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Lift and the leading-edge vortex

Published online by Cambridge University Press:  27 February 2013

C. W. Pitt Ford  and
H. Babinsky
C. W. Pitt Ford
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
H. Babinsky
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
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Abstract

Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15°. The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading- and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin’s circulation theorem, but differs from the values predicted by Wagner’s growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner’s circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner’s lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 720 , 10 April 2013 , pp. 280 - 313
Copyright
©2013 Cambridge University Press

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References

Ames, A., Wong, O. & Komerath, N. 2001  On the flow field and forces generated by a flapping rectangular wing at low Reynolds number. In Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, Progress in Astronautics and Aeronautics, vol. 195, chap. 15, pp. 287–306. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Ansari, S., Zbikowski, R. & Knowles, K. 2006 Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1. Methodology and analysis. J. Aerosp. Engng G 220, 61–83.Google Scholar
Birch, J. M. & Dickinson, M. H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412 (6848), 729–733.CrossRefGoogle Scholar
Bohorquez, F., Samuel, P., Sirohi, J., Pines, D. J., Rudd, L. & Perel, R. 2003 Design analysis and hover performance of a rotating wing micro air vehicle. J. Am. Helicopter Soc. 48 (2), 80–90.Google Scholar
Chow, C.-Y., Huang, M.-K. & Yan, C.-Z. 1985 Unsteady flow about a Joukowski aerofoil in the presence of moving vortices. AIAA J. 23 (5), 657–658.CrossRefGoogle Scholar
Clayton, B. & Massey, B. S. 1967 Flow visualization in water: a review of techniques. J. Sci. Instrum. 44, 2–11.Google Scholar
Dickinson, M. H. & Götz, K. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Expl Biol. 174, 45–64.CrossRefGoogle Scholar
Dickinson, M. H., Lehmann, F. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284 (5422), 1954–1960.Google Scholar
Ellington, C. P. 1999 The novel aerodynamics of insect flight: applications to micro-air vehicles. J. Expl Biol. 202, 3439–3448.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 (6610), 626–630.CrossRefGoogle Scholar
Francis, R. H. & Cohen, J. 1933 The flow near a wing which starts suddenly from rest and then stalls. Aero. Res. Counc. R&M (1561), 90.Google Scholar
Gad-el Hak, M. 1990 Control of low-speed aerofoil aerodynamics. AIAA J. 28 (9), 1537–1552.CrossRefGoogle Scholar
Graftieaux, L., Michard, M. & Grosjean, N. 2001 Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas. Sci. Technol. 12, 1422–1429.Google Scholar
Hu, H., Kumar, A. G., Abate, G. & Albertani, R. 2010 An experimental investigation on the aerodynamic performances of flexible membrane wings in flapping flight. Aerosp. Sci. Technol. 14 (8), 575–586.Google Scholar
Huang, M.-K. & Chow, C.-Y. 1982 Trapping of a free vortex by Joukowski aerofoils. AIAA J. 20 (3), 292–298.Google Scholar
Jones, A. R. & Babinsky, H. 2010 Unsteady lift generation on rotating wings at low Reynolds number. J. Aircraft 47 (3).Google Scholar
Jones, A. R., Pitt Ford, C. W. & Babinsky, H. 2011 Three-dimensional effects on sliding and waving wings. J. Aircraft 48 (2), 633–644.Google Scholar
Lentink, D. & Dickinson, M. H. 2009 Rotational accelerations stabilise leading edge vortices on revolving fly wings. J. Expl Biol. 212, 2705–2719.CrossRefGoogle ScholarPubMed
Liang, C. H., Wang, X. W. & Chen, X. 2010 Inverse Joukowski mapping. Prog. Electromagnetics 19, 113–125.Google Scholar
Minotti, F. 2002 Unsteady two-dimensional theory of a flapping wing. Phys. Rev. E 66, 051907.CrossRefGoogle ScholarPubMed
Morgan, C. E., Babinsky, H. & Harvey, J. K. 2009 Vortex detection methods for use with PIV and CFD data. In 47th AIAA Aerospace Sciences Meeting, Orlando, Florida.CrossRefGoogle Scholar
Peters, D. 2008 Two-dimensional incompressible unsteady aerofoil theory – an overview. J. Fluids Struct. 24 (3), 295–312.Google Scholar
Pines, D. & Bohorquez, F. 2006 Challenges facing future micro-air vehicle development. J. Aircraft 43 (2), 290–305.CrossRefGoogle Scholar
Raffel, M., Willert, C. & Kompenhans, J. 2001 Particle Image Velocimetry: A Practical Guide. Springer.Google Scholar
Saffman, P. G. & Sheffield, J. S. 1977 Flow over a wing with an attached free vortex. Stud. Appl. Maths 57, 107–117.CrossRefGoogle Scholar
Shyy, W., Lian, Y., Tang, J., Liu, H., Trizila, P., Stanford, B., Bernal, L., Cesnik, C., Friedmann, P. & Ifju, P. 2008a Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for mav applications. Acta Mechanica Sin. 24, 351–373.CrossRefGoogle Scholar
Shyy, W., Lian, Y., Tang, J., Viieru, D. & Liu, H. 2008b Aerodynamics of Low Reynolds Number Flyers, Cambridge Aerospace Series, vol. 1, Cambridge University Press.Google Scholar
Slomski, J. F. & Coleman, R. M. 1993 Numerical simulation of vortex generation and capture above an aerofoil. In 31st Aerospace Sciences Meeting and Exhibit, Reno, Nevada.Google Scholar
Usherwood, J. R. & Ellington, C. P. 2002 The aerodynamics of revolving wings I. Model hawkmoth wings. J. Expl Biol. 205 (11), 1547–1564.Google Scholar
Wagner, H. 1925 Uber die enstehung des dynamischen auftreibes von tragflugeln. A. Angew. Math. 17–35.CrossRefGoogle Scholar
Walker, P. 1931 Experiments on the growth of circulation about a wing. Tech. Rep. 1402. Aeronautical Research Committee.Google Scholar
Woods, M. I., Henderson, J. F. & Lock, G. D. 2001 Energy requirements for the flight of micro air vehicles. Aeronaut. J. 105 (2546), 135–149.CrossRefGoogle Scholar
Yilmaz, T. O. & Rockwell, D. 2012 Flow structure on finite-span wings due to pitch-up motion. J. Fluid Mech. 691, 518–545.Google Scholar