Flow of power-law fluids in a cavity driven by the motion of two facing lids - A simulation by lattice Boltzmann method

Journal of Non-Newtonian Fluid Mechanics

Volumn 175-176, Issue , 2012, Pages 10-24

  Mendu, Siva Subrahmanyam ^a   Das, P K ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Anti parallel wall motion; Double sided; Lattice Boltzmann method; Lid driven cavity; Parallel wall motion; Power law fluid

Indexed keywords

DOUBLE SIDED; LATTICE BOLTZMANN METHOD; LID-DRIVEN CAVITIES; POWER LAW FLUID; WALL MOTION;

REYNOLDS NUMBER; VORTEX FLOW;

NON NEWTONIAN FLOW;

EID: 84859635553     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2012.03.007     Document Type: Article

References (50)

1. Chhabra R.P. Bubbles, Drops, and Particles in Non-Newtonian fluids 2007, CRC Press, Boca Raton, FL.
2. Benjamin A.S., Denny V.E. On the convergence of numerical solutions for 2-D flows in a cavity at large Re. J. Comput. Phys. 1979, 33:340-358.
3. 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. 1982, 48:387-411.
4. Jr Calhoon W.H., Roach R.L. A naturally upwind conservative procedure for the Incompressible Navier-Stokes equations on non-staggered grids. Comput. Fluids 1997, 26:525-545.
5. M. Sahin, R G. Owens, A novel fully-implicit finite volume method applied to the lid-driven cavity problem, part I. High Reynolds number flow calculations, Int. J. Numer. Meth. Fluids. 42 (2003) 57-77.
6. Neofytou P. A 3rd order upwind finite volume method for generalized Newtonian fluid flows. Adv. Eng. Softw. 2005, 36:664-680.
7. Bell B.C., Surana K.S. P-version least squares finite element formulation for two-dimensional, incompressible, non-Newtonian, isothermal and isothermal flow. Int. J. Numer. Meth. Fluids 1994, 18:127-162.
8. Zinani F., Frey S. Galerkin least-squares multifield approximations for flows of inelastic non-Newtonian Fluids. J. Fluid Eng. 2008, 130:81507-81514.
9. Cao Z., Esmail M.N. Numerical study on hydrodynamics of short-dwell paper coaters. AIChE J. 1995, 41:1833-1842.
10. Triantafillopoulos N.G., Aidun C.K. Relationship between flow instability in short-dwell ponds and cross directional coat weight non uniformities. TAPPI J. 1990, 73:127-136.
11. Gaskell P.H., Summers J.L., Thompson H.M., Savage M.D. Creeping flow analyses of free surface cavity flows. Theoret. Comput. Fluid Dynam. 1996, 8:415-433.
12. H. Hellebrand, Tape Casting, in: R.J. Brook (Ed.), Processing of Ceramics, Part1, VCH Verlagsgesellschaft mbH, vol. 17A, Weinheim, 1996, pp. 190-265.
13. Leong C.W., Ottino J.M. Experiments on mixing due to chaotic advection in a cavity. J. Fluid Mech. 1989, 209:463-499.
14. Alleborn N., Raszillier H., Durst F. Lid-driven cavity with heat and mass transport. Int. J. Heat Mass Trans. 1999, 42:833-853.
15. Kuhlmann H.C., Wanschura M., Rath H.J. Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures. J. Fluid Mech. 1997, 336:267-299.
16. Kuhlmann H.C., Wanschura M., Rath H.J. Elliptic instability in two-sided lid-driven cavity flow. Eur. J. Mech. B/Fluids 1998, 17:561-569.
17. Blohm CH., Kuhlmann H.C. The two-sided lid-driven cavity: experiments on stationary and time-dependent flows. J. Fluid Mech. 2002, 450:67-95.
18. Albensoeder S., Kuhlmann H.C., Rath H.J. Multiplicity of steady two-dimensional flows in two-sided lid driven cavities. J. Theor. Comput. Fluid Dynam. 2001, 14:223-241.
19. Wahba E.M. Multiplicity of states for two-sided and four-sided lid driven cavity flows. Comput. Fluids 2009, 38:247-253.
20. Arumuga Perumal D., Das A.K. Simulation of incompressible flows in two-sided lid-driven square cavities. Part I-FDM, CFD Lett. 2010, 2:13-24.
21. Benzi R., Succi S., Vergassola M. The lattice Boltzmann equation: theory and applications. Phys. Rep. 1992, 222:145-197.
