Flow-induced vibrations of a tethered circular cylinder

One of the most basic examples of fluid-structure interaction is provided bya tethered bodyin a fluid flow. The tendencyof a tethered buoyto oscillate when excited bywaves is a well-known phenomenon; however, it has only recentlybeen found that a submerged buoywill 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. This paper presents results for the related problem of two-dimensional simulations of the flow past a tethered cylinder. The coupled Navier–Stokes equations and the equations of motion of the cylinder are solved using a spectralelement method. The response of the tethered cylinder system was found to be strongly influenced by the mean layover angle as this parameter determined if the oscillations would be dominated byin-line oscillations, transverse oscillations or a combination of the two. Three branches of oscillation are noted, an in-line branch, a transition branch and a transverse branch. Within the transition branch, the cylinder oscillates at the shedding frequency and modulates the drag force such that the drag signal is dominated bythe lift frequency. 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 synchronized to the vortex shedding frequency of a stationary cylinder, except at veryhigh reduced velocities. Visualizations of the pressure and vorticityin the wake reveal the mechanisms behind the motion of the cylinder.