A multiphase finite element simulation of biological conversion processes in landfills

Worldwide, landfills are the most common way to dispose of waste, but have an impact on the environment as a result of harmful gas and leachate production. Estimating the long-term behaviour of a landfill in regard to this gas production and organic degrading, as well as to settlement and waste water production, is of high importance. Therefore, a model has been developed to simulate these processes. This constitutive model is based on the multiphase Theory of Porous Media. The body under investigation consists of an organic and an inorganic phase as well as a liquid and a gas phase. The equations of the model are developed on the basis of a consistent thermo-mechanical approach including the momentum balance for the solid phase and the mixture, the energy balance for the mixture and the mass balance for the gas phase. All interactions between the constituents such as mass transfers, interaction forces and energy fluxes are taken into consideration. The strongly coupled set of partial differential equations is implemented in the finite element code FEAP. The theoretical framework and the results of meantime successfully performed simulation of a real landfill body will be shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transport and Reaction Processes in Concrete at High Temperatures

Simulating processes in concrete at high temperatures requires coupled formulation of transport and reaction. Transport can be formulated using balance equations for mass and heat as well as constitutive equations. The equations have to be valid in the whole temperature range from 293 K up to 1000 K. Instantaneous thermodynamic equilibrium is assumed for the gas and liquid phase of water substance. Above the critical point of water, only its gas phase exist. This requires a combined mass balance, which contains vapour balance as well as the mass balance of liquid water. Rapid evaporation of water and degradation of cement minerals leads to an enormous pressure increase in the gas phase. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of the microwave drying process of aqueous dielectrics

We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz Field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.     

非饱和土本构关系的混合物理论(Ⅰ)——非线性本构方程和场方程

以混合物理论为基础建立了非饱和土非线性本构方程和场方程.把非饱和土作为3种组分构成的饱和混合物来研究.首先根据土力学成果提出了非饱和土混合物的基本假设,推导出适用于非饱和土混合物的熵不等式;然后采用混合物理论处理本构问题的常规方法得出了非饱和土非线性本构方程;最后把非线性本构方程代入混合物组分动量守恒定律,获得了非饱和土各组分运动的非线性场方程;并且给出了非饱和土混合物的能量守恒方程,从而形成了解决非饱和土混合物热力学过程的完备方程组.     

非饱和土固结的混合物理论（Ⅰ）

非饱和土是由土粒、水、气组成的三相介质，本以混合物理论为基础研究了非饱和土的固结问题。中导出了各向异性多孔介质及非饱和土 的有效应力的理论公式，把有效应力原理和Curie对称原理作为非饱和土的两个重要的本构原理，建立了非饱和 土固结的数学模型：由25个方程求解25个未知量。在增量线性化的情况下，本模型简化为5个控制方程求解5个未知量：3个固相位移、孔隙水压力和孔隙气压力。模型中包含7个材料参数，都可由试验测定，便于工程应用，Biot理论是本模型的特例。     

A coupled multi-component approach for bacterial methane oxidation in landfill cover layers

Methane (CH₄), which has a 25 times higher global warming potential than carbon dioxide (CO₂), can be oxidated by methanotrophic bacteria into carbon dioxide and water. The biological oxidation of methane can be considered in the passive aftercare phase of landfills in order to reduce climate-damaging methane emissions. Methanotrophic bacteria are situated within the landfill cover layer and convert the harmful methane emissions arising from the degradation of organic waste to the less harmful carbon dioxide. Hence, the passive aftercare of landfills in terms of methane oxidation layers is an efficient method to reduce contributions to the greenhouse effect. To model the coupled processes during phase transition from methane to carbon dioxide, the well-known Theory of Porous Media (TPM) combined with the Mixture Theory has been used in order to develop a multi-component Finite Element calculation concept, see [1, 3]. The thermodynamic consistent model analyzes the relevant gas productions of methane, carbon dioxide and oxygen. The model also accounts for the driving phenomena of production, diffusion and advection. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a finite element method for a compressible viscous flow in a MOCVD reactor

We propose a stable finite element method for approximating the flow of a chemically reacting gas mixture in an MOCVD (metal‐organic chemical vapor deposition) reactor. The flow is governed by the full compressible Navier‐Stokes equations extended by transport equations for the chemical species, the energy equations and the equation of state, together with boundary conditions providing information on the reactor geometry and experimental conditions. The equations form a semilinear system with a constraint for which the corresponding pressure term is not the Lagrangian multiplier. An application of our method to a real world model of growth of GaAs shows the consistency with experimental data. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

