基于能谱降阶模型的共振计算方法研究  

Resonance Calculation Method Based on Energy Spectrum Using Reduced Order Model

作　　者：于嘉蕾 张乾 张晋超 赵强 YU Jialei;ZHANG Qian;ZHANG Jinchao;ZHAO Qiang(Fundamental Science on Nuclear Safety and Simulation Technology Laboratory,Harbin Engineering University,Harbin 150001,China;Laboratory for Advanced Nuclear Energy Theory and Applications,Zhejiang Institute of Modern Physics,Department of Physics,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]哈尔滨工程大学、核安全与仿真技术国防重点实验室,黑龙江哈尔滨150001 [2]浙江大学物理学系、浙江近代物理中心、先进核能理论与应用实验室,浙江杭州310030

出　　处：《原子能科学技术》2023年第4期818-827,共10页Atomic Energy Science and Technology

基　　金：国家自然科学基金(12105063);核反应堆系统设计技术重点实验室运行基金(HT-KFKT-24-2021011);核数据重点实验室稳定支持基金(JCKY2021201C154);中核集团“青年英才”项目。

摘　　要：传统的共振计算方法试图对能谱进行诸多近似和预测来实现有效共振自屏截面的计算,但传统方法存在精度与效率难以兼顾的问题。本文采用广义并群理论和降阶模型方法,挖掘复杂能谱的特征,降低共振计算的复杂程度。通过对典型背景截面的超细群能谱的提取,建立能谱样本空间。通过奇异值分解和低秩近似,有效获取代表能谱特征的正交基函数。通过求解考虑正交基函数分布权重下的宽群角通量展开系数,实现目标问题下超细群能谱的重构,并用精细能谱并群计算得到了有效共振自屏截面。初步结果表明,基于能谱降阶模型的共振计算方法能有效预测共振自屏截面,其计算效率与超细群方法相比具备一定的优势。Resonance calculation is one of the most important and difficult parts of core analysis and can dominate the accuracy of the core analysis.There are three methods for resonance computation:ultra-fine group(UFG)method,equivalence method,and subgroup method.Each of the approaches has advantages and disadvantages.UFG method is suitable for rigorous resonance calculation of various reactors,but the efficiency is very low for complex geometry and large-scale core.The equivalent theory has high computational efficiency and is widely used in core calculations.But the equivalence theory uses many assumptions and approximations,and its accuracy and application are limited.Subgroup theory can efficiently calculate resonance self-shield effects for arbitrary geometric problems,but the potential drawback is the limitation on the treatment of the resonance interference effect and the nonuniform temperature distribution.In conclusion,conventional methods have difficulties on balancing the accuracy and efficiency.In this paper,it is proposed to use generalized group condensation theory and reduced order model to extract the features of energy spectra in resonance calculation.Based on the ultrafine group energy spectra under 40 different background sections,the orthogonal bases are generated using these energy spectra.Using singular value decomposition and low rank approximation,the orthogonal basis functions related to energy spectrum characteristics are generated.Based on generalized group condensation theory,the neutron transport equation is solved by orthogonal basis.By solving the broad group angular flux expansion coefficient that considers the weight of orthogonal basis function distribution,the ultra-fine group energy spectrum is reconstructed.Finally,the effective cross-section is calculated by using the ultra-fine group energy condensation.According to the JAERI benchmark,UO 2 fuel cells and MOX fuel cells with different enrichments are designed as problems for this calculation.Numerical results show that the maximum r

关 键 词：共振计算 有效截面 低秩近似 降阶模型 等价理论 

分 类 号：TL329[核科学技术—核技术及应用]