The gamma deposition matrix method for gamma heating calculations for LWRs

Abstract

This paper presents a new method called the gamma deposition matrix (GDM) method to calculate gamma energy deposition without performing a full-core explicit gamma transport calculation. This method computes gamma energy deposition by using the known gamma source and the GDM to perform a simple matrix-vector multiplication. The entries of the GDM represent the gamma energy deposited in a given spatial cell due to a gamma source in another (or the same) spatial cell. Since microscopic cross sections of gamma interactions are insensitive to temperature, and the macroscopic cross sections are insensitive to isotope depletion, the GDM can be pre-calculated and stored in advance and used in the coupled (n,γ) calculations with thermal-hydraulic feedback and core depletion. Three approximations are made to reduce the size and generation time of the GDM: 1) eliminating the dependence of the GDM on gamma energy, 2) neglecting the GDM for gamma deposition far from the gamma source and 3) approximating the GDM for gamma deposition out of a certain range but not too far from the gamma source. Since the second approximation may result in a loss of gamma energy, the third approximation includes a correction technique to conserve the overall gamma energy deposition.The method and all these approximations are proved to be accurate and effective for reducing the memory and runtime for realistic 2D whole-core cases. For a 2D small modular reactor whole core case with 37 assemblies and 289 pins within each assembly, the gamma heating calculation is accelerated by a factor of 3.4 while maintaining satisfactory accuracy.