimental results show that an ultra-highCHF (up to 1020 W/cm2) can be achieved at a modest mass flux of1350 kg/m2 s on DI water.

Nomenclature

Acr cross sectional area of counter flow, m2

As cross sectional area of auxiliary channel, m2

Av contact area between bubble and subcooled fluids, m2

Aw heated surface area of auxiliary channel, m2

Cp heat capacity at atmospheric pressure, J/kg Kd width of auxiliary channel, mDh hydraulic diameter of auxiliary channel, mFo Fourier numberG mass flux, kg/m2 sh heat transfer coefficient at vapor/liquid interface,

W/m2 KH channel height, mhfg latent heat of vaporization, kJ/kgJa Jacob numberkl thermal conductivity of subcooled liquid, W/m Kl length of vapor column entering subcooled liquid, mL length of auxiliary channel, mM number of experimental dataMAE mean absolute error_ml mass flow rate of liquid, kg/s_mv Mass flow rate of vapor, kg/s

n constant numberNu Nusselt numberPr Prantl numberql heat transfer rate of liquid, Wqv heat transfer rate from vapor interface to liquid, Wq00 heat flux, W/m2

q00CHF critical heat flux, W/cm2

R radius of vapor column, mRe Reynolds numberDT increased temperature of subcooled liquid (Tsub–Tin), KTin inlet temperature of liquid, �CTsat saturated temperature of vapor, �CTsub temperature of incoming subcooled liquid, �CDTsub temperature difference between saturated vapor and

incoming subcooled liquid (Tsat–Tsub), KUc Helmholtz critical velocity, m/sUv velocity of vapor, m/sUl velocity of liquid, m/sqv density of vapor, kg/m3

ll dynamic viscosity of liquid, Pa s

Greek symbolsk Rayleigh critical wavelength, mr surface tension, N/mq density, kg/m3

l dynamic viscosity, Pa s

SubscriptsCHF critical heat fluxin inletl liquidrel relativesub subcooled liquidv vapor

Table 1Existing CHF enhancement techniques for flow boiling in microchannels [22].

Techniques Pros* Cons*

Inlet restriction [4,5] CHF+ and HTC+ DP+Reentrant cavity [6,7] CHF+ DP� and

HTC�Tapered manifod [17] CHF+, HTC+ and

DP�Micro/minijet [15,16,23] CHF+, HTC+ and

DP�Micromixer [18] CHF+ and HTC+ DP+Nanofluid [8,24,25] CHF+ DP+ and HTC�Surfactant [14] CHF+ and HTC+ DP�Solution [19,20] CHF+ and HTC+ DP�

Surface modificationNano/microscale coating

[9,10,12,13,21]CHF+ DP+ and HTC�

Surface roughness [26,27] CHF+ and HTC+ DP+

* + increase; � decrease; � little effect or unknown.

W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378 369

Owing to the complexity of CHF mechanisms during flow boil-ing in microchannels, most of the existing CHF models or correla-tions are empirical and semi-empirical [30–32]. According to therecent review on CHF in mini/microchannels conducted by Rodayand Jensen [33], experimental CHF results are inconsistent withexisting models. For instance, there are disagreements with theinfluence of inlet subcooling degree, pressure, exit quality, anddiameter on CHF in existing models [30,34,35]. Additionally, onlya few theoretical CHF models are available for flow boiling inmicrochannels, for example, a theoretical CHF model based oninterfacial waves [3,36], or local liquid thin film dryout [37].However, none of these models considered two-phase oscillations;hence these models are not applicable to the present microchannelconfiguration.

To better understand this CHF enhancement mechanism, asemi-theoretical study in conjunction with experimental investiga-tion is conducted based on fundamental thermal/fluid physics. Todevelop a semi-theoretical CHF model for flow boiling in microchan-nels with high frequency self-sustained two-phase oscillations, allessential thermo-physical properties, for example, thermal conduc-tivity, specific heat, and latent heat of evaporation should be consid-ered. In addition, the mass flux of subcooled liquid is critical to thedirect condensation heat transfer at the vapor/liquid interface,which primarily determined bubble dynamics in the inlet manifoldand CHF condition of subcooling flow boiling [38,39]. Especially, asthe CHF is approaching, vigorous vapor generation resulting fromthin film evaporation leads to reversal vapor flow, which is gov-erned by the Helmholtz and Rayleigh instabilities. Therefore, it iscritical to take account of the interfacial condensation [40].

