Numerical Simulations of Cross-Flow around Four Square Cylinders in an In-Line Rectangular Configuration
A two-dimensional numerical simulation of crossflow
around four cylinders in an in-line rectangular configuration is
studied by using the lattice Boltzmann method (LBM). Special
attention is paid to the effect of the spacing between the cylinders.
The Reynolds number ( Re ) is chosen to be e 100 R = and the
spacing ratio L / D is set at 0.5, 1.5, 2.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0
and 10.0. Results show that, as in the case of four cylinders in an inline
rectangular configuration , flow fields show four different
features depending on the spacing (single square cylinder, stable
shielding flow, wiggling shielding flow and a vortex shedding flow)
are observed in this study. The effects of spacing ratio on physical
quantities such as mean drag coefficient, Strouhal number and rootmean-
square value of the drag and lift coefficients are also presented.
There is more than one shedding frequency at small spacing ratios.
The mean drag coefficients for downstream cylinders are less than
that of the single cylinder for all spacing ratios. The present results
using the LBM are compared with some existing experimental data
and numerical studies. The comparison shows that the LBM can
capture the characteristics of the bluff body flow reasonably well and
is a good tool for bluff body flow studies.
[1] M. M. Zdravkovich, "The effects of interference between circular
cylinders in cross flow," Journal of Fluids and Structures, 1, 1987, pp.
235-261.
[2] A. T. Sayers, "Flow interference between four equispaced cylinders
when subjected to a cross flow," Journal of Wind Engineering and
Industrial Aerodynamics, 31, 1988, pp. 9-28.
[3] A. T. Sayers, "Vortex shedding from groups of three and four
equispaced cylinders situated in cross flow," Journal of Wind
Engineering and Industrial Aerodynamics, 34, 1990, pp. 213-221.
[4] K. Lam, and S. C. Lo, "A visualization study of cross-flow around four
cylinders in a square configuration," Journal of Fluids and Structures, 6,
1992, pp. 109-131.
[5] K. Lam, and X. Fang, "The effect of interference of four equispaced
cylinders in cross flow on pressure and force coefficients," Journal of
Fluids and Structures, 9, 1995, pp. 195-214.
[6] M. M. Zdravkovich, "Flow around circular cylinders", 2003, Oxford
University Press, Oxford.
[7] C. Norberg, "Fluctuating lift on a circular cylinder: review and new
measurements", Journal of Fluids and Structures, 17, 2003, pp. 57-96.
[8] T. Farrant, M. Tan, and W. G. Price, "A cell boundary element method
applied to laminar vortex shedding from array of cylinders in various
arrangement", Journal of Fluids and Structures, 14, 2000, pp. 375-402.
[9] K. Lam, R. M. C. So, and J. Y. Li, "Flow around four cylinders in a
square configuration using surface vorticity method", In: Proceedings of
the Second International Conference on Vortex Methods, Istanbul,
Turkey , 2001a.
[10] K. Lam, J. Y. Li, K. T. Chan, and R. M. C. So, "Velocity map and flow
pattern of flow around four cylinders in a square configuration at low
Reynolds number and large spacing ratio using particle image
velocimetry", In:Proceddings of the Second International Conference on
Vortex Methods, Istanbul, Turkey, 2001b.
[11] K. Lam, W. Q. Gong, and R. M. C. So, "Numerical simulation of crossflow
around four cylinders in an in-line square configuration", Journal of
Fluids and Structures, 1, 2008, pp. 34-57.
[12] O. Inoue, W. Iwakami, and N. Hatakeyama, "Aeolian tones radiated
from flow past two square cylinders in a side-by-side arrangement",
Physics of Fluids, 18, 2006, pp. 1-18.
[13] Y. Rao, Y. S. Ni, and C. F. Liu, "Flow effect around two square
cylinders arranged side by side using lattice Boltzmann method",
International Journal of Modern Physics C, 19, 2008, pp. 1683-1694.
[14] T. Degawa, and T. Uchiyama, "Numerical simulation of bubbly flow
around two tandem square section cylinders by vortex method", Journal
of Mechanical Engineering Science, 222, 2008, pp. 225-234.
