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Transient leading-edge vortex development on a wing rolling in uniform flow

Published online by Cambridge University Press:  21 February 2023

Kevin J. Wabick ,
Kyle C. Johnson ,
Randall L. Berdon ,
Brian S. Thurow Open the ORCID record for Brian S. Thurow [Opens in a new window]  and
James H.J. Buchholz Open the ORCID record for James H.J. Buchholz [Opens in a new window]
Kevin J. Wabick
Affiliation:
Department of Mechanical Engineering/IIHR – Hydroscience & Engineering, University of Iowa, Iowa City, IA 52242, USA
Kyle C. Johnson
Affiliation:
Department of Aerospace and Mechanical Engineering, Auburn University, Auburn, AL 36849, USA
Randall L. Berdon
Affiliation:
Department of Mechanical Engineering/IIHR – Hydroscience & Engineering, University of Iowa, Iowa City, IA 52242, USA
Brian S. Thurow
Affiliation:
Department of Aerospace and Mechanical Engineering, Auburn University, Auburn, AL 36849, USA
James H.J. Buchholz*
Affiliation:
Department of Mechanical Engineering/IIHR – Hydroscience & Engineering, University of Iowa, Iowa City, IA 52242, USA
*
†Email address for correspondence: james-h-buchholz@uiowa.edu
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Abstract

Plenoptic particle image velocimetry and surface pressure measurements were used to analyse the early development of leading-edge vortices (LEVs) created by a flat-plate wing of aspect ratio 2 rolling in a uniform flow parallel to the roll axis. Four cases were constructed by considering two advance coefficients, $J=0.54$ and 1.36, and two wing radii of gyration, $R_g/c=2.5$ and 3.25. In each case, the wing pitch angle was articulated such as to achieve an angle of attack of $33^{\circ }$ at the radius of gyration of the wing. The sources and sinks of vorticity were quantified for a chordwise rectangular control region, using a vorticity transport framework in a non-inertial coordinate system attached to the wing. Within this framework, terms associated with Coriolis acceleration provide a correction to tilting and spanwise convective fluxes measured in the rotating frame and, for the present case, have insignificant values. For the baseline case ($J=0.54, R_g/c=3.25$), three distinct spanwise regions were observed within the LEV, with distinct patterns of vortex evolution and vorticity transport mechanisms in each region. Reducing the radius of gyration to $R_g/c=2.5$ resulted in a more stable vortex with the inboard region extending over a broader spanwise range. Increasing advance ratio eliminated the conical vortex, resulting in transport processes resembling the mid-span region of the baseline case. Although the circulation of the LEV system was generally stronger at the larger advance coefficient, the shear-layer contribution was diminished.

JFM classification

Vortex Flows: Vortex interactions Aerodynamics: Flow-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 957 , 25 February 2023 , A23
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

