Inertial effects of the semi-passive flapping foil on its energy extraction efficiency

The inertia plays a significant role in the response of a system undergoing flow-induced vibrations, which has been extensively investigated by previous researchers. However, the inertial effects of an energy harvester employing the mechanism of flow-induced vibrations have attracted little attention. This paper concentrates on a semi-passive energy extraction system considering its inertial effects. The incompressible Navier-Stokes equations are solved using a finite-volume based numerical solver with a moving grid technique. A partitioned method is used to couple the fluid and structure motions with the sub-iteration technique and an Aitken relaxation, which guarantees a strong fluid-structure coupling. In addition, a fictitious mass is added to resolve the numerical instability aroused by low density ratios. First, at a fixed mass ratio of r = 1, we identify an optimal set of parameters, at which a maximum efficiency of eta = 34% is achieved. Further studies with r ranging from 0.125 to 100 are performed around the optimal parameters. The results show that for the semi-passive flapping energy harvester, the energy harvesting efficiency decreases monotonically with increasing mass ratio. We also notice that the total power extraction stays at a high level with little variation for r < 10; therefore, if we concern more about the amount of power extraction rather than its efficiency, the inertial effects can be neglectable for r < 10. Moreover, since one degree of freedom is released for the semi-passive system, it is possible for the system to automatically determine its optimal operational parameters. We note that the optimal phase difference phi = 82 degrees has been well determined, which leads to a good timing of vortex-foil interactions. We note two different trends on phase difference for the effects of reduced frequency and mass ratio, respectively. By varying the reduced frequency f *, an optimal f * is identified, at which the minimum phase difference is achieved. While the relationship between phase difference and mass ratio is monotonic, a maximum phase difference is achieved at the nearly zero mass ratio. Nevertheless, both trends point to the same optimal phase difference, i.e., phi = 82 degrees at theta(0) = 75 degrees. Furthermore, the relationship between the leading edge vortex and the phase difference is systematically investigated, accounting for the physical reason of existence of the optimal phase difference. (C) 2015 AIP Publishing LLC.