Multiple - Relaxation - Time Lattice Boltzmann Method for Multiphase Flows with High Density and Viscosity Ratios - 10135

In this paper, the lattice Boltzmann method is reviewed for specific applications to numerical simulation of multiphase flow problems. A thorough literature review regarding the multi-phase lattice Boltzmann method was conducted with special focus on flows with large density and viscosity ratios between the two phases. A multiphase model with the capability of handling large-density-ratios is crucial for the modeling efforts at Florida International University since Department of Energy related operations such as the pulsed-air mixing involve air bubbles formed in tanks where the liquid to gas density ratio is approximately 1000. It was observed that there have been four major interface tracking methods developed in the lattice Boltzmann framework, namely; the color method, the free-energy method, ShanChen’s potential method and the index-function method. There have also been other methods proposed such as the hybrid level-set lattice Boltzmann method and the front-tracking lattice Boltzmann method, however, they have not been applied as extensively as the others. Lattice Boltzmann simulations are reported to be unstable when the density ratio between fluids are larger than 10. Of twenty-six papers reviewed on multiphase lattice Boltzmann method with the single-relaxation-time collision model, five have extended the capability of the multiphase methods into fluids with large-density-ratios up to 1000. However, the single-relaxation-time lattice Boltzmann method using the Bhatnagar-Gross-Krook collision model was found to have stability issues when the viscosity of the fluid is reduced or the Reynolds number is increased. Lattice Boltzmann method using the multiple-relaxation-time collision operator was proposed by researchers in order to simulate flows where viscosities are low or the Reynolds number is large. Twenty-five publications were reviewed on multiple-relaxation-time methods, seventeen of which were specific to multiphase flows. Six of the multiple-relaxation-time papers were focused on multiphase flows with large liquid to gas density ratios, which was identified as another source of numerical instabilities observed in multiphase simulations with the lattice Boltzmann method. The multiplerelaxation-time lattice Boltzmann method coupled with the modified index-function approach was observed to be capable of stable simulations of high-density-ratio, low viscosity multiphase flows.