Analysis and evaluations of four models of thermal radiation for densely packed granular systems

Thermal radiation is an important part of heat transfer in granular systems, such as the packed pebble bed of high-temperature gas-cooled reactor (HTGR), bubbling fluidized bed, and other packed granular beds. In this paper, four models of multiple-body radiation within the packed granular bed were proposed and discussed in full integral scales, i.e. black radiation model, uniform radiation model, local radiation model and particle scale radiation model. For particle radiation with black surfaces, the black radiation model was proven to be valid strictly and it agreed with existing correlations and models. The radiative flux in the packed bed increased significantly with the particle emissivity. However, the existed Asakuma radiation model, two-flux model and the newly proposed local radiation model were almost independent of the particle emissivity since the uniform assumption was inappropriate for the gray radiation in the packed bed. The effect of emissivity was handled correctly in the local radiation model without the uniform assumption. Since the computation cost of local radiation model in large-scale granular systems was huge and not applicable in the CFD-DEM simulation, the particle scale radiation model was developed in this study to predict the radiation flux in discrete element method (DEM). It was shown that the effect of particle emissivity was a separable term in the radiative heat transfer equation. The particle scale radiation model provided a good approximation of the local radiation model and enabled efficient prediction of radiative heat transfer in a densely packed bed.