Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T12:12:23.890Z Has data issue: false hasContentIssue false
  • English
  • Français

A Localized Mass-Conserving Lattice Boltzmann Approach for Non-Newtonian Fluid Flows

Published online by Cambridge University Press:  30 April 2015

Liang Wang ,
Jianchun Mi ,
Xuhui Meng  and
Zhaoli Guo
Liang Wang
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, P.R. China State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
Jianchun Mi
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, P.R. China
Xuhui Meng
Affiliation:
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
Zhaoli Guo*
Affiliation:
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
*
*Corresponding author. Email addresses: wlsa0612@gmail.com (L. Wang), jcmi@coe.pku.edu.cn (J. C. Mi), mengxuhui@hust.edu.cn (X. H. Meng), zlguo@hust.edu.cn (Z. L. Guo)
Get access

Abstract

A mass-conserving lattice Boltzmann model based on the Bhatnagar-Gross-Krook (BGK) model is proposed for non-Newtonian fluid flows. The equilibrium distribution function includes the local shear rate related with the viscosity and a variable parameter changing with the shear rate. With the additional parameter, the relaxation time in the collision can be fixed invariable to the viscosity. Through the Chapman-Enskog analysis, the macroscopic equations can be recovered from the present mass-conserving model. Two flow problems are simulated to validate the present model with a local computing scheme for the shear rate, and good agreement with analytical solutions and/or other published results are obtained. The results also indicate that the present modified model is more applicable to practical non-Newtonian fluid flows owing to its better accuracy and more robustness than previous methods.

Keywords

44.05.+e47.11.-j47.56.+rLattice Boltzmann methodnon-Newtonian fluidsmass conservation
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 4 , April 2015 , pp. 908 - 924
Copyright
Copyright © Global-Science Press 2015 

