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Coriolis effect and the attachment of the leading edge vortex

Published online by Cambridge University Press:  05 May 2017

T. Jardin Open the ORCID record for T. Jardin [Opens in a new window]
T. Jardin*
Affiliation:
Institut Supérieur de l’Aéronautique et de l’Espace (ISAE-Supaero), Université de Toulouse, 31055 Toulouse CEDEX 4, France
*
†Email address for correspondence: [email protected]
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Abstract

The role of the Coriolis effect on the attachment of the leading edge vortex (LEV) is investigated. Toward that end, the Navier–Stokes equations are solved in the non-inertial reference frame of a high angle of attack $\unicode[STIX]{x1D6FC}$ rotating wing with the Coriolis term being artificially tuned. Reynolds numbers in the range $Re\in [100;750]$ are considered to identify the interplay between Coriolis and viscous effects. Similarly, artificial tuning of the centrifugal term is achieved to identify the interplay between Coriolis and centrifugal effects. It is shown that (i) the Coriolis effect is the key element in LEV stability for $Re>200$ , (ii) viscous effects are the key element for $Re<200$ and (iii) centrifugal effects have a marginal role. The Coriolis effect is found to promote spanwise flow in the core and behind the LEV, which is known to promote outboard vorticity transport and presumably contributes to stabilizing the aft boundary layer. These mechanisms of LEV stabilization have increased authority as $\unicode[STIX]{x1D6FC}$ decreases.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 820 , 10 June 2017 , pp. 312 - 340
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Copyright
© 2017 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, 239–257.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, 511–517.CrossRefGoogle Scholar
van den Berg, C. & Ellington, C. P. 1997 The three-dimensional leading-edge vortex of a ‘hovering’ model hawkmoth. Phil. Trans. R. Soc. Lond. B 352, 329–340.Google 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
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, 1063–1072.CrossRefGoogle Scholar
Bury, Y. & Jardin, T. 2012 Transitions to chaos in the wake of an axisymmetric bluff body. Phys. Lett. A 376, 3219–3222.Google Scholar
Carr, Z. R., DeVoria, A. C. & Ringuette, M. J. 2015 Aspect-ratio effects on rotating wings: circulation and forces. J. Fluid Mech. 767, 497–525.Google Scholar
Choi, J., Colonius, T. & Williams, D. R. 2015 Surging and plunging oscillations of an airfoil at low Reynolds number. J. Fluid Mech. 763, 237–253.Google Scholar
Ellington, C. P., Van den Berg, C., Willmott, A. P. & Thomas, A. L. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.CrossRefGoogle Scholar
Ferziger, J. H. & Peric, M. 2002 Computational Methods for Fluid Dynamics, 3rd rev. edn. Springer.Google Scholar
Garmann, D. J. & Visbal, M. R. 2014 Dynamics of revolving wings for various aspect ratios. J. Fluid Mech. 748, 932–956.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, 034101.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, 166–192.CrossRefGoogle Scholar
Jardin, T. & David, L. 2014 Spanwise gradients in flow speed help stabilize leading-edge vortices on revolving wings. Phys. Rev. E 90, 013011.Google ScholarPubMed
Jardin, T. & David, L. 2015 Coriolis effects enhance lift on revolving wings. Phys. Rev. E 91, 031001.Google Scholar
Jardin, T. & David, L.2017 Root cut-out effects on the aerodynamics of a low aspect ratio revolving wing. AIAA J. (in press).CrossRefGoogle Scholar
Jardin, T., Farcy, A. & David, L. 2012 Three-dimensional effects in hovering flapping flight. J. Fluid Mech. 702, 102–125.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Kruyt, J. W., van Heijst, G. F., Altshuler, D. L. & Lentink, D. 2015 Power reduction and the radial limit of stall delay in revolving wings of different aspect ratio. J. R. Soc. Interface 12, 20150051.CrossRefGoogle ScholarPubMed
Lentink, D. & Dickinson, M. H. 2009 Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Expl Biol. 212, 2705–2719.CrossRefGoogle ScholarPubMed
Percin, M. & van Oudheusden, B. W. 2015 Three-dimensional flow structures and unsteady forces on pitching and surging revolving flat plates. Exp. Fluids 56, 1–19.CrossRefGoogle 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, 213–225.Google Scholar
Rhie, C. M. & Chow, W. L. 1993 Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21, 1525–1532.CrossRefGoogle Scholar
Ringuette, M. J., Milano, M. & Gharib, M. 2007 Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates. J. Fluid Mech. 581, 453–468.CrossRefGoogle Scholar
Roache, P. J. 1998 Verification and Validation in Computational Science and Engineering. Hermosa.Google Scholar
Taira, K. & Colonius, T. I. M. 2009 Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. J. Fluid Mech. 623, 187–207.Google Scholar
Venkata, S. K. & Jones, A. R. 2013 Leading-edge vortex structure over multiple revolutions of a rotating wing. J. Aircraft 50, 1312–1316.CrossRefGoogle Scholar
Wolfinger, M. & Rockwell, D. 2014 Flow structure on a rotating wing: effect of radius of gyration. J. Fluid Mech. 755, 83–110.CrossRefGoogle Scholar
Zhang, J., Liu, N. S. & Lu, X. Y. 2009 Route to a chaotic state in fluid flow past an inclined flat plate. Phys. Rev. E 79, 045306.Google Scholar