Numerical analysis of shock interaction with a spherical bubble

Abstract

Two-dimensional and three-dimensional computational fluid dynamics studies of a spherical bubble impacted by a supersonic shock wave (Mach 1.25) have been performed to fully understand the complex process involved in shock–bubble interaction (SBI). The unsteady Reynolds-averaged Navier–Stokes computational approach with a coupled level set and volume of fluid method has been employed in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex ring agree very well with the relevant available experimental data. The predicted non-dimensional bubble and vortex velocities are also in much better agreement with the experiment data than values computed from a simple model of shock-induced Rayleigh–Taylor instability (the Richtmyer–Meshkov instability). Comprehensive flow visualization has been presented and analyzed to elucidate the SBI process from the beginning of bubble compression (continuous reflection and refraction of the acoustic wave fronts as well as the location of the incident, refracted and transmitted waves at the bubble compression stage) up to the formation of vortex rings as well as the production and distribution of vorticity. Furthermore, it is demonstrated that turbulence is generated with some small flow structures formed and more intensive mixing, i.e., turbulent mixing of helium with air starts to develop at the later stage of SBI.