Contribution of Mach number on the evolution of Richtmyer-Meshkov instability induced by shock-accelerated square light bubble

TL;DR

This study numerically investigates how different shock Mach numbers influence the evolution and flow morphology of Richtmyer-Meshkov instability induced by a shock-accelerated square helium bubble, revealing significant effects on vortex formation and mixing.

Contribution

It provides a detailed numerical analysis of the impact of shock Mach number on RM instability with a square light bubble, highlighting flow morphology changes and vortex dynamics.

Findings

Higher Mach numbers lead to larger vortex chains and stronger mixing zones.

Shock Mach number significantly affects flow patterns, vortex formation, and bubble deformation.

The study offers comprehensive analysis of shock trajectory and interface evolution at different Mach numbers.

Abstract

The Richtmyer-Meshkov (RM) instability has long been an interesting subject due to its fundamental significance in scientific research, as well as its crucial role in engineering applications. In this study, the contribution of shock Mach number on the evolution of the RM instability induced by a shock-accelerated square light bubble is investigated numerically. The square bubble is composed of helium gas and the surrounding (ambient) gas is nitrogen. Three cases of incident shock strength are considered: Ms = 1.21, 1.7, and 2.1. An explicit mixed-type modal discontinuous Galerkin scheme with uniform meshes is employed to numerically solve a two-dimensional system of unsteady compressible Navier--Stokes--Fourier equations. The numerical results show that the shock Mach number plays an important role during the interaction between a planar shock wave and a square light bubble. The shock Mach number causes significant changes in flow morphology, resulting in complex wave patterns, vorticity generation, vortex formation, and bubble deformation. In contrast to low Mach numbers, high Mach numbers produce the larger rolled-up vortex chains, larger inward jet formation, and a stronger mixing zone with greater expansion. The effects of Mach numbers are explored in detail through phenomena such as the vorticity generation, and evolutions of enstrophy as well as dissipation rate. Finally, the Mach number effects on the time-variations of the shock trajectories and interface features are comprehensively analyzed.