Development of a generalized thermal resistance model for the calculation of effective thermal conductivities in periodic open cellular structures (POCS)

Abstract

Periodic open cellular structures (POCS) are a group of porous media with promising attributes for the use in heat transfer enhancement. They consist of a periodic arrangement of unit cells that offer a vast design freedom and therefore high adaptability to the needs of a specific application. In order to use POCS efficiently, a fundamental understanding of the relation between their geometry and thermal transport properties is essential.This contribution focuses on the investigation and modeling of the effective thermal conductivity. It is based on a homogenization approach that averages the heat conduction properties over an entire unit cell, while neglecting the influence of the fluid. To this end, the investigation provides detailed insight and an important component for the subsequent model development on the overall heat transfer capabilities of POCS, including convection and conjugate heat transfer. A numerical simulation setup is developed, which allows the determination of this quantity in isotropic as well as anisotropic POCS with varying unit cell type, porosity, tapering and strut cross-sectional shape. The results indicate the impact of both struts as well as nodes, on the heat transfer and form the foundation for a new generalized thermal resistance network model. In contrast to similar approaches, the impact of multidimensional heat transfer within the nodes is considered enabling an accurate prediction of the effective thermal conductivity of all POCS investigated in this work. Due to its modularity, it is easily transferable to other unknown geometries, thus contributing to the toolbox for the efficient design of POCS.