多孔介质导热的分形模型

多孔介质中热量传递与多孔介质内部的几何结构有密切的关系，讨论了多孔介质的分形结构和相关的分形维数，利用能量方程，导出了分形维数为D的有限尺度多孔介质中的广义热传导方程，在此基础上，假定热量在多孔介质中的传导路线也是一种分形结构，提出了一个筒化的多孔介质并联通道分形导热模型，求出了基于分形理论的多孔介质有效导热系数表达式。     

A fractal model for determining oxygen effective diffusivity of gas diffusion layer under the dry and wet conditions

In this paper, we propose a new fractal model to determine the oxygen effective diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cell for both the dry and wet conditions. The model considers the GDL structure in terms of tortuosity and area fractal dimensions and also takes the Knudsen effect into account, which has no empirical constant but parameters with physical meanings. The fractal model is verified by the fair agreement with the experimental data and the results obtained from existing models. It is revealed that the Knudsen effect is essential for the understanding of the oxygen transport through the GDL. Under the dry condition, the oxygen effective diffusivity increases with higher area fractal dimension and lower tortuosity fractal dimension. For the wet condition, the water condensation in the GDL of mixed wettability is considered; and it is found that the behavior of oxygen effective diffusivity with liquid saturation depends on the GDL wettability. It is further revealed that for a given liquid saturation, the oxygen effective diffusivity increases with greater area fractal dimension; with the decrease of tortuosity fractal dimension, it also increases, except for the hydrophilic case at high liquid saturation.     

Fractal model for predicting the effective binary oxygen diffusivity of the gas diffusion layer in proton exchange membrane fuel cells

We propose an analytical model to predict the effective binary oxygen diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cells (PEMFCs). In this study, we consider the fractal characteristics of the porous GDL as well as its general microstructure, and we adopt the Bosanquet equation to derive effective diffusivity. The fractal characterization of GDL enables us to model effective diffusivity in a continuous manner while taking into account the effect of pore size distribution. Comparison to two other theoretical models that are generally accepted in the simulation of PEMFCs shows similar trends in all three models, indicating that our proposed model is well founded. Furthermore, the predicted effective binary oxygen diffusivities of two samples show that after treatment with polytetrafluoroethylene (PTFE), the effective binary diffusivity of the GDL decreases. Based on the parametric effect analysis, we conclude that effective binary diffusivity is negatively correlated with tortuosity fractal dimension but positively correlated with the fractal dimension of pore area, porosity, or mean pore diameter. The proposed model facilitates fast prediction of effective diffusivity as well as multi-scale modeling of PEMFCs and thus facilitates the design of the GDLs and of PEMFCs.     

A fractal resistance model for flow through porous media

A fractal model for resistance of flow through porous media is developed based on the fractal characters of porous media and on the pore–throat model for capillary. The proposed model is expressed as a function of the pore–throat ratio, porosity, property of fluid, pore/capillary and particle sizes, fluid velocity (or Reynolds number) and fractal dimensions of porous media. There is no empirical constant and every parameter has clear physical meaning in the proposed model. The model predictions are compared with experiment data, and good agreement is found between them.     

Fractal analysis of Herschel–Bulkley fluid flow in porous media

The Herschel–Bulkley (HB) fluid is the representative fluid which may be reduced to the power-law fluid, Bingham and Newtonian fluids in appropriate conditions. In this paper, fractal models for velocity and the starting pressure gradient for HB fluid in porous media are derived based on fractal characteristics of porous media and capillary model. The proposed models are expressed as a function of fractal dimensions, porosity, maximum pore size and representative length of porous media. Every parameter in the proposed expressions has clear physical meaning, and the proposed models relate the flow characteristics of HB fluid to the structural parameters of porous media. The variation trends of fractal velocity and starting pressure gradient versus different impact factors are shown, and the analytical expressions reveal the physical principles for flow velocity and starting pressure gradient in porous media.     

Study on effective thermal conductivity for porous media using fractal techniques

In this paper, the geometric structure of porous media is described using fractal techniques, and a section particle area fractal dimension d of a porous medium with various porosities is considered with a simplified model. Also an expression of the effective thermal conductivity for soil is presented via a fractal dimension and a model of heat transfer in soil. The results obtained in this paper indicate the effectiveness of the method for determining the effective thermal conductivity by using the section area dimension. © 2000 Scripta Technica, Heat Trans Asian Res, 29(6): 491–497, 2000     

A fractal permeability model for bi-dispersed porous media

In this paper a fractal permeability model for bi-dispersed porous media is developed based on the fractal characteristics of pores in the media. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of particles and clusters, micro-porosity inside clusters, and the effective porosity of a medium. An analytical expression for the pore area fractal dimension is presented by approximating the unit cell by the Sierpinski-type gasket. The pore area fractal dimension and the tortuosity fractal dimension of the porous samples are determined by the box counting method. This fractal model for permeability does not contain any empirical constants. To verify the validity of the model, the predicted permeability data based on the present fractal model are compared with those of measurements. A good agreement between the fractal model prediction of permeability and experimental data is found. This verifies the validity of the present fractal permeability model for bi-dispersed porous media.     

