基于导热反问题的二维圆管内壁面第三类边界条件的反演

Inversion of the Third Boundary Condition on the Inner Wall of a Two-dimensional Pipe Based on Inverse Heat Conduction Problems

对于诸如核电领域中有特殊安全要求或结构完备性要求较高的管道系统,不允许在管道开孔来安装温度传感器测量管道内壁面温度和流体温度,需要寻求一种间接无损的方法来预测或评估管道内壁面温度的分布及变化。在有限元法基础上建立温度场数学模型,基于共轭梯度法进行反问题分析,利用圆管外壁面可测的有限温度信息同时反演出第三类边界条件,即内壁面温度、近内壁流体温度以及表面传热系数,并能够获得整个壁面温度的全貌及其分布特征。计算结果及误差分析表明,此方法的精度较高,共轭梯度法能够准确地反演出该圆管内壁的第三类边界条件。该方法不仅可以为结构应力分析和热疲劳分析提供准确的瞬时热载荷,而且为实现一种无损测温方法提供坚实的理论基础。

The piping system with special safety requirements or higher requirements for structural completeness in nuclear power field, are not allowed to install the temperature sensor through opening pore in the pipe to measure the pipe wall temperature and fluid temperature. A kind of indirect and nondestructive method is in need to predict or evaluate the distribution and variations of the inner wall temperature. The mathematical model of temperature field is established based on the finite element method. And the inverse problem analysis is based on the conjugate gradient methods.The third boundary condition-the inner wall temperature, the fluid temperature near the inner wall, and the convective heat transfer coefficient-is simultaneously inverse solved, and the whole picture and distribution of the wall temperature are obtained. The calculation results and the error analysis indicates that the method is with high accuracy and can inverse estimate the third boundary condition precisely. The method can not only offer exact transient thermal load for the structure stress analysis and thermal fatigue analysis, but also provide a solid theoretical basis for achieving a kind of nondestructive measurement method.