Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors

We present the linear stability analysis of experimental measurements obtained from unsteady flexible pitching panels. The analysis establishes the connections among the wake dynamics, propulsor dynamics, and Froude efficiency in flexible unsteady propulsion systems. Efficiency is calculated from direct thrust and power measurements and wake flowfields are obtained using particle image velocimetry. It is found that for flexible propulsors every peak in efficiency occurs when the driving frequency of motion is tuned to a wake resonant frequency, not a structural resonant frequency. Also, there exists an optimal flexibility that globally maximizes the efficiency. The optimal flexibility is the one where a structural resonant frequency is tuned to a wake resonant frequency. The optimally tuned flexible panels demonstrate an efficiency enhancement of 122%–133% as compared to an equivalent rigid panel and there is a broad spectrum of wake resonant frequencies allowing high efficiency swimming over a wide range of operating conditions. At a wake resonant frequency we find that the entrainment of momentum into the time-averaged velocity jet is maximized.