It is challenging to couple the Helmholtz and Rayleigh instabil-ities [41] in a flow boiling CHF model. The Helmholtz critical veloc-ity of the reversal vapor flow is determined by surface tension andhydraulic diameter of the auxiliary channel. The establishment ofstable vapor columns in the auxiliary channel blocks the liquidsupply to the heating areas, then results in the CHF conditions.The major challenges to develop theoretical CHF model are two-fold: (a) the length of vapor columns varies with the subcoolingliquid flow rate; and (b) the interfacial condensation heat transferrate is difficult to determine. Visualization study of bubble dynam-ics at CHF conditions is conducted to address the former challenge.Additionally, three different interfacial heat transfer coefficient (h)correlations have been used to adopt the best suitable interfacialheat transfer coefficient model for this present condition. Allrelated influences arising from local subcooling near vapor/liquidinterface, conjugate heating, and mass flux are taken account intothe model. Pressure and temperature oscillations have been dis-cussed in our previous studies [16,29].

Fig. 1. Schematic of CHF phenomena in microchannel. (a) architecture of the testing chip, (b) stable vapor column formed at the opening of auxiliary microchannel atG = 900 kg/m2 s.

Fig. 2. Schematic of vapor backflow in an auxiliary channel.

0 200 400 600 800 1000 1200 14000

200

400

600

800

1000

CH

F (W

/cm

2 )

Mass Flux (kg/m2.s)

Present#1#2#3#4#5

Fig. 3. Comparison between the present experimental CHF values and reportedstudies. #1, plain-wall microchannels in Qu and Mudawar’s study [30]. #2, plain-wall microchannels with inlet orifices and #3, structured microchannels with inletorifices in Kuo and Peles’s study [7]. #4, plain-wall microchannels with pressuredrop elements and #5, plain-wall microchannels without pressure drop elements inKuan and Kandlikar’s study [46].

Table 2Comparison of CHF experimental data for DI water.

CHF data by The lengthof heatingarea (mm)

Tin

(�C)G(kg/m2 s)

q00CHF

(W/cm2)

Qu and Mudawar [30] 44.8 30 86–368 107.64–216.76Kuan and Kandlikar [46] 63.5 25.4 46.4–171.9 20.6–54.5Kuo and Peles [7] 10 22 83–303 161.2–645.3Present Experimental study 10 25 200–1350 225.0–1020.0

370 W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378

2. Experimental study

2.1. Experimental apparatus and methods

Micro devices are designed and fabricated to enhance CHF offlow boiling in microchannels. Each micro device consists of four

main channels (H = 250 lm, W = 200 lm, L = 10 mm) with an ori-fice (H = 250 lm, W = 20 lm, L = 400 lm) placed at the inlet ofeach main channel to trap bubbles as shown in Fig. 1. Two auxiliarychannels (H = 250 lm, W = 50 lm, L = 5 mm) are connected at themiddle of each main channel through a 20 lm opening as high-lighted in Fig. 2a. The auxiliary channels are also open to the inletmanifold. The design and fabrication of the microchannel devicewere detailed in our previous studies [16,29]. The experimentalapparatus (including the test module and loop), experimental pro-cedure, and the data reduction method established in our previousstudies are adopted in this work.

In our previous study [13], it was shown that the temperature ofinlet subcooling has negligible effects on CHF. Therefore, CHF datawith an inlet fluid temperature of 25 �C is collected for varyingmass fluxes from 200 to 1350 kg/m2 s. In addition, a uniform heatflux is applied to the bottom of the micro device.

2.2. CHF conditions

It is critical to learn from visualization data at CHF conditions inorder to develop a high fidelity CHF model. In this study, CHF of flow

Fig. 4. The relationship among key parameters that govern CHF.

Fig. 5. (a) CHF phenomena at G = 900 kg/m2 s, (b) Schematic of vapor columnformed at the opening of auxiliary channel. Length of vapor column enteredsubcooled liquid includes two parts: front surface (radius of R � Dh) and sidesurface (side length l).

W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378 371

boiling on deionized (DI) water is explored in a multiple microchan-nel array. Nucleation of bubble first starts on the bottom surface ofthe auxiliary channel. These nucleating bubbles confine quickly andthen expand backwards (reversal vapor flow) in the auxiliary chan-nels as shown in Fig. 2 due to the restriction of the nozzles. Directcondensation occurs at the vapor/liquid interface resulting inshrinkage of the bubble and eventually the bubble collapses inthe auxiliary channels. This action then sucks liquid from inlet man-ifold and forms jetting flows in the main channels through the noz-zles [29]. With further increase in heat flux to some extent, liquidsupply through auxiliary channels is blocked due to stable vaporcolumn and hence bubble collapse ends in auxiliary channels. Inanother word, CHF conditions approach when stable vapor columnsare formed in front of auxiliary channels in the inlet manifold(Fig. 1b) due to equilibrium of heat transfer at the vapor/liquidinterface. The theory of Helmholtz instability is adopted to predictcritical vapor velocity [42–45]. Wave flow is induced by intensevapor flows. Additionally, the critical vapor wavelength of vaporflow is determined by Rayleigh instability [41].

