Skip to main content

Wing Tip Vortices

  • Chapter
Fluid Vortices

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 30))

Abstract

One of the most conspicuous features of an airplane flying at high altitude is its white contrails. These contrails, which are formed by the condensation of engine exhaust water vapour, clearly delineate the location of the wing tip vortices. The contrails are often the first — and perhaps the only — exposure most of us have to wing tip vortices (also referred to as “trailing vortices” or, imprecisely, as “wing wake vortices” or “tip wake vortices”). This chapter aims to explain the origin of tip vortices (§X.l) and review their technological relevance (§X.2). The chapter then summarizes lifting line theory, the simplest finite wing theory (§X.3), and synopsizes our knowledge of tip vortex behaviour (§X.4, §X.5).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Agrawal, S., Barnett, R. M., and Robinson, B. A. 1992 Numerical investigation of vortex breakdown on a delta wing. AIAA J. 30, 584–591.

    Article  ADS  Google Scholar 

  • Arndt, R. E. A. 1983 Cavitation in fluid machinery and hydraulic structures. Ann. Rev. Fluid Mech. 13, 273–328.

    Article  ADS  Google Scholar 

  • Arndt, R. E. A., Arakeri, V. H., and Higuchi, H. 1991 Some observations of tip vortex cavitation. J. Fluid Mech. 229, 269–289.

    Article  ADS  Google Scholar 

  • Arndt, R. E. A. and Keller, A. P. 1992 Water quality effects on cavitation inception in a trailing vortex. J. Fluids Eng. 114, 430–438.

    Article  Google Scholar 

  • Baker, G. R., Barker, S. J., Bofah, K. K., and Saffman, P. 1974 Laser anemometer measurement of trailing vortices in water. J. Fluid Mech. 65, 325–336.

    Article  ADS  Google Scholar 

  • Bandyopadhyay, P. R., Stead, D. J. and Ash, R. L. 1990 The organized structure of a turbulent trailing vortex. 21st Fluid Dynamics, Plasma Dynamics, and Lasers Conference, Seattle, WA.

    Google Scholar 

  • Batchelor, G. K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20, 645–658.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Bertin, J. J. and Smith, M. L. 1989 Aerodynamics for Engineers. Prentice-Hall.

    Google Scholar 

  • Betz, A. 1932 Verhalten von wirbelsystemen. Z. Angew. Math. Mech. 12, 164–174 (also NACA TM-713, 1933).

    Article  Google Scholar 

  • Betz, A. 1919 On airfoil theory with special consideration of rectangular wings. Ph.D. thesis, Gottingen.

    Google Scholar 

  • Brazil, J. 1994 FAA ignored warnings of 757 jet turbulence. Los Angeles Times, Sunday June 5, 1.

    Google Scholar 

  • Brown, G. 1988 personal communication.

    Google Scholar 

  • Campbell, J. F., Chambers, J. R., and Rumsey, C. L. 1989 Observation of airplane flowfields by natural condensation effects. J. Aircraft 26, 593–604.

    Article  Google Scholar 

  • Carlin, G., Dadone, L., and Spencer, R. 1989 Results of an experimental investigation of blade tip vortex modification devices. NASA CR-181853.

    Google Scholar 

  • Chen, C.-L. and McCroskey, W. J. 1988 Numerical simulation of helicopter multi-bladed rotor flow. AIAA paper 88-0046.

    Google Scholar 

  • Chevalier, H. 1973 Flight test studies of the formation and dissipation of trailing vortices. J. Aircraft 10, 14–18.

    Article  Google Scholar 

  • Chigier, N. A. 1974 Vortexes in aircraft wakes. Scientific American March, 76–83.

    Google Scholar 

  • Chigier, N. A. and Corsiglia, V. R. 1972 Wind tunnel studies of wing wake turbulence. J. Aircraft 9, 820–825.

    Article  Google Scholar 

  • Chow, J. S., Zilliac, G. G., and Bradshaw, P. 1993 Measurements in the near-field of a turbulent wingtip vortex. Proceedings of the AIAA 31st Aerospace Sciences Meeting.

    Google Scholar 

  • Chow, J. S., Zilliac, G. G., and Bradshaw, P. 1991 Initial rollup of a trailing wing tip vortex. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.

    Google Scholar 

  • Corsiglia, V. R., Schwind, R. G. and Chigier, N. A. 1973 Rapid scanning three-dimensional hot-wire anemometer surveys of wing-tip vortices. J. Aircraft 10, 752–757.