22. Chen S., Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 1998, 30:329-364.
23. Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond 2001, Oxford University Press, Oxford.
24. Sukop M.C., Thorne D.T. Lattice Boltzmann Modeling: An introduction for Geoscientists and Engineers 2006, Springer, Heidelberg.
25. Hou S., Zou Q., Chen S., Doolen G., Cogley A.C. Simulation of cavity flow by the lattice Boltzmann method. J. Comput. Phys. 1995, 118:329-347.
26. Miller W. Flow in the driven cavity calculated by the lattice Boltzmann method. Phys. Rev. E 1995, 51:3659-3669.
27. 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 2004, 46:921-937.
28. 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. 2006, 15:1855-1862.
29. Cheng M., Hung K.C. Vortex structure of steady flow in a rectangular cavity. Comput. Fluids 2006, 35:1046-1062.
30. Patil D.V., Lakshmisha K.N., Rogg B. Lattice Boltzmann simulation of lid-driven flow in deep cavities. Comput. Fluids 2006, 35:1116-1125.
31. Arumuga Perumal D., Das A.K. Simulation of flow in two-sided lid-driven square cavities by the lattice Boltzmann method. WIT Trans. Eng. Sci. 2008, 59:45-54.
32. Aharonov E., Rothman D.H. Non-Newtonian flow (through porous media): a lattice Boltzmann method. Geophys. Res. Lett. 1993, 20:679-682.
33. S. Gabbanelli, G. Drazer, J. Koplik, Lattice Boltzmann method for non-Newtonian (power-Law) fluids, Phys. Rev. E 72 (2005) 046312-1-046312-7.
34. Sullivan S.P., Gladden L.F., Johns M.L. Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques. J. Non-Newton. Fluid Mech. 2006, 133:91-98.
35. Boyd J., Buick J., Green S. A second-order accurate lattice Boltzmann non-Newtonian model. J. Phys. A: Math. Gen. 2006, 39:14241-14247.
36. Yoshino M., Hotta Y., Hirozane T., Endo M. A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method. J. Non-Newton. Fluid Mech. 2007, 147:69-78.
37. Wang C.-H., Ho J.-R. Lattice Boltzmann modelling of Bingham plastics. Physica A 2008, 387:4740-4748.
38. Vikhansky M. Lattice-Boltzmann method for yield-stress liquids. J. Non-Newton. Fluid Mech. 2008, 155:95-100.
39. Tang G.H., Wang S.B., Ye P.X., Tao W.G. Bingham fluid simulation with the incompressible lattice Boltzmann model. J. Non-Newton. Fluid Mech. 2011, 166:145-151.
40. Ohta M., Nakamura T., Yoshida Y., Matsukuma Y. Lattice Boltzmann simulation of Viscoplastic fluid flows through complex flow channels. J. Non-Newton. Fluid Mech. 2011, 166:404-412.
41. Buick J.M. Lattice Boltzmann simulation of power-law fluid flow in the mixing section of a single-screw extruder. J. Non-Newton. Fluid Mech. 2009, 64:52-58.
42. M.-M. Hedayat, M.-H. Borghei, A. Fakhari, K. Sadeghy, On the use of Lattice-Boltzmann model for simulating lid-driven cavity flows of strain-hardening fluids, Nihon Reoroji Gakkaishi (J. Soc. Rheol. Jpn.) 38 (2010) 201-207.
43. Chai Z., Shi B., Guo Z., Rong F. Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows. J. Non-Newton. Fluid Mech. 2011, 166:332-342.
44. Phillips T.N., Roberts G.W. Lattice Boltzmann models for non-Newtonian flows. IMA J. Appl. Math. 2011, 76:790-816.
45. Lallemand P., Luo Li-Shi Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance and stability. Phys. Rev. E Stat. Phys. Plasmas Fluids Related Interdisc. Topics 2000, 61:6546-6562.
46. Bhatnagar P.L., Gross E.P., Krook M. A model for collision process in gasses. Phys. Rev. 1954, 94:511-525.
47. A. Artoli, Mesoscopic Computational Haemodynamic, Ph.D. Thesis, University of Amsterdam, 2003.
48. Zou Q., He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 1997, 9:1591-1598.
49. He X., Luo L.-S., Dembo M. Some progress in the lattice Boltzmann method: Reynolds number enhancement in simulations. Physica A 1997, 239:276-285.
50. T.C. Papanastasiou, G.C. Georgiou, A.N. Alexandrou, Viscous Fluid Flow, CRC Press, Boca Raton, FL, 2000.