A new Navier-Stokes and Darcy's law combined model for fluid flow in crossflow filtration tubular membranes |
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Authors: | Kamel Damak Abdelmoneim Ayadi Philippe Schmitz |
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Affiliation: | a Gaboratoire Radio Analyse et Environnement, Ecole National d'Ingénieurs de Sfax, BP W, 3038 Sfax, Tunisie b Centre d Etude Fondamentales-Groupe de Mécanique Acoustique et Instrumentation, 66860 Perpignan, France c Institut de Mecanique des Fluides, UMR 5502, 31400 Toulouse, France |
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Abstract: | Numerical simulations were performed for laminar fluid flow in a porous tube with variable wall suction, a model of a crossflow filtration tubular membrane. The variable wall suction is described by Darcy's law, which relates the pressure gradient within a flow stream to the flow rates through the permeable wall. The feed stream in the tube, which flows mainly tangentially to the porous wall, is modelled by the Navier-Stokes equations. A method of coupling the Navier-Stokes and the Darcy equations in a solution scheme was considered to develop a fluid dynamic model of crossflow filtration. The governing equations were solved numerically using a finite difference scheme. The solution depends on both the Reynolds axial and filtration number. Some assumptions adopted in simplified models are discussed. |
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Keywords: | Navier-Stokes Laminar Darcy's law Crossflow filtration Tubular membrane Modelling |
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