Conservative particle weighting scheme for particle collision in gas-solid flows

Even though the particle volume fraction is small in gas-solid flows, the particle-particle collision plays an important role due to the turbulent transport effect and the preferential concentration effect. The direct simulation Monte Carlo (DSMC) method coupled with Eulerian-Lagrangian models for hydrodynamics has been proposed for describing particle-particle collision in gas-solid flows for decades. Huge statistical noise occurs in some less-populated regions (e.g., two edges of log-normal size spectrum of particles) where there are insufficient simulation particle numbers for the DSMC method that tracks the equally weighted simulation particles. To circumvent this difficulty, a new differentially weighted (i.e., conservative particle weighting, CPW) scheme that explicitly conserves mass, momentum and energy during collisions is proposed in the framework of the DSMC method, and a limiting case of high inertia particle flow is simulated to demonstrate its utility in terms of computational precision. Then simulation strategy of coupled DSMC method for particle collision and Lattice Boltzmann-cellular automatic (LB-CA) probabilistic model for hydrodynamics (LB-CA-DSMC) is proposed. The resultant two-phase gas-solid flow model with the consideration of four-way coupling is then used to simulate the gas-solid flows over a backward-facing step. By comparing with the results of LB-CA method (without particle collision) and the experimental measurement, good agreements can be found between the LB-CA method and LB-CA-DSMC method for the case of small mass loading (=0.1), in such a way that the coupling strategy of LB-CA and DSMC is effectively verified. Finally, a “fictitious” gas solid flow over a backward-facing step with bidisperse copper particles injected is calculated, where each simulation particle is represented by variable number weight and the proposed CPW scheme is used to handle collision between differentially-weighted particles. Compared to the results from the conventional equally-weighted DSMC method for particle collision, improved resolution of particle field can be obtained simultaneously by the CPW method for less-populated particles.