Richtmyer-Meshkov instability when a shock wave encounters with a premixed flame from the burned gas Articles uri icon

publication date

  • October 2024

volume

  • 134

International Standard Serial Number (ISSN)

  • 0307-904X

Electronic International Standard Serial Number (EISSN)

  • 1872-8480

abstract

  • We present a linear stability analysis of the Richtmyer-Meshkov instability that develops when a shock wave reaches a sinusoidally perturbed premixed flame from behind. In the hydrodynamic regime, when acoustic contributions dominate the flame growth rate, the problem is analytically addressed by the direct integration of the sound wave equations at both sides of the flame, which are bounded by the reflected and transmitted shock waves and the flame front that acts as a contact surface in the hydrodynamic limit. The resolution involves: a hyperbolic change of variables to modify the triangular spatio-temporal domain, a transformation in the Laplace variable, the resolution of the functional equations in the frequency domain, and the final inverse Laplace transform. The latter involves a novel resolution method that is proven beneficial for long-time dynamics. Asymptotic analysis is also carried out to describe the early time and late time hydrodynamic response. The nonuniform flow field resulting from distorted oscillating shocks is characterized by acoustic, rotational, and entropic disturbances, each of which exerts a substantial influence on flame dynamics. These disturbances contribute to the intricate interplay of factors shaping the behavior of the flame in response to the nonuniform flow. In particular, the sensitivity of local flame propagation to temperature disturbances is investigated. This work contributes to a deeper understanding of Richtmyer-Meshkov instability dynamics and offers insights into instability reduction through the modulation of temperature disturbances generated by the transmitted shock.

keywords

  • bromwich integral; combustion; contour integration; laplace transform; richtmyer-meshkov instability; stability analysis