2.3. Experimental CHF results

Significantly enhanced CHF has been experimentally demon-strated in the microchannels using self-excited and self-sustainedmicrobubble oscillations mechanism [29]. In this study, experi-mental data of CHF is plotted in Fig. 3 for a wide range of massfluxes from 200 kg/m2 s to 1350 kg/m2 s. The maximum CHF valueof 1020 W/cm2 is achieved at a mass flux of 1350 kg/m2 s in thisstudy. Existing CHF values are also compared in Fig. 3.

2.4. Comparisons of CHF experimental results

Such a comparison is hard to make due to the significant varia-tions in the experimental conditions and dimensions of microchan-nels. The objective of this comparison we made here is only toshow efforts that have been done in last decade. CHF experimentalresults in the present microchannel configuration and results in lit-eratures are compared and shown in Table 2. It can be seen fromTable 2 that the present microchannel configuration made signifi-cant progresses using a passive enhancement technique.

3. Semi-theoretical CHF model

3.1. Development of a semi-theoretical CHF model

A semi-theoretical CHF model provides insights into CHF mech-anisms since it is built on a solid understanding of the CHF mech-anisms from experimental studies. Moreover, it is also convenientto implement theoretical and semi-theoretical CHF models. In thispresent study, by incorporating interfacial heat transfer rate with aliquid thin film dryout model, a semi-theoretical CHF model is pro-posed based on an energy conservation analysis in a pair of neigh-boring auxiliary channels. All major thermo/fluidic properties andgeometries are considered in this proposed model. The flow chartin Fig. 4 shows the relationship among key governing parametersof CHF. Heat in auxiliary channels is transported by high frequencybubble growth (from boiling) and collapse (from direct interfacialcondensation) [46]. The direct condensation is determined by heattransfer at the vapor/liquid interface or by forces (such as surfacetension, inertia forces) acting on the interface [47,48]. The heattransfer at the vapor/liquid interface with phase transition highlydepends on local thermo-physical properties, such as liquid con-ductivity, specific heat, latent heat of vapor, density, viscosityand surface tension, etc.; therefore, it is a complex process.

In this study, CHF of flow boiling on the present microchannelconfiguration is assumed to be primarily governed by theHelmholtz instability [44,45]. The Helmholtz instability is inducedby the fast vapor flow in auxiliary channels. Helmholtz criticalvelocity has a relationship with critical vapor wavelength. Hence,Rayleigh instability is applied to predict the critical vapor wave-length of vapor back flow in the auxiliary channels. At CHF, stablevapor columns are formed in front of auxiliary channels. At thiscondition, Helmholtz critical velocity should be equal to vapor jetvelocity. The key characteristics of stable vapor column areexpressed by following equations.

The vapor jet velocity is calculated as

Uv ¼mv

qvAsð1Þ

Helmholtz critical velocity [42] is given by

Uc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi2p � rqv � k

sð2Þ

Rayleigh critical wavelength [41] is determined by

k ¼ffiffiffi2p

p � Dh ð3Þ

Fig. 6. Schematic of two types of liquid thin film dryout modes. (a) Partially developed liquid thin film dryout mode, and (b) fully developed liquid thin film dryout mode.

Fig. 7. Schematic of a counter flow at the opening of an auxiliary channel. Control volume approach was applied to analyze energy conservation during the counter flow.

372 W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378

where, As is cross section area of auxiliary channel, mv is the mass ofvapor flow, qv is density of vapor, r is surface tension, Dh is thehydraulic diameter of auxiliary channels. When Uc ¼ Uv , CHF condi-tions are approached.

To better describe the interfacial heat transfer process, thestable vapor column is divided into two distinct zones, i.e., thefront zone and side zone, as shown in Fig. 5. For a given heat flux,the vapor column length in the side zone varies with mass fluxes.The vapor column in the front zone is assumed as a hemispherewith a diameter of 2Dh according to the experimental observations.Vapor in both front and side zones directly contacts with subcooledliquid and plays an important role in determining CHF of flow boil-ing on the present microchannel configuration.

