Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-10T05:46:50.595Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics

Published online by Cambridge University Press:  10 May 2019

G. Agbaglah Open the ORCID record for G. Agbaglah [Opens in a new window]  and
C. Mavriplis Open the ORCID record for C. Mavriplis [Opens in a new window]
G. Agbaglah*
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada
C. Mavriplis
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow in the near wake of a square cylinder at Reynolds numbers of 205 and 225, corresponding to three-dimensional wake instability modes $A$ and $B$, respectively, and that of the square’s circumscribed circular cylinder are examined by using three-dimensional Navier–Stokes numerical simulations. At small times, prior to the streamwise vortex shedding, a self-similar velocity is observed in the wake and no significant difference is observed in the dynamics of the flows past the square and the circular cylinders. The exponential growth of the three-dimensional instability reaches a saturation regime during this early time for the considered Reynolds numbers. Vortical structures in the wake at long times and shedding frequencies are very close for the square and the circular cylinders. The flow separation on the forward top and bottom corners of the square cylinder have the effect of increasing its effective width, making it comparable with the diameter of the circumscribed circular cylinder. Thus, Floquet multipliers and modes of the associated three-dimensional instabilities are shown to be very close for the two cylinders when using the circumscribed circular cylinder as the basis for a characteristic length scale. Most importantly, the wavenumber with the maximum growth rate, for modes $A$ and $B$, is approximately identical for the two cylinders.

JFM classification

Instability: Nonlinear instability Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 419 - 432
Copyright
© 2019 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

Agbaglah, G., Chiodi, R. & Desjardins, O. 2017 Numerical simulation of the initial destabilization of an air-blasted liquid layer. J. Fluid Mech. 812, 1024–1038.Google Scholar
Agbaglah, G. & Mavriplis, C. 2017 Computational analysis of physical mechanisms at the onset of three-dimensionality in the wake of a square cylinder. J. Fluid Mech. 833, 631–647.Google Scholar
Barkley, D. 2005 Confined three-dimensional stability analysis of the cylinder wake. Phys. Rev. E 71, 017301.Google Scholar
Barkley, D. & Henderson, R. D. 1996 Three dimensional Floquet stability analysis of the wake of circular cylinder. J. Fluid Mech. 322, 215–241.Google Scholar
Blackburn, H. M. & Lopez, J. M. 2003 On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys. Fluids 15, L57–L60.Google Scholar
Blackburn, H. M., Marques, F. & Lopez, J. M. 2005 Symmetry breaking of two-dimensional time-periodic wakes. J. Fluid Mech. 522, 395–411.Google Scholar
Brede, M., Eckelmann, H. & Rockwell, D. 1996 On secondary vortices in the cylinder wake. Phys. Fluids A 8 (8), 2117–2124.Google Scholar
Breuer, M., Bernsdorf, J., Zeiser, T. & Durst, F. 2000 Accurate computations of the laminar flow past a square cylinder based on two different methods: Lattice Boltzmann and finite-volume. Intl J. Heat Fluid Flow 21, 186–196.Google Scholar
Davis, R. W., Moore, E. F. & Purtell, L. P. 1984 A numerical – experimental study of confined flow around rectangular cylinders. Phys. Fluids 27, 46–59.Google Scholar
Fischer, P. F. 1997 An overlapping Schwarz method for spectral element solution of the incompressible Navier–Stokes equations. J. Comput. Phys. 133, 84–101.Google Scholar
Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G.2008 NEK5000: open source spectral element CFD solver, Version 17.0, Argonne National Laboratory, Illinois. Available at: https://nek5000.mcs.anl.gov.Google Scholar
Giannetti, F., Camarri, S. & Luchini, P. 2010 Structural sensitivity of the secondary instability in the wake of a circular cylinder. J. Fluid Mech. 651, 319–337.Google Scholar
Henderson, R. D. 1997 Nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65–112.Google Scholar
Luo, S. C., Tong, X. H. & Khoo, B. C. 2007 Transition phenomena in the wake of a square cylinder. J. Fluids Struct. 23, 227–248.Google Scholar
Ng, Z. Y., Vo, T. & Sheard, G. J. 2018 Stability of the wakes of cylinders with triangular cross-sections. J. Fluid Mech. 844, 721–745.Google Scholar
Ozgoren, M. 2006 Flow structure in the downstream of square and circular cylinders. Flow Meas. Instrum. 17 (4), 225–235.Google Scholar
Robichaux, J., Balachandar, S. & Vanka, S. P. 1999 Three-dimensional Floquet instability of the wake of square cylinder. Phys. Fluids 11 (3), 560–578.Google Scholar
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng Ind. Aerodyn. 49, 79–100.Google Scholar
Saha, A. K., Biswas, G. & Muralidhar, K. 2003 Three-dimensional study of flow past a square cylinder at low Reynolds numbers. Intl J. Heat Fluid Flow 24, 54–56.Google Scholar
Sheard, G. J. 2011 Wake stability features behind a square cylinder: Focus on small incidence angles. J. Fluids Struct. 27, 734–742.Google Scholar
Sheard, G. J., Fitzgerald, M. J. & Ryan, K. 2009 Cylinders with square cross-section: wake instabilities with incidence angle variation. J. Fluid Mech. 630, 34–69.Google Scholar
Sheard, G. J., Hourigan, K. & Thompson, M. C. 2005 Computations of the drag coefficients for low-Reynolds-number flow past rings. J. Fluid Mech. 526, 257–275.Google Scholar
Sohankar, A., Norberg, C. & Davidson, L. 1999 Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. Phys. Fluids 11, 288–306.Google Scholar
Williamson, C. H. K. 1988 The existence of two stages in the transition to three dimensionality of a cylinder wake. Phys. Fluids 31, 3165–3168.Google Scholar
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.Google Scholar