An efficient fluid-structure interaction model for optimizing twistable flapping wings

Spanwise twist can dominate the deformation of flapping wings and alters the aerodynamic performance and power efficiency of flapping wings by changing the local angle of attack. Traditional Fluid-Structure Interaction (FSI) models, based on Computational Structural Dynamics (CSD) and Computational Fluid Dynamics (CFD), have been used to investigate the influence of twist on the power efficiency. However, it is impractical to use them for twist optimization due to the high computational cost. On the other hand, it is of great interest to study the optimal twist of flapping wings. In this work, we propose a computationally efficient FSI model based on an analytical twist model and a quasi-steady aerodynamic model which replace the expensive CSD and CFD methods. The twist model uses a polynomial to describe the change of the twist angle along the span. The polynomial order is determined based on a convergence study. A nonlinear plate model is used to evaluate the structural response of the twisted wing. The adopted quasi-steady aerodynamic model analytically calculates the aerodynamic loads by including four loading terms which originate from the wing's translation, rotation, their coupling and the added-mass effect. Based on the proposed FSI model, we optimize the twist of a rectangular wing by minimizing the power consumption during hovering flight. The power efficiency of optimized twistable and rigid wings is studied. Comparisons indicate that the optimized twistable wings exhibit power efficiencies close to the optimized rigid wings, unless the pitching amplitude at the wing root is limited. When the pitching amplitude at the root decreases by increasing the root stiffness, the optimized rigid wings need more power for hovering. However, with the help of wing twist, the power efficiencies of optimized twistable wings with a prescribed root stiffness are comparable with the twistable wings with an optimal root stiffness. This observation provides an explanation for the different levels of twist exhibited by insect wings. The high computational efficiency of the proposed FSI model allows further application to parametric studies and optimization of flapping wings. This will enhance the understanding of insect wing flexibility and help the design of flexible artificial wings for flapping wing micro air vehicles.