Coupled thermo-hygro-mechanical damage model for concrete subjected to high temperatures

Based on the theory of mixtures, a coupled thermo-hygro-mechanical (THM) damage model for concrete subjected to high temperatures is presented in this paper. Concrete is considered as a mixture composed of solid skeletons, liquid water, water vapor, dry air, and dissolved air. The macroscopic balance equations of the model consist of the mass conservation equations of each component and the momentum and energy conservation equations of the whole medium mixture. The state equations and the constitutive model used in the model are given. Four final governing equations are given in terms of four primary variables, i.e., the displacement components of soil skeletons, the gas pressure, the capillary pressure, and the temperature. The processes involved in the coupled model include evaporation, dehydration, heat and mass transfer, etc. Through the process of deformation failure and the energy properties, the mechanics damage evolution equations are established based on the principle of conversation of energy and the Lemaitre equivalent strain assumption. Then, the influence of thermal damage on the mechanical property is considered.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain,water andgas.In this paper,the consolidation problem of unsaturated soil is investigated basedon the theory of mixture.A theoretical formula of effective stress on anisotropicporous media and unsaturated soil is derived.The principle of effective stress and theprinciple of Curie symmetry are taken as two fundamental constitutive principles ofunsaturated soil.A mathematical model of consolidation of unsaturated soil isproposed,which consists of25 partial differenfial equations with25 unknowns.Withthe help of increament linearizing method,the model is reduced to5 governingequations with5 unknowns,i.e.,the three displacement components of solid phase,thepore water pressure and the pore gas pressure.7 material parameters are involved inthe model and all of them can be measured using soil tests.It is convenient to use themodel to engineering practice.The well known Biot’s theory is a special case of themodel.     

非饱和土半空间Lamb问题及能量传输特性

地球表面绝大多数土层处于非饱和状态, 故采用传统饱和两相介质理论进行动力学分析时, 结果往往与实际情况不符. 针对这一问题, 本文以非饱和半空间作为研究对象, 基于连续介质力学和多孔介质理论, 考虑非饱和多孔介质中各相的质量守恒方程、动量守恒方程、本构方程以及有效应力原理等基本方程, 建立了以骨架位移、孔隙水压力和孔隙气压力为基本未知量的动力学控制方程. 针对非饱和半空间表面在竖向集中简谐荷载作用下的动力学响应及能量传输问题, 建立了频域内经典Lamb问题的轴对称计算模型, 采用Helmholtz分解法, 通过引入势函数Φ和Ψ表示骨架的位移分量, 结合本构方程获得了不同边界条件下半空间表面位移场和能量场等物理量的解析解答, 并通过数值算例对荷载参数(激振频率)、材料参数(饱和度、渗透系数)等影响因素进行了分析与讨论. 结果表明: (1)饱和度的升高或者激振频率下降, 都会提高非饱和半空间的表面位移幅值; (2)当渗透系数下降至一临界值时, 地表位移幅值会趋于一极限值, 并且透水(气)边界与不透水(气)边界条件下渗透系数的影响表现出明显的差异性.      

非饱和多孔介质中热-渗流-力学耦合的混合元法

提出了一个非饱和多孔介质中热-渗流-力学耦合分析的混合有限元 方法. 固相位移、应变和净应力；孔隙水和气的压力、压力空间梯度和Darcy速度；多相混 合介质的温度、温度空间梯度和热流量在单元内均为独立变量分别插值. 基于胡海 昌-Washizu 三变量广义变分原理给出的多孔介质中热-渗流-力学耦合问题控制方程的单元弱形式，导 出了单元公式. 采用共旋公式进行几何非线性分析. 数值结果证明了所提出的单元模拟以 应变局部化为特征的渐进破坏的能力     

Effect of water phase change on temperature distribution in proton exchange membrane fuel cells

A two dimensional, two-phase non-isothermal electrochemical-transport using a fully coupled numerical model is developed to investigate heat transfer and water phase change effects on temperature distribution in a PEM fuel cell. The multiphase mixture is used formulation for the two phase transport process and developed model is treated as a single domain. This process leads to a single set of conservation equations consisting of continuity, momentum, species, potential and energy for all regions of cell. The results indicate that heat release due to condensation of water vapor affects the temperature distribution. When the relative humidity of the cathode is low, phase change would have a small effect on the maximum temperature that appears at the cell inlet, but it has higher effect on temperature variation further down stream towards the exit of cathode channel and its GDL. Under full-humidity conditions, the cell temperature at all regions of cell increases due to the phase change that starts to appear at the inlet, but the maximum effect of phase change occurs further up stream in cathode channel and its GDL. Also, vapor-phase diffusion which provides a new mechanism for heat removal from the cell, affects the cell temperature distribution.     

