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Simulation of Power-Law Fluid Flows in Two-Dimensional Square Cavity Using Multi-Relaxation-Time Lattice Boltzmann Method

Published online by Cambridge University Press:  03 June 2015

Qiuxiang Li ,
Ning Hong ,
Baochang Shi  and
Zhenhua Chai
Qiuxiang Li*
Affiliation:
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
Ning Hong*
Affiliation:
Department of Foundational Courses, Jiangcheng College, China University of Geosciences, Wuhan, 430200, P.R. China
Baochang Shi*
Affiliation:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
Zhenhua Chai*
Affiliation:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
*
Email:[email protected]
Email:[email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
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Abstract

In this paper, the power-law fluid flows in a two-dimensional square cavity are investigated in detail with multi-relaxation-time lattice Boltzmann method (MRT-LBM). The influence of the Reynolds number (Re) and the power-law index (n) on the vortex strength, vortex position and velocity distribution are extensively studied. In our numerical simulations, Re is varied from 100 to 10000, and n is ranged from 0.25 to 1.75, covering both cases of shear-thinning and shear-thickening. Compared with the Newtonian fluid, numerical results show that the flow structure and number of vortex of power-law fluid are not only dependent on the Reynolds number, but also related to power-law index.

Keywords

76A0576M2876D0581T80Multi-relaxation-time lattice Boltzmann methodpower-law fluidshear-thinningshear-thickening
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 1 , January 2014 , pp. 265 - 284
Copyright
Copyright © Global Science Press Limited 2014

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References

[1] Pearson, J. R. A., Tardy, P. M. J., Models of non-Newtonian and complex fluids through porous media, Non-Newton, J. Fluid Mech., 102 (2002), 447–473.Google Scholar
[2] Sullivan, S. P., Gladden, L. F., Johns, M. L., Simulation of power-lawfluid flow through porous media using lattice Boltzmann techniques, Non-Newton, J. Fluid Mech., 133 (2006), 91–98.Google Scholar
[3] Bell, B. C., Surana, K. S., P-version least squares finite element formulation for two dimensional, incompressible, non-Newtonian, isothermal and non-isothermal flow, Numer, Int. J. Meth. Fluids, 18 (1994), 127–162.CrossRefGoogle Scholar
[4] Neofytou, P., A 3rd order upwind finite volume method for generalized Newtonian fluid flows, Adv. Eng. Softw., 36 (2005), 664–680.CrossRefGoogle Scholar
[5] Aharonov, E., Rothman, D. H., Non-Newtonian flow through porous media: a lattice-Boltzmann method, Geophys. Res. Lett., 20 (1993), 679–682.CrossRefGoogle Scholar
[6] Rafiee, A., Modelling of generalized Newtonian lid-driven cavityflow using anSPH method, Anziam. J., 49 (2008), 411–422.Google Scholar
[7] Huang, C. S., Chai, Z. H., and Shi, B. C., Non-Newtonian effect on hemodynamic characteristics of blood flow in stented cerebral aneurysm, Commun. Comput. Phys., 13 (2013), 916–928.Google Scholar
[8] Benzi, R., Succi, S., Vergassola, M., The lattice Boltzmann equation: theory and applications, Phys. Rep., 222 (1992), 145–197.Google Scholar
[9] Aidun, C. K. and Clausen, J. R., Lattice-Boltzmann Method for Complex Flows, Annu. Rev. Fluid Mech., 42 (2010),439–472.Google Scholar
[10] Shan, X. W., Chen, H. D., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47 (1993), 1815–1819.Google Scholar
[11] Ubertini, S., Succi, S., Recent advancesof Lattice Boltzmann techniques on unstructured grids, Prog. Comput. Fluid Dyn., 5 (2005), 85–96.Google Scholar
[12] Yoshino, M., Hotta, Y., Hirozane, T., Endo, M., A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method, Non-Newt, J. Fluid Mech., 147 (2007), 69–78.Google Scholar
[13] Boyd, J., Buick, J., Green, S., A second-order accurate lattice Boltzmann non-Newtonian flow model, J. Phy. A: Math. Gen., 39 (2006), 14241–14247.Google Scholar
[14] Chen, S. Y., Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), 329–364.CrossRefGoogle Scholar
[15] Qian, Y. H., d’Humières, D., Lallemand, P., Lattice BGK models for Navier-Stokes equation, Euorphys. Lett., 17 (1992), 479–484.Google Scholar
[16] d’Humières, D., Generalized lattice Boltzmann equation, in: Rarefied Gas Dynamics: Theory and Simulations, Progress in Astronautics and Aeronautics, AIAA Press, Washington, DC, 159 (1992), 450–458.Google Scholar
[17] Lallemand, P., Luo, L. S., Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, and stability, Phys. Rev. E, 61 (2000), 6546–6562.CrossRefGoogle ScholarPubMed
[18] Ghia, U., Ghia, K. N., Shin, C. T., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48 (1982), 387–411.Google Scholar
[19] Hou, S., Zou, Q., Chen, S. Y., Doolen, G. D., Cogley, A. C., Simulation of cavity flow by the lattice Boltzmann method, J. Comput. Phys., 118 (1995), 329–347.CrossRefGoogle Scholar
[20] Shankar, P. and Deshpande, M., Fluid mechanics in the driven cavity, Annu. Rev. Fluid Mech., 32 (2000), 93–136.Google Scholar
[21] Wu, J. S., Shao, Y. L., Simulation of lid-driven cavity flows by parallel lattice Boltzmann method using multi-relaxation-time scheme, Int. J. Numer. Meth. Fluids, 46 (2004), 921–937.Google Scholar
[22] Chai, Z. H., Shi, B. C., Zheng, L., Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method, Chin. Phys., 15 (2006), 1855–1864.Google Scholar
[23] Zhou, X. Y., Shi, B. C., Wang, N. C., Numerical simulation of LBGK model for high Reynolds number flow, Chin. Phys., 13 (2004), 712–720.Google Scholar
[24] He, N. Z., Wang, N. C., Shi, B. C., Guo, Z. L., A unified incompressible lattice BGK model and its application to three-dimensional lid-driven cavity flow, Chin. Phys., 13 (2004), 40–47.Google Scholar
[25] Zhang, T., Shi, B. C., Chai, Z. H., Lattice Boltzmann simulation of lid-driven flow in trapezoidal cavities, Comput. Fluids, 39 (2010), 1977–1989.Google Scholar
[26] Luo, L. S., Liao, W., Chen, X. W., Peng, Y., and Zhang, W., Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations, Phys. Rev. E, 83 (2011), 056710.Google Scholar
[27] Gabbanelli, S., Drazer, G., Koplik, J., Lattice Boltzmann method for non-Newtonian (power-law) fluids, Phys. Rev. E, 72 (2005), 046312.Google Scholar
[28] Malaspinas, O., Courbebaisse, G., Deville, M., Simulation of generalized Newtonian fluids with the lattice Boltzmann method, Int. J. Mod. Phys. C, 18 (2007), 1939–1949.Google Scholar
[29] Chai, Z. H., Shi, B. C., Guo, Z. L., Rong, F. M., Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows, Non-Newton, J. Fluid Mech., 166 (2011), 332–342.Google Scholar
[30] Tang, G. H., Wang, S. B., Ye, P. X., Tao, W. Q., Bingham fluid simulation with the incompressible lattice Boltzmann model, Non-Newton, J. Fluid Mech., 166 (2011), 145–151.Google Scholar
[31] Guo, Z. L., Zheng, C. G., Shi, B. C., Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chin. Phys., 11 (2002), 366–374.Google Scholar