Energy extraction via Vortex-Induced Vibrations: The effect of spring bistability

Abstract

We study Vortex-Induced Vibration (VIV) of an elastically mounted cylinder placed in uniform flow using numerical simulations based on Immersed Boundary Method and theoretical analysis. We characterize the effect of bistability in elastic potential on energy harvesting from fluid flow, in which the energy generator is modeled as structural damping. A non-dimensional distance of 2β separates the two minima of the bistable spring potential. An increase in the peak energy extraction efficiency and widening of lock-in range is observed for VIV with bistable springs compared to VIV with linear springs, especially for low values of β. We report peak efficiency of 10% for VIV with bistable springs, whereas the peak efficiency for VIV with linear spring is 4%. These results can be explained by the presence of an “Equilibrium Constraint (EC)”, between oscillation amplitude and structure frequency, obtained by balancing the rate of energy production and the rate of energy dissipation due to either structural damping or electrical generators. The EC-based theory predicts that the maximum displacement amplitude depends on damping parameter b∗=2π2m∗ξ/Ur as suggested by Klamo et al. (2005), where m∗ is the solid-to-fluid mass ratio, ξ is the damping ratio and Ur is the reduced velocity of the incident fluid flow. We briefly discuss the wake structures for bistable springs for different β and b∗. We also derive a theoretical expression for oscillation amplitude and energy extraction efficiency for VIV with bistable springs, which agrees well with data from high fidelity numerical simulations, carried out in the present work.