Vortex-induced vibration of two and three-dimensional bodies

We investigate the vortex-induced vibrations of an elastically-mounted rigid cylinder, and an elastically-mounted sphere, in a fluid flow, using extensive force, displacement and vorticity measurements (employing DPIV).;In the case of the elastically-mounted rigid cylinder, we show that there exist two distinct types of response in such systems, depending on whether one has a high or low combined mass-damping parameter (m*zeta). In the classical high-(m*zeta) case, an 'Initial' and 'Lower' amplitude branch are separated by a discontinuous mode transition, whereas in the case of low-(m*zeta), a further higher-amplitude 'Upper' branch of response appears, and there exist two mode transitions. To understand the existence of more than one mode transition we employ two distinct formulations of the equation of motion, one of which uses the 'total force', while the other uses the 'vortex force', due only to the dynamics of vorticity.;The effect of reducing oscillating system mass (characterized by the mass ratio, m* = oscillating mass/displaced fluid mass) on the frequency of the vibrating cylinder is also investigated. We discover the existence of a critical mass ratio, where the oscillating cylinder frequency becomes very large: m*critical=0.54 For very light systems, where m*<m*critical , the regime of flow speeds where large amplitude "resonant" response occurs, extends theoretically to infinity.;We find that an elastically-mounted sphere can oscillate at large amplitudes of the order of a diameter, over a wide range of flow velocities, substantially larger than found in the cylinder vibration problem. Within the range of flow speeds where the oscillation frequency (f) is of the order of the stationary sphere vortex shedding frequency (fvo), we find two modes of periodic vibration, defined as mode I and mode II. Both these modes are associated with the formation of two vortex rings per cycle.;For the sphere, in addition to the response in the flow regime when f = O(fvo), an entirely unexpected large-amplitude periodic mode of oscillations (mode III) is found at much higher flow velocities where fvo >> f. Such an unusual mode of vibration has no counterpart in any other problem in vortex-induced vibrations, to our knowledge.