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The Mott-Smith solution to the regular shock reflection problem

Published online by Cambridge University Press:  18 October 2022

M.Yu. Timokhin*
Affiliation:
Lomonosov Moscow State University, 119991 Moscow, Russia Khristianovich Institute of Theoretical and Applied Mechanics, 630090 Novosibirsk, Russia Moscow Aviation Institute, 125993 Moscow, Russia
A.N. Kudryavtsev
Affiliation:
Khristianovich Institute of Theoretical and Applied Mechanics, 630090 Novosibirsk, Russia
Ye.A. Bondar
Affiliation:
Khristianovich Institute of Theoretical and Applied Mechanics, 630090 Novosibirsk, Russia
*
Email address for correspondence: [email protected]

Abstract

The classical Mott-Smith solution for one-dimensional normal shock wave structure is extended to the two-dimensional regular shock reflection problem. The solution for the non-equilibrium molecular velocity distribution function along the symmetry-plane streamline is obtained as a weighted sum of four Maxwellians. An analysis of applicability of the solution has been performed using the results of direct simulation Monte Carlo calculations for a range of incident shock wave intensities. Accuracy of the solution improves with increasing $Ma_n$, the Mach number normal to the shock front, so that the solution becomes rather accurate for strong shocks with $Ma_n>8$.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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