On the dynamics of a shock-bubble interaction

We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity. Such interactions have been studied experimentally in an attempt to elucidate the mechanisms whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions and re ections of acoustic fronts at the bubble interface. Speci cally, we have reproduced two of the experiments performed by Haas and Sturtevant: a MS = 1:22 planar shock wave, moving through air, impinges on a cylindrical bubble which contains either helium or Refrigerant 22. These ows are modelled using the two-dimensional, compressible Euler equations for a two component uid (air-helium or air-Refrigerant 22). Although simulations of shock wave phenomena are now fairly commonplace, they are mostly restricted to single component ows. Unfortunately, multi-component extensions of successful single component schemes often su er from spurious oscillations which are generated at material interfaces. Here we avoid such problems by employing a novel, nonconservative shock-capturing scheme. In addition, we have utilized a sophisticated adaptive mesh re nement algorithm which enables extremely high resolution simulations to be performed relatively cheaply. Thus we have been able to reproduce numerically all the intricate mechanisms that were observed experimentally (e.g. transition from regular to irregular refraction, cusp formation and shock wave focusing, multi-shock and Mach shock structures, jet formation etc.), and we can now present an updated description for the dynamics of a shock-bubble interaction. 1This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681. 2Supported in part by an NSF Postdoctoral Fellowship, NSF grant #DMS92 03768, ONR grant #N0001492-J-1245, DOE contract #DEFG0288ER25053 and a Packard Fellowship to Leslie Greengard.