Modelling long–range radiation heat transfer in a pebble bed reactor

Abstract

Through the years different models have been proposed to calculate the total effective thermal conductivity in packed beds. The purpose amongst others of these models is to calculate the temperature distribution and heat flux in high temperature pebble bed reactors. Recently a new model has been developed at the North–West University in South Africa and is called the Multi–Sphere Unit Cell (MSUC) model. The unique contribution of this model is that it manages to also predict the effective thermal conductivity in the near wall region by taking into account the local variation in the porosity. Within the MSUC model the thermal radiation has been separated into two components. The first component is the thermal radiation exchange between spheres in contact with one another, which for the purpose of this study is called the short range radiation. The second, which is defined as the longrange radiation, is the thermal radiation between spheres further than one sphere diameter apart and therefore not in contact with each other. Currently a few shortcomings exist in the modelling of the long–range radiation heat transfer in the MSUC model. It was the purpose of this study to address these shortcomings. Recently, work has been done by Pitso (2011) where Computational Fluid Dynamics (CFD) was used to characterise the long–range radiation in a packed bed. From this work the Spherical Unit Nodalisation (SUN) model has been developed. This study introduces a method where the SUN model has been modified in order to model the long–range radiation heat transfer in an annular reactor packed with uniform spheres. The proposed solution has been named the Cylindrical Spherical Unit Nodalisation (CSUN, pronounced see–sun) model. For validation of the CSUN model, a computer program was written to simulate the bulk region of the High Temperature Test Unit (HTTU). The simulated results were compared with the measured temperatures and the associated heat flux of the HTTU experiments. The simulated results from the CSUN model correlated well with these experimental values. Other thermal radiation models were also used for comparison. When compared with the other radiation models, the CSUN model was shown to predict results with comparable accuracy. Further research is however required by comparing the new model to experimental values at high temperatures. Once the model has been validated at high temperatures, it can be expanded to near wall regions where the packing is different from that in the bulk region.