The effect of imposed rotary oscillation on the flow-induced vibration of a sphere

This experimental study investigates the effect of imposed rotary oscillation on the flow-induced vibration of a sphere that is elastically mounted in the cross-flow direction, employing simultaneous displacement, force and vorticity measurements. The response is studied over a wide range of forcing parameters, including the frequency ratio f_R and velocity ratio α_R of the oscillatory forcing, which vary between 0 ≤ f_R ≤ 5 and 0 ≤ α_R ≤ 2. The effect of another important flow parameter, the reduced velocity, U∗, is also investigated by varying it in small increments between 0 ≤ U∗ ≤ 20, corresponding to the Reynolds number range of 5000 ≲ Re ≲ 30 000. It has been found that when the forcing frequency of the imposed rotary oscillations, f_r, is close to the natural frequency of the system, f_nw, (so that f_R = f_r/f_nw ∼ 1), the sphere vibrations lock on to f_r instead of f_nw. This inhibits the normal resonance or lock-in leading to a highly reduced vibration response amplitude. This phenomenon has been termed 'rotary lock-on', and occurs for only a narrow range of f_R in the vicinity of f_R = 1. When rotary lock-on occurs, the phase difference between the total transverse force coefficient and the sphere displacement, φ_total, jumps from 0° (in phase) to 180° (out of phase). A corresponding dip in the total transverse force coefficient C_y(rms) is also observed. Outside the lock-on boundaries, a highly modulated amplitude response is observed. Higher velocity ratios (α_R ≥ 0.5) are more effective in reducing the vibration response of a sphere to much lower values. The mode I sphere vortex-induced vibration (VIV) response is found to resist suppression, requiring very high velocity ratios (α_R > 1.5) to significantly suppress vibrations for the entire range of f_R tested. On the other hand, mode II and mode III are suppressed for α_R ≥ 1. The width of the lock-on region increases with an increase in α_R. Interestingly, a reduction of VIV is also observed in non-lock-on regions for high f_R and α_R values. For a fixed α_R, when U∗ is progressively increased, the response of the sphere is very rich, exhibiting characteristically different vibration responses for different f_R values. The phase difference between the imposed rotary oscillation and the sphere displacement φ_rot is found to be crucial in determining the response. For selected f_R values, the vibration amplitude increases monotonically with an increase in flow velocity, reaching magnitudes much higher than the peak VIV response for a non-rotating sphere. For these cases, the vibrations are always locked to the forcing frequency, and there is a linear decrease in φ_rot. Such vibrations have been termed 'rotary-induced vibrations'. The wake measurements in the cross-plane 1.5D downstream of the sphere position reveal that the sphere wake consists of vortex loops, similar to the wake of a sphere without any imposed rotation; however, there is a change in the timing of vortex formation. On the other hand, for high f_R values, there is a reduction in the streamwise vorticity, presumably leading to a decreased total transverse force acting on the sphere and resulting in a reduced response.