高温作用下混凝土热-水-力耦合损伤分析模型

以混合物理论为基础建立了高温作用下混凝土的热-水-力耦合损伤分析模型．将混凝土视为由固体骨架、液态水、水蒸气、干燥气体和溶解气体共5种组分构成的混合物,模型的宏观平衡方程包括各组分的质量守恒方程、整体的能量守恒方程及动量守恒方程,模型所需的状态方程及本构关系全部给出,最后给出基于4个主要参数（固体骨架位移、气压力、毛细压力和温度）的控制方程．模型考虑了混凝土在高温作用下,水分的蒸发与冷凝、胶结材料的水化及脱水、溶解气的溶解与挥发等相变过程;从材料变形破坏过程中能量耗散特征入手,基于Lemaitre应变等价性假说和能量守恒原理得到力学损伤演化方程,并考虑了高温引起的热损伤对材料力学性能及力学损伤演化规律的影响,建立了热-力耦合损伤本构模型．     

A new multiscale model for flow and transport in unconventional shale oil reservoirs

A new multiscale computational model for two-phase gas/oil flow in a multiporosity shale formation composed of three levels of porosity associated with nano/micro pores and hydraulic fractures is rigorously constructed within the framework of the homogenization procedure in conjunction with the Discrete Fracture Modeling, where fractures are treated as (n-1) interfaces (n=2, 3) immersed in the domain occupied by the matrix. Effective equations are obtained by upscaling the microstructural information of the shale oil formation with matrix composed of three distinct solid phases: the organic matter, constituted by kerogen aggregates containing particles and nanopores with adsorbed gas, and the pyrobitumen network, also containing an organic solid with micropores filled by tight oil and dissolved gas, along with the inorganic solid composed of clay, quartz and calcite, assumed impermeable and free of adsorption. Such distinct solid phases are separated from each other by the network of interparticle pores. Together with the pyrobitumen such a network form the pathways for multiphase flow in the matrix whereas the kerogen aggregates are treated as disconnected inclusions playing the role of storage sites for adsorbed gas. The homogenization of the multiphase flow model of black oil type gives rise to new pressure and saturation equations with effective coefficients strongly correlated with the shale microstructure, volume fractions and total organic content (TOC). Constitutive laws for the effective hydraulic conductivity and retardation parameter, which captures adsorption of methane in the nanopores, are numerically reconstructed by solving the local cell problems arising from the homogenization procedure. In particular the partition coefficient is computed from adsorption isotherms rigorously constructed within the framework of the Thermodynamics of confined gases seated on the Density Functional Theory (DFT). The effective equations in the matrix resemble in form of a generalized black oil model coupled with the two-phase flow model posed in the subdomain occupied by the network of hydraulic fractures. A macroscopic model is obtained by averaging the mass conservation equation across the fracture aperture giving rise to reduced balance laws posed in a network of reduced (n-1)-dimension (n=2, 3) supplemented by a source term arising from the jump in the oil/gas fluxes in the shale matrix. The resultant coupled Discrete Fracture/Multiscale model consists of a first attempt at constructing a rigorous correlation between the nature of the macroscopic multiphase flow equations and the local shale-microstructure mainly characterized by the simultaneous presence of inorganic and organic matters with the latter containing nanopores. Numerical simulations of gas/oil withdrawal are performed to accurately predict hydrocarbon movement in stimulated shale oil formations.     

A three-phase FE-model for the simulation of partially saturated soils

While for many numerical simulations in geotechnics use of a two-phase model is sufficient, separate consideration of all three phases is mandatory for numerical simulations of partially saturated soils subjected to compressed air. This is a common technique frequently applied for temporary ground support in tunnelling. For the numerical simulation of tunnelling using compressed air, a multiphase model for soft soils is developed, in which the individual constituents of the soil – the soil skeleton, the fluid and the gaseous phase – and their interactions are considered. The three phase model is formulated within the framework of the Theory of Porous Media (TPM), based upon balance equations and constitutive relations for the soil constituents and their mixture. Water is modelled as an incompressible and air as a compressible phase. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlocality and thermodynamic restrictions in phase-field models

This work shows two models of nonlocality for the phase field of non-isothermal phase transitions. In one case the constitutive equations involve the phase field through functionals of the phase field over the region of the body; in the other one the nonlocality is represented by functions of the gradient. The second law is expressed in integral form for the whole region of the body. Upon exploitation of the second law inequality, in the case of functions of the gradient, the evolution equation has to involve the variational derivative of the rescaled free energy, thus supporting an assumption common in the literature.     

