Effect of scale on the modeling of radiation heat transfer in packed pebble beds

Thermal radiation is important in high temperature packed pebble bed, which is still poorly understood. The present work is to analyze the effect of spatial scale in modeling thermal radiation of packed pebble beds. The long-range model (full integral scale), short-range model (partial integral scale) and microscopic models (sub-particle scale) are compared and analyzed with reference to existing correlations. In high temperature packed pebble beds, the long-range model takes into account all possible radiation between surrounding spheres, even those that are not direct Voronoi neighbors, whereas the short-range model considers only a portion nearby. It is found that when solid conductivity is much greater than the effective thermal conductivity of radiation (ks ≫ kr or Λ > 10), the long-range model provides better results than the short-range model in predicting the radiative heat exchange. The short-range model overestimates solid conductivity at low temperatures (lower than 1215 °C) when ks ~ O(kr) (or Λ < 10) while underestimating radiative heat exchange. It therefore still provides predictions for total heat exchange that is in good agreement with experimental data in cases where the errors cancel out. Moreover, the short-range radiation model is more computationally efficient than the long-range model and microscopic model to compute view factor between particles of Voronoi neighbors.