Finite element implementation of stress-jump and stress-continuity conditions at porous-medium, clear-fluid interface

Computers and Fluids

Volumn 38, Issue 6, 2009, Pages 1118-1131

  Tan, Hua ^a   Pillai, Krishna M ^a  

^a University of Wisconsin Milwaukee   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITE MICROMECHANICS; FLUIDS; POROUS MATERIALS; TENSORS; THREE DIMENSIONAL;

3D FLOW SIMULATIONS; ANALYTICAL SOLUTIONS; BRINKMAN EQUATIONS; CONTINUITY CONDITIONS; CROSS FLOWS; FE FORMULATIONS; FIBER-MATS; FINITE ELEMENT IMPLEMENTATIONS; FINITE ELEMENTS; FLOW VARIABLES; FLOW-RATE; FLOW-THROUGH; FLUID INTERFACES; GALERKIN; INTERFACE FLOWS; INTERFACIAL CONDITIONS; JUMP CONDITIONS; LIQUID COMPOSITE MOLDING PROCESS; NUMERICAL PREDICTIONS; PARALLEL FLOWS; POROUS MEDIAS; POROUS MEDIUMS; SECOND ORDERS; THREE-DIMENSIONAL FLOWS; UNIT CELLS; VALIDATION STUDIES; VELOCITY PROFILES; VOLUME-AVERAGING METHODS;

FLOW SIMULATION;

EID: 62549164226     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2008.11.006     Document Type: Article

References (43)

