Balancing thrust and energy efficiency: Optimized asymmetric flapping inspired by batoid locomotion

Batoid fishes employ undulating movements to navigate through aquatic environments. Specifically, stingray-like species utilize asymmetric flapping motions, characterized by faster downstrokes to enhance thrust generation. Inspired by these biological mechanisms, this study models flapping motions utilizing a National Advisory Committee for Aeronautics (NACA) 0012 hydrofoil at a Reynolds number of 10 000. By adjusting the amplitudes of the fundamental and second harmonics, diverse flapping kinematics were achieved. The non-dominated sorting genetic algorithm II (NSGA-II) was employed to optimize both thrust and thrust efficiency. From the optimal solutions, six distinct parameter combinations were identified, all featuring relatively brief downstroke durations. This indicates that asymmetric flapping with shorter downstrokes effectively balances thrust and efficiency, resulting in superior performance outcomes. A comprehensive analysis elucidated how each harmonic component influences the timing and intensity of vortex generation and attachment within the flow field. Moreover, the optimized motion closely resembles the natural swimming kinematics observed in batoid fish, suggesting that their locomotion strategies have inherently evolved for efficiency and thrust optimization. These findings provide valuable insights for the design and optimization of biomimetic underwater propulsion systems, facilitating the development of more efficient and adaptable aquatic robots.