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 fu el 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 peb bles, without colliding with a moderator nucleus in between. If the fuel zo ne of the pebble is thought to be of infinite dimensions, the Dancoff facto r becomes equal to the so-called infinite-medium Dancoff factor C-infinity( fk). The C-infinity(fk) has been determined by the evaluation of three exis ting analytical expressions and by two Monte Carlo calculations performed w ith the MCNP-4A code, for various coated-particle densities. The Dancoff fa ctor C-fk can be written as C-infinity(fk) times a correction factor. The l atter has been calculated for different fuel zone radii and pebble shell th icknesses. For the standard pebble, C-fk as a function of the number of coa ted particles has been calculated both analytically and with MCNP. The resu lts of both methods are in good agreement. The analytical calculation metho d is preferred because it consumes practically no CPU rime and obviates the building of MCNP models.