A Comparison of Forces in Two- and Three-Dimensional Flow Past an Oscillating Cylinder Available to Purchase

DNS results are presented for three-dimensional flow past a circular cylinder forced to oscillate both in the transverse and in-line direction with respect to a uniform stream, at Reynolds number equal to 400, and are compared against simulation results for two-dimensional flow. The cylinder follows a figure-eight motion, traversed either counter-clockwise or clockwise in the upper half-plane for a flow stream from left to right. The transverse oscillation frequency is equal to the natural frequency of the Kármán vortex street. The Navier-Stokes equations are solved using a spectral element code, and the forces acting on the cylinder are computed for both three- and two-dimensional flow. The results demonstrate that the effect of cylinder oscillation on the flow structure and forces differs substantially between the counter-clockwise and the clockwise oscillation mode. For the counter-clockwise mode, forcing at low amplitude decreases the flow three-dimensionality, with the wake becoming increasingly three-dimensional for transverse oscillation amplitudes higher than 0.25–0.30 cylinder diameters, with corresponding discrepancies in forces with respect to two-dimensional flow. For the case of clockwise mode, a strong stabilizing effect is found: the wake becomes two-dimensional for a transverse oscillation amplitude of 0.20 cylinder diameters, and remains so at higher amplitudes, resulting in nearly equal values of the force coefficients for three- and two-dimensional flow.