Feedback control of flow-induced vibration of a sphere

The flow-induced vibration of a sphere elastically mounted in the cross-flow direction with imposed feedback rotation was investigated experimentally. The application of rotation provides a means to exercise control over the vibration response of axisymmetric three-dimensional objects. Both the rotational amplitude, which was imposed in proportion to sphere transverse displacement, and the phase of the control signal were varied over a broad parameter space comprising: a non-dimensionalised proportional gain ( $0.5\leqslant K_{p}^{\ast }\leqslant 2$ ); rotation phase ( $0^{\circ }\leqslant \unicode[STIX]{x1D719}_{rot}\leqslant 360^{\circ }$ ), which is the phase between the applied sphere rotation and the transverse displacement; and reduced velocity ( $3\leqslant$ $U^{\ast }\leqslant 20$ ). The corresponding Reynolds number range was ( $3900\lesssim Re\lesssim 25\,800$ ). The structural vibration, fluid forces and wake structure were examined to characterise the effect of the imposed rotation. It was found that the rotation not only altered the magnitude of the vibration response, either amplifying or attenuating the response depending on operating conditions, but it also altered the reduced velocity at which vibrations commenced, the vibration frequency and periodicity and significantly altered the phase between the transverse fluid force and displacement. It was possible to almost completely suppress the vibration in the mode I, mode II and mode III transition regimes for imposed rotation over the ranges $90^{\circ }\lesssim$ $\unicode[STIX]{x1D719}_{rot}\lesssim 180^{\circ }$ , $15^{\circ }\lesssim$ $\unicode[STIX]{x1D719}_{rot}\lesssim 135^{\circ }$ and $0^{\circ }\lesssim$ $\unicode[STIX]{x1D719}_{rot}\lesssim 120^{\circ }$ , respectively. In particular, this could be achieved at effective rotation rates well below those required by using open-loop control (Sareen et al. ,  J. Fluid Mech. , vol. 837, 2018, pp. 258–292). Past the peak of mode II, a ‘galloping-like’ response, similar to that reported by Vicente-Ludlam et al.  ( J. Fluid Mech. , vol. 847, 2018, pp. 93–118) for the circular cylinder, was observed with an increase in vibration amplitude of up to 368 % at the highest reduced velocity tested ( $U^{\ast }=20$ ). Particle image velocimetry measurements revealed a change in the timing and spatial position of the streamwise vortex structures with imposed rotation. Contrary to what has been observed for the circular cylinder, however, no de-synchronisation between vortex shedding and sphere motion was observed.