Improved Model for Flexible Flapping Wings: Considering Spanwise Twisting and Bending

Insect wings and biomimetic wings in flapping-wing micro air vehicles (FWMAVs) are flexible and subject to passive deformations, including spanwise twisting and bending. This raises a typical bilateral fluid–structure interaction (FSI) issue, which is conventionally solved based on combined computational fluid dynamics (CFD) and computational solid dynamics (CSD) methods. To reduce the computational cost of this FSI issue while maintaining a reasonable accuracy, a theoretical model with improved adaptability is proposed here. The improvement results from the consideration of spanwise bending: the distribution of which is formulated by a quadratic polynomial. The aerodynamic force is approximated by a predictive quasi-steady aerodynamic model based on the blade element theory. The FSI iteration at a time step is converged within 0.5 s in our model, whereas a traditional CFD–CSD solution takes about 30 s. Compared to our previous model, the current model can better match the experimental measurements of insect wings. Further analysis reveals that considering spanwise bending affects the stiffness design of flexible flapping wings quantitatively. To maintain a high lift efficiency, the structural stiffness of the wing should be appropriately decreased. Our model provides a refined tool for the wing design in FWMAVs and can promote the development of FWMAVs.