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Bo JIAO, Li-min QIU, Jun-liang LU, Zhi-hua GAN. Liquid film dryout model for predicting critical heat flux in annular two-phase flow[J]. Journal of Zhejiang University Science A, 2009, 10(3): 398~417.

@article{title="Liquid film dryout model for predicting critical heat flux in annular two-phase flow",

author="Bo JIAO, Li-min QIU, Jun-liang LU, Zhi-hua GAN",

journal="Journal of Zhejiang University Science A",

volume="10",

number="3",

pages="398~417",

year="2009",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.A0820322"

}

%0 Journal Article

%T Liquid film dryout model for predicting critical heat flux in annular two-phase flow

%A Bo JIAO

%A Li-min QIU

%A Jun-liang LU

%A Zhi-hua GAN

%J Journal of Zhejiang University SCIENCE A

%V 10

%N 3

%P 398~417

%@ 1673-565X

%D 2009

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.A0820322

TY - JOUR

T1 - Liquid film dryout model for predicting critical heat flux in annular two-phase flow

A1 - Bo JIAO

A1 - Li-min QIU

A1 - Jun-liang LU

A1 - Zhi-hua GAN

J0 - Journal of Zhejiang University Science A

VL - 10

IS - 3

SP - 398

EP - 417

%@ 1673-565X

Y1 - 2009

PB - Zhejiang University Press & Springer

ER -

DOI - 10.1631/jzus.A0820322

**Abstract: **Gas-liquid two-phase flow and heat transfer can be encountered in numerous fields, such as chemical engineering, refrigeration, nuclear power reactor, metallurgical industry, spaceflight. Its critical heat flux (CHF) is one of the most important factors for the system security of engineering applications. Since annular flow is the most common flow pattern in gas-liquid two-phase flow, predicting CHF of annular two-phase flow is more significant. Many studies have shown that the liquid film dryout model is successful for that prediction, and determining the following parameters will exert predominant effects on the accuracy of this model: onset of annular flow, inception criterion for droplets entrainment, entrainment fraction, droplets deposition and entrainment rates. The main theoretical results achieved on the above five parameters are reviewed; also, limitations in the existing studies and problems for further research are discussed.

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[1] Alexander, L.G., Coldren, C.L., 1951. Droplet transfer from suspending air to duct walls. *Industrial & Engineering Chemistry*, **43**:1325-1331.

[2] Andreussi, P., 1983. Droplet transfer in two-phase annular flow. *International Journal of Multiphase Flow*, **9**(6):697-713.

[3] Andreussi, P., Azzopardi, B.J., 1983. Droplet deposition and interchange in annular two-phase flow. *International Journal of Multiphase Flow*, **9**(6):681-695.

[4] Armand, A.A., 1964. Resistance with motion of a two-phase system along horizontal tubes. *Izv. Vses. Teplotekh. Inst*., **1**:16-23.

[5] Asali, J.C., 1984. Entrainment in Vertical Gas-liquid Annular Flow. PhD Thesis, University of Illinois.

[6] Asali, J.C., Hanratty, T.J., Andreussi, P., 1985. Interfacial drag and film height for vertical annular flow. *AIChE Journal*, **31**(6):895-902.

[7] Azzopardi, B.J., 1997. Drops in annular two-phase flow. *International Journal of Multiphase Flow*, **23**(7):1-53.

[8] Azzopardi, B.J., Whalley, P.B., 1980. Artificial Waves in Annular Two-phase Flow ASME Winter Annual Meeting. Published in Basic Mechanisms in Two-phase Flow and Heat Transfer, Chicago, p.1-8.

[9] Azzopardi, B.J., Taylor, S., Gibbons, D.B., 1983. Annular Two Phase Flow in a Large Diameter Tube. International Conference on the Physical Modeling of Multi-phase Flow, Coventry, p.267-282.

[10] Bai, B.F., Huang, R., Guo, L.J., Xiao, Z.J., 2003. Physical model of critical heat flux with annular flow in annulus tubes. *Journal of Engineering Thermophysics*, **24**(2):251-254 (in Chinese).

