Influence of two-phase flow characteristics on critical heat flux in low pressure

In¯uence of two-phase ¯ow characteristics on critical heat ¯ux in lowpressure

Akira Inoue *, Sang-Ryoul Lee

Department of Energy Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuda,

Midori-ku, Yokohama 226, Japan

Received 8 July 1997

Abstract

In the present study, the critical heat ¯ux (CHF) was measured over wide quality range from subcooled boiling to annular-mist

¯ow at the atmospheric pressure. At a low pressure around the atmospheric pressure, the two-phase ¯ow pattern and void fraction

changes easily along the heated length and the ¯ow becomes more complex due to the low density of gas phase. By using Pyrex glass

tube as a test channel installed with a heater rod at the centerline, the two-phase ¯ow situation was observed visually. The ¯ow

pattern was kept nearly constant over the length of test section due to the low power input into the ¯uid. Therefore, the charac-

teristics of CHF could be investigated at each ¯ow patterns of bubbly, slug, annular and annular-mist ¯ow. In the subcooled boiling

region of bubbly ¯ow, the CHF decreased with increase of quality and was less sensitive to ¯ow rate. In the slug ¯ow region, the

CHF showed a minimum value. With more increase of quality in the annular ¯ow, the CHF increased and reached a peak value at a

certain quality depending on ¯ow rate. The peak of CHF occurred almost at a constant vapor mass velocity. In the annular-mist

¯ow region, the CHF decreased with increase of quality. In the region, the e�ect of heated length on the CHF was systematically

measured and validity of an analytical model of CHF considering dryout of liquid was investigated. Ó 1999 Elsevier Science Inc.

All rights reserved.

Keywords: Critical heat ¯ux; Low pressure; Flow pattern

1. Introduction

In boiling two-phase ¯ow, estimation of the criticalheat ¯ux (CHF) is one of the most important subjectsfor the safety of water-cooled reactors and other energysystems involving various heat exchangers. Till now,many studies have been executed to obtain an empiricalcorrelation of the CHF mainly at high pressure withlarge-scale loops from the practical viewpoints of com-mercial water-cooled nuclear reactors [1±5].

Substantially in the boiling two-phase ¯ow, the voidfraction and the ¯ow pattern change along the ¯ow pathdue to quality variation by heating. If it is under thehigh-temperature and high-pressure condition, thechanges are comparatively smooth. However, at low-pressure and low-velocity conditions encountered at an

accidental condition in a nuclear reactor, those changeremarkably along the ¯ow path due to large densitydi�erence between liquid and gas. The void fraction andthe ¯ow pattern are essential parameters for the CHF.Especially, the CHF may be signi®cantly in¯uenced bythe ¯ow pattern of bubbly, slug, annular and annular-mist ¯ow regime because the two-phase ¯ow behaviorsare very di�erent for each ¯ow patterns.

During the past decade, several studies have beenconducted on the CHF under the low-pressure conditionfor the design of evaporators operating at low pressureand boiling-water reactors. Bergles et al. [6] investigatedthe CHF in uniformly heated round tubes where theinlet conditions were subcooled and exit pressures werein the range from 0.172 to 0.862 MPa. At a low-pressurecondition below about 0.35 MPa, they observed that thecurves of CHF exhibited a minimum value at about zerooutlet quality. This is a unique behavior only for low-pressure condition that is not seen at high pressure.They explained the phenomena with the occurrence ofthe slug ¯ow near the zero outlet quality. The unstable¯ow situation and high void fraction of the slug ¯ow

Experimental Thermal and Fluid Science 19 (1999) 172±181

www.elsevier.nl/locate/etfs

* Corresponding author. Present address: Department of Mechani-

cal & Systems Engineering, Faculty of Engineering, Gifu University,

1-1 Yanagido, Gifu-shi, Gifu-ken 501-1193, Japan. Tel/Fax: +81-58-

293-2533. e-mail: [email protected]

0894-1777/99/$ ± see front matter Ó 1999 Elsevier Science Inc. All rights reserved.

PII: S 0 8 9 4 - 1 7 7 7 ( 9 9 ) 0 0 0 1 9 - 9

was assumed to cause momentary vapor blanketing nearheated wall which would result in the CHF even at avery low heat ¯ux. In the net quality region above zero,they observed that the CHF increased with increasingoutlet quality. Reminding that the CHF showed aminimum near zero quality, it is usually impossible toexhibit such behavior with a subcooled inlet conditionbecause of upstream burnout. However, a maximumcould be obtained with a few upstream burnouts. Theyguessed that the trend would be due to ¯ow stabilizationin the transition range of ¯ow pattern from the slug tothe annular ¯ow regime with increasing quality.

