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

Abstract

In this paper, a unified framework for particulate two-phase flow will be 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, i.e., 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 for the continuum gas flow. 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 high concentrated solid particle phase will be modeled by the Eulerian hydrodynamic wave due to the intensive particle-particle collisions, same as the fluid model. At a large Kn number, the dilute solid particle will be sampled and followed by the Lagrangian particle formulation to capture the non-equilibrium transport. In the transition regime, the distribution and evolution of particle and wave in UGKWP are controlled by the local Kn number with a smooth transition between the above limits. The distribution of solid particles in UGKWP is composed of analytical function and discrete particle, where 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 all following aspects: drag force model for different solid particle concentrations; the frictional pressure in inter-particle contacts at high solid-particle concentration; a flux limiting model to avoid solid particles' over-packing; additional nonconservative nozzle and work terms in the governing equation for the gas phase to reflect the local variation of solid volume fraction. Besides, the inter-particle collisions have been refined numerically for the dense particle phase flow through the discretization of the collision term and numerical flux function. The improved method has been applied to gas-particle system with a wide range of solid-particle concentrations. The numerical scheme is tested in a series of 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 accuracy and reliability of the proposed method for gas-particle flow.