Scaling the Power Extraction Efficiency of Three-Dimensional Oscillating Hydrofoils

We present experiments of power extraction performance of combined heaving and pitching NACA 0015 foils of varying aspect ratio (AR). These surface-piercing foils are pitching about their one-third chord at a Reynolds number of Re = 10,000. As expected, the efficiency increases with increasing AR, and the optimal Strouhal number and pitch angle that maximize the efficiency shift to slightly lower and higher values, respectively. We demonstrate that classic Prandtl scaling laws that account for the upwash/downwash effects of finite-span foils can collapse power extraction efficiency performance maps around their peak performance of AR = [3, 4, 6, 8] foils. This simple scaling works well when the effect of the water surface acting as an image plane is accounted for. We further investigate the scaling of the forces and moments, as well as the heave and pitch power. Using the scaling laws, 2D simulations can be corrected for finite-span effect and are compared with the experiments. This study provides an improved understanding of AR effects on the power extraction efficiency of oscillating hydrofoils.