Equivalent group condensation for neutron transport computation in R-Z geometry

Abstract

Recently, equivalent group condensation method which equivalently solves few-group transport equations using angle dependent total cross section had been developed and successfully applied to one-dimensional slab geometry. However, this method has not been verified for multi-dimensional and curvilinear geometries.

In this study, we apply the equivalent group condensation to $r-z$ geometry problems, which is of interest in fast reactor lattice calculations. In a fast reactor lattice calculation, whole-core transport calculations are performed in a simplified $r-z$ geometry to obtain zone dependent flux to be used as weighting spectra for few-group cross sections generation.

We developed an in-house $S_N$ transport code for $r-z$ geometry to investigate the performance of the equivalent group condensation method in multi-dimensional geometry. We also verified the code using the TWODANT code in three benchmark problems with 150 energy groups as fine-group structure.Then we performed group condensation using consistent $P$ approximation, extended transport approximation, and equivalent group condensation method and compared the results.

The results showed that multiplication factor for few-group transport equations condensed using equivalent group condensation was excellent with discrepancy less than 1 pcm compared to fine-group multiplication factor calculated by TWODANT for all problems presented in this study. The other methods produce larger discrepancy and even have convergence problem for particular problems. Therefore, it will be beneficial to implement the equivalent group condensation method in fast reactor lattice calculations for few-group cross sections generation.