Dynamics and forcing of a tethered sphere in a fluid flow

Abstract

Despite the practical significance of studying the case of the tethered sphere in a steady flow, there are almost no laboratory investigations for such a problem, and it was previously unknown whether such a system would tend to oscillate or not. It is also common ocean engineering practice to assume no oscillation effects in predictions of drag and tether angle of a tethered body. The present work demonstrates that a tethered sphere will oscillate remarkably vigorously at a saturation amplitude of close to two diameters peak-to-peak. The oscillations induce an increase in drag and tether angle of the order of around 100% over what is predicted using nonoscillating drag measurements. Analysis of in-line and transverse natural frequencies indicate that these frequencies should have the same value. Our experiments show that the in-line oscillations become phase locked with the transverse oscillations and vibrate at twice the frequency of the transverse motion. The above results suggest that oscillations are highly significant to predictions of sphere response in a steady flow, and should not be neglected. Finally, although response amplitudes show large disparity when plotted against Reynolds number, under a range of different sphere mass ratios (M*) and tether length ratios (L*), we find an excellent collapse of data for the different experiments by plotting the amplitudes versus the reduced velocity VR = U/fnD. This result shows that, for very small structural damping, the response amplitude may be considered as a function of the (normalized) natural frequency, and is only a function of the mass ratio and length ratio in so much as these parameters influence the natural frequency itself. © 1997 Academic Press Limited.