Numerical Simulation of Flows in Conjugated Regions Using the Finite Element Method to Solve the Darcy-Forchheimer Momentum and Energy Equations
Congress: ENCIT
ABSTRACT:
Fluid dynamics with heat transfer problems have complex modeling equations to be solved analytically. Thus, numerical methods, such as the Finite Element Method (FEM), are broadly used in order to simulate such phenomena for any geometry. The current study aims at simulating flows in conjugated regions, where free-flow and porous regions are present. The mathematical modeling is made through mass and momentum equations discretized by the Finite Element Method (FEM) along with the semi-lagrangian technique, where unconditional stability is successfully achieved for the numerical solution in different geometries. The Darcy-Forcheimer term is included in the classical Navier-Stokes equa- tion, so that the resistance imposed by the porous medium is considered in the pressure gradient. The quadratic triangle mesh element fulfil the well-known LBB condition, assuring stability and 2nd order convergence, when compared to sim- pler kinds of elements. Additionally, a mesh convergence is made by comparing results with the literature for meshes with different sizes. As to the temperature, an analysis on how the porous medium interferes in the convective heat transfer is provided, showing that, in conjugated flows, heat transfer is significantly different from one region to the other, due to the effects of the porous medium on convection. A pure convective case is also shown, in order to demonstrate how temperature gradient, associated with a gravitational field can induce convective streamlines in a confined region. The code is written in Python in an optimized object-oriented programming, so that refined meshes are easily used to simulate these phenomena, providing more accurate results as the more elements are used. Also, an optimized method for the semi-lagrangian was implemented, reducing simulation time.