The Magnus effect is a classical fluid dynamic phenomenon associated with rotating bodies immersed in uniform flow. In this study, we numerically investigate the flow past a rotating core–shell cylinder based on the volume-averaged macroscopic equations that are solved by the multiple-relaxation-time lattice Boltzmann method. The effects of the velocity ratio (0 ≤ VR ≤ 6), Darcy number (10−6 ≤ Da ≤ 10−2), and dimensionless thickness (0 ≤ L/D ≤ 1) of the porous layer are investigated on the hydrodynamic force as well as the flow characteristic and pressure coefficient for the rotating core–shell cylinder at a Reynolds number of Re = 40. The results show that the permeation flow through the porous shell induces a confined vortex structure within the porous layer at high Darcy number, while increasing the porous layer thickness suppresses the wake vortex shedding to form an enveloping wake. It is found that the Magnus lift decreases nonlinearly with the porous layer thickness and more rapidly at high Darcy number and velocity ratio. For a thicker porous layer, the Magnus lift decreases with Da more sharply while increases with VR more gradually. The decrease in the drag force with VR at Da = 10−2 depends significantly on L/D. Based on the computed results of lift-to-drag angle, it is found that the porous layer with high permeability can strongly modulate the lift increment at low VR. Two fitting formulas are further developed for rotating core–shell circular cylinders to predict the lift coefficient as a function of L/D and VR at Da = 10−2.
Wang et al. (Thu,) studied this question.