Fracal Theory And Its Applications To Porous Media, Rough Surface And Thermal Contact Conductance

Over the past two decades, fractal geometry theory, which describes the fractal features such as randomicity and scale-independence, etc, has been received much attention in a variety of sciences sand engineering subjects and has extensively been studied both theoretically and experimentally. In order to theoretically identify and recognize the fractal features of structures or patterns existing in nature, some models, methods and techniques have been developed.Firstly, the structural properties of porous media are investigated theoretically based on fractal geometry theory. Construction methods of two types of fractal structures (the Sierpinski carpet and the Menger sponge) are presented, and the expressions for the surface and volume of the structures are derived. Furthermore, two unified models for describing the fractal characters of porous media are derived. The results from the proposed unified models are found to be in good agreement with the available models. The present analysis allows for simulating real porous media with different microstructures and different fractal dimensions, porosity and specific surface area.Secondly, the permeability of porous media is simulated by Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the proposed Monte Carlo technique. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.Thirdly, a new Monte Carlo method is presented for simulating rough surfaces with fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability, thermal and electrical conductivity, etc.) on rough surfaces.Finally, a random number model based on fractal geometry theory is developed to calculate the thermal contact conductance (TCC) of two rough surfaces in contact. This study is carried out by geometrical and mechanical investigations. The present parametric study reveals that the fractal parameters D and G have the important effects on TCC. The TCC by the proposed model is compared with the existing experiment data, and good agreement is observed by fitting parameters D and G. It is also shown that the effect of the bulk resistance on TCC, which is often neglected in existing models, should not be neglected for the relatively larger G and D. The present results show a better agreement with the practical situation than other models'.