# Unsteady Aerodynamic Design of a Flapping Wing Combined with a Bionic Wavy Leading Edge
###### Abstract  
Based on the bionic design of the humpback whale fin, a passive flow control method is proposed to obtain greater flapping lift by applying the wavy leading edge structure to the straight symmetrical flapping wing. The leading edge of the conventional flapping wing is replaced by the wavy shape represented by regular trigonometric function to form a special passive flow control configuration imitating the leading edge of the humpback whale fin. The dynamic aerodynamic performance and flow field characteristics of straight wing and wavy leading edge flapping wing with different parameters are compared and analyzed by CFD numerical simulation. The simulation results show that the wavy leading edge structure changes the flow field of the baseline flapping wing and reduces the pressure on the upper surface of the flapping wing during the process of downward flapping, thereby increasing the pressure difference between the upper and lower surfaces of the flapping wing and increasing the lift. The sensitivity analysis of the design parameters shows that in order to obtain the maximum lift coefficient while losing the least thrust, the smaller amplitude should be selected on the premise of selecting the smaller wavelength. Among the configurations of different design parameters calculated in this paper, the optimal wavy leading edge flapping wing configuration increases the time average lift coefficient by 32.86% and decreases the time average thrust coefficient by 14.28%. Compared with the straight wing, it has better low-speed flight and can withstand greater take-off weight. flapping wing; wavy leading edge; flow control; bionics; computational fluid dynamics (CFD) +
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In 1995, [PERSON] et al. [11] observed the cross section of the whale fins and studied the hydrodynamic performance of the convex structure of the fin limb of the humpback whale for the first time. They pointed out that the wavy leading edge can play a role like the lifting device. Since then, the leading edge wavy configuration has been tried to apply to the study of flow control under various scenarios and conditions. [PERSON] et al. [12] took a typical UAV as the research object and pointed out that compared with the straight wing, the wavy leading edge wing can increase lift and reduce drag and the lift-drag ratio increased by 25%. In addition, by using the oil flow method and PIV technique, they found that the wavy leading edge also makes the height and length of the laminar separation bubble on the straight wing change significantly under the condition of low angle of attack (\(\alpha=6^{\circ}\)) [13]. [PERSON] et al. [14] studied the effect of wavy leading edge on the aerodynamic performance of swept conical SD7032 wing by experiment. The results show that the wavy leading edge can slightly improve the stall performance, and the stall angle of attack can be delayed by 2-4 degrees. However, when the angle of attack is in the range of 7-20 degrees, it makes the lift drag ratio of the original wing decrease by 0-40%. [PERSON] et al. [15] adopted an infinite span rectangular wing with a high radian S1223 airfoil to numerically study the influence of leading edge wavys on its performance and concluded that the wavy structure can completely change the flow structure on the airfoil. The flow separation on the wing surface is limited to the trough of the wavy leading edge, which plays a role in flow control. [PERSON] et al. [16] verified the feasibility of flow control of NACA0015 airfoil by wavy leading edge under low Reynolds number conditions. [PERSON] et al. [17] compared the effect of wavy leading edge structure on swept wings of two different airfoils by numerical and experimental methods, and pointed out that this method has great development potential.