Simulation of Premixed Turbulent Combustion in a Gas Engine using the Immersed Boundary Method and a Level Set Flame Model

An efficient simulation approach for turbulent flame brush propagation is a level set formulation closed by the turbulent flame speed. A formulation of the level set equation with the corresponding treatment of the turbulent mass burning rate that is compatible with standard Finite Volume discretization schemes available in computational fluid dynamics codes is employed. In order to simplify and to speed up the meshing process in complicated geometries (here in gas engines) the immersed boundary method in a continuous formulation, where the forces replacing the boundaries are introduced in the momentum conservation equations before discretization, is employed. In our contribution, aspects of the numerical implementation of the level set flame model combined with the immersed boundary formulation in OpenFOAM are presented. First representative simulation results of a homogeneous methane/air mixture combustion in a simplified engine geometry are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Validation of a coupled FE-model for the simulation of methane oxidation via thermal imaging

To simulate the processes of methane oxidation in landfill cover layers, a new computational model was created. The purpose of the model is to allow a forecast on the performance of methanotrophic activity in landfill cover layers under changing environmental conditions. Therefore, a thermodynamic consistent model based on the well-known Theory of Porous Media (TPM) combined with the mixture theory was developed, which analyzes the relevant gas productions of methane, oxygen and carbon dioxide. Diffusion, advection and conversion processes are considered as well as the energy production during methane oxidation. With the help of the thermal imaging technique a new experimental setup was developed in order to validate the coupled model in terms of the heat generation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

可变形孔隙介质中热、水耦合力学问题的代数多格子分析方法

研究了孔隙介质中包括热和质量传递的全耦合多相流问题的代数多格子分析方法。数学模型包括质量、线性矩、能量平衡方程和本构方程,以位移、毛细压力、汽压和温度为基本变量,模型中采用了考虑毛细压力关系的修正有效应力概念,并考虑相变、热传导、对流和潜热交换(汽化-冷凝),气相是由易混合的干空气和水蒸气组成,视为理想气体。考题显示出较高的计算效率。     

On a model for electromagnetic processes inside and outside a ferromagnetic body

One‐dimensional Maxwell's equations are considered in a ferromagnetic body surrounded by vacuum. Existence and uniqueness of solution for the resulting system of partial differential equations with hysteresis on the whole real line is proved under suitable constitutive hypotheses. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling of electrodynamic-mechanical coupling phenomena in smart magnetoelectroelastic materials

The coupling of electric, magnetic and mechanical phenomena may have various reasons. The famous Maxwell equations of electrodynamics describe the interaction of transient magnetic and electric fields. On the constitutive level of dielectric materials, coupling mechanisms are manyfold comprising piezoelectric, magnetostrictive or magnetoelectric effects. Electromagnetically induced specific forces acting at the boundary and within the domain of a dielectric body are, within a continuum mechanics framework, commonly denoted as Maxwell stresses. In transient electromagnetic fields, the Poynting vector gives another contribution to mechanical stresses. First, a system of transient partial differential equations is presented. Introducing scalar and vector potentials for the electromagnetic fields and representing the mechanical strain by displacement fields, seven coupled differential equations govern the boundary value problem, accounting for linear constitutive equations of magnetoelectroelasticity. To reduce the effort of numerical solution, the system of equations is partly decoupled applying generalized forms of Coulomb and Lorenz gauge transformations [1,2]. A weak formulation is given to establish a basis for a finite element solution. The influence of constitutive magnetoelectric coupling on electromagnetic wave propagation is finally demonstrated with a simple one-dimensional example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some uniqueness and stability results in the theory of micropolar solid-fluid mixture

This paper is devoted to the study of a binary homogeneous mixture of an isotropic micropolar linear elastic solid with an incompressible micropolar viscous fluid. Assuming that the internal energy of the solid and the dissipation energy are positive definite forms, some uniqueness and continuous data dependence results are presented. Also, some estimates which describe the time behaviour of solution are established, provided the above two energies are positive definite forms. These estimates are used to prove that for the linearized equations, in the absence of body loads and for null boundary conditions, the solution is asymptotically stable. Then a uniqueness result under mild assumptions on the constitutive constants is given using the Lagrange-Brun identities method. These mathematical results prove that the approach of a micropolar solid-fluid mixture is in agreement with physical expectations.