    Article  Google Scholar 

  • Critchley, J. B. 1991 Wake vortex -the program in the United Kingdom. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.

    Google Scholar 

  • Crow, S. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.

    Article  ADS  Google Scholar 

  • Crow, S. C. and Bate, E. R. Jr. 1976 Lifespan of trailing vortices in a turbulent atmosphere. J. Aircraft 13, 476–482.

    Article  Google Scholar 

  • Dalton, C. and Wong, X. 1990 The vortex roll-up problem using Lamb vortices for the elliptically loaded wing. Computers and Fluids 18, 139–150.

    Article  Google Scholar 

  • Drummond, A. M., Onno, R., and Panneton, B. 1991 Trajectories and stability of trailing vortices very near the ground. National Research Council of Canada IAR-AN-71

    Google Scholar 

  • Dunham, R. E. Jr. 1976 Unsuccessful concepts for aircraft wake vortex minimization. NASA SP-409, 221–250.

    Google Scholar 

  • Eliason, B. G., Gartshore, I. S., and Parkinson, G. V. 1975 Wind tunnel investigation of Crow instability. J. Aircraft 12, 985–988.

    Article  Google Scholar 

  • Falcão de Campos, J. A. C. 1992 Laser-doppler velocity measurements on tip vortices in non-cavitating and cavitating conditions. ASME Cavitation and Multiphase Flow Forum.

    Google Scholar 

  • Freymuth, P. 1989 Visualizing the connectivity of vortex systems for pitching wings. J. Fluids Eng. 111, 217–220.

    Article  Google Scholar 

  • Gilbert, T. 1991 Aerodynamic effects during minimum-interval takeoffs and aerial refuelling. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.

    Google Scholar 

  • Glauert, H. 1924 A theory of thin airfoils. Brit. Aero. Res. Comm. RM-910

    Google Scholar 

  • Glegg S. A. L. 1991 Prediction of blade wake interaction noise based on a turbulent vortex model. AIAA J. 29, 1545–1551.

    Article  ADS  MATH  Google Scholar 

  • Green, S. I. 1991 Correlating single phase flow measurements with observations of trailing vortex cavitation. J. Fluids Engineering 113, 125–129.

    Article  Google Scholar 

  • Green, S. 1990 Axial velocity distribution in rectangular planform wing trailing vortices. CSME Mech. Eng. Forum.

    Google Scholar 

  • Green, S. I. and Acosta, A. J. 1991 Unsteady flow in trailing vortices. J. Fluid Mechanics 227, 107–134.

    Article  ADS  Google Scholar 

  • Green, S.I, Acosta, A. J., and Akbar, R. 1988 The influence of tip geometry on trailing vortex rollup and cavitation. ASME Cavitation and Multiphase Flow Forum.

    Google Scholar 

  • Greenewalt, C. H. 1975 The flight of birds. Trans. Amer. Phil. Soc. New Series 65, 67 pages.

    Google Scholar 

  • Hart, D. 1991 Cavitation inception in the tip vortex region of an oscillating hydrofoil. ASME Cavitation and Multiphase Flow Forum.

    Google Scholar 

  • Hess, J. L. and Smith, A. M. 0. 1967 Calculation of potential flow about arbitrary bodies. Prog. in the Aero. Sci., 1–138.

    Google Scholar 

  • Higuchi, H., Arndt, R. E. A., Arakeri, V. H., and Killen, J. M. 1989 The structure of tip vortices over a range of cavitation number. 22nd American Towing Tank Conference.

    Google Scholar 

  • Holl, J. W., Arndt, R. E. A., and Billet, M. 1972 Limited cavitation and the related scale effects problem. JSME Proc. 2nd Int. Symp. Fluid Mech. and Fluidics, Tokyo, Japan, 303–314.

    Google Scholar 

  • Kaden, H. 1931 Aufwicklung einer unstabilen unstetigkeitsfläche Ingen. Arch. 2, 140–168.

    Article  Google Scholar 

  • Katz, J. and Galdo, J. B. 1989 The effect of roughness on rollup of tip vortices on a rectangular hydrofoil. J. Aircraft 26, 247–253.

    Article  Google Scholar 

  • Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123–155.

    Article  ADS  Google Scholar 

  • Liu, H.-T., Hwang, P. A., and Srnsky, R. A. 1992 Physical modelling of ground effects on vortex wakes. J. Aircraft 29, 1027–1034.

    Article  Google Scholar 

  • Logan, A. H. 1971 Vortex velocity distributions at large downstream distances. J. Aircraft 8, 930–932.

