Mathematical Model Predicting the Critical Heat Flux of Nuclear Reactors

Journal o Computer Science 01, 8 (1), 1996-007 ISSN 1549-3636 01 doi:10.3844/jcssp.01.1996.007 Pulished Online 8 (1) 01 (http://www.thescipu.com/jcs.toc) Mathematical Model Predicting the Critical Heat Flux o Nuclear Reactors 1 Chien-Hsiung Lee, Lih-Wu Hourng and 3 Kuo-Wei Lin 1 Nuclear Fuels and Materials ivision, Institute o Nuclear Energy Research P.O. Box 3-3, Lungtan, Taoyuan, 3500, R.O.C., Taiwan epartment o Mechanical Engineering, National Central University, Jhongli, 3001, R.O.C., Taiwan 3 epartment o International Business, Hsuan Chuang University, Hsinchu, 3009, R.O.C., Taiwan Received 01-06-08, Revised 01-09-14; Accepted 01-1-1 ABSTRACT Boiling heat transer system keeps a nuclear power plant sae without getting over-heated. Crisis will occur i the dissipated heat lux exceeds the critical heat lux value. This study assumes the low oiling system at high heat lux is characterized y the existence o a very thin liquid layer, known as the sulayer, which is trapped etween the heated surace and the vapor lankets. In the present study, it is hypothesized that the heat transer through the liquid sulayer is dominated y the heat conduction and the sulayer is dried out due to occurrence o Helmholtz instaility as the relative velocity o the vapor lanket to the local liquid in the sulayer reaches a critical value. By recognizing this hypothesis, a theoretical model or low-quality low is developed to predict oiling heat transer and Critical Heat Flux (CHF). To veriy the validity o the present model, the predictions are compared with the experimental data o low oiling heat transer in the simulation o Pressurized Water Reactor (PWR) and Boiling Water Reactor (BWR) conditions. For the PWR low-quality low, the comparison demonstrates that the Helmholtz instaility is the trigger condition or the onset o CHF. Keywords: Nuclear Crisis, Critical Heat Flux (CHF), Helmholtz Instaility, Boiling Heat Transer, Boiling Water Reactor (BWR), Pressurized Water Reactor (PWR), Relative Velocity 1. INTROUCTION In the review o high heat lux oiling mechanisms, many studies have ound the existence o liquid sulayer Sucooled or low-quality orced convective oiling etween the heated surace and the ule layer at high system is utilized in the design o nuclear reactor cores, heat lux conditions. Based on the ormation o the liquid ecause its high heat luxes can e dissipated. Thereore, sulayer, Katto and Yokoya (1968) developed a to protect the heated surace rom overheating or urnout, hydrodynamic model near the CHF according to the a reliale estimation o the oiling heat transer and its consumption o liquid ilm. limitation Critical Heat Flux (CHF) is extremely required Through a measurement o the transient variation o in the low oiling system. In general, the oiling heat heated surace temperature during nucleate pool oiling transer mechanisms are dierent at the low heat lux o water, Chi-Liang and Mesler (1977) conirmed the (q<0.6 CHF) and the high heat lux (q>0.6 CHF) as shown existence o a liquid ilm eneath the growing vapor in Fig. 1. At the ormer condition, most o the heat lux is which is paramount in transerring heat. Bhat et al. provided or nucleation o ules (Fig. 1a); while at the (1983) hypothesized that the heat transer, in the high latter, the oiling heat transer is dominated y the heat heat lux region etween 0.6 CHF and CHF, takes place conduction in the liquid sulayer trapped etween the mainly due to the heat conduction through the liquid heated surace and the vapor lanket (Fig. 1). layer ormed on the heated surace. Corresponding Author: Kuo-Wei Lin, epartment o International Business, Hsuan Chuang University, Hsinchu, 3009, R.O.C., Taiwan 1996

