Wing-wake interaction destabilizes hover equilibrium of a flapping insect-scale wing.

Wing-wake interaction is a characteristic nonlinear flow feature that can enhance unsteady lift in flapping flight. However, the effects of wing-wake interaction on the flight dynamics of hover are inadequately understood. We use a well-validated 2D Navier-Stokes equation solver and a quasi-steady model to investigate the role of wing-wake interaction on the hover stability of a fruit fly scale flapping flyer. The Navier-Stokes equations capture wing-wake interaction, whereas the quasi-steady models do not. Both aerodynamic models are tightly coupled to a flight dynamic model, which includes the effects of wing mass. The flapping amplitude, stroke plane angle, and flapping offset angle are adjusted in free flight for various wing rotations to achieve hover equilibrium. We present stability results for 152 simulations which consider different kinematics involving the pitch amplitude and pitch axis as well as the duration and timing of pitch rotation. The stability of all studied motions was qualitatively similar, with an unstable oscillatory mode present in each case. Wing-wake interaction has a destabilizing effect on the longitudinal stability, which cannot be predicted by a quasi-steady model. Wing-wake interaction increases the tendency of the flapping flyer to pitch up in the presence of a horizontal velocity perturbation, which further destabilizes the unstable oscillatory mode of hovering flight dynamics.