Aspects of the Modeling and Numerical Simulation of Leading-Edge Vortex Flow

  • H. W. M. Hoeijmakers
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


A cell-centered central-difference finite-volume Euler method is applied to the steady subsonic flow about a 65-deg sharp-edged cropped delta wing at incidences close to the incidence at which leading-edge vortex breakdown is observed in wind tunnel experiments. Above a critical value of the incidence the pseudo-time dependent numerical procedure fails to attain a steady-state solution. For the case of subsonic leading-edge vortex flow the occurrence of “solution breakdown” indicates the limits of the domain of applicability of the steady-flow Euler method. In the search for the critical incidence it is found that for a given grid and for a given setting of the parameters controlling the artificial dissipation two distinct, steady-state solutions exist. Analysis of the two solutions obtained at one incidence reveals that within the vortex core above the aft part of the wing these solutions feature remarkably different velocity and vorticity distributions.


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  1. 1.
    Murman, E.M., Rizzi, A.: Applications of Euler Equations to Sharp-Edged Delta Wings with Leading Edge Vortices. ACARD CP412, Paper 15 (1986).Google Scholar
  2. 2.
    Longo, J.M.A.: The Role of the Numerical Dissipation on the Computational Euler-Equations-Solutions for Vortical Flows. AIAA Paper 89–2232 (1989).Google Scholar
  3. 3.
    Hitzel, S.M.: Wing Vortex-Flows up into Vortex Breakdown. A Numerical Simulation. AIAA Paper 89–2232 (1989).Google Scholar
  4. 4.
    O’Neill, P.J., Barnett, R.M., Louie, C.M.: Numerical Simulation of Leading-Edge Vortex Breakdown using an Euler Code. AIAA Paper 89–2189 (1989).Google Scholar
  5. 5.
    Raj, P., Sikora, J.S., Keen, J.M.: Free-Vortex Flow Simulation using a Three-Dimensional Euler Aerodynamic Method. J. of Aircraft, Vol. 25, No. 2 (1988).CrossRefGoogle Scholar
  6. 6.
    Hoeijmakers, H.W.M., van den Berg, J.I.: Application of an Euler-Equation Method to a Sharp-Edged Delta-Wing Configuration with Vortex Flow. AIAA Paper 91–3310 (1991). Also NLR TP 91306.Google Scholar
  7. 7.
    van den Berg, J.I., Hoeijmakers, H.W.M., Sytsma, H.A.: Numerical Investigation into High-Angle-of-Attack Leading-Edge Vortex Flow. AIAA Paper 922600 (1992). Also NLR TP 92248 (1992).Google Scholar
  8. 8.
    Peckham, P.D., Atkinson, S.A.: Preliminary Results of Low Speed Wind Tunnel Tests on a Gothic Wing of Aspect Ratio 1.0. ARC Rep. CP-508 (1957).Google Scholar
  9. 9.
    Elle, B.J.: An Investigation at Low Speed of the Flow near the Apex of Thin Delta Wings with Sharp Leading Edges. ARC Rep. RandM. No. 3176 (1958).Google Scholar
  10. 10.
    Lambourne, N.C., Bryer, D.W.: The Bursting of Leading-Edge Vortices. Some Observations and Discussion of the Phenomenon. ARC Rep. RandM. No. 3282 (1961).Google Scholar
  11. 11.
    Ekaterinaris, J.A., Schiff, L.B.: Numerical Simulation of the Effects of Variation of Angle of Attack and Sweep Angle on Vortex Breakdown over Delta Wings. AIAA-90–3000 (1990).Google Scholar
  12. 12.
    Hall, M.G.: Vortex Breakdown. Annual Review of Fluid Mechanics, Vol. 4, pp. 195–218 (1972).CrossRefGoogle Scholar
  13. 13.
    Elsenaar, A., Hoeijmakers, H.W.M.: An Experimental Study of the Flow Over a Sharp-Edged Delta Wing at Subsonic and Transonic Speeds. AGARD CP-494, Paper 15 (1991).Google Scholar
  14. 14.
    Boerstoel, J.W., Spekreijse, S.P., Vitagliano, P.L.: The Design of a System of Codes for Industrial Calculations around Aircraft and Other Complex Aerodynamic Configurations. AIAA Paper 92–2619 (1992).Google Scholar
  15. 15.
    Jameson, A., Schmidt, W., Turkel, E.: Numerical Solution of Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Scheme. AIAA Paper 81–1259 (1981).Google Scholar
  16. 16.
    Hall, M.G.: A Theory for the Core of a Leading-Edge Vortex. JFM, Vol. 11, pp. 209–227 (1961).CrossRefzbMATHGoogle Scholar
  17. 17.
    Stewartson, K., Hall, M.G.: The Inner Viscous Solution for the Core of a Leading-Edge Vortex. JFM, Vol. 15, pp. 306–318 (1963).CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Hoeijmakers, H.W.M.: Numerical Simulation of Leading-Edge Vortex Flow. NLR TP 91471 (1991).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • H. W. M. Hoeijmakers
    • 1
  1. 1.National Aerospace LaboratoryNLRAmsterdamThe Netherlands

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