Underwater Flight: Hydrodynamics of the Manta Ray

Abstract

Experiments are conducted to better understand the effects of flexibility in generating unsteady bio-inspired propulsion. It is found that by exploiting the effects of flexibility, the thrust production and propulsive efficiency can be up to twice that of a rigid propulsor. The wakes are highly dependent on the input parameters to the system such as the oscillation frequency and chordwise traveling wave wavelength that develops along a flexible surface. In general, the wakes of flexible propulsors tend to concentrate their momentum in the direction of motion whereas the wakes of rigid propulsors have relatively larger momentum in the transverse direction leading to a decrease in propulsive efficiency. A linear stability analysis is conducted on the wakes to determine the wake resonant frequencies. It is found that when the driving oscillation frequency of the apparatus matches the wake resonant frequency there is a local peak in propulsive efficiency. The global peak in efficiency occurs only when the structural resonant frequency of the flexible structure is coincident with the wake resonant frequency, which only occurs under very specific conditions. This implies that there is an optimum flexibility to maximize propulsive efficiency; being either too stiff or too flexible is detrimental to propulsive performance. Since both the structural resonant frequency and wake resonant frequencies are finite, this also suggests that animals must utilize flexible propulsive surfaces if they are to optimize their efficiencies. Finally, a non-dimensional scaling argument is made that is shown to collapse the thrust production, power input to the fluid, and propulsive efficiency for a range of propulsors with various flexibilities and aspect ratio.