Shape optimization to enhance energy harvesting from vortex-induced vibration of a circular cylinder

In previous research on energy harvesting from vortex-induced vibrations (VIVs), the cross section of the structure commonly utilizes basic geometric shapes like circular, ellipse, square, and semicircle. Nevertheless, exploring optimized shapes for energy harvesting from VIV remains an understudied area. To address this gap, this paper employs adjoint-based unsteady shape optimization to increase the efficiency of energy harvesting from VIV of a circular cylinder at low Reynolds numbers. The goal of the optimization is to maximize the plunge-damping derivative of a single-degree-of-freedom transversely vibrating cylinder, which represents the rate of energy injected into the structure by the flow. To facilitate this process, an efficient method to evaluate the gradient of the objective function with respect to shape parameters is provided via the proposed unsteady discrete adjoint method. Results show that, through optimization, the low-pressure region behind the cylinder is significantly enlarged and the separation points move forward, resulting in the faster development of separation vortex and reduced stability of the fluid-structure coupling system. As a consequence, the intensity of VIV as well as the corresponding power generation efficiency is remarkably enhanced, accompanied by a notable expansion in the energy harvesting region.