The aerodynamic performance of passive wing pitch in hovering flight

Insect wings can passively maintain a high angle of attack during each flapping stroke without the aid of the active pitching motion due to the torsional flexibility of the wing basal region. However, there is no clear understanding of how torsional wing flexibility should be designed for achieving optimal aerodynamic performance. In this work, a computational study was conducted to investigate the passive pitching mechanism of a fruit fly wing in hovering flight using a torsional spring model. The torsional wing stiffness was characterized by the Cauchy number, a ratio between the aerodynamic force and the structural elastic force. Different flapping patterns including zero-deviation, figure-8, and oval-shaped flapping trajectories were evaluated along a horizontal stroke plane. The aerodynamic forces and associated unsteady flow structures were simulated using an in-house immersed-boundary-method based computational fluid dynamics solver. A parametric study on the Cauchy number was performed with a Reynolds number of 300. According to the analysis of the aerodynamic performance, we found that a balance of high lift and high lift-to-power ratio can be achieved in a particular range of Cauchy numbers (0.15–0.30) for all different flapping trajectories. This range is consistent with the Cauchy number calculated based on the experimental measurements of a fruit fly in the literature. In addition, 3D wake structures generated by the passive flapping wings were analyzed in detail. The findings of this work could provide important implications for designing more efficient flapping-wing micro-air vehicles.