A Geometric Buckling Expression for Regular Polygons: I. Measurements in Low-Enriched UO₂-H₂O Lattices

Abstract

In the nuclear criticality safety design of a nuclear fuel cycle facility, the geometric buckling of the fuel core is one of the most important quantities used in estimating criticality. When the material buckling value is known for a system consisting of fissile materials, it is possible to judge whether or not the system is subcritical by comparing the material buckling with the geometric buckling. It is widely known that the geometric buckling of a given core can be calculated by using a simple formula for some geometries, e.g., square, cylinder, slab, and sphere.

The experimental results of the geometrical buckling for typical regular polygons are described. Geometric buckling for three types of regular polygons has been measured in light-water-moderated UO₂-H₂O lattices in the tank-type critical assembly at the Japan Atomic Energy Research Institute. Based on the known critical buckling of a given experimental lattice and the measured critical water levels, the horizontal buckling has been evaluated for various sizes of regular hexagonal, square, and regular triangular cores. This method is based on the separability of geometric buckling into horizontal and vertical components. From the measured critical water levels of each core, it was found that the horizontal buckling of the effective core region is inversely proportional to the square of the radius of the circumscribed circle of the core. The geometric buckling B²_g can therefore be expressed in the form of (a_N/R_c)² using the geometric constant a_N. The data for geometric buckling values on these geometries are available for the validation of calculation codes, and the empirical formula for geometric buckling obtained in this study can be applied to the basic criticality safety design of fuel cycle facilities.