    Article  Google Scholar 

  • Margason, R. J. and Lamar, J. E. 1968 Vortex lattice Fortran program for estimating subsonic aerodynamic characteristics of complex planforms. NASA TND-4739.

    Google Scholar 

  • Martin, R. M., Elliott, J. W., and Head, D. R. 1984 Comparison of experimental and analytical predictions of rotor blade vortex interactions using model scale acoustic data. AIAA 84-2269.

    Google Scholar 

  • McCormick, B. W. 1962 On cavitation produced by a vortex trailing from a lifting surface. ASME J. Basic Eng. 84, 369–379.

    Article  Google Scholar 

  • Milne-Thomson, L. M. 1958 Theoretical Aerodynamics. Dover.

    Google Scholar 

  • Moore, D. W. 1974 A numerical study of the roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225–235.

    Article  ADS  MATH  Google Scholar 

  • Munk, M. 1919 Isoperimetric problems in the theory of flight. Ph.D. thesis, Gottingen.

    Google Scholar 

  • O’Connor, L. 1992 Wingtip turbines promise to reduce drag. Mech. Eng. 114, 122.

    Google Scholar 

  • Page, R. D., Clawson, K. L., Garodz, L. J., and Rudis, R. P. 1991 Report on tower fly-by testing. Proceedings of the FAA Wake Vortices Conference. Washington, D.C.

    Google Scholar 

  • Parks, P. C. 1971 A new look at the dynamics of vortices with finite cores. Aircraft Wake Turbulence and its Detection, (ed. J. H. Olsen), Plenum Press.

    Google Scholar 

  • Peyret, R. and Taylor, T. D. 1983 Computational Methods for Fluid Flow. Springer-Verlag.

    Book  MATH  Google Scholar 

  • Platzer, G. P. and Souders, W. G. 1979 Tip vortex cavitation delay with application to marine lifting surfaces -a literature survey. DTNSRDC-79/051.

    Book  Google Scholar 

  • Poling, D. R., Dadone, L., and Telionis, D. P. 1989 Blade-vortex interaction. AIAA J. 27, 694–699.

    Article  ADS  Google Scholar 

  • Pouagare, M. and Delaney, R. A. 1985 Study of three-dimensional viscous flows in an axial compressor cascade including tip leakage effects using a simple-based algorithm. J. Turbomach. 108, 51–58.

    Article  Google Scholar 

  • Prandtl, L. 1919 Tragflugeltheorie. Gottingen Nachrichten, II Mitteilung, 107–137.

    Google Scholar 

  • Prandtl, L. 1922 Applications of Modern Hydrodynamics to Aeronautics. NACA TR 116.

    Google Scholar 

  • Ran, B. and Katz, J. 1992 Measurements of cavitation inception and associated pressure fluctuations in the near field of a turbulent jet. ASME Cavitation and Multiphase Flow Forum.

    Google Scholar 

  • Rao, J. S. 1987 Turbomachine blade vibration. Shock and Vibration Digest 19, 3–10.

    Article  Google Scholar 

  • Rinoue, K. and Stollery, J. L. 1994 Experimental studies of vortex flaps and vortex plates. J. Aircraft 31, 322–329.

    Article  Google Scholar 

  • Robins, R. E. and Delisi, D. P. 1993 Potential hazard of aircraft wake vortices in ground effect with crosswind. J. Aircraft 30, 201–206.

    Article  Google Scholar 

  • Rom, J. 1991 High Angle of Attack Aerodynamics: Subsonic, Transonic, and Supersonic. Springer-Verlag.

    Google Scholar 

  • Rossow, V. 1991 Prospects for alleviation of hazard posed by lift-generated wakes. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.

    Google Scholar 

  • Saffman, P. G. 1991 Approach of a vortex pair to a rigid free surface in viscous fluid. Phys. Fluids A 3, 984–985.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Sami, S., Carmody, T., and Rouse, H. 1967 Jet diffusion in the region of flow establishment. J. Fluid Mech. 27, 231–251.

    Article  ADS  Google Scholar 

  • Sarpkaya, T. 1992 Interaction of a turbulent vortex with a free surface. Proceedings of the Nineteenth Symposium on Naval Hydrodynamics, Seoul, South Korea.

    Google Scholar 

  • Sarpkaya, T. 1989 Computational methods with vortices. J. Fluids Eng. 111, 5–52.

