分形多孔介质导热数值模拟分析

NUMERICAL STUDY OF HEAT CONDUCTION IN FRACTAL POROUS MEDIA

本文基于分形理论构造了不同类型的分形结构来模拟多孔介质,采用有限容积法对其导热问题进行了数值模拟计算,详细分析了基质导热系数、孔隙流体导热系数、孔隙率等因素对其有效导热系数的影响规律。结果发现有效导热系数与基质导热系数、孔隙流体导热系数大致分别成幂函数关系,有效导热系数与孔隙率大致成指数函数关系。并把数值模拟分析结果与文献中的经验公式进行了对比分析,为其提供了数值验证。

Several types of fractals were generated to model the structures of porous media, and heat conduction in these structures was simulated by the finite volume method （FVM）. The influence of the thermal conductivity of solid κs, the thermal conductivity of fluid kf and the porosity s on the effective thermal conductivity κe of these structures was analysed in detail. The calculated results indicate that the relation of effective thermal conductivity κe with thermal conductivity of solid κs and thermal conductivity of fluid kf conforms to a power function, and the relation of effective thermal conductivity ks with porosity s conforms to an exponential function. The numerical results were analysed by comparing with the available empirical formulas from open literatures, and provide verification of these empirical formulas.