Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T13:02:53.543Z Has data issue: false hasContentIssue false
  • English
  • Français

Modification of three-dimensional transition in the wake of a rotationally oscillating cylinder

Published online by Cambridge University Press:  24 December 2009

DAVID LO JACONO ,
JUSTIN S. LEONTINI ,
MARK C. THOMPSON  and
JOHN SHERIDAN
DAVID LO JACONO*
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France CNRS; IMFT; F-31400 Toulouse, France Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
JUSTIN S. LEONTINI
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
MARK C. THOMPSON
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
JOHN SHERIDAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A study of the flow past an oscillatory rotating cylinder has been conducted, where the frequency of oscillation has been matched to the natural frequency of the vortex street generated in the wake of a stationary cylinder, at Reynolds number 300. The focus is on the wake transition to three-dimensional flow and, in particular, the changes induced in this transition by the addition of the oscillatory rotation. Using Floquet stability analysis, it is found that the fine-scale three-dimensional mode that typically dominates the wake at a Reynolds number beyond that at the second transition to three-dimensional flow (referred to as mode B) is suppressed for amplitudes of rotation beyond a critical amplitude, in agreement with past studies. However, the rotation does not suppress the development of three-dimensionality completely, as other modes are discovered that would lead to three-dimensional flow. In particular, the longer-wavelength mode that leads the three-dimensional transition in the wake of a stationary cylinder (referred to as mode A) is left essentially unaffected at low amplitudes of rotation. At higher amplitudes of oscillation, mode A is also suppressed as the two-dimensional near wake changes in character from a single- to a double-row wake; however, another mode is predicted to render the flow three-dimensional, dubbed mode D (for double row). This mode has the same spatio-temporal symmetries as mode A.

JFM classification

Instability: Instability Flow Control: Instability control Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 349 - 362
Copyright
Copyright © Cambridge University Press 2009

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

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.CrossRefGoogle Scholar
Barkley, D., Tuckerman, L. S. & Golubitsky, M. 2000 Bifurcation theory for three-dimensional flow in the wake of a circular cylinder. Phys. Rev. E 61 (5), 5247–5252.CrossRefGoogle ScholarPubMed
Blackburn, H. M. & Lopez, J. M. 2003 On three-dimensional quasi-periodic Floquet instabilities of two-dimensional bluff body wakes. Phys. Fluids 15 (8), L57–L60.CrossRefGoogle Scholar
Blackburn, H. M., Marques, F. & Lopez, J. M. 2005 Symmetry breaking of two-dimensional time-periodic wakes. J. Fluid Mech. 522, 395–411.CrossRefGoogle Scholar
Canuto, C., Hussaini, M., Quarteroni, A. & Zang, T. 1990 Spectral Methods in Fluid Dynamics, 2nd edn. Springer.Google Scholar
Henderson, R. D. 1997 Nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65–112.CrossRefGoogle Scholar
Johnson, S. A., Thompson, M. C. & Hourigan, K. 2004 Predicted low frequency structures in the wake of elliptical cylinders. Eur. J. Mech. B/Fluids 23 (1), 229–239.CrossRefGoogle Scholar
Julien, S., Lasheras, J. C. & Chomaz, J.-M. 2003 Three-dimensional instability and vorticity patterns in the wake of a flat plate. J. Fluid Mech. 479, 155–189.CrossRefGoogle Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods of the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.CrossRefGoogle Scholar
Karniadakis, G. E. & Sherwin, S. J. 2005 Spectral/hp Methods for Computational Fluid Dynamics. Oxford University Press.CrossRefGoogle Scholar
Karniadakis, G. E. & Triantafyllou, G. S. 1992 Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. J. Fluid Mech. 238, 1–30.CrossRefGoogle Scholar
Landman, M. J. & Saffman, P. G. 1987 The three-dimensional instability of strained vortices in a viscous fluid. Phys. Fluids 30, 2339–2342.CrossRefGoogle Scholar
Leontini, J. S., Stewart, B. E., Thompson, M. C. & Hourigan, K. 2006 Wake state and energy transitions of an oscillating cylinder at low Reynolds number. Phys. Fluids 18, 067101.CrossRefGoogle Scholar
Leontini, J. S., Thompson, M. C. & Hourigan, K. 2007 Three-dimensional transition in the wake of a transversely oscillating cylinder. J. Fluid Mech. 577, 79–104.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 1998 a Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85–119.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 1998 b Three-dimensional instabilities in wake transition. Eur. J. Mech. B/Fluids 17, 571–586.CrossRefGoogle Scholar
Marques, F., Lopez, J. M. & Blackburn, H. M. 2004 Bifurcations in systems with Z 2 spatio-temporal and O(2) spatial symmetry. Physica D 189, 247–276.CrossRefGoogle Scholar
Poncet, P. 2002 Vanishing of mode B in the wake behind a rotationally oscillating circular cylinder. Phys. Fluids 16, 2021–2023.CrossRefGoogle Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.CrossRefGoogle Scholar
Ryan, K., Thompson, M. C. & Hourigan, K. 2005 Three-dimensional transition in the wake of bluff elongated cylinders. J. Fluid Mech. 538, 1–29.CrossRefGoogle Scholar
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2003 a A coupled Landau model describing the Strouhal–Reynolds number profile of the three-dimensional wake of a circular cylinder. Phys. Fluids 15, L68–L71.CrossRefGoogle Scholar
Sheard, G., Thompson, M. C. & Hourigan, K 2003 b From spheres to circular cylinders: the stability and flow structures of bluff ring wakes. J. Fluid Mech. 492, 147–180.CrossRefGoogle Scholar
Thiria, B., Goujon-Durand, S. & Wesfreid, J. E. 2006 Wake of a cylinder performing rotary oscillations. J. Fluid Mech. 560, 123–147.CrossRefGoogle Scholar
Thiria, B. & Wesfreid, J. E. 2007 Stability properties of forced wakes. J. Fluid Mech. 579, 137–161.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K., Cheung, A. & Leweke, T. 2006 a Hydrodynamics of a particle impact on a wall. Appl. Math. Modelling 30 (11), 1356–1369.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K., Ryan, K. & Sheard, G. J. 2006 b Wake transition of two-dimensional cylinders and axisymmetric bluff bodies. J. Fluids Struct. 22 (6), 793–806.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K. & Sheridan, J. 1996 Three-dimensional instabilities in the wake of a circular cylinder. Exp. Therm. Fluid Sci. 12, 190–196.CrossRefGoogle Scholar
Thompson, M. C., Leweke, T. & Williamson, C. H. K. 2001 The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15, 607–616.CrossRefGoogle Scholar
Williamson, C. H. K. 1988 The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31 (11), 3165–3168.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Williamson, C. H. K. & Brown, G. L. 1998 A series in 1(Re) to represent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12, 1073–1085.CrossRefGoogle Scholar
Williamson, C. H. K. & Prasad, A. 1993 A new mechanism for oblique wave resonance in the natural far wake. J. Fluid Mech. 256, 269–313.CrossRefGoogle Scholar
Wu, J., Sheridan, J., Welsh, M. C. & Hourigan, K. 1996 Three-dimensional vortex structures in a cylinder wake. J. Fluid Mech. 312, 201–222.CrossRefGoogle Scholar