Journal
JOURNAL OF FLUID MECHANICS
Volume 872, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2019.361
Keywords
propulsion; vortex shedding; vortex streets
Categories
Funding
- Office of Naval Research [N62909-18-1-2091]
- Engineering and Physical Sciences Research Council [1789955]
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Reversed von Karman 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 ${\mathcal{T}}$ of the foil chordline. Two-dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless ${\mathcal{T}}-f$ we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal $St_{{\mathcal{T}}}\rightarrow 1$ . Physically, the product ${\mathcal{T}}f$ expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds $U_{\infty }$ . 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.
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