A 2-D streamline upwind Petrov/Galerkin finite element model for concentration polarization in spiral wound reverse osmosis modules

Journal of Membrane Science

Volumn 244, Issue 1-2, 2004, Pages 129-139

  Ma, Shengwei ^a   Song, Lianfa ^a   Ong, Say Leong ^a   Ng, Wun Jern ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Concentration polarization; Finite element method; Meshing; Numerical simulation; Reverse osmosis; Spiral wound module

Indexed keywords

CONVECTION-DIFFUSION EQUATION; CROSSFLOW DIRECTION; FEED CHANNEL; MEMBRANE SURFACE;

COMPUTER SIMULATION; CONCENTRATION (PROCESS); FINITE ELEMENT METHOD; GALERKIN METHODS; NAVIER STOKES EQUATIONS; OSMOSIS;

OSMOSIS MEMBRANES;

CONCENTRATION; CONVECTION-DIFFUSION EQUATION; FINITE ELEMENT ANALYSIS; POLARIZATION; REVERSE OSMOSIS;

ARTICLE; DIFFUSION; FINITE ELEMENT ANALYSIS; FLOW KINETICS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MEMBRANE; OSMOSIS; POLARIZATION; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; SIMULATION; VELOCITY;

EID: 7444261477     PISSN: 03767388     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.memsci.2004.06.048     Document Type: Article

References (38)