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 (a) () Fig. 1. Liquid-vapor coniguration or up-low oiling wator (a) low heat lux condition (<0.6 CHF) () high heat lux condition (>0.6 CHF) In a susequent paper o Bhat et al. (1986), experimental results o sulayer thickness and requency o vapor mass show good agreement with their previous predictions. Later, many high heat lux models ased on heat conduction in the liquid layer have een reported (Chinm et al., 1989; Jairajpuri and Saini, 1991; Rajvanshi et al., 199). Although all the availale models are developed speciically or pool oiling, Chinm et al. (1989) expected that the same concept o heat conduction through the sulayer may also e applied to low oiling conditions. The sulayer concept with heat alance rather than heat conduction has also een applied in the research o low oiling or predicting the CHF. For example, Haramura and Katto (1983), as ones o the pioneers o the sulayer dry out theory, originally derived a high heat lux model, ased on the heat alance o liquid ilm located etween the heated surace and a vapor lanket, to predict the low oiling CHF on lat plates. Lee and Mudawwar (1988) postulated that CHF occurs when the liquid ilm underneath the vapor lanket dries out due to the oscillation motion o the lanket or an intearnal low oiling system. They emphasized that the onset o sulayer dry out was triggered y Helmhotz instaility in the sulayer-vapor lanket interace whiale as the length o the vapor lanket is equal to the Helmholtz critical wavelength. Later, y replacing the single-phase luid properties with the two-phase homogeneous equilirium luid properties, Lin et al. (1988a; 1988) made an improved sulayer dry out model to extend the applicale range rom the sucooled low oiling to the low-quality saturated low oiling. By accounting or the passage time o the lanket, Katto (1990a; 1990; 199) used the similar idea yet dierent approach to evaluate the HF required to vaporize the liquid ilm underneath the lanket. Celata (1991) suggested that this mechanism may also e applied in the thermal-hydraulics studies o high heat lux, high mass low rate usion reactor. Although thickness o liquid sulayers calculated y Lee and Mudawwar (1988) and Katto (1990a; 1990; 199) models are quite dierent, it is worth to note that the magnitude o sulayer thickness is extremely tiny (order o 10 7 ~10 3 m). It is thus appropriate to hypothesize that the convective oiling heat transer is dominated y the heat conduction through the liquid sulayer at superheated conditions. Thereore, ased on heat conduction in the sulayer, Lin et al. (1994) 1997

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 developed a theoretical model or sucooled low oiling heat transer at high heat lux conditions. Lee and Lin (1993) conducted the low transient CHF experiments in the simulation o Pressurized Water Reactor (PWR) conditions. The experimental data were compared with the predictions o improved model y Lin et al. (1988a). Their results reveal that the sulayer dry out model is appropriate. All o the aore-mentioned theoretical approaches or predicting the low oiling CHF (Lee and Mudawwar, 1988; Lin et al., 1988a; 1988; Katto, 1990a; 1990; 199) acknowledged that the sulayer dry out is triggered y Helmoholtz instaility at the sulayer-vapor lanket interace. However, so ar there is no theoretical model ased on the Helmholtz instaility concept proposed or prediction o occurrence o CHF. In the present study, a critical condition or onset o CHF is derived ased on the Helmholtz instaility at interace o two streams. The relative velocity o two streams is calculated using the heat transer model y Lin et al. (1994). The predicted transient time to the onset o CHF provided reasonale agreement with the Lee and Lin (1993) experimental data.. MATERIALS AN METHOS Based on the oiling coniguration o sucooled low through a vertical tue at the high heat lux conditions as shown in Fig. 1, a theoretical oiling heat transer model was proposed with the ollowing assumptions: In the sucooled low through a vertical tue, the vapor lankets are ormed rom small ules pilling up as vertical distorted vapor cylinders. All the vapor lankets glide up parallel to the heated wall and shield the heated wall rom the cooling o ulk low. As a result, a liquid sulayer