Numerical Simulation of Shock Bubble Interaction with Different Mach Numbers**Supported by the National Natural Science Foundation of China under Grant Nos 11232011 and 11402262, the 111 Project under Grant No B07033, and the China Postdoctoral Science Foundation Funded Project under Grant No 2014M561833.

Abstract

The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high-resolution piecewise parabolic method (PPM), in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers (Ma). The results of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le Métayer, Phys. Fluids 19 (2007) 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the compression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.