Vortex-induced motions of a tethered sphere

Despite the practical significance of studying the vibrations of a tethered sphere in a steady fluid flow, there are almost no laboratory investigations of such a problem, and it was previously unknown whether such a system would tend to oscillate or not. The present work demonstrates that a tethered sphere will oscillate vigorously, at a peak-to-peak amplitude of about two diameters, over a large range of velocities. The RMS amplitude of these oscillations is found to be independent of the tether length when plotted against the reduced velocity V R = U/f n D. However, the saturation value of the RMS is found to vary with the mass ratio. Also interesting is the observed oscillation frequency, at low mass ratios, which does not correspond to either the natural frequency nor the sphere vortex shedding frequency (in the absence of vibrations). The observed large amplitude oscillations also induce an increase in drag and tether angle of the order of 100%. The above results suggest that oscillations are highly significant to predictions of sphere response in a steady flow, and should not be neglected.