Tadashi Ushio

Derivation of optimum polar angle quadrature set for the method of characteristics based on approximation error for the Bickley function

In this paper, dedicated polar angle quadrature sets for the method of characteristics (MOC) are developed, based on the equivalence between MOC and the collision probability method. The discretization error of polar angle in MOC can be considered as an approximation error of the Bickley function used in the collision probability method; the Bickley function is numerically integrated in MOC using a quadrature set for polar direction (i.e., a set of polar angles and weights). Therefore, by choosing an appropriate quadrature set, the approximation error of the Bickley function which appears in MOC can be reduced, thus the calculation accuracy of MOC increases. Quadrature sets from one to three polar angle divisions are derived by minimizing the maximum approximation error of the Bickley function. The newly derived polar angle quadrature set (Tabuchi-Yamamoto or the TY quadrature set) is tested in the C5G7 and 4-loop PWR whole core problems and its accuracy is compared with other quadrature sets, e.g., Gauss-Legendre. The calculation results indicate that the TY quadrature set that is newly developed in the present paper provides better accuracy than the other methods. Since the number of polar angle divisions is proportional to computation time of MOC, utilization of the TY quadrature set will be computationally efficient.

Neutron transport models of AEGIS : An advanced next-generation neutronics design system

Abstract A very rigorous and advanced next-generation neutronics design system, AEGIS (Anisotropic, Extended Geometry, Integrated Neutronics Solver), which is based on the deterministic method, is being developed using advanced computer science technology. The method of characteristics, which has the merit of treating heterogeneous geometry explicitly, is utilized in AEGIS as a neutron transport solver. So, the AEGIS code can explicitly model many types of fuel lattices in both commercial light water reactors (LWRs) and advanced reactors such as Generation IV reactors. The AEGIS code can also treat higher-order anisotropic scattering accurately based on spherical harmonics expansion. To compute a large-scale problem, a nonuniform ray-tracing method is implemented in AEGIS. It utilizes the Gauss-Legendre quadrature weight and the macroband method to decide position and width of ray traces to reduce spatial discretization error efficiently. The transport solution of AEGIS has been verified through various benchmark problems. It was found that the AEGIS code can explicitly treat complicated geometry and can efficiently solve a large-scale problem. These results show that flexibility in handling geometry and the very rigorous neutronics calculation models of AEGIS will contribute to predicting neutronics characteristics accurately, not only for commercial LWRs but also for advanced reactors.

Convergence Improvement of Coarse Mesh Rebalance Method for Neutron Transport Calculations

The coarse mesh rebalance (CMR) is a simple acceleration method that is commonly used for transport calculations though it is conditionally stable, i.e. acceleration failed under certain calculation conditions. In this paper, a new acceleration scheme, i.e. the generalized coarse mesh rebalance (GCMR) method, is proposed and applied to improve convergence property of the CMR method. Definitions of partial neutron currents used in CMR are modified in the present method and convergence property of CMR is improved by the modifications. The proposed method was applied to transport calculations in slab and light water reactor assembly geometries. The calculation results were compared with those by the CMR and the coarse mesh finite-difference (CMFD) acceleration methods, and it was revealed that the present method significantly improves the convergence property of the traditional CMR method. Since the present method can be easily applied to existing transport codes using the CMR method, it is considered as a practical acceleration method.

AEGIS: AN ADVANCED LATTICE PHYSICS CODE FOR LIGHT WATER REACTOR ANALYSES

AEGIS is a lattice physics code incorporating the latest advances in lattice physics computation, innovative calculation models and efficient numerical algorithms and is mainly used for light water reactor analyses. Though the primary objective of the AEGIS code is the preparation of a cross section set for SCOPE2 that is a three-dimensional pin-by-pin core analysis code, the AEGIS code can handle not only a fuel assembly but also multi-assemblies and a whole core geometry in twodimensional geometry. The present paper summarizes the major calculation models and part of the verification/validation efforts related to the AEGIS code.

Neutron anisotropic scattering effect in heterogeneous cell calculations of light water reactors

A study on the anisotropic scattering effects in heterogeneous square cells of light water reactors has been performed using the characteristics method. It was found that the effects of the anisotropic scattering were relatively large for the MOX fuel cell because of the large neutron current from the moderator to the fuel region and the k inf value by the P0 calculation became 0.10–0.16% larger than that by the P5 calculation. With the transport correction, the k inf difference from the P5 calculation became even larger than that from the P0 calculation and the k inf value by the transport correction became 0.18–0.25% larger than that by the P5 calculation for the MOX fuel cell. The transport corrected self-scattering cross sections of the moderator region become smaller than the non-transport corrected ones and the angular flux distribution becomes more anisotropic with the transport correction. Therefore, more neutrons toward the moderator region between the fuel pellets can slow down to the lower energy region with the transport correction. As a result, the k inf value by the transport correction becomes larger than that by the P0 calculation, which is opposite effect to that by the P5 calculation.

