Numerical Modelling of Thermal Dispersion and Viscous Effects in High-Conductivity Porous Materials
Date of Award
Master of Engineering Science
Dr. Anthony Straatman
Transport in porous media has many applications in the sciences and engineering, including filtration, packed bed reactors, groundwater flows, and more recently, enhanced heat transfer. In heat transfer applications, modem graphitic foams have shown great potential due to their high effective thermal conductivity and large internal surface area. Analysis of flow and heat transfer in porous media is typically conducted using volume-averaged equations for the macroscopic flow and thermal fields, rather than directly simulating the pore-level flow. The derivation of the volume-averaged momentum and energy equations, however, introduce new unknowns as it becomes necessary to decompose the velocity and temperature fields into the sum of their volume-average and a spatial deviation. The spatial deviation terms are recast in terms of closure functions, which map the volume-averaged fields onto the pore-level deviations. As a result, the deviation tenns may be recast in terms of the resolved, volume-averaged fields with coefficients defined by the closure functions. The goal of the present work is to examine the details of the pore-level flow in high- conductivity graphitic foams with a spherical void stmcture in order to produce a closed, volume-averaged model for flow and heat transfer in such materials. Due to the high- conductivity of the medium considered here, local thennal non-equilibrium between the fluid and solid phases is assumed to exist. The approach taken in this work is to solve for the flow and closure function fields in an idealized spherical-void-phase porous geometry using a 3-dimensional, unstructured, finite-volume CFD code. Integration of the closure function fields for the thermal closure problem provides results for the thermal dispersion conductivity, modified convecting velocity, and interfacial heat transfer. For the hydrody
namic closure problem, the integration of the closure functions yields the permeability of the medium, as well as an additional form drag term. Results are presented for a range of Reynolds numbers at two porosities. The thermal dispersion conductivity for the idealized graphitic foam considered herein is found to behave quite differently than aluminum foams. The modification to the convecting velocity, which is a result of the pore-level flow fields, was found to have a significant effect on the convection term in the volume-averaged momentum equations. This result is quite interesting considering that this term is nearly always neglected in volume-averaged models. Results are also presented for the interfacial Nusselt number. In terms of the hydrodynamic model, the permeability of the medium is found in addition to the additional form drag term. The form drag term, which accounts for non-Darcian effects, is found to vary non-linearly with Reynolds number, resulting in the need for a cubic velocity term in the volume-averaged momentum equations.
DeGroot, Christopher T., "Numerical Modelling of Thermal Dispersion and Viscous Effects in High-Conductivity Porous Materials" (2009). Digitized Theses. 3886.