Study On Heat Transfer Model Of Vertical Single U-tube Ground Heat Exchanger Of Ground Source Heat Pump

As a renewable energy utilization technology,ground source heat pump(GSHP)has gradually become a research hotspot in the energy saving direction of the construction industry in recent years.Among them,vertical single U-tube ground source heat pump is widely used due to its small footprint and stable performance.The ground heat exchanger is the key device for heat exchange between the ground source heat pump system and the soil,and the rationality of the heat transfer model is critical to the design of the system.However,the existing heat transfer models have some shortcomings.For example,most analytical models ignore the effects of the fluid heat capacity in the tube,the heat capacity of the U-tube,the thermal interference between the two tubes or the nonlinear distribution of fluid temperature,etc,while two-dimensional and three-dimensional numerical models have complex computing time and poor universality.In view of the above deficiencies,this paper proposes three heat transfer models for vertical single U-tube ground heat exchanger,and combines experimental data with other models to verify the accuracy of the these models.Firstly,an analytical model for vertical single U-tube ground heat exchanger is proposed.Based on infinite composite-medium cylindrical source model,and considering the influence of U-tube heat capacity,the average fluid temperature can be calculated,and then combined with a quasi-three-dimensional heat transfer model in borehole,the inlet and outlet fluid temperatures are derived as functions of average fluid temperature and the heat flow,therefore the inlet and outlet fluid temperatures of the U-tube can be calculated.To verify the feasibility of the proposed model,it is applied to a sandbox experiment and compared to other models.The result shows that the inlet and outlet fluid temperatures calculated by the proposed is better than the other models in the whole time period,and the four errors are basically small.The mean absolute errors of the inlet and outlet fluid temperatures predicted are 0.11 ?and 0.09 ?,respectively,and the maximum absolute errors are less than 0.4 ?.Secondly,the analytical model established above assumes that the heat transferwithin the U-tube is a steady state heat transfer,which will cause some errors.Therefore,a hybrid model for vertical single U-tube ground heat exchanger is proposed.The hybrid model consists of two parts: First,the single U-tube is simplified as an equivalent pipe,and a one-dimensional numerical model is established to calculate the average fluid temperature and borehole wall temperature;then based on a quasi-three-dimensional model,the inlet and outlet fluid temperatures of the U-tube are derived as functions of the average fluid temperature and borehole wall temperature,therefore the inlet and outlet fluid temperatures of the U-tube can be calculated.To verify the feasibility of the proposed model,it is applied to an uninterrupted sandbox test and an interrupted sandbox test,and the calculated inlet and outlet fluid temperatures are compared with experimental data and the results of other models.Compared with other models,the fluid temperatures calculated by the proposed model are in better agreement with the experimental data especially during the short time and the interruption time,and four kinds of errors of the model are basically smaller.The absolute errors of the fluid temperatures calculated by the proposed model are less than 0.23 ? except during the early 4hours and the interruption time.Finally,due to the complexity of the ground source heat pump system,the heat flow between the fluid in the U-tube and the surrounding medium may be unknown,and the temperature of the inlet fluid may be known.Therefore,a hybrid model for vertical single U-tube ground heat exchanger under the condition of inlet fluid temperature is proposed.First,based on the above mentioned vertical single U-tube hybrid model,a one-dimensional radial numerical model with variable inlet fluid temperature is established to calculate the average fluid temperature,then,based on the quasi-three-dimensional heat transfer model in the borehole,the borehole wall temperature are derived as functions of average fluid temperature and the inlet fluid temperature,therefore the borehole wall temperature can be calculated,and then the outlet fluid temperatures and the heat flow can be calculated.To verify the feasibility of the proposed model,it is applied to an uninterrupted sandbox test,and thecalculated outlet fluid temperatures and the heat flow are compared with experimental data.The results show that the heat flow calculated by this model has a certain deviation,and the calculated outlet fluid temperatures are in good agreement with the experimental value in the whole time period.In addition,four errors of the outlet fluid temperature and the heat flow are calculated.The maximum absolute error of heat flow is large,while the other three errors are small,and the mean absolute error is 18.02 W.The four errors of the outlet fluid temperature are small,and the maximum absolute error and the mean absolute error are 0.47 ? and 0.05 ?,respectively.