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Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio

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Abstract

We investigate experimentally the effect of aspect ratio ( ) on the time-varying, three-dimensional flow structure of flat-plate wings rotating from rest at 45° angle of attack. Plates of = 2 and 4 are tested in a 50 % by mass glycerin–water mixture, with a total rotation of ϕ = 120° and a matched tip Reynolds number of 5,000. The time-varying, three-component volumetric velocity field is reconstructed using phase-locked, phase-averaged stereoscopic digital particle image velocimetry in multiple, closely-spaced chordwise planes. The vortex structure is analyzed using the \(\mathcal{Q}\)-criterion, helicity density, and spanwise quantities. For both s, the flow initially consists of a connected and coherent leading-edge vortex (LEV), tip vortex (TV), and trailing-edge vortex (TEV) loop; the LEV increases in size with span and tilts aft. Smaller, discrete vortices are present in the separated shear layers at the trailing and tip edges, which wrap around the primary TEV and TV. After about ϕ = 20°, the outboard-span LEV lifts off the plate and becomes arch-like. A second, smaller LEV and the formation of corner vortex structures follow. For = 4, the outboard LEV moves farther aft, multiple LEVs form ahead of it, and after about ϕ = 50° a breakdown of the lifted-off LEV and the TV occurs. However, for = 2, the outboard LEV lift-off is not progressive, and the overall LEV-TV flow remains more coherent and closer to the plate, with evidence of breakdown late in the motion. Inboard of about 50 % span, the = 4 LEV is stable for the motion duration. Up to approximately 60 % span, the = 2 LEV is distinct from the TV and is similarly stable. The = 2 LEV exhibits substantially higher spanwise vorticity and velocity. The latter possesses a “four-lobed” distribution at the periphery of the LEV core having adjacent positive (outboard) and negative (inboard) components, corresponding to a helical streamline structure. Both s show substantial root-to-tip velocity aft of the stable LEV, which drives outboard spanwise vorticity flux; flux toward the root is also present in the front portion of the LEV. For = 2, there is a strong flux of spanwise vorticity from the outboard LEV to the tip, which may mitigate LEV lift-off and is not found for = 4. The TV circulation for each is similar in magnitude and growth when plotted versus the chord lengths travelled by the tip, prior to breakdown. Streamwise vorticity due to the TV induces high spanwise velocity, and for = 2, the tilted LEV creates further streamwise vorticity which corresponds well to spanwise-elongated regions of spanwise velocity. For = 2, the TV influences a relatively greater portion of the span and is more coherent at later times, which coupled with the tilted LEV strongly contributes to the higher overall spanwise velocity and vorticity flux.

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Acknowledgments

This work is supported by the United States Air Force Office of Scientific Research, Grant FA9550-10-1-0281, under the supervision of Dr. Douglas Smith. The authors appreciate the assistance of Adam DeVoria with the setup of the experiment and the exceptional and inordinate service provided by LaVision Inc. We thank the anonymous reviewers for their insightful comments and suggestions that added clarity and strengthened the overall manuscript.

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  1. State University of New York at Buffalo, 318 Jarvis Hall, Buffalo, NY, 14260, USA

    Z. R. Carr, C. Chen & M. J. Ringuette

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Carr, Z.R., Chen, C. & Ringuette, M.J. Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio. Exp Fluids 54, 1444 (2013). https://doi.org/10.1007/s00348-012-1444-8

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