Numerical Study on Oxidation and Dissolution/Precipitation Performances of the ADS Cladding
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摘要: 为开展铅铋合金冷却加速器驱动次临界系统（ADS）堆芯燃料包壳氧化层的生长特性研究，进一步分析存在氧化层的燃料包壳传热，本文建立了ADS包壳氧化层生长和溶解/沉积模型，进一步耦合计算流体动力学（CFD）方法，研究并实现了存在溶解/沉积的包壳氧化层生长和燃料棒温度仿真。对自主设计的多束ADS燃料棒传热和包壳表层氧化、溶解/沉积的研究表明：在高氧浓度下，本文模型与实验吻合度高；最大氧化层厚度、溶解厚度出现在堆芯活性段的高温区，最大沉积厚度出现在低温区的入口端；运行10000 h氧化层总厚度约65 μm，由氧化层引起包壳内外温差增长的最大值为12.20 K。因此，本研究提出的流动液态铅铋环境ADS燃料包壳氧化层生长模型及其数值计算方法可以计算燃料包壳存在氧化层情形的燃料棒温度。
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关键词:
- 加速器驱动次临界系统（ADS） /
- 包壳氧化层 /
- 溶解/沉积 /
- T91不锈钢
Abstract: To investigate the growth characteristics of the oxide scale in the fuel cladding of the lead-bismuth eutectic cooled Accelerator-driven Subcritical System (ADS), and to analyze the heat transfer in the fuel cladding with an oxide scale, the paper proposes a growth and dissolution/deposition model for ADS cladding oxide scale and couple it with the computational fluid dynamics (CFD) method, so as to investigate and realize the simulation of cladding oxide scale growth and fuel rod temperature in the presence of dissolution/deposition. The results of study on fuel rod heat transfer and cladding surface oxidation and dissolution/precipitation of our independently designed multi-beam ADS demonstrate that: the experimental data show a high level of agreement at elevated oxygen concentrations; the maximum oxide scale thickness and dissolution thickness are observed in the high-temperature region of the active zone within the core, while the maximum deposition thickness is in its inlet; the oxide scale reached a thickness of approximately 65 μm after 10000 h, with a maximum increase in temperature difference between the cladding inner and outer surface of 12.20 K. Therefore, ADS fuel cladding surface oxide scale growth model and its numerical calculation method, as proposed in this study, are capable of calculating the fuel rod temperatures for the fuel cladding with oxide scale in the flow liquid lead-bismuth eutectic environment. -
图 2 不同时刻氧化层厚度的实验值[8]与模拟值对比（负数表示向内生长）
Figure 2. Comparison between Simulated Values of Oxide Scale Thickness and Experimental Values at Different Time (Negative Values Represent Inward Growth)
图 5 初始时刻不同高度处流体温度分布云图
Figure 5. Fluid Temperature Distribution Cloud at Different Heights at the Initial Time
图 7 3号燃料棒包壳氧化层分布与生长
Figure 7. Distribution and Growth of Oxide Scale in No. 3 Fuel Rod Cladding
图 8 10000 h时Fe-Cr尖晶石/Fe3O4层厚度和溶解/沉积云图
Figure 8. Thickness and Dissolution/Precipitation Cloud of Fe-Cr Spinel/Fe3O4 at 10000 h
图 9 不同时刻的最高温度和最大温差分布
Figure 9. Distribution of Peak Temperature and Maximum Temperature Difference at Different Time
表 1 元素在LBE内的溶解度[10]
Table 1. Solubility of Some Elements in LBE
元素 a b 温度区间/K Fe 3.14 14190 399~1173 O 1.20 3400 573~1013 a、b—溶解度公式Cs=10a−b/T中的拟合常系数。 
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表 2 消耗1 mol氧对应的吉布斯自由能（400~1000 K）
Table 2. Gibbs Free Energy by Consuming 1 mol O2 (400~1000 K)
反应类型 相应的吉布斯自由能/(J·mol−1) 2Pb+O2=2PbO −437610+199.1·T $\dfrac{3}{2} $Fe+O2=$\dfrac{1}{2} $Fe3O4 −551990+156.9·T
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表 3 相关的参数计算式
Table 3. Expression for Related Parameters
参数 表达式 ${D_{\text{I}}}$ $ D_{\text{I}}=1.22 \times 10^4\exp\left(\dfrac{-27700}{T}\right) \cdot \left[1+1.56 \times 10^6\exp\left(\dfrac{-20100}{T}\right)\right]^{-1} $ ${D_{\text{v}}}$ ${D_{\text{v}}} = 0.177\eta \exp \left( {\dfrac{{ - 14600}}{T}} \right) + 1.16 \times {10^{ - 3}}\left( {1 - \eta } \right)\exp \left( {\dfrac{{ - 8670}}{T}} \right)$ ${K_{\text{I}}}$ ${K_{\text{I}}} = 1.93 \times {10^3}\exp \left( {\dfrac{{ - 43140}}{T}} \right) + 3.01 \times {10^9}\exp \left( {\dfrac{{ - 63270}}{T}} \right)$ ${K_{\text{v}}}$ ${K_{\text{v}}} = 2.04 \times {10^{ - 7}}\exp \left( {\dfrac{{27170}}{T}} \right)$ $a_{{{\text{O}}_{\text{2}}}}^{{\text{ext}}}$ $ a_{\text{O}_{\text{2}}}^{\text{ext}}=\left\{\begin{array}{c}\begin{array}{ll}\mathrm{exp}\left(\dfrac{2\Delta G_{\text{O}\left(\text{PbBi}\right)}^{\text{0}}}{RT}+2\mathrm{ln}\dfrac{M_{\text{PbBi}}}{M_{\text{O}}}+2\mathrm{ln}C_{\text{O}}\right) ,欠氧饱和\mathrm{LBE}环境\end{array} \\ a_{\text{Pb}}^{\text{-2}}\mathrm{exp}\left(\dfrac{2\Delta G_{\text{PbO}}^{\text{0}}}{RT}\right),氧饱和\mathrm{LBE}环境\end{array}\right. $ $a_{{{\text{O}}_{\text{2}}}}^{{\text{int}}}$ $a_{{{\text{O}}_{\text{2}}}}^{{\text{int}}} = a_{{\text{Fe}}}^{{{ - 3/2}}}\exp \left( {\dfrac{{ - 549.05 + 0.1531}}{{RT}}} \right)$ $\eta $ $\eta = {\left[ {1 + 3 \times {{10}^{ - 3}}\exp \left( {\dfrac{{11900}}{T}} \right)} \right]^{ - 1}}$ 参考氧分压为1 bar（1 bar=0.1 MPa）；$\Delta G_{{\text{O}}\left( {{\text{PbBi}}} \right)}^{\text{0}}$、$\Delta G_{{\text{PbO}}}^0$—溶解氧和氧化铅吉布斯自由能；$\eta $—中间变量；MPbBi—铅铋的摩尔质量；MO—氧原子摩尔质量。
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表 4 努塞尔数对比
Table 4. Nu Comparisons
横截面高度/m 0.5 1.0 1.5 2.0 式（17）计算值 21.51 20.77 20.36 20.36 CFD计算值 20.89 20.91 20.90 20.89 相对误差/% 2.89 −0.67 −2.63 −2.61
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