Collapse and Rebound of a Spherical Bubble in Water

TLDR

The study presents numerical solutions describing fluid flow around a collapsing spherical bubble in water. The authors model the bubble dynamics using Lagrangian and characteristic equations, extending solutions beyond the minimum radius to capture rebound and outward pressure wave propagation. The numerical results agree with Gilmore’s theory across a wide Mach range, confirm that an acoustic approximation remains valid at high pressures, and predict pressure wave intensities capable of inducing cavitation damage.

Abstract

Some numerical solutions are presented which describe 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 which propagates outwards into the liquid. The motion during collapse, up to the point where the minimum radius is attained, is determined by solving the equations of motion both in the Lagrangian and in the characteristic form. These are found to be in good agreement with each other and also with the approximate theory of Gilmore which is shown to be accurate over a wide range of Mach number. The liquid flow during the rebound, which occurs after the minimum radius has been attained, is determined from a solution of the Lagrangian equations. It is shown that an acoustic approximation is valid even for fairly high pressures, and this fact is used to determine the peak intensity of the pressure wave as it moves outwards 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.