Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

TL;DR

This paper extends the pseudopotential lattice Boltzmann model to simulate multiphase flows with large density ratios and high Reynolds numbers by introducing an improved forcing scheme and parameter adjustments, enabling more accurate and stable simulations.

Contribution

An improved pseudopotential LB model with enhanced thermodynamic consistency and stability at large density ratios, validated through complex multiphase flow simulations.

Findings

Successfully simulated multiphase flows at density ratios over 500.

Reduced spurious currents and improved numerical stability.

Predicted droplet dynamics consistent with experimental power laws.

Abstract

Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Li et al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/sqrt(a). Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.