Study on the Influence of Geometric Characteristic Parameters on the Neutron Behavior in Four Petal-shaped Helical Fuel Rod
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摘要: 为弥补四叶形花瓣螺旋燃料棒（FPHF）在中子学计算上的不足，进一步确定FPHF几何特征对其中子行为的影响，本文采用DAG-OpenMC构建了FPHF的精确中子学计算模型。从燃料棒直径、截面形状以及螺旋角三个方面研究了FPHF几何特征对中子行为的影响。燃料棒直径取值为3.5、6.3 mm以及9.5 mm；内凹弧与外凸弧比值的取值范围为[0.1, 3.0]；螺旋角取值为[360°, 1080°]。结果表明，燃料棒直径从3.5 mm增大至9.5 mm时，FPHF的径向功率峰因子增大了5.15%，中子注量率分布的不均匀程度增加；内凹弧与外凸弧比值从0.1增大至3.0时，裂变反应速率Rf降低了0.19%，有效增殖系数keff下降了441.5pcm（1pcm=10–5）；螺旋角对燃料棒的慢化效应以及径向注量率分布的影响可以忽略不计。因此，除燃料棒的螺旋角外，本文研究的燃料棒直径与截面形状对FPHF的中子学特征均有明显影响。
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关键词:
- 四叶形花瓣螺旋燃料棒（FPHF） /
- 中子学特性 /
- DAG-OpenMC
Abstract: To address the deficiencies in neutronics calculations of the Four Petal-shaped Helical Fuel Rod (FPHF) and further determine the influence of the geometric characteristics of the FPHF on its neutron behavior, this paper uses DAG-OpenMC to construct an accurate neutronics calculation model of the FPHF. The study examines the impact of the FPHF's geometric characteristics on neutron behavior from three aspects: fuel rod diameter, cross-sectional shape, and helix angle. The fuel rod diameters are set to 3.5 mm, 6.3 mm, and 9.5 mm; the ratio of the concave arc to the convex arc ranges from 0.1 to 3.0; and the helix angle ranges from 360° to 1080°. The results show that when the fuel rod diameter increases from 3.5 mm to 9.5 mm, the radial power peak factor of the FPHF increases by 5.15%, and the non-uniformity of the neutron flux distribution rises. When the ratio of the concave arc to the convex arc increases from 0.1 to 3.0, the fission reaction rate Rf decreases by 0.19%, and the effective multiplication factor drops by 441.5 pcm (1pcm=10–5). The influence of the helix angle on the moderation effect of the fuel rod and the radial flux distribution is negligible. Therefore, except for the helix angle of the fuel rod, both the fuel rod diameter and cross-sectional shape studied in this paper have significant effects on the neutronics characteristics of the FPHF. -
图 3 不同D值的径向快中子与热中子注量率
Figure 3. Radial Fast and Thermal Neutron Flux at Different D Values
图 4 不同C值的燃料棒截面示意图
Figure 4. Schematic Diagram of Fuel Rod Section at Different C Values
图 6 不同C值的径向快中子与热中子注量率
Figure 6. Radial Fast and Thermal Neutron Flux at Different C Values
图 7 不同C值下中子行为示意图
Figure 7. Schematic Diagram of Neutron Behavior at Different C Values
图 8 不同C值下的裂变可回收能量κ值
Figure 8. κ Values of Fission Recyclable Energy at Different C Values
表 1 不同D值下的keff以及六因子
Table 1. keff and Six Factors at Different D Values
D/mm keff keff标准差 p ε f η PFNL PTNL 3.5 1.55410 2.9×10−4 0.62827 1.28971 0.95932 1.99993 0.99999 0.99969 6.3 1.55765 2.8×10−4 0.61841 1.31450 0.95967 1.99942 0.99990 0.99874 9.5 1.56914 3.0×10−4 0.62479 1.31570 0.95736 1.99933 0.99965 0.99761 
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表 2 D从3.5 mm增加到9.5 mm后六因子对keff的贡献值
Table 2. Contribution Value of the Six Factors to keff for D Value Increasing from 3.5 mm to 9.5 mm
贡献类型 ΔVp ΔVε ΔVf ΔVη $ \Delta V_{P_{\mathrm{FNL}}} $ $ \Delta V_{P_{\mathrm{TNL}}} $ Δkeff 贡献价值 −868.0 +3116.0 −318.5 −46.9 −53.3 −325.4 +1503.7 贡献水平/% −57.7 +207.2 −21.18 −3.1 −3.5 −21.6 +100.0
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表 3 不同D值的径向功率峰因子Fq
