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 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.     

Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels

Fluid flow and convective heat transfer of water in sintered bronze porous plate channels was investigated numerically. The numerical simulations assumed a simple cubic structure formed by uniformly sized particles with small contact areas and a finite-thickness wall subject to a constant heat flux at the surface which mirrors the experimental setup. The permeability and inertia coefficient were calculated numerically according to the modified Darcy’s model. The numerical calculation results are in agreement with well-known correlation results. The calculated local heat transfer coefficients on the plate channel surface, which agreed well with the experimental data, increased with mass flow rate and decreased slightly along the axial direction. The convection heat transfer coefficients between the solid particles and the fluid and the volumetric heat transfer coefficients in the porous media predicted by the numerical results increase with mass flow rate and decrease with increasing particle diameter. The numerical results also illustrate the temperature difference between the solid particles and the fluid which indicates the local thermal non-equilibrium in porous media.     

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。     

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。     

含甲烷水合物的石英砂渗透率实验和分形模型对比研究

含水合物的多孔介质渗透率是影响水合物开采的关键参数,多孔介质渗透率与水合物的饱和度密切相关。定量研究多孔介质渗透率随水合物饱和度的变化,对自然界中天然气水合物藏内渗流场的研究具有重要的理论价值。本文以平均粒径为139.612 μm的石英砂为多孔介质,采用稳态注水法测量在不同甲烷水合物饱和度（0 ~ 28.56%）下的石英砂渗透率,将实验数据与两种不同水合物赋存形式（颗粒包裹、孔隙填充）下的石英砂渗透率二维分形模型进行了对比。结果表明,石英砂渗透率比K_r随甲烷水合物饱和度S_h的增大呈现指数减小的趋势。当水合物饱和度低于11.83%时,渗透率比下降缓慢。而当水合物饱和度高于11.83%时,渗透率比下降迅速;当饱和度指数n = 12时,渗透率分形模型与实验数据吻合良好。通过分形模型与实验数据对比,发现当水合物饱和度低于11.83%时,甲烷水合物的赋存形式为颗粒包裹型。在11.83% ~ 28.56%水合物饱和度范围内,甲烷水合物的赋存形式为孔隙填充型。本研究成果量化了石英砂渗透率与甲烷水合物饱和度的关系,确定了含甲烷水合物的石英砂的渗透率分形模型的参数取值。     

基于格子Boltzmann方法的饱和土壤渗流与传热数值模拟

本文利用随机多孔介质生成算法重构了与真实土壤外貌相近的多孔介质几何结构。通过引入不可压耦合双分布格子Boltzmann模型（lattice Boltzmann model ,LBM）对孔隙尺度下单相饱和土壤渗流和传热进行了模拟。着重讨论了不同渗流压差、孔隙率、土壤固体颗粒尺寸分布对流动与传热的影响。结果表明：土壤渗流速度与渗流压差呈线性单调递增关系,平均温度随渗流压差增加而增大,但温升速率逐渐减缓;当孔隙率增大时,渗流速度增加,且当孔隙率大于0.58时,对流换热作用迅速增强,土壤温升速率显著加快;对于相同孔隙率,当土壤固相颗粒尺寸较大时,流动出现典型优先流效应;随着土壤固相颗粒尺寸减小,土壤温度变化逐渐趋于平缓,平均温度降低。     

Permeability of fractal porous media by Monte Carlo simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.     

An Investigation on Transport Properties Near the Wall in Porous Media by Fractal Models

A comprehensive investigation on the wall effects on the transport properties, permeability, thermal conductivity, and thermal dispersion conductivity is performed, based on the fractal models for these properties and the porosity variations near the wall in porous media. The results show that the fractal models for transport properties of porous media can provide good agreement with the conventional models in the region near the wall in porous media. This indicates that the fractal models for transport properties of porous media also hold in the region near the wall in porous media if the wall effects are taken into account.     

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.     

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.     

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.     

Fractal description of microstructures and properties of dynamically evolving porous media

Transport through porous media is encountered in several engineering and biological applications. The porous media can be subjected to changes in structure owing to deposition, erosion, swelling or shrinkage which, in turn, affects the transport properties of the media. A dynamic fractal model (DFM) is developed to describe the evolution in pore structure undergoing deposition using fractal dimensions and to predict the changes in the effective diffusivity in terms of the dynamic fractal dimensions. Evolving microstructures undergoing deposition are analyzed at various saturation levels to determine the effective diffusivity using the dynamic fractal model. The effective diffusivity values of the evolving porous media are compared against existing data in the literature.     

Analysis of seepage characters in fractal porous media

In this paper, the plane-radial and plane-parallel flows for Newtonian fluid in fractal porous media are analyzed. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and on the fractal characteristics of pore size distribution in porous media, the expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows are developed. The obtained expressions are the functions of tortuosity, fractal dimension, maximum and minimum pore diameters, and there are no empirical constant and every parameter has clear physical meaning in the expressions. The pressure distribution equations for plane-radial and plane-parallel flows in fractal porous media are also derived. The pressure and velocity distributions in plane-radial reservoirs are calculated and discussed.     

