# Modeling of liquid film flow in annuli

### Abstract

One of the challenges in thermal-hydraulic analyses of BWRs is correct prediction of dryout occurrence in fuel assemblies. In practical applications the critical powers in fuel assemblies are found from correlations that are based on experimental data. The drawback of this approach is that correlations are valid only for these fuel assemblies on which the experiments have been conducted. Other restrictive factors are the limited ranges of experimental working conditions including pressure, mass flux and axial power distributions. To overcome the above-mentioned limitations, several different approaches have been proposed to predict the dryout occurrence. One of them is to employ a phenomenological model of annular flow, in which the mass transfer between the liquid film and the gas core is based on entrainment and deposition correlations. Most of these correlations are derived from water-air flows in vertical tubes and their applicability to other geometries in general, and rod-bundles in particular, should be analysed. This paper presents an analysis of the entrainment rate in vertical annuli. Using the standard approach to calculate the entrainment rate, one can demonstrate that the results deviate from measurements. It has been shown that modifying the entrainment correlation based on data obtained in the annulus geometry leads to an essential improvement in the predictive capability of the phenomenological model of annular two-phase flow.### References

[1] Adamsson C., Anglart H.: Film flow measurements for high-pressure diabatic annular flow in tubes with various axial power distributions. Nucl. Eng. Des. 236, 2006, pp. 2485-2493.

[2] Andersen P.S., Würtz J.: Adiabatic Steam-Water Annular Flow in an Annular Geometry. Int. J. Multiphase Flow 7, 1981, pp. 235-239.

[3] Anghel I.G., Anglart H.: Post-dryout heat transfer to high-pressure water flowing upward in vertical channels with various flow obstacles. Int. J. Heat Mass Trans. 55, 2012, pp. 8020-8031.

[4] Anglart H., Persson P.: Adiabatic Steam-Water Annular Flow in an Annular Geometry. Int. J. Multiphase Flow 7, 2007, pp. 235-239.

[5] Becker K., Letzter A.: An Experimental Study of the Effect of the Axial Flux Distribution on the Burnout Conditions in a 3650 mm Long Annulus. KTH-NEL-21, Stockholm, Sweden, 1974.

[6] Becker K., Letzter A.: Burnout Measurements for Flow of Water in an Annulus with Two-Sided Heating. KTH-NEL-23, Stockholm, Sweden, 1976.

[7] Behamin D., Persson P., Hedberg S., Blomstrand J.: Loop Studies Simulating – in Annular Geometry – the Influence of the Axial Power Distribution and the Number of Spacers in 8x8 BWR Assemblies. Proc. Two-Phase Flow Group Meeting, Karlsruhe, Germany, 1999.

[8] Bennett A.W., Hewitt G.F., Kearsey H.A., Keeys R.K.F., Pulling D.J.: Studies of Burnout in Boiling Heat Transfer to Water in Round Tubes with Non-Uniform Heating. AERE-R5076, 1966.

[9] Lopez de Bertodano M.A., Assad A.: Entrainment Rate of Droplets in the Ripple-Annular Regime for Small Vertical Ducts. Nucl. Sci. Eng. 129, 1998.

[10] Govan A.H., Hewitt G.F., Owen D.G., Bott T.R.: An Improved CHF Modelling Code. 2nd UK National Heat Transfer Conference, Glasgow, UK, 1988.

[11] Hewitt G.F., Govan A.H.: Phenomenological Modelling of Non-equilibrium Flow With Phase Change. Int. J. Heat Mass Transfer 33(2), pp. 229-242, 1990.

[12] Kataoka I., Ishii M.: Mechanism and Correlation of Droplet Entrainment and Deposition in Annilar Two-Phase Flow. NUREG/CR-2885, ANL-82-44, Argonne National Laboratory, 1982.

[13] Mannov G.: Film Flow Measurements in Concentric Annulus 3500x27.2x17 mm with Heated and Unheated Rod. SDS-65, Danish Atomic Energy Commission, Risö, Denmark, 1973.

[14] Milashenko V.I., Nigmatulin B.I., Petukhov V.V., Trubkin N.I.: Burnout and Distribution of Liquid in Evaporative Channels of Various Lengths, Int. J. Multiphase Flow 15(3), pp. 393-401, 1989.

[15] Moeck E.O.: Annular-Dispersed Two-Phase Flow and Critical Heat Flux. AECL-3656, 1970.

[16] Nigmatulin B.I.: Investigation of Two-Phase Annular Dispersed Flows in Heated Tubes. Appl. Mech. Tech. Phys. 4, pp. 78-88, 1973.

[17] Nigmatulin R.I., Nigmatulin B.I., Khodzhaev Ya.D., Kroshilin V.E.: Entrainment and Deposition Rates in a Dispersed-Film Flow. Int. J. Multiphase Flow 22(1), pp. 19-30, 1996.

[18] Okawa T., Kotani A., Kataoka I., Naito M.: Prediction of Critical Heat Flux in Annular Flow Using a Film Flow Model. J. Nucl. Sci. Techn. 40(6), 2003.

[19] Sugawara S. Miyamoto Y.: FIDAS: Detailed Subchannel Analysis Code Based on the Three-Fluid and Three-Field Model. Nucl. Eng. Des. 120, pp. 147-161, 1990.

[20] Whalley P.B., Hutchinson P., Hewitt G.F.: The Calculation of Dryout in Forced Convection Boiling, Fifth International Heat Transfer Conference. Paper B6.11, Tokyo, Japan,1974.

[21] Whalley P.B., Hutchinson P., Hewitt G.F.: Prediction of Annular Flow parameters for Transient Conditions and for Complex Geometries. European Two-Phase Flow Group Meeting, Haifa, Israel, 1975.

