Hostname: page-component-5db6c4db9b-s6gjx Total loading time: 0 Render date: 2023-03-26T21:42:40.081Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

The three-dimensional transition in the flow around a rotating cylinder

Published online by Cambridge University Press:  30 June 2008

Institut de Mécanique des Fluides de Toulouse, CNRS/INPT/UPS UMR 5502, Toulouse, France
Institut de Mécanique des Fluides de Toulouse, CNRS/INPT/UPS UMR 5502, Toulouse, France
Institut de Mécanique des Fluides de Toulouse, CNRS/INPT/UPS UMR 5502, Toulouse, France
Institut de Mécanique des Fluides de Toulouse, CNRS/INPT/UPS UMR 5502, Toulouse, France
Institut de Mécanique des Fluides et des Solides de Strasbourg, CNRS/ULP UMR 7507, Strasbourg, France


The flow around a circular cylinder rotating with a constant angular velocity, placed in a uniform stream, is investigated by means of two- and three-dimensional direct numerical simulations. The successive changes in the flow pattern are studied as a function of the rotation rate. Suppression of vortex shedding occurs as the rotation rate increases (>2). A second kind of instabilty appears for higher rotation speed where a series of counter-clockwise vortices is shed in the upper shear layer. Three-dimensional computations are carried out to analyse the three-dimensional transition under the effect of rotation for low rotation rates. The rotation attenuates the secondary instability and increases the critical Reynolds number for the appearance of this instability. The linear and nonlinear parts of the three-dimensional transition have been quantified by means of the amplitude evolution versus time, using the Landau global oscillator model. Proper orthogonal decomposition of the three-dimensional fields allowed identification of the most energetic modes and three-dimensional flow reconstruction involving a reduced number of modes.

Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



Badr, H. M., Coutanceau, M., Dennis, S. C. R. & Ménard, C. 1990 Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104. J. Fluid Mech. 220, 459484.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539575.CrossRefGoogle Scholar
Braza, M., Chassaing, P. & Ha-Minh, H. 1986 Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 165, 79130.CrossRefGoogle Scholar
Braza, M., Faghani, D. & Persillon, H. 2001 Successive stages and the role of natural vortex dislocations in three-dimensional wake transition. J. Fluid Mech. 439, 141.CrossRefGoogle Scholar
Cliffe, K. A. & Tavener, S. J. 2004 The effect of cylinder rotation and blockage ratio on the onset of the periodic flows. J. Fluid Mech. 501, 125133.CrossRefGoogle Scholar
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of the time-dependent viscous incompressible flow of fluids with free surface. Phys. Fluids 8, 21822189.CrossRefGoogle Scholar
Ingham, D. B. & Tang, T. 1990 A numerical investigation into the steady flow past a rotating circular cylinder at low and intermediate Reynolds numbers. J. Comput. Phys. 87, 91107.CrossRefGoogle Scholar
Jin, G. & Braza, M. 1993 A non-reflecting outlet boundary condition for incompressible unsteady Navier-Stokes calculations. J. Comput. Phys. 107, 239.CrossRefGoogle Scholar
Kang, S., Choi, H. & Lee, S. 1999 Laminar flow past a rotating circular cylinder. Phys. Fluids 11, 33123321.CrossRefGoogle Scholar
Mittal, S. 2004 Three-dimensional instabilities in flow past a rotating cylinder. J. Appl. Mech. 71, 8995.CrossRefGoogle Scholar
Mittal, S. & Kumar, B. 2003 Flow past a rotating cylinder. J. Fluid Mech. 476, 303334.CrossRefGoogle Scholar
Peaceman, D. W. & Rachford, J. R. 1955 The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Maths. 3, 28.CrossRefGoogle Scholar
Persillon, H. & Braza, M. 1998 Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier-Stokes simulation. J. Fluid Mech. 365, 2388.CrossRefGoogle Scholar
Prandtl, L. 1925 Application of the “magnus effect” to the wind propulsion of ships. Die Naturwissenschaft 13, 93108; transl. NACA-TM-367, June 1926.Google Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard-Von Kàrmàn instability: transient and forced regimes. J. Fluid Mech. 182, 122.CrossRefGoogle Scholar
Stojković, D., Breuer, M. & Durst, F. 2002 Effect of high rotation rates on the laminar flow around a circular cylinder. Phys. Fluids 14, 31603178.CrossRefGoogle Scholar
Stojković, D., Schön, P., Breuer, M. & Durst, F. 2003 On the new vortex shedding mode past a rotating circular cylinder. Phys. Fluids 15, 12571260.CrossRefGoogle Scholar
Tokumaru, P. T. & Dimotakis, P. E. 1993 The lift of a cylinder executing rotary motions in a uniform flow. J. Fluid Mech. 255, 110.CrossRefGoogle Scholar
Williamson, C. H. K. 1992 The natural and forced formation of splot-like vortex dislocations in the transition of a wake. J. Fluid Mech. 243, 393441.CrossRefGoogle Scholar