According to the present experimental studies, two types ofauxiliary channel dryout modes are found to exist. Out of thesetwo modes, the partially liquid thin film dryout mode is observedat low mass fluxes; while the fully liquid thin film dryout modeoccurs at high mass fluxes as illustrated in Fig. 6. In the partiallyliquid thin film dryout mode, only front surface of vapor columncontacts with subcooled liquid. In contrast, the whole vapor col-umn has direct contact with subcooled liquid at the fully liquidthin film dryout mode. Therefore, two CHF models are proposedbased on these two distinct liquid thin film dryout modes.

3.1.1. CHF model based on fully developed liquid thin film dryout modeVapor jets merging from two neighboring auxiliary channels to

form a stable vapor column were observed in CHF conditions. Incase of the fully developed liquid thin film dryout mode (as shownin Fig. 6b), condensation occurs on the side surface and front sur-face of the vapor column. By incorporating direction condensationwith the vapor back flow, a theoretical CHF model is developedusing energy conservation principle:

q00CHF � Aw ¼ h � Av � DTsub þmv � hfg ð4Þ

where

Av ¼ l � H þ Dh � H ð5Þ

Aw ¼ L � d ð6Þ

Aw is area of the heated surface, Av is contact area betweenvapor column and subcooled liquid, and d is width of auxiliarychannel respectively. q00CHF is the critical heat flux and h is the inter-facial heat transfer coefficient. hfg is latent heat of vapor. DTsub isthe temperature difference between saturated vapor and incomingsubcooled liquid. L is the length of heated surface. l represents theside length of vapor column entering subcooled liquid (Fig. 5b).Side length can be measured from flow visualization images.Therefore, a constant number (n) is introduced into the modelrelated to side length of vapor column. n is obtained by:

n ¼ lk

ð7Þ

The constant number (n) is an important parameter to deter-mine the CHF value. Substituting Eqs. (5) and (6) into Eq. (4), thetheoretical CHF model can be expressed as:

q00CHF ¼ h � DTsub n �ffiffiffi2p� pþ 1

� �� Dh

dþ hfg � qv �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2p� r

qv � Dh

s24

35 � H

Lð8Þ

In Eq. (8), DTsub (the temperature difference between saturatedvapor and incoming subcooled liquid) and h (heat transfer coeffi-cient at vapor/liquid interface) are essential to predict CHF.However, it is extremely challenging to accurately determine thesetwo parameters as they are significantly influenced by the

W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378 373

incoming subcooled liquid flow. The effect of mass fluxes on DTsub

is considered and DTsub is estimated at any given axial location inthe later section.

3.1.2. CHF model based on partially developed liquid thin film dryoutmode

Equation (8) is not directly applicable to partially developedthin film dryout CHF condition. A modification is needed only forthe front surface of vapor column contacted with the subcooledliquid (Fig. 6a). Moreover, a small portion of heated surface (L) isstill covered by a thin liquid film. Therefore, the dryout surface inauxiliary channel and condensation area can be expressed by:

Av ¼ Dh � H ð9Þ

Aw ¼ 1� nkL

� �L � d ð10Þ

where, n�kL � 1. n � k represents the length of liquid thin film in the

auxiliary channel (Fig. 6a). Substituting Eqs. (9) and (10) into Eq.(4), the model based on the partially developed thin film dryoutmode becomes:

q00CHF ¼ h � DTsub �Dh

dþ hfg � qv �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2p� r

qv � Dh

s24

35 � H

L� n �ffiffiffi2p� p � Dh

� �ð11Þ

Note that, when n = 0, it means no liquid exists in auxiliarychannels.

In summary, the above two CHF models are developed to pre-dict the CHF for flow boiling in microchannels with high frequencyself-excited two-phase oscillations. These two CHF models areinvestigated upon the energy conservation. It has been shown thatDTsub and h are two critical parameters in determining CHF.

3.2. Estimating DTsub and h

Since the local subcooling temperature varies significantly dur-ing flow boiling processes, it would be more convenient to repre-sent DTsub with a more stable parameter in the above two CHFmodels. It is discussed earlier that DTsub is closely related to sub-cooled liquid mass flux, G and can be represented as a functionof G. The relationship between G and DTsub is studied using thecontrol volume method. As shown in Fig. 7, a counter flow isobserved at the vapor/liquid interface and used to model the inter-facial heat and mass transfer. Based on the energy conservationprinciple, the heat from vapor interface is transferred to the incom-ing subcooled liquid by condensation through the contact area. Thesubcooled liquid surrounding the vapor bubble is then heated upby vapor via condensation and eventually, all the liquids are heatedup by conduction and convection.

The heat transfer rate from vapor interface to liquid is com-puted as:

qv ¼ h � Av � DTsub ð12Þ

Table 3Uncertainties in variables used in uncertainty analysis.

