Numerical modeling of the dynamics of bubble oscillations subjected to fast variations in the ambient pressure with a coupled level set and volume of fluid method.

Abstract

A numerical method for modeling and understanding the dynamics of bubble oscillations subjected to fast variations in the ambient pressure is proposed under low Mach number conditions. In the present work, the method uses a single-fluid continuum formalism of weakly compressible axisymmetric Navier-Stokes equations for the numerical simulation of liquid-gas flows with surface tension and adopts the interface capturing approach based on a coupled level set and volume of fluid (CLSVOF) method for describing the moving and deformed interfaces. To demonstrate the efficacy of the proposed method, first, the numerical results of the radial oscillations of a spherical gas bubble are tested with the numerical solutions of Rayleigh-Plesset equation. Then, the numerical method is applied to reproduce the growth and subsequent collapse of a bubble in an infinite liquid medium observed in experiments. Finally, the numerical simulation of the interaction of two oscillating bubbles at small separation distance is evaluated in response to a moderate step change in the ambient pressure. It is shown that two deformable bubbles undergo coupled radial and oscillatory translational motions which eventually results in the bubbles' attraction and coalescence caused by the secondary Bjerknes forces. The numerical predictions show very good accuracy with the experimental and numerical results reported in the literature.