Resonance Self-Shielding Methods for Fast Reactor Calculations—Comparison of a New Tone’s Method with the Subgroup Method in APOLLO3^Ⓡ

Abstract

This paper presents two resonance self-shielding methods recently implemented in APOLLO3^Ⓡ for fast reactor calculations: a recently developed method, based on Tone’s method, and the subgroup method. Both methods utilize the so-called mathematical probability tables. Numerical results for a pin cell and for a sodium-cooled fast reactor assembly show that Tone’s method produces precision similar to that of the subgroup method while reducing greatly the CPU time. The results also show that utilization of the approximated multicell model in the calculation of collision probabilities noticeably decreases the CPU time as compared to the direct-integration approach, while keeping equivalent accuracy. Finally, our tests show the improvement in the fast neutron spectrum gained by using an incident-energy-dependent fission spectrum instead of the traditional average fission spectrum.

Keywords:

• Resonance self-shielding
• Tone’s method
• subgroup method

Acknowledgments

The authors are particularly grateful to Y.-K. Lee for his help running the SFR TRIPOLI-4^Ⓡ calculations and to Z. Stankovski for his help using the SILENE software for geometry data generation for both APOLLO3^Ⓡ and TRIPOLI-4^Ⓡ. We also thank the reviewers whose comments helped to improve the final paper.

APOLLO3^Ⓡ is a registered trademark of CEA. We gratefully acknowledge AREVA and EDF for their long-term partnership and their support.

TRIPOLI-4^Ⓡ is a registered trademark of CEA. We gratefully acknowledge EDF for its long-term partnership and AREVA for its support.

Notes

^a All cells in the same zone are assumed to have the same averaged flux. Let i denote a region in a cell and I the set of all homologous regions in the zone. The approximated zone CP equations are written as , where and .²³

^b We are currently working different solutions to avoid this limitation of the MCA technique but at present they are not yet available.

^c A first step might consist of including the dependence of the equivalent cross section on the resonant cross section.