| Summary: | 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. === Thesis (M.Sc. (Reactor Science))--North-West University, Potchefstroom Campus, 2007
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