The effect of imposed rotary oscillation on the flow-induced vibration of a sphere
Authors: Sareen A. , Zhao J. , Sheridan J. , Hourigan K. , Thompson M. C. 
Published: September 2018

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.