Coupled model of hygro-thermal behavior of concrete during fire

We present a nonlinear mathematical model for numerical analysis of the behavior of concrete subject to transient heating according to the standard ISO fire curve. The mathematical model consists of the balance equations (conservations laws) with boundary and initial conditions, constitutive laws and material data for concrete at high temperatures. The numerical algorithm based on finite element method for the numerical solution of the energy equation and finite difference method for the mass balance equations is presented. Distributions of temperature, saturation of water and water vapor pressure are demonstrated.     

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)     

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．     

Modelling coupled water and heat transport in a soil–mulch–plant–atmosphere continuum (SMPAC) system

This paper presents a physically based model coupling water and heat transport in a soil–mulch–plant–atmosphere continuum (SMPAC) system, in which a transparent polyethylene mulch is applied to a winter wheat crop. The purpose of the study is to simulate profiles of soil water content and temperature for different stages of wheat growth. The mass and energy balance equations are constructed to determine upper boundary conditions of governing equations. Energy parameters are empirically formulated and calibrated from three-month field observed data. Resistance parameters in the SMPAC system are calculated. The mass and energy equations are solved by an iterative Newton–Raphson technique and a finite difference method is used to solve the governing equations. Water-consuming experiments are performed within the growing period of wheat. The results show that the model is quite satisfactory, particularly for high soil water content, in simulating the water and temperature profiles during the growth of the winter wheat.     

A perturbation solution for bacterial growth and bioremediation in a porous medium with bio-clogging

We investigate a flow problem of relevance in bioremediation and develop a mathematical model for transport of contamination by groundwater and the spreading, confinement, and remediation of chemical waste. The model is based on the fluid mass and momentum balance equations and simultaneous transport and consumption of the pollutant (hydrocarbon) and nutrient (oxygen). Particular emphasis is placed on the study of processes involving the full coupling of reaction, transport and mechanical effects. Dimensional analysis and asymptotic reduction are used to simplify the governing equations, which are then solved numerically.     

Two-dimensional numerical modelling of shallow water flows over multilayer movable beds

The two-dimensional modelling of shallow water flows over multi-sediment erodible beds is presented. A novel approach is developed for the treatment of multiple sediment types in morphodynamics. The governing equations include the two-dimensional shallow water equations for hydrodynamics, an Exner-type equation for morphodynamics, a two-dimensional transport equation for the suspended sediments, and a set of empirical equations for entrainment and deposition. Multilayer sedimentary beds are formed of different erodible soils with sediment properties and new exchange conditions between the bed layers are developed for the model. The coupled equations yield a hyperbolic system of balance laws with source terms. As a numerical solver for the system, we implement a fast finite volume characteristics method. The numerical fluxes are reconstructed using the method of characteristics which employs projection techniques. The proposed finite volume solver is simple to implement, satisfies the conservation property and can be used for two-dimensional sediment transport problems in non-homogeneous isotropic beds without need of complicated three-dimensional equations. To assess the performance of the proposed models, we present numerical results for a wide variety of shallow water flows over sedimentary layers. Comparisons to experimental data for dam-break problems over movable beds are also included in this study.     

Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors

Nonlinear asymptotic Lyapunov stability of the equilibrium state for the balance equations of charge transport in semiconductors based on the maximum entropy principle [A.M. Anile, V. Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Contin. Mech. Thermodyn. 11 (1999) 307–325; V. Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin. Mech. Thermodyn. 12 (2000) 31–51] is proven for a typical 1-D problem.     

Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors

Linear asymptotic Lyapunov stability of the equilibrium state for the balance equations of charge transport in semiconductors based on the maximum entropy principle [A.M. Anile, V. Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Contin. Mech. Thermodyn. 11 (1999) 307–325; V. Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin. Mech. Thermodyn. 12 (2000) 31–51] is proven for a typical two-dimensional problem.     

