1. Introduction
Ground-source heat-pump (GSHP) systems have been widely applied due to their advantages in efficiency, energy conservation, and emission reduction. The GSHP systems use geothermal energy from shallow earth layers as a heat source or a heat sink, and absorb or emit heat to the underground through ground heat exchangers (GHE) to provide refrigeration or heat supply to buildings [
1,
2,
3,
4]. Their first application was in the USA in 1945. The GSHP, as an innovative device, succeeded in revealing its great advantages [
5].The ability of a GHE mainly depends on the structure and thermal properties of the surroundings as well as on the operating conditions. To ensure the performance of a GSHP, the careful design of GHEs is essential [
6,
7].
Various types of GHEs are available on the market. The vertical U-tubes, which are inserted into a borehole and often backfilled with cement, bentonite and sand, are very efficient, but the drilling cost is rather high. Thus, a lot of researchers have aimed to improve the performance of GHEs and reduce the borehole depth [
8]. Jalaluddin and Miyara [
9] built three GHE models, including U-tube, double-tube, and multi-tube, to investigate the effect of tube number. Based on simulation results, during cooling mode, the heat flux of GHE at 22 h increased by 23.7% for the double-tube and 54.2% for the multi-tube. This indicated that the increase in tube number provided a possibility to improve the thermal performance and reduce the drilling cost of the GHEs.
The horizontal and helically coiled GHEs are also good choices for high-efficiency and low-cost [
10,
11]. Congedo et al. [
12] investigated three different tubes (linear, helical and slinky) that influence the performance of GHE by CFD simulations, and the analysis revealed that the helical heat exchanger arrangement performed the best.
The shank spacing is also one of the structural factors on which this study is focused. In order to investigate the factors influencing thermal conductivity and thermal borehole resistance, a sensitivity study based on numerical simulations, considering the effects of the shank spacing, initial thermal distribution and thermal dispersivity, was performed by Wagner et al. [
13]. It was demonstrated that the effects of the first two parameters were just below 10%. On the other hand, thermal dispersivity plays a key role because its influence overestimates the effective thermal conductivity by a factor of 1.2–2.9 as compared to the saturated condition.
Bouhacina et al. [
14] added longitudinal fins to the inner surface of the U-tube to obtain a novel GHE, and then the effects and benefits of this novel GHE were studied numerically. Two models were built to simulate the thermal and dynamic behaviors of a traditional GHE and the novel GHE. The result showed that under the same inlet condition, a greater velocity was noticed in the case of the novel GHE, and the heat exchange was up to 7% more efficient.
Thermal properties have also been considered. Three parameters of the GHE, including subsurface thermophysical properties, pipe materials and operating modes, were investigated by Lous et al. [
15]. The results showed that the porosity, thermal conductivities, and geothermal flux play an important role in the heat transfer. Furthermore, the parameters that affect thermal comportment are primarily the thermal conductivity of the U-tube, the discharge rate of the circulating water and the heat flux.
Several studies have taken the influence of convection into consideration. A CFD simulation of the U-tube was considered by Gustafsson et al. [
16]. A temperature gradient was obtained by setting a lower temperature on the far-field wall and a higher temperature on the tube wall, which induced a velocity gradient in the underground water. This resulted in an increased heat flux. Yang et al. [
17] developed a GHE model that accounts for groundwater advection in a porous media to investigate the influence of groundwater on the thermal distribution. It was discovered that better diffusivity conditions can increase the rate of soil heat diffusion. Thus, the heat buildup can be alleviated. In addition, groundwater advection can efficiently remove the underground heat buildup. Dehkordi and Schincariol [
18] used a fully discretized finite-element model to evaluate the thermal effect and hydrogeological properties of a GHE. The sensitivity of major parameters and thermo-hydrogeological factors that influence the system’s performance, as well as their impact, were analyzed over 6-month and 25-year operation periods. The results indicated that the groundwater flow (>10
−7 m/s), thermal conductivity and thermal gradient between the background and inlet result in a more efficient heat exchange. However, the effect of thermal interference between the branch tubes was overlooked while analyzing the grout thermal conductivity. It can be proved that the thermal interference would be enhanced, and then the GHE efficiency reduced by using thermally enhanced grout.
However, these studies did not thoroughly consider the influencing factors; therefore a comparative analysis is required. In this paper, the vertical GHE applied under different scenarios is evaluated. A three-dimensional unsteady state model for heat transfer in the vertical U-tube GHE is developed, and the influence of underground soil thermal properties, grout materials, inlet water temperature and velocity, and groundwater seepage on the heat transfer in the GHE is analyzed. In the discussion on heat flux, the factors are investigated from different aspects in detail such as the thermal-seepage coupling, thermal interference between branch tubes, turbulent flow in tubes, and recovery of ground temperature.