Estimation of Inner Wall Temperature in a Two-Dimensional Pipeline for Inverse Heat Conduction Problem Based on Green’s Function
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摘要: 核电厂某些管道系统不允许通过开孔安装温度传感器来测量管道内壁温度，需要通过间接无损的方法来获得管道内壁的温度波动。基于格林函数法进行导热反问题分析，利用二维管外壁温度反向推导内壁温度。通过算例验证，并与共轭梯度法进行对比。结果表明，采用格林函数法能够准确地获得管道内壁温度波动；对于采用共轭梯度法难以收敛的厚壁管导热反问题也同样适用，并且由于无需迭代，因此计算效率高很多，更适用于核电厂疲劳监测计算。Abstract: It is not allowed to install the temperature sensor through the opening pore in the pipe to measure the inner wall temperature for some pipe systems in nuclear power plants, and thus it is necessary to find an indirect and non-destructive method to obtain the inner wall temperature fluctuations. The inverse heat conduction problem is analyzed based on Green’s function to achieve the inner wall temperature according to the out wall temperature of the pipeline. It is verified by examples and compared with the conjugate gradient method. Results show that the Green’s function method can accurately catch the inner wall temperature fluctuation of the pipe and is applicable for the thicker wall pipe inverse heat conduction problem which is difficult to converge used by the conjugate gradient method. And because there is no need for iteration, the calculation efficient is much higher, which is more suitable for the fatigue monitoring calculation in nuclear power plants.
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图 2 实验值一100 s时内壁温度径向分布
Figure 2. Radial Temperature Distribution of Inner Wall of Experimental Temperature 1 at 100 s
图 4 实验值二67 s时内壁温度径向分布
Figure 4. Radial Temperature Distribution of Inner Wall of Experimental Temperature 2 at 67 s
图 7 实验值一管道−90°处内壁温度计算值
Figure 7. Calculated Temperatures for Experimental Temperatures 1 at −90°
图 8 实验值二管道90°处内壁温度计算值
Figure 8. Calculated Temperatures for Experimental Temperatures 2 at 90°
表 1 内壁温度反推值最大误差
Table 1. Maximum Error of Calculated Temperature of Inner Wall
内壁实验温度 格林函数反推 共轭梯度法 实验值 内壁径向分布 误差
/℃CPU
时间/s误差
/℃CPU
时间/s实验值一 牛顿多项式 0.1 52 0.42 1045 线性 3.2 52 3.8 1069 实验值二 牛顿多项式 0.1 37 0.97 731 线性 1.5 36 1.9 728 
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