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Int. J. Therm. Sci. (2000) 39, 909–918 2000 Éditions scientifiques et médicales Elsevier SAS. All rights reserved S1290-0729(00)01188-1/FLA An onset of nucleate boiling criterion for horizontal flow boiling Olivier Zürcher a , John R. Thome b , Daniel Favrat a * a Laboratoire d’énergétique industrielle, Département de génie mécanique, École Polytechnique Fédérale de Lausanne LENI-DGM-EPFL, CH-1015 Lausanne, Switzerland b Laboratoire de transfert de chaleur et de masse, Département de génie mécanique, École Polytechnique Fédérale de Lausanne, LTCM-DGM-EPFL, CH-1015 Lausanne, Switzerland (Received 17 April 2000, accepted 24 July 2000) Abstract — A model to predict the onset of nucleate boiling has been successfully developed to differentiate purely convective evaporation from mixed nucleate and convective boiling during evaporation inside a horizontal tube of 14 mm I.D. Based on an extensive database collected for the natural refrigerant ammonia (R-717) over mass velocities from 10 to 140 kg·m -2 ·s -1 , the analysis of the stratified, stratified–wavy and mainly annular flow patterns during evaporation with different heat flux ranges showed very accurate predictions in terms of the local heat transfer coefficient using this new onset of nucleate boiling criterion. 2000 Éditions scientifiques et médicales Elsevier SAS evaporation / local heat transfer coefficient / convection / nucleation / ammonia / substitute refrigerants Nomenclature A cross sectional area ........... m 2 C 0 distribution factor c 0 distribution factor multiplier D diameter ................. m D h hydraulic diameter ........... m d vapor core diameter ........... m G mass velocity .............. kg·m -2 ·s -1 1h evap latent heat ................ J·kg -1 h heat transfer coefficient ......... W·m -2 ·K -1 h L liquid height in the tube ........ m M molecular weight ............ kg·kmol -1 P pressure ................. Pa Pr Prandtl number ˙ q heat flux ................. W·m -2 Re Reynolds number r radius .................. m S contact perimeter ............ m T temperature ............... K u velocity ................. m·s -1 * Correspondence and reprints. [email protected] V drift velocity .............. m·s -1 x vapor quality X tt Martinelli parameter Greek symbols α void fraction δ liquid layer thickness .......... m θ dry dry angle ................ rad θ wet wetted angle ............... rad λ thermal conductivity .......... W·m -1 ·K -1 μ dynamic viscosity ............ Pa·s ξ stratified–wavy angle .......... rad ρ density .................. kg·m -3 σ surface tension ............. N·m -1 ϕ stratified–wavy opening angle ..... rad ψ stratified–wavy wetting angle ..... rad Subscripts A annular cb convective boiling crit critical dry dry i interface L liquid nb nucleate boiling 909

An onset of nucleate boiling criterion for horizontal flow boiling

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Page 1: An onset of nucleate boiling criterion for horizontal flow boiling

Int. J. Therm. Sci. (2000) 39, 909–918 2000 Éditions scientifiques et médicales Elsevier SAS. All rights reservedS1290-0729(00)01188-1/FLA

An onset of nucleate boiling criterion for horizontal flowboiling

Olivier Zürcher a, John R. Thome b, Daniel Favrat a*a Laboratoire d’énergétique industrielle, Département de génie mécanique, École Polytechnique Fédérale de Lausanne LENI-DGM-EPFL,

CH-1015 Lausanne, Switzerlandb Laboratoire de transfert de chaleur et de masse, Département de génie mécanique, École Polytechnique Fédérale de Lausanne,

LTCM-DGM-EPFL, CH-1015 Lausanne, Switzerland

(Received 17 April 2000, accepted 24 July 2000)

Abstract —A model to predict the onset of nucleate boiling has been successfully developed to differentiate purely convectiveevaporation from mixed nucleate and convective boiling during evaporation inside a horizontal tube of 14 mm I.D. Based on anextensive database collected for the natural refrigerant ammonia (R-717) over mass velocities from 10 to 140 kg·m−2·s−1, the analysisof the stratified, stratified–wavy and mainly annular flow patterns during evaporation with different heat flux ranges showed veryaccurate predictions in terms of the local heat transfer coefficient using this new onset of nucleate boiling criterion. 2000 Éditionsscientifiques et médicales Elsevier SAS

evaporation / local heat transfer coefficient / convection / nucleation / ammonia / substitute refrigerants

