Finite-element modelling of combined free/porous flow regimes: simulation of flow through pleated cartridge filters

Mathematical modelling of creeping incompressible Stokes flow and low-permeability Darcy flow are well established and a number of reliable schemes for the simulation of these regimes are available in the literature. However, modelling of combined Stokes/Darcy regimes, such as those encountered in many types of industrial filters, still presents mathematical and practical challenges. In this paper, we present a finite-element model for the prediction and quantitative analyses of the hydrodynamic behaviour of deadend pleated cartridge filters. Elemental discretisation in this scheme is based on the use of unequal order approximation functions for velocity and pressure fields. We show that this discretisation generates unified stabilisation for both Stokes and Darcy equations and prevents 'numerical locking' whilst preserving the geometrical flexibility of the computational grid. Conducting a number of numerical tests, it is shown that the developed model is capable of yielding theoretically expected and accurate simulations for realistic industrially relevant problems. The model is tested for shear thickening non-Newtonian fluids, which represent fluids used in aeronautical applications and in some process industries. This study is part of a multi-disciplinary project undertaken by various investigators for the design and development of high-performance deadend pleated cartridge filters for aeronautical applications. It has been demonstrated that the developed model presents a cost effective, robust and reliable design tool to enable engineers to appraise the operation of such filters.