Fractal Description Of Porous Media And Its Fluid Flow And Heat Transfer Characteristics

Fluid flow and heat transfer in porous media are ubiquitous phenomenon in natural and relevant for practical application, especially have extensive application prospect in soil seepage, wall insulation, phase change heat storage, etc. However, due to the randomness of pore structure, fluid flow and heat transfer in porous media involve extremely complex process. Therefore, the study on the fluid flow and heat transfer in porous media not only have great engineering value but also possess scientific significance in the exploration of microscopic flow and heat transfer mechanism.Until now, the mechanism and inherent law of fluid flow and heat transfer in porous media are still not completely known. Especially, the underlying relationship between the complex pore structure and flow and heat transfer mechanism in porous media is less understood. Moreover, considering the randomness and statistical self-similarity of pore structure, there is a urgent need of developing a geometry model to describe the pore structure characteristics of porous media effectively. In this context, the geometry structure of porous media are regenerated and quantitatively described based on the Fractal Brownian Motion(FBM) model. The theoretical models of seepage, thermal conduction and solid-liquid phase change inside porous media are respectively developed and numerically analyzed. On this basis, the role of pore structure, solid matrix and fluid thermal properties and working condition parameters on the flow and heat transfer behaviors in porous media are also investigated. In addition, a visualization experiment of heat transfer in porous media with solid-liquid phase change are conducted to verify the current theoretical model. In a word, the results are summarized as follows:(1) The theoretical model of fluid flow through porous media is developed and numerically analyzed to investigate the roles of porosity and fractal dimension on liquid flow behaviors in porous media. The results indicate that the velocity distribution in porous media is non-uniform due to the complex pore structure. And the peak velocity magnitude appears in the narrow capillary channel. It is important to note that Darcy's law can't describe the transport properties inside porous media accurately, when Reynolds number Re> 1. In addition, the permeability increases monotonously with the porosity, and there is a rapid increase of permeability for the porosity ?> 0.6. And the fractal dimension also affects the permeability of porous media. The increase of fractal dimension strengthens the transport capacity effectively.(2) The theoretical model of thermal conduction in porous media is developed and numerically analyzed to investigate the roles of porosity, fractal dimension and the ratio of solid matrix and fluid thermal conductivity on heat transfer characteristics of porous media. The results indicate that the temperature and heat flux are unevenly distributed in porous media due to the diffuse distribution of solid matrix. In addition, the effective thermal conductivity decreases monotonously with the porosity, and the decrease trend is slow for the porosity ?>0.6. Moreover, fractal dimension has a negative correlation with the effective thermal conductivity of porous media. The increase of fractal dimension weakens the thermal conduction capacity to same extent.(3) The theoretical model of heat transfer in porous media with solid-liquid phase change is developed and numerically analyzed to investigate the roles of pore structure and working condition parameters on heat transfer characteristics of porous media with solid-liquid phase change. And the results are compared with the melting and solidification processes of pure phase change materials(PCM). The results indicate that the solid-liquid phase interface of pure PCM moves slowly and grows gradually from straight to curve. However, due to the limitation of pore structure, the solid-liquid phase interface of porous media exist an overall hazy phase interface and many independent local phase interfaces. Moreover, the solid matrix of porous media improve the heat transfer characteristics of PCM during the melting process effectively. The temperature of PCM in pores are higher than that of the same location in pure PCM, and the temperature distribution in porous media is more uniform than that of pure PCM. In addition, there is a positive correlation between effective heat transfer coefficient and initial temperature difference. The increase of initial temperature difference increases the temperature gradient through the porous media, and accelerates the progress of melting eventually. It is important to note that porosity has a negative correlation with effective heat transfer coefficient, but it also presents a positive correlation with the total storage heat. Therefore, there is a optimum porosity, make the porous media with PCM not only has better heat storage capacity but also owns a satisfactory heat transfer coefficient. Meanwhile, the fractal dimension also affects the heat transfer characteristics of porous media with solid-liquid phase change. The increase of fractal dimension impairs the effective heat transfer coefficient of melting process, and slows down the progress of arriving the final heat balance state.(4) The visualization experiment of heat transfer in porous media with solid-liquid phase change is developed to observe the evolution of solid-liquid phase and monitor the dynamic temperature characteristics in real time. And the underlying relationship between initial temperature difference and the effective heat transfer coefficient of melting and solidification processes are also established. The experiment research shows that the results of numerical simulation based on the theoretical model of heat transfer in porous structure with solid-liquid phase change is consistent with the experiment results. The solid-liquid phase interface of pure PCM moves slowly and grows gradually from straight to curve. However, due to the limitation of pore structure, the solid-liquid phase interface inside porous media evolves into many independent local phase interfaces, and the evolution rate is faster than that of pure PCM. Obviously, the solid matrix of porous media improve the heat transfer characteristics of PCM during the melting process effectively. The temperature of PCM in pores are higher than that of the same location in pure PCM, and the temperature difference in porous media is smaller than that of pure PCM. In addition, there is a positive correlation between effective heat transfer coefficient and initial temperature difference. The increase of initial temperature difference accelerates the progresses of melting and solidification.