Application of the Chord Method to Obtain Analytical Expressions for Dancoff Factors in Stochastic Media

In this paper the chord method is applied to the computation of Dancoff factors for doubly heterogeneous stochastic media, characteristic of prismatic and pebble bed designs of the Very High Temperature Gas-Cooled Reactor (VHTR), where TRISO fuel particles are randomly distributed in fuel compacts or fuel pebbles that are arranged in a full core configuration. Previous work has shown that a chord length probability distribution function (PDF) can be determined analytically or empirically and used to model VHTR lattices with excellent results. The key observation is that once the chord length PDF is known, Dancoff factors for doubly heterogeneous stochastic media can be expressed as closed-form expressions that can be evaluated analytically for infinite and finite media and semianalytically for a collection of finite media.

Based on the assumption that the chord length PDF in the moderator region between two fuel kernels in a VHTR compact or pebble is exponential, which was shown to be an excellent approximation in previous work, closed-form expressions for Dancoff factors are derived for a range of configurations from infinite stochastic media to finite stochastic media, including multiple finite stochastic media in a background medium (e.g., a pebble bed core). Numerical comparisons with Monte Carlo benchmark results demonstrate that the closed-form expressions for the Dancoff factors for VHTR configurations are accurate over a range of packing fractions characteristic of prismatic and pebble bed VHTRs.