基于本征正交分解降阶的燃耗计算方法研究  

Study on Burnup Calculation Method Based on Proper Orthogonal Decomposition Reduced-order

作　　者：张彬航 毕彦钊 龚瀚源 张永红 袁显宝[2] ZHANG Binhang;BI Yanzhao;GONG Hanyuan;ZHANG Yonghong;YUAN Xianbao(College of Mechanical&Power Engineering,China Three Gorges University,Yichang 443002,China;College of Science,China Three Gorges University,Yichang 443002,China)

机构地区：[1]三峡大学机械与动力学院,湖北宜昌443002 [2]三峡大学理学院,湖北宜昌443002

出　　处：《原子能科学技术》2023年第10期1938-1948,共11页Atomic Energy Science and Technology

基　　金：国家自然科学基金(12275153,12175116,11805112)。

摘　　要：随着堆芯物理计算方法向高保真发展,燃耗区的划分由传统的分米量级降低到厘米量级,全堆燃耗区数量将增加上千倍,燃耗计算精度提升的同时计算代价和复杂度亦陡增。本文研究了基于本征正交分解(POD)降阶的燃耗计算方法,通过建立参数化降阶模型,以1组完备正交基函数实现对各燃耗区燃耗矩阵的快速构造,并进一步研究了离线-在线计算策略以实现高效数值求解。基于JAEA发布的MOX燃料栅元基准题进行了计算分析,数值结果验证了本方法的正确性和可行性。本方法可为有效减少高保真燃耗计算成本、提高计算效率提供参考。The goal of high-fidelity burnup calculations is to accurately describe the nuclide composition of the reactor over its entire lifetime.As the core physics calculation method evolves to high-fidelity,the number of burnup regions will increase thousands of times from the traditional decimeter level to the centimeter level,and the cost and complexity of the burnup calculation will increase steeply while the accuracy of the burnup calculation increases.In this paper,the fuel consumption calculation method based on the proper orthogonal decomposition(POD)reduced-order method was studied.By establishing a parametric reduced-order model(ROM),a set of complete orthogonal basis functions was used to construct the burnup matrix in each burnup region,and further based on the offline-online calculation strategy to achieve efficient numerical solution.In the offline phase,a high-fidelity burnup calculation was performed to obtain the snapshot matrices of reaction rate and neutron flux.Based on singular value decomposition(SVD),a set of basis functions of the burnup matrix and neutron flux were constructed respectively.In the online phase,the neutron flux was obtained from the real-time transport calculation,the parametric ROM and basis functions in the offline stage were used to quickly construct the burnup matrix and then completed the full-life burnup calculation.Based on the benchmark problem of MOX fuel cell released by JAEA,the numerical results verify the correctness and feasibility of this method.For the calculation of k inf,the relative deviation from the full-order model(FOM)is less than 0.5%with only the first-order ROM.For the calculation of nuclear density of heavy nuclides 235 U and 239 Pu,the first-,fifth-and tenth-order ROMs were used for calculation.Comparing with the FOM,the relative deviations are within 5%,0.1%and 0.005%,respectively.However,for the calculation of 155 Gd and 149 Sm,which have larger neutron absorption cross sections,the calculation accuracy of the first-order ROM is poor,the relative devia

关 键 词：燃耗计算 降阶模型 本征正交分解 数值验证 

分 类 号：TL329.2[核科学技术—核技术及应用]