Neutron Energy Groups Research Articles

Method for analysing low-enrichment, light-water cores

A three-group method is developed for analysing light-water UO, cores of low enrichment. The method is composed of a series of sub-routines that are consolidated to produce a set of self-consistent multigroup parameters. The thermal cross-sections are determined by averaging the cross-section over a ‘hardened’ or shifted Maxwellian spectrum, the amount of hardening being a function of the macroscopic absorption-to-slowing-down ratio. The disadvantage factor is calculated using diffusion theory for the moderator and a transport condition at the surface bf the rod, the accuracy of the calculation being comparable to a P-3 calculation. The epithermal capture cross-section of 238U is based on the measurement of Hellstrand including a H barn 1/v absorption, and ignores epithermal self-shielding effects even for very close-packed lattices. The fast-fission factor is calculated relative to the experimental measurements for UO 2. The diffusion coefficients are found by averaging the measured cross-sections over the appropriate neutron flux in each neutron energy group. The slowing-down cross-section is defined as the diffusion coefficient divided by the neutron age, the age being determined by calculating equivalent transport and slowing-down factors relative to light-water measurements. Utilizing the two-dimensional IBM-704 PDQ digital computer code, a comparison is made with the available experimental information using oxide fuel. These experiments, which contain rod-type fuel elements, cover a wide range of 235U enrichment and water-to-uranium ratio. The reactivity and power distribution predictions are very good. The reactivity calculations check to within 2 per cent Δk for all cases, most cases being within 1 per cent Δk.

Minimum Critical Mass in Variable Density and Epithermal Reactors

For thermal reactors and those described by two neutron energy groups it is shown that the adjoint fluxes of multigroup diffusion theory can be expressed as linear combinations of the neutron fluxes even when the moderator density is a function of position. For the case of thermal reactors it is shown that minimum critical mass and constant thermal flux in the core are equivalent. (auth)

Evaluation of a Bank of Slab-type Control Rods

A method for evaluating a bank of slab-type control rods in enriched hydrogenous reactors considering both thermal and epithermal capture was developed within the framework of three neutron energy groups. An absorption area technique that combines diffusion theory in thc fuel moderator region and a transport condition at the control rod boundary is utilized. The effect of the absorption area is to decrease the source strength for the thermal and epithermal energy groups. The epithermal probability for a non-l/ nu absorber is found by an experimental reactivity comparison to a 1/ nu absorber. Assuming that the absorptton area is uniformly distributed throughout the core, a hand calculation can be made which determines the number, size, and composition of rods necessary to achieve a specific cold shutdown margin. (auth)

Application of the Absorption Area Method To Three-Group Diffusion Theory Problems

The absorption area method allows rod absorptions to be considered without treating the rods as discrete boundaries. The source neutrons for a rod absorbing neutron energy group are reduced in proportion to the rod absorption area. This paper presents rod absorption factors based on absorption area calculations that may be applied in any reactor region penetrated by the rods. The factors derived are dependent on the core and rod composition, rod geometry, and include rod interaction effects.