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Abstract

Topological considerations of velocity and skin-friction fields are a powerful tool for flow-field diagnostics and interpretation. We studied in Section 4.4 characteristic properties of three-dimensional attached viscous flow and in Chapter 6 aspects of the interaction between attached viscous flow and its external inviscid flow. In the present chapter we investigate the topology of skin-friction fields of attached viscous flow. Mainly attachment points and lines, but also to a certain extent separation points and lines are considered.

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References

  1. Peake, D.J., Tobak, M.: Three-Dimensional Interaction and Vortical Flows with Emphasis on High Speeds. AGARDograph 252 (1980)

    Google Scholar 

  2. Sears, W.R.: The Boundary Layer of Yawed Cylinders. J. Aeronatical Sc. 15, 49–52 (1948)

    Article  MathSciNet  Google Scholar 

  3. Maltby, R.L.: Flow Visualization in Wind Tunnels Using Indicators. AGARDograph 70 (1962)

    Google Scholar 

  4. Eichelbrenner, E.A.: Three-Dimensional Boundary Layers. Annual Review of Fluid Mechanics 5, 339–360 (1973)

    Article  Google Scholar 

  5. Hirschel, E.H.: On the Creation of Vorticity and Entropy in the Solution of the Euler Equations for Lifting Wings. MBB-LKE122-AERO-MT-716, Ottobrunn, Germany (1985)

    Google Scholar 

  6. Hirschel, E.H.: Evaluation of Results of Boundary-Layer Calculations with Regard to Design Aerodynamics. AGARD R-741, 5-1–5-29 (1986)

    Google Scholar 

  7. Moffat, H.K., Tsinober, A. (eds.): Topological Fluid Mechanics. Proc. IUTAM Symp., Cambridge, GB, 1989. Cambridge University Press (1990)

    Google Scholar 

  8. Délery, J.: Robert Legendre and Henri Werlé: Towards the Elucidation of Three-Dimensional Separation. Annual Review of Fluid Mechanics 33, 129–154 (2001)

    Article  Google Scholar 

  9. Dallmann, U.: Topological Structures of Three-Dimensional Flow Separations. DLR Rep. 221-82 A 07 (1983)

    Google Scholar 

  10. Dallmann, U.: On the Formation of Three-Dimensional Vortex Flow Structures. DLR Rep. 221-85 A 13 (1985)

    Google Scholar 

  11. Eberle, A., Rizzi, A., Hirschel, E.H.: Numerical Solutions of the Euler Equations for Steady Flow Problems. NNFM, vol. 34. Vieweg, Braunschweig Wiesbaden (1992)

    Book  MATH  Google Scholar 

  12. Hirschel, E.H.: Vortex Flows: Some General Properties, and Modelling, Configurational and Manipulation Aspects. AIAA-Paper 96-2514 (1996)

    Google Scholar 

  13. Schlichting, H., Truckenbrodt, E.: Aerodynamics of the Aeroplane, 2nd edn. (revised). McGraw Hill Higher Education, New York (1979)

    Google Scholar 

  14. Wang, K.C.: Boundary Layer Over a Blunt Body at High Incidence with an Open Type of Separation. Proc. Royal Soc., London A340, 33–55 (1974)

    Article  Google Scholar 

  15. Hirschel, E.H., Fornasier, L.: Flowfield and Vorticity Distribution Near Wing Trailing Edges. AIAA-Paper 84-0421 (1984)

    Google Scholar 

  16. Schwamborn, D.: Boundary Layers on Finite Wings and Related Bodies with Consideration of the Attachment-Line Region. In: Viviand, H. (ed.) Proc. 4th GAMM-Conference on Numerical Methods in Fluid Mechanics, Paris, France, October 7-9, 1981. NNFM, vol. 5, pp. 291–300. Vieweg, Braunschweig Wiesbaden (1982)

    Google Scholar 

  17. Zahm, A.F.: Flow and Force Equations for a Body Revolving in a Fluid. NACA Rep. No. 323 (1930)

    Google Scholar 

  18. Lighthill, M.J.: Attachment and Separation in Three-Dimensional Flow. In: Rosenhead, L. (ed.) Laminar Boundary Layers, pp. 72–82. Oxford University Press (1963)

    Google Scholar 

  19. Lugt, H.J.: Introduction to Vortex Theory. Vortex Flow Press, Potomac (1996)

    Google Scholar 

  20. Poincaré, H.: Les points singuliers des équations différentielles. C. R. Acad. Sci. 94, 416–418 (1882), Oeuvres Complètes 1, 3–5 (1882)

    Google Scholar 

  21. Oswatitsch, K.: Die Ablösebedingungen von Grenzschichten. In: Görtler, H. (ed.) Proc. IUTAM Symposium on Boundary Layer Research, Freiburg, Germany, 1957, pp. 357–367. Springer, Heidelberg (1958); Also: The Conditions for the Separation of Boundary Layers. In: Schneider, W., Platzer, M. (eds.) Contributions to the Development of Gasdynamics, pp. 6–18. Vieweg, Braunschweig Wiesbaden, Germany (1980)

    Google Scholar 

  22. Kaplan, W.: Ordinary Differential Equations. Addison-Wesley Publishing Company, Reading (1958)

    MATH  Google Scholar 

  23. Andronov, A.A., Leontovich, E.A., Gordon, I.I., Maier, A.G.: Qualitative Theory of Second-Order Dynamic Systems. J. Wiley, New York (1973)

