Ashurko Yu.M., Kascheev M.V.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia
A complete mathematical model has been developed for the first time for numerical analysisof severe off-design accidents in sodium cooled fast reactors. The developed model enables one to answer the question of the possibility of containment of molten fuel in the reactor vessel. The computational domain under consideration is multiply connected. The mathematical simulation of sub-domains as porous bodies is performed using the laws of conservation of mass, momentum, and energy, written in the form of equations of continuity, motion, and energy in two-dimensional cylindrical coordinates. The problem of formation of heat-generated layer on the lower end shield has been solved. There was obtained solution of the problem on the movement ofvariable mass vapor bubble in liquid. The result have been used to describe the heat sources originated due to vapor condensation above heatgenerated layer.
The developed numerical model is implemented in the form of BRUT computer code. Verification
of the code’s individual blocks has revealed anadequate agreement of the calculation results and available experimental data as well as analytical solution. Using BRUT code there was performed calculation analysis of fast reactor severe accident wherein complete melting of fuel subassemblies in the center of the reactor core and partial melting of peripheral subassemblies are considered. Thereby, in accordance with the calculation results on the considered above accident melted fuel is retained inside of the reactor vessel. The BRUT codewas used for calculation of the postulated severe accident wherein occurs complete melting of fuel subassemblies of reactor core at low power reactor BN.
To effectuate fast evaluations of parameters and,foremost, time of melt-through of designs there was developed mathematical model in which the taskis solved in one-dimensional approach. By the BRUT-O code, developed on the basis of one-dimensionalmathematical model, calculation of accident wherein occurs complete melting of fuel subassemblies in the center of the reactor core and partial melting of peripheral fuel subassemblies is carriedout. It is shown that time for melt contact with the pressure-header upper plate calculated by the BRUT-O code is less than the similar time obtained by the BRUT code to 10%.
1. Kashheev M.V., Kuznecov I.A. Matematicheskoe modelirovanie uderzhaniya rasplavlennogo topliva v korpuse bystrogo reaktora pri tyazheloy avarii. Matematicheskaya model' [Mathematical modeling of
retention of melted fuel in the case of fast reactors under severe accident. Mathematical model]. Teplofizika vysokikh temperatur - High Temperature, 2009, no. 4, pp. 627-632.
2. Kashheev M.V., Kuznecov I.A. Modelirovanie uderzhaniya rasplava v bystrom reaktore pri tyazheloy
avarii [Modeling melt retention in a fast reactor at a severe accident]. Teployenergetika - Thermal
Engineering, 2007, no. 12, pp. 51-56.
3. Kashheev M.V., Kuznecov I.A. Matematicheskoe modelirovanie uderzhaniya rasplava v bystrom reaktore pri tyazheloy avarii [Modeling melt retention in a fast reactor at a severe accident]. Trudy 4 Rossiyskoy nacional'noy konferencii po teploobmenu [Proc. 4th Russian National Conference on Heat Transfer]. Moscow, 2006, pp. 227-230.
4. Kashheev M.V., Kuznecov I.A. Modelirovanie uderzhaniya rasplava v korpuse bystrogo reaktora v usloviyah tyazheloy avarii [Modeling melt retention inthe case of fast reactors under severe accident conditions]. VANT. Series: matematicheskoe modelirovanie fizicheskih processov - PAST. Series: mathematical modeling of physical processes, 2005, no. 3, pp. 53-64.
5. Subbotin V.I. eds. Reshenie zadach reaktornoy teplofiziki na EVM [Solving problems reactor Thermophysics on a computer]. Moscow, Atomizdat Publ., 1979.
6. Gorbis Z.R. Teploobmen i gidromehanika dispersnykh skvoznykh potokov [Heat Transfer and Fluid Mechanics dispersed through streams]. Moscow, Energiia Publ., 1970.
7. Kashheev M.V. Modelirovanie stratifikacii komponentkoriuma pri tyazheloy avarii [Simulation component corium stratification in severe accidents]. Izvestiya vuzov. Yadernaya energetika - Proseedings of Universities. Nuclear Power, 2002, no. 3, pp. 3-13.
8. Lykov A.V. Teoriya teploprovodnosti [The theory of thermal conductivity]. Moscow, Vysshaya Shkola Publ.,1967, 600 p.
9. Kashheev M.V. Dvizhenie parovogo puzyrya peremennoy massy v zhidkosti [The movement of a steam bubble in the liquid of variable weight]. Preprint FEI 3246 - Preprint IPPE 3246. Obninsk, 2014.
10. Florschuetz L.W., Henry C.L., Khan A. Rashid. Growth rates of free vapor bubbles in liquids at uniform superheats under normal and zero gravity conditions. International Journal of Heat and Mass Transfer, 1969, vol. 12, no.11, pp. 1465-1489.
11. Fihtengol'c G.M. Kurs differencial'nogo i integral'nogo ischisleniya [Course of differential and integral calculus]. Moscow, Science Publ., 1969, 800 p.
12. Labuncov D.A., Jagov V.V. Mehanika dvuhfaznyh sistem: Uchebnoe posobie dlja vuzov[Mechanics of two-phase systems: Textbook for high schools]. Moscow, MPEI Publ., 2000, 374 p.
13. Artem'ev V.K. Variant neyavnogo metoda dlya resheniya sistemy uravneniy Nav'e-Stoksa v estestvennykh peremennykh [Option implicit method for solving the Navier-Stokes equations in primitive variables]. Preprint FEI 1962 - Preprint IPPE 1962. Obninsk, 1989.
14. Lipinski R.J., Gronager J.E., Schwarz M. Particle bed heat removal with subcooled sodium: D-4 results
and analysis. Nuclear Technology, 1982, vol. 58, no. 3, pp. 369-378.
15. Kashheev M.V., Kuznecov I.A. Matematicheskoe modelirovanie uderzhaniya rasplavlennogo topliva v korpuse bystrogo reaktora pri tyazhelykh avarii. Rezul'taty rascheta po programme BRUT [Mathematical modeling of retention of melted fuel in the case of fast reactors under severe accident. The calculation results of the program BRUT]. Teplofizika vysokikh temperatur - High Temperature, 2009, no.5, pp. 765-770.
16. Kymalainen O. et. al. Heat Flux Distribution from a Volumetrically Heated Pool with High Rayleigh
Number. Proc. 6th Int. Topical Meeting on Reactor Thermal-Hydraulics. Grenoble, 1993, pp. 47-53.
17. Kashheev M.V. Reshenie zadachi teploprovodnosti dlya kol'cevogo cilindra konechnykh razmerov s vnutrennimi istochnikami tepla [Solution of the problem of thermal conductivity for the annular cylinder of finite size with internal heat sources]. Teploenergetika - Thermal Engineering, 2011, no.2, p. 71-73.
18. Kashheev M.V. Pyat' testovykh zadach [Five test problems]. Preprint FEI 3150 - Preprint IPPE 3150. Obninsk, 2009.
19. Stepanov V.V. Kurs differentsial'nykh uravneniy [Course of differential equations]. Moscow, State Publishing House of physical and mathematical literature, 1959, 468 p.
20. Samarskii A.A., Vabishhevich P.N. Vychislitel'naya teploperedacha[Computational Heat Transfer]. ?oscow, ?ditorial URSS Publ., 2001.
