On the flow generated by rotating flat plates of low aspect ratio
DeVoria, Adam C.
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Low-aspect-ratio propulsors typically allow for high maneuverability at low-to-moderate speeds. This has made them the subject of much recent research aimed at employing such appendages on autonomous vehicles which are required to navigate tumultuous environments. This experimental investigation focuses on the fluid dynamic aspects associated with overly-simplified versions of such biologically-inspired propulsors. In doing so, fundamental contributions are made to the research area. The unsteady, three-dimensional flow of a low-aspect-ratio, trapezoidal flat plate undergoing rotation from rest at a 90° angle of attack and Reynolds numbers of O (10 3 ) is investigated experimentally. The objectives are to develop a straightforward protocol for vortex saturation, and to understand the effects of the root-to-tip flow for different velocity programs. The experiments are conducted in a glass-walled tank, and digital particle image velocimetry is used to obtain planar velocity measurements. A formation-parameter definition is investigated and is found to reasonably predict the state corresponding to the pinch-off of the initial tip vortex across the velocity programs tested. The flow in the region near the tip is relatively insensitive to Reynolds number over the range studied. The component normal to the plate is unaffected by total rotational amplitude while the tangential component has dependence on this angle. Also, an estimate of the first tip-vortex pinch-off time is obtained from the near-tip velocity data and agrees very well with values estimated using circulation. The angle of incidence of the bulk root-to-tip flow relative to the plate normal becomes more oblique with increasing rotational amplitude. Accordingly, the peak magnitude of the tangential velocity is also increased and as a result advects fluid momentum away from the plate at a higher rate. The more oblique impingement of the root-to-tip flow for increasing rotational amplitude is shown to have a distinct effect on the associated fluid dynamic force normal to the plate. For impulsive plate deceleration the time that a non-negligible force exists decreases, while for non-impulsive plate deceleration both this time and the relative force magnitude decrease for larger rotational amplitudes. In a separate set of experiments, force measurements are conducted on a similar plate that performs an advancing stroke from rest followed by a returning stroke. The parameters varied are the rotational amplitude of the motion and the rest time between the advancing and returning strokes. The unsteady normal forces track with the angular acceleration of the plate, with the added mass force peak in the returning stroke being larger than that in the advancing stroke. However, as the rest time is increased, the normal forces generated in each stroke become dynamically similar. The maximum total impulse is calculated from the force measurements and rapidly decays from its largest value at zero rest time and asymptotes to a constant with increased rest time. The direction of this impulse is also calculated and quickly approaches the direction about which the plate motion is symmetric. The largest additional impulse contribution obtained from executing a returning stroke within a finite time is approximately 18%. Increases in rotational amplitude initially increase the maximum total impulse, but it then plateaus at an amplitude of around 90 degrees. For non-zero rest times, any maxima of the impulse in a fixed direction are weak and necessarily reduced from the maximum possible impulse. For a nearly 100 degrees range of directions, the impulse is largest for rotational amplitudes between 75–90 degrees. The results are also applied to three types of propulsive configurations.