Pore-scale Study Of Flow And Heat Transfer In Porous Media Based On Lattice Boltzmann Method

Fluid flow and heat transfer in porous media are among the most fundamental phenomena in the field of fluid dynamics. Problems related are longstanding research topics due to its widely existing in nature and many applications in various engineering fields. According to a large number literature published previously, it is found that, owing to the complexity of the microstructure of porous media and other difficulties encountered in such studies, the physics mechanics behind these phenomena, for example, even the relation between the permeability and the microstructure parameters of porous media, one of the most basic problem, is not understood clearly. In one word, many challenges still exist to go further in these studies.As the studies in other fields, with the rapid development of the computer technology, there are also three main tools to study the phenomena in porous media. They are experimental method, analytical method and numerical simulation. Unlike the experimental method, the cost of numerical simulation is much less; At the same time, numerical simulation can do many things the analytical method cannot do, such as determining the parameters under certain structures of porous media and testing the models obtained from the analytical method. Thus, the method attracts more and more attention of many researchers from the very beginning of its birth. Up to now, the numerical simulations on the study of fluid flow and heat transfer in porous media can be classified into two classes: the pore scale and the REV (Representative Elementary Volume) scale simulation. Also owing to the complexity of the porous media, the traditional numerical methods (such as finite volume method, finite differential method and finite element method, etc) encounter difficulties such as complexity in dealing with irregular boundary conditions, hardness in programming and low performance in parallel computing. Fortunately, the lattice Boltzmann method, which appears in the recent decades, is likely to overcome all these difficulties and can be considered as one of the most promising methods in the studies, especially in the pore scale simulation. So the lattice Boltzmann method is chosen in this thesis to simulate some most basic problem of the fluid flow and heat transfer in porous media in pore scale, and expect to enrich our understanding on these problems by doing so.Our works are composed of two main parts:(1) The estimation of parameters in REV models.In this part, the relation of the permeability and the microstructure parameters is investigated in detail. First we studied the effect of the tortuosity on the permeability by simulate fluid flow in 2D porous media composed of various curve channels via lattice Boltzmann method. The numerical results shows that the square of the tortuosity is inversely proportional to the permeability approximately for the considered cases, which is predicted by the Carman-Kozeny formula. For better predication, the definition of tortuosity based on true flow path is preferred. As a further step in the investigation on the effect of tortuosity, the Kozeny constant in the porous media composed of packed particle models is studied. One point is that the tortuosity here is determined for various models of porous media by solving a diffusion equation in pore scale via lattice Boltzmann method. By doing so we can investigate the effect of tortuosity and shape factor on the Kozeny constant respectively. The numerical results show that two or three regimes can be divided for the relation of Kozeny constant and the porosity instead that the Kozeny constant is a constant for all cases considered. The Kozeny constant shows an exponential increase with the increase of porosity when the porosity is high. The lowest value is about 0.9 for most cases. In the exponential increase regime, the shape factor play a main role for the increase of Kozeny constant. when the value of porosity is lower than 0.90, another regime can be found. In the regime, the change of Kozeny constant is very small. Kozeny constant here can be considered as a constant. In this regime, the shape factor almost unchange, thus the tortuosity here plays a main role now. the particle shape, arrangement, size and difference of 2D and 3D can only change the value of the constant and the length of the regime. When the porosity decrease further, Kozeny constant may decrease or increase. It should be noted that the increase of Kozeny constant with the decrease of porosity can also be found in 3D cases. The fact corrects the view that the phenomenon only appears in 2D cases. If the phenomenon appears, the third regime is conformed. however, which factor will be the main one which affects the Kozeny constant in this regime is not clear now.(2) Test on the validation of the REV models.In this part, the Darcy-Forchheimer-Brinkman model for natural convection in porous media is tested by compare the average Nusselt numbers obtained on the hot wall from both the pore scale and REV scale simulations via lattice Boltzmann method. In this work, the permeability and effective thermal conductivity ratio are determined from pore scale simulation instead of the use of the empirical formula. The numerical results shows that the REV model can be considered as valid under the low Ra number and the homogeneous assumption for the porous media. By comparison of the results using the empirical formula and of the present studies, it is found that, the REV model has the best prediction for the effect of permeability and the worst prediction for that of the thermal conductivity ratio. In the end, the similar conclusion is deduced under different microstructures.We also conduct some other researches related except the above works. The first is about the natural convection in a square cavity containing a rectangular cylinder. The different regimes for flow and heat transfer patterns are obtained. two of them are reported for the first time. the second is about the flow pass two tandem square cylinders under the buoyancy effect. It is found that the critical spacing always exists when Ri < 0 under the considered cases.In summary, two main basic problems in the fluid flow and heat transfer are studied via lattice Boltzmann method. the results obtained enrich our understanding of the problems. In addition, we conduct many numerical experiments on the lattice Boltzmann in the study of fluid flow and heat transfer in porous media. The results show the validation of the method and the works can be considered as a necessary basis for future studies.