Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-11T17:04:54.008Z Has data issue: false hasContentIssue false
  • English
  • Français

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:sbchust@126.com
Email:llqqxxx@126.com
Corresponding author.Email:hn_jxcy@126.com
Email:hustczh@126.com
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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