Scaling the propulsive performance of heaving flexible panels

We present an experimental investigation of flexible panels actuated with heave oscillations at their leading edge. Results are presented from kinematic video analysis, particle image velocimetry, and direct force measurements. Both the trailing edge amplitude and the mode shapes of the panel are found to scale with dimensionless parameters originating from the Euler-Bernoulli beam equation. The time-averaged net thrust increases with heaving frequency, but experiences localized boosts near resonant frequencies where the trailing edge amplitude is maximized. These boosts correspond to local maxima in the propulsive efficiency. For a constant heave amplitude, the time-averaged net thrust coefficient is shown to be a function of Strouhal number over a wide range of conditions. It appears, therefore, that self-propelled swimming (zero net thrust) only occurs over a small range of Strouhal numbers. Under these near-constant Strouhal number conditions, the propulsive economy increases with higher flexibilities and slower swimming speeds.