Comparison of Vortex Cut and Vortex Ring Models for Toroidal Bubble Dynamics in Underwater Explosions

Abstract

The jet impact from a collapsing bubble is an important mechanism of structural damage in underwater explosions and cavitation erosion. The Boundary Integral Method (BIM) is widely used to simulate nonspherical bubble dynamic behaviors due to its high accuracy and efficiency. However, conventional BIM cannot simulate toroidal bubble dynamics, as the flow field transforms from single-connected into double-connected. To overcome this problem, vortex cut and vortex ring models can be used to handle the discontinuous potential on the toroidal bubble surface. In this work, we compare these two models applied to toroidal bubble dynamics in a free field and near a rigid wall in terms of bubble profile, bubble gas pressure, and dynamic pressure induced by the bubble, etc. Our results show that the two models produce comparable outcomes with a sufficient number of nodes in each. In the axisymmetric case, the vortex cut model is more efficient than the vortex ring model. Moreover, we found that both models improve in self-consistency as the number of bubble surface elements (N) increases, with N=300 representing an optimal value. Our findings provide insights into the numerical study of toroidal bubble dynamics, which can enhance the selection and application of numerical models in research and engineering applications.