    MATH  Google Scholar 

  24. Hornung, H., Perry, A.E.: Some Aspects of Three-Dimensional Separation, Part I: Streamsurface Bifurcations. Z. Flugwiss. und Weltraumforsch (ZFW) 8, 77–87 (1984)

    Google Scholar 

  25. Bakker, P.G., de Winkel, M.E.M.: On the Topology of Three-Dimensional Separated Flow Structures and Local Solutions of the Navier-Stokes Equations. In: Moffat, H.K., Tsinober, A. (eds.) Topological Fluid Mechanics. Proc. IUTAM Symp., 1989, pp. 384–394. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  26. Hunt, J.C.R., Abell, C.J., Peterka, J.A., Woo, H.: Kinematical Studies of the Flows Around Free or Surface-Mounted Obstacles; Applying Topology to Flow Visualization. J. Fluid Mechanics 86, 179–200 (1978)

    Article  Google Scholar 

  27. Tobak, M., Peake, D.J.: Topology of Three-Dimensional Separated Flows. Annual Review of Fluid Mechanics 14, 61–85 (1982)

    Article  MathSciNet  Google Scholar 

  28. Davey, A.: Boundary-Layer Flow at a Saddle Point of Attachment. J. Fluid Mechanics 10, 593–610 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  29. Van Dyke, M.: An Album of Fluid Motion. The Parabolic Press, Stanford (1982)

    Google Scholar 

  30. Hirschel, E.H.: Viscous Effects. Space Course 1991, RWTH Aachen, Germany, pp. 12-1–12-35 (1991)

    Google Scholar 

  31. Hirschel, E.H., Weiland, C.: Selected Aerothermodynamic Design Problems of Hypersonic Flight Vehicles, AIAA, Reston, Va. Progress in Astronautics and Aeronautics, vol. 229. Springer, Heidelberg (2009)

    Book  MATH  Google Scholar 

  32. Dallmann, U., Hilgenstock, A., Riedelbauch, S., Schulte-Werning, B., Vollmers, H.: On the Footprints of Three-Dimensional Separated Vortex Flows Around Blunt Bodies. Attempts of Defining and Analyzing Complex Vortex Structures. AGARD-CP-494, 9-1–9-13 (1991)

    Google Scholar 

  33. Schwamborn, D.: Laminare Grenzschichten in der Nähe der Anlegelinie an Flügeln und flügelähnlichen Körpern mit Anstellung (Laminar Boundary Layers in the Vicinity of the Attachment Line at Wings and Wing-Like Bodies at Angle of Attack). Doctoral thesis, RWTH Aachen, Germany, also DFVLR-FB 81–31 (1981)

    Google Scholar 

  34. Hirschel, E.H., Kordulla, W.: Local Properties of Three-Dimensional Separation Lines. Z. Flugwiss. und Weltraumforsch (ZFW) 4, 295–307 (1980)

    Google Scholar 

  35. Hirschel, E.H., Kordulla, W.: Shear Flow in Surface-Oriented Coordinates. NNFM, vol. 4. Vieweg, Braunschweig Wiesbaden (1981)

    Book  Google Scholar 

  36. Schlichting, H., Gersten, K.: Boundary Layer Theory, 8th edn. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  37. Stock, H.-W.: Laminar Boundary Layers on Inclined Ellipsoids of Revolution. Z. Flugwiss. und Weltraumforsch (ZFW) 4, 217–224 (1980)

    Google Scholar 

  38. Hirschel, E.H.: Three-Dimensional Boundary-Layer Calculations in Design Aerodynamics. In: Fernholz, H.H., Krause, E. (eds.) Three-Dimensional Turbulent Boundary Layers. Proc. IUTAM Symp., Germany, pp. 353–365. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  39. Hirschel, E.H.: Basics of Aerothermodynamics, AIAA, Reston, Va. Progress in Astronautics and Aeronautics, vol. 204. Springer, New York (2004)

    Google Scholar 

  40. Cousteix, J.: Analyse théorique et moyens de prévision de la couche limite turbulente tridimensionelle. Doctoral thesis, University of Paris VI, Paris, France (1974); Also: Theoretical Analysis and Prediction Methods for a Three-Dimensional Turbulent Boundary-Layer. ESA TT-238 (1976)

    Google Scholar 

  41. Hirschel, E.H.: Das Verfahren von Cousteix-Aupoix zur Berechnung von turbulenten, dreidimensionalen Grenzschichten. MBB-UFE122-AERO-MT-484, Ottobrunn, Germany (1983)

    Google Scholar 

  42. Kreplin, H.-P., Vollmers, H., Meier, H.U.: Experimental Determination of Wall Shear Stress Vectors on an Inclined Spheroid. In: Proc. DEA-Meeting on Viscous and Interacting Flow-Field Effects, Annapolis MD, USA, pp. 315–332. AFFDL-TR-80-3088 (1980)

    Google Scholar 

  43. Meier, H.U., Kreplin, H.-P.: Experimental Investigation of the Boundary Layer Transition and Separation on a Body of Revolution. Z. Flugwiss. und Weltraumforsch (ZFW) 4, 65–71 (1980)

    Google Scholar 

  44. Meier, H.U., Kreplin, H.-P.: Experimentelle Untersuchung von Ablösephänomenen an einem rotationssymmetrischen Körper. In: DGLR Symposium “Strömungen mit Ablösung”, München, Germany, September 19 & 20. DGLR Reprint 79-071 (1979)

    Google Scholar 

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Hirschel, E.H., Cousteix, J., Kordulla, W. (2014). Topology of Skin-Friction Fields. In: Three-Dimensional Attached Viscous Flow. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41378-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-41378-0_7

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