竖直埋管地热换热器的稳态温度场分析

Analysis on steady-state temperature field around a vertical borehole in geothermal heat exchangers

对竖直埋管在半无限大介质中的稳态传热模型进行了分析讨论。采用虚拟热源法及线性迭加原理给出了其解析解 ,并绘制了其相应的温度分布曲线图 ,指出了现行教科书中由于混淆绝热边界条件与等温边界条件而得出的关于该问题的错误结论。针对工程实际提出了孔壁中点温度和积分平均温度这两个地热换热器孔壁代表性温度的定义 ,给出了两者的适用于工程应用的简明计算公式 ,并对两者进行了比较。基于以上分析 ,进一步讨论了全年冷热负荷不平衡对地热换热器长期性能的影响。

The heat conduction around a vertical borehole is analyzed and discussed. By means of a virtual heat source and the theory of linear superposition, an analytical solution of the steady state temperature distribution in a semi infinite medium with a line source of finite length is obtained, which is a more appropriate model for boreholes in geothermal heat exchangers. Its temperature field has been drawn up. Meanwhile, a mistake on this solution that appears in some handbooks and textbooks is indicated. Two representative borehole wall temperatures, the temperature at the middle of the borehole and the integral mean temperature along the borehole, are defined. Differences between them are compared, and concise expressions for both of them are presented for engineering applications. On this basis the influence of the annual imbalance between heating and cooling loads of the geothermal heat exchangers is discussed on their long term performance.