The Gamma Deposition Matrix Method for Coupled Neutron-gamma Reactor Heating Calculations

Abstract

This thesis concerns the development of an approximate model to predict the energy deposited by gammas following a gamma-release reaction in a light water reactor. This approximate model is an alternative method to the conventional approach of solving the gamma transport equation. Although explicitly solving the gamma transport equation has become possible in recent years thanks to advancements in computing power, it is desirable to come up with a simpler method given the fact that gammas only account for ~10% of energy deposition in LWRs. The new method, called the gamma deposition matrix (GDM) method, calculates gamma energy deposition for coupled (n,γ) iterations without performing an explicit gamma transport calculation. 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. The GDM can be pre-calculated based on a gamma deposition Green's function, which allows gamma energy deposition to be directly computed from the known gamma source by using the GDM to perform a simple matrix-vector multiplication. A significant advantage of the GDM method is that since gammas mainly interact with electrons, gamma cross sections are independent of temperature and depletion. As a result, the GDM is insensitive to thermal feedback and isotopic changes due to depletion, allowing the initial GDM to be used for all (n,γ) iterations throughout a reactor cycle.

Through coupled (n,γ) calculations in MPACT, it is shown that the gamma source spectra do not change over coupled (n,γ) iterations in an LWR. This observation, combined with the fact that the gamma energy deposition is integrated over all gamma energies, leads to the conclusion that the GDM is not a function of gamma energy, resulting in a substantial reduction in the size of the GDM. However, in principle the spatial dependence of the GDM can be prohibitive because the GDM is non-zero for any combination of source and target cells, leading to a huge GDM for full core calculations. In order to further reduce the size of the GDM, the spatial range of the GDM is reduced by neglecting the energy deposition outside a given distance from the source cell. This active region is called a subdomain and the GDM entries are only non-zero for those cells in the subdomain surrounding the source cell. This subdomain model reduces the size of the GDM substantially, with a corresponding reduction in GDM computation time and memory. Since gammas that escape from the subdomain without interaction will result in a loss of energy, an energy preservation scheme is developed that ensures conservation of gamma energy. Numerical results calculated using the energy-independent GDM with the subdomain approximation agree well with reference Monte Carlo calculations. The subdomain approximation is proved to be especially beneficial for large cases. For a small modular reactor whole core case with 37 assemblies and 289 pins within each assembly, using the subdomain approximation along with the energy preservation correction reduces the size of the matrix by ~20 while maintaining satisfactory accuracy.