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.

Experiments are carried out on the interaction and coalescence of two, three and four bubbles with approximately the same sizes, distributed evenly and symmetrically. The bubbles are generated simultaneously by electric discharges, using an in-house designed series circuit, and their interaction is captured using a high-speed camera. Particular attentions are paid to if/when coalescence of bubbles happens, and the motion of the joined bubbles. Some new features are observed, which depend mainly on the dimensionless distance γ bb = d bb /R max , where d bb is the inter-bubble distance and R max is the maximum bubble radius. For γ bb > 2, a jet forms and penetrates each side bubble, directed to the center of the configuration, resulting in a protrusion. Towards the end of collapse, a large portion of bubble gases is compressed into the protrusion from the main part of the toroidal bubble. For γ bb < 2, the bubbles coalesce during expansion, and the part of the joined bubble's surface distal from the center of the configuration collapses faster than elsewhere. The experiments show that the oscillation period of multi-bubbles does not change appreciably without coalescence but increases significantly with coalescence. For three bubbles initiated at collinear positions with γ bb > 2, the jets that form from the side bubbles are towards the middle, and the middle bubble splits into two parts, moving towards the two side bubbles. For γ bb < 2, the side bubbles merge with the middle bubble during expansion, forming an ellipsoid bubble; the joined bubble collapses predominantly from two sides, where two inward jets form towards the end of collapse.

Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document. When citing, please reference the published version. Take down policy While the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.