Lattice Boltzmann method for simulations of gas-particle flows over a backward-facing step

The simulation of turbulent gas–solid flows at the mesoscopic scale is still challenging in fluid mechanics. This paper proposed the Lattice Boltzmann-cellular automata (LB-CA) probabilistic model to simulate gas–solid flows, in which the two-way coupling between the carrier phase and the dispersed phase is considered. In the LB-CA model, the LB subgrid model for high Reynolds number flows is used to describe flow fields at the mesoscopic scale, and the CA probabilistic model utilizing the stochastic process is used to capture transport behavior of discrete solid particles among the same regular lattice nodes as fictitious fluid particles in the LB method. The transport probability of a solid particle to nearest neighboring node directly depends on its actual displacement under other external forces (e.g., drag force, gravity). The two-way coupling is realized by adding external force term for the feedback forcing of particles in the evolution equation of fluid particle density distribution function. The resultant LB-CA model with two-way coupling is then used to simulate gas-particle flows over a backward-facing step. By comparing the present results with experimental measurements and other simulation results from LES (large-eddy simulation)-Lagrangian model, LB-Lagrangian model and two-fluid model, it is found that the LB-CA model is capable of simulating mean and fluctuating velocities of the carrier and dispersed phases and gas-particle covariance with high precision. Generally, the LB-CA method achieves the similar precision with the LES-Lagrangian method, and performs better than some other macroscopic models (such as the two-fluid models).