Nomenclature

A cross sectional area . . . . . . . . . . . m2

C0 distribution factorc0 distribution factor multiplierD diameter . . . . . . . . . . . . . . . . . mDh hydraulic diameter . . . . . . . . . . . md vapor core diameter . . . . . . . . . . . mG mass velocity . . . . . . . . . . . . . . kg·m−2·s−1

1hevap latent heat . . . . . . . . . . . . . . . . J·kg−1

h heat transfer coefficient . . . . . . . . . W·m−2·K−1

hL liquid height in the tube . . . . . . . . m

M molecular weight . . . . . . . . . . . . kg·kmol−1

P pressure . . . . . . . . . . . . . . . . . PaPr Prandtl numberq̇ heat flux . . . . . . . . . . . . . . . . . W·m−2

Re Reynolds numberr radius . . . . . . . . . . . . . . . . . . mS contact perimeter . . . . . . . . . . . . mT temperature . . . . . . . . . . . . . . . Ku velocity . . . . . . . . . . . . . . . . . m·s−1

* Correspondence and [email protected]

V drift velocity . . . . . . . . . . . . . . m·s−1

x vapor qualityXtt Martinelli parameter

Greek symbols

α void fractionδ liquid layer thickness . . . . . . . . . . mθdry dry angle . . . . . . . . . . . . . . . . radθwet wetted angle . . . . . . . . . . . . . . . radλ thermal conductivity . . . . . . . . . . W·m−1·K−1

µ dynamic viscosity . . . . . . . . . . . . Pa·sξ stratified–wavy angle . . . . . . . . . . radρ density . . . . . . . . . . . . . . . . . . kg·m−3

σ surface tension . . . . . . . . . . . . . N·m−1

ϕ stratified–wavy opening angle . . . . . radψ stratified–wavy wetting angle . . . . . rad

Subscripts

A annularcb convective boilingcrit criticaldry dryi interfaceL liquidnb nucleate boiling

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O. Zürcher et al.

ONB onset of nucleate boilingsat saturationStrat stratifiedWavy stratified–wavytp two-phaseV vaporwet wetted

1. RANGE OF APPLICATION ANDSTATE-OF-THE-ART

The substitution of CFC refrigerants in refrigerationsystems, heat pumps and organic Rankine cycles requiresgood knowledge of the heat transfer performance of sub-stitute fluids. A contribution to this international efforthas been undertaken with this study on the natural re-frigerant ammonia (R-717) for evaporation inside a sin-gle horizontal tube, in which the ammonia is heated bycountercurrent flow of water in the annulus of the double-pipe type of test section. This is more appropriate thanelectrical heating for measuring local flow boiling heattransfer coefficients in stratified types of flow and alsoat high vapor qualities where part of the annular liquidfilm has dried out. The global conditions for ammoniawere a saturation temperature of 4◦C, a heat flux rangeof 5–70 kW·m−2 and eleven mass velocities ofG= 10,20,30,40,45,50,55,60,80,120,140 kg·m−2·s−1, cor-

responding to stratified, stratified–wavy, intermittent andannular flow patterns. The flow patterns were observedthrough tubular glass sections at both ends of the 3.1 mlong test section. The heat transfer tube has an internal di-ameter of 14.00 mm, an external diameter of 15.86 mmand is made from a section of welded stainless steel type439 tubing. Its thermal conductivity is 28 W·m−1·K−1.

The local heat transfer measurements were obtainedfrom local heat fluxes and wall superheats. The local walltemperatures were determined from the mean value offour wall thermocouples installed in the wall at two dif-ferent axial locations along the test section (adjusted tothe inner tube wall temperature using Fourier’s heat con-duction law). The local saturation temperature was ob-tained from the vapor pressure curve of pure ammoniaand the local saturation pressure, which was determinedfrom a linear interpolation between the measured inletand outlet pressures. The local heat fluxes were calcu-lated from the slope of splines fit to the enthalpy profilesof the heating water flowing countercurrently in the an-nulus based on the water-side temperature measurements(four locations with four thermocouples at each location)such that local heat transfer coefficients could be mea-sured similar to electrically heated test sections. Also us-ing the enthalpy profile of water and an energy balance,the vapor quality of the refrigerant can be determined ateach of the two wall thermocouple locations.Figure 1depicts a simplified diagram of the test loop.

Figure 1. Simplified diagram of ammonia flow loop.

