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Reflection of multiple incident shock waves and shock interaction train

Published online by Cambridge University Press:  02 April 2025

Zhu-Di Li  and
Chen-Yuan Bai Open the ORCID record for Chen-Yuan Bai [Opens in a new window]
Zhu-Di Li
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beihang University, Beijing 100191, PR China
Chen-Yuan Bai*
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beihang University, Beijing 100191, PR China
*
Corresponding author: Chen-Yuan Bai, baicy@buaa.edu.cn
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Abstract

The reflection of multiple incident shock waves that converge to a single point on the reflecting surface is studied in this paper. The number of the incident shocks, denoted $K$, is arbitrary. The interaction between the reflected shock of one incident shock and the other incident shocks may produce various possible configurations, such as type-I, type-II and type-IV shock interferences. The number of possible reflection configurations is shown to be an exponential function of ($K-1$) with base 2. The possibility of pre-, middle- and post-Mach reflections, which means Mach reflection occurs for the first, middle and last incident shock, is revealed through numerical simulation for $K=3$. For the particular case where the incident shocks are produced by equal variation of wedge surface deflection, the conventional von Neumann condition and detachment condition for the $k\mathrm{th}$ incident shock to have Mach reflection are derived. It is shown that the von Neumann condition for regular reflection is lowered and the detachment condition for Mach reflection is elevated as $k$ increases. The shock reflection patterns for $ K=1,2,\ldots ,10$ are obtained by numerical simulations. We observe a shock interaction train structure, where we have pre-Mach reflection followed by ($K-1$) type-I or type-II shock interferences. We also observe that the Mach stem height decreases with $K$ well above the von Neumann condition and becomes non-monotonic near the von Neumann condition.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves Compressible Flows: Supersonic flow

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A28
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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