A LGA model for fluid flow in heterogeneous porous media

A lattice gas automaton (LGA) model is proposed to simulate fluid flow in heterogeneous porous media. Permeability fields are created by distributing scatterers (solids, grains) within the fluid flow field. These scatterers act as obstacles to flow. The loss in momentum of the fluid is directly related to the permeability of the lattice gas model. It is shown that by varying the probability of occurrence of solid nodes, the permeability of the porous medium can be changed over several orders of magnitude. To simulate fluid flow in heterogeneous permeability fields, isotropic, anisotropic, random, and correlated permeability fields are generated. The lattice gas model developed here is then used to obtain the effective permeability as well as the local fluid flow field. The method presented here can be used to simulate fluid flow in arbitrarily complex heterogeneous porous media.     

A unified theory for cavity expansion in cohesive-frictional micromorphic media

This paper presents a unified theory for both cylindrical and spherical cavity expansion problems in cohesive-frictional micromorphic media. A phenomenological strain-gradient plasticity model in conjunction with a generalized Mohr–Coulomb criterion is employed to characterize the elasto-plastic behavior of the material. To solve the resultant two-point boundary-value problem (BVP) of fourth-order homogeneous ordinary differential equation (ODE) for the governing equations which is not well-conditioned in certain cases, several numerical methods are developed and are compared in terms of robustness, efficiency and accuracy. Using one of the finite difference methods that shows overall better performance, both cylindrical and spherical cavity expansion problems in micromorphic media are solved. The influences of microstructural properties on the expansion response are clearly demonstrated. Size effect during the cavity expansion is captured. The proposed theory is also applied to a revisit of the classic problem of stress concentration around a cavity in a micromorphic medium subjected to isotropic tension at infinity, for which some conclusions made in early studies are revised. The proposed theory can be useful for the interpretation of indentation tests at small scales.     

A unified constitutive model for superalloys

A physically based unified constitutive model is presented for an aircraft engine nickelbase superalloy. The model accounts for deformation modes that can be activated under different stress, time, and temperature combinations. Two internal state variables and a flow function have been utilized to prdict strain rate sensitivity, stress hold creep, strain hold relaxation, monotonic loading, cyclic loading, and thermal mechanical cycling. In the model flow function, creep deformation and plasticity deformation modes have been incorporated over a wide range of temperatures (0.4 < T/T_melt < 0.75). The model is checked with independent isothermal and thermal mechanical experiments. Different temperature ranges are explored to assess model capabilities.     

一种黏弹塑性统一本构模型

经过对大量有关统一本构模型的文献资料分析，指出了现有统一本构模型存在的问题，并通过对材料实验数据的分析，指出了黏弹性现象在实验中的表现，并据此将黏弹性引入到弹性黏塑性统一本构模型之中，建立了黏弹塑性统一本构模型，通过模型的数值模拟证明：模型计算结果无论在变形趋势上，还是在数值精度上都与实验数据符合得很好，克服了此前统一本构模型存在的问题。黏弹塑性统一本构模型的产生将统一本构模型的产生将统一本构理论的内涵扩大到黏弹性范围，进而构造了一个黏弹塑性理论的新框架。     

Experimental studies of model porous media fluid dynamics

The three-dimensional, steady flow velocity components of a viscous, incompressible, Newtonian fluid in model porous media were measured. The model porous geometries were constructed from 3 mm glass rods. A laser Doppler anemometer was used to measure two of the velocity components and the third was calculated by integrating the continuity equation. The effects of viscous drag, inertial flow fields and eddy losses in the model were studied. The results showed that the measured flow was laminar and stable such that micromixing of the fluid was absent. Inertial flow effects were absent due to high viscous drag coefficients.     

Nonstationary model of immiscible fluid flow through porous media

Unsteady two-phase flow through a microinhomogeneous porous medium is considered. A forest growth model — a percolation model that enables nonequilibrium effects to be taken into account — is proposed for describing the dynamics of the process. In the context of the plane problem expressions are obtained for determining the saturation and the characteristic dimensions of the stagnation zones of trapped phase behind the displacement front.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 73–80, November–December, 1993.     

