Resonance Treatment Based on Ultra-fine-group Spectrum Calculation in the AEGIS Code

The resonance calculation method using the ultra-fine-group spectrum calculations in the AEGIS code is explained in detail. By a simple benchmark problem, it is verified that the effect of anisotropic scattering on effective cross-sections is not very large and the isotropic scattering source approximation is adequate in practical resonance calculations in LWRs. Furthermore, some efficient numerical algorithms in the ultra-fine-group calculations to reduce the computation time without large degeneration of accuracy are presented. In addition, the SPH method for energy collapsing of cross-sections is adopted in the AEGIS code to reduce the error of energy collapsing.

Through the comparison with continuous-energy Monte-Calro calculation in the pin-cell geometry, the validity of the resonance treatment in the AEGIS code is verified.     

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

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.     

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

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 pellet's 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.     

不等温分布下燃料棒径向温度相关238U共振吸收截面计算

为精确预测燃料棒径向不等温分布下的²³⁸U共振吸收截面,提出了一种基于求解超细群慢化方程的共振计算方法。该方法通过温度扰动模型,将径向不等温分布对燃料棒能谱的影响分解为每个径向子区对燃料棒能谱的独立影响,从而实现了对不等温分布下的径向相关共振吸收截面的预测。数值结果表明,以MCNP5统计结果为基准,温度扰动模型对²³⁸U共振吸收截面的计算精度相比于传统的均匀碰撞概率超细群方法更高,共振吸收截面的相对偏差在2%以下。温度扰动模型适合进行不等温分布下燃料棒径向的²³⁸U共振吸收截面的精确计算。     

基于特征线法计算的超细群慢化方程求解方法

为实现对复杂几何、复杂能谱组件的精细计算,提出了一种基于特征线的超细群慢化方程求解方法。通过耦合特征线法中的固定源计算,在共振能量范围内建立超细群慢化方程,通过精细能谱获得复杂结构下的共振自屏截面。对典型压水堆栅元问题、带有温度分布的栅元问题、燃料内部存在不均匀性的栅元问题以及板状燃料组件问题进行了计算。结果表明,基于特征线的超细群慢化方程求解方法可精确计算复杂几何、复杂能谱问题,为共振计算提供基准。     

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.