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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 Open the ORCID record for M.Yu. Timokhin [Opens in a new window] ,
A.N. Kudryavtsev Open the ORCID record for A.N. Kudryavtsev [Opens in a new window]  and
Ye.A. Bondar Open the ORCID record for Ye.A. Bondar [Opens in a new window]
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: timokhin@physics.msu.ru
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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 $Ma_n>8$.

JFM classification

Compressible Flows: Shock waves Rarefied Gas Flow: Kinetic theory Compressible Flows: Gas dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 950 , 10 November 2022 , A14
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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