分形多孔介质传热传质过程的格子Boltzmann模拟

针对自然界中实际多孔介质具有的分形特性和随机性,利用中点替代算法和二值化处理构造统计上具有分形特性的随机多孔介质。分析了所构造的多孔介质盒维数与Hurst指数之间的关系。基于随机分形构造的原理,对二维实际多孔介质图像进行了重构。利用两点相关函数,分析了重构图像的结构相关性, 并与实际目标多孔介质的结构特征进行比较。在与解析解对比验证的基础上,将基于二元混合理论的格子Boltzmann模型（LBM）用于模拟多孔介质内流体扩散过程。通过计算不同分形特性的二维多孔介质的有效扩散系数,研究了重构多孔介质的分形维数与有效扩散系数的关系。利用热耦合LBM模型计算多孔介质内传热过程,分析了不同的分形特性对多孔介质蓄热过程的影响。     

Study on the effect of micro geometric structure on heat conduction in porous media subjected to pulse laser

Based on fractal theory, different two-dimensional fractal structures were constructed to simulate the practical porous media. Effective thermal conductivity for porous media was calculated by means of the finite volume method. Theoretical analysis of thermal response in the porous media under various heating conditions was performed with a multi-layer hyperbolic heat conduction model with volumetric heat generation. The results obtained in this paper indicate that pore size and micro distribution have a far-reaching impact on the heat conduction in porous media. If we assumed that both the thermal conductivity and the heat capacity of the solid phase is larger than those of liquid phase, decreasing the pore size and porosity is helpful to enhance the heat transfer in porous media and the peak of temperature increases with pore size and porosity. With the same pore size and porosity, the effect of the pore micro-geometric distribution on heat conduction in porous media is obvious. The method presented in this paper may suggest a valuable approach to theoretically evaluate the effect of pore micro-geometric structure on heat conduction in porous media.     

由吸附等温线分析膨润土的分形孔隙

膨润土是一种多孔的粘土材料，对气相和液相中的污染物均有很好的净化效果。为了了解其对气体的吸附性能，用氮气吸附等温线分析了2种膨润土和1种活性白土的BET比表面积和孔隙分布，并应用基于FHH模型的方法计算了它们的分形维数。结果表明，普通膨润土的分形维数接近2，而活性白土的达到了2．59。讨论了孔隙度、比表面积以及分形维数等参数与吸附量的关系，表明分形维数更能反映膨润土对气体的吸附性能。     

石墨基浸金属多孔材料微观孔隙结构及其分形特征

为定量描述石墨基浸渍金属材料的孔隙结构特征并研究其对浸渍过程的影响规律,在石墨基多孔材料孔隙形成机理研究的基础上,分析形成浸不透孔洞的原因,并运用分形理论对孔隙结构特征进行了描述. 研究表明,石墨基浸渍金属多孔材料的孔隙结构具有典型的分形特征,其基体、孔隙、浸渍金属分形维数分别为1.80~1.85, 1.55~1.65, 1.50~1.55,未浸渍区域的分形维数为1.42~1.60,孔隙率为17.25%~24.85%. 分形维数反映了孔隙结构的非均质性,与采用压汞实验获得的孔隙率变化规律有较好的一致性,证明可用分形维数表征石墨基浸金属材料的孔隙率.     

Multiple linear equation of pore structure and coal–oxygen diffusion on low temperature oxidation process of lignite

This work aimed at studying the feasibility of calculating the coal–oxygen diffusion properties during the low temperature oxidation process of lignite so as to predict its spontaneous combustion process. Coal samples were oxidized in air ambient under different temperatures. Scanning Electron Microscope was used to indicate the surface morphology changes of oxidization. Then, based on fractal theory and flow characteristics, the fractal dimension of gas diffusion in the pore ways was calculated under different temperature. Considering pore size distribution, connectivity distribution and Fick diffusion mechanisms, the relationship between the gas diffusivity change with pore area fractal dimension and porosity was investigated, and multiple linear equation of the coal–oxygen diffusion coefficients and pore parameters was obtained. Comparison between the experimental data and model prediction verifies the validity of the model. The research provides a theoretical basis for the prediction model of coal–oxygen diffusion law.     