[22] Whalley P.B.: The Calculation of Dryout in a Rod Bundle. AERE-R 8319, Harwell, U.K, 1976.

[23] Whalley P.B., Hutchinson P.: Comments on “Adiabatic steam-water annular flow in an Annular Geometry” by P.S. Andersen and J. Würtz, Int. J. Multiphase Flow 7, pp. 241-243, 1981.

[2] Andersen P.S., Würtz J.: Adiabatic Steam-Water Annular Flow in an Annular Geometry. Int. J. Multiphase Flow 7, 1981, pp. 235-239.

[3] Anghel I.G., Anglart H.: Post-dryout heat transfer to high-pressure water flowing upward in vertical channels with various flow obstacles. Int. J. Heat Mass Trans. 55, 2012, pp. 8020-8031.

[4] Anglart H., Persson P.: Adiabatic Steam-Water Annular Flow in an Annular Geometry. Int. J. Multiphase Flow 7, 2007, pp. 235-239.

[5] Becker K., Letzter A.: An Experimental Study of the Effect of the Axial Flux Distribution on the Burnout Conditions in a 3650 mm Long Annulus. KTH-NEL-21, Stockholm, Sweden, 1974.

[6] Becker K., Letzter A.: Burnout Measurements for Flow of Water in an Annulus with Two-Sided Heating. KTH-NEL-23, Stockholm, Sweden, 1976.

[7] Behamin D., Persson P., Hedberg S., Blomstrand J.: Loop Studies Simulating – in Annular Geometry – the Influence of the Axial Power Distribution and the Number of Spacers in 8x8 BWR Assemblies. Proc. Two-Phase Flow Group Meeting, Karlsruhe, Germany, 1999.

[8] Bennett A.W., Hewitt G.F., Kearsey H.A., Keeys R.K.F., Pulling D.J.: Studies of Burnout in Boiling Heat Transfer to Water in Round Tubes with Non-Uniform Heating. AERE-R5076, 1966.

[9] Lopez de Bertodano M.A., Assad A.: Entrainment Rate of Droplets in the Ripple-Annular Regime for Small Vertical Ducts. Nucl. Sci. Eng. 129, 1998.

[10] Govan A.H., Hewitt G.F., Owen D.G., Bott T.R.: An Improved CHF Modelling Code. 2nd UK National Heat Transfer Conference, Glasgow, UK, 1988.

[11] Hewitt G.F., Govan A.H.: Phenomenological Modelling of Non-equilibrium Flow With Phase Change. Int. J. Heat Mass Transfer 33(2), pp. 229-242, 1990.

[12] Kataoka I., Ishii M.: Mechanism and Correlation of Droplet Entrainment and Deposition in Annilar Two-Phase Flow. NUREG/CR-2885, ANL-82-44, Argonne National Laboratory, 1982.

[13] Mannov G.: Film Flow Measurements in Concentric Annulus 3500x27.2x17 mm with Heated and Unheated Rod. SDS-65, Danish Atomic Energy Commission, Risö, Denmark, 1973.

[14] Milashenko V.I., Nigmatulin B.I., Petukhov V.V., Trubkin N.I.: Burnout and Distribution of Liquid in Evaporative Channels of Various Lengths, Int. J. Multiphase Flow 15(3), pp. 393-401, 1989.

[15] Moeck E.O.: Annular-Dispersed Two-Phase Flow and Critical Heat Flux. AECL-3656, 1970.

[16] Nigmatulin B.I.: Investigation of Two-Phase Annular Dispersed Flows in Heated Tubes. Appl. Mech. Tech. Phys. 4, pp. 78-88, 1973.

[17] Nigmatulin R.I., Nigmatulin B.I., Khodzhaev Ya.D., Kroshilin V.E.: Entrainment and Deposition Rates in a Dispersed-Film Flow. Int. J. Multiphase Flow 22(1), pp. 19-30, 1996.

[18] Okawa T., Kotani A., Kataoka I., Naito M.: Prediction of Critical Heat Flux in Annular Flow Using a Film Flow Model. J. Nucl. Sci. Techn. 40(6), 2003.

[19] Sugawara S. Miyamoto Y.: FIDAS: Detailed Subchannel Analysis Code Based on the Three-Fluid and Three-Field Model. Nucl. Eng. Des. 120, pp. 147-161, 1990.

[20] Whalley P.B., Hutchinson P., Hewitt G.F.: The Calculation of Dryout in Forced Convection Boiling, Fifth International Heat Transfer Conference. Paper B6.11, Tokyo, Japan,1974.

[21] Whalley P.B., Hutchinson P., Hewitt G.F.: Prediction of Annular Flow parameters for Transient Conditions and for Complex Geometries. European Two-Phase Flow Group Meeting, Haifa, Israel, 1975.

[22] Whalley P.B.: The Calculation of Dryout in a Rod Bundle. AERE-R 8319, Harwell, U.K, 1976.

[23] Whalley P.B., Hutchinson P.: Comments on “Adiabatic steam-water annular flow in an Annular Geometry” by P.S. Andersen and J. Würtz, Int. J. Multiphase Flow 7, pp. 241-243, 1981.

Published

2015-01-01

How to Cite

ANGLART, Henryk.
Modeling of liquid film flow in annuli.

**Journal of Power Technologies**, [S.l.], v. 94, n. 5, p. 8--15, jan. 2015. ISSN 2083-4195. Available at: <https://papers.itc.pw.edu.pl/index.php/JPT/article/view/587>. Date accessed: 01 aug. 2021.
Section

Nuclear Power

### Keywords

Entrainment rate; Annular flow; Dryout; Annular geometry; BWR

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