2D and 3D flows over counterclockwise rotating cylinders of various cross-sectional shapes at Re = 200 and 1000 and rotation ratio α = π/4 are numerically studied using a newly developed high-order sliding mesh method. It is found that all cylinders experience positive drag and negative lift throughout each rotating period. The circular cylinder has the largest mean forces at Re = 200. In contrast, the elliptic cylinder has the largest mean forces at Re = 1000. It is also noticed that, as the number of edges increases, the rotation frequency becomes less dominant in the flows, and the unsteady force amplitudes decrease. At Re = 1000, the 2D simulations over-predict forces for all cylinders except the elliptic one. Among all the flows, only that about the circular cylinder at Re = 200 is found to be periodic. The flow around the elliptic cylinder exhibits two stable states at Re = 200 and dramatically different flow structures from others at Re = 1000.
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