Spatially two-dimensional mathematical model of the flow hydrodynamics in a channel filled with a net-like spacer

• Published in: Journal of membrane science Vol. 368; no. 1-2; pp. 171 - 183
• Main Authors: Kodým, R., Vlasák, F., Šnita, D., Černín, A., Bouzek, K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.02.2011; Elsevier
• Subjects: Channel filled with a net-like spacer; Chemistry; Colloidal state and disperse state; Computational fluid dynamics; computer software; dialysis; Electrodialysis; equations; Exact sciences and technology; Flow distribution; General and physical chemistry; hydrodynamics; laminar flow; mathematical models; Membranes; pressure; CFD; 3D; 2D; RANS; Computational fluid dynamics; Channel filled with a net-like spacer; Flow distribution; HS; Electrodialysis; Filament; Fluid dynamics; Stokes equation; Hydrodynamics; Two dimensional model; Dimension; Modeling; Geometry; Chemical reduction; Resistance; Liquid; Flow regime; Laminar flow; Distribution; Mathematical model; Structure
• ISSN: 0376-7388; 1873-3123
• DOI: 10.1016/j.memsci.2010.11.042

▶ Novel approach of mathematical modeling of flow hydrodynamics in an electrodialysis unit. ▶ Single channel between two membranes filled with net-like spacer considered. ▶ Simulation of the industrial scale apparatus on an ordinary PC in units of minutes. ▶ Approach based on reduction of the problem dimension from 3D down to 2D. A spatially two-dimensional (2D) mathematical model of the flow hydrodynamics in a flat channel filled with a net-like spacer, for example, typical of the electrodialysis process, was developed and implemented. Subsequently the model was experimentally validated. The model introduced represents a novel CFD (computational fluid dynamic) approach, based on a reduction of the model dimensions from 3D to 2D. This allowed the modeling of systems of industrially relevant geometries on an ordinary personal computer. The simplification is possible because of the structure of the net-like spacer used which consists of two layers of filaments. In the individual layers the filaments are oriented identically. Due to this arrangement the model domain can be separated into two hydraulically interconnected sub-layers, which can be mathematically treated as 2D. The model presented is semiempirical. It includes two empirical coefficients representing hydraulic resistances. They reflect the resistance of spacer filaments to the flow in the normal and tangential direction. The stationary flow of incompressible liquid in the laminar flow regime was calculated. The model equations are based on Navier–Stokes and continuity equations. The pressure loss is described by anisotropic Darcy's law.