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Reflection of a rightward-moving shock wave over a steady oblique shock with post-formed expansion wave

Published online by Cambridge University Press:  02 April 2025

Miaomiao Wang Open the ORCID record for Miaomiao Wang [Opens in a new window]  and
Ziniu Wu Open the ORCID record for Ziniu Wu [Opens in a new window]
Miaomiao Wang*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Ziniu Wu
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
Corresponding author: Miaomiao Wang, mmwang@mail.tsinghua.edu.cn
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Abstract

Reflection of a rightward-moving shock over a steady oblique shock, equivalent to a shock-on-shock interaction, is typically studied with post-formed shock waves. Law, Felthun and Skews (Shock Waves, vol. 13, 2003, pp. 381–394) reported post-formed expansion fan (PFEF) reflection for second-family incident shock. Here, we show that PFEF reflection also exists for first-family incident shock. We derive the critical condition for PFEF reflection in the shock speed Mach number and incident shock angle plane. Our findings indicate PFEF emergence near type post-I region. Numerical simulations reveal that PFEF with rising incident angle can intersect the incident shock, triple point or Mach stem, echoing the Hillier (J. Fluid Mech., vol. 575, 2007, pp. 399–424) three-type classification of shock–expansion fan interactions. The complex shock reflection pattern is essentially composed of an upstream structure linked to the moving shock wave, and a downstream structure linked to the unperturbed oblique shock wave. Under the conditions investigated, the upstream structure is characterized by a Mach reflection of the incident shock over the wall, potentially featuring a triple point formed within the Mach stem. Below this triple point, there is a curved segment of the Mach stem that is close to the wall. As the inclined angle increases, the curved shock may expand and interact with the incident shock, leading to an asymmetric regular reflection, which is a phenomenon that has not been observed previously. The downstream structure is a double $\lambda$ shock structure, with the lower shock resulting from the generation of recompression shock waves.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A19
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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