Unified gas-kinetic wave–particle method for gas–particle two-phase flow from dilute to dense solid particle limit

Abstract

A unified framework for particulate two-phase flow is presented with a wide range of solid particle concentration from dilute to dense limit. The two-phase flow is simulated by two coupled flow solvers, that is, the gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic wave–particle method (UGKWP) for the solid particle phase. The GKS is a second-order Navier–Stokes flow solver. The UGKWP is a multiscale method for all flow regimes. The wave and particle decomposition in UGKWP depends on the cell's Knudsen number (Kn). At a small Kn number, the highly concentrated solid particle phase will be modeled by the Eulerian hydrodynamic wave due to the intensive particle–particle collisions. At a large Kn number, the dilute solid particle will be followed by the Lagrangian particle to capture the non-equilibrium transport. In the transition regime, a smooth transition between the above limits is obtained according to the local Kn number. The distribution of solid particles in UGKWP is composed of analytical function and discrete particle, and both condensed and dilute phases can be automatically captured in the most efficient way. In the current scheme, the two-phase model improves the previous one in many aspects, such as drag force model, the frictional pressure formulation, and flux limiting model. The scheme is tested in many typical gas–particle two-phase problems, including the interaction of shock wave with solid particle layer, horizontal pneumatic conveying, bubble formation, and particle cluster phenomena in the fluidized bed. The results validate the GKS-UGKWP for the simulation of gas–particle flow.