Dottorato in INGEGNERIA AMBIENTALE E IDRAULICA

Titolo della tesi: Lattice Boltzmann modeling of fluid flow and temperature in porous media

The Lattice Boltzmann Equation (LBE) is a minimal form of the Boltzmann kinetic equation. With respect to the more conventional numerical methods commonly used for the study of fluid flow situations, the LBM introduces several advantages, including easy implementation of interfacial dynamics and complex boundaries in porous media; In addition, the convection operator is linear, no Poisson equation for the pressure must be resolved and the translation of the microscopic distribution function into the macroscopic quantities consists of simple arithmetic calculations. In this work, fluid flow through porous media has been modeled by means of the second-order lattice Boltzmann method (LBM). The doubled distribution functions were used for modeling fluid flow and temperature fields. The validation part for evaluating the accuracy of the code was done by estimating Poiseuille flow with two numerical methods including driving the flow with a constant force (i.e. a forcing term), representing the constant pressure gradient, and applying periodic boundary conditions at inlet and outlet of the channel and using inlet boundary condition to drive fluid flow in the channel. Moreover, the temperature field in the channel, Tortuosity and Permeability parameters through the obstacles with the benchmark studies compared. The results have been found in excellent agreement as compared with benchmark solutions. Two numerical approach for modeling porous media were used namely pore-structure (PS) and Representative Elementary Volume (REV) for a wide range of variables. The PS and REV methods have been used to simulate a porous channel with different porosity degrees. This is obtained by means of different arrangements of obstacles located in the channel in case of the PS method and by means of a porosity factor and permeability value in case of the REV method. The permeability factor has been calculated at a first approximation by usual Darcy law. Results are reported in terms of streamlines through the squared obstacles, velocity profiles and pressure drop for different porosity degrees, and a comparison is performed between the methods. The effect of different arrangements of obstacles is evaluated for the same porosity degree and it is highlighted that the various configurations can change the pressure drop (tortuosity effect). The REV method cannot simulate the details of the fluid flow through the porous medium structures compared to the PS method, which is able to better understand the flow field details around the obstacles. Since the porosity factor and configuration of obstacles are two important parameters that affect tortuosity, they were discussed thoroughly. The velocity-based method has been used to compute tortuosity in this pore-structure study. Various effective parameters, including several configurations of obstacles, different Reynolds numbers and the impact of obstacles angle in a wide range on tortuosity were investigated. Tortuosity values were computed after modeling the velocity field under the effect of mentioned effective parameters. Tortuosity- porosity relation in the two random configurations was similar to each other, tortuosity value for In-line arrangement was the lower amount because of open passages throughout. Changing Reynolds number did not has an important effect on Tortuosity. Moreover, the pore-structure modeling was carried out with considering effective parameters on permeability, pressure drop and temperature difference through porous media parts. Results reveal that tortuosity is an essential parameter for staggered and random arrangements compared to in-line ones. It was demonstrated diverting fluid flow from a direct way results in a high tortuosity value. Complex configurations had a higher tortuosity, resulting in efficient heat transfer but a more significant pressure drop. It is declared that the optimum results for maximum efficiency can be achieved based on changing the effective parameters, including porosity, tortuosity, fluid velocity, and configuration of the cold obstacles. Finally, The study shows that the double population model provides reliable results over a wide range of physical parameters and in different situations. We found that a possible forward step in this field of study can be varying the configuration of obstacles with the same porosity factor. In addition, with the same obstacle shape and porosity factor, if we change the angle of the obstacles, we can achieve higher tortuosity values. Keywords: Lattice Boltzmann method; Fluid flow; Temperature; Porous media; Pore-scale model; Representative Elementary Volume model; Porosity; Tortuosity; Permeability