Three dimensional finite element modelling of non-Newtonian fluid flow through a wire mesh
Monofilament cloths are used as the separation media in filtration; woven wire cloths or screens are also used as the media in filters or to enhance the integrity of the filter medium in, for example, filter cartridges. A better understanding of the flow pattern in the woven structure is essential in examining the initial stages of cake filtration as well as the effect of weaves on fouling phenomena within a filter cloth. Due to the complex geometry of a woven cloth, three-dimensional modelling is necessary to correctly visualize the structure of the flow and hence to predict pressure losses. The modelling in a three-dimensional domain was handled using a finite element method which is known to cope with flow domains in complex geometries very effectively. The governing equations of continuity and momentum were solved by a mixed U-V-W-P finite element method and in conjunction with a first order Taylor-Galerkin scheme for temporal discretization. A secondary solution scheme based on a continuous Penalty finite element method in conjunction with theta time stepping method was also used to solve the governing equations. Two robust and reliable computer tools based on these sound and robust numerical techniques have been developed to simulate Newtonian and non-Newtonian fluid flow through a woven wire mesh. Purpose-designed test cases were used to validate the capability of the developed algorithms and were found to give expected numerical predictions. A selection of domains was used to investigate the effect of weave pattern, aperture to diameter ratio and Reynolds number on flow pattern and pressure drop. Based on these domains, simulations were successfully conducted to investigate fluid flow through four basic pore types in a plain weave, twill weave and satin weave. The flow fields in the interstices were illustrated using a commercial graphics software package. The results showed that the weave pattern has a profound effect on the fluid flow pattern and pressure drop across the wire mesh. Simulation results showed that plain weave gives the lowest pressure drop, while satin weave gives the highest pressure drop across the woven cloths. Fluid flow through a plain weave was further investigated in conjunction with the experimental studies of Rushton (1969) using water and Chhabra and Richardson (1985) using shear-thinning fluids. Simulations were tested against experimental data extracted from both studies. The close agreement of the results to those of the available experimental data in literature showed the accuracy and the reliability of the predictions. Personal communication with industrial experts and woven cloth manufacturers have confirmed industrial practice, whereby a plain weave is primarily used due to its lowest flow resistance. This showed that the developed model is capable of generating accurate results for flow of both Newtonian and non-Newtonian fluids through filter media. The model can be used by design engineers as a convenient and effective Computer Aided Design (CAD) tool for quantifying effects of pressure drop. The model can also be extended to describe particle capture on/in the wire mesh and woven filter cloths.