High-Order Numerical Solutions for Rotating Flows with Walls

  • E. Serre
  • I. Raspo
  • O. Czarny
  • P. Bontoux
  • P. Droll
  • M. Schäfer
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 21)


The study of rotating viscous flows with walls has significant importance for many industrial devices. In this approach subsystems of simple geometry coming from realistic geometries are studied using accurate methods (spectral). The three-dimensional incompressible Navier-Stokes equations are solved using a projection scheme. Depending on the aspect ratio of the cavity and on the Reynolds number, annular and spiral patterns of the generic types I and II boundary layer instabilities as well as vortex breakdown phenomena are investigated. Taylor-Couette flows in a finite-length cavity with counter-rotating walls, are also studied. Two complex regimes of wavy vortex and spirals are emphasized for the first time via direct numerical simulation in this configuration


Direct Numerical Simulation Cylindrical Cavity Vortex Breakdown Ekman Layer Spiral Pattern 
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.
    Owen, J. M., Rogers, R. H. (1989) Heat Transfer in Rotating Disk Systems, Vol. 1: Rotor-Stator Systems. Ed. W. D. Morris (Wiley, Taunton, Somerset, England)Google Scholar
  2. 2.
    Owen, J. M., Rogers, R. H. (1995) Heat Transfer in Rotating Disk Systems, Vol. 2: Rotating Cavities. Ed. W. D. Morris (Wiley, Taunton, Somerset, England)Google Scholar
  3. 3.
    Serre, E., Hugues, S. et al. (2001) Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow, Int. J. Heat Fluid Flows 22/1, 82–93CrossRefGoogle Scholar
  4. 4.
    Serre, E., Crespo del Arco, E., Bontoux, P. (2001) Three-dimensional instabilities in an shrouded rotor-stator system, J. Fluid Mech. 434, 65–100MathSciNetzbMATHCrossRefGoogle Scholar
  5. Czarny, O., Serre, E., Bontoux, P. (in print) Direct numerical simulation and identification of complex flows in Taylor-Couette counter-rotating cavities, C. R. Acad. SciGoogle Scholar
  6. 6.
    Serre, E., Pulicani, J. P. (2001) 3D pseudo-spectral method for convection in rotating cylinder, Int. J. of Computers and Fluids 30/4, 491–519MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gauthier, P., Gondret, P., Rabaud, M. (1999) Axisymmetric propagating vortices in the flow between a stationary and a rotating disk enclosed by a cylinder. J. Fluid Mech., 386, 105–127MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Savas, O. (1987) Stability of Bödewadt Fow. J. Fluid Mech. 183, 77–94CrossRefGoogle Scholar
  9. 9.
    Caldwell, D. R., Van Atta, C. W. (1970) Characteristics of Ekman boundary layer instabilities. J. Fluid Mech. 44, 79–95CrossRefGoogle Scholar
  10. 10.
    Faller, A. J. (1991) Instability and transition of the disturbed flow over a rotating disc. J. Fluid Mech. 230, 245–269zbMATHCrossRefGoogle Scholar
  11. 11.
    Andereck, C.D., Liu, S.S., Swinney, H.L. (1986) Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183CrossRefGoogle Scholar
  12. 12.
    Schröder, W., Keller H.B. (1990) Wavy Taylor-Vortex flows via multigridcontinuation methods. J. Comput. Phys. 91, 197–227MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Neitzel, G.P. (1984) Numerical computation of time-dependent Taylor-Vortex flows in finite-length geometries. J. Fluid Mech. 141, 51–66zbMATHCrossRefGoogle Scholar
  14. 14.
    Escudier, M.P. (1984) Observations of the flow produced in a cylindrical container by a rotating end wall, Exps. In Fluids 2, 179–186Google Scholar
  15. 15.
    Blackburn, H. M., Lopez, J. M. (2000) Symmetry breaking of the flow in a cylinder by a rotating end wall, Phys. of Fluids 12, 2698–2701CrossRefGoogle Scholar
  16. 16.
    Pereira, J. C. F., Sousa, J. M. M. (1999) Confined vortex breakdown generated by a rotating cone, J. Fluid Mech. 385, 287–323MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • E. Serre
    • 1
  • I. Raspo
    • 1
  • O. Czarny
    • 1
  • P. Bontoux
    • 1
  • P. Droll
    • 2
  • M. Schäfer
    • 2
  1. 1.L3m FRE 2405 CNRSTechnopole de Chateau-GombertMarseilleFrance
  2. 2.Dept. of Numerical Method inMechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany

Personalised recommendations