Reversed von Kármán streets are responsible for a velocity surplus in the wake of flapping foils, indicating the onset of thrust generation. However, the wake pattern cannot be predicted based solely on the flapping peak-to-peak amplitude A and frequency f because the transition also depends sensitively on other details of the kinematics. In this work we replace A with the cycle-averaged swept trajectory T of the foil chord-line. Two dimensional simulations are performed for pure heave, pure pitch and a variety of heaveto-pitch coupling. In a phase space of dimensionless T −f we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal St T ∼ 1. Physically the product T ⋅ f expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds U ∞ . The new metric offers a unique insight into the thrust producing strategies of biological swimmers and flyers alike as it directly connects the wake development to the chosen kinematics enabling a self similar characterisation of flapping foil propulsion.

Abstract

In this work, we describe the impact of aspect ratio ( $AR$ ) on the performance of optimally phased, identical flapping flippers in a tandem configuration. Three-dimensional simulations are performed for seven sets of single and tandem finite foils at a moderate Reynolds number, with thrust producing, heave-to-pitch coupled kinematics. Increasing slenderness (or $AR$ ) is found to improve thrust coefficients and thrust augmentation but the benefits level off towards higher values of $AR$ . However, the propulsive efficiency shows no significant change with increasing $AR$ , while the hind foil outperforms the single by a small margin. Further analysis of the spanwise development and propagation of vortical structures allows us to gain some insights into the mechanisms of these wake interactions and provide valuable information for the design of novel biomimetic propulsion systems.

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