Analytical models of translationally nonequilibrium dynamics of shock-compressed binary gas mixtures
https://doi.org/10.18384/2949-5067-2023-4-34-48
Abstract
Aim. On the basis of asymptotic and approximate theoretical methods for solving the system of kinetic Boltzmann equations for a shock compressed binary mixture of gases, analytical representations of the distribution functions of the components of the mixture are found.
Methods. Asymptotic and variational methods of mathematical physics were used.
Results. Asymptotic and approximate analytical expressions are found for the distribution functions of components of a shock-compressed binary mixture of gases. For a modification of the Tamm–Mott-Smith method known in the literature, the laws of conservation of mass, momentum and energy fluxes in an arbitrary section inside a shock wave are proved for the first time. Previously, there was no such proof in the literature. The importance of such a proof is due to the fact that when applying the classical Tamm–Mott-Smith method to binary mixtures of gases, it is impossible to ensure compliance with the conservation laws inside the shock wave front.
Research implications. The obtained analytical results are essential both for elucidating the conditions for accelerating the velocities of kinetic processes in the structure of shock waves, and for determining the optimal conditions for conducting appropriate experiments in shock tubes.
About the Authors
M. M. Kuznetsov
Federal State University of Education
Russian Federation
Russian Federation
Mihail M. Kuznetsov – Dr. Sci. (Phys.-Math.), Prof., Department of Fundamental Physics and Nanotechnology
24 ulitsa Very Voloshinoi, Mytishchi 141014, Moscow Region
G. V. Kuznetsov
Federal State University of Education
Russian Federation
Russian Federation
Gleb V. Kuznetsov – Postgraduate Student, Department of Fundamental Physics and Nanotechnology
24 ulitsa Very Voloshinoi, Mytishchi 141014, Moscow Region
V. I. Parenkina
Moscow Aviation Institute (National Research University)
Russian Federation
Russian Federation
Viktorya I. Parenkina – Senior Lecturer, Department 916 “Mathematics”
Volokolamskoe shossse 4, Moscow 125993
D. G. Satyukov
Federal State University of Education
Russian Federation
Russian Federation
Dmitry G. Satyukov – Postgraduate Student, Department of Fundamental Physics and Nanotechnology
24 ulitsa Very Voloshinoi, Mytishchi 141014, Moscow Region
R. F. Halikov
Federal State University of Education
Russian Federation
Russian Federation
Ruslan F. Halikov – Postgraduate Student, Department of Fundamental Physics and Nanotechnology
24 ulitsa Very Voloshinoi, Mytishchi 141014, Moscow Region
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