SCIENCE SPIN-OFFS

[dockzef]

Universal scaling law in drag-to-thrust transition of flapping foils

N. S. Lagopoulos, G. D. Weymouth, B. Ganapathisubramani
(Submitted on 7 Mar 2019)

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 heave-to-pitch coupling. In a phase space of dimensionless T-f we show that the drag-to-thrust transition of all tested modes occurs for a modified Strouhal StT~1. Physically the product T·f expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds U8. 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.

https://arxiv.org/abs/1903.03050