Flow attachment at flow separation lines

On uniqueness problems between wall-flows and off-wall flow fields
  • U. Dallmann
  • H. Gebing
Part of the Acta Mechanica book series (ACTA MECH.SUPP., volume 4)


Evolving flow structures leave definite but not unique “footprints” of the outer (off-wall, mid-air) flow on the wall. Bifurcating flows, characterized by dynamical systems for the velocity field reveal that two-dimensional separation bubbles together with their three-dimensional bifurcations are “embedded” between fully attaching and completely separating three-dimensional flow structures with a possibility that local flow attachment occurs at a separation line. In this respect we show: 1. An unsteady or steady, incompressible flow field can be completely determined by the knowledge of the wall-shear stress and the wall-pressure field without specifying any outer (farfield) boundary conditions. 2. Nonlinearity or time-dependence or an explicit Reynolds number/viscosity dependence which would reflect properties of the Navier-Stokes equations do not affect the structural changes associated with local flow bifurcations which lead to separation bubbles or near-wake vortex flow separations. Only the continuity equation is fulfilled in every case. Therefore, 3. the question is considered how far away from the bifurcation set of parameters the kinematically possible structures remain structurally stable against Navier-Stokes perturbations. This is studied by direct numerical simulations of the structural changes of separated flows around an ellipsoid at angles of attack. It is shown that flow attachment in a region where a separation line forms is possible in a wide range of angles of attack. The dilemma of defining or locating steady streamwise vortices due to open flow separation is considered.


Direct Numerical Simulation Flow Separation Separation Bubble Separation Line Flow Attachment 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Perry, A. E., Chong, M. S.: A description of eddying motions and flow patterns using critical point concepts. Ann. Rev. Fluid Mech. 19, 125–155 (1987).CrossRefADSGoogle Scholar
  2. [2]
    Chong, M. S., Perry, A. E., Cantwell, B. J.: A general classification of three-dimensional flow fields. In: Topological fluid mechanics. Proc. of the IUTAM Symposium, Cambridge, August 13–18, 1989 (Moffatt, H. K., Tsinober, A. eds.), pp. 408–420. Cambridge: Cambridge University Press 1990.Google Scholar
  3. [3]
    Dallmann, U.: Topological structures of three-dimensional vortex flow separation. AIAA-83–1735 (1983) with further details in: On the formation of three-dimensional vortex flow structures DFVLR-IB 221–85 A13 (1985).Google Scholar
  4. [4]
    Dallmann, U.: Three-dimensional vortex structures and vorticity topology. In: Proc. of the IUTAM Symposium on Fundamental Aspects of Vortex Motion, Tokyo, Japan, 1987 (Hasimoto, H., Kambe, T., eds.), pp. 183–189. Amsterdam: North Holland 1988.Google Scholar
  5. [5]
    Bakker, P. G.: Bifurcations in flow patterns. PhD Thesis, Delft University of Technology 1988.Google Scholar
  6. [6]
    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: Topological Fluid Mechanics, Proc. of the IUTAM Symposium, Cambridge, August 13–18, 1989 (Moffatt, H. K., Tsinober, A. eds.), pp. 384–394. Cambridge: Cambridge University Press 1990.Google Scholar
  7. [7]
    Wang, K. C., Zhou, H. C., Hu, C. H., Harrington, S.: Three-dimensional separated flow structure over prolate spheroids. Proc. R. Soc. London Ser. A 421, 73–90 (1990).ADSGoogle Scholar
  8. [8]
    Dallmann, U., Kordulla, W, Vollmers, H., Schulte-Werning, B.: Analysis of the changing topological structures of three-dimensional separated flows. DLR-IB 221–92 Al2 and in: Physics of separated flows (K. Gersten, ed.), pp. 249–256. Braunschweig/Wiesbaden: Vieweg 1993 (Notes on Numerical Fluid Mechanics, Vol. 40).Google Scholar
  9. [9]
    Dallmann, U., Gebing, H., Vollmers, H.: Unsteady three-dimensional separated flows around a sphere — analysis of vortex chain formation. In: Proc. IUTAM Symposium on Bluff-Body Wakes, Dynamics and Instabilities, 7.-11. Sept. 1992, Göttingen (Eckelmann, H. ed.), pp. 27–30. Berlin Heidelberg New York Tokyo: Springer 1993.Google Scholar
  10. [10]
    Schulte-Werning, B.: Numerische Simulation und topologische Analyse der abgelösten Strömung an einer Kugel. DLR-FB 90–43, 1990 ( Dissertation Univ. München, 1990 ).Google Scholar
  11. [11]
    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 flow structures. AGARD CP 494, 9.1–9. 13 (1991).Google Scholar
  12. [12]
    Herberg, T., Dallmann, U.: Untersuchung des dreidimensionalen Wirbelstärkefeldes und der Entstehung von Wirbeln am Deltaflügel. In: Proc. 8. DGLR-Symposium „Strömungen mit Ablösung“, Köln, 10.-12. Nov. 1992, pp. 139–143. DGLR-Bericht 92–07, Bonn: DGLR 1992.Google Scholar
  13. [13]
    Dallmann, U.: Topological structures of three-dimensional flow separations. DFVLR-IB 221–82 A07 (1982).Google Scholar
  14. [14]
    Vollmers, H., Kreplin, H.-P., Meier, H. U.: Separation and vortical-type flow around a prolate spheroid — evaluation of relevant parameters. AGARD-CP-342, 14.1–14. 14 (1983).Google Scholar
  15. [15]
    Wray, A. A., Hunt, J. C. R.: Algorithms for classification of turbulent structures. In: Topological fluid mechanics, Proc. of the IUTAM Symposium, Cambridge, August 13–18, 1989, (Moffatt, H. K., Tsinober, M. A., eds.), pp. 95–104. Cambridge: Cambridge University Press 1990.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • U. Dallmann
    • 1
  • H. Gebing
    • 1
  1. 1.Institute of Theoretical Fluid MechanicsDLRGöttingenFederal Republic of Germany

Personalised recommendations