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高压容器在焊接以后,必须进行去应力退火。对体积庞大的高压容器,应用电红外加热器沿焊缝进行加热并退火是一种最为经济、有效的方法。要正确使用这种方法,必须研究焊缝附近在加热过程中的温度场。本文分析了这种退火方法,提出了研究温度场的物理数学模型,得到了在复杂的边界条件下二维稳定和不稳定温度场的偏微分方程式。在作了两点合理的假定以后,用一种比较巧妙的方法,把一个二维的偏微分方程式转化为两个一维常微分方程式。然后,以数学分析和拉普拉斯变换为工具,求得了在复杂的边界条件下,二维稳定温度场和加热升温过程中二维不稳定温度场的数学分析解。所得的分析解与数值解差不多完全符合。
After the high-pressure vessel welding, stress relief annealing must be carried out. For bulky pressure vessels, the use of electric infrared heaters along the weld heating and annealing is the most economical and effective method. To correctly use this method, you must study the temperature field near the weld during heating. In this paper, we analyze the annealing method and propose a physical mathematic model to study the temperature field. We obtain the partial differential equations of the two-dimensional steady and unstable temperature fields under complicated boundary conditions. After making two reasonable assumptions, a two-dimensional partial differential equation is transformed into two one-dimensional ordinary differential equations in a clever way. Then, with mathematical analysis and Laplace transform, the mathematical analytical solutions of two-dimensional unstable temperature field and two-dimensional unstable temperature field under complex boundary conditions are obtained. The analytical solution obtained is almost exactly in accordance with the numerical solution.