[11] Bennett, A.W., 1969. Measurement of Liquid Film Flow Rates at 1000 Pisa in Upward Steam Water Flow in a Vertical Heated Tube. AERE-R-5809, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[12] Bennett, A.W., Hewitt, G.F., Kearsey, H.A., Keeys, R.K.F., Pulling, D.J., 1966. Studies of Burnout in Boiling Heat Transfer to Water in Round Tubes with Non-uniform Heating. AERE-R-5076, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[13] Brown, D.J., 1978. Disequilibrium Annular Flow. PhD Thesis, University of Oxford.

[14] Brown, D.J., Jensen, A., Whalley, P.B., 1975. Non-equilibrium Effects in Heated and Unheated Annular Two Phase Flow. ASME Paper No. 75-WA/HT-7.

[15] Celata, G.P., Mishima, K., Zummo, G., 2001. Critical heat flux prediction for saturated flow boiling of water in vertical tubes. *International Journal of Heat and Mass Transfer*, **44**(22):4323-4331.

[16] Collier, J.G., 1972. Convective Boiling and Condensation. McGraw-Hill, New York.

[17] Collier, J.G., Hewitt, G.F., 1961. Data on the vertical flow of air-water mixtures in the annular and dispersed flow regions, Part II: film thickness and entrainment data and analysis of pressure drop measurements. *Transactions of the Institution of Chemical Engineers*, **39**:127-144.

[18] Cousins, L.B., Hewitt, G.F., 1968a. Liquid Phase Mass Transfer in Annular Two-phase Flow: Droplet Deposition and Liquid Entrainment. AERE-R-5657, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[19] Cousins, L.B., Hewitt, G.F., 1968b. Liquid Phase Mass Transfer in Annular Two-phase Flow: Radial Liquid Mixing. AERE-R-5693, United Kingdom Atomic Energy Authority. Reactor Group. Atomic Energy Establishment, England.

[20] Cousins, L.B., Denton, W.H., Hewitt, G.F., 1965. Liquid Mass Transfer in Annular Two-phase Flow. Proceedings of Symposium on Two-phase Flow, Exeter, UK, Paper C4.

[21] Dallman, J.C., Jones, B.G., Hanratty, T.J., 1979. Interpretation of Entrainment Measurements in Annular Gas-liquid Flow, Two-phase Momentum Heat and Mass Transfer. Hemisphere, Washington DC, p.681-693.

[22] Dykhno, L.A., Hanratty, T.J., 1996. Use of the interchange model to predict entrainment in vertical annular flow. *Chemical Engineering Communications*, **141-142**:207-235.

[23] Fan, P., Qiu, S.Z., Jia, D.N., 2006. An investigation of flow characteristics and critical heat flux in vertical upward round tube. *Nuclear Science and Techniques*, **17**(3):170-176.

[24] Gill, L.E., Hewitt, G.F., Hitchon, J.W., Lacey, P.M.C., 1962. Sampling Probe Studies of the Gas Core in Annular Two-phase Flow: Part 1: the Effect of Length on Phase and Velocity Distribution. AERE-R-3954, United Kingdom Atomic Energy Authority. Reactor Group. Atomic Energy Establishment, England.

[25] Gill, L.E., Hewitt, G.F., Lacey, P.M.C., 1964. Sampling probe studies of the gas core in annular two-phase flow: II, studies of the effect of phase flowrates on phase and velocity distributions. *Chemical Engineering Science*, **19**(9):665-682.

[26] Gill, L.E., Hewitt, G.F., Roberts, D.N., 1969. Studies of the Behaviour of Disturbance Waves in a Long Vertical Tube. AERE-R-6012, United Kingdom Atomic Energy Authority. Reactor Group. Atomic Energy Establishment, England.

[27] Govan, A.H., 1988. Phenomenological Prediction of Critical Heat Flux. Proceeding of the 2nd UK National Heat Transfer Conference, p.315-326.

[28] Govan, A.H., Hewitt, G.F., Owen, D.G., Bott, T.R., 1988. An Improved CHF Modeling Code. Proceeding of the 2nd UK National Heat Transfer Conference, p.33-48.

[29] Hanratty, T.J., Woods, B.D., Iliopoulos, I., Pan, L., 2000. The roles of interfacial stability and particle dynamics in multiphase flows: a personal viewpoint. *International Journal of Multiphase Flow*, **26**(2):169-190.

