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Aspect-ratio effects on rotating wings: circulation and forces

Published online by Cambridge University Press:  20 February 2015

Zakery R. Carr ,
Adam C. DeVoria  and
Matthew J. Ringuette
Zakery R. Carr
Affiliation:
Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, 318 Jarvis Hall, Buffalo, NY 14260-4400, USA
Adam C. DeVoria
Affiliation:
Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, 318 Jarvis Hall, Buffalo, NY 14260-4400, USA
Matthew J. Ringuette*
Affiliation:
Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, 318 Jarvis Hall, Buffalo, NY 14260-4400, USA
*
†Email address for correspondence: ringum@buffalo.edu
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Abstract

We employ experiments to study aspect ratio ($\def\AR{A\mkern-8muR}\AR$) effects on the vortex structure, circulation and lift force for flat-plate wings rotating from rest at 45° angle of attack, which represents a simplified hovering-wing half-stroke. We use the time-varying, volumetric $\AR =2$ data of Carr et al. (Exp. Fluids, vol. 54, 2013, pp. 1–26), reconstructed from phase-locked, phase-averaged stereoscopic digital particle image velocimetry (S-DPIV), and an $\AR =4$ volumetric data set matching the span-based Reynolds number ($\mathit{Re}$) of $\AR =2$. For $\AR =1{-}4$ and $\mathit{Re}_{\mathit{span}}$ of $O$($10^{3}$–$10^{4}$), we directly measure the lift force. The total leading-edge-region circulation for $\AR =2$ and 4 compares best overall using a span-based normalization and for matching rotation angles. The total circulation increases across the span to the tip region, and is larger for $\AR =2$. After the startup, the total circulation for each $\AR$ has a similar slope and a slow growth. The first leading-edge vortex (LEV) and the tip vortex (TV) for $\AR =4$ move past the trailing edge, followed by substantial breakdown. For $\AR =2$ the outboard, aft-tilted LEV merges with the TV and resides over the tip, although breakdown also occurs. Where the LEV is ‘stable’ inboard, its circulation saturates for $\AR =2$ and the growth slows for $\AR =4$. Aft LEV tilting reduces the spanwise LEV circulation for each $\AR$. Both positive and negative axial flow are found in the first LEV for $\AR =2$ and 4, with the positive component being somewhat larger. This yields a generally positive (outboard) average vorticity flux. The average lift coefficient is essentially constant with $\AR$ from 1 to 4 during the slow growth phase, although the large-time behaviour shows a slight decrease in lift coefficient with increasing $\AR$. The S-DPIV data are used to obtain the lift impulse and the spanwise and streamwise components contributing to the lift coefficient. The spanwise contribution is similar for $\AR =2$ and 4, due to similar trailing-edge vortex interactions, LEV saturation behaviour and total circulation slopes. However, for $\AR =2$ the streamwise contribution is much larger, because of the stronger, coherent TV and aft-tilted LEV, which will create a relatively lower-pressure region over the tip.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 497 - 525
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Copyright
© 2015 Cambridge University Press 

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Footnotes

‡

Present address: CUBRC, Inc., Buffalo, NY 14225, USA.

§

Present address: University of Florida, Gainesville, FL 32611, USA.

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