基于S ierpinski carpet模型的多孔介质迂曲度计算

摘要

Based on the exact self-similar fractal Sierpinski carpet model,it has been studied that the function-al relationship of average tortuosity and porosity,and the functional relationship average tortuosity and mini-mum pore characteristic length and the fractal dimension by solving the distribution function of tortuosity of the control body.The results showed the tortuosity and porosity calculation obey the rule ofΓn =32 -12 φ;the minimum pore characteristic length,the fractal dimension and Euclidean space dimension determine the com-plexity of the internal space of object;the tortuosity of porous media flow lines decreases with the increasing of the internal porosity and increases with the decreasing of the smallest pores characteristic length and pore frac-tal dimension.%基于精确自相似 Sierpinski carpet分形模型，通过求解控制体的迂曲度分布函数，研究了平均迂曲度与孔隙率、最小孔隙特征长度和分形维数的函数关系。结果表明：迂曲度与孔隙率服从Γn＝312－2φ的计算规律；最小孔隙特征长度、分形维数、欧几里得空间维数共同决定了物体内部空间的复杂程度；多孔介质内部流线迂曲度随孔隙率增大而减小，随最小孔隙特征长度、分形维数的减小而增大。