On the well-posed coupling between free fluid and porous viscous flows

International audienceWe present a well-posed model for the Stokes/Brinkman problem with {\em jump embedded boundary conditions (J.E.B.C.)} on an immersed interface. It is issued from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface $\S$ separating the fluid and porous domains. These conditions are well chosen to get the coercivity of the operator. Then, the general framework allows to prove the global solvability of some models with physically relevant stress or velocity jump boundary conditions for the momentum transport at a fluid-porous interface. The Stokes/Brinkman problem with {\em Ochoa-Tapia \& Whitaker (1995)} interface conditions and the Stokes/Darcy problem with {\em Beavers \& Joseph (1967)} conditions are both proved to be well-posed by an asymptotic analysis. Up to now, only the Stokes/Darcy problem with {\em Saffman (1971)} approximate interface conditions was known to be well-posed

Two-phase flow in a chemically active porous medium

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species -- in a one-dimensional macroscopic description --, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor.Comment: 13 pages, 10 figure

Mathematical modeling of channel-porous layer interfaces in PEM fuel cells

In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary. After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them. The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur. We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster

Pressure jump interface law for the Stokes-Darcy coupling: Confirmation by direct numerical simulations

It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, interface law for the effective stress has been a subject of controversy. Recently, a pressure jump interface law has been rigorously derived by Marciniak-Czochra and Mikeli\'c. In this paper, we provide a confirmation of the analytical result using direct numerical simulation of the flow at the microscopic level.Comment: 25 pages, preprin

A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media

In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dynamical and equilibrium properties. Numerical results are presented for the representative 2-dimensional capillary-rise problem pertaining to two closely spaced vertical plates with both identical and disparate wetting properties. Comparison with analytical solutions for these test cases corroborates the accuracy of the presented multiscale model. In addition, we present results for a capillary-rise problem with a non-trivial geometry corresponding to a porous medium

Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension

The XDEM Multi-physics and Multi-scale Simulation Technology: Review on DEM-CFD Coupling, Methodology and Engineering Applications

The XDEM multi-physics and multi-scale simulation platform roots in the Ex- tended Discrete Element Method (XDEM) and is being developed at the In- stitute of Computational Engineering at the University of Luxembourg. The platform is an advanced multi- physics simulation technology that combines flexibility and versatility to establish the next generation of multi-physics and multi-scale simulation tools. For this purpose the simulation framework relies on coupling various predictive tools based on both an Eulerian and Lagrangian approach. Eulerian approaches represent the wide field of continuum models while the Lagrange approach is perfectly suited to characterise discrete phases. Thus, continuum models include classical simulation tools such as Computa- tional Fluid Dynamics (CFD) or Finite Element Analysis (FEA) while an ex- tended configuration of the classical Discrete Element Method (DEM) addresses the discrete e.g. particulate phase. Apart from predicting the trajectories of individual particles, XDEM extends the application to estimating the thermo- dynamic state of each particle by advanced and optimised algorithms. The thermodynamic state may include temperature and species distributions due to chemical reaction and external heat sources. Hence, coupling these extended features with either CFD or FEA opens up a wide range of applications as diverse as pharmaceutical industry e.g. drug production, agriculture food and processing industry, mining, construction and agricultural machinery, metals manufacturing, energy production and systems biology