Density difference driven instabilities in porous media

In the present work, we analyze density driven instabilities in miscible fluids in a random packing of monosized glass spheres (porous medium). The aim of this work is to detect heterogeneities in flow velocity using tracer dispersion because of the sensitivity of this technique. The influence of non-Newtonian rheological properties on the displacement front between two fluids of different densities is particularly studied. We compared the width of the displaced fronts in the case of Newtonian fluids with the same density contrast. Our analysis allows us to find a characteristic gravity number G (ratio between hydrostatic and viscous pressure gradients). A same threshold value of G for Newtonian and non Newtonian solutions is directly related to the structural properties of the porous medium. Received: 30 March 2000     

A two‐scale approach for fluid flow in fractured porous media

A two‐scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid‐saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two‐scale approach and integrated over time. By exploiting the partition‐of‐unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are non‐linear due to the non‐linearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns. Copyright © 2006 John Wiley & Sons, Ltd.     

Experimental investigation of heat transfer through porous media in superfluid helium

An experimental investigation of heat transfer through porous media in superfluid helium has been conducted in the framework of the development of porous electrical insulations for superconducting magnet cables cooled by superfluid helium. Several types of porous media with different characteristics were tested and, in particular, samples with pore size diameters of 0.1 μm, 1 μm, 2 μm, 10 μm and 20 μm. Temperature and pressure were measured between an insulating inner bath and the cryostat bath, communicating only through the porous medium. The cryostat bath is held constant all along the measurement and, for each sample, the tests are performed for bath temperature from 1.4 K to 2.1 K with 0.1 K increment. Depending on the porous medium average pore size diameter, different flow regimes are observed: for porous media with a pore diameter of 0.1 and 1 μm, only the Landau regime is observed whereas for porous media with a pore diameter of 2 μm, we observed the Landau regime and the Gorter-Mellink regime. For samples with a pore diameter of 10 and 20 μm, measurements only permitted to detect the Gorter-Mellink regime. In the laminar regime, the permeability of the samples was determined and it was found that the permeability is constant for bath temperature above 1.9 K whereas it increases as the bath temperature decreases from 1.8 K to 1.4 K. For samples with a pore size diameter of 10 and 20 μm, measurement permits only to observe the turbulent regime and the analysis exhibits a constant average tortuosity for each samples, independently of the bath temperature.     

Ventilation of enclosed porous media by the application of periodic pressure variations

Periodic pressure oscillations applied to the opening of closed containers packed with small beads or granular material result in an enhanced washout of undesired gases from those containers. The amplitude of oscillation pressures need not be higher than a small fraction of an atmosphere and the oscillation frequency is just below the auditory range. The time constant of the washout is reduced by two to three orders of magnitude compared to the passive equilibration by diffusion alone. The mechanism is based on gas dispersion within the gaseous phase of the containers and on gas compressibility. It may be used to remove an undesired gas out of a closed container or space filled with granular material such as solid fuel. It is also useful in the purging of porous material such as active coal.     

BEM modeling of saturated porous media susceptible to damage

This paper deals with the numerical analysis of saturated porous media, taking into account the damage phenomena on the solid skeleton. The porous media is taken into poro-elastic framework, in full-saturated condition, based on Biot’s Theory. A scalar damage model is assumed for this analysis. An implicit boundary element method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and two-dimensional elastostatic problems. The integration over boundary elements is evaluated using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear problem is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficacy.     

Long-time behaviour of multi-component fluid mixtures in porous media

The long-time behaviour of a triply convective-diffusive fluid mixture saturating a porous horizontal layer in the Darcy-Oberbeck-Boussinesq scheme, is investigated. It is shown that the L²- solutions are bounded, uniquely determined (by the initial and boundary data) and asymptotically converging toward an absorbing set of the phase-space. The stability analysis of the conduction solution is performed. The linear stability is reduced to the stability of ternary systems of O.D.Es and hence to algebraic inequalities. The existence of an instability area between stability areas of the thermal Rayleigh number (“instability island”), is found analytically when the layer is heated and “salted” (at least by one “salt”) from below. The validity of the “linearization principle” and the global nonlinear asymptotic stability of the conduction solution when all three effects are either destabilizing or stabilizing, are obtained via a symmetrization.     

