Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
A COMPARISON BETWEEN POROUS AND FREE-FLOW MEDIA USING THE FINITE ELEMENT METHOD TO SOLVE THE GENERALIZED DARCY/FORCHHEIMER EQUATION
Submission Author:
João Paulo Innocente de Souza , RJ
Co-Authors:
João Paulo Innocente de Souza, Gustavo Rabello dos Anjos
Presenter: João Paulo Innocente de Souza
doi://10.26678/ABCM.COBEM2023.COB2023-1061
Abstract
The current study aims at simulating flows in both free-flow and porous regions. The discretization of mass and momentum equations, using the Finite Element Method (FEM), are presented. Also, the semi-lagrangian technique, where unconditional stability is successfully achieved for the numerical solution in different geometries, is developed. For porous and conjugated flows, the Darcy-Forchheimer term is included in the classical Navier-Stokes equation, so that the resistance imposed by the porous medium is considered in the pressure gradient. A second-order spatial convergence is assured for velocity and temperature fields, since a quadratic + linear pair of triangle mesh elements is used, fulfilling the well-known LBB condition. The MINI element is used to verify the results with the literature as well. Energy balance is also made in this work, so that the temperature field can be determined along the domain, evidentiating the differences between free-flow and porous domains with respect to not only pressure and velocity field distribution but also how the medium interferes with heat transfer phenomena. A benchmark validation for the finite element method applied to fluid mechanics is provided and the well-known case of Poiseuille flow is simulated using both media in order to compare the pressure along the channel for the two cases. As expected, a porous medium imposes a higher pressure gradient on the flow, but with lower values for the velocity field. The mass flow for both cases is the same, but a flatter curve is observed in the porous domain due to the effects imposed by the resistance of the medium. Graphical results are shown to illustrate and compare all the cases simulated in this work.
Keywords
FEA, CFD, porous medium, Semi-Lagrangian, Unstructured Mesh, Python
