Numerical Simulation of the Temperature Distribution and the Radionuclide Concentration in a Fuel Element of a Nuclear Reactor
https://doi.org/10.1134/S2304487X2002011X
Abstract
The radial distribution of the temperature in a fuel element of a nuclear reactor has been studied taking into account the boundary conditions of the third kind in five regions with different characteristics. The problem with zero derivative of the temperature on the left boundary of the solution domain has been considered separately as a special case of a boundary condition of the third kind. The numerical simulation has shown that a constant radial distribution of the temperature in the fuel element is established quite quickly. For this reason, stationary heat conduction equations are considered in each of the five regions, and a general solution is obtained for each region. For the case of zero derivative of the temperature on the left boundary, an analytical form of the stationary temperature distribution in all regions is obtained. It has been found that the numerical solution converges quite rapidly to the analytical solution. In addition, the distribution of the concentration of radionuclides is studied taking into account radioactive transformations. The radioactive decay chain of 131Sn has been considered as an example. The results of the numerical simulation are presented in the form of plots of the concentration distribution along the radius of the fuel rod. The main result is a program that allows the numerical simulation of the temperature distribution and concentration of radionuclides under various boundary conditions and for different values of the parameters of the fuel element that can be set by the user of the program.
About the Authors
A. S. Salin
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
References
1. Kudryashov Nikolai A., Khlunov Aleksandr V., Chmykhov Mikhail A., Thermal regimes of high burnup nuclear fuel rod, Com. in Nonlinear Sci. Numerical Simulation, 15, 1240–1252 (2009).
2. Alyushin V. M., Baranov V. G., Kudryashov N. A., Khlunov A. V., Numerical modeling of the temperature distribution in a VVER fuel element, Atomic Energy, Vol. 108, No. 3 (2010).
3. An Chen, Moreira Felippe Celestino, Su Jian, Thermal analysis of the melting process in a nuclear fuel rod, Applied Thermal Engineering, 68, 133–143 (2014).
4. Tang Jiannan, Huang Mei, Zhao Yuanyan, Maqsood Saad, Ouyang Xiaoping, Numerical investigations on the melting process of the nuclear fuel rod in RIAs and LOCAs, International Journal of Heat and Mass Transfer, 124, 990–1002 (2018).
5. Abdul Razak R. K., Afzal Asif, Mohammed Samee A. D., Ramis M. K., Effect of cladding on thermal behavior of nuclear fuel element with non-uniform heat generation, Progress in Nuclear Energy, 11, 1–14 (2019).
6. Poddar Antarip, Chatterjee Rukmava, Chakravarty Aranyak, Ghosh Koushik, Sen Swarnendu, Mukhopadhyay Achintya, A thermal model to characterize the flattening effect of a nuclear fuel element in an anullar channel using simple analytical approach, Progress in Nuclear Energy, 85, 441–453 (2015).
7. Basanskiy E. G., Kolobashkin V. M., Kudryashov N. A., Raschet dvumernogo rasprostranenia primesi v poristoi srede pri nestacionarnoy fil’tracii gaza [Calculation of the two-dimensional distribution of impurities in a porous medium during non-stationary gas filtration], Izv. AS USSR, Fluid and gas mechanics, № 5 (1982) (in Russian).
8. Bondarenko A. G., Kolobashkin V. M., Kudryashov N. A., Rasprostranenie radionuklidov v poristoi srede s uchetom sorbcii i diffuzii [Distribution of radionuclides in a porous medium taking into account sorption and diffusion], Physics Engineering Journal, vol. XXXI, № 6 (1976) (in Russian).
9. Kudryashov N. A., Murzenko V. V., Avtomodel’noe reshenie zadachi osesimmetrichnogo dvizhenia gaza cherez poristuyu sredu pri kvadratichnom zakone soprotivlenia [Self-similar solution to the problem of axisymmetric gas motion through a porous medium with a quadratic law of resistance], Izv. AS USSR, Fluid and gas mechanics, № 4 (1982) (in Russian).
10. Basanskiy E. G., Kolobashkin V. M., Kudryashov N. A., Rasprostranenie radionuclidov cherez razdroblennuyu porodu pod deistviem izbitochnogo davlenia productov vzriva [Propagation of radionuclides through crushed rock under the influence of overpressure of explosion products], Izv. AS USSR, Fluid and gas mechanics, № 2 (1980) (in Russian).
11. Bondarenko A. G., Kolobashkin V. M., Kudryashov N. A., Neravnovesnaya adsorbciya izobarnoi cepochki radionuklidov [Nonequilibrium adsorption of an isobaric chain of radionuclides], Izv. AS USSR, Fluid and gas mechanics, № 3 (1976) (in Russian).
12. Arsenin V. Y., Zyabrev N. B., Kudryashov N. A., O reshenii obratnih zadach konvectivnoy diffuzii i adsorbcii radioactivnogo gaza v poristoi srede [On solving inverse problems of convective diffusion and adsorption of a radioactive gas in a porous medium], Izv. AS USSR, Fluid and gas mechanics, № 3 (1978) (in Russian).
13. Samarskiy A. A., Teoriya raznostnikh skhem [Theory of difference schemes] – 1989, p. 413–427 (in Russian).
14. Kalitkin N. N., Koryakin P. V., Chislennie metodi: v 2 kn. Kn. 2. Metodi matematicheskoy phisiki [Numerical methods: in 2 books. Book 2. Methods of mathematical physics.] – 2013, p. 194–198 (in Russian).
Review
For citations:
Salin A.S., Kudryashov N.A. Numerical Simulation of the Temperature Distribution and the Radionuclide Concentration in a Fuel Element of a Nuclear Reactor. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(2):155-165. (In Russ.) https://doi.org/10.1134/S2304487X2002011X
Views:
109
Email this article 