Modelling of power-law fluid flow through porous media using smoothed particle hydrodynamics

Transport in Porous Media

Volumn 74, Issue 3, 2008, Pages 331-346

  Vakilha, Mehran ^a   Manzari, Mehrdad T ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Anisotropic fibrous media; Darcy's law; Poiseuille flow; Pore scale simulation; Shear thinning fluid; Smoothed particle hydrodynamics

Indexed keywords

CRYSTALLOGRAPHY; FLOW MEASUREMENT; FLOW OF FLUIDS; FLUID DYNAMICS; GROUNDWATER FLOW; HYDRODYNAMICS; INCOMPRESSIBLE FLOW; LAWS AND LEGISLATION; LIQUIDS; NEWTONIAN LIQUIDS; NON NEWTONIAN FLOW; POROUS MATERIALS; REYNOLDS NUMBER; RHEOLOGY; TWO DIMENSIONAL; VISCOUS FLOW;

ANISOTROPIC FIBROUS MEDIA; DARCY'S LAW; NON-NEWTONIAN FLUID FLOWS; NON-NEWTONIAN FLUIDS; POISEUILLE FLOW; PORE SCALE; PORE-SCALE SIMULATION; POROUS MEDIUMS; POWER-LAW FLUIDS; POWER-LAW MODELS; PROJECTION METHODS; REYNOLDS; SHEAR RATES; SHEAR-THINNING; SHEAR-THINNING FLUID; SMOOTHED PARTICLE HYDRODYNAMICS; SMOOTHED-PARTICLE HYDRODYNAMICS METHOD; TEST CASES;

FLUID MECHANICS;

ALGORITHM; COMPUTER SIMULATION; DARCY LAW; FLOW MODELING; HYDRODYNAMICS; INCOMPRESSIBLE FLOW; NON-NEWTONIAN FLUID; POROUS MEDIUM; REYNOLDS NUMBER; SHEAR FLOW; TWO-DIMENSIONAL FLOW;

EID: 50249098098     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-007-9199-z     Document Type: Article

References (35)

