Propulsion by tandem flapping foils

Propulsion by pitching and heaving airfoils and hydrofoils has been a focus of much research in the field of biologically inspired propulsion. Organisms that use this sort of propulsion are self-propelled, so it is difficult to use standard experimental metrics such as thrust and drag to characterize performance. We have constructed a flapping foil robot mounted in a flume on air-bearings that allows for the determination of self-propelled speed as a metric of performance. We have used a pair of these robots to examine the impact of an upstream flapping foil on a downstream flapping foil as might apply to tandem fins of a swimming organism or in-line swimming of schooling organisms. Self-propelled speed and a force transducer confirmed significant thrust augmentation for particular foil-to-foil spacings, phase differences, and flapping frequencies. Flow visualization shows the mechanism to be related to the effective angle of attack of the downstream foil due to the structure of the wake of the upstream foil. This confirms recent computational work and the hypotheses by early investigators of fish fluid dynamics.

The umbilical of the robot provides a restoring force that leads to a streamwise equilibrium position. In our experiments, we start the foils and then tune the flume speed until the robot holds position at its equilibrium position. The flume speed represents the self-propelled speed of the flapping foil system. The robot actually oscillates about the equilibrium position, so to determine the self-propelled speed more precisely, we vary the flume velocity around a rough estimate of the self-propelled speed. This leads to a speed vs. displacement graph that can be fit with a straight line. The self-propelled speed is the value of the linear fit at the streamwise equilibrium position.

The graph to the right shows the self-propelled speed of a tandem foil system as a function of phase difference between the motion of the two foils and the streamwise spacing between the foils. Note that for any given spacing there is a maximum and a minimum self-propelled speed. The positions of these peaks shift as spacing changes. This suggests that the thrust of the downstream foil is modulated by fluid structures shed from the upstream foil and convected downstream. The greater the spacing, the longer it takes for structures in the wake to reach the downstream foil. Therefore, in order for the downstream foil to experience a similar flow field when it is at a certain position as spacing increases, there needs to be an increasing phase lag to allow for the increased convection time.

Lauder, G., Lim, J., Shelton, R., Witt, C., Anderson, E. and Tangorra, J. L. (2011). Robotic models for studying undulatory locomotion. Mar. Tech. Soc. J. 45 (4), 41-55.

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