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]Ubertini, S. and Succi, S., Recent advances of Lattice Boltzmann techniques on unstructured grids, Prog. Comput. Fluid Dyn., 5 (2005), 85’96.CrossRefGoogle Scholar
[2]Boyd, J., Buick, J. and Green, S., A second-order accurate lattice Boltzmann non-Newtonian flow model, J. Phys. A: Math. Gen., 39 (2006), 14241–14247.CrossRefGoogle Scholar
[3]Yong, W. A. and Luo, L. S., Accuracy of the viscous stress in the lattice Boltzmann equation with simple boundary conditions, Phys. Rev. E, 86 (2012), 065701(R).CrossRefGoogle Scholar
[4]Aharonov, E. and Rothman, D. H., Non-Newtonian flow (through porous media): A lattice-Boltzmann method, Geophys. Res. Lett., 20 (1993), 679–682.CrossRefGoogle Scholar
[5]Sullivan, S. P., Gladden, L. F. and Johns, M. L., Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques, J. Non-Newton. Fluid Mech. 133 (2006), 91–98.CrossRefGoogle Scholar
[6]Vikhansky, A., Lattice-Boltzmann method for yield-stress liquids, J. Non-Newton. Fluid Mech., 155 (2008), 95–100.CrossRefGoogle Scholar
[7]Wang, C. H. and Ho, J. R., Lattice Boltzmann modeling of Bingham plastics, Physica A, 387 (2008), 4740–4748.CrossRefGoogle Scholar
[8]Buick, J. M., Lattice Boltzmann simulation of power-law fluid flow in the mixing section of a single-screw extruder, Chem. Eng. Sci., 64 (2009), 52–58.CrossRefGoogle Scholar
[9]Ashrafizaadeh, M. and Bakhshaei, H., A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations, Comput. Math. Appl., 58 (2009), 1045–1054.Google Scholar
[10]Malaspinas, O., Fiétier, N. and Deville, M., Lattice Boltzmann method for the simulation of viscoelastic fluid flows, J. Non-Newtonian Fluid Mech., 165 (2010), 1637–1653.CrossRefGoogle Scholar
[11]Tang, G. H., Wang, S. B., Ye, P. X. and Tao, W. Q., Bingham fluid simulation with the incompressible lattice Boltzmann model, J. Non-Newton. Fluid Mech., 166 (2011), 145–151.CrossRefGoogle Scholar
[12]Ohta, M., Nakamura, T., Yoshida, Y. and Matsukuma, Y., Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels, J. Non-Newton. Fluid Mech., 166 (2011), 404–412.CrossRefGoogle Scholar
[13]Leonardi, C. R., Owen, D. R. J. and Feng, Y. T., Numerical rheometry of bulk materials using a power law fluid and the lattice Boltzmann method, J. Non-Newton. Fluid Mech., 166 (2011), 628–638.CrossRefGoogle Scholar
[14]Bhatnagar, P. L., Gross, E. P. and Krook, M., A model for collision processes in gases. I. Small amplitude processes in charged neutral one-component systems, Phys. Rev., 94 (1954), 511–525.CrossRefGoogle Scholar
[15]Qian, Y. H., d’Humières, D. and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), 479–484.CrossRefGoogle Scholar
[16]Sterling, J. D. and Chen, S., Stability analysis of lattice Boltzmann methods, J. Comput. Phys., 123 (1996), 196–206.CrossRefGoogle Scholar
[17]Niu, X. D., Shu, C., Chew, Y. T. and Wang, T. G., Investigation of stability and hydrodynamics of different lattice Boltzmann models, J. Stat. Phys., 117 (2004), 665–680.CrossRefGoogle Scholar
[18]Gabbanelli, S., Drazer, G. and Koplik, J., Lattice Boltzmann method for non-Newtonian (power-law) fluids, Phys. Rev. E, 72 (2005), 046312.CrossRefGoogle Scholar
[19]Pontrelli, G., Ubertini, S and Succi, S, The unstructured lattice Boltzmann method for non-Newtonian flows, J. Stat. Mech-Theory. E, 2009, doi:10.1088/1742-5468/2009/06/P06005.CrossRefGoogle Scholar
[20]Inamuro, T., A lattice kinetic scheme for incompressible viscous flows with heat transfer, Philos. Trans. Ser. A, Math., Phys. Eng. Sci., 360 (1792) (2002), 477–484.CrossRefGoogle Scholar
[21]Yoshino, M., Hotta, Y., Hirozane, T. and Endo, M., A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method, J. Non-Newton. Fluid Mech., 147 (2007), 69–78.CrossRefGoogle Scholar
[22]Chhabra, R. P., Bubbles, Drops, and Particles in Non-Newtonian Fluids, CRC Press, Boca Raton, 2007.Google Scholar
[23]Bird, R. B., Stewart, W. E. and Lightfoot, E. N., Transport Phenomena, second ed., John Wiely & Sons, New York, 2006.Google Scholar
[24]Neofytou, P., A 3rd order upwind finite volume method for generalized Newtonian fluid flows, Adv. Eng. Softw., 36 (2005), 664–680CrossRefGoogle Scholar
[25]Guo, Z. L., Shu, C., Lattice Boltzmann Method and its Applications in Engineering, World Scientific Press, Singapore, 2013.CrossRefGoogle Scholar
[26]Krüger, T., Varnik, F. and Raabe, D., Shear stress in lattice Boltzmann simulations, Phys. Rev. E, 79 (2009), 046704.CrossRefGoogle Scholar
[27]Papanastasiou, T. C., Flow of materials with yield, J. Rheol., 31 (1987) 385–404.CrossRefGoogle Scholar
[28]Mitsoulis, E., Abdali, S. S. and Markatos, N. C., Flow simulation of Herschel-Bulkley fluids through extrusion dies, Can. J. of Chem. Eng., 71 (1993) 147–160.CrossRefGoogle Scholar
[29]Hussain, Q. E. and Sharif, A. R., Numerical modeling of Helical flow of viscosplastic fluids in eccentric annuli, AIChE. J., 10 (2000) 1937–1946.CrossRefGoogle Scholar
[30]Yu, D., Mei, R. and Shyy, W., A unified boundary treatment in lattice Boltzmann method, New York: AIAA., (2003) 2003–0953.Google Scholar
[31]Hanks, W. H., The axial laminar flow of Yield-Pseudoplastic fluids in a concentric annulus, Ind. Eng. Chem. Process. Des. Dev., 18 (1979) 488–493.CrossRefGoogle Scholar