Optimizing the Efficiency of Batoid-Inspired Swimming

Abstract

Traditional propellers lack the combination of efficiency, maneuverability, and stealth found among swimmers in nature. With this deficiency as motivation, two aspects of batoid-inspired swimming are investigated: flexibility and propulsor-boundary interactions.

In the case of flexibility, direct force measurements on flexible panels reveal that operating in resonance can increase both thrust and efficiency. Gradient-based optimization is used to isolate the resonant modes of one panel, and Particle Image Velocimetry (PIV) is used to study the optimum and near-optimum conditions. Efficiency is globally optimized when (1) the Strouhal number is within an optimal range that varies weakly with amplitude and boundary conditions; (2) the panel is actuated at a resonant frequency of the fluid-panel system; (3) heave amplitude is tuned such that trailing edge amplitude is maximized while the flow along the body remains attached; and (4) the maximum pitch angle and phase lag are chosen so that the effective angle of attack is minimized. The multi-dimensionality and multi-modality of the efficiency response demonstrate that experimental optimization is well-suited for the design of flexible underwater propulsors. Linear beam theory combined with the Lighthill model offers a dimensionless parameter that can be used to tune propulsors to resonant modes. In self-propelled swimming trials, flexibility is found to increase the swimming economy, even at constant Strouhal number, challenging the traditional view that Strouhal number is a primary indicator of efficiency.

Propulsor-boundary interactions are relevant to fish schooling, bodies with multiple fins, and fishes/vehicles that swim near the substrate. In the case of rigid foils operating near a rigid flat boundary, thrust is found to increase monotonically as the foil approaches the ground, and efficiency remains constant. A semi-empirical power law is offered to quantify this behavior, and the same power law is observed in potential flow computations that were run parallel to the experiments. In the near-ground case, momentum jets behind the foil angle away from the ground under most conditions. This angling was also seen in the potential flow computations and is explained using the vortex array model. When propulsors are flexible, propulsive efficiency can increase near the ground in addition to thrust. Direct force measurements on two airfoils pitching side-by-side reveal that thrust or efficiency can be increased or decreased depending on the phase offset between the two airfoils. The momentum jets in the wake of the airfoils either converge or diverge, also depending on the phase offset. When the two foils are 180$^\circ$ out of phase, the forces and flow patterns match those seen in ground effect, as anticipated by the method of images. This behavior is reproduced with an analytical vortex array model. The scaling laws presented here lay a framework for underwater vehicles that use multiple propulsors or swim near the substrate to increase thrust or efficiency.