Rogers et al. [7] measured the CHF for upward ¯owof water in annuli at low ¯ow rates and a constant lowpressure of 0.156 MPa. Also in this study, at mass ve-locities less than 180 kg/m2 s, a minimum CHF wasobserved as the exit quality was raised through zero andall the CHF in the low mass velocity region lied belowthe saturated pool-boiling CHF. However, the CHF atmass velocities higher than 180 kg/m2 s lied above that.It is interesting to recognize that a mass velocity of 180kg/m2 s is equivalent to a coolant inlet ¯ow velocity ofabout 0.2 m/s which was nearly same as the slug vapordrift velocity for the experimental conditions. However,it was not explained why the CHF behaviors becamedi�erent when the super®cial liquid velocity goesthrough the vapor slug rising velocity. They proposed acorrelation only for the data at the higher velocity whichwere over-predicted by the existing correlations.

Mishima and Ishii [8] performed an experiment onthe CHF for low pressure and very low ¯ow rates ofsteam±water upward ¯ow below 40 kg/m2 s in an an-nulus. In the study, they observed that, at the low ve-locities, CHF occurred due to liquid ®lm dryout at the¯ow regime transition from the churn to the annular¯ow. Therefore, they correlated the CHF data by usinga drift ¯ux model transition criterion. However, theypointed out that there should be several more regimes ofCHF except above mentioned and further studies wereneeded to establish the criterion to determine which re-gime of the CHF should occur at low mass velocities. Inthe succeeding research, Mishima et al. [9] investigatedthe relationship between CHF and ¯ow instabilities ofwater ¯owing in a round tube under the atmosphericpressure. The CHF increased linearly as the mass ve-locity increased at a very low-velocity range, where thee�ect of inlet water temperature was small. However, ata high-velocity range, the increasing rate decreased re-markably and the e�ect of inlet water temperature be-came obvious. The transition mass velocity from thelow-velocity to the high-velocity regime was reported tobe about 200 kg/m2 s.

El-Genk et al. [10] also measured the CHF for low¯ow of water in vertical annuli under a low pressure of0.118 MPa. The e�ect of water subcooling on theCHF was indistinguishable in the smaller annuli �e �1:575 and 1:72� and also in the largest annulus �e � 2:0�for mass ¯uxes less than 140 kg/m2 s. However, the CHFvalues increased with the inlet subcooling in the largerannulus at the mass ¯uxes greater than 140 kg/m2 s. The

results suggest that, in the small annuli�e � 1:575 and 1:72�, the water mass ¯ux where the inletsubcooling might a�ect CHF strongly would be higherthan their experimental range. The ¯ow pattern wherethe CHF occurred varied with the annulus ratio and thewater mass ¯ux. While the CHF always occurred at thetransition from annular to annular mist ¯ow inthe smallest annulus �e � 1:575�, it occurred either atthe transition point from churn to annular ¯ow or atfrom slug to churn ¯ow in the larger annuli�e � 1:72 and 2:0�. Based on the results, they suggestedtwo correlations, respectively.

From the above state-of-the-arts, characteristic be-haviors of the CHF at a low pressure and low velocitycan be summarized as follows: (a) The CHF shows aminimum value near zero outlet quality. (b) The e�ect ofinlet water temperature is very small. (c) The CHF issmaller than that of pool boiling and is over-predictedby the existing correlations for high pressure and highvelocity.

However, there are not yet su�cient data to under-stand the details of CHF under low-pressure and low-velocity conditions such as the information about therelationship to the ¯ow pattern and the location of CHFoccurrence. The purpose of present study is to investi-gate the characteristics and mechanisms of CHF in each¯ow pattern under low-pressure condition. To investi-gate the e�ects of ¯ow-pattern on the CHF, it is neces-sary to examine under a simpli®ed ¯ow condition. Inthis study, a circular rod of small diameter is used as aheater rod to keep the input power density small andthen to suppress the change of ¯ow situation along thetest channel. The heater rod is inserted at the center of aPyrex glass channel, so that the ¯ow situation of boilingtwo-phase is observed during the CHF measurements.Two-phase quality condition of wide range from ÿ15%to 50% is made by injecting steam from a boiler intosubcooled water ¯ow at upstream of the test section.

2. Experimental apparatus and ¯ow conditions

The present experimental apparatus is composed of awater circulation loop and a steam supply system asshown in Fig. 1. Subcooled water from a circulationpump is heated up to a setting temperature in a pre-heater and reaches a steam±water mixing device.

