(407a) Direct Numerical Simulation of Particle Rotation Effects in Gas-Solid Flows Using an Immersed Boundary Lattice Boltzmann Method – Relative Effects of the Magnus Lift Force and the Drag Force in Gas-Solid Interactions

A new and efficient direct numerical method with second-order accuracy is developed for fully resolved simulations of incompressible viscous flows laden with rigid particles. The method combines the state-of-the-art immersed boundary method (IBM), the multi-direct forcing method and the lattice Boltzmann method (LBM). First, using the new IB-LB method, steady Stokes flows in ordered arrays of non-rotational and rotational spheres are examined extensively. The results of the non-rotational spheres show excellent agreement with existing theories. The rotational Reynolds number, defined as Rer = ωD²/v, is used to characterize the rotational movement of spheres, where ω,  D and v are the particle’s angular velocity, particle diameter and fluid viscosity, respectively. The solid volume fractions are varied from 0.01 to the close-packing limit. For each solid volume fraction, rotational movements of spheres are simulated at several different rotational Reynolds numbers ranging from 0.1 to O(100). It is found that the Magnus lift force due to particle rotation is directly proportional to the rotational Reynolds number up to O(100), while the drag force is only slightly affected by the increasing rotational Reynolds number. The lift force is very insignificant when rotational Reynolds numbers are lower than 0.1. However, it can be larger than the drag force as rotational Reynolds numbers increase especially at low solid volume fractions. It is shown that, for the ordered arrays of spheres, the lift force is around 43% larger than the drag force at the solid volume fraction of 0.01 and the rotational Reynolds number of 50. In the case with larger solid volume fraction, e.g., 0.5, the lift force can be as big as 39% of the drag force at the rotational Reynolds number of 100. Second, steady Stokes flows in practical random arrays of non-rotational and rotational spheres are also examined extensively. The lift force is also found to be very significant compared to the drag force when rotational Reynolds numbers are up to 100. The lift-to-drag ratio is around 0.68 at the solid volume fraction of 0.1 and the rotational Reynolds number of 50. The lift-to-drag ratio is around 0.15 at the solid volume fraction of 0.6 and the rotational Reynolds number of 100. Third, the simulations of random arrays of spheres with intermediate particle Reynolds number up to O(100) are also performed. It is shown that the lift force becomes less important with the increasing particle Reynolds number, e.g., at the solid volume fraction of 0.1 with a fixed rotational Reynolds number of 50, the lift-to-drag ratio drops from 0.68 to 0.15 when the particle Reynolds number increases from effectively zero to 100. Based on the simulated results, a lift law as well as a new drag law as a function of arbitrary rotational Reynolds numbers, arbitrary particle Reynolds numbers and solid volume fractions is proposed. This study demonstrates that the lift force caused by the particle rotation can be very significant compared to the drag force, especially at low particle Reynolds numbers and low solid volume fractions, and must be considered in practical simulations adopting drag laws, e.g., two-fluid simulations and computational fluid dynamics-discrete element method (CFD-DEM ) simulations.