Analytical Calculation of the Average Dancoff Factor for a Fuel Kernel in a Pebble Bed High-Temperature Reactor

An analytical expression was derived for the average Dancoff factor of a fuel kernel (C^fk) in a pebble of a high-temperature gas-cooled reactor. This Dancoff factor accounts for the probability that a neutron escaping from a fuel kernel enters another fuel kernel, in the same pebble or in other pebbles, without colliding with a moderator nucleus in between. If the fuel zone of the pebble is thought to be of infinite dimensions, the Dancoff factor becomes equal to the so-called infinite-medium Dancoff factor C^fk. The C^fk has been determined by the evaluation of three existing analytical expressions and by two Monte Carlo calculations performed with the MCNP-4A code, for various coated-particle densities. The Dancoff factor C^fk can be written as C^fk times a correction factor. The latter has been calculated for different fuel zone radii and pebble shell thicknesses. For the standard pebble, C^fk as a function of the number of coated particles has been calculated both analytically and with MCNP. The results of both methods are in good agreement. The analytical calculation method is preferred because it consumes practically no CPU time and obviates the building of MCNP models.