Third-order bound of nonlinear composites and porous media under hydrostatic deformation

In this study the third-order variational bound is explicitly derived for nonlinear composites subject to hydrostatic deformation. By formulating the stochastic extreme principle for nonlinear boundary value problems, the third-order upper bound of the potential is derived for nonlinear two-phase composites, which is further explicitly specialized to porous media. Examples of application are provided by applying the derived bound to various cases of composites and porous media characterized with power law nonlinearity.     

Hydrodynamic stability of viscous flow between curved porous channel with radial flow

A linear stability analysis has been presented for the flow between long concentric stationary porous cylinders driven by constant azimuthal pressure gradient, when a radial flow through the permeable walls of the cylinders is present. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius is varied from −100 to 30. The linearized stability equations form an eigenvalue problem which are solved using a numerical technique based on classical Runge-Kutta scheme combined with a shooting method, termed as unit disturbance method. It is observed that radially outward flow and strong inward flow have a stabilizing effect, while weak inward flow has a destabilizing effect on the stability. Profiles of the relative amplitude of the perturbed radial velocities show that radially outward flow shifts the vortices toward the outer cylinder, while radially inward flow shifts the vortices toward the inner cylinder.     

Homogenized free surface flow in porous media for wet‐out processing

This paper presents a novel porous media model for homogenized free surface flow, representing wet‐out composites processing. The model is derived from concepts of homogenization applied to a compressible two‐phase flow, accounting for capillary effects and the concept of relative permeability. Based on mass balance considerations, we obtain a nonlinear set of equations of convection‐diffusion type involving the mixture (fluid) pressure and the degree of saturation as primary fields. A staggered Galerkin finite element approach is employed to decouple the solution. Moreover, the streamline upwind/Petrov‐Galerkin technique is applied to attenuate the oscillations in the saturation solutions. The model accuracy and convergence of the finite element solutions are demonstrated through 1‐dimensional and 2‐dimensional examples, representing resin transfer molding flow processes.     

Resistance of spherical fills in the case of flow of single- and two-phase media

The results of experimental investigations of the hydrodynamic resistance in spherical fills as applied to the cores of nuclear reactors with spherical fuel elements are presented. The experimental setup and the procedures of preparation of models, measurement, and processing of experimental data are described. The criterial dependences satisfactorily describing data on resistance in motion of single- and two-phase media in spherical fills are obtained. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 283–288, March–April, 2009.     

Gate elements at injection locations in numerical simulations of flow through porous media: applications to mold filling

Mold filling in polymer and composite processing is usually modelled as a special case of Darcy flow in porous media. The flow pattern and the time necessary to fill the mold depend on the ‘gate’ locations where resin is injected into the closed mold. In composite manufacturing, these are commonly outlets of small tubes transporting resin from a reservoir and their diameters are several orders of magnitude smaller than the mold dimensions. Similar size issue is also encountered in other applications of flow through porous media, such as oil and water pumping and drilling. Traditionally, these inlets are modelled by pressure or flow rate boundary condition as applied at a node of the finite element mesh that represents the injection gate. The omission of the inlet radius in the model results in a mathematical singularity as the mesh gets refined. The computed pressure or flow field depends on the mesh size and does not converge to the accurate solution, as the finite element mesh is refined. It is possible to deal with this phenomenon by modelling the inlet geometry more accurately but this approach is inefficient, as it requires additional degrees of freedom and, above all, significantly complicates the modelling process if the inlet location is not fixed a priori. This paper presents a more efficient alternate solution. It uses special ‘gate’ elements embedded in the mesh around the injection locations. Instead of adjusting the geometrical modelling of the injection location, the adjacent elements use modified shape functions to accurately model pressure field in the neighbourhood of small radial inlet. The proper pressure field shape‐functions for ‘gate’ elements based on linear finite elements are derived. The implementation in an existing mold filling simulation and how the ‘gate elements’ are automatically selected is described. An example to demonstrate the use of ‘gate’ elements and convergence towards the accurate solution with mesh refinement is presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical investigation of conductance of porous media in high vacuum systems