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An onset of nucleate boiling criterion for horizontal flow boiling

Figure 2. Relative uncertainity for the heat transfer coefficientas a function of heat flux.

Additional information about the experimental setupare available in Zürcher et al. [1] and more detailedinformation can be found in Zürcher [2]. The results ofa propagation of error analysis is shown infigure 2.

The experimental heat transfer coefficients of ammo-nia were influenced by heat flux only in some vapor qual-ity ranges and for some flow pattern types. Based onthe geometrical approach originally proposed by Kattanet al. [3, 4] including the prediction of flow pattern, a newmethod has been developed in Zürcher [2] to predict theonset of nucleate boiling, which differentiates pure con-vective evaporation from combined nucleate and convec-tive boiling.

Kattan et al. [3, 4] showed that even if different heattransfer models exist, such as the superposition, the en-hancement and the asymptotic models, their range of re-liable application is quite limited. They based this con-clusion on a comprehensive database for fluorocarbon re-frigerants covering different flow patterns and establishedthat only heat transfer relations based on local flow pat-tern should today be seriously considered. However, evenif the geometrical two-phase flow model that they pro-posed gave very accurate results in the annular and in theintermittent flow regions, it still suffered some weaknessin the stratified and stratified–wavy regions, even if theirmethod was still several times more precise than any ofthe other approaches tested. The large database, obtainedpresently for ammonia at low mass velocities and objectof this paper, shows an important influence of heat fluxon heat transfer in the stratified and stratified–wavy flowregimes, while no major influence is detected at highermass velocities in the annular flow region.

The flow pattern proposed by Kattan et al. [3] is an im-provement of the flow map of Steiner [5] for HFC refrig-erants where the liquid level in a stratified configurationis calculated as part of the method. Due to the geomet-

rical properties of the stratified configuration, this liquidlevel constitutes by consequence a void fraction. Assum-ing simplified relationships allowing an error of 1.5 %for the expressions of cross-sectional areas, Steiner usedthe assumption of identical pressure gradients for bothseparated phases of the stratified flow pattern domain toobtain a void fraction solution, which is similar to theearlier work of Taitel and Dukler [6]. The heat transferprediction of Kattan et al. [4] is then based on a specificversion for horizontal flow of the original void fractionmodel of Rouhani [7] proposed in [5]. Thus, two differ-ent void fraction models are used for identical conditionsfor the prediction of the flow pattern and the predictionof the heat transfer coefficient, which is not completelycoherent.

If the flow pattern map model proposed by Kattan etal. [3] is very accurate for the five HFC refrigerants intheir database, an empirical modification was proposedby Zürcher et al. [1] to better predict the ammoniaflow patterns experimentally observed, and some furtherimprovements were proposed in [2] to allow a moregeneral flow pattern prediction of both fluorocarbonrefrigerants (like HFC-134a and HFC-407C) and of thenatural refrigerant ammonia.

The new unified method for the prediction of the localheat transfer coefficient during evaporation is proposedin [2]. This paper focuses on a new step in this method,which is the prediction of the onset of nucleate boiling todistinguish between pure convective boiling and mixednucleate and convective boiling two-phase flow. Thus,only the main heat transfer relations used in the predic-tion procedure will be given here and other publicationsabout the flow pattern map and the local heat transfer co-efficient models will be submitted later this year.

2. PROPERTIES OF EACH FLOWPATTERN

The stratified flow pattern (figure 3) is characterizedby the separation of the liquid and vapor phases by asmooth interface. This flow pattern occurs at very lowmass velocities when the Kelvin–Helmholtz instabilitycriterion is counterbalanced by the viscous forces.

From a geometrical point of view, the stratified flowpattern is the best defined flow pattern as the void fractionis a direct function of the wetted angle:

α = 2π − θwet+ sinθwet

2π(1)

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O. Zürcher et al.

Figure 3. Cross-section of stratified configuration.

The precision of the void fraction model used willinfluence the liquid, the vapor and the interface velocities,but also the liquid height in the tube. As the liquid heattransfer coefficient is much larger than the vapor heattransfer coefficient, the liquid height is more importantthan the deviation of the velocities.

