Temperature dependent subgroup formulation with number density adjustment for direct whole core power reactor calculation

The method and performance of the temperature dependent subgroup formulation based on the concept of number density adjustment are presented for the application to the direct whole core calculation of power reactors that involves substantial thermal feedback. The number density of each resonant nuclide is adjusted such that the resulting macroscopic cross section can carry proper temperature dependence even though the microscopic cross section is evaluated at the uniform average temperature. Specifically, the non-uniform temperature distribution is replaced by the corresponding temperature dependent number density distribution and by the uniform temperature for the microscopic cross section of the resonant nuclide. The number density adjustment is introduced not only in the subgroup fixed source problem, but also in the Bondarenko iteration to obtain the effective cross sections for the mixture. The subgroup level dependency of the number density adjustment factor is also introduced. In order to examine the effect of non-uniform temperature profiles on power reactor calculations, the OPR1000 fuel pin problems consisting of several cases having different power levels are constructed. The performance of the proposed method was verified by analyzing the OPR1000 fuel pin problems and by comparing with the corresponding Monte Carlo solutions in the aspect of group-wise cross sections as well as the reactivity. It is demonstrated that the proposed temperature dependent subgroup formulation can predict quite accurately the effects of non-uniform temperature distribution on the fuel temperature coefficients and the shielded cross sections.