Analysis of effective thermal conductivity for circular tubes made with porous media based on fractal theory

Accurately evaluating the relation between heat transfer performance and the complex structure of porous media is still a difficult task. Most previous fractal models of effective thermal conductivity (ETC) are developed to describe the heat-conducting characteristics of a unit cell or a representative elementary volume in porous media, and few models have paid attentions to the ETC for practical circular tubes made with a porous structure based on fractal theory. This paper proposes a new ETC model for a circular tube made with porous media based on fractals, and the validity of the present model is proved by previous models and testing data in the literature, then the effects of intrinsic thermo-physical properties of each component and pore structures on the ETC are discussed. The analysis results indicate that a circular tube made with porous media can improve its heat-insulating performance by about 25% compared with a common parallel circular tube. This can supply an alternative scheme for pipe insulation design in cold/hot fluid supplying systems or air conditioning systems.     

A fractal model for the starting pressure gradient for Bingham fluids in porous media embedded with fractal-like tree networks

In this paper, a fractal model is presented for the starting pressure gradient for Bingham fluids in porous media embedded with fractal-like tree networks. The proposed model relates the starting pressure gradient to the structural parameters of porous media and microstructural parameters of the fractal-like tree networks, the yield stress and fractal dimensions. The model predictions from the present model for the starting pressure gradient are compared with the available expression. Good agreement is obtained between the predictions by the proposed expression Eq. (17) for the starting pressure gradient with those from the available expression.     

含湿非饱和多孔介质的完全分形传热研究

为了探究在含湿情况下多孔介质有效导热率的变化,基于分形理论,考虑多孔介质在含湿时加热过程中相变的影响,结合加热过程中的热量守恒方程和傅里叶导热定律推导出计算有效导热率的新公式。将该模型相关数据代入进行计算,分析了孔隙率、含湿率、面积分形维数和迂曲分形维数对有效导热率的影响。研究发现,孔隙率与有效导热率呈负相关,含湿率与有效导热率呈正相关,分形维数与有效导热率呈负相关。该研究能够反映多孔介质内的传热进程,对于探究微孔结构物质的传热具有一定的指导意义。     

Analysis of permeabilities for slug flow in fractal porous media

Slug flow is one of types of flow in two-phase flow in porous media, and this type of flow widely exists in oil and gas pipelines, underground water reservoirs, and nuclear reactor cooling systems, etc. Study of the mechanisms and characteristics of slug flow in porous media has the great significance in the reservoir engineering, power engineering, aerospace engineering, and chemical engineering etc. In this paper, we propose analytical models for seepage characteristics, both permeabilities and relative permeabilities, for slug flow in a capillary by unit cell approach. Then, we extend the methodology to analyze the seepage characteristics of slug flow in fractal porous media. The proposed relative permeabilities for slug flow in porous media are expressed as a function of micro-structural parameters of porous media and fluid properties, such as maximum and minimum capillary sizes, fractal dimensions, the surface tension, as well as capillary numbers. The parametrical effects on the relative permeabilities are also investigated. The validity of the proposed model for slug flow is verified by comparing the model predictions with the available experimental data.     

A fractal model for the coupled heat and mass transfer in porous fibrous media

This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory.     

燃煤脱硫剂孔隙结构分形特性的研究

脱硫剂孔结构特性对脱硫性能有着重要的影响,其煅烧后的多孔结构是具有自相似性的分形结构.选取4种钙基脱硫剂,在压汞分析实验的基础上,对脱硫剂孔结构的分形特性进行研究,提出了脱硫剂孔隙分形维数的计算方法,并探讨了煅烧温度对分形维数的影响.     

The prediction of effective thermal conductivities perpendicular to the fibres of wood using a fractal model and an improved transient measurement technique

The porous microstructure of wood samples on their sections perpendicular to the fibres were analyzed using the scanning electron microscope images. The fractal dimensions of these images were calculated using the box-counting method, respectively. They are all approximately equal to 1.4, although the distribution and the scale of wood fibres are extremely different. Then, a fractal model for predicting the effective thermal conductivities of wood was established using the thermal resistance method. In addition, we measured the effective thermal conductivity of wood via an improved transient plane source measurement method. The calculated results by the proposed model are in good agreement with the experimental data as well as the literature data. The comparison shows clearly that this fractal model can be used to accurately and effectively predict the effective thermal conductivities perpendicular to the fibres of wood.     

