One-group analytical solution to two-region reactor kinetic model

Abstract

The accurate modeling of nuclear reactor physics is an evolving topic of research that advances as improved methods and models are developed. Contemporary efforts to model nuclear reactors involve computer codes that utilize Monte Carlo and deterministic methods; however, analytical solutions may be just as valid depending on the application. In fact, a set of differential equations, known as the point reactor kinetics equations (PRKEs), can be analytically solved to predict reactor power based on kinetics parameters and applied to instances of rapid reactivity transients by assuming a one effective delayed neutron group point reactor kinetics solution, traditionally termed the prompt jump (PJ) approximation. Recently, analyses performed with a two-region model of the PRKEs investigated the influence of a reactor’s reflector as compared to the one-region PRKEs. Reflectors provide improved neutron economy by decreasing neutron leakage, and are especially important in reactors with small core geometries, such as research reactors. However, the response to a rapid transient in the two-region PRKE model has yet to be investigated despite its potential application, since research reactors often perform rapid transients as part of normal operations and the inclusion of the reflector may significantly alter the modeled response during a rapid reactivity transient.The derivation of a new, one-group solution to the two-region PRKEs is presented and compared with the traditional PJ approximation along with an analytic uncertainty analysis and a discussion on the strengths and weaknesses of each respective model.