Name of variables Error

Mass flux, G 1.0%Voltage supplied by power source, V 0.5%Current supplied by power source, I 0.5%Ambient temperature, T 0.1 �CElectrical power, P 0.7%Electrical resistance, R 0.7%Heat transfer coefficient at vapor/liquid interface, h 9.0%

where, DTsub ¼ Tsat � Tsub.The sensible heat of subcooled liquid is:

ql ¼ _ml � cp � DT ð13Þ

where, _ml ¼ ql � Acr � Ul, the mass flux of subcooled liquid isG ¼ ql � Ul, cp is liquid specific heat and DT ¼ Tsub � Tin.

In the counter flow, heat transfer rate, qv ¼ ql based on energyconservation. Acr is the cross sectional area of counter flow andcan be represent (d:HÞ in the simple form.

Conduction contribution to Tsub through substrate in the chan-nel length direction is ignored by assuming 1-D heat conductionthrough the bottom surface of auxiliary channels as well as dueto high velocity of subcooled liquid flows. Therefore, the tempera-ture of subcooled liquid (Tsub) around the interface is determinedby:

Tsub ¼n �

ffiffiffi2p� pþ 1

� �� Dh � h � Tsat þ G � d � cp � Tin

n �ffiffiffi2p� pþ 1

� �� Dh � hþ G � d � cp

ð14Þ

Then, the local subcooling, DTsub can be expressed as

DTsub ¼G � cp � d � ðTsat � TinÞ

n �ffiffiffi2p� pþ 1

� �� Dh � hþ G � cp � d

ð15Þ

The inlet temperature of DI-water is 25 �C in this study.Substituting Eq. (15) into Eqs. (8) and (11), two CHF models in

Eqs. (16) and (17) are expressed as a function of mass flux, G.

Fully developed liquid thin film dryout model:

q00CHF ¼ h � G � cp � d � ðTsat � TinÞðn �

ffiffiffi2p� pþ 1Þ � Dh � hþ G � cp � d

!n �

ffiffiffi2p� pþ 1

� �"

�Dh

dþ hfg � qv �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2p� r

qv � Dh

s 35 � H

Lð16Þ

Partially developed liquid thin film dryout model:

q00CHF ¼ h � G � cp � d � ðTsat � TinÞn �

ffiffiffi2p� pþ 1

� �� Dh � hþ G � cp � d

0@

1A � Dh

d

24

þhfg � qv �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2p� r

qv � Dh

s 35 � H

L� n �ffiffiffi2p� p � Dh

� � ð17Þ

In these two CHF models, most of critical parameters areincluded. However, the interfacial heat transfer coefficient in Eqs.(16) and (17) is still unknown, which is a key parameter to reflectthe interfacial condensation heat transfer. This process is alsocalled heat transfer controlled condensation [47]. Many correla-tions have been developed for condensation of vapor bubblestranslating in subcooled liquid in previous studies. However, mostof these correlations are developed by considering vapor bubblesrising in a stagnant subcooled liquid. Chen and Mayinger [38] stud-ied condensation of vapor bubbles in slow flowing liquid and pro-posed a correlation to predict Nu as follows:

Nu ¼ 0:185Re0:7Pr0:5 ð18Þ

Zeitoun et al. [49] showed that local subcooling and Jacob num-ber have significant effects on the condensation heat transfer. Inaddition, very limited correlation is found in the literature for steambubbles condensing in flowing subcooled water. Warrier et al. [50]developed a semi-empirical correlation for vapor bubbles conden-sation in subcooled flow boiling considering local subcooling:

Nu ¼ 0:6Re12 Pr

13 1� 1:2Ja9=10Fo2=3� �

ð19Þ

Fig. 8. CHF phenomena at G = 200 kg/m2 s, 600 kg/m2 s, 900 kg/m2 s and 1250 kg/m2 s, the constant number is n = 0, 0.32, 0.745 and 0.96, respectively. Constant number iscalculated by, n ¼ l

k, k ¼ 370 lm.

0 200 400 600 800 1000 1200 1400

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Experimental data Interpolation

Con

stan

t num

ber (

n)

Mass flux (kg/m2s)

Fig. 9. Constant number, n, as a function of mass flux was analyzed by interpolatingexperimental data. Table 4

Constant number, n at the corresponding mass fluxes, G.

