Analysis of nonlinear aerodynamic performance and passive deformation of a flexible flapping wing in hover flight

The flexibility of insect wings and model wings in flapping-wing micro air vehicles (FWMAVs) is crucial to guarantee an economic flight. Since the wing deformation is bilaterally coupled with the aerodynamic force, conventional simulations on this fluid–structure interaction (FSI) problem mostly build up their models using computational fluid dynamics (CFD) and computational solid dynamics (CSD) methods, which requires high computational costs. Alternatively, an analytical model is proposed here for a quick estimate of the aerodynamic performance and passive deformation on flexible flapping wings. The deformation is simplified into a rigid-body rotation at the wing root, a spanwise twist, and a shortening along the span. The aerodynamic force is approximated by a predictive quasi-steady model and the spanwise twist is modeled using a quadratic polynomial. Results show that the introduction of wing flexibility can attenuate the lift generation due to the negative rotational lift and adverse translation–rotation coupling effect after each stroke reversal. The wing with moderate stiffness is recommended to achieve a high lift. An increase of aspect ratio and root cutoff can also enhance the dimensional lift generation, while the most economic wing design has an aspect ratio around 5 and no root cut-off. More importantly, the increase of flapping frequency can only result in a lift enhancement within certain limits. However, the power consumption keeps increasing as the frequency goes up, indicating a significant breakdown of performance. Our findings can uncover the role of wing flexibility in both insects and FWMAVs and therefore contribute to the design of FWMAVs.