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The role of advance ratio and aspect ratio in determining leading-edge vortex stability for flapping flight

Published online by Cambridge University Press:  16 June 2014

R. R. Harbig
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
J. Sheridan*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
M. C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
*
Email address for correspondence: [email protected]

Abstract

The effects of advance ratio and the wing’s aspect ratio on the structure of the leading-edge vortex (LEV) that forms on flapping and rotating wings under insect-like flight conditions are not well understood. However, recent studies have indicated that they could play a role in determining the stable attachment of the LEV. In this study, a numerical model of a flapping wing at insect Reynolds numbers is used to explore the effects of these parameters on the characteristics and stability of the LEV. The word ‘stability’ is used here to describe whether the LEV was attached throughout the stroke or if it was shed. It is demonstrated that increasing the advance ratio enhances vorticity production at the leading edge during the downstroke, and this results in more rapid growth of the LEV for non-zero advance ratios. Increasing the wing aspect ratio was found to have the effect of shortening the wing’s chord length relative to the LEV’s size. These two effects combined determine the stability of the LEV. For high advance ratios and large aspect ratios, the LEV was observed to quickly grow to envelop the entire wing during the early stages of the downstroke. Continued rotation of the wing resulted in the LEV being eventually shed as part of a vortex loop that peels away from the wing’s tip. The shedding of the LEV for high-aspect-ratio wings at non-zero advance ratios leads to reduced aerodynamic performance of these wings, which helps to explain why a number of insect species have evolved to have low-aspect-ratio wings.

Type
Papers
Copyright
© 2014 Cambridge University Press 

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References

Aono, H., Liang, F. & Liu, H. 2008 Near- and far-field aerodynamics in insect hovering flight: an integrated computational study. J. Expl Biol. 211, 239257.Google Scholar
Beem, H. R., Rival, D. E. & Triantafyllou, M. S. 2012 On the stabilization of leading-edge vortices with spanwise flow. Exp. Fluids 52 (2), 511517.Google Scholar
van den Berg, C. & Ellington, C. P. 1997 The three-dimensional leading-edge vortex of a ‘hovering’ model hawkmoth. Phil. Trans. R. Soc. B 352 (1351), 329340.Google Scholar
Birch, J. M. & Dickinson, M. H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412, 729733.CrossRefGoogle Scholar
Birch, J. M., Dickson, W. B. & Dickinson, M. H. 2004 Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers. J. Expl Biol. 207 (7), 10631072.Google Scholar
Bross, M., Ozen, C. A. & Rockwell, D. 2013 Flow structure on a rotating wing: effect of steady incident flow. Phys. Fluids 25 (8), 081901.Google Scholar
Cheng, B., Sane, S. P., Barbera, G., Troolin, D. R., Strand, T. & Deng, X. 2013 Three-dimensional flow visualization and vorticity dynamics in revolving wings. Exp. Fluids 54 (1).CrossRefGoogle Scholar
Dickinson, M. H. & Gotz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Expl Biol. 174 (1), 4565.Google Scholar
Dickinson, M. H., Lehmann, F.-O. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284 (5422), 19541960.CrossRefGoogle ScholarPubMed
Dickson, W. B. & Dickinson, M. H. 2004 The effect of advance ratio on the aerodynamics of revolving wings. J. Expl Biol. 207 (24), 42694281.CrossRefGoogle ScholarPubMed
Dudley, R. & Ellington, C. P. 1990 Mechanics of forward flight in bumblebees. I. Kinematics and morphology. J. Expl Biol. 148, 1952.Google Scholar
Ellington, C. P. 1984a The aerodynamics of hovering insect flight. II. Morphological parameters. Phil. Trans. R. Soc. B 305 (1122), 1740.Google Scholar
Ellington, C. P. 1984b The aerodynamics of hovering insect flight. III. Kinematics. Phil. Trans. R. Soc. B 305 (1122), 4178.Google Scholar
Ellington, C. P. 1999 The novel aerodynamics of insect flight: applications to micro-air vehicles. J. Expl Biol. 202, 34393448.CrossRefGoogle ScholarPubMed
Ellington, C. P., van den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384 (19), 626630.Google Scholar
Fry, S. N., Sayaman, R. & Dickinson, M. H. 2005 The aerodynamics of hovering flight in Drosophila . J. Expl Biol. 208, 23032318.CrossRefGoogle ScholarPubMed
Gopalakrishnan, P. & Tafti, D. K. 2010 Effect of wing flexibility on lift and thrust production in flapping flight. AIAA J. 48 (5), 865877.Google Scholar
Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4 (1), 195218.CrossRefGoogle Scholar
Harbig, R. R., Sheridan, J. & Thompson, M. C. 2013 Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms. J. Fluid Mech. 717, 166192.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, streams, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center for Turbulence Research.Google Scholar
Jardin, T., Farcy, A. & David, L. 2012 Three-dimensional effects in hovering flapping flight. J. Fluid Mech. 702, 102125.CrossRefGoogle Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221246.Google Scholar
Lentink, D. & Dickinson, M. H. 2009 Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Expl Biol. 212 (16), 27052719.Google Scholar
Liu, H. & Aono, H. 2009 Size effects on insect hovering aerodynamics: an integrated computational study. Bioinspir. Biomim. 4, 015002.Google Scholar
Lu, Y., Shen, G. X. & Lai, G. J. 2006 Dual leading-edge vortices on flapping wings. J. Expl Biol. 209, 50055016.CrossRefGoogle ScholarPubMed
Maxworthy, T. 1979 Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1. Dynamics of the ‘fling’. J. Fluid Mech. 93 (1), 4763.CrossRefGoogle Scholar
Morton, B. R. 1984 The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28 (3), 277308.Google Scholar
Nagai, H., Isogai, K., Fujimoto, T. & Hayase, T. 2009 Experimental and numerical study of forward flight aerodynamics of insect flapping wing. AIAA J. 47 (3), 730742.Google Scholar
Poelma, C., Dickson, W. B. & Dickinson, M. H. 2006 Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing. Exp. Fluids 41 (2), 213225.Google Scholar
Rival, D. E. & Wong, J. G.2013 Measurements of vortex stretching on two-dimensional rotating plates with varying sweep. In Proceedings of the 10th International Symposium on Particle Image Velocimetry, Delft, The Netherlands, July 1–3, 2013.Google Scholar
Roache, P. J. 1998 Verification of codes and calculations. AIAA J. 36 (5), 696702.Google Scholar
Sane, S. P. 2003 The aerodynamics of insect flight. J. Expl Biol. 206, 41914208.Google Scholar
Sane, S. P. & Dickinson, M. H. 2001 The control of flight force by a flapping wing: lift and drag production. J. Expl Biol. 204, 26072626.Google Scholar
Shyy, W., Aono, H., Chimakurthi, S. K., Trizila, P., Kang, C. K., Cesnik, C. E. S. & Liu, H. 2010 Recent progress in flapping wing aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 46 (7), 284327.CrossRefGoogle Scholar
Sun, M. 2003 Aerodynamic force generation and power requirements in forward flight in a fruit fly with modelled wing motion. J. Expl Biol. 206 (17), 30653083.CrossRefGoogle Scholar
Usherwood, J. R. & Ellington, C. P. 2002 The aerodynamics of revolving wings I. Model hawkmoth wings. J. Expl Biol. 205 (11), 15471564.Google Scholar
Venkata, S. K. & Jones, A. R. 2013 Leading-edge vortex structure over multiple revolutions of a rotating wing. J. Aircraft 50 (4), 13121316.Google Scholar
Wang, Z. J. 2005 Dissecting insect flight. Annu. Rev. Fluid Mech. 37, 183210.Google Scholar
Wang, Z. J. 2008 Aerodynamic efficiency of flapping flight: analysis of a two-stroke model. J. Expl Biol. 211 (2), 234238.Google Scholar
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Expl Biol. 59, 169230.CrossRefGoogle Scholar
Willmott, A. P. & Ellington, C. P. 1997 The mechanics of flight in the hawkmoth Manduca sexta. I. Kinematics of hovering and forward flight. J. Expl Biol. 200, 27052722.Google 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, 231243.CrossRefGoogle Scholar
Zanker, J. M. 1990 The wing beat of Drosophila melanogaster. I. Kinematics. Phil. Trans. R. Soc. B 327 (1238), 118.Google Scholar

