Direct numerical simulation of low-Reynolds-number flow past arrays of rotating spheres

Immersed boundary-lattice Boltzmann simulations are used to examine the effects of particle rotation, at low particle Reynolds numbers, on flows in ordered and random arrays of mono-disperse spheres. The drag force, the Magnus lift force and the torque on the spheres, are determined at solid volume fractions up to the close-packed limits of the arrays. The rotational Reynolds number based on the angular velocity and the diameter of the spheres is used to characterize the rotational movement of spheres. The results show that the normalized Magnus lift force produced by particle rotation is approximately in direct proportion to the rotational Reynolds number, while the normalized drag force and torque acting on spheres are barely affected by this number. 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 O(10(2)), especially for low solid volume fractions. Based on the simulation results, relations for the Magnus lift force and the torque for both ordered arrays and random arrays of rotating spheres at solid volume fractions from zero to close-packed limits are formulated. Further, the drag force relations in the literature are revised based on existing theories and the present simulation results for both arrays of spheres.