Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-06T15:08:23.324Z Has data issue: false hasContentIssue false
  • English
  • Français

An experimental study of the effect of external turbulence on the decay of a single vortex and a vortex pair

Published online by Cambridge University Press:  22 February 2011

J. P. J. van JAARSVELD ,
A. P. C. HOLTEN ,
A. ELSENAAR ,
R. R. TRIELING  and
G. J. F. van HEIJST
J. P. J. van JAARSVELD
Affiliation:
Eindhoven University of Technology, Department of Applied Physics, PO Box 513, 5600 MB Eindhoven, The Netherlands
A. P. C. HOLTEN
Affiliation:
Eindhoven University of Technology, Department of Applied Physics, PO Box 513, 5600 MB Eindhoven, The Netherlands
A. ELSENAAR
Affiliation:
Eindhoven University of Technology, Department of Applied Physics, PO Box 513, 5600 MB Eindhoven, The Netherlands
R. R. TRIELING*
Affiliation:
Eindhoven University of Technology, Department of Applied Physics, PO Box 513, 5600 MB Eindhoven, The Netherlands
G. J. F. van HEIJST
Affiliation:
Eindhoven University of Technology, Department of Applied Physics, PO Box 513, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: r.r.trieling@tue.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

This study is concerned with the effect of external turbulence on the decay of vortices. Single vortices and vortex pairs were generated with wing(s) mounted in the sidewalls of a wind tunnel. The distance between the two vortices could be adjusted such that they just touched each other or overlapped. The intensity of the turbulence could be controlled with a turbulence grid. The development of the vortex was measured at a number of downstream stations with particle image velocimetry for a range of wing settings. The results indicate that the single vortex can be described by the ‘two length scales’ model of Jacquin, Fabre & Geffroy (AIAA, vol. 1038, 2001, p. 1). A vortex core, which decays like a Lamb–Oseen vortex, is embedded in a region with an almost constant radius and a much lower azimuthal velocity that obeys a ~r−β power law, with r being the radius measured from the vortex centre. For the turbulence levels and the test section length used in this study, the single-vortex behaviour is independent of the external turbulence and in contrast with the decay of the vortex pair that strongly depends on the external turbulence. In the initial stages of the vortex pair evolution, the vortices decay due to cancellation of vorticity at the symmetry plane. At a later stage, Crow oscillations are observed, followed by a breakdown of the vortices. This vortex breakdown might be due to direct turbulent action. The observed behaviour is in agreement with the theoretical model of Crow & Bate (J. Aircraft, vol. 13, 1976, p. 476).

JFM classification

Turbulent Flows: Turbulent Flows Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 214 - 239
Copyright
Copyright © Cambridge University Press 2011

