Application of correction technique using leakage index combined with SPH or discontinuity factors for energy collapsing on pin-by-pin BWR core analysis

A correction technique to capture the spectral interference effect on collapsed cross sections is combined with the superhomogenization (SPH) factor or the discontinuity factor (DF) and is applied to the pin-by-pin core analysis for boiling water reactors (BWRs). The spectral interference effect has relationship with variations of neutron leakage in each pin-cell from the viewpoint of neutron balance. In order to correct collapsed cross sections, a new correction technique, in which the neutron leakage in each pin-cell is used as a correction index, was proposed in the previous study. By this correction technique, the reference coarse group cross sections are well reproduced and the calculation accuracies are improved. However, the reference fine group calculation results could not be reproduced since the correction technique cannot reduce energy collapsing errors. Thus, we combine the correction technique with the SPH factor or the DF to reduce energy collapsing errors. In order to verify and discuss the applicability of the correction technique with the SPH factor or the DF, two-dimensional benchmark calculations considering typical characteristics of BWR cores are carried out. The correction technique with the DF more accurately reproduces the reference fine group calculation results than that with the SPH factor.     

A macroscopic cross-section model for BWR pin-by-pin core analysis

A macroscopic cross-section model used in boiling water reactor (BWR) pin-by-pin core analysis is studied. In the pin-by-pin core calculation method, pin-cell averaged cross sections are calculated for many combinations of core state and depletion history variables and are tabulated prior to core calculations. Variations of cross sections in a core simulator are caused by two different phenomena (i.e. instantaneous and history effects). We treat them through the core state variables and the exposure-averaged core state variables, respectively. Furthermore, the cross-term effect among the core state and the depletion history variables is considered. In order to confirm the calculation accuracy and discuss the treatment of the cross-term effect, the k-infinity and the pin-by-pin fission rate distributions in a single fuel assembly geometry are compared. Some cross-term effects could be negligible since the impacts of them are sufficiently small. However, the cross-term effects among the control rod history (or the void history) and other variables have large impacts; thus, the consideration of them is crucial. The present macroscopic cross-section model, which considers such dominant cross-term effects, well reproduces the reference results and can be a candidate in practical applications for BWR pin-by-pin core analysis on the normal operations.     

An optimization approach to establish an appropriate energy group structure for BWR pin-by-pin core analysis

An optimization approach to establish an appropriate multi-group energy structure for boiling water reactor (BWR) pin-by-pin fine mesh core analysis is proposed. In the present approach, the number of energy groups of cross sections is successively reduced or increased. In order to select an energy group boundary that is removed or added, performances of all possible candidates of energy group structures are tested in multi-assembly geometries. Then, the energy group boundary, which provides the minimum difference of the k-infinity or the pin-by-pin fission rate distribution, is finally removed or added. This procedure is repeated until the number of energy groups reaches to the target value. In order to confirm the applicability of the present approach, the accuracies of the k-infinity and the pin-by-pin fission rate distribution are investigated in various 2 × 2 multi-assembly geometries with the established energy group structure. From the verification results, the differences of the k-infinity and the pin-by-pin fission rate distribution between the reference (fine) and the established (coarse) energy group structure are small in the various 2 × 2 multi-assembly geometries. Therefore, we can conclude that the present approach is efficient to establish an appropriate energy group structure for BWR pin-by-pin fine mesh core analysis.     

A proposal on accuracy estimation method for the sampling-based uncertainty analysis with Monte Carlo simulation technique

The sampling-based uncertainty analysis method is a stochastic approach to estimate response uncertainties caused by the uncertainty in the input parameters. Conventionally, to minimize the effects caused by the Monte Carlo stochastic uncertainty, lots of particle histories have been used for the uncertainty analysis. However, this can cause inefficiencies in the uncertainty analysis. To optimize the calculation efficiency, how the Monte Carlo stochastic uncertainty influences the response uncertainty should be clearly verified. In this study, a method to estimate the accuracy of the response uncertainty is proposed by introducing a standard error and an error propagation theory. Using the proposed method, response uncertainties and standard errors of the multiplication factors for three benchmark problems are evaluated by the Monte Carlo method. Our results show that the proposed method can accurately estimate the accuracy of the response uncertainty caused by the input uncertainty in using the Monte Carlo simulation method. The proposed method can be directly utilized to estimate the accuracy of the sampling-based uncertainty analysis using the Monte Carlo simulation method. Also, it is expected that the proposed method will contribute to an increase in the calculation efficiency in the sampling-based sensitivity and uncertainty analysis.     

Neutron cross section sensitivity analysis of UO2 and MOX core physics experiments on light water reactors

The perturbation theory based on the transport calculation has been applied to study sensitivity of neutron multiplication factors (k_eff's) to neutron cross sections used for the reactivity analysis of UO₂ and MOX core physics experiments on light water reactors. The studied cross sections were neutron capture, fission and elastic scattering cross sections, and a number of fission neutrons, ν. The obtained sensitivities were multiplied to relative differences in the cross sections between JENDL-4.0 and JENDL-3.3 in order to estimate the reactivity effects. The results show that the increase in k_eff, 0.3%Δk/kk′, from JENDL-3.3 to JENDL-4.0 for the UO₂ core is mainly attributed to the decreases in the capture cross sections of ²³⁸U. On the other hand, there are various contributions from the differences in the cross sections of U, Pu, and Am isotopes for the MOX cores. The major contributions to increase in k_eff are decreases in the capture cross sections of ²³⁸U,²³⁸Pu, ²³⁹Pu, and those to decrease in k_eff are decreases in ν of ²³⁹Pu and increases in the capture cross sections of²⁴¹Am. They compensate each other, and the difference in k_eff between JENDL-3.3 and JENDL-4.0 is less than 0.1%Δk/kk′ and relatively small.