Development and verification of a resolved 3D inner particle heat transfer model for the Discrete Element Method (DEM)

Abstract

An implicit 3D heat transfer model is derived to represent resolved heat conduction within spherical and non-spherical particles in the presence of a surrounding fluid. The proposed method, based on a finite difference solution, is integrated into the Discrete Element Method (DEM) applicable to multi-particle systems accounting for the following heat transfer mechanisms: particle–particle, particle–wall, particle–fluid–particle heat conduction, particle–particle radiation and particle–fluid convection. For this purpose, boundary conditions of the second and third kind are formulated. Based on various verifications performed, the underlying sub-approaches of the heat transfer model are validated against resolved FVM simulations performed with the commercial CFD-package ANSYS Fluent. This firstly includes cases with constant heat flux and heat transfer coefficient prescribed for a single particle which allows a basic systematic verification of the implemented model. Secondly particle–particle radiation and particle–particle heat conduction are investigated. These cases are of greater complexity as the resolution of the used heat transfer model and the local heat transfer itself become important. In addition to the thorough model validation on the small scale, heat transfer within packed beds is addressed as large scale cases. To compare the implemented resolved inner particle heat transfer model with literature data, the effective thermal conductivity (ETC) is calculated for packings of thermally thin particles with various particle thermal conductivities. To underline the importance of a resolved 3D heat transfer model in the context of the DEM, material parameters are considered which are attributed to thermally thick particles, thereafter. Here the resolved heat transfer model is compared against the more commonly used unresolved model approach with one constant temperature value associated to a particle. Noticeable differences occur when evaluating heat fluxes within the packing, the time to reach the steady state and for ETC-values obtained. The performed investigations lay the foundation to include the derived resolved DEM inner particle heat transfer model as part of a coupled DEM–CFD framework.