[30] Hay, K.J., Liu, Z.C., Hanratty, T.J., 1996. Relation of deposition to drop size when the rate law is nonlinear. *International Journal of Multiphase Flow*, **22**(5):829-848.

[31] Hewitt, G.F., Pulling, D.J., 1969. Liquid Entrainment in Adiabatic Steam-water Flow. AERE-R-5374, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[32] Hewitt, G.F., Hall-Taylor, N.S., 1970. Annular Two-phase Flow. Pergamon Press, Oxford.

[33] Hewitt, G.F., Govan, A.H., 1990. Phenomenological modeling of non-equilibrium flows with phase change. *International Journal of Heat and Mass Transfer*, **33**(2):229-242.

[34] Hewitt, G.F., Kearsey, H.A., Keeys, R.K.F., 1969. Determination of Rate of Deposition of Droplets in a Heated Tube with Steam-water Flow at 1000 Psia. AERE-R-6118, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[35] Hujghe, J., Mondin, H., 1961. Transfert de chaleur par melange de liquide et de gas en convection force turbulente aves faible vaporisation de la phase liquide. *C. R. Hebd. Seanc. Acad. Sci. Paris*, **253**:395-397.

[36] Hutchinson, P., Whalley, P.B., 1973. A possible characterisation of entrainment in annular flow. *Chemical Engineering Science*, **28**(3):974-975.

[37] Ishii, M., Grolmes, M.A., 1975. Inception criteria for droplet entrainment in two-phase concurrent film flow. *AIChE Journal*, **21**(2):308-318.

[38] Ishii, M., Mishima, K., 1981. Correlation for Liquid Entrainment in Annular Two-phase Flow of Low Viscous Fluid. ANL RAS LWR 81-2, Argonne National Laboratory.

[39] Ishii, M., Mishima, K., 1989. Droplet entrainment correlation in annular two-phase flow. *International Journal of Heat and Mass Transfer*, **32**(10):1835-1846.

[40] Jepson, D.M., 1992. Vertical Annular Flow: the Effect of Physical Properties. PhD Thesis, University of Oxford.

[41] Kataoka, I., Ishii, M., Nakayama, A., 2000. Entrainment and deposition rates of droplets in annular two-phase flow. *International Journal of Heat and Mass Transfer*, **43**(9):1573-1589.

[42] Katto, Y., 1984. Prediction of critical heat flux for annular flow in tubes taking into account the critical liquid film thickness concept. *International Journal of Heat and Mass Transfer*, **27**(6):883-891.

[43] Keeys, R.F.K., 1970. The Effect of Heat Flux on Liquid Entrainment in Steam-water Flow in a Vertical Tube at 1000 Pisa. AERE-R-6294, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[44] Keeys, R.F.K., Ralph, J.C., Roberts, D.N., 1970. Liquid Entrainment in Adiabatic Steam-water Flow at 500 and 1000 Psia. AERE-R-6293, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[45] Lee, D.H., 1965. An Experimental Investigation of Forced Convection Burnout in High Pressure Water: Part 3 Long Tubes with Uniform and Non-uniform Axial Heating. AEEW-R355.

[46] Lee, D.H., Obertelli, J.D., 1963. An Experimental Investigation of Forced Convection Burnout in High Pressure Water: Part 2 Preliminary Results for Round Tubes with Non-uniform Axial Heat Flux Distribution. AEEW-R309.

[47] Lee, K.W., Baik, S.J., Ro, T.S., 2000. An utilization of liquid sublayer dryout mechanism in predicting critical heat flux under low pressure and low velocity conditions in round tubes. *Nuclear Engineering and Design*, **200**(1-2):69-81.

[48] Leman, G.W., 1983. Effects of Liquid Viscosity in Two-Phase Annular Flow. PhD Thesis, University of Illinois.

[49] Lopez de Bertodano, M.A., Jan, C.S., Beus, S.G., 1997. Annular flow entrainment rate experiment in a small vertical pipe. *Nuclear Engineering and Design*, **178**(1-2):61-70.

[50] Magiros, P.G., Dukler, A.E., 1961. Entrainment and Pressure Drop in Concurrent Gas-liquid Flow. Proceedings of the 7th Midwestern Mechanics Conference, p.532-553.

