The motion of a 3D toroidal bubble and its interaction with a free surface near an inclined boundary

The numerical modelling of 3D toroidal bubble dynamics is a challenging problem due to the complex topological transition of the flow domain, and physical and numerical instabilities, associated with jet penetration through the bubble. In this paper, this phenomenon is modelled using the boundary integral method (BIM) coupled with a vortex ring model. We implement a new impact model consisting of the refined local mesh near the impact location immediately before and after impact, and a surgical cut at a high resolution forming a smooth hole for the transition from a singly connected to doubly connected form. This enables a smooth transition from a singly connected bubble to a toroidal bubble. The potential due to a vortex ring is reduced to the line integral along the vortex ring. A new mesh density control technique is described to update the bubble and free surfaces, which provides a high mesh quality of the surfaces with the mesh density in terms of the curvature distribution of the surface. The pressure distribution in the flow field is calculated by using the Bernoulli equation, where the partial derivative of the velocity potential in time is calculated using the BIM model to avoid numerical instabilities. Experiments are carried out for the interaction of a spark generated bubble with a free surface near a boundary, which is captured by using a high speed camera. Our numerical results agree well with the experimental images, for the bubble and free surface shapes for both before and after jet impact. New results are analyzed for the interaction of a toroidal bubble with a free surface near a vertical boundary and a sloping boundary, at both negative and positive angles to the vertical, without and with buoyancy, respectively. After jet impact, the bubble becomes a bubble ring, whose cross section is much thinner at the distal side from the boundary. It subsequently breaks into a crescent shaped bubble. The free surface displays singular features at its intersection with an inclined boundary.