Power extraction from vortex-induced angular oscillations of elliptical cylinder

Using computational methods, we study angular oscillations of an elliptical cylinder attached to a torsional spring, with axis placed perpendicular to a uniform flow, at low Reynolds numbers (Re=100 and Re=200). The equilibrium angle and stiffness of the torsional spring is chosen such that the ellipse reaches stable equilibrium at an angle of roughly 45° with respect to the incoming flow. This configuration leads to large unsteady torque due to asymmetric vortex shedding, which in turn leads to large oscillations of the ellipse. We measure the potential for power-extraction from this setup, by measuring the net dissipation rate in an externally attached angular damper, for different damping coefficients, solid-to-fluid density ratios and Reynolds numbers. The Lattice-Boltzmann method, validated against several test cases, is used to simulate the fluid flow and fluid-structure interaction. For low density ratios, the ellipse tends to oscillate within the first quadrant, while, for higher density ratios, the ellipse, due to its tendency to autorotate, undergoes very large oscillations, covering both the first and fourth quadrant. For a given damping coefficient, the range of density ratios for which the ellipse tends to autorotate widens with increasing Reynolds numbers. We also study lock-in behavior of the ellipse. We find that the frequency spectra of fluid torque have only one peak upto density ratio of 3, and that a secondary peak emerges at higher density ratios. The structure locks on to the frequency of the fundamental fluid mode for low density ratios, even for cases where the structure oscillates over both first and fourth quadrants. The structure locks on to the secondary fluid mode at high density ratios, leading to sustained, high-amplitude oscillations for a large range of density ratios. Power output is maximum for density ratios ranging from 3 and 10, and increases with Reynolds number. Peak efficiency of the generator is 1.7% at Re=200.