orms etween the vapor lankets and the heated wall For high heat lux, the passing period o the vapor lanket ecomes suiciently long as that reported in Hino and Ueda (1985) investigation. Thus, the sulayer seems always exist etween the heated wall and the vapor lanket Since the thickness o the sulayer is very thin with low low rate, it is reasonale to assume that, in the sulayer, the ule generation is ceased and the heat convection can e ignored due to small velocity, the heat transer across the liquid sulayer is dominated y heat conduction Figure shows the temperature distriution in the sulayer and the orce alance on the vapor lanket. As mentioned aove, the q heat lux can e calculated y heat conduction through the thickness o sulayer δ with the temperature dierence o heated wall T w and the vapor lanket T sat. i.e.: k (Tw T sat ) q = δ (1) In this equation k is the conductivity o liquid. By newton s law o cooling, the heat lux also can e expressed as: q = h(t T ) () w From Eq. 1 and, the sucooled oiling heat transer coeicient h can e otained as Eq. 3: h = q / (q δ / k + Tsat T ) (3) Thus to determine the heat transer coeicient, it is needed to calculate the sulayer thickness δ which can e otained y orce alance on the vapor lanket in the axial and the radial directions (Fig. ). For the two-phase low, the eective luid properties such as density ρ and viscosity µ need to e modiied irst..1. Eective Homogeneous Fluid Properties The homogeneous two-phase low model is assumed to e suitale or the present sucooled or low-quality low oiling conditions... Magnitude o True Quality The true quality x can e evaluated y using Saha and Zuer (1974) ormula Eq. 4: xe xd exp(x e / xd 1) x = 1 x exp(x / x 1 d e d (4) where, x e is the thermodynamic equilirium quality and x d is the thermodynamic quality at the point o ule detachment rom that heated wall. The value o x d is Eq. 5: qcp xd = 0.00 ;or Pe < 70000 H k g g q xd = 154 ;or Pe > 70000 H G (5) where, c p the speciic heat capacity o liquid, the inner diameter o the tue, H g is the latent heat o vaporization, G the mass velocity and P e the Peclet numer o liquid. Note that, as x e x d the true quality is identically zero or the single-phase low. 1998

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 Fig.. Schematic diagram o vapor lanke moving in vertical turulent low at high heat lux condition.3. ρ and µ or Homogeneous Flow For the homogeneous two-phase low o true quality x, the luid density ρ is generally given y Eq. 6: 1 x (1 x ) = + ρ ρ ρ g (6) In this equation ρ g and ρ respectively, denote the density o vapor and liquid, while the mean two-phase viscosity µ will e evaluated y using the ormula o ukler et al. (1964) Eq. 7: µ = ρ [xµ gv g + (1 x) µ v ] (7) where, µ g and µ represent the viscosity o vapor and liquid; and v g and v are speciic volume o vapor and liquid, respectively..4. Relative Velocity o Vapor Blanket to Liquid At high heat lux condition, the vapor lanket is ormed y the coalescence o small ules. The vapor lanket is assumed to e a distorted cylinder o length L and diameter, which orms a lat interace near the wall. Consider the orce alance in the axial direction, the relative velocity o the lanket with respect to the liquid will e determined y a alance etween the uoyancy orce F and the drag orce F d Eq. 8 and 9: F + F = 0 (8) B Where: π FB = L ρ g (9) 4 And: 1 Z π F = ρ FCUL (10) 4 in which ρ = ρ -ρ g is the density dierence etween the two phases, C the drag coeicient and U L the relative velocity o the vapor lanket with respect to the liquid at the position corresponding to the centerline o the lanket. The negative sign in Eq. 10 indicates that the direction o the drag orce is opposite to the low direction. Chan and Prince (1965) proposed an expression o the drag coeicient or a small deormed ule Eq. 11: C 48µ = (11) ρ eu L Since the vapor lanket is ormed initially y the coalescence a vertical column o small ules, the 1999