Determination of Effective Thermal Conductivity ForReal Porous Media Using Fractal Theory

INTRODUCTIONPorousmediaisacompositemediathatincludessolidframeandfluidandexistedwidelyintheeajrthbiosphere.Heatandmasstransferinporousmediaisbothanaturalphenomenoninearthbiosphereandaphysicalchemistryprocessinindustries,agricultureandhumanlife.Thusthestudyonheatandmasstransferinporousmediahasbecomeanimportanttasktoscielltistsandengineers.Heatandmasstransferinporousmediaisaverycomplexobject.Therearestillmanydifficultiestodescribethecoupledheatandmasstransferphenomena.Amongthesedifficultie…     

Estimation of thermal and mass diffusivity in a porous medium of complex structure using a lattice Boltzmann method

The thermal and mass diffusivity in a porous medium of complex structure is studied by using the lattice Boltzmann method. The media under consideration include two-dimensional medium with an array of periodically distributed circular and square cylinders, three-dimensional granular medium of overlapping or non-overlapping spherical and cubical inclusions of different size, and randomly generated fibrous medium. The calculated effective diffusivities are in good agreement with existing analytical and numerical results when the inclusions, regardless of their shapes, are not overlapped. For the medium of overlapping inclusions, the effective diffusivity deviates from existing correlations as the inclusion fraction increases. In particular, the deviation increases dramatically if the thermal diffusivity of the inclusion is greater than that of the fluid in the medium for enhanced thermal conduction. A new empirical correlation between the effective diffusivity and the volume fraction for the medium of overlapping inclusions is proposed.     

A fractal permeability model for the gas diffusion layer of PEM fuel cells

In this paper a fractal permeability model for the gas diffusion layer (GDL) of PEM fuel cells (PEMFCs) is presented. The model accounts for the actual microstructures of the GDL in terms of two fractal dimensions, one relating the size of the capillary flow pathways to their population and the other describing the tortuosity of the capillary pathways. In addition, the gas molecule effect is considered by using the Adzumi equation. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of pore and the effective porosity of porous medium without any empirical constants. mercury-intrusion porosimetry was used to measure the microstructures of the GDL. Based on scanning electron microscope (SEM) images, two fractal dimensions are determined by the box-counting method. To verify the validity of the model, the predicted permeability data of the present fractal model were compared with the experimental data supplied by Toray Inc. It is found that the permeability prediction of the model was in accordance with experimental data. This verifies the validity of the present fractal permeability model for the GDL.     

Characteristics of oxygen diffusivity and water distribution by X-ray radiography in microporous media in alternate porous layers of different wettability for moisture control in gas diffusion layer of PEFC

The mass transfer characteristics of the gas diffusion layer (GDL) are closely related to the performance of polymer electrolyte fuel cells. This study investigates the configuration of a new GDL in which two porous media with different wettabilities are alternately arranged (hybrid GDL). The oxygen diffusivity characteristics with respect to water content (saturation) were measured using an experimental system that employs a galvanic oxygen sensor as an oxygen absorber. Furthermore, X-ray radiography was used to observe the internal water distribution in microporous media for GDL to elucidate the enhancement mechanisms of oxygen diffusivity of the new microporous media. It was possible to distinguish between voids and water in microporous media by using X-ray computer tomography. In addition, the water distributions in the new microporous media were visualized and the mechanisms for the high oxygen diffusivity of the hybrid structure of microporous media were clarified.     

Fractal model for prediction of effective hydrogen diffusivity of gas diffusion layer in proton exchange membrane fuel cell

This paper presents a novel prediction model of the effective hydrogen diffusivity for the gas diffusion layer (GDL) in proton exchange membrane fuel cell (PEMFC) by using fractal theory to characterize microstructure. With the consideration of pore-size distribution and Knudsen diffusion effect, a relationship between micro-structural parameters and effective hydrogen diffusivity of GDL is deduced. The prediction of effective hydrogen diffusivities of two samples shows that Knudsen diffusion effect makes the effective diffusivity value decrease, and after being treated with polytetrafluoroethylene (PTFE), carbon paper, a basal material of the GDL, exhibits a lower effective diffusivity value due to the decrease in the pore space and porosity. From the parametric effect study, it can be concluded that effective diffusivity has a positive correlation with pore area fractal dimension D_p or porosity ?, whereas it has a negative correlation with tortuosity fractal dimension D_t.     

A fractal model for gas permeation through porous membranes

Macro and micro porous membranes have been used in many industrial areas. The disordered nature of pore structures in these membranes suggests the existence of a fractal structure formed by the pores. Fractal theory is employed to build the permeation model through these porous membranes. The fractal dimensions for surface pore area and tortuosity of membrane is obtained by box-counting method. Contrary to previous studies which consider only the Poiseulle flow in pores, in this research, the model reflects two gas diffusion mechanisms simultaneously: when the Knudsen number is less than 0.01, the Poiseulle flow is dominant; while when the Knudsen number is greater than 10, the Knudsen flow is dominant; and when the Knudsen number is from 0.01 to 10, the two mechanisms coexist. Contact gas permeation experiments with three porous hydrophobic PVDF membranes are conducted to validate the model. Comparisons between the current model and those from references are made.