# Effect of Wing Corrugation on the Aerodynamic Efficiency of Two-Dimensional Flapping Wings
## 1 Introduction
similarly concluded that the corrugation increases the performance of the wing within the entire range of AoA of (0 to 40)\({}^{\circ}\). Since the largest increase in lift coefficient was found for the largest corrugation [15], even though the orientation of the leading edge is upward, they claimed that the increase in lift coefficient was proportional to the scale of corrugation, regardless of the direction of corrugation. Moreover, their numerical analysis studied the generation of the leading-edge vortex (LEVs), trailing-edge vortex (TEVs), and the vortices in the valley formed by the corrugation. Based on the results for an AoA of 30\({}^{\circ}\), they concluded that the increase in lift coefficient is due to the corrugation on the pressure side of the wing, while the contribution of corrugation to the increase in lift coefficient on the suction side is insignificant. Even though the size of the vortex on the suction side increases for a higher angle of attack, the intensity of the vortex is very small, due to the low velocity. Therefore, it is difficult to observe the effect of corrugation on the suction side. The studies described above were conducted for gliding flight, in which the wings were stationary. From another point of view, [PERSON] et al. [17] investigated the effect of wing corrugation on the aerodynamic performance of a three-dimensional flapping wing. The corrugated wing was modeled by placing the corrugation on the flat plate, ensuring no camber appearance. Through the numerical analysis, they found that at typical mid-stroke angles of attack of (35 to 50)\({}^{\circ}\) in hovering, the average lift of corrugated wing reduced by less than 5%, and this reduction had almost no effect on the mean drag, compared to the rigid flat-plate. [PERSON] et al. [18] also investigated the aerodynamic effects of wing deformation and corrugation of a three-dimensional model hoverfly wing on the aerodynamic performance at hovering condition. They found that the wing deformation contributed to a 9.7% increase in the lift, and the wing corrugation caused a 6.5% decrease in the lift. Thus, they concluded that the wing corrugation was mainly for structural rather than aerodynamic purposes. [PERSON] et al. [19] investigated the effect of corrugation implemented in cambered wings on the aerodynamic performance of three-dimensional flapping wings of the KUBeetle [12]. They numerically tested two types of corrugated wings: the Z wings have five triangle corrugations placed all over the wing chord, and F wings have non-corrugated areas near the leading and trailing edges. Different corrugation heights of (3 and 6)% of chord length were tested for each type of wing. For the Z wing, the lift and drag increased in the downstroke, compared to the non-corrugated wing. However, due to the reversal of the wing profiles in upstroke, the lift and drag were decreased. For the F wing group, the lift and drag were decreased slightly in both downstroke and upstroke. However, the aerodynamic performances of the F wing with a corrugation height of 3% of chord length were very close to those of the non-corrugated curved wing. Therefore, this particular wing was considered suitable to replace the current KUBeetle wing, due to the structural benefits of the corrugated wing. These consistent conclusions on the corrugated wing under three-dimensional flapping motion are mainly due to the fact that these flapping wings experience a high AoA, where the effect of wing corrugation is diminished. In this study, we aimed to search for particular wing corrugations that can enhance aerodynamic efficiency, even for high AoAs. We used the two-dimensional computational fluid dynamics (CFD) model instead of the three-dimensional model to initially assess the aerodynamic performance of various corrugated wings within a shorter time. A commercial software, ANSYS-Fluent, was used for the computation.