Effects of Flexibility on the Aerodynamics of a Hovering Flexible Airfoil at Reynolds Number of 100 to 1000

While biological flyers often display deformed wing structures, the effects of flexibility on the flapping wing aerodynamics remain inadequately understood. We investigate the lift generation and phase dynamics of a flapping flexible wing in hover, between Reynolds number of 100 and 1000 corresponding to small insects, using fully coupled Navier-Stokes equation and linear beam model. The γ scaling, which we recently reported relating the wing tip-deformation to the aerodynamic performance with low flapping-to-natural frequency ratio, is revised to account for wider frequency ratios. The lift averaged over a flapping cycle normalized by effective stiffness scales with the non-dimensional wing tip deformation and the power input scales with the phase lag introduced by the flexibility. It is shown that the phase lag between the prescribed plunging motion and the passive pitch can be varied by adjusting the frequency ratios, capable of producing advanced, synchronized, or delayed rotation modes. Whereas it is widely known that the advanced rotation yields the highest lifts for the rigid wing cases, the highest lift and the optimal efficiency are observed when the motion is in synchronized rotation mode, because the pitch angle is maximal at the midstroke. The main characteristics of the aerodynamic performance remain the same for the whole Reynolds number range considered.