Hostname: page-component-7bb8b95d7b-2h6rp Total loading time: 0 Render date: 2024-09-13T03:59:00.480Z Has data issue: false hasContentIssue false
  • English
  • Français

Amplification of three-dimensional perturbations during parallel vortex–cylinder interaction

Published online by Cambridge University Press:  05 February 2007

X. LIU  and
J. S. MARSHALL
X. LIU
Affiliation:
Department of Mechanical and Industrial Engineering, and IIHR – Hydroscience and Engineering, The University of Iowa, Iowa City, IA 52242, USA
J. S. MARSHALL
Affiliation:
School of Engineering, The University of Vermont, Burlington, VT 05405, USAjeffm@cems.uvm.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A computational study has been performed to examine the amplification of three-dimensional flow features as a vortex with small-amplitude helical perturbations impinges on a circular cylinder whose axis is parallel to the nominal vortex axis. For sufficiently weak vortices with sufficiently small core radius in an inviscid flow, three-dimensional perturbations on the vortex core are indefinitely amplified as the vortex wraps around the cylinder front surface. The paper focuses on the effect of viscosity in regulating amplification of three-dimensional disturbances and on assessing the ability of two-dimensional computations to accurately model parallel vortex–cylinder interaction problems. The computations are performed using a multi-block structured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is examined using a proper-orthogonal decomposition of the Fourier-transformed vorticity field in the azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical vortex waves and for three different Reynolds numbers.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 457 - 478
Copyright
Copyright © Cambridge University Press 2007

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
Brika, D. & Laneville, A. 1997 Wake interference between two circular cylinders. J. Wind Engng Ind. Aerodyn. 72, 61–70.CrossRefGoogle Scholar
Britter, R. E., Hunt, J. C. R. & Mumford, J. C. 1979 The distortion of turbulence by a circular cylinder. J. Fluid Mech. 92, 269–301.CrossRefGoogle Scholar
Fleischmann, S. T. & Sallet, D. W. 1981 Vortex shedding from cylinders and the resulting unsteady forces and flow phenomenon. Part I. Shock Vib. Digest 13 (10), 9–22.Google Scholar
Gamard, S., George, W. K., Jung, D. & Woodward, S. 2002 Application of a ‘slice’ proper orthogonal decomposition to the far field of an axisymmetric turbulent jet. Phys. Fluids 14, 2515–2522.Google Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Hunt, J. C. R. 1973 A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61, 625–706.CrossRefGoogle Scholar
Issa, R. 1985 Solution of the implicit discretized fluid flow equations by operator splitting. J. Comput. Phys. 62, 40–65.Google Scholar
Kiya, M., Arie, M., Tamura, H. & Mori, H. 1980 Vortex shedding from two circular cylinders in staggered arrangement. Trans. ASME: J. Fluids Engng 102, 166–173.Google Scholar
Lai, Y. G. 2000 Unstructured grid arbitrarily shaped element method for fluid flow simulation. AIAA J. 38, 2246–2252.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
Li, J., Chambarel, A., Donneaud, M. & Martin, R. 1991 Numerical study of laminar flow past one and two circular cylinders. Computers Fluids 19 (2), 155–170.CrossRefGoogle Scholar
Mittal, S., Kumar, V. & Raghuvanshi, A. 1997 Unsteady incompressible flows past two cylinders in tandem and staggered arrangements. Intl J. Numer. Meth. Fluids 25, 1315–1344.3.0.CO;2-P>CrossRefGoogle Scholar
Moore, D. W. & Saffman, P. G. 1975 The instability of a straight vortex filament in a strain field. Proc. R. Soc. Lond. A 346, 413–425.Google Scholar
Ramberg, S. 1983 The effects of yaw and finite length upon the vortex wakes of stationary and vibrating circular cylinders. J. Fluid Mech. 128, 81–107.CrossRefGoogle Scholar
Rockwell, D. 1998 Vortex-body interactions. Ann. Rev. Fluid Mech. 30, 199–229.Google Scholar
Sun, J., Li, J. & Roux, B. 1993 Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake. Intl J. Numer. Meth. Fluids 16, 915–929.Google Scholar
Thakur, A., Liu, X. & Marshall, J. S. 2004 Wake flow of single and multiple yawed cylinders. Trans. ASME: J. Fluids Engng 126, 861–870.Google Scholar
Tsai, C. Y. & Widnall, S. E. 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73, 721–733.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Ann. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Zdravkovich, M. M. 1977 Review of flow interference between two circular cylinders in various arrangements. Trans. ASME: J. Fluids Engng 99, 618–633.Google Scholar