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Time history of regular to Mach reflection transition in steady supersonic flow

Published online by Cambridge University Press:  11 July 2011

S. G. LI ,
B. GAO  and
Z. N. WU
S. G. LI
Affiliation:
School of Aerospace Science, Tsinghua University, Beijing 100084, P R China
B. GAO
Affiliation:
School of Aerospace Science, Tsinghua University, Beijing 100084, P R China
Z. N. WU*
Affiliation:
School of Aerospace Science, Tsinghua University, Beijing 100084, P R China
*
†Email address for correspondence: ziniuwu@tsinghua.edu.cn
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Abstract

In this paper, we study the transition from regular to Mach reflection (RR → MR) in the dual solution domain due to the influence of an upstream disturbance, by considering the transition as an evolutionary rather than an abrupt process. From numerical simulation, we observe for the early stage of transition a multiple interaction structure, composed of a triple-shock structure, a type VI shock interaction and a shock/slipline interaction. In the end, we observe a pure unsteady MR structure. Under self-similar assumption of the triple point for the first stage and including additional Mach waves over the slipline for the last stage, we develop an idealized unsteady model to obtain the evolution of the Mach stem height and the time taken for the Mach stem to stabilize. The triple point is found to move at a nearly constant speed in the multiple interaction stage which occupies about one quarter of the transition time. In the pure unsteady MR stage, which occupies the rest of transition, the speed of the triple point drops nonlinearly until the Mach stem stabilizes.

JFM classification

Compressible Flows: Gas dynamics Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 160 - 184
Copyright
Copyright © Cambridge University Press 2011

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