Excitation,inertia, and drag forces on a cylinder vibrating transversely to a steady flow

We present a computational study of the forces on a cylinder oscillating harmonically in the direction perpendicular to a uniform flow. The two-dimensional Navier–Stokes equations are solved on a coordinate system fixed on the cylinder. The Reynolds number is equal to 400. Several oscillation frequencies are considered: (a) resonant forcing, (b) forcing at frequency below the natural frequency of the wake, and (c) forcing at frequency above the natural frequency of the wake. Once the flow has reached a statistical steady state, the lift and drag forces on the cylinder are computed. The lift force in particular is decomposed into one component that is in phase with the velocity (excitation force), and one component that is ${180}^{\circ }$ out of phase with the acceleration (inertia or added mass force). The variation of the forces as a function of the amplitude-over-diameter-ratio is studied in detail. It is found that the scaling of the so-called inertia component of the force with the acceleration of the cylinder can lead to serious problems at small amplitudes of oscillation, and that it is overall preferable to scale both components of the force with the dynamic pressure of the fluid. Through extensive flow visualization, it is shown that changes in the state of the flow are related to the abrupt changes of the forces with the amplitude-over-diameter-ratio. Moreover, qualitative differences are found between the results for the below resonance and the resonant or above resonance forcing. The former are characterized by smooth variation of the hydrodynamic force coefficients and spatially ordered vortex streets. The latter are characterized by continuous and sharp, even jump-like, changes of the forces, and a variety of vortex patterns in the wake, resulting for some combinations of frequency and amplitude of oscillation to spatially disordered vortex streets.