Instability and Mixing of Gas Interfaces Driven by Cylindrically Converging Shock Wave

TL;DR

This study introduces a method to generate pure cylindrically converging shock waves and investigates their role in driving Richtmyer-Meshkov instabilities and fluid mixing, revealing scaling laws and turbulence characteristics post re-shock.

Contribution

The paper presents a novel approach to produce pure cylindrically converging shock waves and analyzes their effects on interface instability and fluid mixing behaviors.

Findings

Fluid mixing is dramatically enhanced after re-shock.

Mixing parameters follow similar temporal laws despite different initial perturbations.

Turbulent kinetic energy spectrum exhibits a $k^{-5/3}$ decay law.

Abstract

In the present paper, an efficient method to generate "pure" cylindrically converging shock wave without a following contact surface is proposed firstly. Then, the Richtmyer-Meshkov instabilities of two interfaces driven by the generated cylindrically converging shock wave and the associated fluids' mixing behaviors are numerically studied. The results show that the instability of the interface is characterized by the growth of perturbation amplitude before re-shock. However, the mixing of fluids is enhanced dramatically after re-shock, which is manifested not only by the evolutions of flow structures but also by the temporal behaviors of mixing parameters. Further investigation shows that, although these two cases are of different initial perturbations, their evolutions of mixing width and other mixing parameters such as molecular mixing fraction, local anisotropy and density-specific volume correlation could achieve the same laws of temporal behavior, especially during the later stage after re-shock. These results to some extent demonstrate that there also exist scaling law and temporal asymptotic behaviors in the mixing zone for cylindrically converging shock wave driven interface. Moreover, the analyses of turbulent kinetic energy spectrums in the azimuthal direction at late stage also witness the $k^{-5/3}$ decaying law of turbulent kinetic energy for the present inhomogeneity flows driven by cylindrically converging shock wave, which further manifests that the fluids' mixing is indeed enhanced at later time after re-shock.