Mass flux, G (kg/m2 s) Constant number, n

200 0600 0.32900 0.7451250 0.96

374 W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378

Kim and Park [51] proposed a correlation to estimate interfacialheat transfer of a large non-spherical condensing vapor bubble insubcooled turbulent flow on water as follows:

Nu ¼ 0:2575Re0:7Pr�0:4564Ja�0:2043 ð20Þ

Thus, the interfacial heat transfer coefficient can be calculated

as: h ¼ Nu klDh

. Vapor column Reynolds number is defined as,

Re ¼ qlUrelDhll

. Hydraulic diameter of auxiliary channel is: Dh ¼ 4AsP

and Urel ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðUv � UlÞ2

q. Where, kl is the conductivity of subcooled

liquid, ll is dynamic viscosity of water. As is the cross section areaof auxiliary channel; P is the perimeter of auxiliary channel.Prandtl number is defined by Pr ¼ cpll

kl. Jacob number is:

Ja ¼ qlcp;lðTsat � TsubÞqvhfg

ð21Þ

Fourier number is a time dependent number and adopted froma simple correlation proposed by Chen and Mayinger [38].

Fo ¼ 1:784Re�0:7Pr�0:5Ja�1:0 ð22Þ

In order to estimate local subcooling from Eq. (15), an expres-sion to calculate Nu is required. In addition, liquid subcooling isrequired to calculate Ja and therefore, Nu. Hence, a trial and error

Table 5DTsub at different mass fluxes, G.

Mass flux, G (kg/m2 s) DTsub (K)

200 35.47250 36.99325 37.01380 37.06430 37.11480 37.18600 37.36750 37.66900 37.941037 38.241150 38.471250 38.701350 38.90

Fig. 10. The dependency of Jacob number, Ja, on the local subcooling, DTsub.

W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378 375

process was adopted to estimate the local subcooling. All thermo-physical properties are calculated according to local temperature.Thermophysical properties of saturated water at atmospheric pres-sure are used in present study.

3.3. Uncertainty analysis

The uncertainties of the measured values as shown in Table 3,are obtained from the manufacturer’s specification sheets, whilethe uncertainties of the derived parameters are calculated usingthe method developed Kline and McClintock [52].

3.4. Mean absolute error (MAE)

Mean absolute error (MAE) is used to evaluate the differencebetween the experimental results and predicted CHF values fromthe developed semi-theoretical model:

MAE ¼ 1M

XM

i¼1

qCHF;exp � qCHF;semi�theoretical

�� ��qCHF;exp

� 100% ð23Þ

Fig. 11. Jacob number as a function of mass flux.

4. Results and discussion

4.1. Correlation of constant number (n) with mass flux

Constant number (n), a dimensionless parameter related to thelength of vapor column (l) and critical wave length (k), is

introduced in this study. According to the observation of CHF phe-nomena, l varies with mass fluxes from 200 kg/m2 s to1250 kg/m2 s and increases with the increase of mass flux, as illus-trated in Fig. 8. Vapor column length, l is measured from flow visu-alization images at different mass flux conditions. Constantnumber, n is calculated using Eqs. (3) and (7). To quantitativelyreflect the influence of l on n, a correlation of n is expressed as afunction of mass flux, G, as shown in Eq. (24). This correlation isgenerated by interpolating experimental results based on fourcases as plotted in Fig. 9 and shown in Table 4. The image resolu-tion is 800 � 160, and sample rate is 22,857 fps. The side length ofvapor column was calculated by counting the number of pixel(4.49 lm/pixel). The uncertainty of the side length of vapor columnis ±10 lm (about ±2 pixels).

The correlation of constant number, n, as a function of massflux, G, can be estimated as:

n ¼ �0:233þ 0:0011G� 9:7� 10�8G2 ð24Þ

4.2. Modeling direct condensation at the vapor/liquid interface

The CHF conditions are strongly influenced by the condensationof vapor column. The depth of vapor column entering subcooledliquid in the inlet manifold is determined by the boiling in auxil-iary channels and the direct condensation. However, the condensa-tion at the moving vapor/liquid interface is complex, especiallywhen coupled with a non-uniform and highly dynamic tempera-ture field. Direct condensation of vapor column in the subcooledliquid is governed by two different phenomena: (1) heat transferat vapor/liquid interface, and (2) inertia force of the subcooled liq-uid. At a small/moderate local subcooling, direct condensation ofvapor column in the subcooled liquid is governed by the vapor/liq-uid interfacial heat transport, whereas, at a higher subcooling, con-densation process is controlled by inertia force of subcooled liquid.In this study, DTsub is obtained for all the mass fluxes and increaseswith increasing mass flux as shown in Table 5. Hence, it can beconcluded that direct condensation is not only influenced by inter-facial heat transfer, but also affected by inertia force of the liquidmass flux, G, in this present condition.

Fig. 12. Comparison of CHF predictions with experimental CHF data.

