یک مدل شبیه سازی دو منطقه ای از لوله عمودی U شکل -مبدل گرمایی زمین و تأیید تجربی آن

Heat transfer around vertical ground heat exchanger (GHE) is a common problem for the design and simulation of ground coupled heat pump (GCHP). In this paper, an updated two-region vertical U-tube GHE analytical model, which is fit for system dynamic simulation of GCHP, is proposed and developed. It divides the heat transfer region of GHE into two parts at the boundary of borehole wall, and the two regions are coupled by the temperature of borehole wall. Both steady and transient heat transfer method are used to analyze the heat transfer process inside and outside borehole, respectively. The transient borehole wall temperature is calculated for the soil region outside borehole by use of a variable heat flux cylindrical source model. As for the region inside borehole, considering the variation of fluid temperature along the borehole length and the heat interference between two adjacent legs of U-tube, a quasi-three dimensional steady-state heat transfer analytical model for the borehole is developed based on the element energy conservation. The implement process of the model used in the dynamic simulation of GCHPs is illuminated in detail and the application calculation example for it is also presented. The experimental validation on the model is performed in a solar-geothermal multifunctional heat pump experiment system with two vertical boreholes and each with a 30 m vertical 1 1/4 in nominal diameter HDPE single U-tube GHE, the results indicate that the calculated fluid outlet temperatures of GHE by the model are agreed well with the corresponding test data and the guess relative error is less than 6%.

Ground coupled heat pump (GCHP) has been showed to be a very efficient method of providing heating and cooling for residential and commercial buildings compared with traditional HVAC equipment and is widely accepted as one of the best renewable energy technology. A typical GCHP system consists of a conventional heat pump coupled with a ground heat exchanger (GHE). In common configurations, the GHE consists of loops installed in a horizontal or vertical style. Currently, for most buildings, a vertical U-tube GHE configuration is usually preferred over horizontal style because it requires less ground area and offers better performance than the horizontal due to smaller seasonal swing in the ground mean temperature. Recent research in the GCHP field has contributed to reducing the life cycle and to broadening the application of this technology. One important research area is modelling, which allows system dynamic simulations to be performed. For GCHP system, simulation is an important tool for system optimization design purpose as well as for investigating long-term system performance. For this a reliable and feasible heat transfer analysis model of GHE is required. Currently, there have been a number of models that can predict transient heat transfer in vertical U-tube GHE. The models are mostly based on either some analytical solutions like line source heat source theory proposed by Ingersoll and Plass [1] and cylindrical heat source theory first presented by Carslaw and Jaeger [2] and Ingersoll et al. [3] and later refined by Deerman and Kavanaugh [4] or numerical solutions like the one proposed by Eskilson’s [5] and Hellstrom [6] that were used for designing vertical boreholes used in GCHP systems.

For the optimum design of GCHP system, it is necessary to estimate its performance and economic feasibility before the installation of the system. In this paper, a two-region analytical solution model, which divided the heat transfer region of vertical U-tube GHE into two parts at the boundary of borehole wall, was proposed and developed to simulate the heat transfer process of a vertical U-tube GHE used in GCHP system. The model considered the effect of fluid temperature along the borehole length and heat interference between two adjacent legs of U-tube simultaneously. The variations of outlet fluid temperature of GHE, borehole wall temperature and COP of heat pump with the operation time are all included and analyzed by an example calculation. The accuracy of the present model is also verified by the experimental data obtained in this paper. The conclusions can be summarized as: (1) The outlet fluid temperature of GHE, borehole wall temperature and COP of heat pump all drop deeply during the startup time, and then the drop extent gradually become tardiness when the operation time exceeds about 200 h. (2) The performance of the GCHP system is very unstable during the starting stage and is strongly affected by the ground initial temperature. But it will reach a quasi-steady state when the operation time exceeds the starting stage and then is affected mainly by the variation of building load. (3) Due to the heat transfer inside borehole is approximately treated as steady-state in the model, the guess accuracy of the model during the startup time (such as the first 7 h in this paper) is affected. But this effect is little and can be neglected for a long-time dynamic simulation of GCHPs. (4) The experimental validations show that the guess absolute error of average outlet temperature of GHE by the model is less than 0.5 °C and the relative error is less than 6%, which is acceptant in engineering application.