外壁恒温条件下单管冻结温度场解析计算

针对外壁恒温条件下单管冻结相变热传导问题，根据冻结峰面分成冻结区和未冻结区，采用变量替换方法进行了温度场解析分析，获得了冻结峰面半径与冻结时间呈平方根关系，以及采用指数积分函数表示冻结区和未冻结区温度以及相应无量纲温度的计算公式；为数值计算简便，给出了冻结温度场中指数积分函数的高精度低阶多项式表示；获得了冻结管壁热流密度的解析算式。通过算例说明了外壁恒温条件下单管冻结温度场的分布规律，结果显示，冻结温度场呈对数型函数分布，且其曲率随冻结时间的增加而迅速减小，以及未冻区范围约为冻结峰面半径的4倍。

Analytical Formulation of Temperature field of single Freezing Pipe with Constant Outer Surface Temperature

In the freeze sinking method, it is required to determine the temperature field of frozen wall and freeze capacity of freezing station. In this paper, aiming at the phase transition of thermal conduction in the outer wall temperature constant condition for a single freezing pipe, frozen field and non-frozen field are separated by the freezing frontal edge, the temperature field is analyzed using the method of variable substitution. The obtained relation between the radius of freezing frontal edge and freezing time follows the square root equation like this form, ，the temperature distribution of frozen field and non-frozen field and the corresponding formula for calculating the dimensionless temperature are expressed by an exponential integral function. For the easiness of numerical calculation, the higher precision and lower derivative polynomial expression of exponential integral function is given. And the analytical formula about the heat flux of freezing pipe’s wall is obtained. The distributing laws of temperature field for a single freezing pipe in the outer wall temperature constant condition are explained by example in the end. The result shows that the temperature field for a single freezing pipe is similar to a logarithmic function, its curvatures decrease with the increment of the freezing days, and unfrozen surface area is longer about 4 times than the radius of the freezing frontal edge.