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 equivalent diameter e and are assumed to e equal to the ule departure diameter (Lee and Mudawwar, 1988) and the latter can e otained rom the correlation o Cole and Rohsenow (1968) Eq. 1: 0.5 1.5 C 4 pt σ ρ sat 1.5 10 g ρ ρ H g g (1) where, σ is the surace tension. Weisman and Pei (1983) indicated that the ules are approximately ellipsoidal with the ratio o long to short ellipse axis eing aout 3:1 in the case o high heat lux. So the length o the vapor lanket L is assumed to e three times o the ule diameter. Comining Eq. 8 through (1) with the relations e = and L =3 gives the relative velocity o the ule with respect to the liquid as Eq. 13: U L = ( ρ ρ g ) 8µ.5. Liquid Velocity Gradient g (13) The local liquid velocity gradient can e evaluated y the orce alance o a vapor lanket in the radial direction and the velocity proile distriution..6. Force Balance in Radial irection The orce alance o a vapor lanket in the radial direction is shown as Fig.. Vapro generation due to sulayer evaporation creates a rate o change o momentum F 1 which pushes the vapor lanket away rom the wall. However, the lateral motion o the lanket is resisted y a lateral orce F R caused y the vapor lanket rotation, which is resulted due to the velocity gradient associated with the liquid oundary layer in the tue. The inertial orce F 1 is given y Eq. 14: U π F = C U L y 4 L R ρ L (16) where, U L is the local liquid velocity and C is a parameter which accounts or the eects o turulent luctuations and local ule concentration on the rotation o the vapor lanket. From a liquid-gas two-phase low experiment in the adiaatic oundary condition, Beyerlein et al. (1985) ound that C is a unction o the average void raction and the liquid Reynolds numer. In the present model or vapor-liquid system with wall heating, the dependences o two-phase Reynolds numer and the oiling numer in the parameter C are taken into account and is modeled y Eq. 17: C = a Re Bo (17) a a3 1 * In which a 1, a and a 3 are empirical constants, Re = G/µ is the eective Reynolds numer or homogeneous low and Bo * is a modiied oiling numer deined as Eq. 18: q Bo = * Bo[(1 x) /1 ] 1 x = α Hg G 1 α (18) In which Bo = q/(gh g ) is the conventional oiling numer and α is the void raction Eq. 19: α = vgx / [vgx + v (1 x)] (19) Upon comining the aove equations, the liquid velocity gradient U L / y can e evaluated as the values o a 1, a and a 3 are treated known quantities, it is Eq. 0: F = ρ V L (14) 1 g U L 3µ q = y gπc ρ ( ρ ρ )H 3 p g g g (0) where, V is the vapor velocity due to evaporation o the sulayerand can e expressed as Eq. 15: V = q / ( ρ gh g) (15) Beyerlein et al. (1985) derived an expression or the lateral orce on a ule in turulent two-phase low in a vertical tue. The lateral orce on the vapor lanket is determined y the relative velocity o the lanket and the gradient o the liquid velocity proile, i.e Eq. 16:.7. Velocity Proile istriution Applying the Karman s three-layer structure o turulent low in a tue, the riction velocity U + can e derived y the non-dimensional wall distance y +, that is Eq. 1a-d: + + + U = y ;or0 < y < 5 (1a) + + + U = 5.0ln y 3.05;or 5 y 30 (1) 000

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 + + + U =.5ln y + 5.5 ;or 30 < y (1c) Where: U = U / τ / ρ, y = y τ ρ / µ (1d) + + w w ( ρ ρ ) ( ) τ δ + / τ / ρ ρ µ w w U = 5.0ln 3.05 + g 8µ g (6) And τ w is wall shear stress which can e otained y Eq. : (G / ρ) τ w = ρ () where, the riction actor is the anning riction actor, can e calculated y Eq. 3: F = 0.046Re 0. (3) The eective value o he velocity gradient causing vapor lanket rotation can e approximated as velocity gradient at the radial position o δ+ / rom the wall. Lee and Mudawwar (1988) ound that the liquid velocity proile around the vapor lanket locates in the uer region and the eective velocity gradient can e calculated rom Eq. (1a-d): U L 1 = 5 τw / ρ y δ + ( / ).8. Thickness o Sulayer (4) Comparing Eq. 0 and 4, the thickness o sulayer δ is otained y: S π τ / ρgc ρ ( ρ ρ )H δ = 3µ q w p g g g (5) Thus, the heat transer coeicient h can e predicted