Aplicação do método de lattice Boltzmann na simulação de meios filtrantes : implementação de códigos para geração do domínio de cálculo e condição de contorno de escorregamento

Abstract

Many studies have been carried out to find the best operating point for filter media, and the mathematical modeling and simulation are becoming a important tool. In this work, a code was built to generate geometric models for filter media from data obtained by statistical analysis and microscopic images, to be used in simulations. Two different approaches (random and uniform distributions) were used to alocate the fiber inside the limits of the filter medium. The OpenLB library, which uses the mesoscopic approach lattice Boltzmann method based on kinetic of gases, was used to calculate the gas flow and estimate the pressure drop through the filter medium. A free slip boundary condition was implemented in OpenLB code, using the mesoscopic approach of specular reflection of the distribution functions. This boundary condition was then applied on the fibers surfaces, with the purpose of correctly represent the slip flow regime. The free slip boundary condition was verificated by simulating flows in confined duct and around obstacles, and the results were compared with data obtained by macroscopic simulations carried out on the commercial package ANSYS Fluent, which solves Navier-Stokes equations, and also with data found in literature. In filter media simulations, the free slip and no-slip boundary conditions were applied on the fibers surfaces and the numerical results of three types of filter media were then compared to experimental data. A better agreement between numerical and experimental data was observed if the free slip boundary condition was used. This confirms the need to consider the proper boundary condition in flows with high Knudsen number. Moreover, an analysis of the influence of the size of the computational domain on the pressure drop was also carried out, in order to determine the smaller size of the geometric model of the filter medium. According to the results, the pressure drop tends to become stable with the increasing of the domain, since the solid fraction is more accurate. This stabilization occurs with better agreement when the ramdon alocation of the fibers are used to distribute the fibers inside the filter medium.