The methodology is described and the results are presented concerning numerical modeling of COPO II Lo experiments on heat transfer in liquid with internal heat generation at very high internal Rayleigh numbers typical for natural convection in a core melt that can appear during progress of severe accident at a nuclear power plant (NPP). The work is keeping in the course of development of CFD-based tool for quantitative analysis of heat transfer in a stratified molten pool of different configurations possible in severe accident scenarios with melt retention in the reactor vessel or in the VVER core catcher. Such CFD methodology would be used for testing of simplified correlation models for simulation of the core melt interaction with NPP structures in system code SOCRAT. During verification the available experimental data on the core melt thermohydraulics were analyzed, and it was concluded that they are insufficient to measures of CFD quality. The data uncertainties, along with the complexities of convective flow, uncertainties of the reactor core melt conditions, limitations of experimental possibilities and of turbulence modeling, actually constrain the multivariate CFD simulations of natural convection at very high Rayleigh numbers. RANS turbulence models only can be efficiently applied here, and they are to be checked for such purposes. In a series of numerical modeling of COPO II Lo experiments and some others, availability of a k-ɛ realizable model with included buoyancy effects was estimated, and the optimal set of CFD options was formed for minimizing numerical artifacts. It was demonstrated that in the investigated range of Rayleigh numbers the k-ɛ model works qualitatively correctly, but is inclined to systematical deformation of the melt boundary heat transfer distribution. This allows one to use this model for qualitative multivariate CFD estimations but requires improvement of the model or finding of its efficient and more exact equivalent.
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Bolshov, L.A., Kondratenko, P.S., and Strizhov, V.F., Free Convection of Free Generating Liquid, UFN, 2001, vol. 171, no. 10, pp. 1051–1070.
Helle, M., Kymalainen, O., and Pessa, E., COPO II-Lo Experiments, IVO Power Engineering LTD, YDINGT1-43, 1997, Transmitted in the frame of the MVI Project, 4th PCRD of the European Community.
Helle, M., Kymalainen, O., and Tuomisto, H., Experimental Data on Heat Flux Distribution from a Volumetrically Heated Pool with Frozen Boundaries, OECD/CSNI Workshop on In-Vessel Core Debris Retention and Coolability, Garching, Germany, March 3–6, 1998.
Bonnet, J.M. and Seiler, J.M., Thermal Hydraulic Phenomena in Corium Pools: The BALI Experiment, ICONE-7, Tokyo, April 19–23, 1999, paper-7057.
Main Results of the First Phase of MASCA Project, OECD MASCA Project, RRC “Kurchatov Institute,” May 2004.
Kukhtevich, I.V., Bezlepkin, V.V., Granovskii, V.S., Khabenskii, V.B., Asmolov, V.G., Beshta, S.V., Sidorov, A.S., Berkovich, V.M., Strizhov, V.F., Khua, M., Rogov, M.F., and Novak, V.P., The Concept of Molten Corium Localization at the Ex-Vessel Stage of BDB Accident of NPP with VVER-1000, Nauchnoprakticheskii seminar “Voprosy besopasnosti AES s VVER” (Scientific-Practical Seminar on Problems of Safety of Nuclear Plants with VVER), St. Petersburg, 2000.
Alvarez, P., Malterre, J., and Seiler, M., Natural Convection in Volume Heated Liquid Pools-the BAFOND Experiments: Proposals for New Correlations, in Science and Technology of Fast Reactor Safety, London: BNES, 1986.
Filippov, A.S., Numerical Simulation of the Experiments on Turbulent Natural Convection at Cylindrical Pool of Heat Generating Liquid, J. Eng. Therm., 2011, no. 1, pp. 1–13.
Fluent 6.2 User Guide, Fluent Inc., Lebanon, NH USA, 2005.
Filippov, A.S., Numerical Simulation of Experiments of Liquid Heat Transfer with Volumetric Heat Generation (Code Fluent), Trudy 4-oi Rossiiskoi natsionalnoi konferentsii po teplomassoobmenu (Proc. 4th Russian National Conf. on Heat and Mass Transfer (RNCT-IV)), Moscow: MPEI, 2006.
Grigoruk, D.D., Strizhof, V.F., and Filippov, A.S., A Numerical Investigation of Heat Transfer of Stratified Melt with Volumetric Heat Release in the Bottom Layer, High Temp., 2008, vol. 46, no. 3, pp. 386–393.
