Upscaling multi-component two-phase flow in porous media with partitioning coefficient

This paper deals with the upscaling of multicomponents two-phase flow in porous media. In this paper, chemical potential equilibrium at the interface between both phases is assumed to be described by a linear partitioning relationship such as Raoult or Henry’s law. The resulting macro-scale dispersion model is a set of two equations related by a mass transfer coefficient and which involves several effective coefficients. These coefficients can be evaluated by solving closure problems over a representative unit-cell. The proposed model is successfully validated through direct analytical and numerical calculations

A two-pressure model for slightly compressible single phase flow in bi-structured porous media

Problems involving flow in porous media are ubiquitous in many natural and engineered systems. Mathematical modeling of such systems often relies on homogenization of pore-scale equations and macroscale continuum descriptions. For single phase flow, Stokes equations at the pore-scale are generally approximated by Darcy’s law at a larger scale. In this work, we develop an alternative model to Darcy’s law that can be used to describe slightly compressible single phase flow within bi-structured porous media. We use the method of volume averaging to upscale mass and momentum balance equations with the fluid phase split into two fictitious domains. The resulting macroscale model combines two coupled equations for average pressures with regional Darcy’s laws for velocities. In these equations, effective parameters are expressed via integrals of mapping variables that solve boundary value problems over a representative unit cell. Finally, we illustrate the behaviour of these equations in a two-dimensional model porous medium and validate our approach by comparing solutions of the homogenized equations with computations of the exact microscale problem

On the use of a Darcy-Forchheimer like model for a macro-scale description of turbulence in porous media and its application to structured packings

In this paper, we propose a methodology to derive a macro-scale momentum equation that is free from the turbulence model chosen for the pore-scale simulations and that is able to account for large-scale anisotropy. In this method, Navier–Stokes equations are first time-averaged to form a new set of equations involving an effective viscosity. The resulting balance equations are then up-scaled using a volume averaging methodology. This procedure gives a macro-scale generalized Darcy–Forchheimer equation to which is associated a closure problem that can be used to evaluate the apparent permeability tensor including inertia effects. This approach is validated through 2D and 3D calculations. Finally, the method is used to evaluate the tensorial macro-scale properties for a gas flow through structured packings

Superfluid Helium Flow in Porous Media

Superfluid helium is primarily used in the field of applied superconductivity. Given the complexity of the magnet geometry and the scales involved, a real 3D simulation of heat transfer in such devices at the micro-channel scale is very difficult, even impossible. However, the repeatability or even periodicity of the structure suggests the possibility of a macro-scale description following a porous medium approach. Which macro-scale model may be used? This largely remains an open field while some answers have been proposed based on experimental or theoretical work

Derivation of an anisotropic Darcy-Forchheimer equation including turbulence effects and its application to structured packings

We propose a methodology to derive a macroscale momentum equation that is free from the turbulence model chosen for the pore-scale simulations and that accounts for large scale anisotropy. In our method, Navier-Stokes equations are first time-averaged to form a new set of equations. Informations that describe the turbulence are embeded in a variable viscosity. This latter results from a pore-scale turbulent simulation and is considered as an input for method. The resulting continuity and momentum equations are then upscaled with regards to the volume averaging methodology to form a Darcy-Forchheimer's equation. The method also provides a closure problem that evaluates the apparent permeability tensor from a turbulent flow field computed over a periodic unit-cell. This approach is validated through 2D and 3D calculations. Finally, the method is used to evaluate the tensorial macro properties of a gas flow through structured packing

Investigation of suitability of the method of volume averaging for the study of heat transfer in superconducting accelerator magnet cooled by superfluid helium.

