Characterization of heat transfer in consolidated, highly porous media using a hybrid-scale CFD approach

Abstract

A pore-scale CFD approach has been adopted to improve the phenomenological understanding of transport phenomena governing heat transfer in consolidated, highly porous media with single-phase fluid flow. The CFD model has already been developed and validated in a previous work [1]. In this contribution, the model has been used to characterize different types of irregular sponge (=open-cell foam) structures and regular porous structures with similar structural parameters, such as e.g. porosity. The results of the convective heat transfer coefficient have been obtained from a local analysis of the simulated temperature and heat flux fields. A dimensionless result analysis in terms of the Nusselt number (Nu) for all sponges investigated yielded one common and consistent functional dependency on the Reynolds number (Re). This Nu-Re-characteristic allows the identification of two main heat transfer regimes present for the laminar flow conditions considered in this work: stagnant fluid heat conduction (Nu ~ Re0 at Re → 0) and boundary-layer dominated heat convection (Nu ~ Re0.5). These findings are in accordance with the classical approaches known from the boundary layer theory and have been used to develop a new physically-based Nu-Re-correlation which is needed for targeted heat exchanger designs. Furthermore, the applicability of the so-called Generalized Lévêque Equation (GLE), i.e. the analogy of heat and momentum transfer processes, has been discussed and is supported by using the results from the CFD analysis. Finally, the CFD model and the physical insights gained for sponges have been used to quantify and analyze the heat transport behavior of consolidated, highly porous media with regular structure – like Kelvin or cubic unit cell structures – while maintaining structural parameters like porosity and specific surface area. Unifying characteristics have been detected and discussed as well as limits of the approach's applicability.