Energy-harvesting characteristics of flapping wings with the free-surface effect

Flapping-wing devices working in an energy-harvesting mode have the advantage of environmental adaptation. To analyze the energy-extraction characteristics of a flapping wing with the free-surface effect, transient-numerical studies were carried out based on the homogeneous two-phase volume-of-flow model, the shear stress transport k–ω turbulence model, and dynamic-grid technology. These studies took into consideration the influences of the dimensionless submergence depth Sd along with the Froude number Fr. The following results were obtained. (1) In the subcritical condition of Fr < 1, there was a critical hydrofoil submergence depth. When it was greater than this critical value, the existence of the free surface was able to promote the energy-extraction efficiency. On the contrary, the closer the flapping wing was to the free surface, the lower its energy-harvesting efficiency was. (2) When the hydrofoil submergence depth was small, the energy-harvesting efficiency first increased and then decreased with the increase in Fr. Furthermore, the smaller Sd was, the faster the energy-extraction efficiency of the flapping wing decreased. While Sd was large, for example Sd > 9, the energy-extraction efficiency first increased and then gradually approached the unbounded-flow condition as Fr increased, but it was always lower than the unbounded-flow case. (3) Compared with the case of unbounded flow, the existence of the free surface affected the motion of the leading-edge vortex, thereby changing the magnitude and direction of the lift force and pitch moment. The relative position of the free-surface wave crest to the wing also affected the pressure distribution around the flapping-wing surface, which in turn affected the energy-harvesting properties. Additionally, Fr affected the formation and shedding of the vortex around the flapping wing, and the movement synchronization between the leading-edge vortex and the flapping wing was extremely important to the energy-harvesting performance.