[en] Highlights: • Tested here are 4 methods for estimating critical rod position, in Monteburns, of a reactor fuel array. • Inverse multiplication methods better predict critical rod position at the cost of more iterations. • A polynomial fit technique can predict most plutonium isotopics to within 5%. - Abstract: This burnup study examined the effect of a predicted critical control rod position on the nuclide predictability of several axial and radial locations within a 4 × 4 graphite moderated gas cooled reactor fuel cluster geometry. To achieve this, a control rod position estimator (CRPE) tool was developed within the framework of the linkage code Monteburns between the transport code MCNP and depletion code CINDER90, and four methodologies were proposed within the tool for maintaining criticality. Two of the proposed methods used an inverse multiplication approach – where the amount of fissile material in a set configuration is slowly altered until criticality is attained – in estimating the critical control rod position. Another method carried out several MCNP criticality calculations at different control rod positions, then used a linear fit to estimate the critical rod position. The final method used a second-order polynomial fit of several MCNP criticality calculations at different control rod positions to guess the critical rod position. The results showed that consistency in prediction of power densities as well as uranium and plutonium isotopics was mutual among methods within the CRPE tool that predicted critical position consistently well. While the CRPE tool is currently limited to manipulating a single control rod, future work could be geared toward implementing additional criticality search methodologies along with additional features.

[en] A novel, hierarchical Haar wavelet basis is introduced and used to discretise the angular dimension of the Boltzmann transport equation. This is used in conjunction with a finite element subgrid scale method. This combination is then validated using two steady-state radiation transport problems, namely a 2D dogleg-duct shielding problem and the 2D C5MOX OECD/NEA benchmark. It is shown that the scheme has many similarities to a traditional equal weighted discrete ordinates ($S_n$) angular discretisation, but the strong motivation for our hierarchical Haar wavelet method is the potential for adapting in angle in a simple fashion through elimination of redundant wavelets. Initial investigations of this adaptive approach are presented for a shielding and criticality eigenvalue example. It is shown that a 60% reduction in the number of angles needed on most spatial nodes - and rising up to 90% on nodes located in high streaming areas - can be attained without adversely affecting the accuracy of the solution.