Effect of Chordwise Flexibility Distribution on Wave-Assisted Flapping Foil Performance

This study investigates the influence of the spatial distribution of flexibility along a propulsor on thrust generation and propulsive efficiency in wave-assisted flapping foils. While flexibility is known to enhance propulsive performance, the role of its chordwise placement remains poorly understood. Here, the effective flexible length is systematically varied by shifting the flexure location along the tail while maintaining constant flexural rigidity and total chord length. Experiments are conducted in quiescent flow at heave frequencies of 0.8 Hz and 1.25 Hz, and non-dimensional heave amplitudes of h* = 0.13 and 0.22. Simultaneous measurements of hydrodynamic forces, flow fields, and tail kinematics are used to quantify performance and elucidate the underlying fluid–structure interactions. The fully flexible configuration consistently achieves higher propulsive efficiency (up to ∼ 164%) across all conditions, which is attributed to enhanced jet persistence and increased streamline vortex spacing, indicative of a more coherent and sustained momentum jet. In contrast, the mid-flexible configuration yields substantially higher thrust (up to ∼ 66%) at the largest heave frequency and amplitude, driven by a pronounced increase in near-wake jet velocity and momentum flux. These results demonstrate that the chord-wise distribution of flexibility governs the trade-off between thrust and propulsive efficiency by modulating wake coherence and momentum transfer. The findings establish flexibility placement as a key design parameter in flapping propulsion and provide physics-based guidelines for enhancing the performance and endurance of wave-driven unmanned surface vehicles.