Prediction and parametric analysis of 3D borehole and total internal thermal resistance of single U-tube borehole heat exchanger for ground source heat pumps

The borehole and total internal thermal resistance are both significant parameters in evaluating the thermal performance of the ground source heat pump.This study aimed to obtain the accurate correlation of the 3D borehole and total internal thermal resistance(R_(b,3D)and R_(a,3D))and analyze the impacts of parameters on the R_(b,3D)and R_(a,3D).Firstly,eight parameters affecting the R_(b,3D)and R_(a,3D),including the borehole diameter,pipe diameter,pipe-pipe distance,borehole depth,soil thermal conductivity,grout thermal conductivity,pipe thermal conductivity,and fluid velocity inside the pipe,were considered and an L-54 design matrix was generated.Then,the 3D numerical model,coupling with the four-resistance model,was proposed to calculate R_(b,3D)and R_(a,3D)for each case.After that,the response surface methodology was employed to obtain and verify the correlation of R_(b,3D)and R_(a,3D),which were compared with the existing resistance calculation methods.Lastly,analysis of variance was carried out to reveal parameters that have statistically significant impacts on the R_(b,3D)and R_(a,3D).Results show that the rationality and accuracy of the correlation of R_(b,3D)and R_(a,3D)can be verified by the determination coefficient and P value of regression model,as well as the P value of lack-of-fit.The existing resistance calculation methods are more or less inaccurate and the discrepancies in some cases can be up to 86.74%and 111.35%for the borehole and total internal thermal resistance.The pipe and grout thermal conductivity,pipe and borehole diameter,and the pipe-pipe distance can be seen as the significant contributory factors to the variation of R_(b,3D)and R_(a,3D).

An Analytical Model for the Thermal Assessment of a Vertical Double U-Tube Ground-Coupled Heat Pump System in Steady-State Conditions

An analytical model was built to predict the thermal resistance of a vertical double U-tube ground-coupled heat pump that operates under steady-state conditions.It included a geometry obstruction factor for heat transfer throughout the backfill medium due to the presence of the second loop.The verification of the model was achieved by the implementation of five different borehole configurations and a comparison with other correlations in the available literature.The model considered a U-tube spacing range between(2)and(4)times the U-tube outside diameter producing a geometry configuration factor range of(0.29-0.6).The results of the model were utilized for the assessment of the DX ground heat exchanger coupled heat pump system.For similar geometrical configurations,the borehole thermal resistance experienced a decrease as the geometry factor increased.The single U-tube borehole thermal resistance was higher than that of the double U-tube heat exchanger by(10-27)%for the examined geometry configurations.The borehole thermal resistance at tube spacing of twice the tube diameter was higher than the predicted value at the triple diameter and fell in the range of(18-34)%.