Universal scaling law for drag-to-thrust wake transition in flapping foils
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 sen...
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Published in | Journal of fluid mechanics Vol. 872 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Cambridge
Cambridge University Press
10.08.2019
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Subjects | |
Online Access | Get full text |
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Summary: | 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
${\mathcal{T}}$
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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ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/jfm.2019.361 |