[51] Mingh, T.Q., 1965. Some Hydrodynamic Aspects of Annular Dispersed Flow, Entrainment and Film Thickness. Two-phase Flow Symposium, Exeter, UK, Paper C2.

[52] Mishima, K., Ishii, M., 1984. Flow regime transition criteria for upward two-phase flow in vertical tubes. *International Journal of Heat and Mass Transfer*, **27**(5):723-737.

[53] Namie, S., Ueda, T., 1972. Droplet transfer in two-phase annular mist flow (PART 1 experiment of droplet transfer rate and distributions of droplet concentration and velocity). *Bulletin JSME*, **15**:1568-1580.

[54] Namie, S., Ueda, T., 1973. Droplet transfer in two-phase annular mist flow (PART 2 prediction of droplet transfer rate). *Bulletin JSME*, **16**:752-764.

[55] Nigmatulin, B.I., Malyshenko, V.I., Shugaev, Y.Z., 1976. Investigation of liquid distribution between the core and the film in annular dispersed flow of steam-water mixture. *Teploenergetika*, **23**(5):66-68.

[56] Okawa, T., Kataoka, I., 2005. Correlations for the mass transfer rate of droplets in vertical upward annular flow. *International Journal of Heat and Mass Transfer*, **48**(23-24):4766-4778.

[57] Okawa, T., Kitahara, T., Yoshida, K., Matsumoto, T., Kataoka, I., 2002. New entrainment rate correlation in annular two-phase flow applicable to wide range of flow condition. *International Journal of Heat and Mass Transfer*, **45**(1):87-98.

[58] Okawa, T., Kotani, A., Kataoka, I., Naito, M., 2003. Prediction of critical heat flux in annular flow using a film flow model. *Journal of Nuclear Science and Technology*, **40**(6):388-396.

[59] Okawa, T., Kotani, A., Kataoka, I., 2004a. Experiments for Equilibrium Entrainment Fraction in a Small Vertical Tube. Proceedings of the 5th International Conference Multiphase Flow, Yokohama, Paper 224.

[60] Okawa, T., Kotani, A., Kataoka, I., Naitoh, M., 2004b. Prediction of the critical heat flux in annular regime in various vertical channels. *Nuclear Engineering and Design*, **229**(2-3):223-236.

[61] Okawa, T., Kotani, A., Kataoka, I., 2005. Experiments for liquid phase mass transfer rate in annular regime for a small vertical tube. *International Journal of Heat and Mass Transfer*, **48**(3-4):585-598.

[62] Olson, R.M., Eckert, E.R.G., 1966. Experimental studies of turbulent flow in a porous circular tube with uniform fluid injection through the tube wall. *Transactions of the ASME Journal of Applied Mechanics*, **33**(4):7-17.

[63] Owen, D.G., Hewitt, G.F., 1986. A Proposed Entrainment Correlation. AERE-R-12279, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[64] Owen, D.G., Hewitt, G.F., 1987. An Improved Annular Two-Phase Flow Model. Proceedings of the 3rd International Conference on Multiphase Flow, the Hague, the Netherlands.

[65] Owen, D.G., Hewitt, G.F., Bott, T.R., 1985. Equilibrium annular flows at high mass fluxes data and interpretation. *PCH Physicochemical Hydrodynamics*, **6**:115-131.

[66] Paleev, I.I., Agafonova, F.A., 1962. Heat Transfer between a Hot Surface and a Gas Flow Entraining Drops of Evaporating Liquid. Proceedings of the 1st All-Union Heat and Mass Transfer Conference, Minsk, p.260-268.

[67] Paleev, I.I., Filippovich, B.S., 1966. Phenomena of liquid transfer in two-phase dispersed annular flow. *International Journal of Heat and Mass Transfer*, **9**(10):1089-1093.

[68] Pan, L., Hanratty, T.J., 2002. Correlation of entrainment for annular flow in vertical pipes. *International Journal of Multiphase Flow*, **28**(3):363-384.

[69] Peng, S.W., 2008. Heat flux effect on the droplet entrainment and deposition in annular flow dryout. *Communications in Nonlinear Science and Numerical Simulation*, **13**(10):2223-2235.

