Effect of wingtip-curve on aerodynamic performance in flapping flexible wings: rectangular versus hawkmoth-like

Insects have various wing morphologies and flapping systems to achieve a highly maneuverable performance at low speed. Among unsteady aerodynamic mechanisms in flapping flights, a leading-edge vortex is a significant key to generating lift stably in insect flights. The leading-edge vortex behavior is correlated with an overall vortical system around flapping wings. In addition, the insects have flexible wing structures that are deformable while flapping their wings. The wing deformations can be easily affected by wing morphologies and kinematic motions, leading to different vortical structures around the flexible wings. Thus, lift enhancement in flapping flexible wings depends on the wing shape and structural deformation in diverse species of insects. Here, by measuring and comparing time-varying force/torque and flow structures of two different flexible wings, rectangular (non-curved, at \(Re\) $\mathit{Re}$ =  ~ 6044) and hawkmoth-like (curved, at \(Re\) $\mathit{Re}$ =  ~ 5309) shapes, it was found that a wingtip curve is a meaningful factor in studying flapping flexible wings. In a flexible case, the hawkmoth-like model had a widened leading-edge vortex region and strengthened circulations around the inner wing, thereby producing more lift (12.7% increase) and achieving better aerodynamic performance (4.8% increase of lift-power ratios). However, despite both flexible models having similar flexural stiffnesses, these features were not observed in the rectangular model, even generating more aerodynamic force even generating more aerodynamic force than the hawkmoth-like model in the rigid case (8.12%, 1.52%, and 16.99% greater in lift, drag, and power, respectively). These were caused by different wingtip motions between two flexible wings during wing reversal, leading to different downwash and corresponding leading-edge vortex structures. These findings demonstrate that the wingtip curve effect might be improved when combined with wing flexibility. They, thus, inspire future research on flapping motions, wing shapes, and structures.