孔隙分布对多孔介质内流动和传热的影响

采用Sierpinski地毯分形技术建立多孔介质内流动和传热模型,通过改变固体基质位置研究了孔隙分布结构对多孔介质内流动特性和热效率的影响,3种孔隙分布为每分形一次固体基质分布在中心位置(A)、分布在中上方(B)和分布在右上方(C),当流体稳定流过多孔介质时,不同的孔隙分布表现出不同流动和传热特性. 结果表明,孔隙分布是影响多孔介质传输特性和传热效率的重要因素,无量纲渗透率k*C>k*B>k*A,多孔介质孔隙率大于0.8时更明显;流体流过不同孔隙分布的多孔介质时,相同孔隙率时与流体接触的固体基质面积A>B>C,传热效果A最佳、C最差. 孔隙分布影响了无量纲局部熵产率,在3种孔隙分布下用Be表示的热传导引起的熵产率占主导.     

Correlations between pore structure parameters and gas permeability of corundum porous materials

Corundum porous materials with different contents of calcium hexaluminate formed in situ were prepared using pure calcium aluminate cement as the calcium source. The surface fractal dimensions of the porous materials were calculated based on the experimental data of mercury intrusion. Correlations between pore structural parameters and the permeability coefficients k₁ and k₂ of the porous materials were then studied based on the grey system theory. The results showed that pores in the corundum porous materials have great fractal characteristics. The surface fractal dimension was a significant pore structural parameter that reflected the complexity of pore shape, pore surface, and pore-size distribution, which had the maximum correlation coefficient with the permeability of this type of porous materials. The apparent porosity and pore-size distribution had relatively high correlation coefficients to the permeability as well. Increasing the apparent porosity and the volume percentage of larger pores, and decreasing the volume percentage of smaller pores all benefited the permeability of the porous materials. In addition, the mean pore size and median pore size showed lower correlation coefficients to the permeability—especially for porous materials with a wide pore-size distribution.     

Prediction of the effective diffusion coefficient in random porous media using the finite element method

A finite-element-based method is presented for evaluating the effective gas diffusion coefficient of porous solids. Using this method, the 3-D micro-scale geometries of the porous solids are constructed under the ANSYS platform by the parametric code; the relation between effective gas diffusivity and micro-scale features of random-distributed porous solids is established. The results show that in random-distributed pore media, there is a percolation threshold ε _p, and this percolation threshold decreases with increasing coordination number of the pore network. The relationship between the effective diffusivity and porosity is strongly nonlinear when the porosity, ε, is less than a certain value ε _L ; for ε > ε _L , the relationship becomes quasi-linear. This dividing point ε _L decreases with increasing coordination number. The larger the coordination number of the pore network, the higher the effective gas diffusivity. Based on the simulation results and observations, a formula relating the effective diffusion coefficient with porosity is proposed.     

Fractal Pore Network Simulation on the Drying of Porous Media

Based on the knowledge of fractal geometry, physics of flow through porous media, and transport process principle, a fractal pore network model for the drying process of a natural porous body was established in this article. This model takes various factors into consideration, such as liquid-phase flow, vapor-phase diffusion, temperature gradient, and pore microstructure characteristic. The drying dynamics characteristics of potato slices were obtained by the simulation of a fractal pore network model. The simulation results of the fractal pore network model were contrasted with those of a regular one and the experimental data, respectively. The wet patches were observed on the potato slices during the drying experiments, and it was validated by the drying simulation. The results indicate that the drying kinetics from the fractal pore network model, as well as the distributions of moisture and temperature inside the porous body, are more consistent with that of the drying experiments than that of the regular one, and the throat size distribution in the pore network of the porous media has a notable influence on the drying process.     

