1 | INTRODUCTION

Flapping-wing micro air vehicle (FWMAV) is a flying robot that mimics the flapping flight of birds or insects, and generates lift and thrust through flapping (Hou et al., 2022). The FWMAV has ideally characteristics such as a small size, a fast take-off, a high maneuverability, flexibility and unique bionic shape (Cao et al., 2019; Nian et al., 2019). The wing, being the main structure that provides lift, thrust and torque, is one of the most important components of the FWMAV.
Corrugated microstructures in insects’ wings are found to be useful in unsteady flows under low Reynolds numbers (R e) for a number of reasons (Flint et al., 2017; Yang et al., 2021). For instance in a dragonfly, their corrugated wings (1) can reduce the increase in drag significantly during flying (Meng et al., 2011; Lian et al., 2014); (2) is 6% higher than the flat wing about lift-to-drag ratio at e.g. α =5 and Re =1400 (Chen et al., 2016); (3) can improve the lift enhancing effect of trailing edge vortex (TEV) with a simple wing kinematic motion (Chen et al., 2015); (4) can enhance the structural strength of wings (Jongerius et al., 2010). In a lowR e environment, a corrugated airfoil can effectively prevent large-scale flow separation and improve the performance with regard to airfoil stall (Hu et al., 2008; Chitsaz et al., 2021). Compared with a flat airfoil, the corrugated wing performs better aerodynamically, although the pressure drag is somewhat increased, the viscous drag is reduced due to the existence of recirculation zones inside the corrugations (Hou et al., 2015). Moreover, corrugation structure has also been found to improve wing rigidity, giving it higher bending and torsion strength (Sunada et al., 2002). In 3D corrugated wings, wing deflection is reduced by 20% and stress is reduced by 95%, compared to a flat plate wing of the same size, making the corrugated wing significantly more stable (Zhang et al., 2018).
Insect wings are complex structures that can passively deform during flight (Hedrick et al., 2015; Sun et al., 2019; Walker et al., 2012). Due to the flexibility of an insect’s wing, its aerodynamics becomes more complicated (Xue et al., 2019). For example, it was found that fruit flies have two distinct aerodynamic force peaks during each flapping stroke during hovering: The flexible wings deform passively during flapping, and the first force peak is due to rapid vortex increase as the wing experiences a fast pitching-up rotation, and the second force peak is associated with wake-capturing (Liu et al., 2019). Both the transient formation and the relatively stable position of the leading-edge vortex (LEV) contribute to the high lift generation of an insect’s wing when it revolves at relatively high angles of attack, and the instantaneous lift depends mostly on the wing’s instantaneous velocity and acceleration (Chen et al., 2020). In the beetle Trypoxylus dichotomus the angle of attack varied significantly along the wingspan during free forward flight with a beat frequency of 38Hz and a flapping angle of 165°. The flexible deformation at different cross sections of the wing is rather variable then (Truong et al., 2012), and the thrust generated by the wing flexibility is decided by aerodynamic forces and inertial forces simultaneously (Yang et al., 2015). Additionally, when transferring from hovering to forward flight, the effect of inertial deformation appeared to be greater than aeroelastic deformation with regard to the instantaneous wing shape (Bergou et al., 2007; Hussein et al., 2019). However, with regard to FWMAV design in comparison to insect functional morphology of flight, many things still have to be cleared up, such as stall at small angles of attack and the detrimental high wind resistance (Li et al., 2022; Liu et al., 2022; Deng et al., 2019; Lian et al., 2003). Beetles (Coleoptera) are a unique group of insects with deployable hindwings that can be folded under the elytra, which probably reduce wing damage when not flying (Sun et al., 2019). The hindwings have successfully combined compatibility between the deformability (instability) required for wing folding with strength (stability) required for flying (Sun et al., 2019; Jeffries et al., 2013). More importantly, the deployable hindwings of beetles seem an ideal model conduce further miniaturization of MAVs in the near future.
In this paper, the microstructure of a cross section of the hindwing was observed. Three corrugated airfoils (CA models) learned from the microscopy imaging of ladybird beetle hindwing were designed. Then aerodynamic performance tests of the models using ANSYS Fluent software were performed. The simulation results were used to investigate the effect of corrugated structural and motion parameters on the aerodynamic behaviors. This research provides relevant enlightenment and reference for corrugated structure design and optimization of bionic FWMAV wings.