Study of the Transient Heat Transfer of a Single-U-Tube Ground Heat Exchanger by Integrating a Forward-Difference Numerical Scheme with an Analytical Technique

Abstract

This study presents the development of a novel computational technique for modeling the transient heat transfer in the outer and inner regions of a single U-tube ground heat exchanger. The modeling approach couples a forward-difference numerical technique with a well-established analytical method with the aim of reducing the two-dimensional axisymmetric heat transfer problem into a one-dimensional problem, which has the benefit of reducing the computational time. Furthermore, the suggested method is numerically stable compared to a full numerical scheme, and the solution converges for a time step of up to 150 min. This is because the suggested method computes the heat transfer of the streaming fluid in the U-tube, which has a lower thermal capacitance, using the analytical technique, resulting in numerical stability at a larger time step, while the full numerical scheme has stability issues at a large time step as it computes the heat transfer of the flowing fluid in the U-tube, which also requires more computational time than the suggested method. In this model, numerical and analytical analyses are coupled with borehole wall temperature. The time-varying temperature histories of the grout material inside the borehole, the borehole wall, and the surrounding soil are presented. In addition, the time variations in the exit fluid temperature and the energy storage within the grout and the outer soil material are presented. The results show that the energy storage in the grout material reaches 62 MJ at the end of 1000 h of ground heat exchanger charging operation, while the energy storage in the surrounding soil can be as high as 7366 MJ. This study also investigates the effect of mass flow rate on the heat transfer performance of the ground heat exchanger.