Numerical simulation of oscillations and rotations of a free liquid droplet using the level set method

Watanabe, Tadashi

In order to develop numerical techniques for two-phase flow simulations, a code solving the Navie-Stokes equations using the level set method is developed and three-dimensional oscillations and rotations of a free liquid droplet are simulated. The oscillations of order 2, 3 and 4 are simulated, and the frequency and the damping for small-amplitude oscillations are shown to agree well with those by the linear theory. Flow fields are visualized, and three-dimensional vortex structures are found to appear around the droplet. It is also found that the number of vortices is the same as the order of oscillation. The effects of initial amplitude and rotation on the oscillation frequency are studied, and it is shown that the oscillation frequency decreases as the initial amplitude increases, while it increases as the rotation rate increases. These nonlinear effects are found to be overestimated by theoretical predictions based on second order perturbations.