Application of numerical methods for predicting energy transport in earth contact systems

Methods for analysing conductive heat flow with applications to underground earth contact systems are reviewed. A discussion and comparison of both the finite difference and finite element methods are presented. The effect of domain discretisation on accuracy for both methods is presented. One- and two-dimensional models are derived and used to solve selected problems. The results for various discretisation domains are compared and constrasted. The application of both the finite difference and finite element approaches to the analysis of heat transfers in an underground building is given. Recommendations are made to aid in the selection of the numerical techniques that are the most appropriate for analysing conductive heat flow problems. Finally, a statement is made on the analysis of the three-dimensional heat and moisture transport problem associated with underground earth contact systems.     

Modified Collocation Trefftz Method for the Geometry Boundary Identification Problem of Heat Conduction

In this article, a meshless numerical algorithm is proposed for the boundary identification problem of heat conduction, one kind of inverse problem. In the geometry boundary identification problem, the Cauchy data is given for part of the boundary. The Neumann boundary condition is given for the other portion of the boundary, whose spatial position is unknown. In order to stably solve the inverse problem, the modified collocation Trefftz method, a promising boundary-type meshless method, is adopted for discretizing this problem. Since the spatial position for part of the boundary is unknown, the numerical discretization results in a system of nonlinear algebraic equations (NAEs). Then, the exponentially convergent scalar homotopy algorithm (ECSHA) is used to efficiently obtain the convergent solution of the system of NAEs. The ECSHA is insensitive to the initial guess of the evolutionary process. In addition, the efficiency of the computation is greatly improved, since calculation of the inverse of the Jacobian matrix can be avoided. Four numerical examples are provided to validate the proposed meshless scheme. In addition, some factors that might influence the performance of the proposed scheme are examined through a series of numerical experiments. The stability of the proposed scheme can be proven by adding some noise to the boundary conditions.     

An experimental data set for benchmarking 1-D,transient heat and moisture transfer models of hygroscopic building materials. Part I: Experimental facility and material property data

As numerical models of heat and moisture transfer in porous building materials advance and numerical investigations increase in the literature, there remains a need for simple accurate and well-documented experimental data for model validation. The aim of this two part paper is to provide such experimental data for two hygroscopic building materials (cellulose insulation and spruce plywood) exposed to 1-D and transient boundary conditions. Part I of this paper describes the transient moisture transfer (TMT) facility used to generate the experimental data as well as the uncertainty and repeatability of the measured data. The measured material properties are also presented to fully document the experimental data set and permit its use by other researchers.     

HYGROTHERMAL STRESS IN A PLATE SUBJECTED TO ANTISYMMETRIC TIME-DEPENDENT MOISTURE AND TEMPERATURE BOUNDARY CONDITIONS

When the temperature and/or moisture at the surfaces of a composite change suddenly, stresses will arise in the composite owing to the nonuniform diffusion of heat and moisture. Recent investigations have shown that under certain conditions the classical uncoupled theory of diffusion can significantly underestimate the coefficient of diffusion. The coupling between heat and moisture is an inherent part of the diffusion process that cannot be neglected on intuitive grounds. This investigation is an inquiry into the influence of antisymmetric boundary conditions on the magnitude of the hygrothermal stresses in a plate made of T300/5208 epoxy material, commonly used in graphite fiber-reinforced composites. Both moisture and temperature boundary conditions are considered. Because of the nonlinear character of the coupled equations, a finite-difference scheme is adopted. Numerical results involving time-dependent moisture, temperature, and stress distributions in the plate are displayed graphically; they show that the stresses derived from the coupled theory differ appreciably from the uncoupled results, both qualitatively and quantitatively. The hygrothermal stresses with coupling taken into account acquire an oscillatory character when the temperature on the plate is raised suddenly; this factor could contribute to material damage. In addition, antisymmetric boundary conditions can either raise or lower the stress levels, depending on time and the transient nature of the applied temperature.     

