Numerical Simulation of Shock Bubble Interaction with Different Mach Numbers

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 (M-a). The results of low M-a cases agree quantitatively with those of experiments [G. Layes, O. Le Metayer, Phys. Fluids 19 (2007) 042105]. With the increase of M-a, 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 M-a is low, while less agreement has been achieved for high M-a cases. In addition, the mixedness between two fluids is enhanced greatly as M-a increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high M-a cases.