Numerical Simulation of Flow Past an Infinite Row of Equispaced Square Cylinders Using the Multi- Relaxation-Time Lattice Boltzmann Method

Authors: S. Ul. Islam, H. Rahman, W. S. Abbasi, N. Rathore

Abstract:

In this research numerical simulations are performed, using the multi-relaxation-time lattice Boltzmann method, in the range 3 ≤ β = w[d] ≤ 30 at Re = 100, 200 and 300, where β the blockage ratio, w is the equispaced distance between centers of cylinders, d is the diameter of the cylinder and Re is the Reynolds number, respectively. Special attention is paid to the effect of the equispaced distance between centers of cylinders. Visualization of the vorticity contour visualization are presented for some simulation showing the flow dynamics and patterns for blockage effect. Results show that the drag and mean drag coefficients, and Strouhal number, in general, decrease with the increase of β for fixed Re. It is found that the decreasing rate of drag and mean drag coefficients and Strouhal number is more distinct in the range 3 ≤ β ≤ 15. We found that when β > 15, the blockage effect almost diminishes. Our results further indicate that the drag and mean drag coefficients, peak value of the lift coefficient, root-mean-square value of the lift and drag coefficients and the ratio between lift and drag coefficients decrease with the increase of Re. The results indicate that symmetry boundary condition have more blockage effect as compared to periodic boundary condition.

Keywords: Blockage ratio, Multi-relaxation-time lattice Boltzmann method, Square cylinder, Vortex formation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1105787

References:

[1] M. Cheng, and P. M. Moretti, “Experimental study of the flow field downstream of a single tube row,” Experimental Thermal Fluid Science, vol.1, 1988, pp. 69-74.
[2] A. Okajima, “Strouhal numbers of rectangular cylinders,” Journal of Fluid Mechanics, Cambridge, U.K. vol. 123, 1982, pp. 379-398.
[3] R. W. Davis, E. F. Moore, and L. P. Purtell, “A numerical experimental study of confined flow around rectangular cylinders,” Physics of Fluids, Part A, vol. 27, 1984, pp. 46-59.
[4] R. Franke, W. Rodi, and B. Schonung, “Numerical calculation of Laminar Vortex Shedding flow past cylinders,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 35, 1990, pp. 237-257.
[5] A. Sohankar, L. Davidson, and C. Norberg, “Numerical simulation of unsteady flow around a square two-dimensional cylinder,” Twelfth Australian Fluid Mechanics Conference, The University of Sydney, Australia. 1995, pp. 517-520.
[6] A. Sohankar, C. Norberg, and L. Davidson, “Simulation of threedimensional flow around a square cylinder at moderate Reynolds numbers,” Physics of Fluids. vol.11, 1999, pp. 288-306.
[7] A. K. Saha, K. Muralidhar, and G. Biswas, “Transition and Chaos in two-dimensional flow past a square cylinder,” Journal of Engineering Mechanics, vol.126, 1999, pp. 523-532.
[8] D. B. Ingham, T. Tang, and B. R. Morton, “Steady two-dimensional flow through a row of normal flat plates,” Journal of Fluid Mechanics, vol. 210, 1990, pp.281-302.
[9] B. Fornberg, “Steady incompressible flow past a row of circular cylinders,” Journal of Fluid Mechanics, vol. 225, 1991, pp. 655-678.
[10] D. B. Ingham, and B. Yan, “Fluid flow around cascades,” Zangew Mathematical Physics, vol. 44, 1993.
[11] R. Natarajan., B. Fornberg, and A. Acrivos, “Flow past a row of flat plates at large Reynolds numbers,” Proceedings of Royal Society London A, vol. 441, 1993, pp. 211-235.
[12] S. R. Kumar., A. Sharma., and A. Agarwall, “Simulation of flow around a row of square cylinders,” Journal of Fluid Mechanics, vol. 606, 2008, pp.369-397.
[13] S. U. Islam and C. Y. Zhou, “Numerical simulation of flow around a row of circular cylinders using the lattice Boltzmann method,” Information Technology Journal, vol.8. , 2009, pp. 513-520.
[14] S. Ul. Islam, H. Rahman, and W. S. Abbasi, “Grid independence study of flow past a square cylinder using the multi-relaxation-time lattice Boltzmann method,” International Journal of Mathematical, Computational, Physical and Quantum Engineering, World Academy of Science, Engineering and Technology, vol. 8, 2014, pp. 972-982.
[15] S. Ul. Islam, W. S. Abbasi, and H. Rahman, “Force statistics and wake structure mechanism of flow around a square cylinder at low Reynolds numbers,” International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, vol. 8, 2014, pp. 1397-1403.
[16] Y. Dazchi, M. Renwei, L. S. Luo, and S. Wei, “Viscous flow computations with the method of lattice Boltzmann equation,” Progress in Aerospace Sciences, vol. 39, 2003, pp. 329-367.