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Linear interaction of two-dimensional free-stream disturbances with an oblique shock wave

Published online by Cambridge University Press:  01 July 2019

Zhangfeng Huang Open the ORCID record for Zhangfeng Huang [Opens in a new window]  and
Huilin Wang
Zhangfeng Huang*
Affiliation:
Department of Mechanics, Tianjin University, Tianjin300072, PR China State Key Laboratory of Aerodynamics, China Aerodynamic Research and Development Center, Mianyang, Sichuan621000, PR China
Huilin Wang
Affiliation:
Department of Mechanics, Tianjin University, Tianjin300072, PR China
*
†Email address for correspondence: hzf@tju.edu.cn
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Abstract

The problem of interaction between disturbances and shock waves was solved by a theoretical approach called linear interaction analysis in the mid-twentieth century. More recently, great progress has been made in analysing shock–turbulence interactions by direct numerical simulation. However, an unsolved theoretical problem remains: What happens when no acoustic waves are stimulated behind the shock wave? The concept of a damped wave is introduced, which is a type of excited plane wave. Based on this, the dispersion and amplitude relationships between any incident plane wave and resulting stimulated waves are constructed analytically, systematically and comprehensively. The physical essence of damped waves and the existence of critical angles are clarified. It is demonstrated that a damped wave is a complex number space solution to the acoustic dispersion relationship under certain conditions. It acts as a bridge connecting fast and slow acoustic waves at the position where the $x$ component of the group velocity is zero. There are two critical angles that can excite fast and slow acoustic waves, which determine the conditions that stimulate a damped wave. Our results show good agreement with theoretical and simulation results. The contribution of each excited wave to the transmission coefficient is evaluated, the distribution of the transmission coefficient is analysed and application to an engineering wedge model is performed.

JFM classification

Boundary Layers: Boundary layer receptivity Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 1179 - 1205
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Copyright
© 2019 Cambridge University Press 

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Footnotes

‡

The original version of this article was published with incorrect author information. A notice detailing this has been published and the error rectified in the online PDF and HTML copies.

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