Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

Abstract

In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. In this study, the gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of local particle phase Knudsen number. The UGKWP is an appropriate method for the capturing of the multiscale transport mechanism in the particle phase through its coupled wave-particle formulation. In the regime with intensive particle collision, the evolution of solid particle will be followed by the analytic wave with quasi-equilibrium distribution; while in the rarefied regime the non-equilibrium particle phase will be captured through particle tracking and collision, which plays a decisive role in recovering particle trajectory crossing behavior. The gas phase in the multiphase system is assumed to be stay in the continuum flow regime, and its evolution is mainly controlled by the Navier-Stokes equations with the interaction with particle phase. The gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the highly collision regime for the particles, no particles will be sampled in UGKWP and the wave formulation for solid particle with the hydrodynamic gas phase will reduce the system to the two-fluid Eulerian model. On the other hand, in the collisionless regime for the solid particle, the free transport of solid particle will be followed in UGKWP, and coupled system will return to the Eulerian-Lagrangian formulation for the gas and particle. The scheme will be tested for in all flow regimes, which include the non-equilibrium particle trajectory crossing, the particle concentration under different Knudsen number, and the dispersion of particle flow with the variation of Stokes number. A experiment of shock-induced particle bed fluidization is simulated and the results are compared with experimental measurements. These numerical solutions validate suitability of the proposed scheme for the simulation of gas-particle multiphase flow.

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

“…In the continuum flow regime, UGKWP will automatically get back to the gas-kinetic scheme (GKS), which is a kinetic theory-based Navier-Stokes solver [59,58,21,65,5]. Besides gas flow, UGKWP has also been used in the study of radiative transfer, plasma, and two phase flow [25,28,63]. The special wave and particle decomposition in UGKWP makes it suitable for the simulation of both dense (wave) and dilute solid-particle (particle) phase easily.…”

“…For the particulate two phase flow, the gas phase will be followed by the GKS and solidparticle phase by the UGKWP, and final scheme is called GKS-UGKWP for convenience. For the dilute monodisperse particulate flow, a previous GKS-UGKWP has been developed [63]. Based on the UGKWP for the solid-particle phase, the sampled particles depends on the local particle's cell's Knudsen number.…”