圆形翅片管换热器计算模型与算法收敛性研究

Research on the Calculation Model and Algorithm Convergence of Cylindrical Fin-tube Heat Exchanger

本文以单排换热管为换热单元,建立了圆筒形翅片管换热器的分排参数数学模型,并提出采用二分法迭代求解换热方程组的数值求解方法,重点讨论了在对单排换热管进行迭代求解时出现的收敛性问题。本文提出两个迭代判据条件,并给出通过求解条件方程零点的方法确定迭代变量(各排换热管的进水温度)的下限值。对模型进行验证,结果表明各排换热管的进水温度迭代下限值是总进水温度的线性递增函数。在总进水温度较低的情况下,该方法可以避免迭代计算进入不合理区间,保证算法稳定收敛。

Cylindrical fin-tube is a new type of heat exchanger,and its mathematical calculation model has not been researched sufficiently.This study establishes a row-parameter model to realize the numerical calculation of cylindrical fin-tube heat exchangers,i.e.,the exchanger is divided into a network of single-row heat exchange tubes and each row is regarded as a heat exchanging unit.The numerical method presents an iterative solution of heat transfer equations using dichotomy method.Herein,the convergence problem in the iterative solution of single-row tubes was discussed in detail.Two iterative criteria were mentioned to guarantee the correct lower limit of the iteration variable(inlet temperature of water of each row).The algorithm was verified,and the results showed that the lower limit of the iteration variable is a linearly increasing function of the inlet water temperature of the heat exchanger.Moreover,for pipelines close to the water outlet of the heat exchanger,the lower limit temperature is higher than the total inlet temperature,which means that the algorithm has practical physical meaning,and could avoid the iteration into the unreasonable interval.