1. G. Belfort Synthetic Membrane Processes: Fundamentals and Water Applications 1984 Academic Press Orlando
2. E. Matthiasson, and B. Sivik Concentration polarization and fouling Desalination 35 1980 59
3. L. Song, and S. Yu Concentration polarization in cross-flow reverse osmosis AIChE J. 45 1999 921
4. S.S. Sablani, M.F.A. Goosen, R. Al-Belushi, and M. Wilf Concentration polarization in ultrafiltration and reverse osmosis: a critical review Desalination 141 2001 269
5. H. Miyoshi, T. Fukuumoto, and T. Kataoka A consideration of flow distribution in an ion exchange compartment with spacer Desalination 42 1982 47
6. I.S. Kang, and H.N. Chang The effects of turbulence promoters on mass transfer-numerical analysis and flow visualization Int. J. Heat Mass Transfer. 25 1982 1167
7. W.W. Focke, and P.G.J.M. Nuijens Velocity profile caused by a high porosity spacer between parallel plates (membrane) Desalination 49 1984 243
8. A.R. Da Costa, and A.G. Fane Net-type spacers: effects of configuration on fluid flow path and ultrafiltration flux Ind. Eng. Chem. Res. 33 1994 1845
9. D. Van Gauwbergen, and J. Baeyens Macroscopic fluid flow conditions in spiral-wound membrane elements Desalination 110 1997 287
10. Z. Cao, D.E. Wiley, and A.G. Fane CFD simulations of net-type turbulence promoters in a narrow channel J. Membrane Sci. 185 2001 157
11. S.K. Karode, and A. Kumar Flow visualization through spacer filled channels by computational fluid dynamics I. Pressure drop and shear rate calculations for flat sheet geometry J. Membrane Sci. 193 2001 69
12. J. Schwinge, D.E. Wiley, and D.F. Fletcher Simulation of the flow around spacer filament between narrow channel walls 1. Hydrodynamics Ind. Eng. Chem. Res. 41 2002 2977
13. S. Srinivasan, C. Tien, and W.N. Gill Simultaneous development of velocity and concentration profiles in reverse osmosis systems Chem. Eng. Sci. 22 1967 417
14. D.E. Wiley, and D.F. Fletcher Techniques for computational fluid dynamics modeling of flow in membrane channels J. Membrane Sci. 211 2003 127
15. S. Srinivasan, and C. Tien Simplified method for the prediction of concentration polarization in reverse osmosis operation for multi-component systems Desalination 7 1969 133
16. L. Song, and M. Elimelech Theory of concentration polarization in crossflow filtration J. Chem. Soc. Faraday Trans. 91 1995 3389
17. S. Bhattacharya, and S.-T. Hwang Concentration polarization, separation factor, and Peclet number in membrane processes J. Membrane Sci. 132 1997 73
18. M. Elimelech, and S. Bhattacharjee A novel approach for modeling concentration polarization in crossflow membrane filtration based on the equivalence of osmotic pressure model and filtration theory J. Membrane Sci. 145 1998 223
19. T.K. Sherwood, P.L.T. Brian, R.E. Fisher, and L. Dresner Salt concentration at phase boundaries in desalination by reverse osmosis Ind. Eng. Chem. Fundam. 4 1965 113
20. P.L.T. Brian Concentration polarization in reverse osmosis desalination with variable flux and incomplete salt rejection Ind. Eng. Chem. Fundam. 4 1965 439
21. D. Bhattacharyya, S.L. Back, and R.I. Kermode Predication of concentration polarization and flux behavior in reverse osmosis by numerical analysis J. Membrane Sci. 40 1990 231
22. E. Pellerin, E. Michelitsch, K. Darcovich, S. Lin, and C.M. Tam Turbulent transport in membrane modules by CFD simulation in two dimensions J. Membrane Sci. 100 1995 139
23. K. Madireddi, R.B. Babcock, B. Levine, J.H. Kim, and M.K. Stenstrom An unsteady-state model to predict concentration polarization in commercial spiral wound membranes J. Membrane Sci. 157 1999 13 34
24. L. Huang, and M.T. Morrissey Finite element analysis as a tool for crossflow membrane filter simulation J. Membrane Sci. 155 1999 19
25. A.S. Berman Laminar flow in channels with porous walls J. Appl. Phys. 24 1953 1232
26. A.N. Brooks, and T.J.R. Hughes Streamline upwind Petrov/Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Methods Appl. Mech. Eng. 32 1982 199
27. S. Idelsohn, N. Nigro, M. Storti, and G. Buscaglia A Petrov/Galerkin formulation for advection-diffusion Comput. Methods Appl. Mech. Eng. 136 1996 27
28. P.S. Bernard, and J.M. Wallace Turbulent Flow: Analysis, Measurement and Predication 2002 Wiley
29. G. Schock, and A. Miquel Mass transfer and pressure loss in spiral wound modules Desalination 64 1987 339
30. T.C. Papanastasiou, M. Malamataris, and K. Ellwood A new outflow boundary condition Int. J. Numer. Methods Fluids 14 1992 567
31. J.C. Heinrich, S.R. Idelsohn, E. Onate, and C.A. Vionnet Boundary conditions for finite element simulations of convective flows with artificial boundaries Int. J. Numer. Meth. Eng. 39 1996 1053
32. F. Padilla, Y. Secretan, and M. Leclerc On open boundaries in the finite element approximation of two-dimensional advection-diffusion flows Int. J. Numer. Meth. Eng. 40 1997 2493
33. G.F. Carey, and R. Krishnan Penalty finite element method for the Navier-Stokes equations Comput. Methods Appl. Mech. Eng. 42 1984 183
34. T.M. Shih, C.H. Tan, and B.C. Hwang Equivalence of artificial compressibility method and penalty-function method Numer. Heat Transfer, B: Fundam. 15 1989 127
35. T.J. Chung Finite Element Analysis in Fluid Dynamics. 1978 McGraw-Hill New York
36. O.C. Zienkiewicz, and R.L. Taylor The Finite Element Method V3: Fluid Dynamics fifth edition 2000 Butterworth Heinemann Oxford
37. U. Merten, H.K. Lonsdale, and R.L. Riley Boundary-layer effects in reverse osmosis Ind. Eng. Chem. Fundam. 3 1964 210
38. W.N. Gill, C. Tien, and D.W. Zeh Analysis of continuous reverse osmosis systems for desalination Int. J. Heat Mass Transfer. 9 1966 907