On the other hand, steam saturated at 0.7 MPa issupplied from a boiler and is superheated by the de-crease of pressure to 0.3 MPa after passing through athrottle valve. The steam ¯ow rate is measured by one ofthe three calibrated ori®ce ¯ow meters of di�erent range.The steam is injected into a water ¯ow through a sin-tered metal ®lter of 50 lm in the particle diameter. Thedevice is located at 1000 mm upstream of the testchannel as shown in Fig. 2(c). Large pressure dropacross the sintered ®lter suppresses pulsation of steam¯ow rate induced by the latent pressure pulsation in atwo-phase ¯ow channel. Also the volume between the¯ow control valve and the ®lter was kept as small as

A. Inoue, S.-R. Lee / Experimental Thermal and Fluid Science 19 (1999) 172±181 173

possible for the same purpose. The temperature and thepressure of superheated steam are measured just beforethe mixing device. By the above injection method, a two-phase ¯ow with uniform bubbles is obtained, whichclosely simulates a boiling two-phase ¯ow.

Two kinds of test channels were made of a Pyrexglass tube of 21.0 and 13.0 mm in inner diameter and1000 mm in length. Graphite rod of 2.1 mm in outerdiameter and 30±750 mm in length were used as the testheater rod. It is installed at the center of the test channelas shown in Fig. 2(a). Two copper rods of 4 mm in di-ameter were set at the both ends of heater rod along thecenterline of the test channel, which serves as the elec-trodes. Both ends of the heater rod were plated withcopper in 15 mm length and amalgamated in a mercury±nitric acid solution to reduce electric contact resistanceas shown in Fig. 2(b). Its upper end is fastened to thecopper electrode with a mechanical holder at 20 mmdistance from the outlet of test channel and the otherend is dipped into a mercury pond dug on the top of thelower copper electrode.

Connecting part between the Pyrex tube and thesteam±water mixing device was designed to serve as the

lower electrode as shown in Fig. 2(c). The voltage dropacross the heater rod was measured through a pair ofthin wires attached to the copper electrodes and thecurrent was measured by a calibrated shunt.

Pressure drop over the test channel in¯uences thebubble generation and growth according to the localpressure. On this account, a pressure tap was attached tothe glass tube wall at the same level as that of thedownstream end of the heater rod where most of theCHFs occurred. Two-phase ¯ow from the test section isseparated in a steam separator located at the top of testchannel. The steam is released to the atmosphere andthe water is recirculated into the main loop.

All experiments were conducted with keeping thetotal mass ¯ow rate constant when the steam ¯ow ratewas changed. After setting all the experimental condi-tions, power input into the heater rod was raised grad-ually up to CHF. The CHF was ascertained by physicalburnout of the heater rod. The CHF was calculatedfrom the electric power input at the instance of theburnout. The position of burnout occurrence, Lb (dis-tance from the bottom end of heater rod) was also re-corded, where the local quality, xb, was calculated fromthe following energy balance:

Wli hli� ÿ hls� � Wvi hvi� ÿ hvs� � LbQt

LhA� xb Wli� � Wvi�hlv:

�1�In the present experiments, the data uncertainties

were estimated from the law of error propagation. The¯ow rate measurements have an uncertainty of �3%depending on the each ori®ces used. The critical heat¯ux was calculated from the electric power input intothe heater and its uncertainty was estimated within�2%. The uncertainty for measured pressure was �1%,and that for the calculated quality was �4% neglectingthe heat loss from the outer wall of test section.

3. Characteristics of the CHF in various ¯ow patterns

3.1. Bubbly ¯ow region

The bubbly ¯ow was observed at a subcooled con-dition of xb50 for every mass ¯ow rates and tubediameters. Although the equilibrium quality over across-section was minus, many bubbles were observedaround the heater rod at a high input power near theCHF. However, when the large bubbles were detachedfrom the heater wall into the liquid ¯ow, those werequickly condensed and did not grow up to a large slugbubble. Therefore, there were no signi®cant oscillationsof ¯ow rate, void fraction and pressure.

In this region, the CHF data were correlated wellwith the equilibrium quality, xb, at the burnoutpoint.The e�ect of ¯ow velocity was very weak when itwas less than 1 m/s. However, the e�ect could not beneglected at high velocity. The velocity e�ect at highvelocity was considered to be due to the forced con-

Fig. 1. Experimental loop.

