Physical splitting of nonlinear effects in high-velocity stable flow through porous media

Advances in Water Resources

Volumn 29, Issue 1, 2006, Pages 30-41

  Panfilov, M ^a   Fourar, M ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b CNRS   (France)

Author keywords

Darcy; Forchheimer; High Reynolds; Navier Stokes; Nonlinear correction; Permeability; Porous media; Streamlines; Vortex

Indexed keywords

CHANNEL FLOW; COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; HEAT CONVECTION; NAVIER STOKES EQUATIONS; NONLINEAR EQUATIONS; POROUS MATERIALS; REYNOLDS NUMBER; STREAM FLOW; VISCOUS FLOW; VORTEX FLOW;

FLOW STRUCTURE; FORCHHEIMER EQUATION; HIGH-VELOCITY STABLE FLOW; NONLINEAR CORRECTION; NONLINEAR EFFECTS; STREAMLINE DEFORMATION;

FLOW OF WATER;

DARCY LAW; FLOW MODELING; FLOW VELOCITY; POROUS MEDIUM; VORTEX;

EID: 28444448010     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2005.05.002     Document Type: Article

References (44)

1. N. Ahmed D.K. Sunuda Nonlinear flow in porous media J Hydr Div Proc ASCE 95 HY6 1969 1847
2. Barrère J. Modélisation des écoulements de Stokes et Navier-Stokes en milieux poreux. PhD thesis, Université Bordeaux I, France, 1990.
3. Beliashevsky NN, Bugai NG. Hydraulic structure of porous flow in an individual pore under nonlinear regime. In: Republican proceedings, Hydromechanics, Ukrainian Academy of Sciences 1974;26:64-69 [in Russian].
4. A. Bourgeat E. Marusic-Paloka Loi d'écoulement non-linéaire entre deux plaques ondulées C R Acad Sci Paris Ser I 321 1995 115-1120
5. M. Buès M. Panfilov C. Oltean Macroscale model and inertia-viscous effects for Navier-Stokes flow in a radial fracture with corrugated walls J Fluid Mech 504 2004 41-60
6. G. Chavetau Cl. Thirriot Régimes d'écoulements en milieu poreux et limite de la loi de Darcy La Houille Blanche 2 1967 141-148
7. K. Cieślicki A. Lasowska Przeplyw wody w modelu przestrzeni porowej w świetle równania Forchheimera Archiwum Górnictwa 31 1 1986 63-71
8. O. Coulaud P. Morel J.P. Caltagirone Numerical modelling of nonlinear effects in laminar flow through a porous medium J Fluid Mech 190 1988 393-407
9. F.A. Dulien M.I. Azzam Flow rate - pressure gradient measurement in periodically nonuniform capillary tube AIChE J 19 1973 222-229
10. J.P. Du Plessis J.H. Masliyah Mathematical modelling of flow through consolidated isotropic media Transport Porous Media 3 1988 145-161
11. D.A. Edwards M. Shapiro P. Bar-Yoseph M. Shapira The influence of Reynolds number upon the apparent permeability of spacially periodic arrays of cylinders Phys Fluids A 2 1 1989 45-55
12. S. Ergun Fluid flow through packed columns Chem Eng Prog 48 1952 89-95
13. M. Firdaouss J.-L. Guermond P. Le Quéré Nonlinear corrections to Darcy's law at low Reynolds numbers J Fluid Mech 343 1991 331-350
14. M. Firdaouss J.-L. Guermond Sur l'homogénéisation des équations de Navier-Stokes à faible nombre de Reynolds C R Acad Sci Paris Ser I 320 1995 245-251
15. P. Forchheimer Wasserbewegung durch boden Zeit Vereines Deutscher Ingnieure 45 49 1901 1736-1741
16. M. Fourar G. Radilla R. Lenormand C. Moyne On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media Adv Water Resourc 27 2004 669-677
17. D. Geertsma Estimating the coefficient of inertial resistance in fluid flow through porous media SPE J 14 5 1974 445-450
18. C.K. Ghaddar On the permeability of unidirectional porous media: A parallel computational approach Phys Fluids 7 11 1995 2563-2586