The annular flow pattern (figure 4) is obtained whenthe liquid wets all the tube periphery and the vapor flowsat the center of the tube. Due to gravity, the film thicknessis not constant around the periphery. The annular flowpattern has been considered to be reached as soon asthe motion of the liquid flowing at the top of the tubewas comparable to the one of the liquid at the bottomof the tube. Globally, the heat transfer coefficient forannular flows is characterized by a constant increasewith increasing the vapor quality, until the breakup ofthe liquid film at the top of the tube occurs. At thispoint, the heat transfer coefficient reaches a peak and thendecreases very rapidly towards the value of the all vaporheat transfer coefficient.

The annular flow pattern (figure 5), from a geometricalpoint of view and assuming no liquid entrainment in thevapor core, is fully determined with void fraction as longas the annular flow pattern is characterized by an allwetted perimeter and a circular vapor core of diameterd .The vapor core may either be centered or eccentric withrespect to the central axis of the tube. The particular casewhere no liquid droplets are entrained in the vapor coreis called the ideal annular configuration, where

α =(d

D

)2

(2)

The stratified–wavy flow pattern (figure 6) is character-ized by a wavy interface on the liquid. This flow pattern

Figure 4. Annular flow pattern of pure ammonia flowing atx = 81% and G= 122kg·m−2·s−1.

Figure 5. Cross-section of ideal annular configuration.

is a transitional one where waves exist but these are of areduced magnitude and are not able to reach the top ofthe tube. In a cross-sectional view, the interface is curved(figure 7). Based on the heat transfer results where thegeneral function of heat transfer is different for each flowpattern, the stratified–wavy region is considered to be atransition regime between the smooth interface regiondefined by the stratified flow pattern and the all-wettedand quite uniform mean distributed velocity in the liquidphase occurring for annular flow. Some flows that obvi-ously wetted all the perimeter were found to be betterdescribed by the stratified–wavy model than the annularmodel when the liquid at the top of the tube was flowingvery slowly, or at a noticeably different velocity than theliquid at the bottom of the tube.

The stratified–wavy flow pattern is more difficultto represent geometrically since the wetted angle isan independent variable. As shown infigure 7, the

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An onset of nucleate boiling criterion for horizontal flow boiling

Figure 6. Stratified–wavy flow pattern of pure ammonia flowingat x = 80% and G= 41 kg·m−2·s−1.

Figure 7. Modeling of the stratified–wavy flow pattern basedon the intersection of two circles.

liquid cross-sectional surface can be modeled by theintersection of the inner tube wall and a second circlecentered at 0′ with a radius ofR0. The parametrizationof the circle is set as a function of two angles, calledhere thehalf wetting angleψ and themoon angleϕ.The difference between these two angles is called the

stratified–wavy angleξ . Void fraction is very important inthe determination of the velocities of both phases and thelocation of the interface, which influence the convectiveheat transfer term; but the geometry of the stratified–wavy flow represented by the wetted angle also greatlyinfluences the two-phase heat transfer coefficient. Thevoid fraction corresponding tofigure 7is

α = 1− 1

π

[(ψ − 1

2sin(2ψ)

)− sin2ψ

sin2 ξ

(ξ − 1

2sin(2ξ)

)](3)

3. VOID FRACTION MODELS

Zuber and Findlay [8] showed that void fraction isa parameter that depends on the flow properties, e.g.,the velocity distribution. Thus, different void fractionmodels have been used, depending on flow pattern, forthe prediction of the flow pattern map and the heattransfer coefficient in our new heat transfer model.

The separated flow model of Taitel and Dukler [6]has been used in the stratified flow region. Applied toa horizontal tube, the void fraction solution is obtainedwhen

X2tt

[(SL)

1.2

(1− α)3]

−[(SV + Si)

0.2

α2

(SV + Si

α+ Si

1− α)]= 0 (4)

whereXtt is the turbulent–turbulent Martinelli parameterandS is the contact perimeter (liquid to wall, vapor towall and interface). As there is no particular advantagein the use of the nondimensional variables proposedby Taitel and Dukler [6], equation (4) is similar to theoriginal expression for horizonal flow, but expressed interms of void fraction and dimensional perimeters.

