Construction of a model for calculating average tortuosity of porous media based on optimal fractal structure

Abstract

The distribution of pores and skeletons in porous media materials are irregular, and its distribution of curved pore channels is uneven and complex. The bending degree of pores affects the internal heat transfer process. The tortuosity is not only a parameter to describe the bending degree of pore channels, but also is one of the important structural basic parameters of porous media materials. According to the porosity of the porous media materials, Sierpinski carpet model is established to characterize its structures. The calculation model of the average tortuosity of the porous media materials is derived by using the average value of the route of the heat flow through Sierpinski carpet. In order to find the best fractal unit structure and the number of iterations in the average tortuosity calculation model, an optimization discriminant model is established. The results of the average tortuosity calculation model of this model and the other three scholars are compared, and their average relative errors are calculated to be all less than 1 %, indicating that the average tortuosity calculation model established in this study is effective and reliable. The average tortuosity prediction model is related to the fractal unit structure and stage of the carpet, and there is no empirical constant in this model. It can be used to calculate the average tortuosity of other porous media materials, providing a new idea for calculating the average tortuosity.