Heat and mass transfer in a cross-flow membrane-based enthalpy exchanger under naturally formed boundary conditions

Heat and mass transfer mechanisms in a cross-flow parallel plate membrane-based enthalpy exchanger for heat and moisture recovery from exhaust air streams are investigated. The flow is assumed laminar and hydrodynamically fully developed, but developing in thermal and concentration boundaries. Contrary to the traditional methods to assume a uniform temperature (concentration) or a uniform heat flux (mass flux) boundary condition, in this study, the real boundary conditions on the exchanger surfaces are obtained by the numerical solution of the coupled equations that govern the transfer of momentum, thermal energy, and moisture in the two cross-flow air streams and through the membrane. The naturally formed heat and mass boundary conditions are then used to calculate the local and mean Nusselt and Sherwood numbers along the cross-flow passages, in the developing region and thereafter. A comparison was made with those results under uniform temperature (concentration) and uniform heat flux (mass flux) boundary conditions, for rectangular ducts of various aspect ratios. An experiment is done to verify the prediction of outlet moisture content.     

Hybrid numerical method applied to transient hygrothermal analysis in an annular cylinder

A hybrid numerical method of the Laplace transformation and the finite difference is applied to solve the transient hygrothermal problem of an infinitely long annular cylinder, in which the temperature and moisture coupling at the inner and outer surfaces is taken into account in the boundary conditions. By a combining method of the Laplace transformation and the finite difference, the general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed by the method of matrix operation and Fourier series technique. The transient distributions of temperature, moisture, displacement, stresses of the annular cylinder in the real domain are calculated numerically. The presented method is also applicable to multiplayer annular cylinders and to other types of boundary conditions.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL HEAT AND MOISTURE TRANSFER DURING DRYING OF A RECTANGULAR OBJECT

The present article deals with the numerical modeling of heat and moisture transfer during the drying process of a two-dimensional (2-D) rectangular object subjected to convective boundary conditions. As is common in solids drying, it is assumed that drying takes place as a simultaneous heat and moisture transfer whereby moisture is vaporized by means of a drying fluid (e.g., air), which passes over a moist object. The governing equations representing the drying process in a 2-D rectangular object are discretized using an explicit finite-difference approach, and a computer code is developed to predict the temperature and moisture distributions inside the object. Moreover, the results obtained from the present model are compared with the experimental data available in the literature, and considerably high agreement is found.     

Investigation of heat and moisture migration in unsaturated soil under natural boundary conditions

Theoretical and experimental investigations were conducted to determine the heat and moisture migration in unsaturated soil under natural surface boundary conditions. Theoretically, a new model of heat and moisture migration in unsaturated porous media was developed, in which the gradients of volume water content, temperature, and partial vapor pressure were considered as the main driving forces which influence the process of heat and moisture migration in unsaturated soil. A set of coupled, nonlinear, partial differential equations were developed, which are related dynamically to the surface boundary conditions. Heat and moisture migration in sandy soil under solar radiation and air convection were studied experimentally. Temperature, volume water content, and water table evaporation were measured under unsteady conditions. The predictions are in good agreement with experimental data from a fairly sandy soil. © 1999 Scripta Technica, Heat Trans Asian Res, 28(1): 3–17, 1999     

A COMPUTATIONAL MODEL OF COUPLED HEAT AND MOISTURE TRANSFER WITH PHASE CHANGEIN GRANULAR SUGAR DURING VARYING ENVIRONMENTAL CONDITIONS

As part of a comprehensive effort to predict the development of caking in granular materials, a mathematical model is introduced to model simultaneous heat and moisture transfer with phase change in porous media when undergoing temperature oscillations/cycling. The resulting model partial differential equations were solved using finite-volume procedures in the context of the PHYSICA framework and then applied to the analysis of sugar in storage. The influence of temperature on absorption/desorption and diffusion coefficients is coupled into the transport equations. The temperature profile, the depth of penetration of the temperature oscillation into the bulk solid, and the solids moisture content distribution were first calculated, and these proved to be in good agreement with experimental data. Then, the influence of temperature oscillation on absolute humidity, moisture concentration, and moisture migration for different parameters and boundary conditions was examined. As expected, the results show that moisture near boundary regions responds faster than farther away from them with surface temperature changes. The moisture absorption and desorption in materials occurs mainly near boundary regions (where interactions with the environment are more pronounced). Small amounts of solids moisture content, driven by both temperature and vapour concentration gradients, migrate between boundary and center with oscillating temperature.     

