Non-spherical bubble dynamics of underwater explosions in a compressible fluid

This paper is concerned with the bubble dynamics of underwater explosion in a compressible liquid flow whose Mach number, based on characteristic liquid velocities, is O(10−1). We will study this phenomenon based on weakly compressible theory using the method of matched asymptotic expansions. As a result, the inner flow near the bubble to second order is described by Laplace's equation with the compressible effects appearing only in the far field condition. The problem can thus be modelled approximately using the boundary integral method. Validations are performed against the Keller equation for spherical bubbles and available experimental data for “small-charge” explosions for non-spherical bubbles under the action of buoyancy. The computation traces jet impact, the transition of the bubble from a singly connected to a doubly connected form, and the recombining of a doubly connected to a singly connected form, and the further repeated transitions. The computational result of the bubble shapes correlates well with experimental data to the end of the second oscillation. The first collapse, which we call the “principal collapse,” is the most severe in terms of energy loss. The damping of the bubble oscillation is alleviated by the buoyancy effects and reduced with the buoyancy parameter.