Research and verification on calculation method of multi-ring fuel resonance
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摘要: 针对多环燃料精确共振计算的难题，提出并建立了基于全局局部耦合的多环燃料共振计算方法，其中局部计算中采用超细群方法求解共振核素有效自屏截面。采用多环燃料组件问题对该共振计算方法的精度、效率进行了评估，并进一步将该方法应用于高通量工程试验堆二维和三维全堆芯问题分析中。结果表明：基于全局局部耦合的多环燃料共振计算方法在精度和效率上都比传统子群方法更好；采用全局局部耦合的多环燃料共振计算方法模拟全堆芯问题中，特征值、功率分布均与参考解吻合较好。Abstract:
Background Accurate resonance calculation for multi-ring fuel elements remains a significant challenge in reactor physics due to the complex spatial self-shielding effects and strong mutual interference between resonant nuclides. Traditional resonance methods, such as the subgroup method, often struggle to achieve a balance between computational efficiency and accuracy when dealing with such configurations. This is particularly critical for high-fidelity analysis of advanced reactors and experimental facilities like the high-flux engineering test reactor, where precise characterization of resonance phenomena is essential for predicting core performance and safety parameters.Purpose This study aims to address the limitations of existing resonance calculation methods for multi-ring fuel systems by developing a novel global-local coupling framework. The primary objectives are to enhance the accuracy of effective self-shielding cross-section computation for resonant nuclides, improve computational efficiency, and validate the method’s applicability for both assembly-level and full-core simulations.Methods A multi-ring fuel resonance calculation method based on the global-local coupling method (MRFRCM) was proposed specifically for multi-ring fuel analysis. In this approach, when handling global spatial effects, the entire multi-ring fuel is treated as an integrated black body. This process simplifies the multi-ring fuel problem into an equivalent rod-type fuel problem for calculating the global Dancoff correction factor. Subsequently, an equivalent one-dimensional local problem is established through a conservation-based search of the Dancoff correction factor. Finally, the problem is reverted to a one-dimensional multi-ring fuel configuration, where the ultra-fine group method is employed to obtain precise self-shielding cross-sections. The method was implemented and tested on multi-ring fuel assembly problems to evaluate its precision and efficiency. Furthermore, it was applied to two-dimensional and three-dimensional full-core models of a high-flux engineering test reactor to assess its performance in practical scenarios.Results The proposed method demonstrated superior accuracy and computational efficiency compared to the traditional subgroup method. In assembly-level calculations, the global-local approach reduced errors in effective cross-section estimation while maintaining competitive computation times. For full-core simulations, the results showed good agreement with reference solutions. The method also exhibited robust performance in handling complex geometries and heterogeneous material configurations.Conclusions The MRFRCM provides an effective solution for high-accuracy resonance modeling in multi-ring fuel systems. It significantly outperforms the traditional subgroup method in both precision and efficiency, making it suitable for large-scale reactor physics applications. The successful application to 2D and 3D full-core analyses confirms its practicality and reliability for simulating high-fidelity reactor core behavior. Future work will focus on extending the method to broader energy ranges and more complex reactor types. -
图 1 多环燃料全局局部耦合分析流程
Figure 1. Global-local coupling analysis process of multi-ring fuel
图 2 多环燃料黑体处理过程（红色代表燃料，灰色代表包壳，白色代表慢化剂）
Figure 2. Black-body treatment of multi-ring fuel (red area represents the fuel region, gray area represents the cladding region, and white area represents the moderator region.)
图 3 多环燃料等效一维问题搜索
Figure 3. Search process of an equivalent one-dimensional model for multi-ring fuel
图 4 多环燃料一维求解模型的建立
Figure 4. Establishment of a one-dimensional solving model for multi-ring fuel
图 7 第1环燃料235U和238U所有共振能群微观吸收截面及相对偏差计算结果
Figure 7. All resonance energy group self-shielding cross-sections and biases of 235U and 238U for the No. 1 ring fuel
图 9 第6环燃料235U和238U所有共振能群微观吸收截面及相对偏差计算结果
Figure 9. All resonance energy group self-shielding cross-sections and biases of 235U and 238U for the No. 6 ring fuel
图 8 第4环燃料235U和238U所有共振能群微观吸收截面及相对偏差计算结果
Figure 8. All resonance energy group self-shielding cross-sections and biases of 235U and 238U for the No. 4 ring fuel
图 10 不同方案堆芯布置NECP-X程序建模图
Figure 10. Core layout geometry model for different schemes by NECP-X
图 12 高通量工程试验堆堆芯布置方案1二维全堆归一化组件功率及偏差分布图
Figure 12. Normalized assembly power and bias distribution of HFETR two-dimensional core layout scheme 1
图 14 高通量工程试验堆堆芯布置方案3二维全堆归一化组件功率及偏差分布图
Figure 14. Normalized assembly power and bias distribution of HFETR two-dimensional core layout scheme 3
图 13 高通量工程试验堆堆芯布置方案2二维全堆归一化组件功率及偏差分布图
Figure 13. Normalized assembly power and bias distribution of HFETR two-dimensional core layout scheme 2
图 15 方案4堆芯径向布置NECP-X程序建模图
Figure 15. Core layout geometry model for scheme 4 by NECP-X
图 16 高通量工程试验堆堆芯布置方案1三维全堆径向积分归一化组件功率及偏差分布图
Figure 16. Radial integrated normalized assembly power and bias distribution of HFETR three-dimensional core layout scheme 1
图 17 高通量工程试验堆堆芯布置方案4三维全堆径向积分归一化组件功率及偏差分布图
Figure 17. Radial integrated normalized assembly power and bias distribution of HFETR three-dimensional core layout scheme 4
图 18 高通量工程试验堆堆芯布置方案1三维全堆轴向积分归一化组件功率及偏差分布图
Figure 18. Axial integrated normalized power and bias distribution of HFETR three-dimensional core layout scheme 1
图 19 高通量工程试验堆堆芯布置方案4三维全堆轴向积分归一化组件功率及偏差分布图
Figure 19. Axial integrated normalized power and bias distribution of HFETR three-dimensional core layout scheme 4
表 1 单环燃料栅元问题特征值及偏差结果
Table 1. Eigenvalue and bias results for single-ring fuel cell problem
method eigenvalue bias/10−5 calculation time/s reference 1.72257 ±2.0×10−5/ / MRFRCM 1.72300 43 2.38 TSG 1.72300 43 426.72 
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表 2 高通量工程试验堆不同堆芯布置方案二维全堆特征值计算结果
Table 2. Eigenvalue and bias results for different two-dimensional core layout schemes of HFETR
scheme reference keff NECP-X keff bias/10−5 scheme 1 1.04074 ±2.0×10−51.04177 103 scheme 2 1.03544 ±4.0×10−51.03784 240 scheme 3 1.03091 ±2.0×10−51.03066 −25
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表 3 高通量工程试验堆不同堆芯布置方案三维全堆特征值计算结果
Table 3. Eigenvalue and bias results for different three-dimensional core layout schemes of HFETR
scheme reference keff NECP-X keff bias/10−5 scheme 1 1.00131 ±2.0×10−51.00102 −29 scheme 4 1.00109 ±4.0×10−51.00096 −13
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