Numerical simulation of two- and three-dimensional two-phase fluid motion by lattice Boltzmann method

Abstract

This study describes the numerical simulations of two-phase fluid motions under gravity by the lattice Boltzmann method (LBM), in which the fluid motions result from collision and translation of mesoscopic particles and the interface interaction in multiphase fluids can be reproduced in a self-organizing way. Our aims are to examine the applicability of LBM to the numerical analysis of bubble motions in comparison with the two-dimensional results by the Volume Of Fluid (VOF) method based on the Navier–Stokes and the liquid-volume convective equations, and to develop the three-dimensional binary fluids model, consisting of two sets of distribution functions to represent the total fluid density and the density difference, which introduces the repulsive interaction consistent with a free energy function between fluid particles. We included the buoyancy terms due to the density difference between two phases in the lattice Boltzmann equations, and simulated the motions of single bubble and two bubbles rising in a duct, calculating the surface tension from the Laplace's law represented by the non-dimensional numbers, Eotvos and Morton numbers. In the two-dimensional simulations, the results by LBM agree with those by the VOF method. The three-dimensional simulation of two bubble interaction shows that the upper bubble takes a shape of skirt as the lower bubble approaches due to the wake formation, and they coalesce into a single bubble eventually. These results prove the validity of the buoyancy model proposed here and the applicability of LBM to the quantitative numerical analysis of two-phase fluid motions.