19. R.E. Hayes A. Afacan B. Boulanger An equation of motion for an incompressible Newtonian fluid in a packed bed Transport Porous Media 18 1995 185-198
20. A. Houpeurt Etude analogique de l'écoulement radial circulaire transitoire des gaz dans les milieux poreux Rev Inst Fr Petr 8 4 1953 129-151
21. D. Koch A.J.C. Ladd Moderate Reynolds number flows through periodic and random arrays of aligned cylinders J Fluid Mech 349 1997 31-66
22. L.D. Landau E.M. Liphshits Hydrodynamics 1986 Nauka Moscow [in Russian]
23. H. Ma D.W. Ruth The microscopic analysis of high Forchheimer number flow in porous media Transport Porous Media 13 1993 139-160
24. J.D. McFarland P.M. Dranchuk Visualisation of the transition to turbulent flow in porous media Can Petrol Technol 15 2 1976 71-77
25. C.C. Mei J.-L. Auriault The effect of weak inertia on flow through a porous medium J Fluid Mech 222 1991 647-663
26. A. Mikelić Effets inertiels pour un écoulement stationnaire visqueux incompressible dans un milieu poreux C R Acad Sci Paris Ser I 320 1995 1289-1294
27. A. Mikelić U. Hornung Homogenization and porous media 1996 Springer
28. E.M. Minsky On the turbulent flow through porous media Dokl Acad Nauk SSSR 58 3 1951 409-412
29. Muskat M. The flow of homogeneous fluids through porous media. International Human Resources Development Corporation, Reprint, 1982.
30. Panfilova I, Buès M, Panfilov M, Bouet Y. Paradoxe de symétrie et loi macroscopique d'écoulement aux grands nombres de Reynolds en milieux poreux. In: 5èmes Journées d'études sur les milieux poreux, Marseille, France, Novembre 2001;6-7:105-6.
31. M. Panfilov C. Oltean I. Panfilova M. Buès Singular nature of nonlinear macroscale effects in high-rate flow through porous media C R Acad Sci Paris Ser Mécanique 331 2003 41-480
32. M. Rasoloarijaona J.-L. Auriault Nonlinear seepage flow through a rigid porous medium Eur J Mech B/Fluids 13 2 1994 177-195
33. D.W. Ruth H. Ma Numerical analysis of viscous, incompressible flow in a diverging-converging RUC Transport Porous Media 13 1993 161-177
34. A.E. Scheidegger The physics of flow through porous media 1960 Macmillan New York
35. G. Scheneebeli Expérience sur la limite de validité de la loi de Darcy et l'apparition de turbulence dans un écoulement de filtration La Houille Blanche 2 1955 41
36. R. Skawinski Przeplyw wody w ośrodkach porowatych Archiwum Górnictwa 31 1 1986 111-123
37. E. Skjetne J.-L. Auriault High-velocity laminar and turbulent flow in porous media Transport Porous Media 36 1999 131-147
38. E. Skjetne A. Hansen J.S. Gudmunsson High-velocity flow in a rough fracture J Fluid Mech 383 1999 1-28
39. H.P.A. Souto C. Moyne Dispersion in two-dimensional periodic porous media. Part I. Hydrodynamics Phys Fluids 9 8 1997 2243-2252
40. Tran P. Corrections non linéaires à la loi de Darcy et dispersion en milieux poreux périodiques anisotropes. PhD thesis, Université Paris 6, France, 2000.
41. V.I. Volkov V.A. Mukhin V.E. Nakoriakov Investigation of flow structure in porous media J Prikladnoi Chimii 31 1 1981 101-110
42. S. Whitaker The Forchheimer equation: Theoretical development Transport Porous Media 25 1996 27-61
43. J.-C. Wodie T. Levy Correction non linéaire de la loi de darcy C R Acad Sci Paris Ser II 312 1991 157-161
44. D.E. Wright Nonlinear flow through granular media J Hydraul Div Proc Amer Soc Civ Eng 94 HY4 1868 851-872