Numerical analysis of energy harvesting property and wake evolution characteristics for semi-passive flapping airfoil with various pitching amplitudes

The energy harvesting potential of flapping airfoils has garnered significant research interest, inspired by the natural movements of birds and marine creatures. In this study, a semi-passive flapping airfoil device with a prescribed pitching motion was examined using a transient numerical simulation method that employed an overlapping grid technique. The influence of pitching amplitude (\({\theta }_{m}\)) on the energy harvesting characteristics of the flapping airfoil device was analyzed using the momentum theorem and dynamic mode decomposition. The results suggested that the energy harvesting efficiency of the semi-passive flapping device varied with \({\theta }_{m}\), increasing gradually from \({\theta }_{m}\) = 10° until reaching a peak at \({\theta }_{m}\) = 80°, after which it started to decline. Lift-induced work was identified as the dominant factor contributing to the flapping energy harvesting. The wake structures of the flapping device with different \({\theta }_{m}\) values could be categorized into three types: the BVK (\({\theta }_{m}\) < 30°), mS (\({\theta }_{m}\) = 30°–50°), and 2S + mS (\({\theta }_{m}\) > 50°) types. As \({\theta }_{m}\) increased, large-scale vortices merged with adjacent small-scale vortices of the same rotation direction while suppressing small-scale vortices with the opposite rotation direction, leading to a reduction in the number of small vortices and rapid dissipation along the flow direction. The momentum theorem was utilized to identify that the vortical force term C_y^(V) and the local fluid acceleration term C_y^(A) predominantly contribute to the energy harvesting efficiency. Under small pitching amplitudes, the dynamic mode decomposition revealed a stripe-like pattern in all the modes. As the wake transitioned to the mS type, Mode1 exhibited three rows of shedding vortices. When the wake transformed to the 2S + mS type, the vortex structures within Mode1 reorganized into two orderly rows of vortices, while higher order modes dissipated rapidly along the flow direction.