[15] Y. Shimizu, and Y. Tanida, "Fluid forces acting on cylinders of
rectangular cross-section", Trans. JSME, 16, 1978, pp. 465-485.
[16] A. Okajima, "Strouhal numbers of rectangular cylinders", Journal of
Fluid Mechanics, 123, 1982, pp. 379-398.
[17] C. Norberg, "Flow around rectangular cylinders: Pressure forces and
wake frequencies", Journal of Wind Engineering and Industrial
Aerodynamics, 49, 1993, pp. 187-196.
[18] A. Sohankar, L. Davidson, and C. Norberg, "Numerical simulation of
unsteady flow around a square two-dimensional cylinder", The Twelfth
Australian Fluid Mechanics Conference, The University of Sydney,
Australia, 1995, pp. 517-520.
[19] S. U. Islam, and C. Y. Zhou, "Characteristics of flow past a square
cylinder using the lattice Boltzmann method", to be published in
Information Technology Journal.
[20] Z. Guo, B. Shi, and N. Wang, "Lattice BGK Model for Incompressible
Navier-Stokes Equation", Journal of Computational Physics, 165, 2000,
pp. 288-306.
[21] P. L. Bhatnagar, E. P. Gross, M. Krook, "A model for collision processes
in gases. 1. small amplitude processes in charged and neutral onecomponent
systems", Phys. Rev. 94, 1954, pp. 511-514.
[22] S. Chapman, T. Cowling, and D. Burnet, "The mathematical theory of
non-uniform gases. An account of the kinetic theory of viscosity,
thermal conduction, and diffusion in gases", Cambridge University
Press, 3rd edition, 1990.
[23] Y. Dazhi, M. Renwei, L. S. Luo, and S. Wei, "Viscous flow
computations with the method of lattice Boltzmann equation", Progress
in Aerospace Sciences 39, 2003, pp. 329-367.
[1] M. M. Zdravkovich, "The effects of interference between circular
cylinders in cross flow," Journal of Fluids and Structures, 1, 1987, pp.
235-261.
[2] A. T. Sayers, "Flow interference between four equispaced cylinders
when subjected to a cross flow," Journal of Wind Engineering and
Industrial Aerodynamics, 31, 1988, pp. 9-28.
[3] A. T. Sayers, "Vortex shedding from groups of three and four
equispaced cylinders situated in cross flow," Journal of Wind
Engineering and Industrial Aerodynamics, 34, 1990, pp. 213-221.
[4] K. Lam, and S. C. Lo, "A visualization study of cross-flow around four
cylinders in a square configuration," Journal of Fluids and Structures, 6,
1992, pp. 109-131.
[5] K. Lam, and X. Fang, "The effect of interference of four equispaced
cylinders in cross flow on pressure and force coefficients," Journal of
Fluids and Structures, 9, 1995, pp. 195-214.
[6] M. M. Zdravkovich, "Flow around circular cylinders", 2003, Oxford
University Press, Oxford.
[7] C. Norberg, "Fluctuating lift on a circular cylinder: review and new
measurements", Journal of Fluids and Structures, 17, 2003, pp. 57-96.
[8] T. Farrant, M. Tan, and W. G. Price, "A cell boundary element method
applied to laminar vortex shedding from array of cylinders in various
arrangement", Journal of Fluids and Structures, 14, 2000, pp. 375-402.
[9] K. Lam, R. M. C. So, and J. Y. Li, "Flow around four cylinders in a
square configuration using surface vorticity method", In: Proceedings of
the Second International Conference on Vortex Methods, Istanbul,
Turkey , 2001a.
[10] K. Lam, J. Y. Li, K. T. Chan, and R. M. C. So, "Velocity map and flow
pattern of flow around four cylinders in a square configuration at low
Reynolds number and large spacing ratio using particle image
velocimetry", In:Proceddings of the Second International Conference on
Vortex Methods, Istanbul, Turkey, 2001b.
[11] K. Lam, W. Q. Gong, and R. M. C. So, "Numerical simulation of crossflow
around four cylinders in an in-line square configuration", Journal of
Fluids and Structures, 1, 2008, pp. 34-57.
