Kenichi Tada

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

The pin-by-pin fine-mesh core calculation method is considered as a candidate next-generation core calculation method for BWR. In this study, the diffusion and simplified P3 (SP3) theories are applied to the BWR pin-by-pin fine-mesh calculation. The performances of the diffusion and SP3 theories for cell-homogeneous pin-by-pin fine-mesh calculation for BWR are evaluated through comparison with a cell-heterogeneous detailed transport calculation by the method of characteristics (MOC). Two-dimensional, 2 × 2 multi-assemblies geometry is used to compare the prediction accuracies of the diffusion and SP3 theories. The 2 × 2 multi-assemblies geometry consists of 9 × 9 UO2 fuel assemblies that have two different enrichment splittings. To minimize the cell-homogenization error, the SPH method is applied for the pin-by-pin fine-mesh calculation. The SPH method is a technique that reproduces a result of heterogeneous calculation using that of homogeneous calculation. The calculation results indicated that the diffusion theory shows a discrepancy larger than that of the SP3 theory on the pin-wise fission rate distribution. In contrast to the diffusion theory, the SP3 theory shows a much better accuracy on the pin-wise fission rate distribution. The computation time using the SP3 theory is about 1.5 times longer than that using the diffusion theory. The BWR core analysis consists of various calculations, e.g., the cross section interpolation, neutron flux calculation, thermal hydraulic calculation, and burn-up calculation. The function of the calculation time for the neutron flux calculation is usually less than half in the typical BWR core analysis. Therefore, the difference in the calculation time between the diffusion and SP3 theories would have no significant impact on the calculation time of the BWR core analysis. For these reasons, the SP3 theory is more suitable than the diffusion theory and is expected to have sufficient accuracy for the 2 × 2 multi-assemblies geometry used in this study, which simulates a typical situation of the actual BWR core.

Treatment of Staggered Mesh for BWR Pin-by-Pin Core Analysis

In this paper, the neutron current interpolation (NCI) method is proposed to treat the staggered mesh on the basis of the Simplified P3 (SP3) theory code. In the NCI method, the response matrix formulation is applied to the SP3 theory code, and neutron partial currents at assembly boundary are interpolated using low-order polynomial functions, i.e., flat, linear or quadratic function. The pin-by-pin fine-mesh core analysis method is considered as a candidate next-generation core calculation method for BWR. Since the number of fuel rods in BWR assembly is increased with the higher burn-up, the different types of assembly may be adjacent in a BWR core. Therefore, when the cell-homogenized pin-by-pin analysis method is applied to the BWR core analysis, it must have a capability to treat the staggered mesh. Our previous study indicates that the SP3 theory is appropriate for pin-by-pin BWR calculations. However, the SP3 theory code that can treat the staggered mesh has not been developed so far. For these reasons, the treatment method of the staggered mesh is investigated to develop such SP3 theory code. The performances of the NCI method are evaluated through comparison with the cell-heterogeneous detailed transport calculations by the method of characteristics (MOC). Two-dimensional, 2 × 2 multi-assembly geometries are used to compare the prediction accuracy of the NCI method. The 2 × 2 multi-assembly geometries consist of 9 × 9 UO2 and 10 × 10 MOX fuel assemblies. The calculation results indicate that the prediction accuracy of the NCI method is similar to that of the detailed transport calculation method.

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.

Application of Quick Subchannel Analysis Method for Three-Dimensional Pin-by-Pin BWR Core Calculations

Three-dimensional pin-by-pin core analysis is considered to be a candidate for the next-generation BWR core calculation method. In our previous study, the applicability of the transport and burnup calculations for a three-dimensional pin-by-pin BWR core analysis was investigated. However, the thermal-hydraulics calculation has not yet been studied in this framework. In the conventional core analysis code, the bundlewise thermal-hydraulics calculation is adopted. In the actual core analysis, the power distribution inside a fuel assembly is tilted at the region adjacent to a control blade or the core peripheral region. In these regions, the consideration of the subchannel-wise void distribution has an impact on the fission rate distribution. Therefore, an evaluation of the detailed void distribution inside an assembly, i.e., the incorporation of the subchannel wise void distribution, is desirable for the pin-by-pin BWR core analysis. Although several subchannel analysis codes have been developed, these subchannel analysis codes generally require a large computational effort to estimate the subchannel-wise void distribution in a whole BWR core. Therefore, to analyze a whole BWR core within a reasonable computation time, it was necessary to apply a fast subchannel analysis code. In this paper, a quick subchannel analysis code dedicated to pin-by-pin BWR core analysis is newly developed, and the void distribution of the present subchannel analysis code is compared with the prevailing subchannel analysis code NASCA using three-dimensional single-assembly geometries. Since the present subchannel analysis code is used for a coupled neutronics/thermal-hydraulics analysis, the results of the coupling calculation are also compared with those of NASCA. The calculation result indicates that the void distribution difference between NASCA and the present subchannel analysis code is slightly less than 10%. This result indicates that the prediction accuracy of the present subchannel analysis code will be reasonably appropriate for a pin-by-pin BWR core analysis. Furthermore, the results show that the calculation time of the present subchannel analysis code is only 10 min for a hypothetical three-dimensional ABWR quarter-core geometry using a single CPU. This calculation time is sufficient for a pin-by-pin BWR core analysis.