A Parameter Study of Shock Focusing Phenomenon for Shock-Elliptic Bubble Interaction

Impulsive acceleration of a spherical gas-density inhomogeneity by a planar shock is referred to as the classical shock-bubble interaction or SBI. The applications of this flow class cover a wide range of scales, spanning from shock-wave lithotripsy and supersonic combustion to inertial confinement fusion and shocked interstellar media.

Depending on media and bubble parameters, two distinct classes of flows – divergent and convergent shock refractions – take place. The resulting effects of bubble distortion and vorticity deposition and development are well studied. Another, less explored SBI feature is shock focusing phenomenon, or SFP, which takes place for both divergent and convergent shock refraction patterns, although the mechanisms of focusing shocks formation and collapsing (cumulation) are completely different.

Apart from Mach number M of incident shock and Atwood number A of bubble gas, SFP features are strongly dependent on bubble elongation e. Several SFP patterns – internal (Fig. 1), external and transitional – are distinguished according to the position of cumulation point relative to distorted bubble boundary.

Fig. 1 An internal SFP pattern for converging shock refraction case (M=2, A=0.5, e=1.4): early stage (left) and shortly before the cumulation (right). Bottom edge is the axis of symmetry; white arrows indicate local shock propagation directions.

The present study continues and expands the investigation [1] of interaction of a shock with elliptical bubbles using Euler’s equations. A parameter study is performed for Mach number, Atwood number and bubble shape. A qualitative dependence of SFP pattern type and intensity is determined (see Fig. 2 for an example for A=0.5). Three-dimensional simulations are performed in order to determine non-axisymmetrical features of SBI-induced shock focusing process.

This study is supported by Russian Scientific Fond (project №14-11-00773).

Fig. 2 A qualitative dependence of SFP pattern and peak pressure on Mach number M and bubble elongation e for A=0.5. Patterns are coded by color: orange is external, yellow is transitional and green is internal cumulation type.

1. Georgievskii P.Yu., Levin V.A., Sutyrin O.G. Cumulation Effect upon the Interaction between a Shock and a Local Gas Region with Elevated or Lowered Density // Fluid Dynamics. 2011. V. 46. No. 6 P. 967–974. DOI: 10.1134/S0015462811060147