Optimization of energy harvesting efficiency of an oscillating hydrofoil: Sinusoidal and Non-sinusoidal trajectories

We determine the feasibility of applying optimization algorithms to an oscillating hydrofoil's motion trajectory to determine maximum efficiency of energy capture. Optimization is performed using the Nelder-Meade downhill simplex method. The objective function is the energy captured measured experimentally in run-time with an oscillating hydrofoil capable of measuring mechanical energy capture in a laboratory flume. For sinusoidal trajectories, optimization is performed over pitch and heave amplitudes as well as frequency; this system is shown to be capable of optimization in run-time. The optimum efficiency of 30{\%} is found for a pitch amplitude of 70$^{\circ}$, a heave amplitude of 0.8*chord and a dimensionless frequency of 0.13. To treat non-sinusoidal trajectories, we expand them in a truncated Fourier series and consider the coefficients of this series as variables for optimization. The sinusoidal case is simply an extreme case of such a truncated Fourier series, with only one term in the series retained. We present a systematic method for optimization over general non-sinusoidal trajectories by including more and more terms in the Fourier series.