Free-pitching flapping-foil turbines with imposed sinusoidal heave

Abstract

This work investigates the dynamics of a semi-passive flapping-foil with a prescribed sinusoidal heave motion and a passive pitch motion with the objective of extracting energy from an oncoming fluid flow. This implies that the heave motion is mechanically driven while the foil is elastically supported in pitch. The pitch motion therefore results from the interaction of the foil with the flow and its elastic supports, namely springs and dampers. Numerical simulations have been conducted at a Reynolds number of 3.9×106 based on the chord length. Positive efficiencies and periodic pitch motions of large amplitude are obtained when the frequency of the pitch motion synchronizes itself to the frequency of the prescribed heave motion. The conditions under which it happens are explored. The results of this study demonstrate that an optimal power-generation performance can be maintained over large variations of the moment of inertia and pitch stiffness, provided that they are properly scaled. This is achieved by combining these two structural parameters into a single effective parameter: the effective pitch stiffness coefficient. Moreover, four different positions of the pitch axis are considered, ranging from the leading edge to the three-quarter-chord point. By adjusting the governing structural parameters adequately, efficiencies exceeding 40% can be achieved with all four positions of the pitch axis, with a maximum of 46.0% obtained when the pitch axis is located at the quarter-chord point. It is found that a phase lag near 90° between the heave and the pitch motions is only optimal with this specific position of the pitch axis. It needs to be larger than 90° when the pitch axis is located upstream of the quarter-chord point and smaller than 90° when it is located downstream of this position.