    Article  Google Scholar 

  • Sarpkaya, T. 1983 Trailing vortices in homogeneous and density-stratified media. J. Fluid Mech. 136, 85–109.

    Article  ADS  Google Scholar 

  • Sarpkaya, T. and Daly, J. J. 1987 Effect of ambient turbulence on trailing vortices. J. Aircraft 24, 399–404.

    Article  ADS  Google Scholar 

  • Schreier, J., 1982 Fluctuating forces and rotor noise due to main rotor -tail rotor interaction. Association Aeronautique et Astronautique de France, 8th European Rotorcraft Forum.

    Google Scholar 

  • Schrenk, O. 1940 Simple approximation method for obtaining spanwise lift distribution. NACA TM-948.

    Google Scholar 

  • Shekarriz, A., Fu, T. C, Katz, J., Liu, H.L., and Huang, T.T. 1992 Study of junction and tip vortices using particle displacement velocimetry. AIAA J. 30, 145–152.

    Article  ADS  Google Scholar 

  • Shekarriz, À., Fu, T. C, Katz, J., and Huang, T.T. 1993 Near-field behavior of a tip vortex. AIAA J. 31, 112–118.

    Article  ADS  Google Scholar 

  • Simonich, J. C., McCormick, D. C, and Lavrich, P. L. 1993 Role of leading-edge vortex flows in prop-fan interaction noise. J. Aircraft 30, 255–261.

    Article  ADS  Google Scholar 

  • Singh, P. I. and Uberoi, M. S. 1976 Experiments on vortex stability. Physics of Fluids 19, 1181–1188.

    Google Scholar 

  • Smith, J. H. B. 1986 Vortex Flows in Aerodynamics. Ann. Rev. Fluid Mech. 18, 221–242.

    Article  ADS  Google Scholar 

  • Spreiter, J. R. and Sacks, A. H. 1951 The rolling up of the trailing vortex sheet and its effect on the downwash behind wings. J. Aero. Sci. 18, 21–32.

    MathSciNet  MATH  Google Scholar 

  • Srinivasan, G. R., Baeder, J. D., Obayashi, S., and McCroskey, W. J. 1992 Flow-field of a lifting rotor in hover: A Navier-Stokes simulation. AIAA J. 30, 2371–2378.

    Article  ADS  MATH  Google Scholar 

  • Srinivasan, G. R., McCroskey, W. J., Baeder, J. D., and Edwards, T. A. 1986 Numerical simulation of tip vortices of wings in subsonic and transonic flows. AIAA 86-1095.

    Google Scholar 

  • Stahl, W. H., Mahmood, M., and Asghar, A. 1992 Experimental investigations of the vortex flow on delta wings at high incidence. AIAA J. 30, 1027–1033.

    Article  ADS  Google Scholar 

  • Stinebring, D. R., Farrell, K. J., and Billet, M. L. 1991 The structure of a three dimensional vortex at high Reynolds number. J. Fluids Eng. 113, 496–503.

    Article  Google Scholar 

  • Teske, M. E., Bilanin, A. J., and Barry, J. W. 1993 Decay of aircraft vortices near the ground. AIAA J. 31, 1531–1533.

    Article  ADS  Google Scholar 

  • Thomas, A. S. W. 1985 Aircraft viscous drag reduction technology. Lockheed Horizons 19, 22–32.

    Google Scholar 

  • Thompson, D. H. 1975 Experimental study of axial flow in wing tip vortices. J. Aircraft 12 990–991.

    Google Scholar 

  • Tu, E. L. 1994 Vortex-wing interaction of a close-coupled canard configuration. J. Aircraft 31, 314–321.

    Article  Google Scholar 

  • Wake, B. E. and Sankar, N. L. 1989 Solutions of the Navier-Stokes equations for the flow about a rotor blade. J. American Helicopter Society 34, 13–23.

    Article  Google Scholar 

  • Webber, G. W. and Dansby, T. 1983 Wing tip devices for energy conservation and other purposes -experimental and analytical work in progress at the Lockheed-Georgia Company. Can. Aero. Space J. 29, 105–120.

    Google Scholar 

  • Werlé, H. 1974 Le tunnel hydrodynamique au service de la recherche aérospatiale. ONERA-156. (see also van Dyke, M. 1982 An Album of Fluid Motion. Parabolic.)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Green, S.I. (1995). Wing Tip Vortices. In: Green, S.I. (eds) Fluid Vortices. Fluid Mechanics and Its Applications, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0249-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0249-0_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4111-9

  • Online ISBN: 978-94-011-0249-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics