Advertisement

Spherical Couette flow with superimposed throughflow

  • Karl Bühler
Conference paper
  • 603 Downloads
Part of the Lecture Notes in Physics book series (LNP, volume 549)

Abstract

This work deals with the generalization of the spherical Couette flow from a closed flow into an open flow system. A superimposed throughflow in meridional direction leads to novel flow structures and stability behaviour. A analytical solution for the superposition of the spherical Couette and the source-sink flow is given for the creeping flow. Numerical simulations for steady and time-dependent rotationally symmetric solutions are presented for a large Reynolds number range. These solutions represents the non-uniqueness of the supercritical spherical Couette flows. Their symmetry with respect to the equator and time-behaviour depends strongly on the throughflow Reynolds number. The experiments show the rich variety of supercritical solutions depending on the rotation and throughflow parameters. Rotationally symmetric vortices and spiral vortices are realized in steady and time-dependent form. For the pure source-sink flow the instabilities are formed like banana shaped structures. The existence regions and transitions between the different modes of flow are presented in maps. For the rotationally symmetric states there is a good agreement between theory and experiments.

Keywords

Reynolds Number Meridional Plane Meridional Direction Taylor Number Taylor Vortex 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. Sawatzki, J. Zierep: Das Stromfeld im Spalt zwischen zwei konzentrischen Kugelflächen, von denen die innere rotiert. Acta Mechanica 9, pp.13–35(1970)CrossRefGoogle Scholar
  2. 2.
    M. Wimmer: Experiments on a viscous fluid flow between concentric rotating spheres, J. Fluid Mech. 78, pp. 317–335(1976)CrossRefADSGoogle Scholar
  3. 3.
    I.M. Yavorskaya, N.M. Astav'eva: Numerical analysis of the stability and nonuniqueness of spherical Couette flow. Notes on Num. Fluid Mech. 2, pp.305–315 (1980)Google Scholar
  4. 4.
    F. Bartels: Taylor vortices between two concentric rotating spheres. J.Fluid Mech. 119, pp.287–303 (1982)CrossRefGoogle Scholar
  5. 5.
    P.S. Marcus, L. Tuckerman: Simulation of flow between concentric rotating spheres, Part 1 and Part 2, J. Fluid Mech. 185, pp. 1–65 (1987)zbMATHCrossRefADSGoogle Scholar
  6. 6.
    J. Zierep: Special solutions of the Navier-Stokes equations in the case of spherical geometry. Rev.Roum. Math., TOME XXVII, 3, pp.423–428 (1982)MathSciNetGoogle Scholar
  7. 7.
    K. Bühler: Strömungsmechanische Instabilitäten zäher Medien im Kugelspalt. Fortschritt-Ber. VDI, Reihe 7 Nr.96 Düsseldorf 1985Google Scholar
  8. 8.
    K. Bühler: Symmetric and asymmetric Taylor vortex flow in spherical gaps. Acta Mechanica 81, pp.3–38 (1990)CrossRefMathSciNetGoogle Scholar
  9. 9.
    C. Egbers: Zur Stabilität der Strömung im konzentrischen Kugelspalt. Dissertation Universität Bremen (1994)Google Scholar
  10. 10.
    K. Bühler, J. Zierep: Dynamical instabilities and transition to turbulence in spherical gap flows. Advances in Turbulence, Ed.:G. Comte-Bellot and J. Mathieu, Springer Berlin pp.16–26 (1987)Google Scholar
  11. 11.
    C. Egbers, H.J. Rath: Routes to chaos in rotating fluid flows. Advances in Fluid Mechanics and Turbomachinery, Springer pp.147–168 (1998)Google Scholar
  12. 12.
    K. Nakabayashi: Transition of Taylor-Görtler vortex flow in spherical Couette flow. J. Fluid Mech. 132, pp.209–230 (1983)CrossRefADSGoogle Scholar
  13. 13.
    K. Bühler, N. Polifke: Dynamical behaviour of Taylor vortices with superimposed axial flow. Proc. Nato-Workshop Streitberg, ed. Busse & Kramer, Plenum Press pp. 21–29 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Karl Bühler
    • 1
  1. 1.University of Applied ScienceOffenburgGermany

Personalised recommendations