174 A. Inoue, S.-R. Lee / Experimental Thermal and Fluid Science 19 (1999) 172±181

vection cooling of liquid ¯ow. The heat ¯ux, qc, by theforced convection cooling could be estimated using thefollowing correlation by Clark and Rosenow [11]:

qc � 0:023Re0:8 Pr0:33 DTsat;b� � DTsub;b�

� 1

� De

Lb

� �0:7!

kl

De

; �2�

where DTsat;b and DTsub;b are superheat and subcooling atthe instance of CHF, respectively. Usually, DTsat;b isestimated as 25±30 K in a saturation pool boiling.However, this value might be di�erent for the forcedconvection boiling. On this account, the superheats nearthe CHF condition were actually measured by usingplatinum wire of 0.3 mm in diameter and 150 mm longin the same test channel. The DTsat;b was summarizedwith the following correlation:

DTsat;b � 15:0� 0:98DTsub;b: �3�Namely, the superheat near the CHF increases lin-

early with the liquid subcooling and is not so much in-¯uenced by the ¯ow velocity. By substituting Eq. (3) intoEq. (2) and subtracting the qc from the qb, the results of

qbo � qb ÿ qc were described in Figs. 3(a) and (b). Thedata were compared with the empirical correlations forsubcooled pool boiling by Zuber et al. [12], Gunther andKreith [13] and Ellion [14]. The behavior of qbo againstxb is similar to those for the pool boiling. Conclusively,the following correlation including xb was obtained forall the present data after the Zuber's correlation [12]:

q�bo �qb ÿ qc

qvhlvU �� K1 ÿ K2xb; �4�

where

U � � ql ÿ qv� �grq2

v

� �1=4

; �5�

where K1 � 0:19 and K2 � 6:35 for D � 13 mm, andK1 � 0:11 and K2 � 5:96 for D � 21 mm, respectively,from the least square ®tting.

For the saturated pool boiling with a horizontal wire,Kutateladse [15] and Zuber et al. [12] obtained that K1 isequal to 0.16 and 0.2, respectively. The in¯uences of¯ow velocity and channel diameter on the CHF weresmall. This implies that the mechanism of CHF in thebubbly ¯ow regime is similar to that of pool boiling.

Fig. 2. Details of experimental apparatus: (a) test section, (b) heating rod, and (c) mixing device.


3.2. Slug ¯ow region

The slug ¯ow regime starts when a coalesced bubble(slug bubble) occupies the whole channel cross-sectionand the bubble grows up in length with increase of

quality. In this region, there were observed serious¯uctuations of the ¯ow velocity, the void fraction andthe pressure drop.

Relationship between qb and xb for the present ex-perimental data in the slug ¯ow region is shown in Fig.4. In the ®gure, the dotted lines indicate the observedtransition boundaries of slug-annular ¯ow. The transi-tion quality, xtsa, was estimated as follows:

xtsa � Wsa

Wt

DD0

; �6�

where Wsa � 14:6 kg/m2 s in the present experimentalconditions of Wt � 72±789 kg/m2 s and D � 0:021 m.That is, the transition from the slug to the annular ¯owoccurred at a constant steam mass velocity regardless oftotal mass ¯ow rate. According to the drift ¯ux model,these boundaries were estimated to correspond to theaverage void fraction of a� 0.7±0.75. Fig. 4 shows thebehaviors of qb against xb. Here qb has a minimum valueat about 0.1% quality for all Wt. The minimum value ofqb increases with total mass velocity and is correlated asfollows:

q�bmin � Ks1 � Ks2

Wt

qvU �

� �; �7�

where q�bmin � qbmin=�qvhlvU �� and Ks1 � 0:027; Ks2 �0:00048. When Wt ! 0; q�bmin approaches Ks1 � 0:027.According to Eq. (4), Ks1 � 0:11 for the bubbly ¯ow.That is, at the zero mass velocity, q�bmin becomes smallerby about 1/4 times than that in the bubbly ¯ow.

The values of qb are essentially scattered in the slug¯ow region. According to the measurements by a plat-inum wire as mentioned in the previous chapter, the walltemperature started to ¯uctuate from very low heat ¯uxof about one-tenth of qb. The wall temperature increasedtransiently by several ten degrees when a slug bubblepassed by the heater rod. This indicates that local dryoutoccurs on the heater wall, and then it is recovered to alow temperature when a successive liquid slug passes by.Therefore, it may be considered that the physicalburnout of heater occurs when the wall temperaturecannot be recovered by the passage of a liquid slug. Inthe slug ¯ow region, it is concluded that the CHF ismainly in¯uenced by the characteristic pulsating be-

Fig. 4. Relation between CHF and quality in the slug ¯ow region.

Fig. 3. Relation between CHF and quality in subcooled region: (a)

D � 0:013 m, and (b) D � 0:021 m.


havior of the slug ¯ow and not by the bubble formationnear the wall.

Successively when the successive slug bubbles arecoalesced to in®nite length at a higher quality, the ¯owregime changes to the annular ¯ow.

