Lattice Boltzmann Method For Multiphase Flows With High Density Ratios

Abstract

This thesis describes the Lattice Boltzmann Method (LBM) and its application to single and multiphase flows. The LBM algorithm using Single Relaxation Time (SRT) and Multi Relaxation Time (MRT) models are studied. In particular, a new MRT multiphase model is developed, based upon the SRT multiphase model of Banari et al. (2014). A unified LBM approach is used with separate formulations for the phase field, the pressureless Naiver-Stokes (NS) equations and the correction of the pressureless velocity field by solving a Poisson equation. To validate the current model, computations for various Reynolds numbers (Re) were performed to simulate 2D lid driven cavity flow. Results show excellent comparison with those in the literature. The multiphase model was verified with two fluid Poiseuille flow, static and rising bubbles. The method was also used to simulate 2D single and multiple mode Rayleigh-Taylor instability (RTI). A good comparison between the present numerical results and those in the literature at large Re with high density ratio and various values of surface tension coefficient in single mode and multiple mode RTI are made, respectively. The multiphase LB model has been extended using MRT collision operator to study various breaking dam problems with both dry and wet bed, expanding the range of the possible density ratios and Re which was impossible with SRT. The simulations show agreement with those in the literature. Moreover, grid convergence was studied using both acoustic and diffusive scaling for standing wave simulations with high density ratios. The use of MRT was found to improve the stability for high density ratio. Results with density ratio up to 1000 at large Re = 1000 were obtained using MRT model.