Table 3. Radial Power Peak Factor at Different D Values
D/mm Fq 3.5 1.0471 9.5 1.1010
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表 4 不同D值下的核反应速率
Table 4. Nuclear Reaction Rates at Different D Values
D/mm Ra Rf Rs $ \alpha = {{R_{\text{γ }}^{{}^{235}{\text{U}}}} \mathord{\left/ {\vphantom {{R_{\text{γ }}^{{}^{235}{\text{U}}}} {R_{\text{f}}^{{}^{235}{\text{U}}}}}} \right. } {R_{\text{f}}^{{}^{235}{\text{U}}}}} $ 3.5 0.96850 0.63563 24.30486 0.23898 9.5 0.96501 0.64126 24.73698 0.24193
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表 5 不同C值下的keff以及六因子
Table 5. keff and Six Factors at Different C Values
C keff keff标准差 p ε f η PFNL PTNL 0.1 1.57469 3.0×10−4 0.62607 1.31377 0.95908 1.99940 0.99985 0.99853 0.3 1.57342 2.9×10−4 0.62547 1.31403 0.95906 1.99941 0.99985 0.99849 0.6 1.57176 2.8×10−4 0.62446 1.31460 0.95919 1.99938 0.99984 0.998514 0.9 1.57012 3.1×10−4 0.62365 1.31485 0.95922 1.99937 0.99985 0.99855 2.0 1.56661 3.0×10−4 0.62178 1.31580 0.95931 1.99939 0.99984 0.99851 3.0 1.56381 3.2×10−4 0.62069 1.31597 0.95923 1.99939 0.99983 0.99843
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表 6 C值从0.1增加到3.0后六因子对keff的贡献值
Table 6. Contribution Value of Six Factors to keff for C Value Increasing from 0.1 to 3.0
贡献类型 ΔVp ΔVε ΔVf ΔVη $ \Delta V_{P_{\mathrm{FNL}}} $ $ \Delta V_{P_{\mathrm{TNL}}} $ Δkeff 贡献价值 −550.1 106.4 9.9 −0.4 −2.9 −6.1 −441.5 贡献水平/% +124.6 −24.1 −2.2 +0.1 +0.6 +1.4 −100.0
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表 7 不同C值的径向功率峰因子Fq
Table 7. Radial Power Peak Factor at Different C Values
C Fq 0.1 1.0747 3.0 1.0850
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表 8 不同C值下的核反应速率
Table 8. Nuclear Reaction Rates at Different C Values
C Ra Rf Rs $ \alpha = {{R_{\text{γ }}^{{}^{235}{\text{U}}}} \mathord{\left/ {\vphantom {{R_{\text{γ }}^{{}^{235}{\text{U}}}} {R_{\text{f}}^{{}^{235}{\text{U}}}}}} \right. } {R_{\text{f}}^{{}^{235}{\text{U}}}}} $ 0.1 0.96912 0.64478 24.53809 0.24183 3.0 0.96822 0.64351 24.50130 0.24186
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表 9 不同β值的径向功率峰因子Fq
Table 9. Radial Power Peak Factor at Different β Values
β/(°) Fq 360 1.0841 540 1.0915 720 1.0830 900 1.0835 1080 1.0892
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表 10 不同 β 值下的keff以及六因子
Table 10. keff and Six Factors at Different β Values
β/(°) keff keff标准差 p ε f η PFNL PTNL 360 1.55977 3.0×10−4 0.61845 1.31665 0.95959 1.99937 0.99985 0.99857 540 1.55969 3.0×10−4 0.61842 1.31684 0.95951 1.99938 0.99985 0.99849 720 1.55970 2.7×10−4 0.61844 1.31684 0.95948 1.99937 0.99985 0.99851 900 1.55937 2.7×10−4 0.61804 1.31737 0.95950 1.99935 0.99984 0.99851 1080 1.55935 3.0×10−4 0.61830 1.31697 0.95943 1.99937 0.99984 0.99846
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表 11 不同β值下的核反应速率
Table 11. Nuclear Reaction Rates at Different β Values
β/(°) Ra Rf Rs $ \mathit{\mathit{\alpha}}=R_{\text{γ }}^{^{235}\text{U}}\mathord{\left/\vphantom{R_{\text{γ }}^{^{235}\text{U}}R_{\text{f}}^{^{235}\text{U}}}\right.}R_{\text{f}}^{^{235}\text{U}} $ 360 0.96821 0.63735 24.34101 0.24283 540 0.96897 0.63821 24.33805 0.24263 720 0.96785 0.63758 24.37022 0.24256 900 0.96806 0.63782 24.33916 0.24274 1080 0.96945 0.63840 24.34675 0.24254
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