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Wake transition in the flow around two circular cylinders in staggered arrangements

  • BRUNO S. CARMO (a1), SPENCER J. SHERWIN (a1), PETER W. BEARMAN (a1) and RICHARD H. J. WILLDEN (a1)

Abstract

The wake transition of the flow around two circular cylinders placed in staggered arrangements with fixed streamwise separation of 5D and cross-stream separation varying from 0 to 3D has been studied. The wake transition is compared to that of a single isolated cylinder. Linear stability analysis utilizing Floquet theory and direct numerical simulations using a spectral/hp element spatial discretization were carried out. The unstable modes that first appear in the wake transition of the flow around a single cylinder, which are the long-spanwise-wavelength mode A and the short-spanwise-wavelength mode B, are also found in the flow around the staggered arrangements. However, a third mode, referred to as mode C, is also present in the wake transition of the flow around staggered arrangements, depending on the relative positioning of the cylinders. This mode has an intermediate spanwise wavelength and period-doubling character. The structure and onset characteristics of mode C are analysed and the nonlinear character of the bifurcation for this mode is investigated.

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Akbari, M. H. & Price, S. J. 2005 Numerical investigation of flow patterns for staggered cylinder pairs in cross-flow. J. Fluids Struct. 20, 533554.
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. & Sorensen, D. 1999 LAPACK Users' Guide, 3rd edn. SIAM.
Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215241.
Blackburn, H. M. & Lopez, J. M. 2003 On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys. Fluids 15, 5760.
Blackburn, H. M., Marques, F. & Lopez, J. M. 2005 Symmetry breaking of two-dimensional time-periodic wakes. J. Fluid Mech. 522, 395411.
Carmo, B. S. 2005 Numerical investigation of the flow around two cylinders in tandem arrangements. Msc dissertation, Escola Politécnica – University of São Paulo, Brazil.
Dušek, J., Le Gal, P. & Fraunié, P. 1994 A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264, 5980.
Gerrard, J. H. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25, 401443.
Golub, G. H. & Van Loan, C. F. 1996 Matrix Computations, 3rd edn. Johns Hopkins University Press.
Henderson, R. D. 1997 Nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65112.
Henderson, R. D. & Barkley, D. 1996 Secondary instability of the wake of a circular cylinder. Phys. Fluids 8, 16831685.
Karniadakis, G. E. 1990 Spectral Element–Fourier methods for incompressible turbulent flows. Comput. Meth. Appl. Mech. Engng 80, 367380.
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414443.
Karniadakis, G. E. & Sherwin, S. J. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press.
Lehoucq, R. B. & Sorensen, D. C. 2000 Implicit restarted Arnoldi method (section 7.6). In Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (ed. Bai, Z., Demmel, J., Dongarra, J., Ruhe, A. & van der Vorst, H.), pp. 166185. SIAM.
Leweke, T. & Williamson, C. H. K. 1998 Three-dimensional instabilities in wake transition. Eur. J. Mech. B/Fluids 17, 571586.
Marques, F., Lopez, J. M. & Blackburn, H. M. 2004 Bifurcations in systems with Z2 spatio-temporal and O(2) spatial symmetry. Physica D 189, 247276.
Mizushima, J. & Suehiro, N. 2005 Instability and transition of flow past two tandem circular cylinders. Phys. Fluids 17, 104107.
Noack, B. R. & Eckelmann, H. 1994 A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297330.
Persillon, H. & Braza, M. 1998 Physical analysis of the tansition to turbulence in the wake of a circular cylinder by three-dimensional navier-stokes simulation. J. Fluid Mech. 365, 2388.
Posdziech, O. & Grundmann, R. 2001 Numerical simulation of the flow around an infinitely long circular cylinder in the transition regime. Theore. Computat. Fluid Dyn. 15, 121141.
Provansal, M., Mathis, C. & Boyer, L. 1987 Bérnard-von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 122.
Robichaux, J., Balachandar, S. & Vanka, S. P. 1999 Three-dimensional Floquet instability of the wake of a square cylinder. Phys. Fluids 11, 560578.
Saad, Y. 1992 Numerical Methods for Large Eigenvalue Problems. Manchester University Press.
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, 147180.
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, 4578.
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2005 a Subharmonic mechanism of the mode C instability. Phys. Fluids 17, 111702.
Sheard, G. J., Thompson, M. C., Hourigan, K. & Leweke, T. 2005 b The evolution of a subharmonic mode in a vortex street. J. Fluid Mech. 534, 2338.
Sumner, D., Price, S. J. & Païdoussis, M. P. 2000 Flow-pattern identification for two staggered circular cylinders in cross-flow. J. Fluid Mech. 411, 263303.
Thompson, M. C., Hourigan, K. & Sheridan, J. 1996 Three-dimensional instabilities in the wake of a circular cylinder. Exp. Therm. Fluid Sci. 12, 190196.
Thompson, M. C., Leweke, T. & Williamson, C. H. K. 2001 The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15, 607616.
Williamson, C. H. K. 1988 The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31, 31653168.
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345407.
Wu, J., Sheridan, J., Welsh, M. C., Hourigan, K. & Thompson, M. C. 1994 Longitudinal vortex structures in a cylinder wake. Phys. Fluids 6, 28832885.
Zdravkovich, M. M. 1972 Smoke observations of wakes of tandem cylinders at low reynolds numbers. Aero. J. 76, 108114.
Zdravkovich, M. M. 1977 Review of flow interference between two circular cylinders in various arrangements. Trans. ASME: J. Fluids Engng 99, 618633.
Zhang, H.-Q., Fey, U., Noack, B. R., König, M. & Eckelmann, H. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779794.
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Wake transition in the flow around two circular cylinders in staggered arrangements

  • BRUNO S. CARMO (a1), SPENCER J. SHERWIN (a1), PETER W. BEARMAN (a1) and RICHARD H. J. WILLDEN (a1)

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