Fluid flow in fractured and fracturing porous media: A unified view

Fluid flow in fractures that pre-exist or propagate in a porous medium can have a major influence on the deformation and flow characteristics. With the aim of carrying out large-scale calculations at reasonable computing costs, a sub-grid scale model has been developed. While this model was originally embedded in extended finite element methods, thereby exploiting some special properties of the enrichment functions, we will herein show that, using proper micro–macro relations, in particular for the mass balance, sub-grid scale models can be coupled to a range of discretisation methods at the macroscopic scale, from standard interface elements to isogeometric finite element analysis.     

A unified mesh refinement method with applications to porous media flow

A unified algorithm is presented for the refinement of finite element meshes consisting of tensor product Lagrange elements in any number of space dimensions. The method leads to repeatedly refined n-irregular grids with associated constraint equations. Through an object-oriented implementation existing solvers can be extended to handle mesh refinements without modifying the implementation of the finite element equations. Various versions of the refinement procedure are investigated in a porous media flow problem involving singularities around wells. A domain decomposition-type finite element method is also proposed based on the refinement technique. This method is applied to flow in heterogeneous porous media. © 1998 John Wiley & Sons, Ltd.     

A unified plasticity model for cyclic behaviour of clay and sand

This paper presents the development and an experimental evaluation of a simple unified bounding surface plasticity theory for modelling the stress–strain behaviour of sand and clay under both drained and undrained cyclic loading conditions. The model concerned is called CASM-c, which is based on the unified critical state model CASM developed by Yu [Yu, H.S., 1995. A unified critical state model for clay and sand. Civil Engineering Research Report No. 112.08.1995. University of Newcastle, NSW 2308, Australia; Yu, H.S., 1998. CASM: a unified state parameter model for clay and sand. International Journal of Numerical and Analytical Methods in Geomechanics 22, 621–653]. CASM is a relatively simple model as it only requires seven model constants, five of which are the same as those used in the modified Cam-clay model. All these constants have clear physical meanings and may be easily determined from the results of triaxial tests. A key advantage of CASM over many other existing critical state models lies on its simplicity and unified nature as it can model the behaviour of both clay and sand.The extension of the model CASM presented in this paper consists of adopting the bounding surface plasticity theory and treating the reloading and unloading processes differently when calculating the hardening modulus. As a result, a smooth transition of stiffness and gradual accumulation of permanent strain and/or pore pressure in unload–reload cycles as well as the hysteretic behaviour can be reproduced. The results of model simulations show an encouraging agreement with experimental data from triaxial tests subjected to both one-way and two-way cyclic loading conditions.     

A LGA model for dispersion in heterogeneous porous media

The lattice gas automaton (LGA) model proposed in the previous paper is applied to the problem of simulating dispersion and mixing in heterogeneous porous media. We demonstrate here that tracer breakthrough profiles and longitudinal dispersion coefficients can be computed for heterogeneous porous media.     

A Cosserat shell model for interphases in elastic media

This study is concerned with the modeling of interphases in elastic media in general, and in composite materials in particular. The aim is to replace a boundary value problem consisting of a three-phase configuration, say that of fiber-interphase-matrix, by a simpler problem which involves the fiber and matrix only, plus certain matching conditions which simulate the interphase. The simplest of such known representations replaces a thin interphase by a “perfect contact interface” (a single surface) across which the displacements and tractions are assumed to be continuous. Another classical model replaces a thin and soft interphase by a “spring-type interface”, across which the tractions are continuous, but the displacement field undergoes a discontinuity. In the present paper, a Cosserat shell model of the interphase is derived which successfully models the original interphase in a unified manner, for the full range of its material parameters relative to those of the neighboring media. The model is derived in the setting of three-dimensional linear elasticity with small deformations and displacements. Comparisons with an existing exact solution of a coated fiber in an infinite matrix show that it performs extremely well even for moderately thick interphases.     