In the field of applied superconductivity, there is a growing need to better understand heat transfers in superconducting accelerator magnets. Depending on the engineering point of view looked at, either 0-D, 1-D, 2D or 3D modeling may be needed. Because of the size of these magnets, alone or coupled together, it is yet, impossible to study this numerically for computational reasons alone without simplification in the description of the geometry and the physics. The main idea of this study is to consider the interior of a superconducting accelerator magnet as a porous medium and to apply methods used in the field of por-ous media physics to obtain the equations that model heat transfers of a superconducting accelerator magnet in different configurations (steady-state, beam losses, quench, etc.) with minimal compromises to the physics and geometry. Since the interior of a superconducting magnet is made of coils, collars and yoke filled with liquid helium, creating channels that interconnect the helium inside the magnet, an upscaling method provides models that describe heat transfer at the magnet scale and are suitable for numerical studies. This paper presents concisely the method and an example of application for super-conducting accelerator magnet cooled by superfluid helium in the steady-state regime in considering the thermal point of view

Modélisation des écoulements dans les garnissages structurés : de l'échelle du pore à l'échelle de la colonne

Une colonne de séparation d'air réalise un écoulement liquide-gaz à contre courant dans une structure complexe, le garnissage. Au sein de ce garnissage, l'écoulement du liquide est du type film drainé par gravité, alors que l'écoulement du gaz est turbulent. La fonction de ces contacteurs est de développer une surface d'échange interfaciale aussi grande que possible pour favoriser le transfert d'un composé chimique de la phase liquide vers la phase vapeur (et inversement) tout en offrant des pertes de charge raisonnables. Ces dispositifs sont constitués par l'assemblage de plaques métalliques ondulées, avec ou sans perforations, où deux plaques adjacentes sont respectivement inclinées d'un angle et son opposé par rapport à l'axe de la colonne. Ce type de contacteur peut être considéré comme un milieu poreux bi-structuré avec un taux de porosité élevé. Les écoulements peuvent être décrits à deux échelles : une échelle du pore et une échelle macroscopique. A cause de cette double structuration, la modélisation macroscopique des écoulements dans ce type de structure reste un problème difficile. En particulier, les mécanismes macroscopiques qui entraînent l'étalement d'un jet dans les garnissages sont incompris. Par ailleurs, une difficulté de modélisation supplémentaire est due aux effets liés à la turbulence. Au cours de cette thèse, nous avons développé, à partir d'une méthode de changement d'échelle, un modèle complet pour simuler les écoulements et le transfert de matière dans les colonnes équipées de garnissages structurés. Notre étude se focalise sur les trois points suivants. Premièrement, nous avons obtenu, à l'aide d'une prise de moyenne volumique, une loi de Darcy-Forchheimer qui inclue les effets de la turbulence. Ensuite, pour modéliser la dispersion radiale du liquide dans la colonne, nous avons trouvé pratique de séparer la phase liquide en deux films distincts, qui s'écoulent sur chaque plaque ondulée selon des directions préférentielles différentes. Ces phases fictives ne sont pas indépendantes puisque de la matière peut passer de l'une à l'autre au niveau des points de contact entre les feuilles ondulées. Finalement, nous avons proposé un modèle macroscopique pour simuler le transport d'espèces chimiques dans un système diphasique, multiconstituants. Tous les paramètres effectifs qui apparaissent dans ce modèle sont évalués à partir de solutions analytiques ou numériques de l'écoulement à la petite échelle. Les résultats de simulation ont été comparés avec succès à des mesures expérimentales obtenues en laboratoire ou sur pilote industriel

Numerical Investigation of Thermal Counterflow of He II Past Cylinders

We investigate numerically, for the first time, the thermal counterflow of superfluid helium past a cylinder by solving with a finite volume method the complete so-called two-fluid model. In agreement with existing experimental results, we obtain symmetrical eddies both up- and downstream of the obstacle. The generation of these eddies is a complex transient phenomenon that involves the friction of the normal fluid component with the solid walls and the mutual friction between the superfluid and normal components. Implications for flow in a more realistic porous medium are also investigated

Numerical Investigation of Heat Transfer in a Forced Flow of He II

In this paper, we use the complete two-fluid model to simulate transient heat transfer for a forced flow of He II at high Reynolds number following the setup of the experiments performed by Fuzier, S. and Van Sciver, S., “Experimental measurements and modeling of transient heat transfer in forced flow of He II at high velocities,” Cryogenics, 48(3–4), pp. 130 – 137, (2008). A particular attention has been paid to the heat increase due to forced flow without external warming. The simulation are performed using HellFOAM , the helium superfluid simulator based on the OpenFOAM technology. Simulations results are then compared to the experimental data