A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

Theoretical modelling of momentum transfer function of bi-disperse porous media

The aim of this paper is to obtain the momentum transfer coefficient between the two phases, denoted by f and p, occupying a bi-disperse porous medium by mapping the available experimental data to the theoretical model proposed by Nield and Kuznetsov. Data pertinent to plate-fin heat exchangers, as bi-disperse porous media, were used. The measured pressure drops for such heat exchangers are then used to give the overall permeability which is linked to the porosity and permeability of each phase as well as the interfacial momentum transfer coefficient between the two phases. Accordingly, numerical values are obtained for the momentum transfer coefficient for three different fin spacing values considered in the heat exchanger experiments.

Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls

This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.

TRANSIENT NATURAL CONVECTION FLOW IN A RECTANGULAR CAVITY FILLED WITH A POROUS MATERIAL WITH LOCALIZED HEATING FROM BELOW AND THERMAL STRATIFICATION

The transient natural convection flow with thermal stratification in a rectangular cavity filled with fluid saturated porous medium obeying Darcy's law has been studied. Prior to the time t* = 0, the flow in the cavity is assumed to be motionless and all four walls of the cavity are at the same constant temperature. At time t* = 0, the temperatures of the vertical walls are suddenly increased which vary linearly with the distance y and at the same time on the bottom wall an isothermal heat source is placed centrally. This sudden change in the wall temperatures gives rise to unsteadiness in the problem. The horizontal temperature difference induces and sustains a buoyancy driven flow in the cavity which is then controlled by the vertical temperature difference. The partial differential equations governing the transient natural convection flow have been solved numerically. The local and average Nusselt numbers decrease rapidly in a small time interval after the start of the impulsive change in the wall temperatures and the steady state is reached quickly. The time required to reach the steady state depends on the Rayleigh number and the thermal stratification parameter.

Instabilities in a fluid overlying an inclined anisotropic and inhomogeneous porous layer

In this paper, linear stability analysis on a Newtonian fluid film flowing under the effect of gravity over an inclined porous medium saturated with the same fluid in isothermal condition is carried out. The focus is placed on the effect of the anisotropic and inhomogeneous variations in the permeability of the porous medium on the shear mode and surface mode instabilities. The fluid-porous system is modelled by a coupled two-dimensional Navier-Stokes/Darcy problem. The perturbation equations are solved numerically using the Chebyshev collocation method. Detailed stability characteristics as a function of the depth ratio (the ratio of the depth of the fluid layer to that of the porous layer), the anisotropic parameter (the ratio of the permeability in the direction of the basic flow to that in the direction transverse to the basic flow) and the inhomogeneity functions are presented.

Stability of Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous layer

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

Influence Of Rayleigh Effect Combined With Marangoni Effect On The Onset Of Convection In A Liquid Layer Overlying A Porous Layer

The coupling mechanism of Rayleigh effect and Marangoni effect in a liquid-porous system is investigated using a linear stability analysis. The eigenvalue problem is solved by means of a Chebyshev tau method. Results indicate that there are three coupling modes between the Rayleigh effect and the Marangoni effect for different depth ratios. (C) 2008 Elsevier Ltd. All rights reserved.

Thermocapillary Convection In An Inhomogeneous Porous Layer

A new model consisting of an inhomogeneous porous medium saturated by incompressible fluid is investigated. We focus on the effects of inhomogeneity for the streamline patterns and instabilities of the system. Influences of the 'mean porosity' and gradient of distributions of porosity are also emphasized. The results cannot be obtained by studying the media with constant porosity as carried out by other researchers, and have not been discussed before.

A geometry model for tortuosity of flow path in porous media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.

Instabilities of a liquid film flowing down an inclined porous plane

The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy's law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio d, the Darcy number delta, and the Beavers-Joseph coefficient alpha(BJ) on the instability of the system.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.

A coupled hydro-mechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method

The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr-Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. © 2013 Elsevier Ltd.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Deposition of silver nanoparticles in geochemically heterogeneous porous media: predicting affinity from surface composition analysis.

The transport of uncoated silver nanoparticles (AgNPs) in a porous medium composed of silica glass beads modified with a partial coverage of iron oxide (hematite) was studied and compared to that in a porous medium composed of unmodified glass beads (GB). At a pH lower than the point of zero charge (PZC) of hematite, the affinity of AgNPs for a hematite-coated glass bead (FeO-GB) surface was significantly higher than that for an uncoated surface. There was a linear correlation between the average nanoparticle affinity for media composed of mixtures of FeO-GB and GB collectors and the relative composition of those media as quantified by the attachment efficiency over a range of mixing mass ratios of the two types of collectors, so that the average AgNPs affinity for these media is readily predicted from the mass (or surface) weighted average of affinities for each of the surface types. X-ray photoelectron spectroscopy (XPS) was used to quantify the composition of the collector surface as a basis for predicting the affinity between the nanoparticles for a heterogeneous collector surface. A correlation was also observed between the local abundances of AgNPs and FeO on the collector surface.