Three-Dimensional Numerical Simulation of Laminar Turbulent Transition and its Control by Periodic Disturbances

  • L. Kleiser
  • E. Laurien
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

The laminar-turbulent transition process in plane Poiseuille flow is simulated by numerical integration of the three-dimensional time-dependent Navier-Stokes equations using a spectral method. The classical peak-valley splitting mode of secondary instability is considered. Detailed comparison with experiments has demonstrated very satisfactory agreement up to the 1-spike stage. Visualizations of the development of three-dimensional flow structures are presented including timelines of fluid markers. It is found that the A vortex structure appearing in flow visualizations does not consist of a vortex tube as the usual interpretation of the vortex loop concept suggests. A numerical study of transition control by superposition of purely two-dimensional waves shows that efficient control is possible at an early stage of the transition process but fails once significant three-dimensional disturbances are present.

Keywords

Vortex Milling Vorticity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    S.A. Orszag, A.T. Patera, JFM 128 (1983) 347–385CrossRefMATHADSGoogle Scholar
  2. [2]
    Th. Herbert, AIAA paper 83–1759 (1983) and AIAA paper 84–0009 (1984)Google Scholar
  3. [3]
    Th. Herbert, Secondary instability of shear flows, in AGARD Report No. 709 (1984)Google Scholar
  4. [4]
    W.S. Saric, V.V. Kozlov, V.Ya. Levchenko, AIAA paper 84–0007 (1984)Google Scholar
  5. [5]
    M. Nishioka, M. Asai, S. Iida, Proc. IUTAM Symposium on Laminar-Turbulent Transition, Stuttgart, 1979 (Springer Verlag, 1980 ) 37–46Google Scholar
  6. [6]
    M. Nishioka, M. Asai, Proc. IUTAM Symposium on Turbulence and Chaotic Phenomena, Kyoto, 1983Google Scholar
  7. [7]
    V.V. Kozlov, M.P. Ramasanov, Fluid Dynamics 18 (1983) 30–33CrossRefADSGoogle Scholar
  8. [8]
    Th. Herbert, Fluid Dyn. Trans. 11 (1983) 77–126Google Scholar
  9. [9]
    L. Kleiser, Numerische Simulationen zum laminar-turbulenten UmschlagsprozeD der ebenen Poiseuille-Strömung. Dissertation, Karlsruhe, 1982 (Report KfK 3271, Kernforschungszentrum Karlsruhe)Google Scholar
  10. [10]
    L. Kleiser, Springer Lecture Notes in Physics 170 (1982) 280–285CrossRefADSGoogle Scholar
  11. [11]
    L. Kleiser, U. Schumann, in R.G. Voigt et al. (ed.), Spectral Methods for Partial Differential Equations, SIAM, Philadelphia 1984, 141–163Google Scholar
  12. [12]
    L. Kleiser, in H.L. Jordan. (ed.), Nonlinear Dynamics in Trans-critical Flows, Springer Lecture Notes in Engineering, to appearGoogle Scholar
  13. [13]
    A. Wray, M.Y. Hussaini, AIAA paper 80–0275 (1980)Google Scholar
  14. [14]
    F.R. Hama, Phys. Fluids 5 (1962) 644–650CrossRefMATHADSGoogle Scholar
  15. [15]
    F.X. Wortmann, Springer Lecture Notes in Physics 148 (1981) 268–279CrossRefADSGoogle Scholar
  16. [16]
    D.R. Williams, H. Fasel, F.K. Hama, to appear in JFMGoogle Scholar
  17. [17]
    R.W. Milling, Phys. Fluids 24 (1981) 979–981CrossRefADSGoogle Scholar
  18. [18]
    H.W. Liepmann, D.M. Nosenchuck, JFM 118 (1982) 201–204CrossRefADSGoogle Scholar
  19. [19]
    A.S.W. Thomas, JFM 137 (1983) 233–250CrossRefADSGoogle Scholar
  20. [20]
    E. Laurien, L. Kleiser, to appear in ZAMMGoogle Scholar

Copyright information

© Springer-Verlag, Berlin, Heidelberg 1985

Authors and Affiliations

  • L. Kleiser
    • 1
  • E. Laurien
    • 1
  1. 1.Institute for Theoretical Fluid MechanicsDFVLRGöttingenGermany

Personalised recommendations