Filippov, A.S., Strizhov, V.Th., and Tarasov, O.V., Molten Pool Models Validation and Cross-Verification: CFD&SOCRAT Code, 17th Int. Conf. on Nucl. Eng., ICONE17, Brussels, 2009.
Grigoruk, D.G., Kondratenko, P.S., and Nikolskii, D.V., Numerical Simulation of Free Convention of Heat Generating Liquid in an Axially Symmetric Closed Volume, Inzh.-Fiz. Zh., 2008, vol. 81, no. 2, pp. 280–289.
Abalin, S., Gmidoi, I., Semenov, V., Surenkov, A., and Strizhov, V., The Results and Analysis of the RASPLAV Salt Tests, Proc. RASPLAV Seminar, Garching, Germany, 2000.
Bolshov, L.I. and Strizhov, V.F., SOCRAT-The System of Codes for Realistic Analysis of Severe Accidents, Proc. ICAPP’06 Reno, NVUSA, 2006, paper 6439.
Computer Code Manuals, Reference Manual, vers. 2.1, NUREG/CR-6119, vol. 2, rev. 4, SAND2008-xxxx, Sandia National Laboratories, Albuquerque, NM, September 2008.
Guillard, G., Pignet, S., Jacq, F., Majumdar, P., and Siméone, A., ASTEC V1 Code: DIVA Physical Modeling, rev. 1, Note Technique SEMCA-2007-316, Kadarash, France, October 2007.
Filippov, A.S., Drobyshevsky, N.I., Kisselev, A.E., Strizhov, V.F., and Fokin, A.L., SOCRAT/HEFEST Code: Models of VVER Core Melt Interaction with Reactor Structures under Severe Accident Conditions, Izv. RAN, Energet., 2010, no. 3, pp. 4–24.
Ozrin, V., Tarasov, O., Strizhov, V., and Filippov, A., AModel for Calculating Composition and Density of the Core Melt in the Water-Moderated Water-Cooled Reactor in Case of Severe Accident, Thermal Eng., 2010, vol. 57, no. 13, pp. 1099–1111.
Filippov, A.S., Mosunova, N.A., and Strizhov, V.F., Modeling of Melt Behavior in VVER Vessel Using SOCRAT/HEFEST Code, Izv. RAN, Energet., 2010, no. 3, pp. 43–82.
Tran, C.T., Kudinov, P., and Dinh, T.N., An Approach to Numerical Simulation and Analysis of Molten Corium Coolability in a Boiling Water Reactor Lower Head, Nucl. Eng. Design, 2010, vol. 240, pp. 2148–2159.
Theofanous, T.G., Liu, C., Additon, S., Angelini, S., Kymiliinen, O., and Salmassi, T., In-Vessel Coolability and Retention of a Core Melt, Nucl. Eng. Design, 1997, vol. 169.
Grigoruk, D.G. and Kondratenko, P.S., Heat Transfer Focusing Effect in Multicomponent Fluid with Internal Heat Generation, High Temperature, 2000, vol. 39, no. 1, pp. 161/162.
Kondratenko, P.S., Nikolskii, D.V., Samharadze, N.N., and Tchizhov, M.E., Free Convention of Heat Generating Liquid in a Hemispherical Closed Volume, 2011, vol. 49, no. 5, pp. 751–757.
Bernaz, L. et al., Thermal Hydraulic Phenomena in Corium Pools: Numerical Simulation with TOLBIAC and Experimental Validation with BALI, Proc. In-Vessel Core Debris Retention and Coolability Workshop, Garching, Germany, 1998, pp. 185–193.
Yang, H. and Zhu, Z., Numerical Simulation of Turbulent Rayleigh-Benard Convection, Int. Comm. Heat Mass Transfer, 2006, vol. 33, pp. 184–190.
Omri, M. and Galanis, N., Numerical Analysis of Turbulent Buoyant Flows in Enclosures: Influence of Grid and Boundary Conditions, Int. J. Therm. Sci., 2007, vol. 46, pp. 727–738.
Trias, F.X., Gorobets, A., Soria, M., and Oliva, A., Direct Numerical Simulation of a Differentially Heated Cavity of Aspect Ratio 4 with Rayleigh Numbers up to 1011, Part I: Numerical Methods and Time-Averaged Flow, Int. J. Heat. Mass Transfer, 2010, vol. 53, pp. 665–673.
