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Numerical study of flow past four square-arranged cylinders using spectral element method. (English) Zbl 1290.76109
Summary: Flow past around four cylinders which are arranged as a square shape at a Reynolds number of 200 is numerically investigated with a spectral element method. To validate the numerical method for incompressible Navier-Stokes equations, benchmark problems of flow past a single and two tandem cylinders are employed, with the numerical results in a good agreement with the available literatures. Then the study concentrates on the flow characteristics of two groups of cases, respectively, with incidence angle $$\alpha=0^\circ$$ and $$\alpha=45^\circ$$. By changing the spacing ratios $$L/D$$ from 1.5 to 4.0 ($$L$$ is the center-to-center distance and $$D$$ the cylinder diameter), the flow characteristics, including the flow patterns, statistical force parameters such as the drag and lift coefficients as well as wake oscillation frequencies (Strouhal numbers) are investigated. Numerical results show that in each case there are around three wake flow patterns which are more related with the spacing ratio. In addition, the force parameters are highly affected by the flow patterns.

MSC:
 76M22 Spectral methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76M10 Finite element methods applied to problems in fluid mechanics
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 [1] Yoon, H. S.; Chun, H. H.; Kim, J. H.; Park, I. L.R., Flow characteristics of two rotating side-by-side circular cylinder, Comput Fluids, 38, 466-474, (2009) · Zbl 1237.76207 [2] Harichandan, A. B.; Roy, A., Numerical investigation of low Reynolds number flow past two and three circular cylinders using unstructured grid CFR scheme, Int J Heat Fluid Flow, 31, 154-171, (2010) [3] Liang, C.; Premasuthan, S.; Jameson, A., High-order accurate simulation of low-Mach laminar flow past two side-by-side cylinders using spectral difference method, Comput Struct, 87, 812-827, (2009) [4] Sumner, D., Two circular cylinders in cross-flow: a review, J Fluids Struct, 26, 849-899, (2010) [5] Nicolle, A.; Eames, I., Numerical study of flow through and around a circular array of cylinders, J Fluid Mech, 679, 1-31, (2011) · Zbl 1241.76146 [6] Kang, S., Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers, Phys Fluid, 15, 2486-2498, (2003) · Zbl 1186.76270 [7] Carmo, B. S.; Sherwin, S. J.; Bearman, P. W.; Willden, H. J., Wake transition in the flow around two circular cylinders in staggered arrangements, J Fluid Mech, 597, 1-29, (2008) · Zbl 1133.76018 [8] Igarashi, T.; Suzuki, K., Characteristics of the flow around three circular cylinders arranged in-line, Bull. JSME, 27, 2397-2404, (1984) [9] Bao, Y.; Zhou, D.; Huang, C., Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second order characteristic-based split finite element method, Comput Fluids, 39, 882-899, (2010) · Zbl 1242.76109 [10] Lam, K.; Li, J.; So, R. M.C., Force coefficients and Strouhal numbers of four cylinders in cross flow, J Fluids Struct, 18, 305-324, (2003) [11] Lam, K.; Li, J. Y.; Chan, K. T.; So, R. M.C., Flow pattern and velocity field distribution of cross-flow around four cylinders in a square configuration at a low Reynolds number, J Fluids Struct, 17, 665-679, (2003) [12] Lam, K.; Gong, W. Q.; So, R. M.C., Numerical simulation of cross-flow around four cylinders in an in-line square configuration, J Fluids Struct, 24, 34-57, (2008) [13] Lin, Z.; Lin, Y. F.; Lam, K., Large-eddy simulation of flow around cylinder arrays at a subcritical Reynolds number, J Hydrodyn, 20, 403-413, (2008) [14] Brooks, A. N.; Hughes, T. J.R., Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput Methods Appl Mech Eng, 32, 199-259, (1982) · Zbl 0497.76041 [15] Hughes, T. J.R.; Franca, L. P.; Hulbert, G. M., A new finite element formulation for computational fluid dynamics: VIII. the Galerkin/least-squares method for advective-diffusive equations, Comput Methods Appl Mech Eng, 73, 173-189, (1989) · Zbl 0697.76100 [16] Zienkiewicz, O. C.; Codina, R., A general algorithm for compressible and incompressible flow, part I: the split, characteristic-based scheme, Int J Numer Methods Fluids, 20, 869-885, (1995) · Zbl 0837.76043 [17] Bao, Y.; Zhou, D.; Zhao, Y. J., A two-step Taylor-characteristic based Galerkin method for incompressible flows and its application to flow over triangular cylinder with different incidence angles, Int J Numer Methods Fluids, 62, 1181-1208, (2010) · Zbl 1423.76328 [18] Blackburn, H. M.; Sherwin, S. J., Formulation of a Galerkin spectral element-Fourier method for three-dimensional incompressible flows in cylindrical geometries, J Comput Phys, 197, 759-778, (2004) · Zbl 1106.76418 [19] Karniadakis, G. E.; Sherwin, S. J., Spectral/hp element methods for CFD, (1999), Oxford University Press Oxford · Zbl 0954.76001 [20] Blackburn, H. M.; Lopez, J. M., Modulated waves in a periodically driven annular cavity, J Fluid Mech, 667, 336-357, (2011) · Zbl 1225.76142 [21] Blackburn, H. M.; Sheard, G. J., On quasi-periodic and subharmonic Floquet wake instabilities, Phys Fluid, 22, (2010), 031701-1-4 · Zbl 1188.76014 [22] Blackburn, H. M.; Sherwin, S. J.; Barkley, D., Convective instability and transient growth in steady and pulsatile stenotic flows, J Fluid Mech, 607, 267-277, (2008) · Zbl 1145.76374 [23] Blackburn, H. M.; Barkley, D.; Sherwin, S. J., Convective instability and transient growth in flow over a backward-facing step, J Fluid Mech, 603, 271-304, (2008) · Zbl 1151.76470 [24] Sheard, G. J.; Thompson, M. C.; Hourigan, K., From spheres to circular cylinders: the stability and flow structures of bluff ring wakes, J Fluid Mech, 492, 147-180, (2003) · Zbl 1063.76539 [25] Norberg, N., Fluctuating lift on a circular cylinder: review and new measurements, J Fluids Struct, 17, 57-96, (2003) [26] Fey, U.; Konig, M.; Eckelmann, H., A new Strouhal-Reynolds-number relationship for the circular cylinder in the range 47
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