The zonal approach applied to the simulation of the radiative heat transfer in a packed pebble bed

Abstract

The Fukushima Daiichi Nuclear Disaster highlighted the importance of nuclear safety and the importance of modeling a nuclear reactor under diverse conditions. Applied to pebble bed reactors, these diverse conditions include taking into account the macroscopic temperature gradient through the bed. At high temperatures the thermal radiation component of the effective thermal conductivity becomes the dominant heat transfer mode and the short-range and long-range radiation must be properly taken into account. The Multi-Sphere Unit Cell (MSUC) model was developed to address the shortcomings in the conduction and radiation components of the effective thermal conductivity model. Although the conduction component was properly addressed, the long-range component of the thermal radiation component still had some shortcomings. The Zonal Approach, which is a network-type approach, was suggested to replace the thermal radiation component of the MSUC model due to its simplicity, capability to model long-range radiation and its relatively fast solution time. The participating medium of the Zonal Approach was changed from a semi-transparent porous medium to a medium containing surfaces to accommodate the large spheres in-side a packed bed. The emission and absorption from volume zones effectively changed to surface-to-surface exchange. The volume-to-surface and volume-to-volume direct ex-change areas were re-derived to accommodate the changes in the volume zones. The attenuation factors for both the simple cubic and random packed beds were derived. The derived attenuation factor for the random bed included the wall region, near-wall region and bulk region. The zones were also subdivided to account for non-isothermal sphere surface temperatures. The thermal radiation results from the adapted Zonal Approach were compared to the results from a Computational Fluid Dynamics (CFD) package using surface-to-surface radiation only without solid models to eliminate the effect of heat transfer from solid conduction. The results were generally in good agreement with the CFD results, but it highlighted the importance of an accurate attenuation factor. The conduction component from the MSUC model was coupled to the Zonal Approach and the results were compared to the Near-wall Thermal Conductivity Test Facility (NWTCTF) experimental results for a simple cubic and a random packed bed. The predicted heat was in good agreement with the experimental results but the predicted thermal resistance was too low. The Zonal Approach generally predicted the thermal radiation well for both the simple cubic and random packed beds. The subdivision of the control volumes or zones eliminated the need for a conductivity correction parameter needed to correct non-isothermal sphere surfaces. With further improvement of certain components the accuracy of the results can be improved.