On the stability of piston-driven planar shocks Articles uri icon

publication date

  • June 2023

start page

  • 1

end page

  • 38


  • 964

International Standard Serial Number (ISSN)

  • 0022-1120

Electronic International Standard Serial Number (EISSN)

  • 1469-7645


  • 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.


  • Industrial Engineering


  • gas dynamics; shock waves