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Analytical models of translationally nonequilibrium dynamics of shock-compressed binary gas mixtures

https://doi.org/10.18384/2949-5067-2024-3-50-57

Abstract

Aim: to find statistical distributions of molecules and their pairs in a shock-compressed gas mixture based on the modified Tamm-Mott-Smith method.
Methodology. Theoretical methods of mathematical physics were used.
Results. It is shown that the single-particle modified Tamm-Mott-Smith statistical distribution for a shock-compressed gas mixture is essentially four-modal. This makes it possible to satisfy both the conditions of conservation of mass, momentum and energy fluxes inside the shock wave front, and to significantly simplify the systems of moment equations used in numerical calculations. Analytical representations are obtained for all types of distribution functions of pairs of molecules in a shock compressed binary mixture of gases.
Research implications. The obtained analytical results are essential for clarifying the question of the need to take into account translational disequilibrium in determining the velocity coefficients of energetically activated inelastic collisions inside shock wave fronts

About the Authors

M. Kuznetsov
Federal State University of Education
Russian Federation

Mikhail M. Kuznetsov (Moscow) – Dr. Sci. (Phys.-Math.), Assoc. Prof., Prof., Department of Fundamental Physics and Nanotechnology

ulitsa Radio 10A, build. 2, Moscow 105005



Ju. Kuleshova
Federal State University of Education
Russian Federation

Juliya D. Kuleshova (Zhukovsky, Moscow region) – Cand. Sci. (Phys.-Math.), Assoc. Prof., Department of Higher Algebra, Mathematical Analysis and Geometry

ulitsa Radio 10A, build. 2, Moscow 105005



D. Satyukov
Federal State University of Education
Russian Federation

Dmitry G. Satyukov (Moscow) – Postgraduate Student, Department of Fundamental Physics and Nanotechnology

ulitsa Radio 10A, build. 2, Moscow 105005



References

1. Kuznetsov, M. M., Kuznetsov, G. V., Parenkina, V. I., Satyukov, D. G. & Halikov, R. F. (2023). Analytical models of translationally nonequilibrium dynamics of shock-compressed binary gas mixtures. In: Bulletin of the Federal State University of Education. Series: Physics and Mathematics, 4, 36–48. DOI: 10.18384/2949-5067-2023-4-34-48 (in Russ.).

2. Tanenbaum, B. S. & Scott, R. M. (1966). Comments on “Kinetic-Theory Approach to the Problem of Shock-Wave Strukture in a Binary Mixture”. In: Physics of Fluids, 9 (5), 1048– 1049. DOI: 10.1063/1.1761772

3. Bratos, M. & Herczynski, R. (1983). Shock waves in noble gases and their mixtures. In: Archives of Mechanics (Archiwum Mechaniki Stosowanej), 35 (2), 215–239.

4. Kulikov, S. V., Ternovaya, O. I. & Chereshnev, S. L. (1993). Specificity of translational nonequilibrium in the shock wave front in a single-component gas. In: Soviet Journal of Chemical Physics, 12 (3), 340–342 (in Russ.).

5. Kulikov, S. V., Ternovaya, O. I. & Chereshnev, S. L. (1994). Specificity of the evolution of the distribution of one-component gas molecules by relative velocities in the shock wave front. In: Combustion, Explosion, and Shock Waves, 30 (4), 140–144 (in Russ.).

6. Kuznetsov, M. M. & Kuleshova, J. D. (2012). Increase in rates of Kinetic Processes inside the Bimodal Hypersonic Shock Wave. In: Heat Transfer Research, 43 (3), 228–236. DOI: 10.1615/HeatTransRes.v43.i3.30.

7. Kuznetsov, M. M., Kuleshova, Ju. D. & Smotrova, L. V. (2012). On the increase of the kinetic processes rates in Tamm – Mott-Smith shock wave model. In: Bulletin of the Moscow Region State University. Series: Physics and Mathematics, 2, 108–116 (in Russ.).

8. Kuznetsov, M. M., Kuleshova, Ju. D. & Smotrova, L. V. (2012). The translational nonequilibrium effect in the Tamm – Mott-Smith shock wave model. In: Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 3, 84–86 (in Russ.).


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ISSN 2949-5083 (Print)
ISSN 2949-5067 (Online)