3.3. Annular ¯ow region

After the slug ¯ow region, the CHF increases withthe critical quality and the increasing rate becomeslarger with the increase of total mass velocity as shownin Fig. 4. In the annular ¯ow region, the ¯ow ¯uctuatedstill extensively and the CHFs were scattered. As xb in-creases at a constant mass ¯ow rate, the two-phase ve-locity increases and the ¯uctuation is suppressed. As aresult, the CHF increases with the critical quality.

Figs. 5 and 6(a) and (b) show the behaviors of CHF,qb, after the slug ¯ow region against the critical quality,xb, and the steam mass velocity, Wv, respectively. At ®rstqb increases with xb and Wv. At a higher quality, thereappears a peak of the CHF, where entrained dropletswere observed. The behavior of CHF showed drasticdi�erences before and after the peak point. Therefore, itis de®ned here that a quality region from the slug-an-nular boundary to the peak point is the annular ¯ow

regime. Since the slip velocity between a steam and aliquid ®lm ¯ow increases with xb, the interface shearstress and the entrainment from liquid ®lm increasesabruptly near a quality, xbmax where the CHF shows apeak value. Conclusively, liquid ®lm ¯ow rate decreaseswith quality and the ¯ow pattern changes to the annu-lar-mist ¯ow.

The relationship between xbmax and Wt at the peak iswell correlated as follows:

Wtxbmax � Wv � 30±35 kg=m2

s �8�Namely, the peak of qb appears at a constant steam

mass velocity as shown in Figs. 6(a) and (b). Accordingto the calculation of steam velocity at the peak pointusing the drift ¯ux model, the peak point corresponds tothe steam velocity of 42±50 m/s at the present systempressure. In case that the vapor velocity is much largerthan that of liquid ®lm, that is, Uv ÿ U1 � Uv, the Webernumber is determined only by the vapor velocity.Therefore, the condition that the droplet entrainmentfrom liquid ®lm becomes signi®cant is described by aconstant steam ¯ow rate as like Eq. (8).

On the other hand, according to Ishii and Grolmer[16], the vapor velocity, U �e , where droplet entrainmentstarts, is correlated as follows:

Fig. 5. Relation between CHF and quality in the annular and annular-

mist ¯ow region: (a) D � 0:013 m, and (b) D � 0:021 m.

Fig. 6. Relation between CHF and steam mass velocity: (a) D � 0:013

m, and (b) D � 0:021 m.


U �e � 3:7rg ql ÿ qv� �

q2v

� �1=4

: �9�

From the above equation, the mass velocity at thestarting point of droplet entrainment is estimated suchthat Wv � qvU �e � 16:8 kg/m2 s. Then, the value of Wv

obtained from Eq. (8) at the peak is about two timeslarger than that at the beginning point of droplet en-trainment. The value of Wv corresponds to that for thepeak of entrainment ¯ow rate by Collier's data [17].

3.4. Annular-mist ¯ow region

Annular-mist ¯ow region is a quality region higherthan xbmax corresponding to the peak of qb. As shown inFig. 5(a) and (b), qb decreases with xb at a constant Wt

due to decrease of liquid ®lm ¯ow rate. The qb decreaseswith increase of Wt at a constant xb especially in thehigher quality region of the annular-mist ¯ow region.Namely, the decreasing rate of qb with increase of xb

becomes more signi®cant as Wt increases. As Wv in-creases in proportion to Wt at a constant xb, the shearstress at a vapor±liquid interface increases with Wt.Then, the entrainment rate increases enough for theliquid ®lm ¯ow rate to decrease. This behavior ofthe CHF at the annular-mist ¯ow is similar to that ofthe existing experimental results at high pressure.

However, if qb is arranged against Wv as in Figs. 6(a)and (b), qb increases with increase of Wt even in thehigher quality region. The reason can be explained asfollows. As mentioned previously, in case that the vaporvelocity is much larger than that of liquid ®lm, theWeber number is determined only by the vapor velocityand the amount of entrainment is so too.

The CHF in this region occurs by dry patch or dry-out of liquid ®lm so that the positions of the CHFsconcentrate on the downstream end of the heater rod.

4. The e�ect of heated length in the annular-mist ¯owregion

It has been said generally that CHF decreased withincrease of total ¯ow rate at a constant quality in theannular ¯ow regime. However, as shown later, thisfeature can be observed only in a higher quality regionof the annular-mist ¯ow regime.

Fig. 7 shows the in¯uence of heated length on CHFin the annular-mist ¯ow region when Wt is equal to 114kg/m2 s. As the heater length decreases from 0.75 to 0.03m, the CHF increases in the entire quality region. Thequality that corresponds to the peak of CHF, whichserves as the transition boundary from the annular andthe annular-mist ¯ow regime, shifts to a little highervalue from xb � 0:2 in Lh > 0:2 m. For every heaterlength, as xb increases more from xbmax, the CHF de-creases gradually.

