Application of Power Function Model of Gas Leakage in Tightness Test of Double-wall Containment Annulus
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摘要: 双层安全壳核电机组的环廊密封性是核安全的重要保证，需在机组装料前完成测试。气体泄漏幂函数模型在计算民用建筑泄漏时比二次函数模型有更大的压力适用范围和更高的精度。本文以气体泄漏幂函数模型为基础，推导了环廊泄漏率的计算模型，以及带环廊负压修正的幂函数拟合方案，并采用某双层安全壳环廊密封性试验实测数据对该计算模型进行验证。结果表明，本文计算模型比带环廊负压修正的二次函数拟合方案和国外某公司使用的线性拟合方案有更高的精度，与双层安全壳实际泄漏情况更加吻合。Abstract: The tightness of the annulus of the nuclear power unit with double-wall containment is an important guarantee of nuclear safety, which needs to be tested before the unit is loaded. The power function model of gas leakage has a wider range of pressure application and higher accuracy than the quadratic function model for calculating the leakage of civil buildings. In this paper, based on the power function model of gas leakage, the calculation model of annulus leakage rate and the power function fitting scheme with annulus negative pressure correction are derived, and the calculation model is verified by the measured data of a double-wall containment annulus tightness test. The results show that the calculation model in this paper has higher accuracy than the quadratic function fitting scheme with annulus negative pressure correction and the linear fitting scheme used by a foreign company, and is more consistent with the actual leakage of double-wall containment.
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Key words:
- Double-wall containment /
- Annulus /
- Tightness /
- Leakage rate
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图 1 环廊泄漏率试验典型压力循环曲线
Figure 1. Typical Pressure Cycle Curve of Annulus Leakage Rate Test
图 2 内外压力平衡过程中环廊气体平均温度
Figure 2. Average Temperature of Annulus Gas during Internal and External Pressure Balance
图 4 使用幂函数对循环2的拟合结果
Nm3—在0℃、1个标准大气压下的气体体积
Figure 4. Fitting Result of Cycle 2 Using Power Function
图 5 循环2各压差下泄漏率的幂函数拟合残差
Figure 5. Power Function Fitting Residual of Leakage Rate under Each Pressure Difference in Cycle 2
表 1 使用幂函数进行拟合的结果
Table 1. Results of Fitting with Power Function
试验循环 $ {C'_{\text{e}}} $ $ {m'_{\text{e}}} $ $ {P'_{{\text{dr}}}} $/Pa RSS r2 环廊泄漏率/(Nm3·h−1) Pdd=620 Pa Pdd=1303 Pa 循环2 0.6145 0.680 88 62.8 0.9993 43.87 76.92 循环3 0.4976 0.705 46 63.5 0.9995 43.84 76.19 循环4 0.5357 0.698 67 21.2 0.9996 43.99 77.12 循环5 0.5311 0.699 61 44.5 0.9995 44.22 77.26 循环6 0.4239 0.732 71 43.6 0.9995 42.92 77.55 
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表 2 使用二次函数进行拟合的结果
Table 2. Results of Fitting with Quadratic Function
试验循环 RSS r2 $ {P'_{{\text{dr}}}} $/Pa 环廊泄漏率/ (Nm3·h−1) Pdd=620 Pa Pdd=1303 Pa 循环2 72.2 0.9992 135 44.00 78.00 循环3 84.7 0.9994 85 43.97 77.10 循环4 23.5 0.9995 115 44.11 78.05 循环5 47.7 0.9994 115 44.81 78.95 循环6 46.2 0.9995 105 42.97 78.59
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表 3 使用线性函数进行拟合的结果
Table 3. Results of Fitting with Linear Function
试验循环 RSS r2 环廊泄漏率/ (Nm3·h−1) Pdd=620 Pa Pdd=1303 Pa 循环2 855.8 0.9904 41.95 76.87 循环3 1174.7 0.9915 41.58 75.50 循环4 315.8 0.9936 43.19 77.27 循环5 634.1 0.9924 43.54 77.05 循环6 741.5 0.9918 40.66 78.58
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表 4 3种拟合方案的比较
Table 4. Comparison of Three Fitting Methods
项目 线性拟合 二次函数拟合 幂函数拟合 RSS取值范围 315.8~1174.7 23.5~84.7 21.2~63.5 r2取值范围 0.9904~0.9936 0.9992~0.9995 0.9993~0.9996 $ {P'_{{\text{dr}}}} $取值区间/Pa 85~135 46~88 试验结果的最大偏差/ (Nm³·h−1) Pdd=620 Pa 1.52 1.00 0.85 Pdd=1320 Pa 1.55 1.04 0.82 试验结果的标准差/ (Nm³·h−1) Pdd=620 Pa 1.18 0.66 0.50 Pdd=1320 Pa 1.10 0.70 0.51
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