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Reflection of moving shock wave over Prandtl–Meyer expansion waves

Published online by Cambridge University Press:  26 September 2025

Miao-Miao Wang Open the ORCID record for Miao-Miao Wang [Opens in a new window]  and
Zi-Niu Wu Open the ORCID record for Zi-Niu Wu [Opens in a new window]
Miao-Miao Wang*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Zi-Niu Wu*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
Corresponding authors: Miao-Miao Wang, mmwang@mail.tsinghua.edu.cn; Zi-Niu Wu, ziniuwu@tsinghua.edu.cn
Corresponding authors: Miao-Miao Wang, mmwang@mail.tsinghua.edu.cn; Zi-Niu Wu, ziniuwu@tsinghua.edu.cn
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Abstract

This study examines the reflection of a rightward-moving shock (RMS) over expansion waves, dividing the reflection structure into three components. The first component analyses the pre- and post-interaction parts of the expansion waves, categorising primary flow patterns into four types with defined transition criteria, visualised through Mach contours. The second component investigates the curved perturbed shock. Through numerical simulations, the influence of increasing shock strength on the flow structures is displayed. A triple point forms for an RMS of the first family, and the Mach stem height increases with the increase of shock strength. When the RMS is strong enough, a vortex forms in the near-wall region, which acts like a wedge to distort the near-foot part of the RMS. The third component, the near-foot region, is analysed using a one-dimensional Riemann problem approach. The calculated wave speeds are used to mark waves in Mach contours for eight cases. The position of the waves indicates that the left-going shock for an RMS of the first family or the right-going shock for an RMS of the second family corresponds to the foot of the RMS. This can explain the finding that the right-hand side of an RMS of the first family or the left-hand side of an RMS of the second family is disturbed. The regions to have different wave patterns solved from the one-dimensional Riemann problem are displayed in the original Mach number–shock speed Mach number plane.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A5
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© The Author(s), 2025. Published by Cambridge University Press

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