Neutron diffusion and multiplication in reactor lattices

The systematic variation of neutron flux distribution and buckling measurements as a function of fuel loading in a sub-critical assembly (natural uranium, graphite moderated) have been investigated in a symmetrical square configuration at the centre. Some control rod effectiveness studies have been carried out on the same pattern. The results have been correlated on the basis of Diffusion Theory. For full assembly cases lattice parameters were calculated, and compared with Syrett's model for graphite moderated reactors and are in good agreement. The correlation of partially filled assembly cases (clean core and vacancy) was based on the concept of reflector savings calculated by both One- and Two-group theory formulation in an infinite plane slab system and on Two-group heterogeneous theory (source-sink) for finite systems. The results confirm that the homogenised concept of reactor lattices (Wigner-Sietz) holds well down to 36 fuel elements. For fewer numbers of fuel elements, serious deviations become apparent compared with heterogeneous theory which predicts results correctly down to 16 - 9 fuel elements. Curves of K-co and B- vs. number of fuel elements and reflector savings vs. reflector thickness have been drawn and show the physical breakdown of the first theory. The flux distributions by heterogeneous theory are also much better than the, homogenised theory for small numbers of fuel elements. All these results (clean core) were also analysed by numerical methods and compared. The analysis of the control rod (mild steel, transparent to fast neutrons) effects has been based on (a) super-cell calculations and (b) the heterogeneoAs theory. The experimental predictions have wide variations in comparison to the super-cell calculations and are in good agreement with heterogeneous theory if diffusion area of the fueled lattice is used to calculate the controlled reactivity.