In the annular flow region, a void fraction modelof Rouhani [7] has been used. Rouhani et al. [7] pro-posed a correlation based on the drift flux model ofZuber and Findlay [8] for vertical flow. Steiner in theVDI-Wärmeatlas [5] proposed a version of the Rouhanimodel applied to horizontal flow based on experimentaldata. The general expression of the drift flux model is

α = x

ρV

[C0

(x

ρV+ 1− x

ρL

)+ VV

G

]−1

(5)

Steiner [5] proposed the following distribution parameter,based on a horizontal configuration in agreement with

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O. Zürcher et al.

experimental data:

C0= 1+ c0(1− x) (6)

wherec0= 0.12 and the weighted mean drift velocity ofthe vapor is

VV = 1.18(1− x)[σg(ρL − ρV)

ρ2L

]1/4

(7)

The stratified–wavy flow is a central region betweenthe stratified and the annular flow regions. The transi-tion between the two flow pattern geometries is adaptedwith equation (5), where along the stratified–wavy to an-nular boundary the distribution parameterC0 is basedon Rouhani withc0 = 0.12, and the neededC0 to re-produce at a constant vapor quality, along the stratifiedto stratified–wavy boundary the void fraction obtainedwith the Taitel and Dukler [6] model. Into the stratified–wavy flow region, the value ofc0 is obtained by the lin-ear interpolation of the respective values ofc0 along thetwo transition boundaries (stratified to stratified–wavyand stratified–wavy to annular) at a given vapor quality.While there is no physical justification for this interpola-tion, it allows a continuous void fraction solution acrossthe transition boundaries, i.e. the evolution of the voidfraction solution in the stratified-wavy flow region froma separated flow model (Taitel and Dukler) near the strat-ified flow region to a drift flux model (Rouhani) near theannular flow region.

With this, the stratified–wavy flow pattern will betreated with the drift flux model. This is motivated bythe good agreement of this model to the two-phasesituations where there is a notable interaction betweenthe two phases. This is the case for annular flow and thestratified–wavy flow patterns, which tend to the annularflow configuration.

4. ONSET OF NUCLEATE BOILINGCRITERION

Nucleate boiling is related to the nucleation of vaporbubbles in the liquid at the wall. This disturbes theliquid layer at the heated wall by the rapid growth ofthe bubbles. Due to the surface tension forces, a givenamount of heat is needed for the onset of nucleate boiling.Steiner and Taborek [9] used the following criterion:

q̇ONB= 2σTsathcb,0

rcritρV1hevap(8)

where rcrit = 0.3·10−6 m is the critical bubble radiusrecommended for usual extruded tube materials andhcb,0is theall liquid convective heat transfer coefficient.

In pool boiling, the heat flux needed to activateboiling sites (defined in equation (8)) represents therequired temperature difference for the onset of thisphenomenon. Naturally, this onset value depends onthe thermal resistance of the liquid layer, representedthrough the liquid convective heat transfer coefficient.Thus, because of the increases of the void fraction andthe liquid mean velocity, the convective heat transfercoefficienthcb,0 is not constant, and generally increaseswith increasing local vapor quality.

Prior flow boiling models combining the contributionof nucleate and convective boiling, such as Steiner andTaborek [9], are defined with theall liquid convectiveheat transfer coefficient. Thisall liquid convective coef-ficient is naturally calculated with theall liquid velocityand consequently with the tube diameter. Thus, the esti-mation of the temperature difference into the liquid layeris strongly overestimated as the vapor quality increases.

It is proposed here instead to define the onset ofnucleate boiling (ONB) in two-phase flow with a morerealistic convective heat transfer coefficient called thecritical convective heat transfer coefficient. The idea isto consider that the heat transfer of the two-phase flowis only convective below ONB, and to define a criticalheat flux value at which nucleation is activated. Whenthe needed heat flux is obtained, the liquid heat transfercoefficient can be correlated with an asymptotic model.

Starting from the ONB criterion used by Steinerand Taborek [9] (equation (8)), a new relation for theminimum heat flux for the onset of nucleate boilingduring evaporation is proposed to be

q̇ONB,x = 2σTsathcb,crit

rcritρV1hevap(9)

wherehcb,crit is the convective heat transfer coefficientoccurring during evaporation at the current vapor quality,and at the most advantageous location in the liquid crosssection. As convective boiling is inversely proportionalto the liquid thickness, the onset of nucleate pool boilingshould occur at the location where the liquid thicknessis the largest. Thus, the critical convective boiling heattransfer coefficient is defined as

hcb,crit = CRemδ Pr0.4L

λL

δcrit(10)

where the values of the two constantsC = 0.01361 andm = 0.6965 are based on experimental results of pure

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An onset of nucleate boiling criterion for horizontal flow boiling

Figure 8. Determination of the leading constant C and theReynolds number exponent m assuming pure convective heattransfer, based on ammonia measurements in annular flow.