y sustituting Eq. 5 into Eq. 3..9. Velocity o Vapor Blanket To determine the onset o CHF, it is needed to calculate the velocity o vapor lanket U which can e approximated as the superposition o the local liquid velocity at the radial position o δ+ / rom the wall and the relative vapor lanket velocity. Thereore, the velocity o the vapor lanket can e calculated rom Eq. 1 and 13, it is Eq. 6:.10. Critical Velocity or Oneset o CHF Figure 3 represents the low oiling coniguration o sucooled or low-quality low immediately just eore and occurrence o CHF. This phenomenon is called Helmholt instaility which causes a wavy motion o the sulayer-vapor lanket interace. Based on the concept o Helmholtz instaility as the relative velocity o the two streams, i.e., the liquid in the sulayer and the vapor in the vapor lanket, reaches a critical value, a wavy motion o the interace is induced. ue to the instaility nature, the amplitude o the wavy motion can e ampliied. The critical value will e evaluated ased on the ollowing assumptions: The length o the lanket changes suddenly to the Helmholtz critical wavelength when the vapor lanket velocity reaches the critical valueand the sulayer also adjust its thickness The vapor lanket touches the heated surace as result o the Helmholtz instaility, the dry patch persists and spreads very quickly, which induces a sudden rise in wall temperature CHF occurs when the rate o sulayer mass loss y evaporation exceeds the mass low rate o the liquid entering the sulayer rom the core region.11. Thickness o Sulayer Since CHF is postulated to occur as a result o Helmholtz instaility, the length o the sulayer and the vapor lanket are assumed to e equal to the Helmholtz critical wavelength L H, as shown in Fig. 3a, i.e Eq. 7: L πσ( ρ +ρ ) = a (7) ρ ρ g H g(uh U m) In which U H, is the critical velocity o the vapor lanket to onset o CHF, U m the liquid velocity in the sulayer. Since U H is always much higher than U m, the aove expression can e reduced to: L πσ( ρ +ρ ) = (8) ρ ρ g H guh 001

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 sulayer, G m the liquid mass lux lowing into the sulayer, can e express as Eq. 30: Gm = ρ (UH U m) ρ UH (30) Since H g = C p and in general, T sat = T m the second term in RHS o Eq. 9 can e neglected. Thereore, comining Eq. 8 through (30) gives δ H the thickness o the sulayer as Eq. 31: πσq ( ρ +ρ ) δ = (31) ρ ρ c g H 3 ghguh (a).1. Relative Velocity o Capor Blanket to Liquid Near the CHF condition, the relative velocity o the vapor lanket to local liquid U LH can e determined y a alance etween the uoyancy orce F B and the drag orce F Eq. 33 and 34: F + F = 0 (3) B Where: π FB = L H( ρ ρ g)g (33) 4 And: 1 π F = ρ CU LH (34) 4 In which C is the drag coeicient, can e evaluated through the Chan and Prince (1965) Eq. 35: () Fig. 3. The proposed sulayer dry out mechanism (a) Just eor CHF () Occurrence o CHF Since the occurrence o CHF is a result o local sulayer dry out, the minimum critical heat lux q c necessary to evaporate the mass lux in the sulayer (see Fig. 3a is: qclh = G mδ H[Hg + C p (Tsat T m)] (9) where, δ H is the thickness o the sulayer to onset o CHF, T m the temperature o the liquid entering the C 48µ = (35) ρ ULH Comining Eq. 8 and 3 through 35 gives the relative velocity o the vapor lanket: U πσ( ρ ρ ) g g LH = 1µ ρρguh.13. Critical Velocity o Vapor Blanket (36) The critical velocity o the vapor lanket is derived y the supersession o local liquid velocity at the radial position o δ H + / rom the wall and the lanket relative velocity U H which can e otained rom Eq. 1 and 36. it is Eq. 37: 00

