Computational Study of Three-Dimensional Flow Past an Oscillating Cylinder Following a Figure Eight Trajectory

The paper presents a computational study of three-dimensional flow past a cylinder forced to oscillate in a uniform stream, following a figure-eight trajectory. Flow simulations were performed for Re = 400, for different cases, defined in terms of the oscillation mode ('counter-clockwise' or 'clockwise'), for values of the ratio, F, of the transverse oscillation frequency to the Strouhal frequency close to 1.0. The results demonstrate that, for F <= 1.0, counter-clockwise cylinder motion is associated with positive power transfer from the flow to the cylinder, corresponding to excitation; for the clockwise motion, power transfer is negative at intermediate to high amplitudes, corresponding to damping. For the clockwise mode, in the range F = 0.9-1.1, a transition to two-dimensional vortex street is identified for transverse oscillation amplitude exceeding a critical value. This results from the induced suction of vortices, which moves vortex formation and shedding closer to the cylinder surface, thus resulting in a narrower wake, characterized by an effective lower Reynolds number. Both oscillation modes are characterized by higher harmonics in the lift force spectrum, with the third harmonic being very pronounced, while even harmonics are present for the case of clockwise mode, resulting from a wake transition to a "S + P" mode.