376 W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378

Studies showed that the interfacial heat transfer is greatly influ-enced by Jacob number (Ja) [53]. Ja represents the ratio of the sen-sible heat of liquid to the latent heat of vapor. It is a criterion forinterfacial heat and mass transfer. Jacob number, Ja is expressedin Eq. (21). The thermophysical properties of vapor and subcooledliquid are assumed to be constant at a given temperature. Hence, itcan be seen from Eq. (21) that Ja depends on local subcooling,DTsub. The dependency of Ja on DTsub plotted in Fig. 10.Figure shows that Ja increases with DTsub. Previous experimentalstudies have shown that Ja is closely related to the thermal bound-ary layer thickness around the vapor column [54]. When Ja > 100,the thermal boundary layer is thin and unstable due to local con-densation effects [38,47,53], resulting in an increased condensa-tion heat transfer rate and liquid inertia is the dominant factorfor this condensation. Conversely, at a small value of Ja (Ja < 80),the thermal boundary layer becomes thicker, resulting in adecreased interfacial heat transfer rate [47].

Therefore, the study of Ja (related to interfacial heat transfer)relationship to mass flux of subcooled liquid (related to inertiaforce) is critical to understand the condensation process. The rela-tionship between Ja and G is investigated based on Eqs. (15) and(21), and plotted in Fig. 11. From figure, it can be seen that Jaincreases from 108.05 to 118.71 for mass fluxes from 200 kg/m2 sto 1350 kg/m2 s.

Table 6Comparison of present CHF model and existing models/correlations.

Reference Recommended channel sizeand fluid

Correlation of CHF

Kosar et al. [31] Dh = 0.227 mm water q00CHF ¼ 0:0035Ghfg We�0:12

Bowers and Mudawar[32]

Dh = 0.51–2.54 mm R-113q00CHF ¼ 0:16Ghfg We�0:19 L

dh

� ��0

Qu and Mudawar [30] Dh = 0.38–2.54 mm R-113 andwater

q00CHF ¼ 33:43GhfgWe�0:21 qGqL

� �Current theoretical

study (1)Dh = 0.083 mm water q00CHF ¼ h � G�cp �d�ðTsat�TinÞ

ðn�ffiffi2p�pþ1Þ�Dh �hþG�cp �d

�hand Park [51] Correlation]

Current theoreticalstudy (2)

Dh = 0.083 mm water q00CHF ¼ h: G�cp �d�ðTsat�Tin Þðn:ffiffi2p�pþ1Þ�Dh �hþG�cp �d

� �hWarrier et al. [50] Correlatio

4.3. Prediction of the present theoretical CHF model and comparisonswith existing models/correlations

As shown in Fig. 8, the auxiliary channels under the CHF condi-tions are shown to be fully dryout at a mass flux range of200 kg/m2 s to 1250 kg/m2 s. As a result, partially developed liquidthin film dryout model is not applicable to predict CHF on theseconditions. According to the fully developed liquid thin film dryoutmodel in combination with correlation of constant number, n, CHFcan be predicted. Three different interfacial heat transfer coeffi-cient (h) correlations have been used, namely, Chen andMayinger [38] correlation, Warrier et al. [50] correlation and Kimand Park [51] correlation to adopt the best suitable interfacial heattransfer coefficient model for this present condition. Additionally,the theoretical predictions are compared with experimental dataat a mass flux range of 200 kg/m2 s to 1350 kg/m2 s as shown inFig. 12. It can be seen from figure that the CHF model based onChen and Mayinger [38] correlation and Warrier et al. [50] correla-tion over predict the experimental data with a MAE of 70% and 32%respectively, whereas, Kim and Park [51] correlation under predictthe experimental data with a MAE of 25%. This large deviation ofCHF model based on Chen and Mayinger correlation with experi-mental data is due to the different operating condition and inaccu-racy in local temperature measurement. Chen and Mayingercorrelation was proposed based on bubble condensation in slowflowing subcooled liquid and bulk temperature was consideredinstead of local liquid temperature. Warrier et al. and Kim andPark correlation were proposed based on bubble condensation insubcooled flow boiling and local temperature (local subcooling)was incorporated in terms of Ja. Therefore, higher accuracy isobtained in CHF model with experimental data due to the similar-ities in operating condition and measurement accuracy. Warrieret al. correlation was proposed at atmospheric pressure, whereasKim and Park correlation was proposed at low pressure. Though,this present study is conducted at atmospheric pressure, higherdeviation in Warrier et al. correlation may be due to the inaccuracyin predicting Fo.

