Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T15:20:26.896Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of a trailing vortex from a perturbed wing

Published online by Cambridge University Press:  10 July 2017

G. Fishman Open the ORCID record for G. Fishman [Opens in a new window] ,
M. Wolfinger  and
D. Rockwell
G. Fishman*
Affiliation:
Department of Mechanical Engineering, Lehigh University, Bethlehem, PA 18015, USA
M. Wolfinger
Affiliation:
Department of Mechanical Engineering, Lehigh University, Bethlehem, PA 18015, USA
D. Rockwell
Affiliation:
Department of Mechanical Engineering, Lehigh University, Bethlehem, PA 18015, USA
*
†Email address for correspondence: gef213@lehigh.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The structure of a trailing vortex from a wing undergoing small amplitude, low frequency heaving motion is investigated using space–time representations determined from stereo particle image velocimetry. The evolution of the vortex shows large fluctuations of axial velocity deficit and circulation during the oscillation cycle. Correspondingly, large variations of swirl ratio occur and onset of pronounced azimuthal vorticity arises. At a given cross-section of the vortex, the pattern of azimuthal vorticity moves around its axis in an ordered fashion as both it and the pattern of velocity defect increase in magnitude and scale. When the swirl ratio attains its minimum value during the oscillation cycle, and this value lies below the theoretically established critical threshold for amplification of azimuthal modes, the magnitude and scale of the pattern of azimuthal vorticity is maximized. Subsequent increase of the swirl ratio yields attenuation of the azimuthal vorticity. Onset of pronounced azimuthal vorticity when the swirl ratio decreases involves rapid amplification, then disruption, of axial vorticity fluctuation.

JFM classification

Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 701 - 721
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Barnes, C. J., Visbal, M. R. & Gordnier, R. E. 2015 Analysis of streamwise-oriented vortex interactions for two wings in close proximity. Phys. Fluids 27, 015103.CrossRefGoogle Scholar
Batchelor, G. K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20, 645–658.Google Scholar
Birch, D. & Lee, T. 2005 Investigation of the near-field tip vortex behind an oscillating wing. J. Fluid Mech. 544, 201–241.Google Scholar
Calderon, D. E., Wang, Z., Gursul, I. & Visbal, M. R. 2013 Volumetric measurements and simulations of the vortex structures generated by low aspect ratio plunging wings. Phys. Fluids. 25, 067102.Google Scholar
Chang, J. W. & Park, S. O. 2000 Measurement in the tip vortex roll-up region of an oscillating wing. AIAA J. 38, 1092–1095.CrossRefGoogle Scholar
Cleaver, D. J., Wang, Z., Gursul, I. & Visbal, M. R. 2011 Lift enhancement by means of small-amplitude airfoil oscillations at low Reynolds numbers. AIAA J. 49, 2018–2032.Google Scholar
Crouch, J. D. 2005 Airplane trailing vortices and their control. C. R. Phys. 6, 487–499.Google Scholar
Delbende, I., Chomaz, J. & Huerre, P. 1998 Absolute/convective instabilities in the batchelor vortex: a numerical study of the linear impusle response. J. Fluid Mech. 355, 229–254.Google Scholar
Delbende, I. & Rossi, M. 2005 Nonlinear evolution of a swiriling jet instability. Phys. Fluids. 17, 044103.Google Scholar
Eckhoff, K. S. 1984 A note on the instability of columnar vortices. J. Fluid Mech. 145, 417–421.Google Scholar
Garmann, D. J. & Visbal, M. R.2014 Unsteady interactions of a wandering streamwise-oriented vortex with a wing. AIAA Paper 2014-2105.Google Scholar
Garmann, D. J. & Visbal, M. R. 2015 Interactions of a streamwise-oriented vortex with a finite wing. J. Fluid Mech. 767, 782–810.Google Scholar
Garmann, D. J. & Visbal, M. R.2016a Unsteady evolution of the tip vortex on a stationary and oscillating naca0012 wing. AIAA Paper 2016-0328.Google Scholar
Garmann, D. J. & Visbal, M. R.2016b Further investigations of the tip vortex on an oscillating naca0012 wing. AIAA Paper 2016-4343.Google Scholar
Gerontakos, P. & Lee, T. 2006 Active trailing-edge flap control of oscillating-wing tip vortex. AIAA J. 44, 2746–2754.Google Scholar
Hummel, D. 1983 Aerodynamic aspects of formation flight in birds. J. Theor. Biol. 104 (3), 321–347.Google Scholar
Jacquin, L. & Pantano, C. 2002 On the persistence of trailing vortices. J. Fluid Mech. 471, 159–168.CrossRefGoogle Scholar
Kim, D. & Gharib, M. 2010 Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp. Fluids 49, 329–339.Google Scholar
Lawson, N. J. & Wu, J. 1997 Three-dimensional particle image velocimetry: error analysis of stereoscopic techniques. Meas. Sci. Technol. 8, 897–900.Google Scholar
Lee, T. 2007 Effectiveness of dynamically deflected tab control of a tip vortex. AIAA J. 45, 2994–3002.CrossRefGoogle Scholar
Leibowich, S. & Stewartson, K. 1983 A sufficient condition for the instability of columnar vortices. J. Fluid Mech. 126, 335–356.Google Scholar
Lissaman, P. B. S. & Schollenberger, C. A. 1970 Formation flight of birds. Science 168, 1003–1005.Google Scholar
Mayer, E. W. & Powell, K. G. 1992 Viscous and inviscid instabilities of a trailing vortex. J. Fluid Mech. 245, 91–114.Google Scholar
Moore, D. W. & Saffman, P. G. 1973 Axial flow in laminar trailing vortices. Proc. R. Soc. Lond. A 333, 491–508.Google Scholar
Olendraru, C. & Sellier, A. 2002 Viscous effects in the absolute-convective instability of the batchelor vortex. J. Fluid Mech. 459, 371–396.Google Scholar
Panagakos, A. & Lee, T. 2006 Tip vortex control via an active trailing-edge tab. J. Aircraft 43, 1152–1158.Google Scholar
Prasad, A. K. 2000 Stereoscopic particle image velocimetry. Exp. Fluids 29, 103–116.CrossRefGoogle Scholar
Ramaprian, B. R. & Zheng, Y. 1998 Near field of the tip vortex behind an oscillating rectangular wing. AIAA J. 36, 1263–1269.Google Scholar
Rockwell, D. 1998 Vortex-body interactions. Annu. Rev. Fluid Mech. 30, 199–229.Google Scholar
Savas, O. 2005 Experimental investigations on wake vortices and their alleviation. C. R. Phys. 6, 415–429.Google Scholar
Spalart, P. R. 1998 Airplane trailing vortices. Annu. Rev. Fluid Mech. 30, 107–138.Google Scholar
Viola, F., Arratia, C. & Gallaire, F. 2016 Mode selection in trailing vortices: harmonic response of the non-parallel batchelor vortex. J. Fluid Mech. 790, 523–552.Google Scholar
Visbal, M. R.2011 Three-dimensional flow structure on a heaving low-aspect-ratio wing. AIAA Paper 2011-219.Google Scholar
West, G. S. & Apelt, C. J. 1982 The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds numbers between 104 and 105 . J. Fluid Mech. 114, 361–377.Google Scholar
Yilmaz, T. O. & Rockwell, D. O. 2010 Three-dimensional flow structure on a maneuvering wing. Exp. Fluids 48, 539–544.Google Scholar