An economical method for the determination of group constants for reactor lattices

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Virginia Polytechnic Institute and State University

The development of an economical method for determining accurately group constants of hexagonal and rectangular cells is considered in this dissertation. The mathematical model constructed for this purpose has the capability to characterize the group constants for the entire range of the neutron spectrum. Furthermore, this model is also rigorous enough to predict the group constants with the required accuracy for a specific range of interest in the energy spectrum and for a variety of energy group configurations.

The model is implemented separately for the fast and thermal energy regions. These regions are subsequently coupled via the source term. The construction of the model for the fast energy range has been pursued by implementing the transport equation specialized in a two-region cell. The regions are coupled via the escape probability functions. The model for the thermal energy range has been attained by implementing the appropriate Nelkin and Honeck amplitude functions within the kernels of the transport equation. The Nelkin amplitude function is utilized for treating light water moderated systems, and the Honeck amplitude function relates to heavy water moderated systems.

The group constants calculated with the economical model have been benchmarked with those computed by the VIM Monte Carlo code. The values obtained for the group constants agree within 1-2% with those computed by VIM for the fast energy region. The agreements for the thermal energy region are within 2-3%. The CPU running time of the implemented model is about 3 1/2 minutes for a four group configuration. On the other hand a typical VIM run comprising 25,000 neutron histories and a four-group structure expends about 30 minuts of CPU time for light water moderated systems. Moreover, similar VIM runs utilizing heavy water as moderator require over one hour of CPU time. Therefore, the implemented model makes utilization of computer resources with a cost advantage of a factor of 10 or better as compared to VIM. This economical benefit of the implemented model enables it to be coupled directly with fuel depletion codes, whereby the group constants and the fuel isotopics are updated at relatively short time intervals. On the other hand, the coupling of VIM with burnup codes would result in prohibitively expensive CPU costs.