Some dynamical characteristics of a non-spherical bubble in proximity to a free surface

Abstract

The motions of a gas bubble in proximity to a free surface with and without buoyancy force, as well as in shallow water are simulated based on a numerical time integration coupled with three-dimensional boundary integral spatial solution. The fluid is assumed to be inviscid, incompressible, and the flow irrotational. The unsteady Bernoulli equation is applied on the free surface and bubble surface as one of the boundary conditions of the Laplace equation for the potential. Improvements have been made in the mesh generation of the free surface and rigid boundary, the modeling of the toroidal bubble after the jet impact and the investigation into the combined effects on the motion of a bubble in the presence of the rigid bottom and free surface. The growth and collapse of a gas bubble together with the formation of the toroidal bubble after the jet impact are simulated. The shapes and positions of the bubble, the trajectories and velocities of the poles of the bubble as well as the pressure distributions in the fluid under different standoff distances and buoyancy parameters are obtained to better illuminate the mechanism underlying the motions of gas bubble and free surface. When a bubble is initiated sufficiently close to a free surface, the free surface spike and the second accelerating phenomenon of the free surface during the collapse phase can be observed. The buoyancy force has significant effects on the jet formation and development within the bubble and it may reverse the direction of the liquid jet when exceeding the effect of the Bjerknes force induced by the free surface. The large contortions in the shallow water and the formation of the high-pressure region between the bubble and the free surface are captured when the bubble is close enough to the rigid bottom and the free surface.