convective heat transfer in annular flow (seefigure 8).The film Reynolds number referred to a liquid layer is

Reδ = 4ρLuLδ

µL(11)

Based on the geometrical representations of the flowpatterns, the critical layer thickness applied to stratifiedflow (seefigure 3) is

δcrit,Strat= D2

(1− cos

θwet

2

)(12)

For stratified–wavy flow pattern, the critical layer thick-ness is (seefigure 7)

δcrit,Wavy= D2

(1− cosψ + cosϕ

1+ cos(ψ − ϕ))

(13)

The annular flow liquid thickness varies between themean film thickness and twice its value (seefigure 5) as

δcrit,A =D − d = 2 · D2

(1−√α) (14)

Here twice the mean liquid layer is chosen as it corre-sponds to the thickest possible liquid layer in annular hor-izontal flow. It occurs along the stratified–wavy to annu-lar flow transition and gives the smallest onset value. TheONB criterion is larger when the mean liquid thickness isconsidered at the bottom of the tube, but still with twicethe liquid layer, the calculated ONB value was higherthan most experimental heat fluxes.

Based on the present experimental database, goodagreement has been obtained using a critical bubbleradius in equation (9) ofrcrit = 0.38·10−6 m (best fit withrespect to the experimental data).

At the present experimental conditions, the ONBvalue is easily reached for stratified flow and sometimesfor stratified–wavy flow, while no occurrence has beenobtained for annular flow within the range of the heatfluxes tested.

5. EXPERIMENTAL RESULTS

In figures 9and10, a comparison is made between theexperimental and the predicted heat transfer coefficientsfor pure ammonia at 4◦C in a smooth tube of 14 mm I.D.The experimental results are plotted as squares, and thepredicted coefficients, calculated with the experimentalconditions of each individual data point, are plotted as abold line. The dashed line with triangles represents theratio of the experimental heat flux to the ONB heat fluxcalculated with equation (9). Even if there is no physicalmeaning of theline between two calculated points, ithelps to better visualize the relationship and improvereadability. The data are for stratified and stratified–wavy flows at 20 kg·m−2·s−1 and for stratified–wavyand annular flows at 80 kg·m−2·s−1. The complete heattransfer calculation procedure cannot be detailed here,but will be later submitted to publication.

When the experimental heat flux is higher than theONB heat flux value, the liquid heat transfer coefficientis calculated with the following asymptotic model. If theexperimental heat flux is lower than the onset value, thenucleate boiling heat transfer coefficienthnb is set to zero(pure convective heat transfer of the liquid):

hwet=[(hcb,L)

3+ (hnb)3]1/3 (15)

wherehcb,L is the liquid convective heat transfer coeffi-cient calculated with the forced convection relation ap-plied to a thin liquid layer:

hcb,L = 0.01361Re0.6965δ Pr0.4

LλL

δ(16)

andhnb is the nucleate pool boiling heat transfer coeffi-cient calculated with Cooper [10], which is

hnb= 55

(P

Pcrit

)0.12[− log

(P

Pcrit

)]−0.55

M−0.5q̇0.67

(17)The two-phase flow heat transfer coefficient is thenobtained with

htp= θdryhV + (2π − θdry)hwet

2π(18)

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O. Zürcher et al.

Figure 9. Comparison of experimental results (squares) to the new model (bold lines) of ammonia at G= 20 kg·m−2·s−1, and ratio ofthe experimental heat flux to the onset of nucleate boiling value (dashed lines).

Figure 10. Comparison of experimental results (squares) to the new model (lines) of ammonia at G= 80 kg·m−2·s−1, and ratio of theexperimental heat flux to the onset of nucleate boiling value (dashed lines).

where θdry is the angle measured from the center ofthe cross-section and expresses the angle occupied bythe vapor phase whilehV is the convective vapor heattransfer coefficient calculated with the Dittus–Boeltercorrelation:

hcb,V = 0.023Re0.8DV Pr0.4VλV

D(19)

The term(2π−θdry) in equation (18) represents the anglewetted by the liquid phase (seefigure 3). This involves,

of course, the knowledge of the geometrical distributionof both the liquid and vapor phases in the cross-section.Hence, use of a flow pattern map is imperative.

