Transverse vortex-induced vibration of a circular cylinder on a viscoelastic support at low Reynolds number

The effect of a viscoelastic-type structural support on vortex-induced vibration (VIV) of a circular cylinder has been studied computationally for a fixed mass ratio (m^∗=2.546) and Reynolds number (Re=150). Unlike the classical case of VIV where the structural support consists of a spring and damper in parallel, this study considers two springs and one damper, where the two springs are in parallel and the damper is in series with one of the springs. This spring/damper arrangement is similar to the Standard Linear Solid (SLS) model used for modelling viscoelastic behaviour. The viscoelastic support (SLS type) is governed by the following two parameters: (a) the ratio of spring constants (R), and (b) the damping ratio (ζ). The focus of the present study is to examine and understand the varied response of the cylinder to VIV as these parameters are varied. For small ζ and R, the cylinder response shows characteristics similar to the classical case, where the amplitude response is composed of an upper- and the lower-type branch. The presence of upper-type branch at low Re is evident through the peak lift force, frequency and phase response of the cylinder. As the damping ratio is increased, the vibration amplitude decreases and hence the upper-type branch disappears. There exists a critical value of ζ=1 beyond which the amplitude again increases asymptotically. The non-monotonic variation of amplitude response with ζ is presented in the form of the ”Griffin plot”. The amplitude, force, frequency and phase-difference response of cylinder were found to be mirror symmetric in log(ζ) about ζ=1. In addition, the effect of R at the critical value of damping, ζ=1, was studied. This show that the amplitude decreases with an increase of R, with suppression of the response branches for high R values. The results suggest that a careful tuning of the damping may be effectively employed both to enhance power output for energy extraction applications or to suppress flow-induced vibration.