The Green’s Function-Based Thermal Analysis of a Spherical Geothermal Tank in a Semi-Infinite Domain
The Green’s Function-Based Thermal Analysis of a Spherical Geothermal Tank in a Semi-Infinite Domain
复制标题
半无限域中球形地热罐基于格林函数的热分析
DOI：
10.1115/1.4054568
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Yin, Huiming
中科院分区：
文献类型：
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作者：
Wang, Tengxiang;Wu, Chunlin;Zhang, Liangliang;Yin, Huiming
将具有平面界面的双材料无限域的绿色函数应用于球形地下储热罐的热分析。球热源的热传递是由球域上的绿色函数的积分导出的。由于储罐的导热系数与土壤的导热系数不同，采用Eshelby等效夹杂法（EIM）模拟储罐与土壤的导热系数失配。为了简单起见，在地面上具有近似均匀温度的地面由双材料无限域来模拟，该无限域在地面上方是完全导电的。研究了两种情况下的地下热传导：第一，考虑了从地表到地下的稳态均匀热通量，由于导热系数失配，热通量被水箱的存在所干扰。通过引入一个给定的温度梯度或特征温度梯度来研究储罐附近的局部温度场。其次，当水箱中的水与土壤之间存在温差时，水箱与土壤之间的热传递取决于水箱尺寸、传导率和温差，这为水箱尺寸的换热设计提供了指导。模型框架可以扩展到二维情况下，周期性的，或瞬态热传递问题的地热井操作。为这些应用提供了相应的绿色函数。
The Green’s function of a bimaterial infinite domain with a plane interface is applied to thermal analysis of a spherical underground heat storage tank. The heat transfer from a spherical source is derived from the integral of the Green’s function over the spherical domain. Because the thermal conductivity of the tank is generally different from soil, the Eshelby’s equivalent inclusion method (EIM) is used to simulate the thermal conductivity mismatch of the tank from the soil. For simplicity, the ground with an approximately uniform temperature on the surface is simulated by a bimaterial infinite domain, which is perfectly conductive above the ground. The heat conduction in the ground is investigated for two scenarios: First, a steady-state uniform heat flux from surface into the ground is considered, and the heat flux is disturbed by the existence of the tank due to the conductivity mismatch. A prescribed temperature gradient, or an eigen-temperature gradient, is introduced to investigate the local temperature field in the neighborhood of the tank. Second, when a temperature difference exists between the water in the tank and soil, the heat transfer between the tank and soil depends on the tank size, conductivity, and temperature difference, which provide a guideline for heat exchange design for the tank size. The modeling framework can be extended to two-dimensional cases, periodic, or transient heat transfer problems for geothermal well operations. The corresponding Green’s functions are provided for those applications.