Non-linear finite element models were developed to simulate transient heat and mass transfer in the soil surrounding the ground heat exchangers of ground-coupled heat pumps (GCHPs) operating in the cooling mode. Parametric studies were performed with two dimensional horizontal cross sectional models. The heat transfer and temperature distributions yielded excess errors less than 6% and 3%, respectively, when compared to analytical solutions. Two constant temperature sources performed equivalent heating as one constant temperature source having twice the radius. For constant heat flux sources, the equivalent radius was found to be increased by ?2. A heat flux equivalent radius (tau_h,eqv) was developed and shown to be more consistent than the geometric radius (tau_g,eqv). All equivalent radii varied with time and source separation. A heat exchanger effectiveness for two sources, (epsilon_A), was introduced based on an earlier definition for one source. Effectiveness was found to be independent of a dimensionless temperature variable that included temperatures of the tubes and soil, and varied only with separation distance at steady state. Thermal short circuiting was defined as 1 ? epsilon_A and ranged from 38% to 47% in the reasonable installation separation range. Non-homogenous media were modeled by varying backfill thermal conductivity. Maximum heat transfer was achieved with a fictitious backfill thermal conductivity of 1,000 W/m-K, while measured bentonite backfill conductivities were less than 2 W/m-K. The overall heat transfer increased with backfill thermal conductivity but epsilon_A decreased. Therefore, the backfill effectiveness of Couvillion was used to rank backfill performance. The range of the backfill effectiveness was from 45% for touching bentonite backfill tubes to 60% for the fictitious backfill at a separation of seven l/Do. Moisture migration was incorporated into the numerical finite element model by formulating coupled partial differential equations for non-linear heat and mass transfer. Simulations with decreasing soil moisture contents resulted in lower thermal conductivity and performance degradation. Increasing the bore hole size improved the efficiency (decreased thermal short circuiting) by as much as 20%. In addition, higher conductivity fictitious backfills improved efficiency by up to an additional 20%. However, cost savings in both cases had a negligible effect compared to the bore hole cost.
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机译：开发了非线性有限元模型，以模拟在冷却模式下运行的地面耦合热泵（GCHP）的地面换热器周围土壤中的瞬态传热和传质。用二维水平横截面模型进行参数研究。与分析解决方案相比，传热和温度分布产生的误差分别小于6％和3％。两个恒温源进行的加热等效于一个半径为两倍的恒温源。对于恒定的热通量源，发现等效半径增加了φ2。发展了热通量等效半径（tau_h，eqv），并显示出比几何半径（tau_g，eqv）更一致。所有等效半径随时间和源分离而变化。根据一个源的更早定义，引入了两个源（epsilon_A）的热交换器效率。发现有效性独立于无量纲的温度变量，该变量包括管子和土壤的温度，并且仅在稳定状态下随分离距离而变化。热短路定义为1？在合理的安装间隔范围内，epsilon_A为38％至47％。通过改变回填热导率对非均质介质进行建模。假想的回填热导率为1,000 W / m-K，实现了最大的传热，而测得的膨润土回填电导率小于2 W / m-K。总的热传递随着回填热导率的增加而增加，但ε_A减小。因此，使用Couvillion的回填效果来对回填效果进行排名。回填效果的范围从接触膨润土回填管的45％到虚拟回填的60％（间隔为7 l / Do）。通过为非线性传热和传质建立耦合偏微分方程，将水分迁移纳入数值有限元模型。降低土壤水分含量的模拟导致较低的热导率和性能下降。增加钻孔尺寸可将效率提高（减少热短路）达20％。此外，更高电导率的虚拟回填可将效率提高多达20％。但是，与钻孔成本相比，在两种情况下节省的成本都可以忽略不计。
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