The Evolution of a Gas Bubble Near an Inclined Wall

The nonlinear dynamics of a gas bubble close to an inclined wall is investigated numerically. The fluid is assumed to be inviscid and incompressible and the flow irrotational. A time-integration boundary integral method is used to solve the Laplace equation for the velocity potential to calculate the shape and position of the bubble. Improvements to the previous research on this subject have been made in the surface triangulation of the initial spherical bubble, the integration of the influence coefficients, the calculations of the normal vector and tangential velocity vector at a node, the time integration scheme, etc. Comparisons have been carried out between the results of the present three-dimensional model and the results of a validated axis-symmetrical bubble code (Wang et al., 1996a,b, 1998) for axis-symmetrical cases. The comparisons demonstrate the robustness and accuracy of the present method. Simulations have been carried out for a gas bubble initiated at 3.0R _m, 2.0R _m, and 1.0R _m (R _m being defined as the maximum radius of the bubble) from an inclined wall with various buoyancy parameters and wall angles. All the simulations are performed at high resolution and without numerical instabilities occurring nearly up until the re-entrant jet impacts on the opposite bubble surface. The following qualitative features have been observed. When a bubble is initiated at $3.0R_{rm m}$ or more away from an inclined wall, the jet is roughly symmetric; the jet direction is roughly the same as that of the motion of the bubble centroid, which can be approximately predicted by the Kelvin impulse theory. When a bubble is initiated around 2.0R _m from a wall, the jet is obviously asymmetric and inclined upwards; the Kelvin impulse theory can only be used to predict the location where the jetting occurs, but it can no longer be used to predict the jet direction. When a bubble is initiated at 1.0R _m or less near an inclined wall and the buoyancy and Bjerknes attraction are comparable, the jet is roughly in the upward direction. Received 6 August 1997 and accepted 9 April 1998