1. Aharonov, E., Rothman, D.H.: Non-Newtonian flow through porous media, a lattice Boltzmann method. Geophys. Res. Lett. 20 (8), 679-682 (1993)
2. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, 1st ed. Wiley, New York (1960)
3. Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1972)
4. Bernsdorf, J., Brenner, G., Durst, F.: Numerical analysis of the pressure drop in porous media flow with lattice Boltzmann (BGK) automata. Comput. Phys. Commun. 129 (1-3), 247-255 (2000)
5. Bonet, J., Lok, T.S.L.: Variational and momentum preservation aspects of smoothed particle hydrodynamics formulations. Comput. Methods Appl. Mech. Eng. 180 (1-2), 97-115 (1999)
6. Cancelliere, A., Chang, C., Foti, E., Rothman, D.H., Succi, S.: The permeability of a random medium: Comparison of simulation with theory. Phys. Fluids A 2 (12), 2085-2088 (1990)
7. Cao, J., Kitanidis, P.K.: Adaptive finite element simulation of Stokes flow in porous media. Adv. Water Resour. 22 (1), 17-31 (1998)
8. Carreau P.J., De Kee D.C.R., Chhabra R.P.: Rheology of Polymeric Systems. Hanser Gardner Publications (1997)
9. Chaplain, V., Allain, C., Hulin, J.P.: Tracer dispersion in power-law fluids flow through porous media: Evidence of a cross-over from logarithmic to a power-law behavior. Eur. Phys. J. B 6 (2), 225-231 (1998)
10. Chen, S., Diemer, K., Doolen, G.D., Eggert, K., Fu, C., Gutman, S., Travis, B.J.: Lattice gas automata for flow through porous media. Physics D 47 (1-2), 72-84 (1991)
11. Chorin, A.J.: Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (104), 745-762 (1968)
12. Colagrossi, A., Landrini, M.: Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 191 (2), 448-475 (2003)
13. Durst, F., Haas, R., Interthal, W.: The nature of flows through porous media. J. Non-Newt. Fluid Mech. 22 (2), 169-189 (1987)
14. Fox R.W., McDonald A.T. (1994) Introduction to Fluid Mechanics, 4th edn. Wiley
15. Gingold, R.A., Monaghan, JTJ.: Smoothed particle hydrodnamics: theory and application to nonspherical stars. Mon. Not. Roy. Astr. Soc. 181 (2), 375-389 (1977)
16. Hosseini, S.M., Manzari, M.T., Hannani, S.K.: A fully explicit three-step SPH algorithm for simulation of non-Newtonian fluid flow. Int. J. Numer. Methods Heat Fluid Flow 17 (7), 715-735 (2007)
17. Idris, Z., Orgeas, L., Geindreau, C., Bloch, J.F., Auriault, J.L.: Microstructural effects on the flow law of power-law fluids through fibrous media. Model. Simul. Mater. Sci. Eng. 12, 995-1015 (2004)
18. Kopenon, A., Kataja, M., Timonen, J.: Permeability and effective porosity of porous media. Phys. Rev. E 56 (3), 3319-3325 (1997)
19. Koshizuka, S., Tamako, H., Oka, Y.: A particle method for incompressible viscous flow with fluid fragmentation. Comput. Fluid Dyn. J. 4 (1), 29-46 (1995)
20. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82 (12), 1013-1024 (1977)
21. Monaghan, J.J.: Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30 (2), 543-574 (1992)
22. Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136 (1), 214-225 (1997)
23. Orgeas, L., Idris, Z., Geindreau, C., Bloch, J.F., Auriault, J.L.: Modelling the flow of power-law fluids through anisotropic porous media at low-pore Reynolds number. Chem. Eng. Sci. 61, 4490-4502 (2006)
24. Pearson, J.R.A., Tardy, P.M.J.: Models of non-Newtonian and complex fluids through porous media. J. Non-Newt. Fluid Mech. 102 (2), 447-473 (2002)
25. Rodriguez, S., Romero, C., Sargenti, M.L., Muller, A.J., Saez, A.E., Odell, J.A.: Flow of polymer solutions through porous media. J. Non-Newt. Fluid Mech. 49 (1), 63-85 (1993)
26. Shao, S., Lo, E.Y.M.: Incompressible SPH method for simulating newtonian and non-newtonian flows with a free surface. Adv. Water Resour. 26 (7), 787-800 (2003)
27. Spaid, M.A.A., Phelan, F.R.: Lattice Boltzmann methods for modeling microscale flow in fiborous porous media. Phys. Fluids 9 (9), 2468-2474 (1997)
28. Sullivan, S.P., Gladden, L.F., Johns, M.L.: Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques. J. Non-Newt. Fluids Mech. 133 (2-3), 91-98 (2006)
29. Takeda, H., Miyama, S.M., Sekiya, M.: Numerical simulation of viscous flow with smoothed particle hydrodynamics. Prog. Theor. Phys. 92 (5), 939-960 (1994)
30. Tartakovsky, A.M., Meakin, P.: Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics. Adv. Water Resour. 29 (10), 1464-1478 (2006)
31. Watkins, S.J., Bhattal, A.S., Francis, N., Turner, J.A., Whitworth, A.P.: Astron. Astrophys. Suppl. Ser. Adv. Water Resour 119 (1), 177-187 (1996)
32. Whitaker, S.: Flow An porous media, I: a theoretical derivation of Darcy's law. Transp. Porous Media 1 (1), 3-25 (1986)
33. Woods, J.K., Spelt, P.D.M., Lee, P.D., Selerland, T., Lawrence, C.J.: Creeping flows of power-law fluids through periodic arrays of elliptical cylinders. J. Non-Newt. Fluid Mech. 111, 211-228 (2003)
34. Yiotis, A.G., Psihogios, J., Kainourgiakis, M.E., Papaioannou, A., Stubos, A.K.: A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media. Colloids Surf. A: Physicochem. Eng. Asp. 300, 35-49 (2007)
35. Zhu, Y., Fox, P.J.: Simulation of pore-scale dispersion in periodic porous media using smoothed particle hydrodynamics. J. Comput. Phys. 182 (2), 622-645 (2002)