Fig. 8 shows the relationship between qbLh and Lh inthe annular-mist region. If the ®lm ¯ow rate at the inlet

of the heater were a dominant factor of liquid ®lmdryout, qbLh would be kept constant even when thedryout was the mechanism of CHF in this condition.However, it would increase with Lh if the deposition ofdroplets to the ®lm ¯ow should prevail. In Fig. 8, qbLh

increases in proportion to Lh except for the cases ofLh < 0:2 m. The intersection values at Lh ! 0 corres-pond to the inlet ®lm ¯ow rate and the slope at Lh > 0:2m means the deposition rate of droplets. As xb increasesfrom 0.2 to 0.7, the slope decreases by about 0.25. Thismeans that the deposition rate decreased due to decreaseof a droplet density with quality. The data in Lh < 0:2 m

Fig. 7. E�ects of heating length on CHF �qb ÿ xb�.

Fig. 8. E�ects of heating length on CHF �qbLh ÿ Lh�.


indicate that the CHF is caused by any mechanism ex-cept for the dryout, for example, by departure fromnucleate boiling under a liquid ®lm.

5. Location of CHF occurrence

Although the two-phase ¯ow situations change littlealong with the length of heater rod in the present ex-periment, the CHF will occur at a location of theweakest situation. In the case of uniform heating, it isusual that the CHF location concentrates on thedownstream end of the heater rod, because thickness ofbubble boundary layer, void fraction and liquid ®lmthickness change integrally along the heated length.However, if any local conditions, such as generation oflarge bubbles near the heated wall by pulsating ¯ow,become prevailing parameter, the CHF location wouldbe scattered.

In Fig. 9, the relationship between CHF locationand xb in a positive quality region was shown forvarious heater lengths from 0.35 to 0.75 m. Generallyspeaking, the locations concentrated on the down-stream end in the subcooled boiling region. However,as xb became close to 0, the two-phase ¯ow ¯uctuatedmore intensively and the CHF locations were scattered.Subsequently, the CHF locations were scattered mostin the slug ¯ow region. Also in the annular ¯ow ofsmall xb, the ¯ow ¯uctuation was so intensive still thatthe scatter of CHF location remained remarkable.However, as xb increased and ¯ow ¯uctuation wassuppressed, the location tended to concentrate on thedownstream end of the heater rod.

6. Considerations

The mechanism of CHF is considered as follows:when a heated surface is dried out partially at any in-stance and then if it cannot be rewetted again, the sur-face temperature increases abruptly and cannot recoverto a lower temperature. The cause of the partial surfacedryout is di�erent in each two-phase ¯ow patterns. Inthe bubbly ¯ow, the cause of dryout is similar to that ofthe pool boiling, where it is caused mainly by a largebubble coalesced near the heated surface. Cooling byliquid ¯ow is e�ective only at the outside of bubbleboundary layer, so that the in¯uence of ¯ow rate on theCHF is not so outstanding in the subcooled region.However, the e�ect of liquid subcooling on it is strongbecause the subcooled liquid ¯ow condenses steambubbles and suppresses their coalescence.

In the slug ¯ow region, the CHF is a�ected by thethickness and the length of liquid ®lm beneath the slugbubble and its passing velocity. It was ascertained ex-perimentally that the liquid ®lm partially dried out evenat much lower heat ¯ux than the CHF, because the ¯owvelocity and the thickness were very small and ¯uctu-ated. Considering the low CHF value in this region,bubbles generated in the liquid ®lm are few and a�ectlittle the dryout of the ®lm. At that time, whether thepartial dryout leads to the CHF or not is determined bywhether it can be rewetted or not when consecutiveliquid slug passes. As quality increases in the region, theCHF increases because the liquid ®lm velocity increasesand the ¯ow pattern changes to the annular ¯ow whichis comparatively stable.

With increasing quality in the annular ¯ow, the ¯owvelocity of liquid ®lm increases and the ¯uctuating fea-ture of ¯ow is suppressed due to the increasing shearstress at the interface. These result in the increase ofCHF. In this region, dry patches might be formed bybubbles generated in the liquid ®lm layer due to the highheat ¯ux. The occurrence of CHF will be determined bywhether the dry patch is rewetted again or not. Whentotal ¯ow rate increases at a same quality, the inertiaforce of ®lm ¯ow increases. So that the e�ect of mass¯ow rate on the CHF is signi®cant in this region.However, the present experimental data of CHF weresmaller by one over than those estimated with the as-sumption of total dryout of liquid ®lm. Therefore, thee�ect of ¯ow ¯uctuation on the CHF is thought to bestill signi®cant in the annular ¯ow.

