Fourier expansion as an aid in the solution of the diffusion equation for three-dimensional power distributions in water reactors

Abstract

The problem of predicting axial power peaking factors in water moderated reactors is not adequately solved by so called coarse mesh methods for the solution of the neutron diffusion equation. The Fourier Expansion method, briefly described, gives an essentially continuous representation of axial power shapes and therefor a higher precision in the peaking factors.—It does this with a precision equivalent to fine mesh 3D methods. Yet, it is shown to require a factor 5–10 less numerical work than fine mesh. Applications to 3D core power calculations for different types of water reactor (the HWR, BWR and PWR) are illustrated by a range of measured and calculated axial power distributions. These applications have been collected from 10 years of experience with the method. The comparisons show that the Fourier Expansion method is well suited to LWR applications.