The collapse of a spherical cavity in a compressible liquid

Abstract

This paper presents numerical solutions for the flow in the vicinity of a collapsing spherical bubble in water. The bubble is assumed to contain a small amount of gas and the solutions are taken beyond the point where the bubble reaches its minimum radius up to the stage where a pressure wave forms and propagates outwards into the liquid. The motion up to the point where the minimum radius is attained, is found by solving the equations of motion both in the Lagrangian and in the characteristic forms. These are in good agreement with each other and also with the approximate theory of Gilmore which is demonstrated to be accurate over a wide range of Mach number. The liquid flow after the minimum radius has been attained is determined from a solution of the Lagrangian equations. It is shown that an acoustic approximation is quite valid for fairly high pressures and this fact is used to determine the peak intensity of the pressure wave at a distance from the center of collapse. It is estimated in the case of typical cavitation bubbles that such intensities are sufficient to cause cavitation damage.