A matrix model of particle-scale radiative heat transfer in structured and randomly packed pebble bed

Thermal radiation in pebble bed is very hard to compute accurately and efficiently since it occurs between the surfaces no matter how far they are. Herein, radiative heat flux and effective thermal conductivity were derived mathematically by a matrix model to present the thermal radiation between particles in pebble beds. For structured packing, the transient radiative heat transfer is proven to be similar to thermal diffusion. This study proposed a correlation to predict the radiation exchange factor under different porosity. Radiative effective thermal conductivity was found to grow slightly with void fractions. For random pebble beds, a regression model of the multi-layer neural network was trained by large datasets to compute the view factor matrix efficiently. With the trained model and GPU acceleration, it is feasible to perform real-time-simulation of full-range radiations inside large-scale pebble beds, even for real reactors (e.g. HTR-PM). A thermal radiation simulation of the decay heat removal of a real reactor adopted this model as a demonstrative application and showed that the highest temperature is still within the design limitation of the packed bed.