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D’Yakov–Kontorovich instability in planar reactive shocks

Published online by Cambridge University Press:  19 September 2019

César Huete Open the ORCID record for César Huete [Opens in a new window]  and
Marcos Vera Open the ORCID record for Marcos Vera [Opens in a new window]
César Huete*
Affiliation:
Grupo de Mecánica de Fluidos, Universidad Carlos III, Av. Universidad 30, 28911 Leganés, Spain
Marcos Vera
Affiliation:
Grupo de Mecánica de Fluidos, Universidad Carlos III, Av. Universidad 30, 28911 Leganés, Spain
*
†Email address for correspondence: chuete@ing.uc3m.es
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Abstract

The standard D’Yakov and Kontorovich (DK) instability occurs when a planar shock wave is perturbed and then oscillates with constant amplitude in the long-time regime. As a direct result, pressure perturbations generated directly behind the shock propagate downstream as non-evanescent sound waves, an effect known as spontaneous acoustic emission (SAE). To reach the DK regime, the slope of the Rankine–Hugoniot curve in the post-shock state must satisfy certain conditions, which have usually been related to non-ideal equations of state. This study reports that the DK instability and SAE can also occur in shocks moving in perfect gases when exothermic effects occur. In particular, a planar detonation, initially perturbed with a wavelength much larger than the detonation thickness, may exhibit constant-amplitude oscillations when the amount of heat released is positively correlated with the shock strength, a phenomenon that resembles the Rayleigh thermoacoustic instability. The opposite strongly damped oscillation regime is reached when the shock strength and the change in the heat released are negatively correlated. This study employs a linear perturbation model to describe the long-time and transient evolution of the detonation front, which is assumed to be infinitely thin, and the sound and entropy–vorticity fields generated downstream.

JFM classification

Compressible Flows: Shock waves Compressible Flows: Detonation waves Instability: Parametric instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 54 - 84
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Copyright
© 2019 Cambridge University Press 

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