MODELING THE INITIAL MOTION OF LARGE CYLINDRICAL AND SPHERICAL BUBBLES

A two-dimensional, transient, finite difference technique based on a volume fraction specification of the free surface position and accounting for the effects of surface tension is shown to accurately predict the initial motion of large cylindrical and spherical bubbles. The predictions compare very favourably with the experimental data of Walters and Davidson. The initial acceleration of cylindrical and spherical bubbles is properly predicted as g and 2g respectively. The penetration of a tongue of liquid from below is the dominant process by which large deformations from the original shape take place and is well predicted by the model in both cases. For the spherical case the eventual transition into a toroidal bubble is demonstrated and the circulation associated with a rising toroidal bubble as a function of its volume upon release is shown to agree very well with experiments. Iterative linear equation-solving techniques applicable to the special nature of the linear system resulting from such a free surface specification are surveyed and a simple Jacobi iteration based on red-black ordering is found to perform well. The impact of the free surface on the relaxation of the linear system and the convergence criteria is also explored.