Reactivity Effect of Non-Uniformly Distributed Fuel in Fuel Solution Systems

Abstract

A numerical method to determine the optimal fuel distribution for minimum critical mass, or maximum k-effective, is developed using the Maximum Principle in order to evaluate the maximum effect of non-uniformly distributed fuel on reactivity. This algorithm maximizes the Hamiltonian directly by an iterative method under a certain constraint—the maintenance of criticality or total fuel mass. It ultimately reaches the same optimal state of a flattened fuel importance distribution as another algorithm by Dam based on perturbation theory.

This method was applied to two kinds of spherical cores with water reflector in the simulating reprocessing facility. In the slightly-enriched uranyl nitrate solution core, the minimum critical mass decreased by less than 1% at the optimal moderation state. In the plutonium nitrate solution core, the k-effective increment amounted up to 4.3Δk within the range of present study.

KEYWORDS:

• optimization reactivity
• minimum critical mass
• maximum k-effective
• Maximum Principle
• non-uniformly distributed fuel
• fuel importance
• perturbation theory
• uranyl nitrates
• plutonium nitrates
• reprocessing