[12] O. Inoue, W. Iwakami, and N. Hatakeyama, "Aeolian tones radiated
from flow past two square cylinders in a side-by-side arrangement",
Physics of Fluids, 18, 2006, pp. 1-18.
[13] Y. Rao, Y. S. Ni, and C. F. Liu, "Flow effect around two square
cylinders arranged side by side using lattice Boltzmann method",
International Journal of Modern Physics C, 19, 2008, pp. 1683-1694.
[14] T. Degawa, and T. Uchiyama, "Numerical simulation of bubbly flow
around two tandem square section cylinders by vortex method", Journal
of Mechanical Engineering Science, 222, 2008, pp. 225-234.
[15] Y. Shimizu, and Y. Tanida, "Fluid forces acting on cylinders of
rectangular cross-section", Trans. JSME, 16, 1978, pp. 465-485.
[16] A. Okajima, "Strouhal numbers of rectangular cylinders", Journal of
Fluid Mechanics, 123, 1982, pp. 379-398.
[17] C. Norberg, "Flow around rectangular cylinders: Pressure forces and
wake frequencies", Journal of Wind Engineering and Industrial
Aerodynamics, 49, 1993, pp. 187-196.
[18] A. Sohankar, L. Davidson, and C. Norberg, "Numerical simulation of
unsteady flow around a square two-dimensional cylinder", The Twelfth
Australian Fluid Mechanics Conference, The University of Sydney,
Australia, 1995, pp. 517-520.
[19] S. U. Islam, and C. Y. Zhou, "Characteristics of flow past a square
cylinder using the lattice Boltzmann method", to be published in
Information Technology Journal.
[20] Z. Guo, B. Shi, and N. Wang, "Lattice BGK Model for Incompressible
Navier-Stokes Equation", Journal of Computational Physics, 165, 2000,
pp. 288-306.
[21] P. L. Bhatnagar, E. P. Gross, M. Krook, "A model for collision processes
in gases. 1. small amplitude processes in charged and neutral onecomponent
systems", Phys. Rev. 94, 1954, pp. 511-514.
[22] S. Chapman, T. Cowling, and D. Burnet, "The mathematical theory of
non-uniform gases. An account of the kinetic theory of viscosity,
thermal conduction, and diffusion in gases", Cambridge University
Press, 3rd edition, 1990.
[23] Y. Dazhi, M. Renwei, L. S. Luo, and S. Wei, "Viscous flow
computations with the method of lattice Boltzmann equation", Progress
in Aerospace Sciences 39, 2003, pp. 329-367.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:62454", author = "Shams Ul Islam and Chao Ying Zhou and Farooq Ahmad", title = "Numerical Simulations of Cross-Flow around Four Square Cylinders in an In-Line Rectangular Configuration", abstract = "A two-dimensional numerical simulation of crossflow
around four cylinders in an in-line rectangular configuration is
studied by using the lattice Boltzmann method (LBM). Special
attention is paid to the effect of the spacing between the cylinders.
The Reynolds number ( Re ) is chosen to be e 100 R = and the
spacing ratio L / D is set at 0.5, 1.5, 2.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0
and 10.0. Results show that, as in the case of four cylinders in an inline
rectangular configuration , flow fields show four different
features depending on the spacing (single square cylinder, stable
shielding flow, wiggling shielding flow and a vortex shedding flow)
are observed in this study. The effects of spacing ratio on physical
quantities such as mean drag coefficient, Strouhal number and rootmean-
square value of the drag and lift coefficients are also presented.
There is more than one shedding frequency at small spacing ratios.
The mean drag coefficients for downstream cylinders are less than
that of the single cylinder for all spacing ratios. The present results
using the LBM are compared with some existing experimental data
and numerical studies. The comparison shows that the LBM can
capture the characteristics of the bluff body flow reasonably well and
is a good tool for bluff body flow studies.", keywords = "Four square cylinders, Lattice Boltzmann method, rectangular configuration, spacing ratios, vortex shedding.", volume = "3", number = "9", pages = "1119-10", }
