High resolution numerical simulation of a shock-accelerated refrigerant-22 bubble

Abstract

Computational results are presented for an evolving Refrigerant-22 bubble after its interaction with a Mach 1.22 shock wave. Initially, the bubble is kept stationary in surrounding air, presenting a fast/slow interface to the approaching shock wave. We solve the Euler equations in two dimensions using the low dissipation AUSMD algorithm coupled with a ninth-order upwind scheme for the convective terms and a four-stage third-order Runge–Kutta time integration scheme. The high resolution solver reveals intricate details of vorticity generation during and after the interaction. In the early phase, the detected wave structure matches with available experimental and computational results. Going beyond what is available in literature, we show how the central jet that has drawn attention of researchers could be explained by observing the Richtmyer–Meshkov instability driven mushroom structure that appears behind a cylindrical blast wave set off near the ground. Initial growth of vorticity generated by the baroclinic torque, appearance of opposite signed vorticity during emergence of the transmitted wave, interaction of vortices of various sizes and their accumulation in regions of intense mixing are all captured well. Tracking the area within the bubble where mole fraction of Refrigerant-22 is between 0.05 to 0.8, we show that mixing of air and Refrigerant-22 is increases with a period of time. Fourier spectra of streamwise kinetic energy is indicative of redistribution of energy to lower Fourier modes during long time bubble growth. This redistribution of energy occurs through merger of vortices during their interaction.