Numerical simulation of two- and three-dimensional. two-phase fluid motionby lattice Boltzmann method

This study describes the numerical simulations of two-phase fluid motions u nder gravity by the lattice Boltzmann method (LBM), in which the fluid moti ons result from collision and translation of mesoscopic particles and the i nterface interaction in multiphase fluids can be reproduced in a self-organ izing way. Our aims are to examine the applicability of LBM to the numerica l 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 liq uid-volume convective equations, and to develop the three-dimensional binar y fluids model, consisting of two sets of distribution functions to represe nt 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 be tween two phases in the lattice Boltzmann equations, and simulated the moti ons of single bubble and two bubbles rising in a duct, calculating the surf ace tension from the Laplace's law represented by the non-dimensional numbe rs, Eotvos and Morton numbers. In the two-dimensional simulations, the resu lts by LBM agree with those by the VOF method. The three-dimensional simula tion 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 c oalesce into a single bubble eventually. These results prove the validity o f the buoyancy model proposed here and the applicability of LBM to the quan titative numerical analysis of two-phase fluid motions. (C) 2000 Elsevier S cience B.V. All rights reserved.