Diffuse interface model for high speed cavitating underwater systems

High speed underwater systems involve many modelling and simulation difficulties related to shocks, expansion waves and evaporation fronts. Modern propulsion systems like underwater missiles also involve extra difficulties related to non-condensable high speed gas flows. Such flows involve many continuous and discontinuous waves or fronts and the difficulty is to model and compute correctly jump conditions across them, particularly in unsteady regime and in multi-dimensions. To this end a new theory has been built that considers the various transformation fronts as ‘diffuse interfaces’. Inside these diffuse interfaces relaxation effects are solved in order to reproduce the correct jump conditions. For example, an interface separating a compressible non-condensable gas and compressible water is solved as a multiphase mixture where stiff mechanical relaxation effects are solved in order to match the jump conditions of equal pressure and equal normal velocities. When an interface separates a metastable liquid and its vapor, the situation becomes more complex as jump conditions involve pressure, velocity, temperature and entropy jumps. However, the same type of multiphase mixture can be considered in the diffuse interface and stiff velocity, pressure, temperature and Gibbs free energy relaxation are used to reproduce the dynamics of such fronts and corresponding jump conditions. A general model, based on multiphase flow theory is thus built. It involves mixture energy and mixture momentum equations together with mass and volume fraction equations for each phase or constituent. For example, in high velocity flows around underwater missiles, three phases (or constituents) have to be considered: liquid, vapor and propulsion gas products. It results in a flow model with 8 partial differential equations. The model is strictly hyperbolic and involves waves speeds that vary under the degree of metastability. When none of the phase is metastable, the non-monotonic sound speed is recovered. When phase transition occurs, the sound speed decreases and phase transition fronts become expansion waves of the equilibrium system. The model is built on the basis of asymptotic analysis of a hyperbolic total non-equilibrium multiphase flow model, in the limit of stiff mechanical relaxation. Closure relations regarding heat and mass transfer are built under the examination of entropy production. The mixture equation of state (EOS) is based on energy conservation and mechanical equilibrium of the mixture. Pure phases EOS are used in the mixture EOS instead of cubic one in order to prevent loss of hyperbolicity in the spinodal zone of the phase diagram. The corresponding model is able to deal with metastable states without using Van der Waals representation.     

Formulation of thermo-hydro-mechanical coupling behavior of unsaturated soils based on hybrid mixture theory

Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.     

Boiling in Porous Media: Model and Simulations

We present a modelization of the heat and mass transfers within a porous medium, which takes into account phase transitions. Classical equations are derived for the mass conservation equation, whereas the equation of energy relies on an entropy balance adapted to the case of a rigid porous medium. The approximation of the solution is obtained using a finite volume scheme coupled with the management of phase transitions. This model is shown to apply in the case of an experiment of heat generation in a porous medium. The vapor phase appearance is well reproduced by the simulations, and the size of the two-phase region is correctly predicted. A result of this study is the evidence of the discrepancy between the air – water capillary and relative permeability curves and water – water vapor ones.     

FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model

The phenomenon of liquefaction is one of the most important subjects in Earthquake Engineering and Coastal Engineering. In the present study, the governing equations of such coupling problems as soil skeleton and pore water are obtained through application of the two-phase mixture theory. Using au-p (displacement of the solid phase-pore water pressure) formulation, a simple and practical numerical method for the liquefaction analysis is formulated. The finite difference method (FDM) is used for the spatial discretization of the continuity equation to define the pore water pressure at the center of the element, while the finite element method (FEM) is used for the spatial discretization of the equilibrium equation. FEM-FDM coupled analysis succeeds in reducing the degrees of freedom in the descretized equations. The accuracy of the proposed numerical method is addressed through a comparison of the numerical results and the analytical solutions for the transient response of saturated porous solids. An elasto-plastic constitutive model based on the non-linear kinematic hardening rule is formulated to describe the stress-strain behavior of granular materials under cyclic loading. Finally, the applicability of the proposed numerical method is examined. The following two numerical examples are analyzed in this study: (1) the behavior of seabed deposits under wave action, and (2) a numerical simulation of shaking table test of coal fly ash deposit.     