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 g g H ( ρ + ρ ) πσqc g + τ 3 wρ τ ghguh w ρ ρ UH = 5.0ln 3.05 ρ µ πσ( ρ ρ ) g + 1µ ρ ρ U (37) Thus, the critical lanket velocity U H can e predicted y the numerical iteration. 3. RESULTS AN ISCUSSION 3.1. Veriication o Heat Transer Model By a regression analysis o 31 experimental data in the simulation o Light Water Reactors (LWRs) conditions (P = 6.9~15.5MPa), that is conducted y Lin et al. (1994), empirical constants a 1, a and a 3 are ound to e 0.50, 1.0 and.1, respectively, Fig. 4 provides a comparison o predicted and experimental heat transer coeicient or sucooled low oiling at high heat lux (0.6 CHF < q<chf). The predictions agree well with the experimental dataand the majority o data points all within the error and o 40%. Gungor and Winterton (1986) evaluated the various correlations or sucooled low oiling, y comparing with measured data, they reported that the correlations y Moles and Shaw (197); Shah (1977) and Gungor and Winterton (1986) are the est ones among others. Thereore, the aove mentioned three correlations are selected in the study o sucooled low oiling heat transer coeicients. The comparison o these correlations with the experimental data is in Tale 1. The correlations y Moles and Shaw (197) and Gungor and Winterton (1986) that perormed well with the high pressure (6.9MPa~15.5 MPa) oiling data give mean deviation o 3.7% (Moles and Shaw, 197) and 46.1% (Gungor and Winterton, 1986), this error is closed to the report or sucooled low iling data at the pressure rom 13. to0000.3 MPa. The correlation y Moles and Shaw present a etter agreement with the experimental data within average deviation o 3.9% and mean deviation o 3.7%. However, this correlation is derived y direct dimensionless analysisand no signiicant physical meanings. Since the present model is developed ased on the high heat lux mechanisms o vapor lanket and heat conduction in sulayer, it is superior to other correlations. 3.. Veriication o Steady-State CHF To veriy the trigger condition or onset o CHF, it is needed to examine the comparison etween the critical value U H and the vapor lanket velocity U as CHF occurs. Fig. 4. Comparison o the predicted heat transer coeicient with the experimental data at high heat lux Tale 1. The statistical results or predicting oiling heat transer coeicient y the various correlation Correlation Numer o points A(%) M(%) Gungor and Interton 31 45.4 46.1 Moles and Shaw 31 3.9 3.7 Shah 31 75.4 76.0 Present model 31 1.6 18.6 Thereore, an analysis o relation etween U H and U will e study ased on a total o 36 data points o sucooled and low-quality saturated low oiling water included in the taular CHF data o the USSR Academy o Sciences (Collier, 1981), at the conditions o P = 6.9 17.6MPa, G = 1000~5000 kg m s and α = 0.07. The analysis provided the Average eviation (A) o 5.3% and mean deviation o.8%. Thus, ased on the Helmholtz instaility at the sulayer-vapor lanket interace is the trigger condition or the onset o CHF as the lanket velocity reaches a critical value, this hypothesis is appropriate. 3.3. Veriication o Tr0061nsient CHF Lee and Lin (1993) conducted an experiment low transient CHF in the simulation o PWR at the linear mass low decay rate rom 0.1 to 30%/s. Figure 5 shows the variation o the inlow mass velocity and the wall temperature with the transient time at the low decay rate o 0.1%/s. The onset o CHF is determined at the exit o the test section while the wall temperature excursion occurred, since the arupt drop and the ollowed jump in wall temperature implies rewetting and dry out process o liquid ilm underneath the vapor lanket. 003

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 Fig. 5. The variation o the inlow mass velocity and the wall temperature with the transient time at the low decay rate o 0.1%/s Fig. 6. The variation o sulayer thickness and vapor lanket velocity with the transient time at the low decay rate o 0.1%/s 004

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 Fig. 7. The relation etween the transient time to CHF and the low decay rate Fig. 8. Comparison o the predicted time to CHF with the experimental data under simulating PWR low transient 005