分形多孔介质的孔隙特性对气体扩散的影响

采用随机行走方法建立了分形多孔介质生成模型,生成的颗粒在形貌上与真实多孔颗粒接近,且能够反映其固有分形特征。在此模型基础上,根据经典分子动理论建立扩散控制方程,对气体在多孔介质中的扩散进行数值模拟。分析了比表面积、平均孔径、孔隙率等孔隙特性参数对扩散的影响,获得了分形多孔介质中气体扩散系数与平均孔径的函数关系。结果表明,扩散系数随平均孔径的增大以幂函数形式增大,相应的指数表征扩散系数对平均孔径的敏感度,其值随孔隙率的增大呈线性减小。     

ANALYSIS OF PERMEABILITY FOR ELLIS FLUID FLOW IN FRACTAL POROUS MEDIA

This work studies the flow characteristics of Ellis fluid in saturated porous media. A fractal model is developed for the effective permeability of Ellis fluid flow in porous media based on the assumptions that porous media consist of a bundle of tortuous capillaries, whose size distribution and tortuosity follow the fractal scaling laws. The average flow velocity and the effective permeability for Ellis fluid flow in porous media are derived. The proposed fractal model does not contain any empirical constant, and every parameter in the model has clear physical meaning. The model predictions are compared with the measured data, and good agreement between them is obtained.     

分形多孔介质中气体的非稳态扩散

通过引入平均修正系数修正Fick第二扩散定律得到了描述分形多孔介质气体非稳态扩散的理论方程。基于“塞状流”扩散实验法建立了分形多孔介质非稳态扩散实验系统,对3个孔隙结构不同的分形多孔介质样品进行了非稳态扩散实验,通过实验对理论方程进行验证和修正。结果表明,Fick第二扩散定律不适用于分形多孔介质中气体非稳态扩散,分形多孔介质中气体非稳态扩散存在一定规律,且多孔介质孔隙结构不同其扩散规律不同。     

生物质焦分形维数计算

采用压汞法的实验数据,计算两种分形模型下生物质焦样的分形维数。其中根据Menger海绵模型计算得到的分形维数Dm的值在2．7～3．1之间,基于热力学关系的分形模型计算得到的分形维数Dr的值在2．7～2．9之间。分析认为第二种模型更好的描述了焦样的孔隙结构,Dr的值比Dm的值更为合理。实验结果表明,分形维数与生物质种类有关,树叶焦样的分形维数整体上大于稻壳焦样的分形维数。生物质焦样的平均孔径与分形维数有关。总的来看,同一生物质焦样的分形维数随着平均孔径的增大而减小。     

CAPILLARY NETWORK MODELS FOR TRANSPORT IN PACKED BEDS: CONSIDERATIONS OF PORE ASPECT RATIO

The conventional analysts for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed Tor unconsolidated and grainy media.     

Strategy for predicting effective transport properties of complex porous structures

Measurements of effective transport properties of porous media, such as effective diffusivity and permeability, are well established by several experimental techniques. Effective transport properties can be also calculated from the spatially 3D reconstructed porous media, where the morphology characteristics required for the reconstruction are obtained from electron microscopy images. Here we demonstrate the reconstruction of porous alumina catalyst carrier with bimodal pore size distribution. Multi-scale concept is employed for the computation of effective diffusivity and permeability of reconstructed porous media and calculated effective transport properties are compared with transport parameters experimentally determined in Graham diffusion and simple permeation cell. The limitations of current state-of-the-art reconstruction techniques for porous media with broad pore size distribution are discussed. We show that the contribution of nano-pores towards the total diffusion flux is significant and cannot be neglected, but it is reasonable to neglect the contribution of nano-pores towards the sample permeability.     

MICROSCOPIC DETERMINATION OF TRANSPORT PARAHETERS IN DRYING POROUS MEDIA

The flow and distribution of liquid and vapor in the pore space of drying porous media are represented by a simple network model that incorporates the microscopic mechanisms. A method akin to Monte Carlo and molecular dynamics approaches is described for calculating from any such model the macroscopic, 'volume- averaged', or effective transport parameters: relative permeabilities for pressure-driven flow, effective diffusivities for molecular diffusion, and so on.

