Hostname: page-component-f554764f5-sl7kg Total loading time: 0 Render date: 2025-04-10T20:52:35.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Cylinders with square cross-section: wake instabilities with incidence angle variation

Published online by Cambridge University Press:  10 July 2009

GREGORY J. SHEARD ,
MATTHEW J. FITZGERALD  and
KRIS RYAN
GREGORY J. SHEARD*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
MATTHEW J. FITZGERALD
Affiliation:
AMOG Consulting, Sea Technology House, 19 Business Park Drive, Monash Business Park, Notting Hill, VIC 3168, Australia
KRIS RYAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The wakes behind square cylinders with variation in incidence angle are computed over a range of Reynolds numbers to elucidate the three-dimensional stability and dynamics up to a Reynolds number of Re = 300, based on the projected height of the inclined square cylinder. Three-dimensional instability modes are predicted and computed using a linear stability analysis technique and three-dimensional simulations, respectively. Depending on the incidence angle, the flow is found to transition to three-dimensional flow through either a mode A instability, or a subharmonic mode C instability. The mode A instability is predicted as the first-occurring instability at incidence angles smaller than 12° and greater than 26°, with the mode C instability predicted between these incidence angles. At a zero-degree angle of incidence, the wake instabilities closely match modes A, B and a quasi-periodic mode predicted in earlier studies behind square and circular cylinders. With increasing angle of incidence, the three-dimensional wake transition Reynolds number first increases from Re = 164 as the mode A instability weakens, before decreasing again beyond an incidence angle of 12° as the wake becomes increasingly unstable to the mode C instability, and then again to the mode A instability as the incidence angle approaches 45°. A spanwise autocorrelation analysis from computations over a cylinder span 20 times the square cross-section side length reveals that beyond the onset of three-dimensional instabilities, the vortex street breaks down with patterns consistent with spatio-temporal chaos. This effect was more pronounced at higher incidence angles.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 630 , 10 July 2009 , pp. 43 - 69
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.)