In the annular-mist ¯ow region, as quality increases,the interface shear stress between a vapor and a liquid®lm ¯ow increases further due to increase of vapor ve-locity. Accordingly, the droplet entrainment increases,and then both the ¯ow rate and the thickness of theliquid ®lm decrease. Generally, it seemed that nucleateboiling was suppressed due to the e�cient cooling byevaporation. Therefore, in the case that a heated lengthis su�ciently long and CHF is small, the CHF can beestimated by the assumption of total dryout of liquid®lm. However, when the heated length is short and theCHF is large, the assumption overestimates the CHFFig. 9. Location of CHF occurrence.


value. In this case, formation of dry patches by bubblegeneration in a liquid ®lm might be an importantmechanism of CHF. The solid line in Fig. 8 indicates theestimated values assuming formation of dry patch in theliquid ®lm on a heated surface. In the analysis of drypatch, the following are considered:1. Flow rates of liquid ®lm and entrained droplets are

estimated by Collier's correlation [17].2. Liquid ®lm velocity on the heater rod is assumed as

the universal pro®le based on the shear stress at theheating rod surface, which is estimated by pressuredrop measurement.

3. Droplet deposition rate to the heater rod is calculatedwith a di�usion coe�cient of ed � 0:45ev where ev isan eddy di�usivity of turbulence in a gas phase.

4. The minimum ®lm thickness is determined from thebalance of a surface tension force, shear stresses atliquid ®lm of both sides and a momentum of a liquid®lm ¯ow deduced by Zuber and Staub [18].As shown in Fig. 7, when the heated length is longer

than 0.35 m, the estimation of CHF shows goodagreement with the experiment data. However, if it isless than 0.2 m, the CHF is quite overestimated in a lowquality region of the annular-mist ¯ow.

In the case of a real fuel assembly of LWR where theheated length is long and the heat ¯ux is large, several¯ow patterns exist at a same time in a ¯ow channel. Inthis case, serious trouble may take place in the slug ¯owregion under low-pressure condition, because the CHFshows a minimum value there among all the ¯ow pat-terns.

7. Conclusions

Characteristics of the critical heat ¯ux were investi-gated experimentally in the various ¯ow patterns ofboiling two-phase ¯ow at the atmospheric pressure. Theresults of this study are summarized as follows:1. The behaviors of CHF are remarkably di�erent in

each ¯ow pattern.2. In the subcooled bubbly ¯ow region, the mechanism

of CHF resembles that of pool boiling. The in¯uenceof mass velocity on the CHF is very weak. However,the liquid subcooling a�ects the CHF signi®cantly.The CHF is well correlated by Eq. (4) which is similarto the correlation for pool boiling by Zuber et al. [12]and Kutateladse [15].

3. In the slug ¯ow region, the CHF shows a minimumvalue due to the ¯ow ¯uctuation.

4. In annular ¯ow region, the CHF increases with in-creases of quality and mass velocity, and the increas-ing rate is signi®cantly enhanced by increase of massvelocity. The increase of CHF is due to suppression ofthe ¯ow ¯uctuation by increases of quality and massvelocity.

5. In the transition region from the annular to the annu-lar-mist ¯ow, the CHF shows a peak value. The peakappeared almost at the same vapor mass velocity of30±35 kg/m2 s regardless of total mass velocity.

6. In the annular-mist ¯ow region, the CHF decreaseswith increase of quality. The decreasing rate becomeslarger with increase of total mass velocity. So that, ina high quality region, the CHF decreases with in-crease of total mass velocity at a same quality. Thischaracteristic trend appears when the CHF data arearranged as a function of the critical quality. If thedata are arranged against vapor mass velocity, thoseincrease with total mass velocity at a same vapormass velocity, and decrease with increase of a vapormass velocity at a same total ¯ow rate. Namely, inthis region, the vapor slip velocity dominates dropletentrainment and the CHF resultantly.

7. The CHF model by the assumption of total dryout ofliquid ®lm showed a good agreement with the exper-imental data when a heated length was larger than300 mm in the high quality region of annular-mist¯ow.

8. The CHF almost occurs at the downstream end of aheated length in the bubbly and the annular-mist¯ow. However, in the slug and the lower quality re-gion of the annular ¯ow, the location of CHF is scat-tered due to the characteristic ¯ow ¯uctuation.

