Fluid forces on a square cylinder in oscillating flows with non-zero-mean velocities

The unsteady forces on a square cylinder in sinusoidally oscillating flows with non-zero-mean velocities are investigated numerically by using a weakly compressible-flow method with three-dimensional large eddy simulations. The major parameters in the analysis are Keulegan-Carpenter number (KC) and the ratio between the amplitude and the mean velocities of the approaching flow (A_R). By varying the values of KC and A_R the resulting drag and lift of the cylinders are analyzed systematically at two selected approaching-flow attack angles (0 and 22.5°). In the case of the non-zero attack angle, results show that both the drag and lift histories can be adequately described by Morison equations. However, Morison equations fail to correctly describing the lift history as the attack angle is zero. In addition, when the ratio of A_R/KC is near the Strouhal number of the bluff-body flow, the resulting drag is promoted due to the occurrence of resonance. Based on the results of systematic analyses, finally, the mean and inertia force coefficients at the two selected attack angles are presented as functions of KC and A_R based on the Morison relationships.