Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T06:21:25.532Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional instability of the flow around a rotating circular cylinder

Published online by Cambridge University Press:  30 July 2013

Jan O. Pralits ,
Flavio Giannetti  and
Luca Brandt
Jan O. Pralits*
Affiliation:
DICCA, University of Genoa, Via Montallegro 1, 16145 Genoa (GE), Italy
Flavio Giannetti
Affiliation:
DIIN, University of Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy
Luca Brandt
Affiliation:
Linné Flow Centre, KTH Mechanics, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: jan.pralits@unige.it
Get access Rights & Permissions [Opens in a new window]

Abstract

The two-dimensional stationary flow past a rotating cylinder is investigated for both two- and three-dimensional perturbations. The instability mechanisms are analysed using linear stability analysis and the complete neutral curve is presented. It is shown that the first bifurcation in the case of the rotating cylinder occurs for stationary three-dimensional perturbations, confirming recent experiments. Interestingly, the critical Reynolds number at high rotation rates is lower than that for the stationary circular cylinder. The spatial characteristics of the disturbance and a qualitative comparison with the results obtained for linear flows suggest that the stationary unstable three-dimensional mode could be of hyperbolic nature.

JFM classification

Wakes/Jets: Vortex streets Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 730 , 10 September 2013 , pp. 5 - 18
Copyright
©2013 Cambridge University Press 

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.)

References

Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.Google Scholar
Barnes, F. H. 2000 Vortex shedding in the wake of a rotating circular cylinder at low Reynolds numbers. J. Phys. D: Appl. Phys. 33, L141–L144.Google Scholar
Caulfield, C. P. & Kerswell, R. R. 2000 The nonlinear development of three-dimensional disturbances at hyperbolic stagnation points: a model of the braid region in mixing layers. Phys. Fluids 12 (5), 1032–1043.Google Scholar
ElAkoury, R., Braza, M., Perrin, R., Harran, G. & Hoarau, Y. 2008 The three-dimensional transition in the flow around a rotating cylinder. J. Fluid Mech. 607, 1–11.Google Scholar
Friedlander, S. & Vishik, M. M. 1991 Instability criteria for the flow of an inviscid incompressible fluid. Phys. Rev. Lett. 66, 2204–2206.Google Scholar
Giannetti, F. & Luchini, P. 2007 Structtural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.Google Scholar
Kang, S., Choi, H. & Lee, S. 1999 Laminar flow past a rotating circular cylinder. Phys. Fluids 11 (11), 3321.Google Scholar
Leblanc, S. & Godeferd, F. S. 1999 An illustration of the link betwen ribs and hyperbolic instability. Phys. Fluids 11 (2), 497–499.Google Scholar
Lifschitz, A. & Hameiri, E. 1991 Local stability conditions in fluid dynamics. Phys. Fluids A 3 (11), 2644–2651.CrossRefGoogle Scholar
Linh, D.T. T. 2011 Flow past a rotating circular cylinder. PhD thesis, Department of Mechanical Engineering, National University of Singapore.Google Scholar
Luchini, P., Giannetti, F. & Pralits, J. O. 2008 Structural sensitivity of linear and nonlinear global modes. In Proceedings of 5th AIAA Theoretical Fluid Mechanics Conference, Seattle, Washington, USA, Paper AIAA-2008-4227.Google Scholar
Mittal, S. 2004 Thee-dimensional instabilities in flow past a rotating cylinder. J. Appl. Mech. 71, 89–95.Google Scholar
Mittal, S. & Kumar, B. 2003 Flow past a rotating cylinder. J. Fluid Mech. 476, 303–334.Google Scholar
Noack, B. R. & Eckelmann, H. 1994 A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297–330.Google Scholar
Pralits, J. O., Brandt, L. & Giannetti, F. 2010 Instability and sensitivity of the flow around a rotating circular cylinder. J. Fluid Mech. 650, 513–536.Google Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.Google Scholar
Rao, A., Leontini, J., Thompson, M. C. & Hourigan, K. 2013 Three-dimensionality in the wake of a rotating cylinder in a uniform flow. J. Fluid Mech. 717, 1–29.Google Scholar
Stojković, D., Breuer, M. & Durst, F. 2002 Effect of high rotation rates on the laminar flow around a circular cylinder. Phys. Fluids 14 (9), 3160–3178.Google Scholar
Stojković, D., Schön, P., Breuer, M. & Durst, F. 2003 On the new vortex sheddng mode past a rotating circular cylinder. Phys. Fluids 15 (5), 1257–1260.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.Google Scholar
Yildirim, I., Rindt, C. C. M., van Steenhoven, A. A., Brandt, L., Pralits, J. O. & Giannetti, F. 2008 Identification of shedding mode ii behind a rotating cylinder. In Seventh European Fluid Mechanics Conference, Manchester, UK. Book of abstracts, p. 371.Google Scholar