Abstract
Separated flows around a rotating circular cylinder and flows around an airfoil with a rotating cylinder are investigated by a vortex method applied to moving walls. The random walk method is used to simulate the diffusion of vorticity and linear vortex distribution is used to represent a body.
Computations are performed for the unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest at Reynolds number Re =1000 and velocity ratios Uc/U∞=0.5 and 2.0. Good agreements are obtained between numerical results and the flow visualization by Badr et al. (1990). The lift coefficient obtained here, which is much smaller than that obtained by the potential theory shows that the viscous effects for the circulation around the rotating cylinder are correctly computed by this method.
Numerical solutions for flows around an impulsively started airfoil with a rotating cylinder at different speed ratios Uc/U∞=0.0, 2.0, 4.0, Re=10000 and incidence α=24° are obtained. The Kutta condition is satisfied automatically at the trailing edge immediately after an impulsive start, and the starting vortex is observed. As Uc/U∞ increases, the separated region is reduced in size and an increase in circulation is observed. Leading edge separation is controlled at Uc/U∞ = 2.0 and 4.0. Numerical results suggest that inverse circulation shed from the rotating cylinder cancels the circulation at the separated region and suppresses separation.