A unified potential-based cohesive model of mixed-mode fracture

A generalized potential-based constitutive model for mixed-mode cohesive fracture is presented in conjunction with physical parameters such as fracture energy, cohesive strength and shape of cohesive interactions. It characterizes different fracture energies in each fracture mode, and can be applied to various material failure behavior (e.g. quasi-brittle). The unified potential leads to both intrinsic (with initial slope indicators to control elastic behavior) and extrinsic cohesive zone models. Path dependence of work-of-separation is investigated with respect to proportional and non-proportional paths—this investigation demonstrates consistency of the cohesive constitutive model. The potential-based model is verified by simulating a mixed-mode bending test. The actual potential is named PPR (Park-Paulino-Roesler), after the first initials of the authors’ last names.     

Jots - a mathematical model of microscopic fluid flow in porous media

The model described in this paper is an approach to simulating flow through porous media on a microscopic scale. It is based on a variation of diffusion limited aggregation. The model is shown to match coreflood average saturation profiles and production histories as predicted by Darcy's equations while generating saturation distributions resembling viscous fingering. The model also is shown to simulate the limiting cases of infinite mobility ratio and zero flow rates as previously modeled by diffusion limited aggregation and percolation theory. With some simplifying assumptions, differential equations very similar to Darcy's equations are derived from the microscopic interpretation of fluid behavior in porous media used in this model.     

A mixed damage model for unsaturated porous media

The aim of this study is to present a framework for the modeling of damage in continuous unsaturated porous geomaterials. The damage variable is a second-order tensor. The model is formulated in net stress and suction independent state variables. Correspondingly, the strain tensor is split into two independent thermodynamic strain components. The proposed framework mixes micro-mechanical and phenomenological approaches. On the one hand, the effective stress concept of Continuum Damage Mechanics is used in order to compute the damaged rigidities. On the other hand, the concept of equivalent mechanical state is introduced in order to get a simple phenomenological formulation of the behavior laws. Cracking effects are also taken into account in the fluid transfer laws. To cite this article: C. Arson, B. Gatmiri, C. R. Mecanique 337 (2009).     

A resistance model for flow through porous media

A new model for resistance of flow through granular porous media is developed based on the average hydraulic radius model and the contracting–expanding channel model. This model is expressed as a function of tortuosity, porosity, ratio of pore diameter to throat diameter, diameter of particles, and fluid properties. The two empirical constants, 150 and 1.75, in the Ergun equation are replaced by two expressions, which are explicitly related to the pore geometry. Every parameter in the proposed model has clear physical meaning. The proposed model is shown to be more fundamental and reasonable than the Ergum equation. The model predictions are in good agreement with the existing experimental data.     

A unified spray model for engine spray simulation using dynamic mesh refinement

This study is based on dynamic mesh refinement and uses spray breakup models to simulate engine spray dynamics. It is known that the Lagrangian discrete particle technique for spray modeling is sensitive to gird resolution. An adequate spatial resolution in the spray region is necessary to account for the momentum and energy coupling between the gas and liquid phases. This study uses a dynamic mesh refinement algorithm that is adaptive to spray particles to increase the accuracy of spray modeling. On the other hand, the accurate prediction of the spray structure and drop vaporization requires accurate physical models to simulate fuel injection and spray breakup. The present primary jet breakup model predicts the initial breakup of the liquid jet due to the surface instability to generate droplets. A secondary breakup model is then responsible for further breakup of these droplets. The secondary breakup model considers the growth of the unstable waves that are formed on the droplet surface due to the aerodynamic force. The simulation results are compared with experimental data in gasoline spray structure and liquid penetration length. Validations are also performed by comparing the liquid length of a vaporizing diesel spray and its variations with different parameters including the orifice diameter, injection pressure, and ambient gas temperature and density. The model is also applied to simulate a direct-injection gasoline engine with a realistic geometry. The present spray model with dynamic mesh refinement algorithm is shown to predict the spray structure and liquid penetration accurately with reasonable computational cost.     

A perturbation solution for non-Newtonian fluid two-phase flow through Porous media

In this paper, the mathematical problem of weak non-Newtonian fluid two-phase flow through porous media, including the effect of capillary pressure, is solved by singular perturbation method in combination with regular perturbation method. The asymptotic analytical solutions of the fractional flow function and the wetting phase saturation are obtained. The results are verified by numerical calculations and by classical solutions for corresponding Newtonian case. The influences of the non-Newtonian exponent and capillary pressure are discussed.