Comparison and Extension of Dancoff Factors for Pebble-Bed Reactors

A method is developed for the computation of infinite-medium Dancoff factors for spherical kernels with a stochastic packing as used in high-temperature reactors. The method is used to compute Dancoff factors that are then compared to those obtained by four preexisting methods from the literature. The older methods assume either infinitesimally small kernels with a random distribution, or finite kernels with some assumptions. In the new method, the infinite-medium Dancoff factor is calculated rigorously by numerically integrating the Dancoff factor of two adjacent finite-size kernels over their surfaces and relative positions. It turns out that for practical pebble-bed fuel designs, as currently envisioned, all four methods give results accurate (i.e., compatible with one another) within 2%, but that larger deviations are observed for extreme cases (either at high or low dilution).

A Monte Carlo program, named INTRAPEB, was 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 the pebble. For the Dancoff factor, the analytical results from literature agree very well with the new computational approach. 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 the derivation of the analytical methods. If the previously developed analytical methods need improvement, this could be achieved by using a more forwardly peaked neutron distribution.

A second program, named PEBDAN, was written to calculate the average value and the space dependency of the interpebble 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 using a Monte Carlo ray-tracing method. The packing distribution obtained in this code reproduces the principal features of experimental data; however, the predicted radial porosity profile of the packed bed displays less-pronounced oscillations (i.e., lower peaks) and a slightly larger average porosity value. Because of the larger first-flight escape probability of neutrons, the Dancoff factors drop several tens of percent along the inner and outer reflector of the core.