Optimization of Nonsinusoidal Twisting Motion for Enhanced Aerodynamic Performance of Three-Dimensional Flapping Wings

The combined motion of flapping and twisting in a flapping wing can achieve high propulsion efficiency. However, prior research has predominantly concentrated on the analysis of 2D airfoils subjected to sinusoidal twisting motion. Nevertheless, the influence of nonsinusoidal motion patterns on the aerodynamic performance of 3D wings is significant, yet most studies focus on the hovering state without flow, with few extending to forward flight conditions. To obtain the optimal nonsinusoidal twisting motion pattern for 3D flapping wings, this paper designs a custom function based on the concept of piecewise functions and proposes an optimization framework based on surrogate models. The study finds that the optimal motion pattern results in a drag coefficient approximately 76.4% lower and a propulsion efficiency about 73.5% higher than that of the baseline motion pattern. Moreover, a simplified method for rapidly calculating the lift coefficient is introduced. It was discovered that the differences in twisting patterns lead to variations in the effective angle of attack and effective inflow velocity over time, which subsequently affect the generation and shedding of leading-edge vortices, resulting in a fundamental change in the mechanisms of aerodynamic force generation. In comparison to wings following sinusoidal motion patterns, wings following a square wavelike motion pattern, characterized by prolonged periods of large twisting angles and brief rapid twists, demonstrate a drag coefficient reduction of approximately 34.2% and an increase in propulsion efficiency of about 45.2%.