共查询到8条相似文献,搜索用时 15 毫秒
1.
In the quest (i) to determine the form of the boundary conditions that must be applied at a fluid/porous interface and (ii)
to determine the value of the jump parameters that appear in the expression for these boundary conditions, two different approaches
are commonly considered: the so-called one-domain and two-domain approaches. These approaches are commonly thought to be different,
and they are thus sometimes compared to each other to determine the value of jump parameters. In this article, we show that
the two-domain and discontinuous one-domain approaches are actually strictly equivalent, provided that the latter is mathematically
interpreted in the sense of distributions. This equivalence is shown in details for a heat conduction problem and for the
more classical Darcy-Brinkman problem. We show in particular that interfacial jumps are introduced in the discontinuous one-domain
approach through Dirac delta functions. Numerical issues are then discussed that show that subtle discretization truncation
errors give rise to large variations that can be mis-interpreted as the sign of the existence of jump parameters. 相似文献
2.
The flow of non-Newtonian fluids through two-dimensional porous media is analyzed at the pore scale using the smoothed particle
hydrodynamics (SPH) method. A fully explicit projection method is used to simulate incompressible flow. This study focuses
on a shear-thinning power-law model (n < 1), though the method is sufficiently general to include other stress-shear rate relationships. The capabilities of the
proposed method are demonstrated by analyzing a Poiseuille problem at low Reynolds numbers. Two test cases are also solved
to evaluate validity of Darcy’s law for power-law fluids and to investigate the effect of anisotropy at the pore scale. Results
show that the proposed algorithm can accurately simulate non-Newtonian fluid flows in porous media. 相似文献
3.
The macroscopic model governing coupled electro-chemo-mechanical phenomena in expansive clays is revisited within a rigorous
homogenization procedure applied to the microscopic governing equations which describe the local interaction between charged
clay particles and a binary monovalent aqueous electrolyte solution. The up-scaling of the microscopic electro-hydro-dynamics
leads to a two-scale approach wherein the macroscopic model appears governed by a fully coupled form of Onsager’s reciprocity
relations, mass conservation equations and a modified Terzaghi’s effective stress principle. In addition, the two-scale approach
provides microscopic representations for the effective coefficients which are exploited herein to obtain further insight in
the constitutive behavior of the electrochemical parameters and the swelling pressure. Among other effects, we show that these
microscopic closure relations are mainly dictated by the spatial variability of a microscale electric potential which satisfies
a local version of the Poisson–Boltzmann problem in a periodic unit cell, The proposed framework allows to address various
relevant still open issues regarding the constitutive behavior of swelling systems, Among them we give particular emphasis
on the analysis of the influence of the fluctuation and distortion of the electrical double layer upon the magnitude of the
electrochemical coefficients and the precise local conditions for the validity of the symmetry of Onsager’s relations. 相似文献
4.
We consider the compressible steady state air flow in a porous medium caused by an extraction well and governed by Darcy's law. For a homogeneous soil matrix we have derived formulas (in 2-D and 3-D) to determine the effective radius of a single well depending on the well position and the depth of the domain. For inhomogeneous case (in 2-D) the influence of the heterogeneity, well position and the depth of the water table on the effective radius and on the pressure at the well is studied. 相似文献
5.
Computation of Jump Coefficients for Momentum Transfer Between a Porous Medium and a Fluid Using a Closed Generalized Transfer Equation 总被引:1,自引:0,他引:1
Francisco J. Valdés-Parada José Alvarez-Ramírez Benoît Goyeau J. Alberto Ochoa-Tapia 《Transport in Porous Media》2009,78(3):439-457
The momentum transfer between a homogeneous fluid and a porous medium in a system analogous to the one used by Beavers and
Joseph (J Fluid Mech 30:197–207, 1967) is studied using volume averaging techniques. In this article, we present a closed
generalized momentum transport equation (GTE) that is valid everywhere and is expressed in terms of position-dependent effective
transport coefficients, which are computed from the solution of associated closure problems previously reported. A combination
of the velocity profiles from the GTE in the definition of the excess terms that define the jump coefficients allows their
computation using numerical techniques. The calculations are in concordance with those resulting from the work of Goyeau et al.
(Int J Heat Mass Transf. 46:4071–4081, 2003), showing a strong dependence with the porosity. In addition, the effects of the
roughness of the boundary on the computation of the position-dependent permeability tensor in the inter-region are also analyzed. 相似文献
6.
Moura Neto F. Paes Leme P. J. Amaral Souto H. P. Vargas A. S. 《Transport in Porous Media》1998,33(3):205-226
Homogenization techniques are used to upscale from pore to laboratory or field scale viscous and second grade nonNewtonian flow in a porous medium. Nonlinear forms of Darcy's law are obtained and analysed under a series of symmetry properties. The general case of displacement of one of these fluids by another with different properties is considered and a linear stability analysis is performed. 相似文献
7.
Francisco J. Valdés-Parada Jose Alvarez-Ramirez Benoît Goyeau J. Alberto Ochoa-Tapia 《Transport in Porous Media》2009,78(3):459-476
In this paper, mass transfer at the fluid–porous medium boundaries is studied. The problem considers both diffusive and convective
transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that
is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction
and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved
as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., ), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a
microporous medium. 相似文献
8.
In Part I Moyne and Murad [Transport in Porous Media 62, (2006), 333–380] a two-scale model of coupled electro-chemo-mechanical phenomena in swelling porous media was derived by
a formal asymptotic homogenization analysis. The microscopic portrait of the model consists of a two-phase system composed
of an electrolyte solution and colloidal clay particles. The movement of the liquid at the microscale is ruled by the modified
Stokes problem; the advection, diffusion and electro-migration of monovalent ions Na+ and Cl− are governed by the Nernst–Planck equations and the local electric potential distribution is dictated by the Poisson problem.
The microscopic governing equations in the fluid domain are coupled with the elasticity problem for the clay particles through
boundary conditions on the solid–fluid interface. The up-scaling procedure led to a macroscopic model based on Onsager’s reciprocity
relations coupled with a modified form of Terzaghi’s effective stress principle including an additional swelling stress component.
A notable consequence of the two-scale framework are the new closure problems derived for the macroscopic electro-chemo-mechanical
parameters. Such local representation bridge the gap between the macroscopic Thermodynamics of Irreversible Processes and
microscopic Electro-Hydrodynamics by establishing a direct correlation between the magnitude of the effective properties and
the electrical double layer potential, whose local distribution is governed by a microscale Poisson–Boltzmann equation. The
purpose of this paper is to validate computationally the two-scale model and to introduce new concepts inherent to the problem
considering a particular form of microstructure wherein the clay fabric is composed of parallel particles of face-to-face
contact. By discretizing the local Poisson–Boltzmann equation and solving numerically the closure problems, the constitutive
behavior of the diffusion coefficients of cations and anions, chemico-osmotic and electro-osmotic conductivities in Darcy’s
law, Onsager’s parameters, swelling pressure, electro-chemical compressibility, surface tension, primary/secondary electroviscous
effects and the reflection coefficient are computed for a range particle distances and sat concentrations. 相似文献