DOI 10.15507/2079-6900.23.202104.394–411

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 76D05, 76M12

Numerical modeling of the formation of D-T mixture spherical layer in micro-targets of LTS

E. Yu. Kireicheva1, E. A. Veselova1, Yu. N. Deryugin1, T. F. Mamedova2

1FSUE RFNC - VNIIEF (Sarov, Russia

2National Research Mordovia State University (Saransk, Russia)

Abstract. The article presents a two-dimensional economical computational model of the formation of D-T mixture cryogenic layer in a spherical shell. The model is based on the description of the motion of the gas phase in the Boussinesq approximation. The thermal problem is a Stefan problem with a gas-solid phase transition. The technique is based on the finite volume method, the use of a structured mobile grid, whose movement is associated with the separation of the phase front, implicit approximations and the method of splitting two-dimensional equations in directions into one-dimensional equations. It is numerically shown that, due to natural radioactivity, the target is symmetrized. A calculated estimation of the symmetrization time for one geometry of the target with different filling coefficients is carried out.

Key Words: cryogenic target, Navier-Stokes equation in the Boussinesq approximation, finite volume method, structured mobile grid

For citation: E. Yu. Kireicheva, E. A. Veselova, Yu. N. Deryugin, T. F. Mamedova. Numerical modeling of the formation of D-T mixture spherical layer in micro-targets of LTS. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 23:4(2021), 394–411. DOI: https://doi.org/10.15507/2079-6900.23.202104.394–411

Submitted: 14.09.2021; Revised: 12.11.2021; Accepted: 16.11.2021

Information about the authors:

Ekaterina Yu. Kireicheva, Leading Economist, Russian Federal Nuclear Center (24 Druzhby St., Sarov 607181, Russia), ORCID: https://orcid.org/0000-0003-1614-3420, kireycheva@gmail.com

Elena A. Veselova, Senior Researcher, Department of the Institute of Theoretical and Mathematical Physics, Russian Federal Nuclear Center (46b Chkalova St., Sarov 607182, Russia), ORCID:https://orcid.org/0000-0002-9042-3415, sarov333@gmail.com

Yuriy N. Deryugin, Chief Researcher, Department of the Institute of Theoretical and Mathematical Physics, Russian Federal Nuclear Center (22 Yunosti St., Sarov 607182, Russia), D. Sci. (Physics and Mathematics), ORCID: https://orcid.org/0000-0002-3955-775X, dyn1947@yandex.ru

Tatyana F. Mamedova, Professor of the Department of Applied Mathematics, Differential equations and Theoretical Mechanics, National Research Mordovia State University (50 years of October st., Saransk 430019, Russia), Ph. D. (Physics and Mathematics), ORCID: https://orcid.org/0000-0002-7582-216X, mamedovatf@yandex.ru

All authors have read and approved the final manuscript.

Conflict of interest: The authors declare no conflict of interest.

Creative Commons Attribution 4.0 International License This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License.