Article purchase

Temporarily unavailable

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
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. & Sherwin, S. J. 2004 Formulation of a Galerkin spectral element-Fourier method for three-dimensional incompressible flow in cylindrical geometries. J. Comput. Phys. 197, 759–778.CrossRefGoogle Scholar
Carmo, B. S., Sherwin, S. J., Bearman, P. W. & Willden, R. H. J. 2008 Wake transition in the flow around two circular cylinders in staggered arrangements. J. Fluid Mech. 597, 1–29.CrossRefGoogle Scholar
Dutta, S., Panigrahi, P. K. & Muralidhar, K. 2008 Experimental investigation of flow past a square cylinder at an angle of incidence. J. Engng Mech.-ASCE 134 (9), 788–803.CrossRefGoogle Scholar
Henderson, R. D. 1997 nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65–112.CrossRefGoogle Scholar
Henderson, R. D. & Barkley, D. 1996 Secondary instability in the wake of a circular cylinder. Phys. Fluids 8, 1683–1685.CrossRefGoogle Scholar
Inoue, O. & Yamazaki, T. 1999 Secondary vortex streets in two-dimensional cylinder wakes. Fluid Dyn. Res. 25 (1), 1–18.CrossRefGoogle Scholar
Karasudani, T. & Funakoshi, M. 1994 Evolution of a vortex street in the far wake of a circular cylinder. Fluid Dyn. Res. 14 (6), 331–352.CrossRefGoogle Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.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
Landau, L. D. & Lifshitz, E. M. 1976 Mechanics. Third Edition. Pergamon Press.Google Scholar
Lehoucq, R. B., Sorenson, D. C. & Yang, C. 1998 ARPACK Users' Guide. SIAM.CrossRefGoogle Scholar
Leweke, T. & Provansal, M. 1994 Model for the transition in bluff body wakes. Phys. Rev. Lett. 72 (20), 3174–3177.CrossRefGoogle ScholarPubMed
Leweke, T. & Provansal, M. 1995 The flow behind rings: bluff body wakes without end effects. J. Fluid Mech. 288, 265–310.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85–119.CrossRefGoogle Scholar
Luo, S. C., Chew, Y. T. & Ng, Y. T. 2003 Characteristics of square cylinder wake transition flows. Phys. Fluids 15 (9), 2549–2559.CrossRefGoogle 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.CrossRefGoogle Scholar
Mansy, H., Yang, P.-M. & Williams, D. R. 1994 Quantitative measurements of three-dimensional structures in the wake of a circular cylinder. J. Fluid Mech. 270, 277–296.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 (3/4), 247–276.Google Scholar
Mittal, R. & Balachandar, S. 1996 Direct numerical simulation of flow past elliptic cylinders. J. Comput. Phys. 124, 351–367.CrossRefGoogle Scholar
Ranjan, R., Dalal, A. & Biswas, G. 2008 A numerical study of fluid flow and heat transfer around a square cylinder at incidence using unstructured grids. Numer. Heat Transfer A-Appl. 54 (9), 890–913.CrossRefGoogle Scholar
Robichaux, J., Balachandar, S. & Vanka, S. P. 1999 Three-dimensional Floquet instability of the wake of a square cylinder. Phys. Fluids 11 (3), 560–578.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
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, 54–66.CrossRefGoogle Scholar
Sheard, G. J. 2009 Cylinders with elliptical cross-section: wake stability with variation in angle of incidence. In IUTAM Symposium on Unsteady Separated Flows and their Control (ed. Braza, M. & Hourigan, K.), Proceedings of the IUTAM Symposium “Unsteady Separated Flows and their Control”, Corfu, Greece, 18–22 June 2007, IUTAM Bookseries. Vol. 14, ISBN: 978-1-4020-9897-0.Google Scholar
Sheard, G. J., Leweke, T., Thompson, M. C. & Hourigan, K. 2007 Flow around an impulsively arrested circular cylinder. Phys. Fluids 19 (8), 083601.CrossRefGoogle Scholar
Sheard, G. J. & Ryan, K. 2007 Pressure-driven flow past spheres moving in a circular tube. J. Fluid Mech. 592, 233–262.CrossRefGoogle Scholar
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2003 From spheres to circular cylinders: the stability and flow structures of bluff ring wakes. J. Fluid Mech. 492, 147–180.CrossRefGoogle Scholar
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2004 From spheres to circular cylinders: non-axisymmetric transitions in the flow past rings. J. Fluid Mech. 506, 45–78.CrossRefGoogle Scholar
Sheard, G. J., Thompson, M. C., Hourigan, K. & Leweke, T. 2005 The evolution of a subharmonic mode in a vortex street. J. Fluid Mech. 534, 23–38.CrossRefGoogle Scholar
Shraiman, B. I., Pumir, A., van Saarloos, W., Hohenberg, P. C. & Chaté, H. 1992 Spatiotemporal chaos in the one-dimensional complex Ginzburg–Landau equation. Physica D 57 (3–4), 241–248.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 (2), 288–306.CrossRefGoogle Scholar
Taneda, S. 1959 Downstream development of wakes behind cylinders. J. Phys. Soc. Jpn 14 (6), 843–848.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. & Provansal, M. 2001 a Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15, 575–585.CrossRefGoogle Scholar
Thompson, M. C., Leweke, T. & Williamson, C. H. K. 2001 b The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15, 607–616.CrossRefGoogle Scholar
Tong, X. H., Luo, S. C. & Khoo, B. C. 2008 Transition phenomena in the wake of an inclined square cylinder. J. Fluids Struct. 24 (7), 994–1005.CrossRefGoogle Scholar
Williamson, C. H. K. 1988 a Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids 31, 2742–2744.CrossRefGoogle Scholar
Williamson, C. H. K. 1988 b The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31, 3165–3168.CrossRefGoogle Scholar
Williamson, C. H. K. 1992 The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393–441.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Williamson, C. H. K. & Prasad, A. 1993 Wave interactions in the far wake of a body. Phys. Fluids A-Fluid Dyn. 5 (7), 1854–1856.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
Zhang, H., Noack, B. R., König, M. & Eckelmann, H. 1995 On the transition of the circular cylinder wake. Phys. Fluids 7 (4), 779–793.CrossRefGoogle Scholar