Analysis of arbitrarily shaped planar cracks in three-dimensional isotropic hygrothermoelastic media

In the present article, a planar crack of arbitrary shape embedded in three-dimensional isotropic hygrothermoelastic media is investigated. Based on the general solutions and Hankel transform technique, the fundamental solutions for unit-point and extended displacement discontinuities (EDD; including the displacement discontinuities, moisture concentration discontinuity, and the temperature discontinuity) are derived. The EDD boundary integral equations for an arbitrarily shaped, planar crack in the hygrothermoelastic medium are established in terms of the EDD. Utilizing the boundary integral equation method, the singularities of near-crack front fields are analyzed, and the stress, moisture flux, and heat flux intensity factors are all derived in terms of the EDD. As a special case, the analytical solution for a penny-shaped crack under uniform combined loadings is presented. The EDD boundary element method is proposed for numerical simulation. The numerical result for a penny-shaped crack subjected to uniform mechanical–moisture–thermal loading is compared with the analytical solution to verify the correctness of the proposed method. Two coplanar elliptical cracks subjected to combined loadings are simulated as an application, and the influences of applied loadings and the ellipticity ratio are discussed.     

A building corner model for hygrothermal performance and mould growth risk analyses

Combined multidimensional analysis of heat, air and moisture transport through porous building elements is barely explored in the literature due to many difficulties such as modeling complexity, computer run time, numerical convergence and highly moisture-dependent properties. In this way, a mathematical model considering a combined two-dimensional heat, air and moisture transport through unsaturated building upper corners is presented. In order to improve the discretized model numerical stability, the algebraic equations are simultaneously solved for the three driving potentials: temperature, vapor pressure and moist air pressure gradients. In the results section, the convective effects caused by air stagnation are analyzed in terms of heat flux and mould growth risk for different boundary conditions, showing the importance of a detailed hygrothermal analysis – which is normally disregarded by simulation tools – for accurately predicting building energy consumption, indoor air quality, thermal comfort or mould growth risk.     

Heat and moisture transfer in fibrous thermal insulation with tight boundaries and a dynamical boundary temperature

Prefabricated, lightweight building elements are widely used in the building construction sector. Such elements consist of fibrous thermal insulation encapsulated between two metal sheets. Under various circumstances, moisture can appear in the insulation matrix. Since the temperature of the boundary metal sheets changes dynamically with meteorological conditions, heat and mass transfer between boundaries appear in this case. This paper presents a transient model of the heat and mass transfer, including the sorption and condensation processes. A numerical model considers the dynamical changing of the boundary temperatures. A parametric study considering different amplitudes of temperature change, different moisture masses and different thicknesses of the insulation matrix was made. It was found that a relatively small mass of water in the insulation matrix can result in a significantly increased average heat flux during a periodic cycle. The numerical code was verified with experiments, which showed good agreement with the numerics.     

Determination of the gasket load drop at large size welding neck flange joints in the case of nonlinear gasket model

In this paper, the new hydrobulging technology is described for manufacturing giant ellipsoidal tank heads which could only be made through press and welding before. First, the head is divided into skirt and center parts; the skirt part is formed through traditional technology, while the center part is formed through hydrobulging. Then these two parts are welded together and if the shape and dimensions of the center part after hydrobulging are those of the required ellipsoidal head, then a whole ellipsoidal head is produced. The experiment was performed by hydrobulging plates in pairs under different boundary conditions to form the centre part of an ellipsoidal head. The deformations of the experimental work were measured and calculated and were compared with those of a standard ellipsoidal curvature which were nearest to the experimental curvatures. Finally numerical simulation of the hydrobulging plates in pairs under stiff boundary conditions was done using FEM.     

