【作者】 张东辉；

【导师】 施明恒；

【作者基本信息】 东南大学 ， 工程热物理， 2003， 博士

【摘要】 分形理论给多孔介质传热传质研究提供了一种新的视角!本论文对分形多孔介质中斐克扩散、和压力弥散和热传导过程进行了全面和系统的分析。本文首先采用有限容积法分析了分形多孔介质中的热传导过程，多孔介质可以视为二元混合介质，计算中发现分形结构中的导热规律非常复杂，基质与孔隙之间存在着很强的相互换热，当不考虑孔隙气体中的导热时，本文所构造的随机Sierpinski地毯上导热系数与基质率(基质百分含量)大多呈指数关系，这与Archie定律的结果是-致的。进一步模拟计算发现：分形结构中的温度分布和热流分布存在自相似性，与结构紧密关联!上述模拟的结果使我们对分形多孔介质中的热传输规律有了更深的了解。在第三章中，对物质在分形介质中的布朗运动作了初步分析，并依此建立了分形介质的扩散模型，并对不同分形结构下影响扩散过程的主要因素作了初步分析，斐克定律不再适用。物质在分形多孔介质中的扩散受到质量分形维数和谱维数的影响很大，分析表明：物质的分形介质中的扩散是一种不均匀扩散，扩散过程可以认为是一个标度过程，大部分气体粒子沿着结构中最短路径的方向扩散，有效扩散系数和系统的尺度之间存在指数下降关系。第四章将蒙特卡罗(随机模拟)方法应用于多孔介质中的物质传输过程,采用通道逾渗模型，对不同孔隙通道联结率下的弥散规律进行了分析。模拟中发现：在渗流阈值附近，确实存在着反常弥散和优势通道现象，网格中的压力分布也和全部联通时完全不一样。由于在逾渗阈值附近，网格可视为近似分形结构，对二维网格,纵向弥散系数和尺度之间存有指数增加关系!流体微团的概率密度分布函数也表现出多重分形特征!这实际上表明了逾渗阈值附近的弥散是一种典型的非线性弥散过程!为了更深入地了解物质在多孔介质中的运移，本论文进行了土柱模拟实验，将含颜料的水分渗入不同类型的土壤中，然后对其不同深度的剖面进行观察，并且进行了图像分析，发现颜料的分布满足分形特征，水分在土壤中的运移存在优势流现象，受到大孔隙的影响很大，这与上述随机模拟的结果是一致的。最后一章本论文对新老有机碳在土壤当中的迁移积累进行了数值模拟，分析了不同参数对有机碳扩散的影响，得到了不同年龄的有机碳在土壤中的分布规律，这为进一步预估中国土壤中的有机碳动态变化打下了基础。本论文所作出的分析计算和实验研究，对建立符合实际情况的多孔介传热传质模型具有很好的参考价值!更多还原

【Abstract】 Fractal theory would offer a new sight on heat and mass transfer in porous media. This paper mainly deals with the research on the mass diffusion, dispersion and heat conduction in fractal porous media.Firstly, heat conduction in fractal porous media is analyzed and simulated by use of finite volume method in this paper. Fractal porous media can be simplified as a kind of binary mixture with different thermal conductivities. The calculated results show that heat transfer in fractal porous media is very complicated, the thermal coupling effect of matrix with pore structure is studied. When heat transfer in pore structure is neglected, the effective thermal conductivity for random Sierpinski Carpet is scaled up with the percent of matrix, which is described by the classic Archie’s law. All these results are helpful to understand heat conduction mechanism in porous media.Then, Brownian motion in fractal sierpinski carpet is discussed in the third chapter. The random walk in fractal sierpinski carpet is demonstrated as a scaled process. The Fick law is not applicable in fractal media. The spectral dimension is estimated by Monte Cario(random walk) method. The calculated results show that mass diffusion in fractal media is non-homogeneous and nonlinear. The diffusion coefficient is scaled up with porosity percent. The gas diffusion is simulated using diffusion equation in fractal porous media .Dispersion process in porous media is analyzed and simulated by use of Monte Carlo method in this paper. Many unusual phenomena near the percolation threshold caused by random pore removal or blockage is found. First, the grid pressure distribution is Anomalous ; Secondly, the dispersion is much slowly than in Euclidean space. Thirdly, there is a preferential path for dispersion flow near the percolation threshold; Fourth, the longitudinal dispersivity is scaled with grid length. At last, the probability density function shows multi-fractal characteristic, which is Gauss distribution in Euclidean space.The experimental study is designed to observe the flow process by use of morphological method in different kind of soils. Macropore geometry is subsequently characterized by using fractal dimensions of staining patterns on horizontal cross-sections. The results prove that water flow in structured clay soils is strongly influenced by the presence of macro-pores and their geometries. The preferential flow is found widely in the un-destructed soils.A math-physical model of vertical transport of organic carbon in soil is introduced. Numerical simulation of distribution of SOC in soil profiles is conducted ? Influence of some parameters are analyzed, such as: D(diffusion rates), v (coefficient of convection).Double or three compartments model of SOC is used. It is found that the diffusion process for different compartments of organic carbon in soil is very differently. This model could also calculated the accumulation of SOC in soil per year, which is helpful to understand the dynamic process of organic carbon storage in soil.The analytical and experimental results obtained in this work will be greatly valuable and significant for the understanding of heat and mass transfer mechanism in fractal porous media.更多还原