Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow

  • E. A. Christensen
  • J. N. Sørensen
  • M. Brøns
  • P. L. Christiansen
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

This presentation introduces a low-dimensional model for an incompressible, viscous, rotating fluid flow in a cylindrical vessel. The low-dimensional model is formed by projecting the transport equations on some subspace, spanned by known solutions to the discretized Navier-Stokes equations. Using the software package PATH, a program that analyses finite non-linear ODE-systems, such as our low-dimensional model, we find the bifurcation path with the Reynolds number as modelparameter. Thus, the transition from a stationary to a periodic solution in physical space is recognized as a super-critical Hopf-bifurcation in low-dimensional space.

Further aspects are to determine the bifurcations in space for all aspect ratios, and even further to give the dynamical concepts of a given fluid flow system.

Keywords

Vortex Soliton Vorticity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. P. Escudier, Observations of the flow produced in a cylindrical container by a rotating endwall, Experiments in Fluids, 2, pp 189–196, 1984 ).CrossRefADSGoogle Scholar
  2. [2]
    M. Brans, Bifurcations and Instabilities in the Greitzer Model for Compressor System Surge, Math. Engng Ind., Vol. 1, No. 1, (1988).Google Scholar
  3. [3]
    O. Daube and J. N. Sorensen, Simulation numerique de l’ecoulement periodique axisymetrique dans une cavite cylindrique, C.R. Acad. Sci. Paris, 308, 2, pp 443–469, (1959).Google Scholar
  4. [4]
    J. N. Sorensen and O. Daube, Direct simulation of flow structures initiated by a rotating cover in a cylindrical vessel, Adv. in Turb., pp 383–390, Springer (1989).Google Scholar
  5. [5]
    J. N. Sorensen Ta Phuoc Loc, High—Order Axisymmetric Navier—Stokes Code Description and Evaluation of Boundary Conditions, Int. J. for Num. Meth. in Fluids, Vol. 9, 1517–1537, (1989).CrossRefADSGoogle Scholar
  6. [6]
    C. K. Petersen, PATH — User’s Guide, Dept. of Applied Math. and Nonlinear Studies, University of Leeds, (1988).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • E. A. Christensen
    • 1
  • J. N. Sørensen
    • 2
  • M. Brøns
    • 3
  • P. L. Christiansen
    • 1
  1. 1.Laboratory of Applied Mathematical PhysicsThe Technical University of DenmarkLyngbyDenmark
  2. 2.Department of Fluid MechanicsThe Technical University of DenmarkLyngbyDenmark
  3. 3.Mathematical InstituteThe Technical University of DenmarkLyngbyDenmark

Personalised recommendations