A Novel Numerical Scheme for Outlet Boundary Conditions in Large Density Ratio Lattice Boltzmann Model

Abstract

In the past decades, the Lattice Boltzmann method has gained much success in variety fields especially in multiphase flow, porous media flow, and other complex flow, and become a promising method for computational fluid dynamic (CFD). The outlet boundary condition (OBC) and its numerical scheme are critical issues in CFD, which may influence the accuracy and stability of the calculation. The common OBCs i.e. Neumann boundary condition (NBC), extrapolation boundary condition (EBC), and convection boundary condition (CBC), which have been widely investigated in single-phase LB model, have rarely been investigated in multiphase LB model. The previous research on the OBCs for two-phase LB model only aims at small density ratio. While in most industrial applications, the density ratio often ranges from a hundred to a thousand, and a large density ratio would bring some problems such as parasitic current and bad stability in LB method. Lee and Fischer have proposed an improved LB model which is suitable for large density ratio two-phase flow. In order to assess the OBCs for large density ratio LB model, the OBCs are investigated. And it is found that the existing OBC numerical scheme cannot be directly applied to the large density ratio LB model. In present study, a novel numerical scheme for the OBCs is proposed assuming that the outlet velocity is gained by the outlet boundary condition instead of the momentum equation which is an improvement of previous scheme, and it can be used in large density ratio LB model. The performance of the proposed OBC scheme is examined for different density ratios. The results show that the proposed OBC scheme could converge in a stable manner. Comparing with the reference flow condition, the CBC scheme shows a better performance than the NBC scheme and the EBC scheme. The NBC scheme would lead a large droplet deformation, large velocity peaks at the outlet, and large errors for both small and large density ratio. And the EBC scheme keeps a good droplet shape, but it would lead large velocity peaks at the outlet and large error when large density ratio is considered. The CBC scheme always shows superior performance including a good droplet shape, smooth outlet velocity profile, and small errors no matter whether the density ratio is small or large. Hence the CBC scheme could be applied in large density ratio LB model for the outlet boundary condition, which has a good accuracy and stability in the calculation.