(445c) DNS of Flow Past Arrays of Rotating Spheres: Computational Aspects and Results for the Drag Force, Magnus Lift Force and Torque

A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The most recently developed techniques, such as the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles, are adopted in the new IB-LBM. The IB-LBM is further improved with the implementation of high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The IB-LBM then is used to examine the effects of particle rotation, at low and intermediate particle Reynolds numbers, on flows in simple cubic and random arrays of mono-disperse spheres. The drag force, the Magnus lift force and the torque exerted on spheres, are determined at solid volume fractions up to the close-packed limits of the arrays. To compute the Magnus lift force due to particle rotation, a procedure is formulated to eliminate the influence of the force produced by the anisotropy of random arrays of spheres. Along with this procedure, detailed computational aspects of obtaining these physical quantities will be addressed. In this study, the rotational Reynolds number based on the angular velocity and diameter of spheres, is used to characterize the rotational movement of spheres. It is found that, the Magnus lift force is negligible relative to the magnitude of the drag force when the rotational Reynolds number is low. However, it can be very significant and even larger than the drag force, as the rotational Reynolds number increases up to hundreds, especially for low solid volume fractions. Based on the simulation results, relations of the drag force, the Magnus lift force and the torque at solid volume fractions from zero up to the close-packed limit for a wide range of particle Reynolds numbers and rotational Reynolds numbers are formulated for random arrays of rotating spheres.