Numerical Modeling of Transport in Metal Foam Using an Idealized Geometrical Cell

Abstract

Open-cell metal foam is a class of modern porous media that possesses high thermal conductivity, large accessible surface area per unit volume and high porosities (often greater than 90%). The high porosity means very low weight. The microstructure of the foam is web-like. Internal flow inside the foam is complex and includes flow reversal, destruction of boundary layers and vigorous mixing. All of these attributes make metal foam a very attractive heat transfer core for many applications, e.g. heat exchange and reactors. The rather complex and intrinsically random architecture of the foam is virtually impossible to capture exactly. In this dissertation, a unit cell geometrical model was developed that can be used to understand fluid flow behavior and heat transfer through open-cell metal foam. In particular, two numerical models were constructed to simulate, first, the fluid flow and pressure drop inside aluminum foam; second, forced convection heat transfer between the aluminum foam and air. The Navier-Stokes and the governing energy equation were directly solved and the velocity and temperature fields were obtained using COMSOL. The details of the modeling process are given in this dissertation. The pressure drop results were compared to experimental data, from which the permeability, form drag coefficient and hydrodynamic entry length could be calculated. The commercial foam that was used in the experiment had 10 pores per inch, with a porosity of 91.2%. Air was forced to flow inside the foam using an open loop wind tunnel. Good agreement between the modeling and experimental results were obtained, within the velocity range of the study. To validate the heat transfer model, numerical air temperatures were compared to the volume-averaged analytical predictions, and to physical experimental data. The volume-averaged analytical formulation employed the Darcy-extended Brinkman model for momentum, and the non-thermal-equilibrium two-energy-equation model for the temperatures of the solid and the fluid phases inside a channel filled with foam, and heated at its top and bottom bounding surfaces by a uniform heat flux. The physical experiment was conducted on 20-pores-per-inch commercial aluminum foam, with a porosity of 90 %. Local air temperatures were measured inside a commercial aluminum foam cylinder heated at its outer wall by a constant heat flux, and cooled by forced air flow. A comparison showed good agreement between the numerical, experimental and the analytical air temperatures, within the thermally fully-developed region. The results are encouraging and lend confidence to the modeling approach, which paves the way for investigating other phenomena inside the foam.