地源热泵竖直埋管的有限长线热源模型

A Model of Finite-length Linear Heat-source for the Vertical Embedded Pipe of a Ground-source Heat Pump

对地热换热器竖直埋管的非稳态传热模型进行了分析讨论。采用虚拟热源和格林函数法给出了半无限大介质中有限长线热源产生的非稳态温度场的解析解表达式。与稳态温度场的解进行比较 ,讨论了温度场达到名义上的“稳态”所需的时间 ,同时对于达到稳态时的温度场也进行了分析 ,指出了现行教科书中关于该问题的错误 ,提出了稳态时两个地热换热器孔壁代表性温度的定义 ,并对两者进行了比较 ,进而给出了可供工程应用的简化计算公式。基于以上分析 。

Analyses and discussions were conducted of a non steady heat transfer model for the vertical embedded pipe of a geothermal heat exchanger. With the use of a virtual heat source and Green function method obtained is an analytical solution expression for the non steady temperature field generated by a finite length linear heat source in semi infinite large media. By way of comparison with a steady state temperature field solution discussed is the time required for the temperature field to attain a nominal 'steady state'. Meanwhile, an analysis is performed of the temperature field when it has reached a steady state. In this connection a mistake that appeared in current textbooks was indicated. Two representative steady state borehole wall temperatures, i.e., the temperature at the middle of the borehole and the integral mean temperature along the borehole, are defined. A comparison of the difference between these two temperatures has led to a simplified calculation formula, suitable for engineering applications. On the basis of the above analyses discussed further is the impact of the annual imbalance between heating and cooling loads of geothermal heat exchangers on their long term performance.