NomenclatureA cross-sectional area ¯ow channel (m2)c proportional constantDe equivalent diameter of test channel

(m)D inner diameter of test channel (m)d droplet diameter (m)g gravity (m/s2)h enthalpy (J/kg)K1;K2 constant of Eq. (4)Ks1;Ks2 constant of Eq. (7)Lb location of the CHF from the bottom

of heater (m)Lh total heated length (m)Pr Prandtl numberqb critical heat ¯ux (W/m2)qbo qb ÿ qc (W/m2)q�bo nondimensional heat ¯ux by Eq. (4)qc heat ¯ux by convective cooling

�W=m2�Qt total heat input (W)Re Reynolds numberDTsat;b superheat at CHF (K)DTsub;b subcooling at CHF (K)U ¯ow velocity (m/s)U � characteristic velocity by Eq. (5)U �e velocity of entrainment starting by

Eq. (9)W mass velocity �kg=m2 s�We Weber numberx qualitya average void fractioned di�usion coe�cient of droplet


References

[1] T.G. Theofanous, The boiling crisis in nuclear reactor, Int. J.

Multiphase Flow 6 (1980) 69±95.

[2] M.M. Shah, A generalized graphical method for predicting CHF

in uniformly heated vertical tubes, Int. J. Heat Mass Transfer 22

(1979) 557±568.

[3] A.E. Bergles, Burnout in boiling heat transfer, Part II: Subcooled

and low quality forced convection systems, Nucl. Safety 18 (1977)

154±167.

[4] A.E. Bergles, Burnout in boiling heat transfer, Part III: High-

quality forced convection systems, Nucl. Safety 20 (1979) 671±

689.

[5] Y. Katto, H. Ohno, An improved version of the generalised

correlation of critical heat ¯ux for the forced convective boiling in

uniformly heated vertical tubes, Int. J. Heat Mass Transfer 27

(1984) 1641±1648.

[6] A.E. Bergles, R.F. Lopina, M.P. Fiori, Critical-heat-¯ux and

¯ow-pattern observations for low-pressure water ¯owing in tubes,

Trans. ASME J. Heat Transfer (1967) 69±74.

[7] R.T. Rogers, M. Salcudean, A.E. Tahir, Flow boiling critical heat

¯uxes for water in a vertical annulus at low pressure and

velocities, Proceedings of the Seventh International Heat Transfer

Conference, Munich, vol. 4, Paper No. FB28, 1982.

[8] K. Mishima, M. Ishii, Experimental study on natural convection

boiling burnout in an annulus, Proceedings of the Seventh

International Heat Transfer Conference, Munich, vol. 4, Paper

No. FB23, 1982.

[9] K. Mishima, H. Nishihara, I. Michiyoshi, Boiling burnout and

¯ow instabilities for water-¯owing in a round tube under

atmospheric pressure, Int. J. Heat Mass Transfer 28 (1985)

1115±1129.

[10] M.S. El-Genk, S.J. Haynes, S.H. Kim, Experimental studies of

critical heat ¯ux for low ¯ow of water in vertical annuli at near

atmospheric pressure, Int. J. Heat Mass Transfer 31 (1988) 2291±

2304.

[11] J.A. Clark, W.M. Rosenow, Trans. ASME 76 (1954) 554.

[12] N. Zuber, M. Tribus, J.W. Westwater, The hydrodynamic crisis

in pool boiling of saturated and subcooled liquids, Proceedings of

the Second International Heat Transfer Conference, vol. 27, 1961.

[13] F.C. Gunther, F. Kreith, Heat Transfer and Fluid Mechanics

Institute, 113, 1949.

[14] M.E. Ellion, Jet Prop. Lab. Memo, No. 20-88, 1954.

[15] S.S. Kutateladse, A hydrodynamic theory of changes in the

boiling process under free convection, Izv. Akad. Nzuk. SSSR 4

(1951) 529.

[16] M. Ishii, M.A. Grolmer, Inception criteria for droplet entrain-

ment in two-phase cocurrent ®lm ¯ow, AIChE J. 21-2 (1975) 308.

[17] J.G. Collier, G.F. Hewitt, Data on the vertical ¯ow of air±water

mixtures in the annular and dispersed ¯ow regions, Part 2,

AERE-R 3455, 1960.

[18] N. Zuber, F. Staub, Int. J. Heat Mass Transfer 9 (1966) 897.

ev eddy di�usivity of gas phasekl conductivity of liquid (W/mK)q density �kg=m3�r surface tension (N/m)

Subscriptsb at critical heat ¯uxi inletl liquidmax maximummin minimumo outlets saturationt totalv vapor


Influence of two-phase flow characteristics on critical heat flux in low pressure

Documents

Transcript of Influence of two-phase flow characteristics on critical heat flux in low pressure