基于改进缺陷因子方法的FCM燃料有效多群截面计算方法研究

全陶瓷微胶囊封装（FCM）燃料是重要的候选事故容错燃料，与传统燃料相比，FCM燃料的双重非均匀性使得其有效多群截面计算面临较大的挑战。本文提出一种改进的缺陷因子方法来处理FCM燃料在共振能区和非共振能区的自屏效应，实现FCM燃料的等效均匀化。通过颗粒丹可夫因子守恒来构建新的等效模型以克服传统的体积权重等效模型无法考虑燃料棒间自屏的影响；在共振能量段，基于新的等效一维球模型求解超细群慢化方程获得共振能量段的超细群缺陷因子；在非共振能量段，利用新等效模型的特征值计算获得快群和热群的多群缺陷因子；在此基础上实现FCM燃料棒的等效均匀化。本方法已在高保真中子学程序NECP-X上实现，并在一系列工况下进行了测试，与蒙特卡罗程序的比较表明，本方法能处理不同情况下的双重非均匀性，并可获得准确的有效自屏截面。

Advanced Disadvantage Factor Method for Homogenized Effective Cross Section Calculation in FCM fuel

Conventional PWR fuel only needs to consider the single heterogeneity between fuel rods, but FCM fuel also needs to consider the double heterogeneity between particles and matrix. Disadvantage factor method is a typical method to solve double heterogeneity. But there are still some problems in this method. Firstly, the equivalent model for calculating the disadvantage factor is established by the conservation of volume weight, which introduces the assumption that the particles are uniformly distributed in the infinite matrix and cannot consider the macroscopic heterogeneity. Secondly, the disadvantage factor in the non-resonace energy region is obtained by ensuring the conservation of first flight collision probability in the 3D penetration model, but this method cannot meet the requirements of high-precision calculation in FCM fuel. To solve these problems, this paper proposes an improved disadvantage factor method based on the previous work. The improved disadvantage factor method mainly makes two improvements on the traditional method. Firstly, equivalent one-dimensional sphere model based on the Dancoff factor replaces the volume-weight equivalent model. Secondly, in the processing of non-resonance energy range, eigenvalue calculation is used in the new model to obtain multi-group disadvantage factors. This method was implemented in NECP-X and verified in different working conditions and problems of different scales. All the results are in good agreement with the reference solutions, which proves that the proposed method can effectively deal with the double heterogeneity in FCM fuel and obtain accurate effective multi-group cross sections.