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Scaling law for the lift force of autorotating falling seeds at terminal velocity

Published online by Cambridge University Press:  27 November 2017

Injae Lee  and
Haecheon Choi Open the ORCID record for Haecheon Choi [Opens in a new window]
Injae Lee
Affiliation:
Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Korea
Haecheon Choi*
Affiliation:
Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Korea
*
†Email address for correspondence: choi@snu.ac.kr Also at Institute of Advanced Machines and Design, Seoul National University, Seoul 08826, Korea
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Abstract

We provide a scaling law for the lift force of autorotating falling seeds at terminal velocity to describe the relation among the lift force, seed geometry and terminal descending and rotating velocities. Two theories, steady wing-vortex theory and actuator-disk theory, are examined to derive the scaling law. In the steady wing-vortex theory, the strength of a leading-edge vortex is scaled with the circulation around a wing and the lift force is modelled by the time derivative of vortical impulse, whereas the conservations of mass, linear and angular momentum, and kinetic energy across the autorotating falling seed are applied in the actuator-disk theory. To examine the validity of the theoretical results, an unsteady three-dimensional numerical simulation is conducted for flow around an autorotating seed (Acer palmatum) during free fall. The sectional lift coefficient predicted from the steady wing-vortex theory reasonably agrees with that from the numerical simulation, whereas the actuator-disk theory fails to provide an estimation of the sectional lift coefficient. The weights of 11 different species of autorotating falling seeds fall on the scaling law derived from the steady wing-vortex theory, suggesting that even a simple theoretical approach can explain how falling seeds support their weights by autorotation once the circulation from a leading-edge vortex is properly included in the theory.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 406 - 420
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Copyright
© 2017 Cambridge University Press 

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