Modelling the wetting and cooking of a single cereal grain

Three models are presented for the wetting of whole grains ofcereal. Two are for temperatures below gelatinization temperatures,one of which incorporates the effects of swelling of the grain.A third model is presented for wetting of a grain at temperaturesabove gelatinization, and hence cooking the grain. The modelsare developed as partial differential equations, and solvedin a variety of ways. A model that ignores swelling at temperaturesbelow gelatinization is solved for wetting times by using theconcept of mean action time, which reduces the problem to anexactly solvable linear Poisson equation. The other two models,which include swelling and cooking respectively, are solvedapproximately, taking advantage of the steep nonlinear diffusionfronts that develop. The aim of the modelling is to improveunderstanding of the cooking of whole-grain cereals prior toprocessing into breakfast cereals. Moisture penetration curvesare obtained and compared. Regions where the penetration rateis approximately linear are noted, suggesting that nonlineardiffusion equations are a promising way to model grain wettingand cooking.     

Tubuloglomerular feedback in a dynamic nephron

A dynamic model for a short-looped mammalian nephron is developed to study tubuloglomerular feedback (TGF). Evolution equations for salt and urea concentrations and for fluid flux in the nephron are derived and coupled to a resistance network that serves as a schematic model of the glomerulus and associated structures. The evolution equations, which are semi-linear hyperbolic partial differential equations, are solved by the method of flux-corrected transport. The implementation and testing of this method is described and numerical results are presented. This investigation suggests that: (i) the concentrating nephron exhibits high gain, i.e., a small increase in single nephron glomerular filtration rate produces a large increase in the salt concentration of tubular fluid in the cortical thick ascending limb at the macula densa; (ii) the nephron, as a concentrating system, acts as a low-pass filter, i.e., high frequency pressure oscillations (1 Hz) of a prescribed amplitude at the proximal tubule produce relatively low amplitude oscillations in tubular concentrations, while low frequency oscillations (1/30 Hz) produce relatively high amplitude oscillations in tubular concentrations; and (iii) as a consequence of long time delay in TGF, some perturbations in afferent arteriolar blood pressure induce sustained periodic oscillations similar to those observed in recent experiments.     

重建极性连续统理论的基本定律和原理(Ⅶ)——增率型

目的是建立微极连续统增率型的较为完整的运动方程,边界条件和能率方程.为此,先给出较为完整的变形梯度及其逆的定义.接着推导出各种应力率和偶应力率间的新关系式.最后,作为一种特殊情形得到连续统力学的耦合的增率型运动方程、边界条件和能率方程.     

Two-fluid and population balance models for subcooled boiling flow

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUSIG (MUltiple-SIze-Group) model implemented in the computer code CFX4.4 is further developed to accommodate the wall nucleation at the heated wall and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison using empirical relationships for the active nucelation site density and local bubble diameter is also investigated. Good agreement is achieved with the local radial void fraction, bubble Sauter diameter and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency through the consideration of additional momentum equations or developing an algebraic slip model to account for bubble separation.     

重建极性连续统理论的基本定律和原理(Ⅵ)——质量和惯性守恒定律

重建极性连续统理论的耦合型质量和惯性的守恒定律和局部守恒方程以及跳变条件.为此推导出新的变形梯度、线元、面元和体元的物质导数,并给出广义Reynolds输运定理.把这些结果和作者以前推导出的耦合型动量、动量矩和能量的基本定律和有关原理结合在一起就大体上构成极性连续统理论相当完整的耦合型基本定律、局部守恒和均衡方程及原理体系.从此体系可以根据常用的局部化方法给出耦合型的非局部质量和惯性守恒方程以及动量、动量矩和能量均衡方程.     