[70] Rossum, J.J.V., 1951. Experimental investigation of horizontal liquid films: wave formation, atomization, film thickness. *Chemical Engineering Science*, **11**(2):35-52.

[71] Saito, T., Hughes, E.D., Carbon, M.W., 1978. Multi-fluid modeling of annular two-phase flow. *Nuclear Engineering and Design*, **50**(2):225-271.

[72] Schadel, S.A., Leman, G.W., Binder, J.L., Hanratty, T.J., 1990. Rates of atomization and deposition in vertical annular flow. *International Journal of Multiphase Flow*, **16**(3):363-374.

[73] Singh, K., Pierre, C.C.S., Crago, W.A., Moeck, E.O., 1969. Liquid film flowrates in two-phase flow of steam and water at 1000 psia. *AIChE Journal*, **15**(1):51-56.

[74] Steen, D.A., Wallis, G.B., 1964. The Transition from Annular to Annular Mist Concurrent Two Phase Down Flow. AEC Report NYO-3114-2.

[75] Sugawara, S., 1990. Droplet deposition and entrainment modeling based on the three-fluid model. *Nuclear Engineering and Design*, **122**(1-3):67-84.

[76] Ueda, T., 1979a. Droplet entrainment rate and droplet diameter in annular two-phase flow. *Bulletin JSME*, **45**:127-135.

[77] Ueda, T., 1979b. Entrainment rate and size distribution of entrained droplets in annular two-phase flow. *Bulletin JSME*, **22**:1258-1265.

[78] Ueda, T., Inoue, M., Nagatome, S., 1981. Critical heat flux and droplet entrainment rate in boiling of falling liquid films. *International Journal of Heat and Mass Transfer*, **24**(7):1257-1266.

[79] Utsuno, H., Kaminaga, F., 1998. Prediction of liquid film dryout in two-phase annular-mist flow in a uniformly heated narrow tube development of analytical method under BWR conditions. *Journal of Nuclear Science and Technology*, **35**(9):643-653.

[80] Wallis, G.B., 1961. Flooding Velocities for Air and Water Vertical Tubes. AEEW-R-123, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[81] Wallis, G.B., 1969. One-dimensional Two-phase Flow. McGraw-Hill, New York.

[82] Whalley, P.B., 1977. The calculation of dryout in a rod bundle. *International Journal of Multiphase Flow*, **3**(6):501-515.

[83] Whalley, P.B., Jepson, D.M., 1994. Entrainment and Deposi tion in Annular Gas-liquid Flow: the Effect of Fluid Physical Properties. Proceedings of the 10th International Heat Transfer Conference, Brighton, UK, p.289-294.

[84] Whalley, P.B., Hewitt, G.F., Hutchinson, P., 1973. Experimental Wave and Entrainment Measurements in Vertical Annular Two-phase Flow. AERE-R-7521, United Kingdom Atomic Energy Authority, Reactor Group, Atomic Energy Establishment, England.

[85] Whalley, P.B., Hutchinson, P., Hewitt, G.F., 1974. Calculation of Critical Heat Flux in Forced Convection Boiling. Proceedings of the 5th International Heat Transfer Conference, Tokyo, Japan, p.290-294.

[86] Wicks, M., Dukler, A.E., 1960. Entrainment and pressure drop in concurrent gas-liquid flow: air water in horizontal flow. *AIChE Journal*, **6**(3):463-468.

[87] Willetts, I.P., 1987. Non-aqueous Annular Two-phase Flow. PhD Thesis, University of Oxford.

[88] Woodmansee, D.E., Hanratty, T.J., 1969. Mechanism for the removal of droplets from a liquid surface by a parallel air flow. *Chemical Engineering Science*, **24**(2):299-307.

[89] Wurtz, J., 1978a. Entrainment in Annular Steam-water Flow. European Two-phase Flow Group Meeting, Stockholm, Paper A4.

[90] Wurtz, J., 1978b. An experimental and Theoretical Investigation of Annular Steam-water Flow in Tubes and Annuli at 30 to 90 bar. Riso Report No. 372, Riso National Laboratory.

[91] Yanai, M., 1971. Study on Boiling Heat Transfer in a Flow Channel. PhD Thesis, Kyoto University.

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