不排水条件下土石混合料双轴压缩离散元模拟

基于离散单元法构建了考虑碎石形状的柔性边界不排水双轴压缩模型,研究了11组不同含石量土石混合料在不排水条件下的宏细观力学特性。研究发现,(1)土石混合料强度随含石量增加先增后减,含石量超过约60%时形成碎石骨架,强度快速增长;含石量约80%时强度和内摩擦角最大;含石量增加,混合料黏聚力逐渐减小。(2)不排水受载下,土石混合料孔隙水压力先正后负、先增后减。含石量较小时,含石量增加,混合料孔隙水压力变化较小,混合料在碎石骨架形成初期孔隙水压力增加;碎石骨架完全形成后最大孔隙水压力减小。(3)含石量小于约30%时,混合料应变局部化呈规则剪切带,随后含石量增加破坏规则剪切带,当含石量约为80%时,混合料再次形成规则剪切带。含石量增加,配位数逐渐减小,颗粒间接触力在含石量小于60%时随含石量增加缓慢增长,超过70%时则快速增长。     

Bubbles in liquids with phase transition

In the forthcoming second part of this paper a system of balance laws for a multi-phase mixture with many dispersed bubbles in liquid is derived where phase transition is taken into account. The exchange terms for mass, momentum and energy explicitly depend on evolution laws for total mass, radius and temperature of single bubbles. Therefore in the current paper we consider a single bubble of vapor and inert gas surrounded by the corresponding liquid phase. The creation of bubbles, e.g. by nucleation is not taken into account. We study the behavior of this bubble due to condensation and evaporation at the interface. The aim is to find evolution laws for total mass, radius and temperature of the bubble, which should be as simple as possible but consider all relevant physical effects. Special attention is given to the effects of surface tension and heat production on the bubble dynamics as well as the propagation of acoustic elastic waves by including slight compressibility of the liquid phase. Separately we study the influence of the three phenomena heat conduction, elastic waves and phase transition on the evolution of the bubble. We find ordinary differential equations that describe the bubble dynamics. It turns out that the elastic waves in the liquid are of greatest importance to the dynamics of the bubble radius. The phase transition has a strong influence on the evolution of the temperature, in particular at the interface. Furthermore the phase transition leads to a drastic change of the water content in the bubble. It is shown that a rebounding bubble is only possible, if it contains in addition an inert gas. In Part 2 of the current paper the equations derived are sought in order to close the system of equations for multi-phase mixture balance laws for dispersed bubbles in liquids involving phase change.     

A Continuum Theory of Multispecies Thin Solid Film Growth by Chemical Vapor Deposition

A continuum theory for the chemical vapor deposition of thin solid films is proposed, in which a flowing, chemically reacting, gaseous mixture is coupled to the bulk of a growing thin film via the equations that govern the morphological evolution of the interface separating them. The vapor-film interface is viewed as a surface of zero thickness capable of sustaining mass and endowed with thermodynamic variables that account for its distinct structure. We consider situations in which species diffusion and heat conduction occur in all three phases (vapor, bulk and surface), with the former mechanism augmented by the convective transport of particles in the gas. Special attention is given to the chemical reactions that occur both in the vapor and on the film surface. Ours is a conceptual framework based on conservation laws for chemical species, momentum and energy, together with a separate balance of configurational forces. These balances are supplemented by an appropriate version of the second law which is used to develop suitable constitutive relations for each of the phases. In particular, we investigate the case of an elastic film, deposited on a rigid substrate and in contact with a reacting, multispecies, ideal vapor, whose surface behaves like an anisotropic, chemically reactive, multicomponent, ideal lattice gas. In addition to recovering the standard equations that describe the behavior of the gas and film phases, we derive the coupled PDE's that govern the interfacial morphological, chemical, and thermal evolution. In particular, the constitutively augmented interfacial configurational force balance provides a “kinetic relation” linking the thermodynamic “driving force” at the film surface to the growth rate. The special cases of (i) negligible interfacial species densities, and (ii) local (mechanical) equilibrium of both multi- and single-species films are investigated.     

多孔介质在压力梯度作用下的热质耦合数值模拟

多孔介质干燥导致热质耦合传输过程。本文基于连续介质力学的宏观尺度,对多孔介质的热、湿和气三者耦合迁移进行数值模拟,研究压力梯度对热质传输的影响。多孔介质传质机理主要为水汽和空气的对流和扩散传输、吸附水在含湿量梯度作用下的自由扩散和其在温度梯度即Soret效应驱动下的流动。采用Galerkin加权余量的有限元方法,提出了...     

