Numerical investigation of toroidal bubble dynamics in a compressible fluid based on boundary integral method

Abstract

The external liquid compressibility cannot be ignored because the speed of the bubble jet emerging at the end of bubble collapse reaches hundreds of meters per second. Additionally, when the bubble jet penetrates the surface of a bubble, a toroidal bubble forms and the singly connected flow domain changes to a doubly connected topology. As the Biot–Savart law is based on the assumption of incompressibility, the vortex ring model is very difficult to extend to compressible fluids. This paper describes the use of the boundary integral method to establish a numerical model of a toroidal bubble, considering the external liquid compressibility and the internal gas wave effect. A cut is introduced into the fluid domain so that it can be considered as singly connected, with the discontinuity of velocity across this cut equal to the circulation of the flow. Furthermore, the initial bubble condition is calculated by the volume acceleration model. The numerical model is validated through comparisons with experimental data from underwater explosions. The numerical results are found to correlate well with the experimental results. Then, the influence of buoyancy parameters and the internal gas wave effect on toroidal bubble dynamics in a gravitational field is investigated.