Kazuya Yamaji

Advanced resonance self-shielding method for gray resonance treatment in lattice physics code GALAXY

A new resonance self-shielding method based on the equivalence theory is developed for general application to the lattice physics calculations. The present scope includes commercial light water reactor (LWR) design applications which require both calculation accuracy and calculation speed. In order to develop the new method, all the calculation processes from cross-section library preparation to effective cross-section generation are reviewed and reframed by adopting the current enhanced methodologies for lattice calculations. The new method is composed of the following four key methods: (1) cross-section library generation method with a polynomial hyperbolic tangent formulation, (2) resonance self-shielding method based on the multi-term rational approximation for general lattice geometry and gray resonance absorbers, (3) spatially dependent gray resonance self-shielding method for generation of intra-pellet power profile and (4) integrated reaction rate preservation method between the multi-group and the ultra-fine-group calculations. From the various verifications and validations, applicability of the present resonance treatment is totally confirmed. As a result, the new resonance self-shielding method is established, not only by extension of a past concentrated effort in the reactor physics research field, but also by unification of newly developed unique and challenging techniques for practical application to the lattice physics calculations.

Integration of equivalence theory and ultra-fine-group slowing-down calculation for resonance self-shielding treatment in lattice physics code GALAXY

A new hybrid resonance self-shielding treatment method in reactor physics field is developed by integrating equivalence theory and ultra-fine-group slowing-down calculation from the theoretical point of view. In the conventional equivalence theory, scattering source approximation and taking no account of resonance interference effect cause prediction error of effective cross-section. By reviewing the derivation scheme of neutron flux in the equivalence theory, the essence of the ultra-fine-group treatment is effectively incorporated. A new form of energy-dependent flux is based on multi-term rational equation, but the scattering source can be solved by the way similar to the slowing-down equation. The accurate non-fuel flux is also considered without direct heterogeneous calculation. The new method can also efficiently eliminate the multi-group condensation error by a semi-analytical reaction rate preservation scheme between ultra-fine and multi-group treatments. The present method is implemented in Mitsubishi Heavy Industries, Ltd. lattice physics code GALAXY. From comparisons of neutronics parameters between GALAXY and a continuous energy Monte-Carlo code, applicability of the new method for lattice physics calculations is confirmed. GALAXY achieves high accuracy with short computation time. Therefore, it can be efficiently applied to generation of the nuclear constants used in the nuclear design and safety analysis of commercial light water reactors.

Simple and Efficient Parallelization Method for MOC Calculation

A parallelization method that does not entail much data communication and allowseasy implementation was developed for the method of characteristics (MOC). In the parallelization method, azimuthal angles were grouped to compute, on the same processor, theangular flux before and after the reflection on the outer boundary. The method can be easily applied to existing MOC codes without the highly technical knowledge on efficientdata communication in parallel computing. It was implemented into the GALAXY code and numerical comparisons were performed. As a result, computation speedup by a factor of 9 to 10 and good parallel efficiencies of 70 to 80% were achieved by using twelve processors. The speedup benefits the practical reactor core design using MOC codes. Other thanthe parallel efficiency, the proposed method allows easy implementation because no drastic change in the conventional algorithm for existing sequential process codes is needed. This is carried out with the absence of data communication between processors during the inner iteration of MOC with the proposed method.

Depletion Calculations for PWR Assemblies including Burnable Absorbers with Lattice Code PARAGON

Most of the lattice physics codes, used for routine core design calculations, are based on the spatial flat-flux assumption representation to solve the neutron transport equation. Consequently for regions (like fuel or control rods) with strong flux gradient, a fine computational mesh becomes required for better accuracy of the predictions. In the case of a PWR assembly, this situation particularly occurs with Gadolinia fuel (UO2-Gd2O3) or Erbia fuel (UO2- Er2O3) rods. The aim of this study is to determine, for UO2-Gd2O3 and UO2-Er2O3 pins, the optimal number of computational fuel mesh rings that preserves good accuracy and at the same time is consuming minimum computational running time. This study will be carried out using PARAGON lattice physics code. PARAGON is a two-dimensional neutron/gamma transport code used mainly to generate the group constants for core simulator codes such as ANC. PARAGON (with its new module SDDM) can treat the multi-region resonance self-shielding effect for all resonant isotopes in the fuel rods micro-regions including Gd spatial concentration variation due to burnup depletion. With this capability, PARAGON does not use the pre-tabulated Gd effective cross-sections that are usually generated with a super-cell calculation model. The power distribution used during the fuel integrity evaluation of the fuel rods with burnable absorbers will be also discussed in this paper. By comparing the power profiles of UO2 and absorber rods, it is found that the UO2 values are more limiting and consequently they can be used for conservative evaluations.

Validation of a New Lattice Physics Code GALAXY for PWRs

A new lattice physics and assembly calculation code GALAXY with the 172 energy-group ENDF/B-VII.0 library has been developed. GALAXY generates few group nuclear constants used in a new core simulator COSMO-S. The GALAXY code uses the many enhanced calculation method for more explicit treatment of neutronics characteristics. The outline of enhanced methods used in GALAXY and the qualification results are shown in this paper. From the qualifications in the continuous energy Monte Carlo benchmark, critical experiment analyses and post irradiation examination (PIE) analyses, GALAXY with the library was validated and the applicability of GALAXY to PWR nuclear design was confirmed.Copyright

