A methodology for material design applied to porous media with flow

Two methodologies to design the microstructure of porous materials are presented in this work. The methodologies are based on shape and topology optimization and allow to identify layouts of the microstructure of a periodic cells using criteria such as maximizing the effective properties, minimizing the energy losses, or maximizing the mixing of a dispersed solute. The porous materials studied are made of a mixture of a heterogeneous solid matrix with its void filled with fluids. There exist two relevant length scales in the model materials:, a microscale, which is associated with the pores, and a large scale associated with the overall part.;The governing equations for the microscale and the large scale are related through the effective properties. These effective properties are derived using the theory of homogenization. Expressions derived using homogenization for effective properties such as permeability, dispersivity are computed using finite element analysis and validated with experimental results. Shape and topology optimization are used to find the optimal shape and layout of the microstructure.;In shape optimization, an algorithm is developed to find an optimal shape of the pores in the microstructure for a given criterion for single and multiphase flow. Three different shapes for the solid region of the microstructure were analyzed: circular, elliptic and rectangular geometries. The macroscopic fluid flow and solute transport equations were solved based of the effective properties computed for the optimized microstructure. The velocity and solute fields were compared with those computed from a microstructure form by square array of identical porosity as of the optimized microstructure. The result showed that the optimized microstructure has a significant improvement in reducing energy loss during fluid flow and increasing mixing of the dispersed solute.;Topology optimization is then used to design porous media for two different objective functions: minimizing dissipation power and maximizing dispersive power. The governing equations were solved using finite element analysis and the sensitivity is computed using an adjoint problem based of the approach. The results were evaluated by comparing the macroscopic fluid flow for the optimal microstructure with the flow obtained for a microstructures formed by square array with same porosity as the optimized microstructure.