A finite element model for hygrothermal analysis of masonry walls with FRP reinforcement

Modeling of moisture migration and heat transfer in fiber reinforced polymer (FRP) composite upgraded masonry structures is of great importance, since the interfacial adhesive between the reinforcing FRP laminate and the host masonry is prone to moisture damages. In this paper, a generic theoretical formulation was first developed to model moisture and heat transport in a layered structure consisting of distinct materials. This formulation was based on the framework of the hygrothermal model presented by Philip and De Vries for a monolithic porous medium. Finite element implementation of the formulation was subsequently used to model moisture and heat transport in an FRP reinforced masonry block. Analytical results were then compared with experimental data to validate the model. Parametric studies were then performed for a concrete block with a reinforcing FRP laminate partially covering one surface. The results showed that changing temperature gradient affects the moisture distribution considerably. This effect was found particularly significant at the concrete/FRP interface where a drastic change in local temperature gradient is present.     

重建极性连续统理论的基本定律和原理(Ⅲ)--Noether定理

对现有的各种偶应力理论进行了认真的再研究，目的是要提出一个耦合型的Noether定理并由此重新建立偶应力弹性动力学的较为完整的守恒定律和相应的均衡方程．这里给出了新的各种守恒定律和均衡方程的具体形式，并建立起从给定的不变性要求所得到的这类守恒定律的确切属性．最后，由这里的结果自然地推导出各种特殊情形；并可自然地过渡到微极连续统的结果．     

Thermal radiation effects on magnetohydrodynamic free convection heat and mass transfer from a sphere in a variable porosity regime

A mathematical model is presented for multiphysical transport of an optically-dense, electrically-conducting fluid along a permeable isothermal sphere embedded in a variable-porosity medium. A constant, static, magnetic field is applied transverse to the cylinder surface. The non-Darcy effects are simulated via second order Forchheimer drag force term in the momentum boundary layer equation. The surface of the sphere is maintained at a constant temperature and concentration and is permeable, i.e. transpiration into and from the boundary layer regime is possible. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. Increasing porosity (ε) is found to elevate velocities, i.e. accelerate the flow but decrease temperatures, i.e. cool the boundary layer regime. Increasing Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing both porosity and radiation parameters.     

A two-dimensional finite volume method for transient simulation of time- and scale-dependent transport in heterogeneous aquifer systems

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Plauck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the same problems.     

Numerical modelling of bubbly flows with and without heat and mass transfer

In this paper, modelling gas–liquid bubbly flows is achieved by the introduction of a population balance equation combined with the three-dimensional two-fluid model. For gas–liquid bubbly flows without heat and mass transfer, an average bubble number density transport equation has been incorporated in the commercial code CFX5.7 to better describe the temporal and spatial evolution of the geometrical structure of the gas bubbles. The coalescence and breakage effects of the gas bubbles are modelled according to the coalescence by the random collisions driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Local radial distributions of the void fraction, interfacial area concentration, bubble Sauter mean diameter, and gas and liquid velocities, are compared against experimental data in a vertical pipe flow. Satisfactory agreements for the local distributions are achieved between the predictions and measurements. For gas–liquid bubbly flows with heat and mass transfer, boiling flows at subcooled conditions are considered. Based on the formulation of the MUSIG (multiple-size-group) boiling model and a model considering the forces acting on departing bubbles at the heated surface implemented in the computer code CFX4.4, comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter, interfacial area concentration, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter, interfacial area concentration and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress through the consideration of additional momentum equations or developing an algebraic slip model to account for the effects of bubble separation.     

Two-dimensional modelling of the river Rhine

The system for operational water level forecast and prediction of (fortunately not daily) pollutant transport for the river Rhine is in daily use. This model is based on the Saint-Venant or one-dimensional shallow water equations.The model is augmented by additional terms and equations to model the effect of dead zones and the transport of soluble components.The next step is to move towards two-dimensional models. An important problem that arises is that the domain of the fluid is not fixed by the given data, but depends on the water level and is therefore part of the solution of the model. Even worse, depending on the topography of the river bed, even the topology of the fluid domain may change, as islands may appear at low water and get flooded at high water situations.