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Numerical simulations of flow through channels with T-junction. (English) Zbl 1426.76099
Summary: The paper deals with numerical solution of laminar and turbulent flows of Newtonian and non-Newtonian fluids in branched channels with two outlets. Mathematical model of the flow is based on the Reynolds averaged Navier-Stokes equations for the incompressible fluid. In the turbulent case, the closure of the system of equations is achieved by the explicit algebraic Reynolds stress (EARSM) turbulence model. Generalized non-Newtonian fluids are described by the power-law model. The governing equations are solved by cell-centered finite volume schemes with the artificial compressibility method; dual time scheme is applied for unsteady simulations. Channels considered in presented calculations are of constant square or circular cross-sections. Numerical results for laminar flow of non-Newtonian fluid are presented. Further, turbulent flow through channels with perpendicular branch is simulated. Possible methods for setting the flow rate are discussed and numerical results presented for two flow rates in the branch.

76D05 Navier-Stokes equations for incompressible viscous fluids
76A05 Non-Newtonian fluids
76F10 Shear flows and turbulence
76M12 Finite volume methods applied to problems in fluid mechanics
Full Text: DOI
[1] Barth, W.; Branets, L.; Carey, G., Non-Newtonian flow in branched pipes and artery models, International Journal for Numerical Methods in Fluids, 57, 531-553, (2008), ISSN: 1097-0363 · Zbl 1198.76163
[2] Bodnar, T.; Sequeira, A., Numerical simulation of the coagulation dynamics of blood, Computational and Mathematical Methods in Medicine, 4, 83-104, (2008), ISSN: 1748-6718 · Zbl 1145.92011
[3] Bodnar, T.; Sequeira, A.; Prosi, M., On the shear-thinning and viscoelastic effects of blood flow under various flow rates, Applied Mathematics and Computation, 217, 5055-5067, (2011), ISSN: 0096-3003 · Zbl 1276.76098
[4] Chhabra, R. P.; Richardson, J. F., Non-Newtonian flow in the process industries, (1999), Biddles Ltd., Guildford and King’s Lynn Great Britain
[5] Chorin, A. J., A numerical method for solving incompressible viscous flow problems, Journal of Computational Physics, 2, 1, 12-26, (1967), ISSN: 0021-9991 · Zbl 0149.44802
[6] A.O. Demuren: Calculation of turbulence-driven secondary motion in ducts with arbitrary cross-section. AIAA Paper, 90-0245, 1990.
[7] A. Hellsten: New advanced k-ω turbulence model for high-lift aerodynamics, in: 42nd AIAA Aerospace Sciences Meeting, Reno, Nevada, 2004.
[8] Huang, H.-Ch.; Li, Z.-H.; Usmani, A. S., Finite element analysis of non-Newtonian flow, (1999), Springer-Verlag London
[9] P. Louda, K. Kozel, J. Přı´hoda: Numerical modelling of turbulent flow over three dimensional backward facing step, in: T. Lajos, J. Vad, (Eds.), Conference on Modelling Fluid Flow CMFF’06, pp. 448-455, Budapest, 2006, Budapest University of Technology and Economics, ISBN 963 420 872 X.
[10] Louda, P.; Kozel, K.; Přı´hoda, J., Numerical solution of 2D and 3D viscous incompressible steady and unsteady flows using artificial compressibility method, International Journal for Numerical Methods in Fluids, 56, 1399-1407, (2008), ISSN: 0271-2091 · Zbl 1151.76019
[11] P. Louda, K. Kozel, K. Přı´hoda, L. Beneš, T. Kopáček, Numerical solution of incompressible flow through branched channels, Computers and Fluids, in press, doi:10.1016/j.compfluid.2010.12.003. · Zbl 1433.76110
[12] Menter, F. R., Two-equation eddy-viscosity turbulence models for engineering applications, AIAA Journal, 32, 8, 1598-1605, (1994), ISSN: 0001-1452
[13] Miller, D. S., Internal flow. A guide to losses in pipe and duct systems, (1971), The British Hydromechanics Research Association Cranfiled, Bedford, England, p. 329
[14] Oka, K.; Ito, H., Energy losses at tees with large area ratios, Journal of Fluids Engineering-Transactions of the Asme, 127, 110-116, (2005), ISSN: 0098-2202
[15] Paz, D.; Einav, S.; Raderer, F.; Trubel, W., Numerical model and experimental investigation of blood flow through a bifurcation - interaction between an artery and a small prosthesis, Asaio Journal, 43, 326-333, (1997), ISSN: 1058-2916
[16] Robertson, A. M.; Sequeira, A.; Kameneva, M. V., Hemorheology, (2008), Birkhäuser Verlag Basel, Switzerland
[17] Robertson, A. M., Review of relevant continuum mechanics, (2008), Birkhäuser Verlag Basel, Switzerland
[18] Sváček, P., On approximation of non-Newtonian fluid flow by the finite element method, Journal of Computational and Applied Mathematics, 218, 1, 167-174, (2008), ISSN: 0377-0427 · Zbl 1388.76154
[19] Štigler, J., Tee junction as a pipeline net element. part 1. A new mathematical model, Journal of Mechanical Engineering, 57, 5, 249-262, (2006), ISSN: 0039-2472
[20] Štigler, J., Tee junction as a pipeline net element. part 2. coefficients determination, Journal of Mechanical Engineering, 57, 5, 263-270, (2006), ISSN: 0039-2472
[21] J. Štigler, T-part as an element of the pipe-line system, The introduction of the mathematical model of the fluid flow in T-part for the arbitrary angle of the adjacent branch, in: 25th IAHR Symposium on Hydrualic Machinery and Systems, September 20-24, 2010 Timisoara Romania, 2010 IOP Conference Series, Earth Environ. Sci. 12 012102, 10 pp.
[22] Sunmi, L.; Eunok, J., A two-chamber model of valveless pumping using the immersed boundary method, Applied Mathematics and Computation, 206, 2, 876-884, (2010), ISSN: 0096-3003 · Zbl 1163.76011
[23] Vimmr, J.; Jonášová, A., Non-Newtonian effects of blood flow in complete coronary and femoral bypasses, Mathematics and Computers in Simulation, 80, 6, 1324-1336, (2010), ISBN 0378-4754 · Zbl 1193.92030
[24] S. Wallin, Engineering turbulence modeling for CFD with a focus on explicit algebraic Reynolds stress models, Ph.D. Thesis, Royal Institute of Technology, Stockholm, 2000.
[25] Wallin, S.; Johansson, A. V., An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows, Journal of Fluid Mechanics, 403, 89-132, (2000), ISSN: 0022-1120 · Zbl 0966.76032
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