Forecast of the thermal regime of an underground storage facility for heat-generating materials under mixed convection conditions
The paper presents the results of a study by numerical simulation methods of the thermal regime of an underground facility for long-term storage of spent nuclear fuel in the version of an built-in reinforced concrete structure. A multiphysical computer model in a two-dimensional setting was built in the COMSOL program. The mathematical model is based on the continuity equation, Navier-Stokes equations and the general heat transfer equation. The conditions of mixed convection are taken into account in the «incompressible ideal gas» approximation, in which the thermophysical parameters of air are a function of temperature only. The choice of thermophysical parameters of different parts of the model and a set of boundary conditions for the solved ones are substantiated. For two parameters of the model, the following values are taken: the air flow rate which provides the velocity at the input boundary of 0.01, 0.03 and 0.05 m/s, and the effective thermal conductivity of the material of the integrated design is 1.0 and 2.0 W/(m⋅K). Numerical experiments were performed for a period of up to 5 years of fuel storage. The formation features of the velocity fields in the facility are noted when the values of these parameters are changed. Special emphasis is given to the fundamental difference between the non-stationary structure of the velocity fields predicted in the model of an «incompressible ideal gas» and the «frozen» picture of aerodynamic parameters in the model of an incompressible fluid. An analysis is made of the dynamics of spatial distributions of temperature fields in different areas of the model. The distribution features of maximum temperature values in the different areas of the model are also noted. It is shown that the requirements for not exceeding the criterion temperature values are met when the facility is operated under conservative ventilation conditions in terms of the air flow rate and the thermal conductivity coefficient of the material of the built-in structure. The dynamics of heat flows directed into the rock mass through the base and from the surface of the built-in structure into the air is analyzed. The heat flow dominance from the structure surface is noted. Finally, the influence of the effective coefficient of thermal conductivity of the material of the built-in structure and the air flow rate on the value of heat fluxes into the air and rock mass is demonstrated.
- Melnikov N.N., Konukhin V.P., Naumov V.A., Amosov P.V., Gusak S.A., Naumov A.V., Katkov Y.R. Spent Nuclear Fuel of Ship Power Plants in the European North of Russia. Part II. Apatity. KNTs RAN Publ., 2003, 209 p. (in Russian).
- Melnikov N.N., Konukhin V.P., Naumov V.A., Amosov P.V., Gusak S.A., Naumov A.V., Katkov Y.R., Smirnov Yu.G., Orlov A.O., Rybin Yu.Yu. Concept of Underground Storage of Spent Nuclear Fuel for Marine Nuclear Power Plants on the Kola Peninsula. Vestnik MGTU, 2006, v. 9, iss. 3, pp. 408-418 (in Russian).
- Dry Storage Facilities for Spent Nuclear Fuel. NP Safety Requirements-035-02. Vestnik Gosatomnadzora Rossii, 2002, iss. 3, pp. 51-58 (in Russian).
- Safety Rules for Storage and Transportation of Nuclear Fuel at Nuclear Energy Facilities NP-061-05. Available at: https://files.stroyinf.ru/Data1/47/47340/ (accessed Jan 20, 2020) (in Russian).
- Kalinkin V.I., Kritsky V.G., Tokarenko A.I., Tikhonov N.S., Razmashkin N.V., Serova A.L., Balitskaya A.N. Storage of Spent Nuclear Fuel of Power Reactors: Preprint. St-Petersburg. VNIPIET Publ., 2009, 124 p. (in Russian).
- Naumov V.A., Gusak S.A. A Study on Formation Regularities of Heat Sources in the Cask Type Storage Facilities for Spent Nuclear Fuel of the Low-Power Rectors. Vestnik Kol’skogo Nauchnogo Tsentra RAN. 2019, iss. 2 (11), pp. 105-115; DOI: https://doi.org/10.25702/KSC.2307-5228.2019.11.2.105-115 (in Russian).
