On the lift-optimal aspect ratio of a revolving wing at low Reynolds number

Lentink & Dickinson (2009 J. Exp. Biol. 212, 2705–2719. (doi:10.1242/jeb.022269)) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a va...

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Bibliographic Details
Published in:Journal of the Royal Society interface 2018-06, Vol.15 (143), p.20170933-20170933
Main Authors: Jardin, T., Colonius, T.
Format: Article
Language:English
Subjects:
Acceleration
Aerodynamics
Axes of rotation
Balances (scales)
Birds
Computational fluid dynamics
Computer simulation
Convergence
Coriolis force
Cyclones
Flapping And Revolving Wings
Fluid flow
High lift
Hovering
Insects
Life Sciences–Engineering interface
Low aspect ratio
Reynolds number
Seeds
Vortex Flows
Wings
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Summary:Lentink & Dickinson (2009 J. Exp. Biol. 212, 2705–2719. (doi:10.1242/jeb.022269)) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.
ISSN:1742-5689
1742-5662
DOI:10.1098/rsif.2017.0933