A theoretical study of the coupling between a vortex-induced vibration cylindrical resonator and an electromagnetic energy harvester

This paper presents a theoretical study of the coupling between a vortex-induced vibration (VIV) cylindrical resonator and its associated linear electromagnetic generator. The two-equation mathematical model is based on a dual-mass formulation in which the dominant masses are the stator and translator masses of the generator. The fluid–structure interaction implemented in the model equations follows the so-called 'advanced forcing model' whose closure relies on experimental data. The rationale to carry out the study is the fact that in these types of configurations there is a two-way interaction between the moving parts in such a way that their motions influence each other simultaneously, thereby affecting the energy actually harvested. It is believed that instead of mainly resorting to complementary numerical simulations, a theoretical model can shed some light on the nature of the interaction and, at the same time, provide scaling laws that can be used for practical design and optimization purposes. It has been found that the proposed configuration has a maximum hydrodynamic to mechanical to electrical conversion efficiency (based on the VIV resonator oscillation amplitude) of 8%. For a cylindrical resonator 10 cm long with a 2 cm diameter, this translates into an output power of 20 to 160 mW for water stream velocities in the range from 0.5 to 1 m s⁻¹. (paper)