In high vacuum systems or materials that have fine capillaries, the molecular transport can be characterized as being free-molecular flow regime. In this flow regime intermolecular interactions can be ignored and flow is determined entirely by molecule-surface collisions. The transport of gases and volatile compounds through porous media and filters with variety of geometries is of great interest in various industrial applications. Although the effect of porosity on gas flow in the most of the flow regimes has been explored, but there are a few investigations on gas transport in porous media and filers at free-molecular regime. In this investigation gas transport in porous media with various porosities and geometries is explored. Test Particle Monte-Carlo (TPMC) method is employed. The walls are assumed to be diffusive. The skeletal portion of the porous media (frame) is modelled by solid spheres. The developed numerical scheme is validated with non porous cases. The effect of porosity, sphere sizes of frame, porous geometry, gas type and temperature on the conductance is examined. The simulations are performed for a porous pipe and porous nozzle. Results demonstrate that porosity and filtration highly affects the conductance of pipe and nozzle and causes great pressure drop in high vacuum systems. The increase of sphere sizes at constant porosity causes conductance to grow. The gas type and temperature of gas affects the conductance of pipe and nozzle too.     

Numerical modelling of void inclusions in porous media

Numerical modelling of porous flow in a low‐permeability matrix with high‐permeability inclusions is a challenging task because the large ratio of permeabilities ill‐conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill‐conditioning and is more efficient than heterogeneous Darcy flow. Copyright © 2003 John Wiley & Sons, Ltd.     

Exact solution of the Navier–Stokes equations for the pulsating Dean flow in a channel with porous walls

Analytical solutions of the equations of motion of a Newtonian fluid for the fully developed laminar flow between two concentric cylinders are presented, when an oscillating circumferential pressure gradient is imposed (finite gap oscillating Dean flow). The walls of the cylinders are porous, so that a radial flow can be superimposed. The analytical solution is examined for a variety of values of the dimensionless parameters, which are the transverse radial Reynolds number, the Womersley number and the ratio of the radii of the cylinders.     

恒压下树脂在双尺度多孔介质中的流动特性

基于复合材料液态模塑(LCM)工艺过程中存在半饱和区域的实验现象以及对预制体双尺度效应的逐步认识, 一些学者提出用沉浸模型来研究双尺度多孔介质的不饱和流动。通过体积均匀化方法描述了双尺度多孔介质复合材料液态模塑工艺模型的特征, 得到含有沉浸项的双尺度多孔介质的质量守恒方程, 并采用有限元法对方程进行数值求解, 通过具体算例计算了考虑双尺度效应时恒压树脂注射下不同时段的压力分布状态, 得到树脂在填充过程中流动前沿半饱和区域从出现到消失的过程, 采用不同注射压力进行模拟并比较。结果表明, 与单尺度多孔介质模型不同, 双尺度多孔介质模型更能反映实际树脂填充过程中出现的半饱和区域现象。     

First-order indicators for the estimation of discrete fractures in porous media

Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modelled as interfaces that interact with the surrounding matrix. We propose a new technique for the estimation of the location and hydrogeological properties of a small number of large fractures in a porous medium from given distributed pressure or flow data. At each iteration, the algorithm builds a short list of candidates by comparing fracture indicators. These indicators quantify at the first order the decrease of a data misfit function; they are cheap to compute. Then, the best candidate is picked up by minimization of the objective function for each candidate. Optimally driven by the fit to the data, the approach has the great advantage of not requiring remeshing, nor shape derivation. The stability of the algorithm is shown on a series of numerical examples representative of typical situations.