The proposed semi-theoretical CHF models are also comparedto existing CHF models/correlations as summarized inTable 6 and plotted in Fig. 13. These three correlations are well rec-ognized among numerous CHF correlations of flow boiling inmini/microchannels. As shown in Fig. 13, the semi-empirical corre-lation developed by Kosar et al. [31] can be extended to the oper-ating range of mass fluxes in present study. The Kosar’s correlationis shown to agree well with the experimental CHF data with MAE of10.3% on DI-water. This prediction is even slightly better than oursemi-theoretical model developed in this study. This could be aresult of the similarities in the microchannel configurations anddryout mechanisms between the Kosar’s research and our presentstudy. Specifically, inlet orifices are used in both microchannel

MAE(%)

10.3:54 117.2

1:1L

dh

� ��0:36 76.3

�ðn �

ffiffiffi2p� pþ 1Þ � Dh

d þ hfg � qv :ffiffiffiffiffiffiffiffiffiffiffiffi

2p�r

qv �Dh

q i� H

L [h is calculated based on Kim 25

n �ffiffiffi2p� pþ 1

� �� Dh

d þ hfg � qv �ffiffiffiffiffiffiffiffiffiffiffiffi

2p�r

qv �Dh

q i� H

L . [h is calculated based on

n]

32

0 200 400 600 800 1000 1200 14000

400

800

1200

1600

2000

2400 Experimental data Present study (1) Present study (2)

Three correlations: Ali Kosar [31] Qu and Mudawar [30] Bowers [32]

CHF(

W/c

m2 )

Mass flux (kg/m2s)

Overprediction

Underprediction

Fig. 13. Comparison of CHF results between theoretical CHF model and correlationsby other researchers.

W. Li et al. / International Journal of Heat and Mass Transfer 88 (2015) 368–378 377

configurations to regulate two-phase flows. CHF mechanisms andcriteria behind these two configurations could be same, i.e., hydro-dynamic instabilities. Surface tension force is dominant duringflow boiling in microchannels [55]. Weber number that measuresthe relative importance of the fluid’s inertia to surface tensioncan well represent the critical role of surface tension force in gov-erning CHF conditions. These reasons may lead to a great agree-ment between the Kosar’s correlation and our semi-theoreticalmodel. It is noted that the operating range of mass fluxes (41–302 kg/m2 s) and range of effective heat fluxes (28–445 W/cm2)in Kosar’s study is smaller compared to the present study.

Additionally, the correlation developed by Bowers et al. [32]overpredicts CHF values and Qu’s correlation [30] underpredictsCHF over the entire mass flux range with a large discrepancy.These large deviations may be attributed to differences in channeldimensions, applicable mass fluxes, heating area, etc. By compar-ing these two correlations to Kosar’s correlation, it is found thatthe heater size and channel hydraulic diameter were not consid-ered in Kosar’s correlation. However, Bowers’ and Qu’s correlationsemployed a ratio of L/d. This ratio may be a possible reason for theresulting large deviations. Moreover, the ratio of liquid and vapordensity was taken into account in Qu’s correlation.

5. Conclusions

In this study, CHF of flow boiling in microchannels withself-excited and self-sustained high frequency two-phaseoscillations is experimentally and theoretically studied. Asemi-theoretical CHF model is developed bad on energy conserva-tion principles and the Helmholtz instability and Rayleigh instabil-ity theories. Previous CHF models and empirical CHF correlationsare compared to the present theoretical CHF model. Majorconclusions are summarized as follows:

1. A microbubble-excited actuation mechanism can significantlyenhance CHF in microchannels during flow boiling in a passiveway. Formation of stable vapor columns in auxiliary channels isthe primary reason resulting in CHF conditions.

2. The direct condensation of vapor significantly alters the tem-perature of subcooled liquid. Jacob number increases with theincreasing mass flux.

3. According to the observations of CHF phenomena, the length ofvapor columns entering into subcooled liquid varies with massfluxes (Fig. 8). Consequently, two theoretical CHF models are

developed based on two possible liquid thin film dryout modes.The developed theoretical CHF models in this study can predictexperimental data with a MAE of 25% and 32%.

4. Existing recognized CHF correlations in mini/micro-channelsare also compared to present study. The semi-empirical correla-tion developed by Kosar shows a great agreement with theexperimental data because of the similarities in the microchan-nel configuration and CHF mechanisms.

5. The theoretical CHF model developed in this study considerseffects of thermo-physical properties, geometries, and flow con-ditions. The development of the theoretical CHF model providesinsights into the CHF mechanisms. However, further investiga-tion is needed to estimate accurate local subcooling and interfa-cial vapor to liquid heat transfer coefficient.

Conflict of interest

None declared.

Acknowledgements

This work was supported the US Department of Defense, Officeof Naval Research under the Grant N000141210724 (ProgramOfficer Dr. Mark Spector).

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