Ph.D. Thesis Defense by Jeffrey A. Favorite
Monday, March 2, 1998

(Dr. Weston M. Stacey, Advisor)

"Variational Methods Applied to Nuclear Reactor Space-Time Neutronics"


Variational methods have been applied to make a number of improvements to the standard methods of computational nuclear reactor space-time neutronics. Most of the expense of kinetics calculations is associated with the calculation of spatial neutron flux distributions during the transient in order to accurately evaluate the integral parameters - primarily the reactivity - that determine the time-dependence of the reactor power level. Variational methods provide a means for accurately estimating these integral parameters without the necessity of frequent and expensive recomputation of the spatial neutron distribution. Previously existing variational functionals have been extended and two new functionals have been developed and applied to develop more accurate estimates for the reactivity. A previous variational estimate of the static reactivity worth of a perturbation has been improved to eliminate a numerical problem associated with large, negative reactivities. This development extends the range of perturbations whose reactivity worth can be estimated accurately using the initial static neutron flux distribution. A new variational estimate of the dynamic reactivity has been developed that for the first time accounts for the effect of delayed neutrons in holding back flux shifts following changes in the reactor configuration, which is very important in large light water reactors. This development allows even more accurate estimates of reactivity changes during a transient, again without the necessity of spatial neutron flux distribution calculations. The variational static and dynamic reactivity estimates have been adapted for use with the widely used quasistatic method (the IQS method) for space-time neutronics. This development results in a substantial improvement in the computational efficiency of the quasistatic method because fewer flux shape calculations were required when the variational reactivity estimates were used. A variational formulation of the quasistatic method based on the integro-differential form of the kinetics equations that more accurately accounts for the delayed neutron holdback effect has also been developed. Finally, a self-consistent spatial approximation method for computing neutron flux distributions has been developed by applying an existing variational functional. The new spatial approximation method provides a self-consistent procedure for the widely used "nodal" methods, which use detailed local spatial flux shapes to construct average integral parameters to represent large regions (nodes) with detailed spatial fine-structure, solve the nodal balance equations for the average flux distribution over the reactor, then combine the global average and detailed local flux distributions to obtain a detailed flux distribution over the reactor. The advantage of the new method is that it is self-consistent in its definition of the homogenized nodal parameters, the construction of the global nodal equations, and the reconstruction of the detailed flux distribution.