Chien-Hsiung Lee et al. / Journal o Computer Science 8 (1) (01) 1996-007 Tale. The statistical results or predicting transient time to CHF y the various correlations Correlation No. o points A(%) M(%) EPRI-1 15-40.8-40.8 BandW- 15-1. 13.9 Lin, Lee and Pei 15-5.7-5.7 Present model 15-17.8 0.6 The experimental data will e compared with present model predictions. In present study, the predicted time to onset o CHF is determined as the lanket velocity is reached the critical velocity. Figure 6 show the variation a vapor lanket velocity and sulayer thickness with the transient time at the conditions o T in = 90 C, P = 15.5MPa, G initial = 3800 kg m sec and low decay rate =0.1%/. The CHF is occurred when U is equal to U H, it is worth to note that the thickness o sulayer is very near zero during the occurrence o CHF, this is a good evidence or sulayer dry out model. In Fig. 7, as the low decay rate increase rom 0.1-30%/s, it is shown that the experimental and the predicted transient time to CHF is decreased. Figure 8 provides a comparison o the predicted and measured time to ones o CHF. The prediction agrees well with the experimental dataand the majority o data points all within the error ank o 30% The well-known CHF correction o BandW- (Gellerstedy, 1969), EPR-1 (Fighetti and Reddy, 1983) and Lin et al. (1988a) are used to predict the onset o CHF in comparison with the present model. The comparison is shown in Tale. Only the BandW- correlation with 13.9% o mean deviation is etter than the prediction o present model. But the process rom oiling heat transer to the onset o CHF only can e demonstrated y the present model, this is why the present model is superior to the other correlations. 4. CONCLUSION A theoretical model ased on the Helmholtz instaility has een developed or the evaluation o heat transer perormance and occurrence o CHF in lowquality low oiling prolem. For prediction o the heat transer coeicient and the critical heat lux, the validity o the present model has een demonstrated y comparing with the existing experimental data and empirical corrections. However, it is worthy to note that the present model is developed ased on the low and heat transer mechanisms. Thereore, unlike most o the previous models, the present one is o more physical meanings. It is elieved that the present theoretical model is also useul to the analysis o the cooling technology related to the low oiling heat transer. 5. REFERENCES 1. Beyerlein, S.W., R.K. Cossman and H.J. Richter, 1985. Prediction o ule concentration proiles in vertical turulent twophase low. Int. J. Mul. Flow, 11: 69-641. OI: 10.1016/0301-93(85)90083-7. Bhat, A.M., J.S. Saini and R. Prakash, 1986. Role o macrolayer evaporation in pool oiling at high heat lux. Int. J. Heat Mass Trans., 9: 1953-1961. OI: 10.1016/0017-9310(86)90014-1 3. Bhat, A.M., R. Prakash and J.S. Saini, 1983. Heat transer in nucleate pool oiling at high heat lux. Int. J. Heat Mass Trans., 6: 833-840. OI: 10.1016/S0017-9310(83)80107-0 4. Celata, G.P., 1991. A review o recent experiments and predictions aspects o urnout at very high heat luxes. Proceedings o the International Journal Multiphase Flows Conerence, (IJMFC 91), pp: 31-40. 5. Chan, B.K.C. and R.G.H. Prince, 1965. istillation studies-viscous drag on a gas ule rising in a liquid. AIChE, J. 11: 176-19. OI: 10.100/aic.690110139 6. Chi-Liang, Y. and R.B. Mesler, 1977. A study o nucleate oiling near the peak heat lux through measurement o transient surace temperature. Int. J. Heat Mass Trans., 0: 87-840. OI: 10.1016/0017-9310(77)9011-0 7. Chinm, P., J.Y. Hwang and T.L. Lin, 1989. The mechanism o heat transer in transition oiling. Int. J. Heat Mass Trans., 3: 1337-1349. OI: 10.1016/0017-9310(89)90033-1 8. Cole, R. and W.R. Rohsenow, 1968. Correlation o ule departure diameters or oiling o saturated liquids. Proceedings o the Chemical Enginring Progress Symposym, (CEPS 68), pp: 11-13. 9. Collier, J.G., 1981. Convective Boiling and Condensation. nd Edn., McGraw-Hill, New York, ISBN-10: 0070117985, pp: 435. 10. ukler, A.E., M. Wicks and R.G. Cleveland, 1964. Frictional pressure drop in two-phase low: B. An approach through similarity analysis. AIChE J., 10: 38-51. OI: 10.100/aic.690100118 006

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