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Interaction of two-dimensional spots with a heat releasing/absorbing shock wave: linear interaction approximation results

Published online by Cambridge University Press:  28 May 2019

G. Farag ,
P. Boivin Open the ORCID record for P. Boivin [Opens in a new window]  and
P. Sagaut Open the ORCID record for P. Sagaut [Opens in a new window]
G. Farag
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2 UMR 7340, Marseille, France
P. Boivin*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2 UMR 7340, Marseille, France
P. Sagaut
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2 UMR 7340, Marseille, France
*
†Email address for correspondence: pierre.boivin@univ-amu.fr
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Abstract

The canonical interaction between a two-dimensional weak Gaussian disturbance (entropy spot, density spot, weak vortex) with an exothermic/endothermic planar shock wave is studied via the linear interaction approximation. To this end, a unified framework based on an extended Kovásznay decomposition that simultaneously accounts for non-acoustic density disturbances along with a poloidal–toroidal splitting of the vorticity mode and for heat release is proposed. An extended version of Chu’s definition for the energy of disturbances in compressible flows encompassing multi-component mixtures of gases is also proposed. This new definition precludes spurious non-normal phenomena when computing the total energy of extended Kovásznay modes. Detailed results are provided for three cases, along with fully general expressions for mixed solutions that combine incoming vortical, entropy and density disturbances.

JFM classification

Turbulent Flows: Compressible turbulence Reacting Flows: Detonations Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , pp. 865 - 895
Copyright
© 2019 Cambridge University Press 

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