Validation of a New Core Simulator COSMO-S for PWRs

A new PWR nuclear design code system, GALAXY/COSMO-S, has been developed by Mitsubishi Heavy Industries, Ltd. (MHI) with support of Osaka University and Nagoya University. The code system has been developed based on today’s popular techniques such as MOC and semi-analytical nodal expansion method for GALAXY and COSMO-S, respectively. These codes employ several new features to improve calculation accuracy and efficiency of commercial PWR design calculations. Especially, a new robust cross section representation model based on the concept of quality engineering is introduced in GALAXY/COSMO-S system. The new representation model is intended to cover all PWR operating conditions ranging from cold shut down to hot full power. The robustness of the cross section representation model is achieved by fitting equation including cross term effect by fuel temperature, moderator density and moderator temperature. The fitting equation is determined based on Akaike’s Information Criteria (AIC) instead of empirical ways. It is the first challenge to apply the concept of quality engineering technique, which is widely used in manufacturing field, to the cross-section representation model. In order to demonstrate the applicability of COSMO-S for PWR core designs, several benchmark calculations simulating an assembly models, multi assembly models and a typical commercial plant were performed. Reactivity and power distribution were compared with the reference results prepared by GALAXY and current core design code. The results of these comparisons show excellent agreements with the references. These results validate the applicability of the GALAXY/COSMO-S system with a new cross section model for PWR core design.© 2010 ASME

Ultra-fine-group resonance treatment using equivalent Dancoff-factor cell model in lattice physics code GALAXY

ABSTRACT In order to achieve highly accurate resonance calculations with short computation time , a new ultra-fine-group resonance calculation method is developed. The ultra-fine-group method has a limitation in practical design applications of large and complicated geometries in fuel assembly level due to its long computation time. Therefore, we developed an enhanced one-dimensional (1D) cylindrical pin-cell model to achieve both high calculation accuracy and short computation time. In the enhanced 1D cylindrical pin-cell modeling, moderator radius is adjusted to preserve each fuel pellets Dancoff factor obtained in the exact 2D fuel lattice arrangement. We call this model the ‘equivalent Dancoff-factor’ cell model. This model can accurately consider heterogeneity effects in PWR fuel assemblies and can represent effective cross sections obtained by the ultra-fine-group calculations in the complicated 2D square lattice arrangements. The present method is implemented with Mitsubishi Heavy Industries, Ltd. lattice physics code GALAXY. From the comparisons of neutron multiplication factors and pin power distributions between GALAXY and a continuous-energy Monte Carlo code, applicability of the present method to lattice physics calculations is confirmed. Application of GALAXY with the present method achieves high accuracy with short computation time in normal operations and accident conditions including low moderator density conditions.

Radially and azimuthally dependent resonance self-shielding treatment for general multi-region geometry based on a unified theory

ABSTRACT A unified resonance self-shielding method, which can treat general sub-divided fuel regions, is developed for lattice physics calculations in reactor physics field. In a past study, a hybrid resonance treatment has been developed by theoretically integrating equivalence theory and ultra-fine-group slowing-down calculation. It can be applied to a wide range of neutron spectrum conditions including low moderator density ranges in severe accident states, as long as each fuel region is not sub-divided. In order to extend the method for radially and azimuthally sub-divided multi-region geometry, a new resonance treatment is established by incorporating the essence of sub-group method. The present method is composed of two-step flux calculation, i.e. ‘coarse geometry + fine energy’ (first step) and ‘fine geometry + coarse energy’ (second step) calculations. The first step corresponds to a hybrid model of the equivalence theory and the ultra-fine-group calculation, and the second step corresponds to the sub-group method. From the verification results, effective cross-sections by the new method show good agreement with the continuous energy Monte-Carlo results for various multi-region geometries including non-uniform fuel compositions and temperature distributions. The present method can accurately generate effective cross-sections with short computation time in general lattice physics calculations.

Recent improvements of reactor physics codes in MHI

This paper introduces recent improvements for reactor physics codes in Mitsubishi Heavy Industries, Ltd(MHI). MHI has developed a new neutronics design code system Galaxy/Cosmo-S(GCS) for PWR core analysis. After TEPCO’s Fukushima Daiichi accident, it is required to consider design extended condition which has not been covered explicitly by the former safety licensing analyses. Under these circumstances, MHI made some improvements for GCS code system. A new resonance calculation model of lattice physics code and homogeneous cross section representative model for core simulator have been developed to apply more wide range core conditions corresponding to severe accident status such like anticipated transient without scram (ATWS) analysis and criticality evaluation of dried-up spent fuel pit. As a result of these improvements, GCS code system has very wide calculation applicability with good accuracy for any core conditions as far as fuel is not damaged. In this paper, the outline of GCS code system is described briefly and recent relevant development activities are presented.

Verification of Control Rod Assembly Homogenization for LMFBR With a New Lattice Physics Code GALAXY-H

A new FBR lattice physics code GALAXY-H has been developed by Mitsubishi Heavy Industries, Ltd. (MHI). GALAXY-H is a hexagonal version of GALAXY, which is a two dimensional transport calculation code for PWR assembly. GALAXY-H generates assembly nuclear constants used in the FBR core calculation code. The methodology of flux calculation for GALAXY-H is based on the method of characteristics (MOC) as well as GALAXY. The fuel assemblies of Japanese demonstrated and commercial FBRs are intended to contain the inner duct called FAIDUS where molten fuel is removed to prevent re-critical at severe accident. One of the objectives for developing GALAXY-H is to treat the inner duct and wrapper tube configurations exactly. In this paper, the method generating nuclear constants of control rod assembly is developed with multi-assembly model to exclude the super-cell model that has been used in FBR design so far. Besides, GALAXY-H employs the SPH method for reduction of homogenization error, which is popular method in LWR design. From this, the advanced nuclear constants calculation method for FBR control rod assembly is developed and the basic applicability of FBR nuclear design by using GALAXY-H is confirmed.Copyright