The paper presents computational results of three-dimensional flow past a cylinder forced to oscillate: (a) transversely with respect to a uniform stream, and (b) both transversely and in-line with respect to a uniform stream, following a figure-eight trajectory. For a flow from left to right the figure-eight is traversed counter-clockwise in the upper half-plane. DNS of the Navier-Stokes equations for three–dimensional flow is performed using a spectral element code. Computations are carried out for a Reynolds number equal to 400, at a transverse oscillation frequency equal to the natural frequency of the Kármán vortex street. For both oscillation modes, the transverse oscillation amplitude is varied from zero to 0.60 cylinder diameters. The forces on the cylinder are calculated and related to flow structure in the wake. The results indicate that, in general, the presence of in-line oscillation increases the magnitude of forces acting on the cylinder, as well as the power transfer from the flow to the structure. Flow visualizations indicate that, for the figure-eight mode, low-amplitude forcing tends to reduce the wake three-dimensionality. However, at high oscillation amplitudes, the wake structure is found to become more complex at increasing amplitude.
Derivation of Vortex Method from Navier-Stokes Equations. Three-Dimensional Flow.
