Experiments in Fluids

, Volume 47, Issue 2, pp 321–331 | Cite as

Flow past a delta wing with a sinusoidal leading edge: near-surface topology and flow structure

  • T. Goruney
  • D. Rockwell
Research Article


The near-surface flow structure and topology on a delta wing of low sweep angle, having sinusoidal leading edges of varying amplitude and wavelength, are investigated using a stereoscopic technique of high-image-density particle image velocimetry at a Reynolds number of 15,000. Identification of critical points, in conjunction with surface-normal vorticity and velocity, provides a basis for determining the effectiveness of a given leading edge. At high angle of attack, where large-scale three-dimensional separation occurs from the wing with a straight leading edge, an amplitude of the leading-edge protuberance as small as one-half of one percent of the chord of the wing can substantially alter the near-surface topology. When the amplitude reaches a value of four percent of the chord, it is possible to completely eradicate the negative focus of large-scale, three-dimensional separation, in favor of a positive focus of attachment. Moreover, alteration of the near-surface topology is most effective when the ratio of the wavelength to amplitude of the sinusoidal leading edge is maintained at a small value.


Vorticity Particle Image Velocimetry Saddle Point Laser Sheet Leading Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Bakker PG, de Winkel MEM (1990) On the Topology of three-dimensional separated flow structures and local solutions of the Navier-Stokes equations. In: Moffatt HK, Tsinober A (eds) Proceedings of the IUTAM Symposium, 13–18 August 1989, Cambridge, UK. Topological fluid mechanics. Cambridge University Press, CambridgeGoogle Scholar
  2. Bearman PW, Owen JC (1998) Reduction of bluff-body drag and suppression of vortex shedding b the introduction of wavy separation lines. J Fluids Struct 12:123–130CrossRefGoogle Scholar
  3. Bushnell DM, Moore KJ (1991) Drag reduction in nature. Annu Rev Fluid Mech 23:65–79CrossRefGoogle Scholar
  4. Chapman GT, Yates LA (1991) Topology of flow separation on three-dimensional bodies. Appl Mech Rev 44(7):329CrossRefMathSciNetGoogle Scholar
  5. Chong MS, Perry AE, Cantwell B (1990) A general classification of three-dimensional flow fields. Phys Fluids A (Fluid Dyn) 2(5):765–777CrossRefMathSciNetGoogle Scholar
  6. Dallman U (1983) Topological structures of three-dimensional vortex flow separation in AIAA-83-1735Google Scholar
  7. Delery J (2001) Robert Legendre, Henri Werlé: toward the elucidation of three-dimensional separation. Annu Rev Fluid Mech 33:129–154CrossRefGoogle Scholar
  8. Depardon S, Lasserre JJ, Boueilh JC, Brizzi LE, Boree J (2005) Skin friction pattern analysis using near-wall PIV. Exp Fluids 39:805–818CrossRefGoogle Scholar
  9. Depardon S, Lasserre JJ, Brizzi LE, Borée J (2007) Automated topology classification method for instantaneous velocity fields. Exp Fluids 42:697–710CrossRefGoogle Scholar
  10. Earnshaw PB, Lawford JA (1964) Low-speed wind tunnel experiments on a series of sharp-edged delta wings. Aeronautical Research Council. R&M 3424Google Scholar
  11. Fish FE, Lauder GV (2006) Passive and active flow control by swimming fishes and mammals. Annu Rev Fluid Mech 38:193–224CrossRefMathSciNetGoogle Scholar
  12. Foss JF (2004) Surface selections and topological constraint evaluation for flow field analyses. Exp Fluids 37:883–898CrossRefGoogle Scholar
  13. Fouras A, Soria J (1998) Accuracy of out-of-plane vorticity measurements derived from in-plane velocity field data. Exp Fluids 25:409–430CrossRefGoogle Scholar
  14. Gordnier RE, Visbal MR (2003) Higher-order compact difference scheme applied to the simulation of a low sweep delta wing flow AIAA Paper 2003-0620. In: 41st AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV, JanuaryGoogle Scholar
  15. Goruney T (2008) Investigation of flow structure on a stationary and pitching delta wing of moderate sweep angle using stereoscopic particle image velocimetry. Ph.D. Dissertation. Lehigh University, BethlehemGoogle Scholar
  16. Hunt JCR, Abel CJ, Peterka J, Woo H (1977) Kinematical studies of the flows around free-surface-mounted obstacles. J Fluid Mech 86:179–200CrossRefGoogle Scholar