REFERENCES

Acharya, M. & Metwally, M.H. 1992 Unsteady pressure field and vorticity production over a pitching airfoil. AIAA J. 30 (2), 403–411.CrossRefGoogle Scholar
Akkala, J.M. & Buchholz, J.H.J. 2017 Vorticity transport mechanisms governing the development of leading-edge vortices. J. Fluid Mech. 829, 512–537.CrossRefGoogle Scholar
Birch, J.M. & Dickinson, M.H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412, 729–733.CrossRefGoogle Scholar
Bridges, D.H. 2010 Toward a theoretical description of vortex wake asymmetry. Prog. Aerosp. Sci. 46, 62–80.CrossRefGoogle Scholar
Bross, M., Ozen, C.A. & Rockwell, D. 2013 Flow structure on a rotating wing: effect of steady incident flow. Phys. Fluids 25, 081901.CrossRefGoogle Scholar
Carr, Z., Chen, C. & Ringuette, M.J. 2012 The effect of aspect ratio on the three-dimensional vortex formation of rotating flat-plate wings. 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Nashville, Tennessee. AIAA Paper 2012-912.Google Scholar
Chen, L., Wang, L., Zhou, C., Wu, J. & Cheng, B. 2022 Effects of Reynolds number on leading-edge vortex formation dynamics and stability in revolving wings. J. Fluid Mech. 931, A13.CrossRefGoogle Scholar
Chen, L., Wu, J. & Cheng, B. 2019 Volumetric measurement and vorticity dynamics of leading-edge vortex formation on a revolving wing. Exp. Fluids 60, 12.CrossRefGoogle Scholar
Eldredge, J.D. & Jones, A.R. 2019 Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech. 51 (1), 75–104.CrossRefGoogle Scholar
Eldredge, J.D., Wang, C. & Ol, M.V. 2009 A computational study of a canonical pitch-up, pitch-down wing maneuver. 39th AIAA Fluid Dynamics Conference. San Antonio, TX. AIAA Paper 2009-3687.Google Scholar
Ellington, C.P., van den Berg, C., Willmott, A.P. & Thomas, A.L.R. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.CrossRefGoogle Scholar
Eslam Panah, A., Akkala, J.M. & Buchholz, J.H.J. 2015 Vorticity transport and the leading-edge vortex of a plunging airfoil. Exp. Fluids 56, 160.CrossRefGoogle Scholar
Fahringer, T.W., Lynch, K.P. & Thurow, B.S. 2015 Volumetric particle image velocimetry with a single plenoptic camera. Meas. Sci. Technol. 26 (11), 1–25.CrossRefGoogle Scholar
Garmann, D.J., Visbal, M.R. & Orkwis, P.D. 2013 Three-dimensional flow structure and aerodynamic loading on a revolving wing. Phys. Fluids 25 (3), 034101.CrossRefGoogle Scholar
Himmelskamp, H. 1947 Profile investigations on a rotating airscrew (PhD dissertation, Göttingen, 1945), M.A.P. Völkenrode, Report and Translation No. 832, Göttingen.Google Scholar
Jardin, T. 2017 Coriolis effect and the attachment of the leading edge vortex. J. Fluid Mech. 820, 312–340.CrossRefGoogle Scholar
Jardin, T. & David, L. 2014 Spanwise gradients in flow speed help stabilize leading-edge vortices on revolving wings. Phys. Rev. 90, 013011.Google ScholarPubMed
Jardin, T. & David, L. 2015 Coriolis effects enhance lift on revolving wings. Phys. Rev. E 91, 031001.CrossRefGoogle ScholarPubMed
Johnson, K.C., Thurow, B.S., Wabick, K.J., Berdon, R.L. & Buchholz, J.H.J. 2020 Vortex topology of a pitching and rolling wing in forward flight. Exp. Fluids 61, 221.CrossRefGoogle Scholar
Kim, D. & Gharib, M. 2010 Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp. Fluids 49, 329–339.CrossRefGoogle Scholar
Kuo, C.H. & Hsieh, J.K. 2001 Unsteady flow structure and vorticity convection over the airfoil oscillating at high reduced frequency. Exp. Therm. Fluid Sci. 24, 117–129.CrossRefGoogle Scholar
Lentink, D. & Dickinson, M.H. 2009 a Biofluiddynamic scaling of flapping, spinning, and translating fins and wings. J. Expl Biol. 212, 2691–2704.CrossRefGoogle ScholarPubMed
Lentink, D. & Dickinson, M.H. 2009 b Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Expl Biol. 212, 2705–2719.CrossRefGoogle ScholarPubMed
Lim, T.T., Teo, C.J., Lue, K.B. & Yeo, K.S. 2009 On the prolong attachment of leading edge vortex on a flapping wing. Mod. Phys. Lett. B 23 (03), 357–360.CrossRefGoogle Scholar
Maxworthy, T. 1981 The fluid dynamics of insect flight. Annu. Rev. Fluid Mech. 13, 329–350.CrossRefGoogle Scholar
Mendez, M.A., Raiola, M., Masullo, A., Discetti, S., Ianiro, A., Theunissen, R. & Buchlin, J.M. 2017 POD-based background removal for particle image velocimetry. Exp. Therm. Fluid Sci. 80, 181–192.CrossRefGoogle Scholar
Mulleners, K., Kindler, K. & Raffel, M. 2012 Dynamic stall on a fully equipped helicopter model. Aerosp. Sci. Technol. 19, 72–76.CrossRefGoogle Scholar
Ol, M.V. & Gharib, M. 2003 Leading-edge vortex structure of nonslender delta wings at low Reynolds number. AIAA J. 41, 16–26.CrossRefGoogle Scholar
Onoue, K. & Breuer, K.S. 2017 A scaling for vortex formation on swept and unswept pitching wings. J. Fluid Mech. 832, 697–720.CrossRefGoogle Scholar
Ozen, C.A. & Rockwell, D. 2012 Flow structure on a rotating plate. Exp. Fluids 52 (1), 207–223.CrossRefGoogle Scholar
Pitt Ford, C.W. & Babinsky, H. 2013 Lift and the leading edge vortex. J. Fluid Mech. 720, 280–313.CrossRefGoogle Scholar
Potter, M.C. & Foss, J.F. 1982 Fluid Mechanics. Great Lakes Press, Inc.Google Scholar
Shih, C. & Ho, C.M. 1994 Vorticity balance and time scales of a two-dimensional airfoil in an unsteady free stream. Phys. Fluids 6 (2), 710–723.CrossRefGoogle Scholar
Visbal, M.R. & Shang, J.S. 1989 Investigation of the flow structure around a rapidly pitching airfoil. AIAA J. 27 (8), 1044–1051.CrossRefGoogle Scholar
Wojcik, C.J. & Buchholz, J.H.J. 2014 a Parameter variation and the leading-edge vortex of a rotating flat plate. AIAA J. 52, 348–357.CrossRefGoogle Scholar
Wojcik, C.J. & Buchholz, J.H.J. 2014 b Vorticity transport in the leading-edge vortex on a rotating blade. J. Fluid Mech. 743, 249–261.CrossRefGoogle Scholar
Wolfinger, M. & Rockwell, D. 2015 Transformation of flow structure on a rotating wing due to variation of radius of gyration. Exp. Fluids 56, 137.CrossRefGoogle Scholar
Wong, J.G., Kriegseis, J. & Rival, D.E. 2013 An investigation into vortex growth and stabilization for two-dimensional plunging and flapping plates with varying sweep. J. Fluids Struct. 43, 231–243.CrossRefGoogle Scholar
Wong, J.G., laBastide, B.P. & Rival, D.E. 2017 Flow separation on flapping and rotating profiles with spanwise gradients. Bioinspir. Biomim. 12, 0026008.CrossRefGoogle ScholarPubMed
Yilmaz, T. & Rockwell, D. 2012 Flow structure on finite-span wings due to pitch-up motion. J. Fluid Mech. 691, 518–545.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T.M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar