Numerical Study Of Heat Transfer In Porous Media Based On Renormalization Group Transform

As a functional composite material,porous material has been widely used with its unique advantages in insulation.However,due to the complex structure of porous materials,it is difficult to describe the characteristics accurately using mathematical tools.So,breakthrough progress in theoretical prediction of transfer process in porous media has not been made in recent years.Based on the renormalization group transformation method,heat transfer process in fractal porous media was studied.A new iterative algorithm is proposed in this paper to try to improve the computational efficiency and accuracy of numerical simulation.On the basis of the conclusions obtained above,an approximation algorithm is further proposed to calculate the effective thermal conductivity of random porous media.The main research work and achievements of this paper can be summarized as follows:(1)A lot of porous media existed in nature have been proved to have fractal features.On the bases of the self-similarity characteristics of fractal porous media,2D Sierpinski carpets and 3D Menger sponge models which have strict self-similarity are constructed by using geometric iterative method to study the thermal performance of porous media.In order to make the study closer to reality and with higher availability,several different types of random fractal porous structures which have statistical self-similarity characteristics are also be produced by using the Quartet Structure Generation Set(QSGS)method correspondingly.(2)According to the self-similarity characteristic of fractal porous media,a new iterative algorithm is proposed based on renormalization group transform theory to improve the efficiency of traditional finite volume method.The results show the new algorithm can bring about great improvement in numerical calculating speed and efficiency.The accuracy can also be improved to some extent at the same time.(3)GEM equation,based on the thermoelectricity analogy theory,is commonly used in engineering practice to predict the effective thermal conductivity of porous media.There are only two variables,porosity and structure factor n,contained in this equation.On the basis of the self-similarity of fractal porous media and the renormalization group transformation method,an approximation algorithm is proposed to get the relatively accurate n.By comparing with the experimental results quoted from other researchers,the algorithm is proved to be effective in accurately predicting the thermal performance of the fractal porous materials,regular or random structures.(4)Over the application of thermal conductivity of real porous foam aluminum structure,the specific implementation principle and the calculation process of renormalization group transformation method are put forward.The results show that the iterative approximation algorithm of renormalization group transformation is universally applicable.In respect of the superiority of GEM equation in predicting the effective thermal conductivity of porous media,the influence factors of the approximation algorithm of renormalization group transformation in calculating the structural factors are discussed.The results show that the sampling scale and the sampling position of porous media structure have little effect on the structural factors,and the errors caused by these sampling factors are almost negligible in a certain range.