Two-dimensional characterization of particle entrainment over a downstream obstacle

This study conducts a two-dimensional numerical investigation of the particle entrainment in the presence of a large downstream circular obstacle, and aims to deepen the understanding of the entrainment mechanism and propose a dimensionless number to describe the entrainment threshold. With the coupled lattice Boltzmann and discrete element method, direct numerical simulations are conducted for a wide range of obstacle-to-particle radius ratios (2<R_o/R_p<8 ) and Reynolds numbers (38≤Re≤160). The results show that the low-pressure separated vortex due to the obstacle is the fluid structure to entrain the particle by vortex stretching at low R_o/R_p (2<R_o/R_p<3.8). Based on this mechanism, a dimensionless number defined as the ratio of the vertical drag force to the particle gravity is proposed, which can be understood as a generalized Shields number including the additional effect of the obstacle radius, and it approaches the constant value of 2.5198 at the critical conditions of entrainment. In addition, we find that at high R_o/R_p (5.6≤R_o/R_p≤8.0), the particle is too far from the separated vortex to undergo sufficient vertical drag force, and thus its inertia should be small enough to ensure the entrainment. In this situation, the entrainment threshold is well described by the Stokes number, which approaches the constant value of 0.2134. At the moderate R_o/R_p (3.8≤R_o/R_p≤5.6) the drag force of separated vortex and the low particle inertia are both essential to realize the particle entrainment.