Numerical simulations of the flow-induced vibrations of tethered bluff bodies

One of the most basic examples of fluid-structure interaction is provided by a tethered cylinder or sphere in a fluid flow. The tendency of a tethered sphere to oscillate when excited by waves is a well-known phenomenon and it has only recently been found that the same system will act in a similar fashion when exposed to a uniform flow at moderate Reynolds numbers, with a transverse peak-to-peak amplitude of approximately two diameters over a wide range of velocities. The present paper presents results of DNS of the flow past a tethered cylinder. The coupled Navier-Stokes equations and the equations of motion of the cylinder are solved using a spectral element method. The fluid forces acting on the cylinder as well as the tension in the tether are computed and used to determine the resulting motion of the object. It is found that the mean amplitude response is greatest at high reduced velocities, i.e. when the cylinder is oscillating predominantly transverse to the fluid flow. Furthermore, the oscillation frequency is found to correspond to the vortex shedding frequency of a stationary cylinder, except at high reduced velocities. This is in contrast to a tethered sphere in which the oscillation frequency does not correspond to either the vortex shedding frequency or the natural frequency. Visualizations of the vortex structures in the wake reveal the mechanisms behind the motion of the cylinder, and suggest that the induced oscillations are highly significant in the prediction of cylinder response in a steady flow.