1. Joseph D.D., Nield D.A., and Papanicolaou G. Nonlinear equation governing flow in a saturated porous medium. Water Res Res 18 (1982) 1049-1052
2. Hsu C.T., and Cheng P. Thermal dispersion in a porous medium. Intl J Heat Mass Transfer 33 (1990) 1587-1597
3. Kladias N., and Prasad V. Experimental verification of Darcy-Brinkman-Forchheimer flow model for natural convection in porous media. J Thermophys 5 (1991) 560-576
4. Vafai K., and Kim S.J. Fluid mechanics of the interface region between aporous medium and a fluid layer-an exact solution. Intl J Heat Fluid Flow 11 (1990) 254-256
5. Nield D.A. The limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous medium and at an interface. Intl J Heat Fluid Flow 12 (1991) 269-272
6. Beavers G.S., and Joseph D.D. Boundary condition at a naturally permeable wall. J Fluid Mech 30 (1967) 197-207
7. Saffman P.G. On the boundary condition at the surface of a porous medium. Stud Appl Maths 50 (1971) 93-101
8. Taylor G.I. A model for the boundary condition of a porous material: part 1. J Fluid Mech 49 (1971) 319-326
9. Larson R.E., and Higdon J.J.L. Microscopic flow near the surface of two-dimensional porous media, part 1: axial flow. J Fluid Mech 166 (1986) 449-472
10. Larson R.E., and Higdon J.J.L. Microscopic flow near the surface of two-dimensional porous media, part 2: transverse flow. J Fluid Mech 178 (1987) 119-136
11. Salinger A.G., Aris R., and Derby J.J. Finite element formulations for large-scale, coupled flows in adjacent porous and open fluid domains. Int J Numer Meth Fluids 18 (1994) 1185-1209
12. Gartling D.K., Hickox C.E., and Givler R.C. Simulation of coupled viscous and porous flow problems. Comput Fluid Dyn 7 (1996) 23-48
13. Nassehi V. Modelling of combined Navier-Stokes and Darcy flows in crossflow membrane filtration. Chem Eng Sci 53 (1998) 1253-1265
14. Brinkman H.C. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl Sci Res A1 (1947) 27-34
15. Neale G., and Nader W. Practical significance of Brinkman's extension of Darcy's law: coupled parallel flows within a channel and a bounding porous medium. Can J Chem Engng 52 (1974) 475-478
16. Martys N., Bentz D.P., and Garboczi E.J. Computer simulation study of the effective viscosity in Brinkman's equation. Phys Fluids 6 (1994) 1434-1439
17. Sahraoui M., and Kaviany M. Slip and no-slip velocity boundary conditions at interface of porous, plain media. Int J Heat Mass Transfer 35 (1995) 927-943
18. James D.F., and Davis A.M. Flow at the interface of a model fibrous porous medium. J Fluid Mech 426 (2001) 47-72
19. Costa V.A.F., Oliveira L.A., Baliga B.R., and Sousa A.C.M. Simulation of coupled flows in adjacent porous and open domains using a control-volume finite-element method. Numer Heat Transfer, Part A 45 (2004) 675-697
20. Ochoa-Tapia J.A., and Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid I: theoretical development. Int J Heat Mass Transfer 38 (1995) 2635-2646
21. Ochoa-Tapia J.A., and Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid II: comparison with experiment. Int J Heat Mass Transfer 38 (1995) 2647-2655
22. Ochoa-Tapia J.A., and Whitaker S. Momentum jump condition at the boundary between a porous medium and a homogeneous fluid: inertial effects. J Porous Media 1 (1998) 201-217
23. Valdes-Parada F.J., Goyeau B., and Ochoa-Tapia J.A. Jump momentum boundary condition at a fluid-porous dividing surface: derivation of the closure problem. Chem Eng Sci 62 15 (2007) 4025-4039
24. Valdes-Parada F.J., Goyeau B., and Ochoa-Tapia J.A. Diffusive mass transfer between a microporous medium and an homogeneous fluid: jump boundary conditions. Chem Eng Sci 61 5 (2006) 1692-1704
25. Kuznetsov A.V. Influence of the stress jump condition at the porous-medium/clear-fluid interface on a flow at a porous wall. Int. Commun. Heat Mass Transfer 24 (1997) 40-410
26. Kuznetsov A.V. Analytical investigation of Coette flow in a composite channel partially filled with a porous medium and partially filled with a clear fluid. Int J Heat Mass Transfer 41 (1998) 2556-2560
27. Chandesris M., and Jamet D. Boundary conditions at a planar fluid-porous interface for a poiseuille flow. Int J Heat Mass Transfer 49 13-14 (2006) 2137-2150
28. Chandesris M., and Jamet D. Boundary conditions at a fluid-porous interface: an a priori estimation of the stress jump coefficients. Int J Heat Mass Transfer 50 17-18 (2007) 3422-3436
29. Tan H, Chen X, Pillai KM, Papathanasiou TD. Boundary conditions at the interface between the clear-fluid and porous medium domains'. In: Ninth international conference on flow processes in composite materials, Montreal; 2008.
30. Reddy J.N. Penalty-finite-element analysis of 3-D Navier-Stokes equations. Comput Meth Appl Mech Eng 35 (1982) 87-106
31. Reddy J.N., and Gartling D.K. The finite element method in heat transfer and fluid dynamics (2000), CRC, New York
32. Donea J., and Huerta A. Finite element methods for flow problems (2003), John Wiley & Sons Ltd., England
33. Kaviany M. Principles of heat transfer in porous media (1991), Springer, New York
34. Tachie M.F., James D.F., and Currie I.G. Velocity measurements of a shear flow penetrating a porous medium. J Fluid Mech 493 (2003) 319-343
35. Nield D.A., and Bejan A. Convection in porous media (1992), Springer, New York
36. Rudd C.D., Long A.C., Kendall K.n., and Mangin C.G.E. Liquid molding technologies: resin transfer moulding, structural reaction injection moulding and related processing techniques (1997), Woodhead Publishing Ltd.
37. Parnas Richard.S., and Salem Andrew.J. A comparison of the unidirectional and radial in-plane flow of fluids through woven composite reinforcements. Polymer Compos 14 5 (1993) 383-394
38. Ngo N.D., and Tamma K.K. Microscale permeability predictions of porous fibrous media. Int J Heat Mass Transfer 44 (2001) 3135-3145
39. Nordlund M., and Lundstrom T.S. Numerical study of the local permeability of noncrimp fabrics. J Compos Mater 39 (2005) 929-947
40. Tan H., Roy T., and Pillai K.M. Variations in unsaturated flow with flow direction in resin transfer molding: an experimental investigation. Compos Part A 38 8 (2007) 1872-1892
41. Gebart B.R. Permeability of unidirectional reinforcements for RTM. J Compos Mater 26 (1992) 1100-1133
42. Roy T., and Pillai K.M. Characterization of dual-scale fiber mats for unsaturated flow in liquid composite molding. Polymer Compos 26 6 (2005) 756-769
43. Hua Tan, Languri Ehsan M, Pillai Krishna M, Permeability prediction of dual-scale fibrous structure using the unit cell. In: Ninth international conference on flow processes in composite materials, Montreal; 2008.