Spatial effects in Dancoff factor calculations for pebble-bed HTRs

A Monte-Carlo program, named INTRAPEB, is written to calculate the average value and the space-dependency of the Dancoff factor of one single fuel pebble, as well as the angular distribution of neutrons escaping from the pebble. For the Dancoff factor, the analytical results from literature agree very well with ours. However, for a cubic packing of particles, as is usually modeled in MCNP calculations, a larger Dancoff factor is found for the pebble. The angular distribution of neutrons escaping from the moderator zone of a pebble is much more forwardly peaked than the cosine angular distribution assumed in analytical methods. A second program, named PEBDAN, is written to calculate the average value and the space dependency of the inter-pebble Dancoff factor (the probability that a neutron escaping from the fuel zone of a pebble crosses a fuel particle in another pebble) and the pebble-pebble Dancoff factor (the probability that a neutron escaping from the fuel zone of a pebble crosses the fuel zone of another pebble). In this program, the coordinates of the pebbles in a randomly packed bed are determined, after which the Dancoff factors are calculated by a Monte Carlo ray-tracing method. Compared with experiments, the radial porosity profile of the packed bed shows less pronounced peaks and a slightly larger average value. Due to the larger first-flight escape probability of neutrons, the Dancoff factors drop several tens of percents along the inner and outer reflector of the core. (authors)