Trias, F.X., Gorobets, A., Soria, M., and Oliva, A., Direct Numerical Simulation of a Differentially Heated Cavity of Aspect Ratio 4 with Ra-Number up to 1011, Part II: Heat Transfer and Flow Dynamics, Int. J. Heat Mass Transfer, 2010, vol. 53, pp. 674–683.
Ahlers, G., Grossmann, S., and Lohse, D., Heat Transfer and Large Scale Dynamics in Turbulent Rayleigh-Bé nard Convection, Rev. Mod. Phys., 2009, vol. 81, pp. 503–537.
Lee, S.D., Lee, J.K., and Suh, K.Y., Natural Convection Thermo Fluid Dynamics in a Volumetrically Heated Rectangular Pool, Nucl. Eng. Design, 2007, vol. 237, pp. 473–483.
Kenjeres, S. and Hanjalic, K., LES, T-RANS and Hybrid Simulations of Thermal Convection at High Ra Numbers, Int. J. Heat Fluid Flow, 2006, vol. 27, pp. 800–810.
Kiš, P. and Hervig, H., The Near Wall Physics and Wall Functions for Turbulent Natural Convection, Int. J. Heat Mass Transfer, 2012, vol. 55, pp. 2625–2635.
You, J.Y. and Kwon, O.J., Blending of SAS and Correlation-Based Transition Models for Flow Simulation at Supercritical Reynolds Numbers, to appear in Comput. Fluids, 2012.
Filippov, A.S., Numerical Simulation of Turbulent Heat Transfer in Oxidic Melt at Corium Catcher of NPP with VVER-1200, J. Eng. Therm., 2011, no. 2, pp. 161–173.
Gaus-Liu, A., Miassoedov, T., Cron, and Wenz, T., In-Vessel Melt Pool Coolability Test-Description and Results of LIVE Experiments, Int. Conf. on Nuclear Energy for New Europe, Bled, Slovenia, September 14–17, 2009.
Asmolov, V., Ponomarev-Stepnov, N.N., Strizhov, V., and Sehgal, B.R., Challenges Left in the Area of In-Vessel Melt Retention, J. Nucl. Eng. Design, 2001, vol. 209, pp. 87–96.
Peric, M., A Finite Volume Method for the Prediction of Three-Dimensional Fluid Flow in Complex Ducts, PhD thesis, Imperial College, University of London, 1985.
Versteeg, H.K. and Malalasekera, W., An Introduction to Computational Fluid Dynamics. The Finite Volume Method, New York: Longman, 1995.
Chen, Z.J. and Przekwas, A.J., A Coupled Pressure-Based Computational Method for Incompressible/Compressible Flows, J. Comput. Phys., 2010, vol. 229, pp. 9150–9165.
Shih, T.-H., Liou, W.W., Shabbir, A., Yang, Z., and Zhu, J., A New k-ɛ Eddy-Viscosity Model for High Reynolds Number Turbulent Flows. Model Development and Validation, Comp. Fluids, 1995, vol. 24, no. 3, pp. 227–238.
Physical Values, Handbook, Grygoryev, I.S. and Meylikhov, E.Z., Eds., Moscow, 1991.
Al-Arabi, M. and El-Riedy, M.K., Natural Convection Heat Transfer from Isothermal Horizontal Plates of Different Shapes, Int. J. Heat Mass Transfer, 1976, vol. 19, p. 1399.
Kutateladze, S.S., Heat Transfer and Hydraulic Resistances, Handbook, Moscow, 1990.
Niemela, J.J., Skrbek, L., Sreenivasan, K.R., and Donnelly, R.J., Turbulent Convection at Very High Rayleigh Numbers, Nature, 2000, vol. 404, no. 6780, pp. 837–840.
Chavanne, X., Chilla, F., Chabaud, B., Castaing, B., and Hebral, B., Turbulent Rayleigh-Bernard Convection in Gaseous and Liquid He, Phys. Fluids, 2001, vol. 13, no. 5, pp. 1300–1320.
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Filippov, A.S., Tarasov, O.V. Simulation of COPO II Lo experiments on natural convection of heat generating liquid at high Rayleigh numbers. J. Engin. Thermophys. 23, 112–128 (2014). https://doi.org/10.1134/S1810232814020040
- Heat Transfer
- Nusselt Number
- Natural Convection
- Rayleigh Number
- Molten Pool