Computational investigation of vortex structure and breakdown over a delta wing at supersonic pitching maneuver

  • M. Hadidoolabi
  • H. Ansarian
Technical Paper


Unsteady compressible flows over a 60° swept delta wing with a sharp leading edge undergoing pitching maneuvers are computationally studied. Emphasis in this study is on possible supersonic flow structures and vortex breakdown during the pitching motion of a delta wing. Unstructured grid, kω SST turbulence model and a dual-time implicit time integration were used. Accurate simulations were performed for various Mach numbers, initial and final angles of attack, and pitch rates to cover different flow structures and phenomena associated with them. The contours obtained by the numerical results which show the flow structures were compared with experimental visualization images. Variations of flow patterns, pressure coefficient on the wing surface, and the lift coefficient during a pitching maneuver are investigated. Vortex breakdown was observed for both subsonic and supersonic flows and its impact on the lift coefficient during the motion was shown.


Delta wing Supersonic flow Vortex structure Vortex breakdown Pitching maneuver 

List of symbols




Drag coefficient


Lift coefficient


Pressure coefficient


Mach number


Pitch rate




Velocity magnitude

x, y, z

Cartesian coordinate


Angle of attack

\(\dot{\alpha }\)

Rate of angle of attack change


Sweep angle







Component normal to the leading edge

Free stream condition





  1. 1.
    Gursul I, Gordnier R, Visbal M (2005) Unsteady aerodynamics of nonslender delta wings. Prog Aerosp Sci 41(7):515–557CrossRefGoogle Scholar
  2. 2.
    Gursul I (2004) Recent developments in delta wing aerodynamics. Aeronaut J 108(1087):437–452CrossRefGoogle Scholar
  3. 3.
    Rockwell D (1993) Three-dimensional flow structure on delta wings at high angle-of-attack: experimental concepts issues. In: 31st aerospace science meeting and exhibit, Reno, Nevada, Paper No. 93-0550Google Scholar
  4. 4.
    Visbal MR (1993) Computational and physical aspects of vortex breakdown on delta wings. In: 33rd aerospace science meeting and exhibit, Reno, Nevada, paper no. 95-0585Google Scholar
  5. 5.
    Maltby RL, Engler PB, Keating RFA (1963) Some exploratory measurements of leading-edge vortex positions on a delta wing oscillating in heave. Aeronautical Research Council, Research and Memorandum, No. 3410, LondonGoogle Scholar
  6. 6.
    Lambourne NC, Bryer DW, Maybrey JFM (1969) The behaviour of the leading-edge vortices over a delta wing following a sudden change of incidence. Aeronautical Research Council, Research and Memorandum, No. 3645, LondonGoogle Scholar
  7. 7.
    Gursul I (2005) Review of unsteady vortex flows over slender delta wings. J Aircr 42(2):299–319CrossRefGoogle Scholar
  8. 8.
    Gad-el-Hak M, Ho CM (1985) Pitching delta wing. AIAA J 23(11):1660–1665CrossRefGoogle Scholar
  9. 9.
    Gursul I, Yang H (1995) On fluctuations of vortex breakdown location. Phys Fluids 7(1):229–231CrossRefGoogle Scholar
  10. 10.
    Gursul I, Ho CM (1994) Vortex breakdown over delta wings in unsteady freestream. AIAA J 32(2):433–436CrossRefGoogle Scholar
  11. 11.
    Visbal MR, Gordnier RE (1995) Pitch rate and pitch-axis location effects on vortex breakdown onset. J Airc 32(5):929–935CrossRefGoogle Scholar
  12. 12.
    Atta R, Rockwell D (1987) Hysteresis of vortex development and breakdown on an oscillating delta wing. AIAA J 25(11):1512–1513CrossRefGoogle Scholar
  13. 13.
    LeMay SP, Batill SM, Nelson RC (1990) Vortex dynamics on a pitching delta wing. J Airc 27(2):131–138CrossRefGoogle Scholar
  14. 14.
    Lin JC, Rockwell D (1995) Transient structure of vortex breakdown on a delta wing. AIAA J 33(1):6–12CrossRefGoogle Scholar
  15. 15.
    Magness C, Robinson O, Rockwell D (1993) Instantaneous topology of the unsteady leading edge vortex at high angle of attack. AIAA J 31(8):1384–1391CrossRefGoogle Scholar
  16. 16.
    Yavuz MM, Elkhoury M, Rockwell D (2004) Near-surface topology and flow structure on a delta wing. AIAA J 42(2):332–340CrossRefGoogle Scholar
  17. 17.
    Goruney T, Rockwell D (2010) Effect of pitch rate on near-surface topology on a delta wing. AIAA J 48(6):1207–1220CrossRefGoogle Scholar
  18. 18.
    Stanbrook A, Squire LC (1964) Possible types of flow at swept leading edges. Aeronaut Q 15(2):72–78CrossRefGoogle Scholar
  19. 19.
    Miller DS, Wood RM (1984) Leeside flows over delta wings at supersonic speeds. J Airc 21(9):680–686CrossRefGoogle Scholar
  20. 20.
    Szodruch JG, Peake DJ (1980) Leeward flow over delta wings at supersonic speeds. Report NASA-TM No. 81187Google Scholar
  21. 21.
    Seshadri SN, Narayan KY (1988) Possible types of flow on lee-surface of delta wings at supersonic speeds. Aeronaut J 5:185–199CrossRefGoogle Scholar
  22. 22.
    Brodetsky MD, Krause E, Nikiforov SB et al (2001) Evolution of vortex structures on leeward side of a delta wing. J Appl Mech Tech Phys 42(2):243–254CrossRefGoogle Scholar
  23. 23.
    Vorropoulos G, Wendt JF (1983) Laser velocimetry study of compressibility effect on the flow field of a delta wing. Report AGARD CP No. 342Google Scholar
  24. 24.
    Brodetsky MD, Shevchenco AM (1990). Some features of a separated flow and supersonic vortex structure at the leeside of a delta wing. In: Proceedings of the IUTAM symposium on separated flows and jets, Berlin, pp 341–344Google Scholar
  25. 25.
    Imai G, Fujii K, Oyama (2006) A. Computational analyses of supersonic flows over a delta wing at high angles of attack. In: 25th International Congress of the Aeronautical Sciences (ICAS), Hamburg, GermanyGoogle Scholar
  26. 26.
    Oyama A, Ito M, Imai G et al (2008) Mach number effect on flow field over a delta wing in supersonic region. In: 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Paper No. 354Google Scholar
  27. 27.
    Schiavetta LA, Boelens OJ, Fritz W (2006). Analysis of transonic flow on a slender delta wing using CFD. In: 24th Applied aerodynamics conference, San Francisco, CA, Paper No. 3171Google Scholar
  28. 28.
    Schiavetta LA, Badcock KJ, Cummings RM (2007) Comparison of DES and URANS for unsteady vortical flows over delta wings. In: 46th AIAA aerospace sciences meeting and exhibit, Reno, Nevada, Paper No. 1085Google Scholar
  29. 29.
    Younis Y, Bibi A et al (2009) Vortical flow topology on windward and leeward side of delta wing at supersonic speed. J Appl Fluid Mech 2(2):13–21Google Scholar
  30. 30.
  31. 31.
    Hadidoolabi M, Ansarian H (2017) Investigation of supersonic flow over a pitching delta wing using surface pressure measurements and numerical simulations. Chin J Aeronaut (in press)Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Malek Ashtar University of TechnologyTehranIran

Personalised recommendations