Water Evaporation Versus Condensation in a Hygroscopic Soil

The liquid/vapour phase change of water in soil is involved in many environmental geotechnical processes. In the case of hygroscopic soils, the liquid water is strongly adsorbed on the solid phase and this particular thermodynamic state can highly influence the phase change kinetics. Based on the linear Thermodynamic of Irreversible Processes ideas, the non-equilibrium phase change rate is written as a linear function of the water chemical potential difference between the liquid and vapour state. In this relation, the system is characterized by a phenomenological coefficient that depends on the state variables. Using an original experimental set-up able to analyze the response of a porous medium subjected to non-equilibrium conditions, the phase change coefficient is determined in various configurations. This paper focuses on the influence of the gas phase pressure and underlines that a low gas pressure decreases the phase change kinetics. Then, evaporation and condensation processes are compared showing an asymmetric behaviour. These experimental results are interpreted from a microscopic point of view by relying on recent works dealing with molecular dynamics numerical simulation of the liquid/gas interface.     

非饱和土-隧道系统动力响应计算的波函数法

针对非饱和地基土中埋置隧道的三维动力响应计算问题, 提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱壳的振动控制方程与非饱和土的波动方程.根据隧-土交界面与地表面处的应力、位移以及孔隙流体压力等边界条件,利用平面波与柱面波的转换性质,实现了隧道内作用单位简谐载荷时隧道衬砌与土体系统动力响应的耦合求解.通过与既有单相弹性介质2.5维有限元-边界元法、两相饱和多孔介质2.5维有限元-边界元法以及三相非饱和介质Pip in Pip半解析法的计算结果进行对比, 验证了本文计算方法的可靠性. 最后,基于该方法, 通过算例分析了不同饱和度下非饱和土-隧道系统的动力响应特征.结果表明, 饱和度对土体动位移与超孔隙水压力的幅值响应有较大影响.该方法的非饱和地基土参数退化后,也可用来计算和分析饱和地基土或单相弹性地基土与隧道系统的动力响应.      

Internal flow numerical simulation of a cross‐flow fan in refrigerant operating condition using user‐defined functions

In the paper, a cross‐flow fan in refrigerant operating condition is systematically simulated using user‐defined functions. Three‐dimensional simulations are acquired with Navier–Stokes equations coupled with k–ε turbulence model, and internal flow characteristics of an indoor split‐type air conditioner are obtained, which is mainly composed of cross‐flow fan and heat exchanger. It has systematically been simulated in the isothermal flow condition that the performance of cross‐flow fan may be reduced easily with dry or humid air, and in the refrigerant operating condition in which user‐defined functions are applied to the humid air, considered as a mixture of dry air and vapor. A density‐modulated function is adopted to deal with the condensation of the vapor at the heat‐transfer region approximately. The results show flow mechanism of the two gas‐phase flow, including phase‐vary process. The distribution of the parameters is not uniform at the inlet of the machine, the intensity and position of pressure and velocity vary along the axial direction of the fan, the distribution of vapor volume fraction and turbulent intensity in heat‐transfer region is obtained, and the external characteristic data of the indoor machine are obtained and analyzed. Compared with the experimental data, the calculated characteristic curves and designed parameters are on target. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.     

Stability of the evaporation and condensation surfaces in a porous medium

The stability of a phase transition interface which separates the soil regions saturated with water and humid air, respectively, is investigated. The humid air region contacting with the atmosphere is assumed to be located above the water-saturated region. Water flows through the porous medium in the lower region, while diffuse vapor transfer is implemented in the upper region. Two cases corresponding to water evaporation and vapor condensation are considered. In the first case water flows out from the porous aquifer, evaporates, and comes out into the atmosphere. In the second case, during condensation, the atmospheric moisture saturates soil. The problem is solved in the steady-state case. The investigation of linear stability carried out by means of the normal mode method shows that the evaporation surface can be unstable in both nonwettable and wettable soils in the presence of the capillary pressure gradient. Depending on the parameters, the condensation surface can be unstable also in the neutral medium.     

黏弹性准饱和土中球空腔动力特性

在频率域内研究了内水压力作用下分数导数型黏弹性准饱和土中球空腔的稳态动力响应. 通 过引入与孔隙率有关的应力系数合理地确定了介质和孔隙水共同承担的内水压力值. 将土骨 架和衬砌分别视为具有分数导数本构模型的黏弹性体和多孔柔性材料, 基于Biot两相介质模 型, 通过引入位移势函数解耦得到了内水压力作用下分数导数型黏弹性准饱和土中半封闭球 形空腔的位移、应力和孔隙水压力解析表达式. 考察了物性和几何各参数对球形空腔动力响 应的影响, 结果表明: 分数导数本构模型更合理地描述了土体的动力学行为; 饱和度对应力 和孔隙水压力影响较大, 而对位移影响较小.