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Numerical Modeling of the Transient Thermal Interference of Vertical U-Tube Haet Exchangers
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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.
Muraya, Norman K. (1994). Numerical Modeling of the Transient Thermal Interference of Vertical U-Tube Haet Exchangers. Available electronically from