Scaling laws for the thrust production of flexible pitching panels

Abstract

We present experimental results on the role of flexibility and aspect ratio in bio-inspired aquatic propulsion. Direct thrust and power measurements are used to determine the propulsive efficiency of flexible panels undergoing a leading-edge pitching motion. We find that flexible panels can give a significant amplification of thrust production of $\mathscr{O}(100{\unicode{x2013}} 200\hspace{0.167em} \% )$ and propulsive efficiency of $\mathscr{O}(100\hspace{0.167em} \% )$ when compared to rigid panels. The data highlight that the global maximum in propulsive efficiency across a range of panel flexibilities is achieved when two conditions are simultaneously satisfied: (i) the oscillation of the panel yields a Strouhal number in the optimal range ($0. 25\lt \mathit{St}\lt 0. 35$) predicted by Triantafyllou, Triantafyllou & Grosenbaugh (J. Fluid Struct., vol. 7, 1993, pp. 205–224); and (ii) this frequency of motion is tuned to the structural resonant frequency of the panel. In addition, new scaling laws for the thrust production and power input to the fluid are derived for the rigid and flexible panels. It is found that the dominant forces are the characteristic elastic force and the characteristic fluid force. In the flexible regime the data scale using the characteristic elastic force and in the rigid limit the data scale using the characteristic fluid force.

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

“…The scaling is also consistent with recent experiments performed in water [47]. The consistency between the g-scaling and the water experiments can be shown as follows.…”

“…More recently, a similar experiment has been performed in water [47] from which a scaling relationship for forward flight was observed as…”

“…In our study, we considered the added mass as an external fluid dynamic force, which is included in the definition of g. Alternatively, because added mass is proportional to the acceleration, a modified natural frequency can be established that includes the effects of added mass, i.e. the empirical frequency ratio f* [47].…”

A fast Chebyshev method for simulating flexible-wing propulsion

“…These studies have demonstrated that flexibility can drastically improve propulsive performance, especially when a wing or fin is driven near resonance [51,50,21,54,69]. Several studies even performed optimization to uncover wing properties and/or actuation strategies that deliver peak performance [94,2,57,73,69].…”

“…Several studies even performed optimization to uncover wing properties and/or actuation strategies that deliver peak performance [94,2,57,73,69]. All of the studies mentioned above, though, considered only the simplest material distributions, such as uniform flexibility [33,2,4,51,50,21,57,69] or flexibility that is localized through a torsional joint [84,54].…”