  17. Johari H, Henoch C, Custodio D, Levshin A (2007) Effects of leading edge protuberances on airfoil performance. AIAA J 45:2634–2642CrossRefGoogle Scholar
  18. Johari H, Henoch C, Custodio D (2008) Visualization of flow on hydrofoils with leading edge protuberances. In: 13th international symposium on flow visualization, 1–4 July, Nice, FranceGoogle Scholar
  19. Legendre R (1956) Séparation de l’ecoulement laminaire tridimensional. La Rech Aéronautique 54:3–8Google Scholar
  20. Legendre R (1977) Lignes de Courant d’un Écoulement Permanent, Deécollement et Separation. La Rech Aérospatiale 6:327–335Google Scholar
  21. Miklosovic DS, Murray MM, Howle LE, Fish FE (2004) Leading-edge tubercles delay stall on Humpback Whale (Megaptera Novaeangliae) flippers. Phys Fluids 16:L39–L42CrossRefGoogle Scholar
  22. Miklosovic DS, Murray MM, Howle LE (2007) Experimental evaluation of sinusoidal leading-edges. J Aircr 44(4):1404–1408CrossRefGoogle Scholar
  23. Owen JC, Szewezyk AA, Bearman PW (2000) Suppression of Kármán vortex shedding, gallery of fluid motion. Phys Fluids 12:1–13CrossRefGoogle Scholar
  24. Paterson EG, Wilson RV, Stern F (2003) General-Purpose Parallel Unsteady RANS CFD Code for Ship Hydrodynamics, IIHR Hydroscience Engineering Report 531. University of Iowa, Iowa City, IowaGoogle Scholar
  25. Perry AE, Chong MS (1987) A description of eddying motions and flow patterns using critical-point concepts. Annu Rev Fluid Mech 19:125–155CrossRefGoogle Scholar
  26. Perry AE, Chong MS (2000) Flow visualization: techniques and examples. In: Smiths A, Lim TT (eds) Interpretation of flow visualization, chap 1. Imperial College Press, LondonGoogle Scholar
  27. Perry AE, Fairlie DB (1974) Critical points in flow patterns. Adv Geophys 18B:299–315Google Scholar
  28. Perry AE, Hornung H (1984) Some aspects of three-dimensional separation, Part II: vortex skeletons. Z Flugwiss Weltraumforsch 8:155–160Google Scholar
  29. Prasad AK, Jensen K (1995) Scheimpflug stereocamera for particle image velocimetry in liquid flows. Appl Opt 34(30):7092–7099CrossRefGoogle Scholar
  30. Sahin M, Sankar LN, Chandrasekhara MS, Tung C (2003) Dynamic stall alleviation using a deformable leading edge concept: a numerical study. J Aircr 40(1):77–85CrossRefGoogle Scholar
  31. Squire LC, Maltby RL, Keating RFA, Stanbrook A (1962) Flow visualization in wind tunnels using indicators, Part I: the surface oil flow technique. Technical Report, AGARDOGRAPHGoogle Scholar
  32. Su W, Liu M, Liu Z (1990) Topological structures of separated flows about a series of sharp-edged delta wings at angles-of-attack up to 90°. In: Moffatt HK, Tsinober A (eds) Proceedings of the IUTAM Symposium,13–18 August 1989, Cambridge, UK. Topological fluid mechanics. Cambridge University Press, CambridgeGoogle Scholar
  33. Taylor GS, Gursul I (2004) Unsteady vortex flows and buffeting of a low sweep delta wing, AIAA 2004-1066, 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NVGoogle Scholar
  34. Tobak M, Peake J (1982) Topology of three-dimensional separated flows. Annu Rev Fluid Mech 14:61–85CrossRefMathSciNetGoogle Scholar
  35. Verhaagen, Bossuyt (2006) Flow on a delta wing apex collection of technical papers. In: 44th AIAA Aerospace Sciences Meeting, vol 5, pp 3056–3066Google Scholar
  36. Watts P, Fish FE (2001) The influence of passive, leading edge tubercles on wing performance. In: Proceedings of twelfth international symposium on Unmanned Untethered Submersibles Technology, Durham New Hampshire: Auton, Undersea Systems InstituteGoogle Scholar
  37. Yavuz MM (2006) Origin and control of the flow structure and topology on delta wings. Ph.D. Dissertation. Lehigh University, BethlehemGoogle Scholar
  38. Yavuz MM, Elkhoury M, Rockwell D (2004) Near-surface topology and flow structure on a delta wing. AIAA J 42(2):332–340CrossRefGoogle Scholar
  39. Zang W, Prasad AK (1997) Performance evaluation of a Scheimpflug stereocamera for particle image velocimetry. Appl Opt 36(33): 8738–8744Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and MechanicsLehigh UniversityBethlehemUSA

Personalised recommendations