Flow around a tethered cylinder, the effect of tether length at high layover angles

Tethered cylinder systems constitute a natural extension of the lightly damped, hydro-elastically mounted cylinder. In this case, the cylinder is constrained to travel along an arc prescribed by the tether length. The analysis of the tethered cylinder system is hampered by the dependence of the natural frequency of the system on both the fluid forces acting on the system and the curved motion (which in turn alters the added mass coefficient away from unity). These difficulties have precluded prior studies considering the natural frequency or reduced velocity as a controlling parameter, making direct comparison with the hydro-elastically mounted cylinder system difficult. nvestigation considers the case of a tethered cylinder at low Reynolds number (Re=200) for a mass ratio m⁎=0.2. It notes a local maximum in the amplitude of oscillation when the normalized tether length L ⁎ ≃ 2.0 , in agreement with prior studies. By instead considering the amplitude of oscillation in a rotational framework, we are able to explain the existence of this peak, and identify two regions of amplitude response, the first region exists for very small tether lengths ( L ⁎ ≲ 0.3 ), while the second exists for larger tether lengths. The transition from small tether lengths to large tether lengths exhibits the highest amplitude angular oscillations. l wake states are also considered for a tethered cylinder which is oscillating about a horizontal mean layover angle. By considering these wake states, coupled with the definition of the natural frequency, an estimate of the added mass coefficient is made. Here we predict that C A ≃ 0.5 for a tether length of L⁎=1.5. This prediction is based not only on the tether length, but also on the amplitude of oscillation, and hence is Reynolds number dependent.