Numerical simulation of a shock–helium bubble interaction

Abstract

We solve the Euler equations to compute the interaction of a Mach 1.22 shock wave with a helium bubble contaminated by 28% air by mass. A ninth-order upwind scheme is used to calculate the left and the right states of the primitive variables as required by the AUSMD algorithm. The low numerical dissipation of the AUSMD algorithm makes it an ideal choice for computing long-time behavior of the bubble after the shock passes over it. The algorithm combines well with the high spectral accuracy of the ninth-order upwind scheme. The basic trends in the evolving bubble match with earlier experimental and numerical observations. Effect of numerical schemes and grid sizes is also observed for this study. The Euler solver captures a large number of small-scale rolled-up vortices originally generated by the baroclinic torque term in the vorticity transport equation and later enhanced by the Kelvin–Helmholtz instability. Numerical schlieren, mass fraction, and vorticity contour plots are used to visualize the turbulent mixing zone that is a key feature of the translating and deforming bubble.