Computing Shock Waves in Cloud Cavitation

Abstract

This paper presents a numerical investigation of some of the phenomena involved in the nonlinear dynamics of a homogeneous bubbly mixture bounded by an oscillatory wall. This problem represents an idealization of the flow in a typical vibratory cavitation damage device. Results are presented showing that wave steepening and ultimately shock wave formation occur as the magnitude of the excitation increases. The propagation characteristics of the waves through the bubbly medium have also been studied. Strong pressure peaks of short duration, corresponding to the coherent collapse of the bubble clusters, are computed and accurately resolved, both in space and time. As the amplitude of the excitation is increased a series of period doubling bifurcations occurs. The nonlinear dynamics of the oscillating bubble cluster are observed to follow a subharmonic route to chaos.