Harbig et al. supplementary material

Flow structures around an AR=2.91 wing at J=0.5 and ReR=613. Vortex structures are visualised by iso-Q surfaces coloured by spanwise vorticity to indicate direction, green is positive and blue is negative.

Download Harbig et al. supplementary material(Video)
Video 6.1 MB

Harbig et al. supplementary material

Flow structures around an AR=2.91 wing at J=0 and ReR=613. Vortex structures are visualised by iso-Q surfaces coloured by spanwise vorticity to indicate direction, green is positive and blue is negative.

Download Harbig et al. supplementary material(Video)
Video 5.1 MB

Harbig et al. supplementary material

Flow structures around an AR=7.28 wing at J=0.5 and ReR=613. Vortex structures are visualised by iso-Q surfaces coloured by spanwise vorticity to indicate direction, green is positive and blue is negative.

Download Harbig et al. supplementary material(Video)
Video 3.7 MB

Harbig et al. supplementary material

Flow structures around an AR=2.91 wing at J=0 and ReR=7668. Vortex structures are visualised by iso-Q surfaces coloured by spanwise vorticity to indicate direction, green is positive and blue is negative.

Download Harbig et al. supplementary material(Video)
Video 7.1 MB

Harbig et al. supplementary material

Flow structures around an AR=2.91 wing at J=0.5 and ReR=7668. Vortex structures are visualised by iso-Q surfaces coloured by spanwise vorticity to indicate direction, green is positive and blue is negative.

Download Harbig et al. supplementary material(Video)
Video 9.9 MB

Harbig et al. supplementary material

Flow structures around an AR=7.28 wing at J=0.5 and ReR=7668. Vortex structures are visualised by iso-Q surfaces coloured by spanwise vorticity to indicate direction, green is positive and blue is negative.

Download Harbig et al. supplementary material(Video)
Video 8.3 MB