On-The-Fly Prediction of Macroscopic Cross-Section Spatial Response to TH Perturbations Through Transfer Functions: Theory and First Results

Monte Carlo (MC) codes are widely used for the accurate modeling of nuclear reactors. However, efficient inclusion of thermal-hydraulic (TH) feedback within the MC calculation sequence is still an open problem. The issue is emphasized when coupled MC-TH calculations are needed to model the burnup evolution using multiple depletion steps. Among the techniques proposed to solve this problem is the utilization of stabilized Picard iteration in conjunction with a low-order prediction step. The latter is composed of a prediction block for cross sections and a fast deterministic solver that uses the cross sections to obtain a prediction of the power profile. The predicted power is then used as an improved guess for the next MC calculation, therefore leading to faster convergence for the overall algorithm. In this paper, we propose a new prediction block in which one-group cross sections are calculated through convolution of the TH scalar fields with MC-generated generalized transfer functions (GTFs). First-order perturbation theory is then utilized to calculate the power profile from the updated cross sections. A version of this prediction block using a simple fast Fourier transform–based approximation of the GTF is tested against a boiling water reactor unit-cell with realistic density profile and axial reflectors. The analysis was limited to the feedback between neutronics and coolant density variation. Good agreement was observed for both the spatial power and the one-group macroscopic cross-section profiles, which were compared to the reference MC results. This agreement was also preserved near the boundary, where the spatial flux gradients are maximum due to proximity to the axial reflectors.