Research of Double-Heterogeneity Physical Boundary on Dispersed Particle-type Systems
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摘要: 弥散颗粒系统由于双重非均匀性而无法用传统中子学计算程序描述，直接采用体积均匀化方法处理会带来反应性计算偏差。本文通过分析弥散颗粒燃料及不同类型弥散颗粒可燃毒物的体积均匀化反应性计算偏差及其与光学长度的关系，提出将计算偏差的影响因素整合为修正光学长度，提出了弥散颗粒系统双重非均匀性的物理边界，当修正光学长度大于10−4时，体积均匀化方法的反应性计算偏差将大于100pcm（1pcm=10−5），需要考虑弥散颗粒系统的双重非均匀性。Abstract: Dispersed particle-type systems cannot be described with traditional neutronics calculation programs because of the double-heterogeneity (DH), and the direct use of Volumetric Homogenization Method (VHM) will bring reactivity calculation deviation. In this paper, by analyzing the calculation deviation of volumetric homogenization reactivity of dispersed particle fuel and different types of dispersed particle burnable poison and its relationship with optical length, it is proposed that the influence factors of calculation deviation shall be integrated into corrected optical length. The physical boundary of double-heterogeneity of dispersed particle-type system is proposed. When the corrected optical length is greater than 10−4, the reactivity calculation deviation of the volumetric homogenization method will be more than 100pcm, so the double-heterogeneity of the dispersed particle-type system needs to be taken into account.
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图 1 弥散颗粒在基体中随机分布示意图
Figure 1. Schematic Diagram of Random Distribution of Dispersed Particles in Matrix
图 2 弥散颗粒燃料栅元体积均匀化方法反应性偏差
Figure 2. Reactivity Deviation of Volumetric Homogenization Method on Dispersed Particle Fuel Cell
图 3 弥散颗粒可燃毒物栅元体积均匀化方法反应性偏差
Figure 3. Reactivity Deviation of Volumetric Homogenization Method on Burnable Poison Cell of Dispersed Particle
图 4 不同富集度下体积均匀化反应性计算偏差与修正光学长度关系
Figure 4. Relationship between Calculation Deviation of Volumetric Homogenization Reactivity and Corrected Optical Length under Different Enrichments
图 5 不同颗粒相体积下体积均匀化方法反应性计算偏差与修正光学长度关系
Figure 5. Relationship between Calculation Deviation of Volumetric Homogenization Reactivity and Corrected Optical Length under Different Particle Phase Volumes
图 6 体积均匀化反应性计算偏差与光学长度关系
Figure 6. Relationship between Calculation Deviation of Volumetric Homogenization Reactivity and Optical Length
表 1 燃料栅元主要参数
Table 1. Main Parameters of Fuel Cell
参数名 参数值 栅距/cm 1.26 燃料区半径/cm 0.4096 气隙厚度/cm 0.0084 Zr包壳厚度/cm 0.057 Zr包壳密度/(g·cm−3) 6.5 慢化剂密度/(g·cm−3) 1.0 
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表 2 弥散颗粒燃料及可燃毒物颗粒模型参数取值
Table 2. Model Parameter Values for Dispersed Particle Fuel and Burnable Poison Particle
参数名 参数值 可燃毒物类型 Ag/In/Cd/Hf/B4C/Dy2O3/Er2O3/Eu2O3/Gd2O3 可燃毒物颗粒半径/μm 10~250 可燃毒物颗粒体积份额/% 1~10 燃料富集度/% 10~90 燃料颗粒类型 UO2 燃料颗粒半径/μm 100~400 燃料颗粒体积份额/% 3~30 燃料颗粒芯体富集度/% 10~90 弥散颗粒燃料系统基体 Zr
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