American Nuclear Society

Home / Publications / Journals / Nuclear Science and Engineering / Volume 180 / Number 1

A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel—II: Verifications

Sooyoung Choi, Chidong Kong, Deokjung Lee, Mark L. Williams

Nuclear Science and Engineering / Volume 180 / Number 1 / May 2015 / Pages 41-57

Technical Paper /

First Online Publication:March 9, 2015
Updated:April 27, 2015

A new methodology has been developed recently to treat resonance self-shielding in systems for which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. The theoretical development adopts equivalence theory in both micro- and macro-level heterogeneities to provide approximate analytical expressions for the shielded cross sections, which may be interpolated from a table of resonance integrals or Bondarenko factors using a modified background cross section as the interpolation parameter. This paper describes the first implementation of the theoretical equations in a reactor analysis code. To reduce discrepancies caused by use of the rational approximation for collision probabilities in the original derivation, a new formulation for a doubly heterogeneous Bell factor is developed in this paper to improve the accuracy of doubly heterogeneous expressions. The methodology is applied to a wide range of pin cell and assembly test problems with varying geometry parameters, material compositions, and temperatures, and the results are compared with continuous-energy Monte Carlo simulations to establish the accuracy and range of applicability of the new approach. It is shown that the new doubly heterogeneous self-shielding method including the Bell factor correction gives good agreement with reference Monte Carlo results.

Questions or comments about the site? Contact the ANS Webmaster.