Resonant response and optimal energy harvesting of an elastically mounted pitching and heaving hydrofoil

The aeroelastic response and energy harvesting performance of an elastically mounted hydrofoil subject to a prescribed pitching motion are experimentally studied using a cyber-physical force-feedback control system in a uniform flow. By taking advantage of this cyber-physical system, we systematically sweep through the parameter space of the elastic support (stiffness, damping, and mass) for various frequencies of the prescribed pitching motion. It is found that the flow-induced heave amplitude and the energy harvesting performance are both strongly affected by the frequency ratio between the prescribed pitching frequency and the natural frequency of the system and the damping coefficient. In particular, for a fixed damping coefficient, the maximum flow-induced heave amplitude is achieved at the resonant condition (frequency ratio of 1), which also gives rise to the highest energy harvesting performance. At this resonance condition, though a smaller damping produces a larger heave amplitude, the optimal energy harvesting performance is obtained consistently at an intermediate damping coefficient of 1.5. In addition, at the resonance condition, the heave amplitude, or Strouhal number, and the hydrodynamic forces on the foil are both found to collapse well for different reduced frequencies, suggesting a similarity in the vortex dynamics generated by the elastically mounted system. A low-order model based on classical vibration theory is formulated to reproduce the power coefficient using the damping coefficient and Strouhal number, and we find that the power coefficient predicted by the model agrees well with that measured in the experiment over the range of reduced frequency explored.