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## On numerical simulation of cooling the porous heat-releasing objects in the mode of forced filtration with given gas consumption

The unsteady gas flow through porous heat-releasing element is considered. Such processes is referred to actual problems in the context of organization the cooling process of energy release spots, which appear due to different disasters [1]. Mathematical modelling of cooling the porous objects with energy-releasing sources by gas, with the given pressure gradient on the open boundaries were conducted earlier in one- [2], two- [3, 4] and three-dimensional [5] statements. Given gas pressure on the inlet boundary allows to describe processes of forced filtration as well as gravitational convection, when gas isn't pressurized. However, in the case of pressurized filtration the more convenient to control not the pressure but gas consumption, how it usually takes place under the combustion in the regime of filtration combustion [6].

Numerical scheme for calculation of gas filtration through porous object with heat-emitted spots with given gas consumption on the inlet is offered in this study. Calculation data are made comparison with previous results which were gotten from calculations of gas filtration through porous self-heating medium with given pressure gradient. The speed of process stabilization and processes when stabilization is impossible, but the unlimited heating takes place, are investigated.
The work was made with support of RFBR (grant 16-01-00103-а).

References
[1] Maslov V.P., Myasnikov V.P., Danilov V.G. Mathematical model of safety block at the Chernobyl A-plant. Moscow, Nauka Publ., 1987. 144 p. (in Russian).
[2] Lutsenko N.A. Unsteady conditions of cooling of the porous fuel element // Matematicheskoe modelirovanie. Vol. 17, no. 3, 2005. Pp. 120-128 (in Russian).
[3] Levin V.A., Lutsenko N.A. Numerical modelling of two-dimensional gas flow through porous heat-releasing elements. // Vychislitelnie tehnologii. Vol. 11, no. 6, 2006. Pp. 44-58 (in Russian).
[4] Levin V.A., Lutsenko N.A. Time-dependent gas flows through axisymmetrical porous heat-evolutional objects // Matematicheskoe modelirovanie. Vol. 22, no. 3, 2010. Pp. 26-44 (in Russian).
[5] Lutsenko N.A. Numerical modeling of three dimensional time-dependent gas through porous objects with energy-releasing sources // Computational continuum mechanics. Vol. 9, no. 3, 2016. Pp. 331-344. http://dx.doi.org/10.7242/1999-6691/2016.9.3.27
[6] Kislov V.M., Glazov S.V., Salgansky E.A., Kolesnikova Yu.Yu., Salganskaya M.V. Coal gasification by a mixture of air and carbon dioxide in the filtration combustion mode // Combustion, Explosion, and Shock Waves. Vol. 52, issue. 3, 2016. Pp. 320-325. DOI: 10.1134/S0010508216030102.

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