Effect of aspect ratio on the energy extraction efficiency of three-dimensional flapping foils

Abstract

Numerical simulations are used to investigate the effect of variation of the aspect ratio and the structure of pitching motions on the energy extraction efficiency and wake topology of flapping foils. The central aim is to predict the energy extraction performance and efficiency of a flapping-foil-based energy harvesting system (EHS) in realistic working conditions with finite aspect ratios. A sinusoidal heaving motion is imposed upon the foil, as well as both a sinusoidal pitching motion and a variety of trapezoidal-like periodic pitching motions. The simulations employ a finite-volume method with body-fitted moving grids, allowing the capture of flow structure near the foil surface. A detailed analysis of the hydrodynamic performance shows two peaks per periodic cycle in the lift force time histories or equivalently, the energy extraction time histories. The first primary peak corresponds to an effective angle of attack around 15.4°, indicating good attachment of the flow on the foil surface without significant flow separation. The secondary peak corresponds to a leading edge vortex (LEV) travelling on the foil surface. The shape of the LEV is altered markedly as the aspect ratio varies, and consequently the secondary peak in the lift force time history is strongly affected by the effects of three-dimensionality for foils with smaller aspect ratios. By examining the relationship between energy extraction efficiency and aspect ratio, a critical aspect ratio of AR = 4 is identified for sinusoidal pitching motions, below which the three-dimensional low-aspect-ratio characteristics dominate the flow evolution. Therefore, the compromise between higher energy extraction efficiency and lower costs of manufacturing and installation suggests that an aspect ratio around AR = 4 is the most appropriate choice for a real EHS. Furthermore, although trapezoidal-like pitching motions are known to improve the efficiency in flows restricted to two dimensions, particularly for non-optimal angle of attack, the efficiency of such flows is even more strongly affected by three-dimensional motions, with substantial efficiency loss even for AR = 8. This suggests that the implementation of efficiency improvement strategies obtained by two-dimensional studies should be treated with caution when extended to real three-dimensional flows.