Gas-solid two-phase flows are widely encountered in many industrial processes, and computational fluid dynamics (CFD) simulations of gas-solid two-phase flows are useful for both practical and academic interests. In this work, we present an alternate Euler-Lagrange approach based on the lattice Boltzmann method (LBM) to describe the gas flow and transport behaviors, which is completely different from the finite-difference, finite-volume and finite-element numerical technique are used to solve gas flows based on the Navier-Stokes equations or volume-averaged Navier-Stokes equations (Zhang et al., 2014). For exploring the flow, transport and reaction details at the gas-solid interface, and to explore the constitutive laws for the simulations at the scales above, a lattice Boltzmann based direct numerical simulation (DNS) of the gas flow around each particle and its interaction with the particle surfaces is proposed by Wang et al. (2010). It does not have to establish boundary links at all, thus avoids a stair-step representation of the particle surface in Ladd’s (1994) method and produces a smooth transition across the stepwise interface with sub-grid resolution at the moving boundaries (Zhou et al., 2011). Taking advantage of the inherent parallelism of LBM and the attractive Flops/Price ratio of graphics processing units (GPUs), we implemented GPU parallel computing of this algorithm and conducted large-scale DNS of gas–solid suspension, with 1,166,400 solid particles for a two-dimensional system and 129,024 particles for a three-dimensional system on a Mole-8.5 system. Large-scale DNS reveals that the standard drag correlation expressed in terms of the solid volume fraction and the Reynolds number is not adequate, the magnitude and form of the heterogeneity should be considered in the drag correlation explicitly (Zhou et al., 2014), and meso-scale structures singificantly influence the statistical properties of particles in gas-solid flows. Due to DNS extremely limited by the computational cost and practically not feasible for industrial applications, we also proposed a lattice Boltzmann based discrete particle simulation (DPS) for gas-solid two-phase flows (Wang et al., 2013). The partial saturation concept has been extended to model the objects much smaller than the cell spacing (i.e. porous media), and both the linear and nonlinear drag effects of the solid phase (media) have been considered in the lattice Boltzmann based DPS for the first time (Wang et al., 2013). It is noteworthy that the similar computational strategy has been implemented in lattice Boltzmann based DNS (Wang et al., 2010) of gas-solid two-phase flows where the modified LBE was used with particles size much larger than the cell spacing, and in lattice Boltzmann based DPS (Wang et al., 2013) of gas-solid two-phase flows where the modified LBE was used model the objects much smaller than the cell spacing. Finally, two different Euler-Lagrange numerical methods in hydrodynamic modeling and simulation of gas-solid two-phase flows at different levels have been developed and implemented in the framework of LBM.
Ladd A.J.C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech.271:285-309 (1994).
Wang L.,Zhou G.,Wang X.,Xiong Q.,Ge W. Direct numerical simulation of particle-fluid systems by combining time-driven hard-sphere model and lattice Boltzmann method. Particuology 8, 379-382(2010).
Wang L., Zhang B., Wang X., Ge W., Li J. Lattice Boltzmann based discrete simulation for gas-solid fluidization. Chem. Eng. Sci. 101:228 -239 (2013).
Xiong Q., Li B., Zhou G., Fang X., Xu J., Wang J., He X., Wang X., Wang L., Ge W., Li J. Large-scale DNS of gas–solid flows on Mole-8.5. Chem. Eng. Sci. 71: 422–430(2012).
Zhou G., Wang L., Wang X., Ge W. Galilean-invariant algorithm coupling immersed moving boundary conditions and Lees-Edwards boundary conditions, Phys. Rev. E 84, 066701(2011)
Zhou G., Xiong Q., Wang L., Wang X., Ren X., Ge W. Structure-dependent drag in gas–solid flows studied with direct numerical simulation. Chem. Eng. Sci. 116: 9–22(2014).
Zhang J., Wang L., Ouyang J. Lattice Boltzmann model for the volume-averaged Navier-Stokes equations. Europhys. Lett. 107(2):20001(2014).