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

REFERENCES

Bailey, S. C. C., Hultmark, M., Schumacher, J., Yakhot, V. & Smits, A. J. 2009 Measurements of local dissipation scales in turbulent pipe flows. Phys. Rev. Lett. 103, 014502 (1–4).CrossRefGoogle Scholar
Bailey, S. C. C. & Tavoularis, S. 2008 Measurements of the velocity field of a wing-tip vortex, wandering in grid turbulence. J. Fluid Mech. 601, 281–315.CrossRefGoogle Scholar
Bandyopadhyay, P. R., Stead, D. J. & Ash, R. L. 1991 Organized nature of a turbulent trailing vortex. AIAA J. 29, 1627–1633.CrossRefGoogle Scholar
Bearman, P., Heyes, A., Lear, C. & Smith, D. 2006 Natural and forced evolution of a counter-rotating vortex pair. Exp. Fluids 40, 98–105.CrossRefGoogle Scholar
Bearman, P., Heyes, A., Lear, C. & Smith, D. 2007 Evolution of a forced counter-rotating vortex pair for two selected forcing frequencies. Exp. Fluids 43, 501–507.CrossRefGoogle Scholar
Beninati, M. L. & Marshall, J. S. 2005 An experimental study of the effect of free-stream turbulence on a trailing vortex. Exp. Fluids 38, 244–257.CrossRefGoogle Scholar
Betz, A. 1932 Verhalten von Wirbelsystemen. Z. Angew. Math. Mech. 12, 146–174.CrossRefGoogle Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177–191.CrossRefGoogle Scholar
de Bruin, A. C., Hegen, G. H., Rohne, P. B. & Spalart, P. R. 1996 Flow field survey in trailing vortex system behind a civil aircraft model at high lift. AGARD Symp. Trondheim 25, 1–12.Google Scholar
Cantwell, B. & Rott, N. 1988 The decay of a viscous vortex pair. Phys. Fluids 31, 3213–3224.CrossRefGoogle Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.CrossRefGoogle Scholar
Crow, S. C. & Bate, E. R. 1976 Lifespan of trailing vortices in a turbulent atmosphere. J. Aircraft 13, 476–482.CrossRefGoogle Scholar
Devenport, W. J., Rife, M. C., Liapis, S. I. & Follin, G. J. 1996 The structure and development of a wing-tip vortex. J. Fluid Mech. 312, 67–106.CrossRefGoogle Scholar
Devenport, W. J., Vogel, C. M. & Zsoldos, J. S. 1999 Flow structure produced by the interaction and merger of a pair of co-rotating wing-tip vortices. J. Fluid Mech. 394, 357–377.CrossRefGoogle Scholar
Devenport, W. J., Zsoldos, J. S. & Vogel, C. M. 1997 The structure and development of a counter-rotating wing-tip vortex pair. J. Fluid Mech. 332, 71–104.CrossRefGoogle Scholar
Green, G. C. 1986 An approximate model of vortex decay in the atmosphere. J. Aircraft 23, 566–573.CrossRefGoogle Scholar
Holzäpfel, F., Gerz, T., Darracq, D., Moet, H., Garnier, F. & Ferreira Gago, C. 2003 Analysis of wake vortex decay mechanisms in the atmosphere. Aerosp. Sci. Technol. 7, 263–275.CrossRefGoogle Scholar
Holzäpfel, F., Hofbauer, T., Gerz, T. & Schumann, U. 2000 Aircraft wake vortex evolution and decay in idealized and real environments: methodologies, benefits and limitations. In Proceedings of the Euromech Colloquium 412, Advances in LES of Complex Flows, Munich, Germany, 4–6 October 2000 (ed. Rudi, W. & Friedrich, R.). Kluwer.Google Scholar
Iversen, J. D. 1976 Correlation of turbulent trailing vortex decay data. J. Aircraft 40, 323–331.Google Scholar
van Jaarsveld, J. P. J. 2008 Wind tunnel experiments on wake-vortex decay in external turbulence. Masters thesis (no. R-1726-A), Eindhoven University of Technology, Department of Applied Physics, Fluid Dynamics Laboratory, Eindhoven.Google Scholar
Jacquin, L., Fabre, L. & Geffroy, P. 2001 The properties of a transport aircraft wake in the extended near field: an experimental study. AIAA 1038, 1–41.Google Scholar
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.CrossRefGoogle Scholar
Kaden, H. 1931 Aufwicklung einer unstabilen Unstetigkeits Fläche. Ing.-Arch. II 1931, 140–168.CrossRefGoogle Scholar
Liu, H.-T. 1992 Effects of ambient turbulence on the decay of a trailing vortex wake. J. Aircraft 20, 255–263.CrossRefGoogle Scholar
Marshall, J. S. & Beninati, M. L. 2005 External turbulence interaction with a columnar vortex. J. Fluid Mech. 540, 221–245.CrossRefGoogle Scholar
Miyazaki, T. & Hunt, J. C. R. 2000 Linear and nonlinear interactions between a columnar vortex and external turbulence. J. Fluid Mech. 402, 349–378.CrossRefGoogle Scholar
Roberts, L. 1975 Persistence and decay of wake vorticity. In AGARD Conference on Flight/Ground Testing Facilities Correlation, AGARD CP 187, pp. 9-1–9-19.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Sarpkaya, T. 1998 Decay of wake vortices of large aircraft. AIAA J. 36, 1671–1679.CrossRefGoogle Scholar
Sarpkaya, T. & Daly, J. 1987 Effect of ambient turbulence on trailing vortices. J. Aircraft 24, 399–404.CrossRefGoogle Scholar
Spalart, P. 1998 Airplane trailing vortices. Annu. Rev. Fluid Mech. 30, 107–138.CrossRefGoogle Scholar
Squire, H. B. 1965 The growth of a vortex in turbulent flow. Aeronaut. Q. 10, 302–306.CrossRefGoogle Scholar
Takahashi, N., Ishii, H. & Miyazaki, T. 2005 The influence of turbulence on a columnar vortex. Phys. Fluids 17, 035105.CrossRefGoogle Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–211.Google Scholar
Tombach, I. 1973 Observations of atmospheric effects on vortex wake behaviour. J. Aircraft 10, 641–647.CrossRefGoogle Scholar
Uberoi, M. 1979 Mechanisms of decay of laminar and turbulent vortices. J. Fluid Mech. 90, 241–255.CrossRefGoogle Scholar
Westerweel, J. 1993 Digital particle image velocimetry: theory and applications. PhD thesis, Technische Universiteit Delft, Delft.Google Scholar
Winckelmans, G., Cocle, R., Dufresne, L., Capart, R., Bricteux, L., Daeninck, G., Lonfils, T., Duponcheel, M., Desenfans, O. & Georges, L. 2006 Direct numerical simulation and large-eddy simulation of wake vortices: going from laboratory conditions to flight conditions. In ECCOMAS CFD Conference, Swansea, Wales, UK.Google Scholar
Winckelmans, G. S. & Jeanmart, H. 2001 VLES of aircraft wake vortices in a turbulent atmosphere: a study of decay. In ECCOMAS CFD Conference, Swansea, Wales, UK.Google Scholar
Zeman, O. 1995 The persistence of trailing vortices: a modelling study. Phys. Fluids A 7, 135–143.CrossRefGoogle Scholar