Nonsimilar Effects in the Collapsing of an Empty Spherical Cavity in Water

Abstract

The flow field behind, and the motion of an empty spherical cavity collapsing in water are calculated by means of a perturbation technique similar to Sakurai's theory for blast waves in gases. In order that the higher approximations may be uniformly valid, the radius coordinate is modified in accordance with Lighthill's principle. The present scheme applies only to the latter half of the collapse process when the cavity speed is highly supersonic and extends Hunter's self-similar solution to account for nonsimilar effects due to the finite sound speed at the interface as well as the finite cavity radius of curvature. The first-order theory is worked out for a sample cavity of initial radius 1 cm collapsing under a constant ambient pressure of 6 atm. The necessary coupling with the initial conditions is obtained from the results of some earlier numerical calculations. The present results indicate that while the nonsimilar effects modify the distributions of flow parameters, the cavity trajectory is practically unchanged from the self-similar law. Very high pressures are shown to accompany cavity collapse even at moderately high collapse speeds.