Publication: On the stability of piston-driven planar shocks
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2023-06-10
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Cambridge University Press
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Abstract
We present a theoretical and numerical stability analysis for a piston-driven planar
shock against two-dimensional perturbations. The results agree with the well-established
theory for isolated planar shocks: in the range of hc < h < 1 + 2M2, where h is the
Dyakov-Kontorovich (DK) parameter related to the slope of the Rankine-Hugoniot
curve, hc is its critical value corresponding to the onset of the spontaneous acoustic
emission (SAE) and M2 is the downstream Mach number, non-decaying oscillations
of shock-front ripples occur. The effect of the piston is manifested in the presence
of additional frequencies occurring by the reflection of the sonic waves on the piston
surface that can reach the shock. An unstable behaviour of the shock perturbation is
found to be possible when there is an external excitation source affecting the shock,
whose frequency coincides with the self-induced oscillation frequency in the SAE regime,
thereby being limited to the range hc < h < 1 + 2M2. An unstable evolution of the shock
is also observed for planar shocks restricted to one-dimensional perturbations within
the range 1 < h < 1 + 2M2. Both numerical integration of the Euler equations via the
method of characteristics and theoretical analysis via Laplace transform are employed to
cross-validate the results.
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Keywords
Gas dynamics, Shock waves
Bibliographic citation
Calvo-Rivera, A., Velikovich, A. L., & Huete, C. (2023). On the stability of piston-driven planar shocks. Journal of Fluid Mechanics, 964(A33)