Response Effects Due to Polygonal Representation of Pores in Porous Media Thermal Models

Abstract

\n Physics models — such as thermal, structural, and fluid models — of engineering systems often incorporate a geometric aspect such that the model resembles the shape of the true system that it represents. However, the physical domain of the model is only a geometric representation of the true system, where geometric features are often simplified for convenience in model construction and to avoid added computational expense to running simulations. The process of simplifying or neglecting different aspects of the system geometry is sometimes referred to as “defeaturing.” Typically, modelers will choose to remove small features from the system model, such as fillets, holes, and fasteners. This simplification process can introduce inherent error into the computational model.Asimilar event can even take place when a computational mesh is generated, where smooth, curved features are represented by jagged, sharp geometries. The geometric representation and feature fidelity in a model can play a significant role in a corresponding simulation’s computational solution. In this paper, a porous material system — represented by a single porous unit cell — is considered. The system of interest is a two-dimensional square cell with a centered circular pore, ranging in porosity from 1% to 78%. However, the circular pore was represented geometrically by a series of regular polygons with number of sides ranging from 3 to 100. The system response quantity under investigation was the dimensionless effective thermal conductivity, k*, of the porous unit cell. The results show significant change in the resulting k* value depending on the number of polygon sides used to represent the circular pore. In order to mitigate the convolution of discretization error with this type of model form error, a series of five systematically refined meshes was used for each pore representation. Using the finite element method (FEM), the heat equation was solved numerically across the porous unit cell domain. Code verification was performed using the Method of Manufactured Solutions (MMS) to assess the order of accuracy of the implemented FEM. Likewise, solution verification was performed to estimate the numerical uncertainty due to discretization in the problem of interest. Specifically, a modern grid convergence index (GCI) approach was employed to estimate the numerical uncertainty on the systematically refined meshes. The results of the analyses presented in this paper illustrate the importance of understanding the effects of geometric representation in engineering models and can help to predict some model form error introduced by the model geometry.