The method is to map representative small samples of pore space onto regular networks that have equivalent mean coordination and are made up of biconical pore segments intersecting in pore bodies, all dimensions being drawn from measured or estimated distributions. Evaporation and meniscus curvature, vapor movement by diffusion away from menisci and viscous flow toward them are described by one-dimensional local approximations. The resulting large set of ordinary differential and algebraic equations is solved by computer. Solutions from several such realizations are averaged to determine relative permeability to liquid, capillary pressure, and effective diffusivity of vapor as functions of liquid saturation and drying history. The results are to be used for interpreting, interpolating, and extrapolating experimental measurements of the same quantities.     

构建微波冷冻干燥质扩散系数的一种新方法

针对现有微波冷冻干燥模型中必须依靠实验以确定扩散系数的问题．提出一种构建扩散系的新方法。根据毛细管低压气体输运理论，利用物料本身的细微结构、气体分子平均自由程、气体状态参数和气体物性参数来构建扩散系数，在此基础上建立微波冷冻干燥模型。并结合牛肉的微波冷冻干燥行模型可靠性分析。结果表明，新建模型能够很好地描述微波冷冻干燥过程温度场的变化及其特征．升过程干燥曲线的理论值与实验值之间的相对误差小于10％。     

多孔介质的孔隙特性对气体扩散过程影响的直接数值模拟

引言多孔介质内的扩散过程广泛存在于化工、能源、环境和生物等领域,例如石油天然气开采、污水处理、填充床化学反应、催化剂和生物组织内的质量传递等,使得多孔介质内传质现象的研究尤为重要[1-2]。多孔介质由于结构和形状各异,难以有准确、有效且简单的描述方法,因而研究变得极为     

不同秸秆生物炭的孔隙结构及其差异

基于低温氮气吸附的研究方法,对水稻秸秆、玉米秸秆、小麦秸秆制备的生物炭进行了孔结构研究,用BET方程、BJH方程和t-plot方法分别计算得到生物炭的比表面积、孔径分布和微孔数据,利用FHH模型计算了孔隙分形维数。研究表明：不同温度不同材料都对生物炭的孔结构有较大影响,随着热解温度的升高水稻秸秆生物炭和小麦秸秆生物炭的BET比表面积和总孔容呈先增加后降低的趋势,而玉米秸秆生物炭的孔隙度随着热解温度升高持续增加;3种秸秆生物炭的孔径分布均以中孔为主,孔隙内部以Ⅱ型孔为主;水稻秸秆、玉米秸秆、小麦秸秆制备的生物炭都具有很好的分形特征,分形维数(D)分别为2.545 4~2.669 3、2.629 7~2.689 5、2.577 3~2.597 2,表明这3种生物炭孔隙结构比较复杂,非均质性强,其中水稻秸秆生物炭和小麦秸秆生物炭均在500 ℃条件下有较高的分形维数,分别是2.669 3和2.597 2,玉米秸秆生物炭则在700 ℃条件下有较高的分形维数,为2.689 5。     

A critical look into effects of electrode pore morphology in solid oxide fuel cells

Knudsen diffusion, an important form of gas transport in sub‐micro/nanoscale porous electrodes of solid oxide fuel cells (SOFCs), is evaluated typically based on the assumption of isotropic cross‐sections of electrode pores. As a consequence, errors are induced in the evaluation of gas transport and polarization loss of SOFCs with irregular, anisotropic pore morphology. Here, a numerical model is derived to investigate the impact of pore morphology on Knudsen diffusivity and effective total diffusivity in porous SOFC electrodes. Based on the model, the correlation between pore morphology and important parameters of SOFCs, including limiting current density (LCD) and concentration polarization (CP), is evaluated. As the aspect ratio of pore cross‐section increases, the gas diffusivity in SOFC electrodes decreases, and then nontrivial variations in LCD and CP are induced. This work facilitates the accurate evaluation of gas transport in SOFCs as well as the rational design of electrode microstructure of SOFCs. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2312–2317, 2017