Numerical Analysis of Coupled Stokes/Darcy Flows in Industrial Filtrations

Abstract

Free flow channel confined by porous walls is a feature of many of the natural and industrial settings. Viscous flows adjacent to saturated porous medium occur in cross-flow and dead-end filtrations employed primarily in pharmaceutical and chemical industries for solid-liquid or gas-solid separations. Various mathematical models have been put forward to describe the conjugate flow dynamics based on theoretical grounds and experimental evidence. Despite this fact, there still exists a wide scope for extensive research in numerical solutions of these coupled models when applied to problems with industrial relevance. The present work aims towards the numerical analysis of coupled free/porous flow dynamics in the context of industrial filtration systems. The free flow dynamics has been expressed by the Stokes equations for the creeping, laminar flow regime whereas the flow behaviour in very low permeability porous media has been represented by the conventional Darcy equation. The combined free/porous fluid dynamical behaviour has been simulated using a mixed finite element formulation based on the standard Galerkin technique. A nodal replacement technique has been developed for the direct linking of Stokes and Darcy flow regimes which alleviates specification of any additional constraint at the free/porous interface. The simulated flow and pressure fields have been found for flow domains with different geometries which represent prototypes of actual industrial filtration equipment. Results have been obtained for varying values of permeability of the porous medium for generalised Newtonian fluids obeying the power law model. A series of numerical experiments has been performed in order to validate the coupled flow model. The developed model has been examined for its flexibility in dealing with complex geometrical domains and found to be generic in delivering convergent, stable and theoretically consistent results. The validity and accuracy of the simulated results has been affirmed by comparing with available experimental data.

Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization

“…We refer to [10], [13], [14], [27], [36] and references therein. In such setting, the authors used general interface conditions introduced by Ochoa-Tapia and Whitaker in [29].…”

Pressure-driven flow in a channel with porous walls

“…Furman 2008, filtration (see e.g. Hanspal et al 2006), material processing (see e.g. Le Bars & Worster 2006), biological interfaces (see e.g.…”

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

“…Many of the applications considered use a Newtonian fluid in both the Stokes and Darcy regions, where the motivating problem is often a coupled surface water / groundwater model (see, for instance, [6,14,18,22,24,27,28]). Our interest in coupled flows arises from filtration applications, which continues to be an active area of research (see, for instance, [3,12,20,26,23]).…”