Shock-bubble interactions: Features of divergent shock-refraction geometry observed in experiments and simulations

The interaction of a planar shock wave with a spherical bubble in divergent shock-refraction geometry is studied here using shock tube experiments and numerical simulations. The particular case of a helium bubble in ambient air or nitrogen (A approximate to -0.8) is considered, for 1.4 < M < 3.0. Experimental planar laser diagnostics and three-dimensional multifluid Eulerian simulations clearly resolve features arising as a consequence of divergent shock refraction, including the formation of a long-lived primary vortex ring, as well as counter-rotating secondary and tertiary upstream vortex rings that appear at late times for M >= 2. Remarkable correspondence between experimental and numerical results is observed, which improves with increasing M, and three-dimensional effects are found to be relatively insignificant. Shocked-bubble velocities, length scales, and circulations extracted from simulations and experiments are used successfully to evaluate the usefulness of various analytical models, and characteristic dimensionless time scales are developed that collapse temporal trends in these quantities. Those linked directly to baroclinicity tend to follow time scales based on shock wave speeds, while those linked to interface deformation and vortex- or shear-induced motion tend to follow a time scale based on the postshock flow speed, though no single time scale is found to be universally successful. (c) 2008 American Institute of Physics.