Cross section adjustment method based on random sampling technique

A cross section adjustment method based on the random sampling technique is proposed. In the proposed method, correlations among cross sections and core parameters are used instead of sensitivity coefficients of cross sections, which are necessary in the conventional method. The correlations are statistically estimated by the random sampling technique. The proposed method is theoretically consistent with the conventional method and provides comparable adjusted cross sections when sufficient number of random sampling is taken into account. The proposed method would be suitable for practical light water reactor (LWR) core analysis since estimation of sensitivity coefficients, which requires considerable computational cost in typical LWR problems, is not necessary. Through a benchmark problem in simple pin-cell geometry, adjusted cross sections by the present and the conventional cross section adjustment method are compared. The adjusted cross sections by the present method well reproduce the conventional ones, thus the feasibility of the present method is confirmed.

Uncertainty Quantification of LWR Core Characteristics Using Random Sampling Method

Abstract Uncertainties of various neutronics characteristics in commercial boiling water reactor (BWR) and pressurized water reactor (PWR) cores due to cross-section covariance are evaluated by the Latin Hypercube Sampling (LHS) method, which is an efficient random sampling algorithm. Thermal-hydraulic feedback and burnup effects are fully and explicitly taken into account using a licensing-grade core simulator. Uncertainties for various core characteristics are evaluated by the statistical processing of core calculation results based on the LHS method. The calculation results indicate that uncertainty of critical eigenvalue (i.e., core reactivity) in the BWR core is comparable to that of a typical PWR core. On the other hand, uncertainties of assembly relative power distribution and maximum assembly burnup in the present BWR core are much smaller than those of the present PWR core. The strong thermal-hydraulic feedback effect in the BWR core significantly contributes to the difference of uncertainties in BWR and PWR cores.

Important fission product nuclides identification method for simplified burnup chain construction

A method of identifying important fission product (FP) nuclides which are included in a simplified burnup chain is proposed. This method utilizes adjoint nuclide number densities and contribution functions which quantify the importance of nuclide number densities to the target nuclear characteristics: number densities of specific nuclides after burnup. Numerical tests with light water reactor (LWR) fuel pin-cell problems reveal that this method successfully identifies important FP nuclides included in a simplified burnup chain, with which number densities of target nuclides after burnup are well reproduced. A simplified burnup chain consisting of 138 FP nuclides is constructed using this method, and its good performance for predictions of number densities of target nuclides and reactivity is demonstrated against LWR pin-cell problems and multi-cell problem including gadolinium-bearing fuel rod.

The Characteristics and Subgroup Methods in Square Light Water Reactor Cell Calculations

Abstract The effect caused by the circular approximation of the geometry for cell calculations in light water reactors is studied using the continuous-energy Monte Carlo code MVP. It was found that the kinf values were underestimated with this approximation of the geometry, especially in the case of a mixed-oxide fuel cell. To treat the square geometry, including the resonance calculation, KRAM-B was developed based on the two-dimensional neutron transport code KRAM as a deterministic cell calculation code. KRAM-B solves the neutron transport equation using a combination of the subgroup method and the characteristics method. The subgroup method is able to perform the resonance calculation faster than the ultrafine energy group calculation and predict the resonance cross section more accurately than the Dancoff factor method. It was found that the kinf values and the effective microscopic resonance cross sections by KRAM-B agreed well with the reference MVP results.

Design of a gadolinia bearing mixed-oxide fuel assembly for pressurized water reactors

Abstract A study on neutronics design of a gadolinia (Gd 2 O 3 ) bearing mixed-oxide (MOX) fuel assembly (MOX-UO 2 (Gd 2 O 3 ) assembly) was performed for the purpose of suppressing the use of fresh lumped burnable poison rods (BPRs). The MOX-UO 2 (Gd 2 O 3 ) assembly investigated consists of MOX and UO 2 (Gd 2 O 3 ) fuel rods, which have already been verified through both fabrication and irradiation experiences. In all, 16 UO 2 (10 wt% Gd 2 O 3 ) fuel rods are located at every corner and the peripheral region of the MOX-UO 2 (Gd 2 O 3 ) assembly in order to reduce the power peaking of MOX fuel rods due to the thermal neutron inflow, and to reduce the reactivity penalty at the end of cycle (EOC). Since fresh BPRs are not expected to be inserted and UO 2 (Gd 2 O 3 ) fuel rods are located at every corner of the assembly, the number of splits in plutonium (Pu) content can be only two, which is less than three splits required for a standard MOX assembly. Core characteristics of an equilibrium core loaded with MOX-UO 2 (Gd 2 O 3 ) assemblies are evaluated and it is verified that adoption of the MOX-UO 2 (Gd 2 O 3 ) assembly is effective to avoid the use of fresh BPRs with securing both the core safety and cycle length. The simplication of the splits in Pu content is also supposed to be beneficial, since it has the possibility of reduce MOX fuel fabrication costs.