Numerical Study Of Heat Conduction And Fluid Flow In Fractal Porous Media

Heat conduction and fluid flow are the two important processes of heat and mass transfer in porous media. Previous studies indicate that the transports in porous media are determined not only by the properties of solid and fluid but also by the structural characteristics of porous media such as the size, shape, location, interconnectivity of pores. Because the Euclidean geometry has a limitation in describing the structures of pores, traditional treatment of porous media has to employ the continuous medium assumption and the volumetric averaging method, which make it difficult to consider the influence of microstructures of pores on the heat conduction and fluid flow in porous media, and thus the application of those existing porous media theories has some fundamental limitations.Taking into account the structural complexity in the study of transport phenomena in porous media, fractal models are proposed to model the structures of porous media, and then numerical simulations are performed for the heat conduction and fluid flow in the fractal porous media by the finite volume method and the lattice Boltzmann method respectively, and some general laws are gained.Chapter 2 briefly introduces the structural characteristics of porous media firstly, and then we review the four kinds of structural models of porous media whose advantages and drawbacks are analyzed and summarized, and explain the reasons and necessity of introducing the fractal models. Then we introduce briefly the basic conceptions and theory of fractal geometry, and indicate that the natural porous media are fractal objects in a certain range of length scales. Finally, based on the fractal theory several types of fractal structures are generated to model the structures of porous media.In Chapter 3, heat conduction model in fractal porous media is founded and heat conduction in fractal porous media is simulated numerically by the finite volume method (FVM). The influences of the thermal conductivity of solid, the thermal conductivity of fluid, the porosity, and the structural characteristics of pores on the effective thermal conductivity of fractal porous media are analyzed in detail. The numerical results are analyzed by comparing with the available empirical formulas from open literatures, and provide numerical verification of those empirical formulas. The calculating results indicate that: (1) for the deterministic fractals the relation of effective thermal conductivity with the thermal conductivity of solid or fluid conforms to a power function, and the relation of effective thermal conductivity with porosity conforms to an exponential function. (2) For the random fractals, the porosity is the most important factor that determines the effective thermal conductivity of fractal porous media, but the size and spatial distribution of pores, especially the spatial distribution of the bigger pores, do have substantive influences. (3) The periodicity in structures is not equal to the periodicity in heat conduction for the random fractals, that is very useful and worthy while we generating the porous structure models or preparing experimental samples.In Chapter 4, fractal theory and lattice Boltzmann method are combined to study the fluid flow through porous media. The flow fields are simulated for different porosity and different pressure gradient. The results show that: (1) the flow field structures of flow in fractal porous media exhibit fractal characteristics. (2) The volume flow rate is proportional to the hydraulic gradient in the direction of flow, which indicates that the flows in fractal porous media obey Darcy's Law for the range of flow and pressure level studied in this work. When the hydraulic gradient is given, the volume flow rate goes higher when porosity increases, and the relation of volume flow rate with porosity conforms to an exponential function. (3) LBM is suitable for studying the fluid flow in fractal porous media. It is possible to reveal the phenomenon and rules of flow in complex porous structures more in depth by combining fractal theory with lattice Boltzmann method to study the fluid flow in porous media.Finally, a summary of the thesis work and recommendation for future work are given.