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

  • A. Sareen (a1), J. Zhao (a1), J. Sheridan (a1), K. Hourigan (a1) and M. C. Thompson (a1)...

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 $\unicode[STIX]{x1D6FC}_{R}$ of the oscillatory forcing, which vary between $0\leqslant f_{R}\leqslant 5$ and $0\leqslant \unicode[STIX]{x1D6FC}_{R}\leqslant 2$ . The effect of another important flow parameter, the reduced velocity, $U^{\ast }$ , is also investigated by varying it in small increments between $0\leqslant U^{\ast }\leqslant 20$ , corresponding to the Reynolds number range of $5000\lesssim Re\lesssim 30\,000$ . 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 $f_{R}=f_{r}/f_{nw}\sim 1$ ), 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, $\unicode[STIX]{x1D719}_{total}$ , jumps from $0^{\circ }$ (in phase) to $180^{\circ }$ (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 ( $\unicode[STIX]{x1D6FC}_{R}\geqslant 0.5$ ) 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 ( $\unicode[STIX]{x1D6FC}_{R}>1.5$ ) to significantly suppress vibrations for the entire range of $f_{R}$ tested. On the other hand, mode II and mode III are suppressed for $\unicode[STIX]{x1D6FC}_{R}\geqslant 1$ . The width of the lock-on region increases with an increase in $\unicode[STIX]{x1D6FC}_{R}$ . Interestingly, a reduction of VIV is also observed in non-lock-on regions for high $f_{R}$ and $\unicode[STIX]{x1D6FC}_{R}$ values. For a fixed $\unicode[STIX]{x1D6FC}_{R}$ , when $U^{\ast }$ 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 $\unicode[STIX]{x1D719}_{rot}$ 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 $\unicode[STIX]{x1D719}_{rot}$ . 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.

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