生物质热燃气多孔介质直燃机理与脱焦特性研究

为研究含焦油的生物质热燃气在多孔介质中的燃烧机理与焦油燃烧脱除特性,采用固相实体颗粒堆积法模拟多孔介质,通过分析燃烧过程中反应器内温度、热流密度以及反应动力学速率等参数场的分布特征,揭示了当量比对生物质热燃气多孔介质燃烧过程的显著影响作用.研究表明,焦油燃烧脱除过程中直接氧化反应速率高是决定焦油出口浓度小、转化率高的关...     

土体渗透变形及渗透破坏过程中分形特征初探

根据天然土体及室内配制土样颗粒分析、干密度、渗透、渗透变形试验结果,基于土体分形理论计算了土体质量分维数,土体孔隙度、不均匀系数、中值粒径、干密度、渗透系数与分维数关系密切。当分维数较大时,表示小于某粒径颗粒累积含量较少,颗分曲线越平缓,土体有粗化现象,不均匀系数及中值粒径都在增大,孔隙度减小,干密度增大。利用土体分维数可判断出土体渗透破坏形式（如管涌、流土）,土体发生渗透破坏后分维数减小,渗透破坏过程中分维数逐渐减小,并随流失颗粒粒径的增大而加速减小。     

华中粉砂岩粗粒土粒径级配分形特性研究

研究不同应力状态下颗粒粒径级配演化规律是分析土体应力状态、评价其工后变形的关键。基于质量-粒径分形模型从分形角度阐述了粗粒土粒径级配曲线探究依据,设计了5种不同分形维数的粒径级配,分析了土体颗粒空间分布特性;通过三轴剪切试验及颗粒筛分试验,探究了不同分形维数粗粒土偏应力峰值前后应力应变曲线性态分布及剪应力峰值、内摩擦角、分形维数因子等参数变化规律。结果表明,土体粒径范围随分形维数越大而更宽泛;应力应变曲线随分形维数及围压增大而存在应变软化向应变硬化过渡的趋势,偏应力峰值随分形维数增加而增大,内摩擦角呈先减小后增大的变化规律。粗粒土分形维数变化因子与相对围压呈线性函数关系,方程斜率及截距仍与相对围压呈线性函数关系,据此建立了考虑围压及初始分形维数的经验方程,为从分形角度来设计与优化粗粒土粒径级配而达到提高其力学强度等提供了参考依据。     

The influences of thermophysical properties of porous media on superadiabatic combustion with reciprocating flow

The influences of thermophysical properties of porous media on superadiabatic combustion with reciprocating flow is numerically studied in order to improve the understanding of the complex heat transfer and optimum design of the combustor. The heat transfer performance of a porous media combustor strongly depends on the thermophysical properties of the porous material. In order to explore how the material properties influence reciprocating superadiabatic combustion of premixed gases in porous media (short for RSCP), a two‐dimensional mathematical model of a simplified RSCP combustor is developed based on the hypothesis of local thermal non‐equilibrium between the solid and the gas phases by solving separate energy equations for these two phases. The porous media is assumed to emit, absorb, and isotropically scatter radiation. The finite‐volume method is used for computing radiation heat transfer processes. The flow and temperature fields are calculated by solving the mass, moment, gas and solid energy, and species conservation equations with a finite difference/control volume approach. Since the mass fraction conservation equations are stiff, an operator splitting method is used to solve them. The results show that the volumetric convective heat transfer coefficient and extinction coefficient of the porous media obviously affect the temperature distributions of the combustion chamber and burning speed of the gases, but thermal conductivity does not have an obvious effect. It indicates that convective heat transfer and heat radiation are the dominating ways of heat transfer, while heat conduction is a little less important. The specific heat of the porous media also has a remarkable impact on temperature distribution of gases and heat release rate. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 336–350, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20120     

Study on boiling heat transfer in liquid saturated particle bed and fluidized bed

An investigation on the effects of solid particles on boiling heat transfer enhancement is performed. The range of particle diameter is from millimeter to nanometer. The experimental results show that boiling heat transfer can be enhanced greatly by adding the solid particle into the liquid whether in fixed particle bed or in fluidized particle bed. The boiling enhancement is closely related to the particle size, the initial bed depth and the heat flux applied. The experiments show that boiling characteristics are greatly changed when a particle layer is put on the heated surface. The major effects of fixed particle bed on nucleate pool boiling heat transfer are the nucleation, bubble moving and thermal conductivity effect. A boiling heat transfer correlation is obtained to predict the boiling heat transfer coefficients in a liquid saturated porous bed. A volumetric convection mechanism of boiling heat transfer enhancement by fluidized particles is proposed. The calculated results from the model suggested in this paper agree reasonably with the experimental values.     

干湿循环对土体级配分形特性影响分析

为分析粗粒土受水体干湿循环作用时颗粒级配演化规律,采用颗粒筛分试验统计干湿循环作用后土体颗粒粒径分布,引入颗粒质量-粒径分形模型计算粒径分形曲线(GFC)及分形维数(D),揭示了D随围压及干湿循环次数变化的规律,量化了干湿循环作用对粗粒土D的影响,并建立了计算方程。结果表明,等效替代缩尺法对GFC及D影响较小;制样及筛分过程导致D增大0.63%,室内试验方法引起粗粒土颗粒破碎效应不可忽略。低围压条件下(围压小于0.60MPa),D随围压增大及干湿循环次数增多而增大,剪切作用及水体干湿循环作用加剧了粗粒土颗粒破碎效应。所建粗粒土D计算模型为评价干湿循环对涉水工程填筑土体级配劣化效应提供了依据。