多孔材料等效导热系数与分形维数关系的数值模拟研究  

Numerical simulation of relationship between thermal conductivity of porous material and fractal dimension

作　　者：李守巨[1] 刘迎曦[1] 于贺[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《岩土力学》2009年第5期1465-1470,共6页Rock and Soil Mechanics

基　　金：国家重点基础研究发展规划项目(No.2007CB714006);国家自然科学基金重点项目(No.90815023)

摘　　要：采用有限元方法模拟了多孔材料的导热系数与孔隙率和分形维数之间的非线性关系。有限元模型中的固体骨架和孔隙根据孔隙率的大小随机生成,模型中的材料参数和单元属性用ANSYS中的APDL参数化语言赋值。根据有限元随机模拟断面的热流密度分布和稳态热传导傅立叶定律,计算在不同孔隙率条件下的等效导热系数。研究表明,多孔材料模型等效导热系数随着孔隙的增加而线性减小。在孔隙率为常数的条件下,模型等效导热系数随着模型比例因子的增加而呈指数增加。等效导热系数随着孔隙分形维数的增加而减小,随着固体颗粒分形维数的增加而增加。The relationship between thermal conductivity of porous material and ffactal dimension is numerically simulated by using finite element method. The solid matrix and pore space are generated randomly according to material porosity; and material parameters and element properties are changed by ANSYS parameter design language. The effective thermal conductivity is computed according to thermal flux through some section computed by FEM and Fourier heat transform law. The investigation shows that the effective thermal conductivity linearly decreases with increasing porosity; the effective thermal conductivity of FEM model will increase in exponential function with the increase of scaling factor while the material porosity is constant. The effective thermal conductivity will decrease in exponential fimction with the increase of fractal dimension of porosity space and increase in exponential function with the increase of fractal dimension of solid matrix.

关 键 词：多孔材料 等效导热系数 分形维数 随机数值模拟 有限元方法 

分 类 号：O242[理学—计算数学]