Solution of the multigroup analytic nodal diffusion equations in 3-dimensional cylindrical geometry

Abstract

Nodal diffusion methods have been used extensively in nuclear reactor calculations specifically for their performance advantage, but also their superior accuracy. In this work a nodal diffusion method is developed for three-dimensional cylindrical geometry. Recent developments in the Pebble Bed Modular Reactor (PBMR) project have sparked renewed interest in the application of different modelling methods to its design, and naturally included in this effort is a nodal method for cylindrical geometry. More specifically, the Analytic Nodale Method (ANM) has been applied to numerous reactor problems with much success. The multi-group ANM is applied to Cartesian geometry in the Necsa developed OSCAR-3 code system used for the calculation of MTR and PWR type nuclear reactors. However, in support of the PBMR project, a need has arisen to include the ANM in cylindrical geometry. The ANM is based on a transverse integration principle, resulting in a set, of one-dimensional equations containing inhomogeneous sources. The issue of applying this method to 3D cylindrical geometry has never been satisfactorily addressed, due to difficulties in performing the transverse integration, and a proposed solution entails the use of conformal mapping in order to circumvent these difficulties. This approach should yield a set of 1D equations with an extra, geometrically dependent., "ghost" source. This thesis describes the mathematical development of the conformal mapping approach, as well as the numerical analysis via a developed FORTRAN test code. The code is applied to a series of test problems, ranging from idealized constructions to realistic PBMR 400 MW designs. Results show that the method is viable and yields much improved accuracy and performance, similar to what may be expected from nodal methods.