Calculation and Analysis of Multiscale Coupling of Dispersion Plate-type Fuel
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摘要: 弥散型板状燃料两相弥散材料的多尺度特点对其性能研究提出了挑战。为准确分析与评价U3Si2/Al弥散型板状燃料在堆内的性能，在已有的U3Si2/Al弥散型芯体的等效物性、行为模型基础上，针对等效芯体较为复杂的蠕变特性，建立其蠕变衰减系数模型以准确模拟两相复合材料的蠕变行为。同时，构建了三维燃料板模型、一维颗粒球模型，并提出了将三维燃料板模型与一维颗粒球模型耦合的跨尺度耦合方法，以在宏观分析的同时，获取燃料芯体各部位微观颗粒行为。基于跨尺度多物理场耦合分析工具，开展针对弥散型燃料的多物理场分析，并对燃料颗粒的尺寸与体积份额的影响进行了评估。结果显示，增加颗粒的尺寸和体积份额只略微提高燃料中心温度，影响可忽略；当体积份额从30%提升到40%时，燃料颗粒应力增加11.6%。Abstract: The multi-scale characteristics of two-phase dispersion materials in dispersion-type plate fuel pose challenges to its performance research. To accurately analyze and evaluate the in-pile performance of U3Si2/Al dispersion-type plate fuel, based on the existing equivalent physical properties and behavior model of U3Si2/Al dispersion fuel meat, the creep attenuation coefficient model was established to accurately simulate the creep behavior of two-phase composites, particularly focusing on the complex creep characteristics of the equivalent fuel meat. Additionally, a three-dimensional macroscopic fuel plate model and a one-dimensional sphere model were constructed, and a multi-scale coupling method was proposed to couple these models, enabling simultaneous simulation at both scales. Based on the multi-scale multi-physics coupling analysis tool, the multi-physical field analysis of U3Si2/Al dispersion-type fuel was conducted, and the impact of fuel particle size and volume fraction was evaluated. The results inidcate that increasing the particle size and volume fraction only slightly increases the central temperature of the fuel; however, when the volume fraction increases from 30% to 40%, the fuel particle stress increases by 11.6%.
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图 1 MMC蠕变衰减系数与颗粒体积份额的关系
Figure 1. Relationship Between MMC Creep Reduction Factor and Particle Volume Fraction
图 2 RVE模型与不同等效单元模型在蠕变作用下的应变变化
Figure 2. Strain Variation under Creep for RVE and Different Equivalent Models
图 5 跨尺度耦合模型计算结果同其他模型的对比
Figure 5. Comparison of Calculation Results of Multi-scale Coupling Model with Other Models
图 6 各模型燃料颗粒与基体界面处径向与环向应力对比
Figure 6. Comparison of Radial and Hoop Stresses at the Fuel Particle-Matrix Interface for Each Model
图 7 1/8 JRR-3M标准燃料元件示意图
Figure 7. Schematic Diagram of 1/8 JRR-3M Standard Fuel Element
图 8 等效芯体静水压力分布及其关键部位微观颗粒径向应力分布
A、D、E、F、G、H—关键部位编号
Figure 8. Hydrostatic Pressure Distribution of the Equivalent Fuel Meat and Radial Stress Distribution of Microscopic Particles at Key Locations
图 9 各位置处燃料径向应力随燃料板最高燃耗的变化
Figure 9. Variation of Fuel Radial Stress at Various Positions with Maximum Burnup of Fuel Plate
图 11 不同燃料颗粒半径下宏观芯体中心颗粒温度分布
Figure 11. Distribution of Particle Temperature at the Center of Macroscopic Fuel Meat for Different Fuel Particle Radii
图 12 不同燃料颗粒半径下宏观芯体A点处燃料应力随燃耗的变化
Figure 12. Variation of Fuel Stress at Point A in the Macroscopic Fuel Meat with Burnup for Different Fuel Particle Radii
图 13 不同体积份额下芯体中心处一维颗粒温度分布
Figure 13. Temperature Distribution of One-Dimensional Particle at the Fuel Meat Center under Different Volume Fraction
图 14 不同体积份额下芯体中心体应变随燃耗的变化
Figure 14. Variation of Fuel Meat Center Volumetric Strainwith Burnup under Different Volume Fraction
图 15 不同体积份额下芯体应力最大点（A点）应力随燃耗变化
Figure 15. Variation of Stress with Burnup at the Maximum Stress Point (A) of the Fuel Meat under Different Volume Fraction
图 16 包壳B点VonMises应力随燃耗的变化
Figure 16. Variation of Von Mises Stress with Burnup at Point B of the Fuel Cladding
图 17 A点燃料颗粒的径向应力随燃耗变化
Figure 17. Variation of Radial Stress with Burnup at Point A of Fuel Particle
表 1 跨尺度耦合方法综合验证算例输入参数
Table 1. Input Parameters for Verification Cases of Multi-Scale Coupling Method
参数名 参数值 体积份额/% 40 颗粒尺寸/μm 25 压力/MPa 300 温度/K 400 裂变率/ (s−1·cm−3) 1.2×1014 时间/s 1×107 最大燃耗/%FIMA（FIMA表示已裂变
原子数与初始的总装料金属原子数之比）10.0 
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表 2 跨尺度耦合模拟输入参数
Table 2. Input Parameters for Multi-Scale Coupling Simulation
参数名 参数值 芯体等效体功率/(W·m−3) 3.68636×109×cos[(y/0.77)×3.14)]
（y为Y轴坐标，m）最大快中子注量率/(m−2·s−1) 2.0×1018 最大燃耗/%FIMA 20 冷却剂温度/K 313.15 对流换热系数/(W·m−2·K−1) 25000 冷却剂压力/MPa 0.152
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