- Rzhevsky V.V., Novik G.Ya. Fundamentals of Rock Physics. Moscow. Nedra Publ., 1978, 390 p. (in Russian).
- COMSOL Documentation. Available at: https://www.comsol.ru/documentation (accessed Jan 20, 2020) (in Russian).
- Release 17.0 Documentation for ANSYS. Swanson Analysis Systems, Inc. 2016.
- Schelyaev A. FlowVision-modern Russian mathematical modeling tool. Available at: https://sapr.ru/article/21879 (accessed Jan 20, 2020) (in Russian).
- Amosov P.V., Podshivalova A.V. Modeling of the Thermal Regime of an Underground Storage Facility for Heat-Emitting Radiation-Hazardous Materials. Vestnik MGTU. 2010, v. 13, iss. 3, pp. 562-566 (in Russian).
- Amosov P.V., Podshivalova A.V. Features of the Thermal Regime of an Underground Object of Insulation of Heat-Generating Materials (Container Version). Izvestia Vysshikh Uchebnykh Zawedeniy. Yadernaya Energetika, 2010, no. 3, pp. 133-140 (in Russian).
- Egorov V.I. Application of Computers for Solving Problems of Thermal Conductivity. Tutotial. St. Petersburg. SP GU ITMO Publ., 2006, 77 p. (in Russian).
- Amosov P.V., Novozhilova N.V. Two-dimensional numerical simulation of atmosphere aerothermodynamic of open pit. Proc. of the All-Russian Sci.-Tech. Conf «Ekologicheskaya strategiya razvitiya gornodobyvayuschej otrasli – formirovanie novogo mirovozzreniya v osvoenii prirodnyh resursov». Apatity. Gornyj Institut Kol’skogo Nauchnogo Tsentra RAN Publ., 2014, pp. 153-159 (in Russian).
- Amosov P.V., Kozyrev S.A., Nazarchuk O.V. Development of a computer model of aerothermodynamics of the pit open atmosphere in ANSYS FLUENT. Izvestiya Sankt-Peterburgskogo Gosudarstvennogo Tekhnologicheskogo Instituta (Tehnicheskogo Universiteta), 2018, iss. 44 (70), pp. 121-125; DOI: https://doi.org/10.15217/issn1998984-9.2018.44.121 (in Russian).
- Earth Science. Vol. 21: Handbook of Physical Constants of Rocks. Moscow. Mir Publ., 1969, 543 p. (in Russian).
- Vargaftik N.B. Handbook of Thermophysical Properties of Gases and Liquids. Moscow. Nauka Publ., 1972, 720 p. (in Russian).
- Pekhovich A.I., Zhidkikh V.M. Calculations of the Thermal Regime of Solids. Leningrad. Energia Publ., 1968, 304 p. (in Russian).
- Handbook (Cadastre) of Physical Properties of Rocks. N.V. Melnikov, V.V. Rzhevsky, M.M. Protodyakonov (Eds). Moscow. Nedra Publ., 1975, 279 p. (in Russian).
- Physical Properties of Rocks and Minerals (Petrophysics): Handbook of Geophysics. N.B. Dortman (Ed.). Moscow. Nedra Publ., 1984, 455 p. (in Russian).
- Horai K. Thermal conductivity of rock-forming minerals. Journal of Geophysical Research. 1971, v. 76, iss. 5, pp. 1278-1308.
- Chirkin V.S. Thermophysical Properties of Nuclear Engineering Materials. Moscow. Atomizdat Publ., 1968, 485 p. (in Russian).
- Melnikov N.N., Konukhin V.P., Naumov V.A., Amosov P.V., Gusak S.A., Naumov A.V., Orlov A.O., Smirnov Yu.G., Karavaeva E.V., Novozhilova N.V., Klimin S.G. Scientific and Engineering Aspects of Safe Storage and Disposal of Radiation-Hazardous Materials in the European North of Russia. Apatity. KNTS RAN Publ., 2010, 305 p. (in Russian).