Figure 9shows experimental and predicted heat trans-fer coefficients atG = 20 kg·m−2·s−1 in a region withsome pure stratified, but mainly with stratified–wavy flowpatterns. The upper mean heat flux (q̇ = 17.8 kW·m−2)has been treated over the full range with the asymptoticmodel which involves a nucleation boiling contribution.The mean heat flux was clearly higher than the onset

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An onset of nucleate boiling criterion for horizontal flow boiling

value obtained with equation (9) while for the lower heatflux (q̇ = 5.40 kW·m−2) the mean heat flux applied onthe liquid was of the same order of magnitude as the onsetvalue. Due to the noncontinuous heat transfer predictionbetween the pure convective and the asymptotic models,some jumps appear in the prediction showing the inter-mittence of asymptotic and pure convective liquid heattransfer coefficients. Nevertheless, it must be noted thatthe upper and lower values of the jump still define clearlyan accurate prediction.

The predictions forG = 20 kg·m−2·s−1 involve theuse of the stratified–wavy wetted angle. Even if this an-gle is still very close to the stratified one, the proposedprediction shows accurate results in a domain where thenumber of free parameters is the largest. It is also impor-tant to observe that the general tendency of the stratified–wavy heat transfer coefficient is a slow monotonic de-crease during evaporation. Using the complete heat trans-fer procedure, the standard deviation of the tests atG =20 kg·m−2·s−1 is 33.4 % for the lower mean heat flux and27.1 % for the larger mean heat flux. In contrast, the Gun-gor and Winterton (1987) flow boiling correlation with itsstratification correction factor mispredicts these data byabout a factor of 2 (see [1]).

Figure 10 shows complete evaporation at differentheat flux ranges. The heat flux level was not high enoughto reach the onset of nucleate boiling in the annularflow configuration. A few experimental points at highheat flux reached the onset value, but based on theexperimental points, no specific enhancement of the heattransfer coefficient existed in our database. Due to this,the pure convective liquid coefficient has been applied tothe full range of evaporation in annular flow. Rememberalso that the critical liquid height defined for annular flowis twice the liquid layer thickness. As the annular flowregime is well established, the cross-sectional geometryis better represented by a pure axisymmetric flow than anannular flow at the onset of dryout limit (refer tofigure 5).Thus, the real heat flux needed for onset of nucleateboiling in annular flow has not been reached during theseexperiments, even if the ratio of the experimental heatflux to the onset of nucleate boiling value is close to onein figure 10.

This last remark is not to be considered in the otherflow regimes. At a mean heat flux ofq̇ = 32.5 kW·m−2,the model uses the asymptotic approach in the stratified–wavy region, while a transition from asymptotic to pureconvective is shown on the same graph at a mean heatflux of q̇ = 17.8 kW·m−2 at a vapor quality ofx = 18 %.The standard deviation of the tests atG= 80 kg·m−2·s−1

is 25.0 % for the lower mean heat flux and 12.9 % for the

larger mean heat flux. Note that these standard deviationsin annular flow are strongly affected by the data in thepartial dryout region after the peak because of the rapiddecrease of the heat transfer coefficient; before dryout thepredictions are very precise.

6. CONCLUSION

A criterion to differentiate pure convective evapora-tion from combined nucleate and convective heat transferduring evaporation has been proposed. The approach ofSteiner and Taborek [9] has been modified to include thereal mean flow conditions of the liquid and a geometri-cal modelization of the liquid cross-section. It has beenshown that the experimental influence of the heat flux onthe local heat transfer coefficient has been accurately de-tected with the new onset of nucleate boiling criterion.Included in the complete procedure of heat transfer co-efficient prediction, which is based on a flow map pre-diction, a mean weighted coefficient and an asymptoticmodel in the case of mixed convective and nucleate boil-ing heat transfer, the standard deviations of the proposedcases were all less than 35.0 %. These values overstatethe actual deviations of the method since many data werepurposely taken near flow regime transitions and at veryhigh vapor qualities, which are the most difficult to pre-dict.

Acknowledgements

This work has been carried out at the Laboratory forIndustrial Energy Systems (LENI), Swiss Federal Insti-tute of Technology in Lausanne (EPFL). The project hasbeen supported financially by the EPFL, the Swiss Fed-eral Office of Energy (OFEN) and Research grant 800-RPfrom the American Society of Heating, Refrigerationand Air-Conditioning Engineers (ASHRAE), which aregratefully acknowledged.

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[14] Zürcher O., Thome J.R., Favrat D., Development ofa diabatic two-phase flow pattern map for horizontal flowboiling, to be submitted.

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