Flow-induced vibration of a near-wall circular cylinder with a small gap ratio at low Reynolds numbers

Abstract

Numerical simulations of flow-induced vibration of a near-wall circular cylinder with a small gap (e) to diameter (D) ratio (e∕D=0.1) at low Reynolds numbers 55≤Re≤200 (based on the incoming velocity U∞ and the diameter D) are performed using a finite volume method by means of modified OpenFOAM codes. As the cylinder is very close to the wall, remeshing is regularly applied during the body oscillation to avoid over-distortion of the grid. A model to account for the collision of the cylinder with the wall is adopted, in which when the gap between the cylinder and the wall is smaller than a critical value, the direction of its velocity is reversed. Simulations are made for low mass ratio, relevant to the cases in hydrodynamics. The results show the anti-clockwise vortices in the wake are suppressed by the shear flow in the boundary layer near the wall and only one single vortex (“1S”) is periodically shed downstream. The unchanged vortex shedding mode indicates that the motion amplitude generally increases with the reduced velocity first and then decreases after reaching a peak, and there is no obvious hysteretic transition. As Re increases, the largest root-mean-square of the in-line displacements Xrms and the mean transverse amplitude AY increase, and the reduced velocity U∗ corresponding to the largest vibration amplitude decreases. The collision with the wall slightly increases the vibration frequency. In addition, potential and vortex force components in the total fluid force are computed and further investigated. The results indicate that the total fluid force is dominated by the vortex force component and that other harmonic modes of the vortex force coefficient CL,V (or the total fluid force coefficient CL,T) except the first one becomes more significant and their dominant mode will shift to the second harmonic mode as the dominant vibration frequency fY∗ becomes close to the natural frequency in still water fn∗ (or the natural frequency in vacuum fvac∗), the vibration displacement Y(t) is very much dominated by the first mode. Moreover, it is found that the wall has significant effect on the equivalent stiffness of the cylinder at e∕D=0.1. The largest vibration amplitudes appear at larger frequencies than the natural frequency at all Re. The equation for the equivalent stiffness proposed in the present study is able to rectify the ratio of the vibration frequency to the natural frequency at resonance.