The use of flux ratios to homogenize squared absorber cells

A difficult problem of homogenizing over a cell region not bounded by a zero surface perpendicular current, or in other words, reflective conditions, is considered in this paper. One of the methods is to form flux ratios, for the homogenized region, between the fluxes obtained for the detailed, non-homogenized, layout of the region and the corresponding fluxes for the homogenized version of the region. In this note we demonstrate the utility of homogenization flux ratios. The inaccuracy related to a simple-minded homogenization is demonstrated on a simple 1-D example. The simple analysis shows an over-prediction of 0.6% in the potency of the square absorber cell. More realistic 2-D calculations demonstrated the validity of this result. The method of Flux Ratios, when properly applied, will assure an accurate estimation of the reactivity of an absorber cell in a lattice of fuel cells. Flux ratios must be derived for a model describing the cylindrical details of the absorber, over a model in which the absorber has been homogenized into a square. It was shown that failure to apply flux ratios in the manner described above, and in more detail throughout the article, may lead to over-predictions of the reactivity of absorber cells in a magnitude from 1 to 3%.