Experimental and numerical validation of hygrothermal transfer in brick wall

In this paper, a mathematical model dealing with a coupled heat, air, and moisture transfer in a building envelope was developed. Based on the three-following driving potential: vapor pressure, dry air pressure, and temperature, an application on a hygrothermal behavior of a real wall was carried out for different climatic conditions. For this purpose, a characterization of the heat and moisture properties of the materials constituting the wall made with red brick and cement mortar was carried out in the laboratory. This was used to evaluate experimentally the input parameters of the model as a function of relative humidity. To validate the numerical model, an experimental platform was improved. The wall was set up in a double-climatic chamber with different boundary conditions, and then the temperature and humidity evolutions were recorded using several sensors within the wall thickness. The results have highlighted a good agreement between numerical simulation results and experimental ones.     

Unsteady numerical simulation of the cooling process of vertical storage tanks under laminar natural convection

The transient cooling of a fluid initially at rest inside a vertical cylinder submitted to heat losses through the walls is studied. The study is restricted to laminar flow conditions. In order to identify the relevant non-dimensional groups that define the unsteady natural convection phenomenon that occurs, a non-dimensional analysis is carried out. The long-term behaviour of the fluid is modelled by formulating a prediction model based on global balances. A parametric study by means of several multidimensional numerical simulations led to correlate the Nusselt number and the transient mean fluid temperature, in order to feed the global model proposed. Special attention is given to the appropriateness of the spatial and time discretisation adopted, the verification of the numerical solutions and the post-processing tasks carried out in order to obtain the correlations. The most relevant particularities of the numerical model developed are also pointed out.     

Three dimensional numerical modeling of simultaneous heat and moisture transfer in a moist object subjected to convective drying

The drying behavior of a moist object subjected to convective drying is analyzed numerically by solving heat and moisture transfer equations. A 3-D numerical model is developed for the prediction of transient temperature and moisture distribution in a rectangular shaped moist object during the convective drying process. The heat transfer coefficients at the surfaces of the moist object are calculated with an in-house computational fluid dynamics (CFD) code. The mass transfer coefficients are then obtained from the analogy between the thermal and concentration boundary layer. Both these transfer coefficients are used for the convective boundary conditions while solving the simultaneous heat and mass transfer governing equations for the moist object. The finite volume method (FVM) with fully implicit scheme is used for discretization of the transient heat and moisture transfer governing equations. The coupling between the CFD and simultaneous heat and moisture transfer model is assumed to be one way. The effect of velocity and temperature of the drying air on the moist object are analyzed. The optimized drying time is predicted for different air inlet velocity, temperature and moisture content. The drying rate can be increased by increasing the air flow velocity. Approximately, 40% of drying time is saved while increasing the air temperature from 313 to 353 K. The importance of the inclusion of variable surface transfer coefficients with the heat and mass transfer model is justified.     

Sensitivity analyses of convective and diffusive driving potentials on combined heat air and mass transfer in hygroscopic materials

ABSTRACT

The focus of this paper was to examine the contribution of two key mechanisms—moisture convection and diffusion–on heated air and moisture transfer in porous building envelopes and to define the validity of the sub-models. A numerical simulation was performed and is focused on the one-dimensional problem for drying test boundary conditions. Thereafter, a detailed parametric analysis was carried out in order to investigate the influence of typical nondimensional parameters. Results show that convection is a prominent driving potential with respect to the diffusion process when the hygric state is stable between the environment and the envelope.     

利用移动网格技术模拟冰融化过程中的传热问题

用计算流体动力学中的贴体坐标下移动网格技术分析了一类典型具有移动界面的流动融化传热问题,即Stefan问题。流场的计算采用控制容积法,控制方程的离散扩散项采用中心差分法,对流项采用QUICK格式。通过计算表明,这种技术可以非常好地捕捉由于融化引起的界面运动和变形的位置,能获得准确的融化曲线及温度场的演化过程。从中可总结出努谢尔特效或传热系数的变化趋势,找出在自然对流情况下,方冰柱的融化规律和固液界面形状的变化。     

Boundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless method

We study the stable numerical identification of an unknown portion of the boundary on which either a Dirichlet or a Robin boundary condition is provided, while additional Cauchy data are given on the remaining known part of the boundary of a two-dimensional domain, in the case of steady state anisotropic heat conduction problems. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method [53]. The optimal value for the regularization parameter is chosen according to Hansen’s L-curve criterion [17]. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples in both smooth and piecewise smooth geometries.