# Abstract

Many researchers numerically investigated U-tube underground heat exchanger using a two-dimensional simplified pipe. However, a simplified model results in large errors compared to the data from construction sites. This research is carried out using a three-dimensional full-size model. A model validation is conducted by comparing with experimental data in summer. This article investigates the effects of fluid velocity and buried depth on the heat exchange rate in a vertical U-tube underground heat exchanger based on fluid–structure coupled simulations. Compared with the results at a flow rate of 0.4 m/s, the results of this research show that the heat transfer per buried depth at 1.0 m/s increases by 123.34%. With the increase of the buried depth from 80 to 140 m, the heat transfer per unit depth decreases by 9.72%.

## 1 Introduction

Considering global energy emission issues of fossil fuels, renewable energy sources (such as solar and geothermal energies) have been focused on by many researchers. Various phase change materials (PCMs) have been widely used in renewable energy applications [1]. Li et al. [2] proposed a novel solar thermal system coupling with active PCM heat storage wall, which met a time balance between the solar supply and demand. A ground source heat pump (GSHP), like vertical U-tube GSHP, has been widely used for the exploitation of geothermal energy due to its advantages, such as energy-saving and eco-friendly utilizations. A vertical U-tube underground heat exchanger has a high initial investment, which is needed to put forward an accurate heat transfer model for a reduction in initial investment of energy systems [3].

Based on an investigation of fluid–structure coupled simulations, a three-dimensional heat transfer model about the vertical U-tube GSHP will be proposed in this article; and this model will use independent programming development of user-defined functions in the software ANSYS FLUENT 18.0 [4]. To discuss the effects of fluid velocity and buried depth on heat transfer performance of a vertical U-tube ground heat exchanger (GHE), inlet velocities are set to 0.4, 0.6, 0.8, and 1.0 m/s under the same buried depth of 120 m. With the same inlet velocity of 0.6 m/s, the thermal performance of the vertical U-tube GHE is also investigated under different buried depths of 80, 100, 120, and 140 m.

## 2 Methodologies

The test system consists of a vertical U-tube GHE, ground-coupled heat pump unit, circulation pump, and data acquisition system with measuring devices (like thermocouples, thermometers, and flow meters). These measuring devices mainly collect temperature and flow rates of supply water and return water of the GHE. A diagram is represented in Figure 1.

### Figure 1

It is a complex heat transfer process between the vertical U-tube GHE and the surrounding soil, and some assumptions are made to simplify the model.

For one assumption that the topsoil is not affected by solar radiation, the whole soil has an initial temperature as denoted by equation (1) [5]. Thermal resistance of all contact surfaces is given to be 0.

*T*is the temperature at a given depth (K).

*T*

_{s}is reference temperature at 0 m, and its value is 282.15 K.

*T*

_{d}is temperature gradient of 0.03 K/m, and

*Z*is buried depth (m).

A three-dimensional model has been established with a scale of 1:1. Figure 2 shows the computational domain of the vertical U-tube GHE.

### Figure 2

The external and internal diameters of the U-pipe are 32 and 26.2 mm, respectively. It is a distance of 100 mm between two branches of the U-pipe. The buried depth of the U-pipe is 120 m, and the soil depth is 121 m. The diameters of the borehole and the surrounding soil are 250 mm and 10 m, respectively.

The computational domain consists of PE pipe, working fluid, backfill, and surrounding soil. Table 1 shows the thermophysical properties of materials, as provided by Tianjin Geothermal Exploration and Development-Design Institute.

Term | Density (kg/m^{3}) |
Specific heat (J/kg K) | Thermal conductivity (W/m K) |
---|---|---|---|

PE pipe | 940 | 2,300 | 0.65 |

Water | 998.2 | 4,182 | 0.6 |

Backfill material | 1,860 | 840 | 3 |

Soil | 1,990 | 1,380 | 1.7 |

Initial backfill, PE pipe, and soil are supposed to start at temperature values from equation (1). Based on the boundary conditions during the tests, the inlet velocity is set to 0.6 m/s, and the inlet temperature changes with time, as shown in equation (2), is as follows:

*T*

_{i}is inlet temperature (K), and

*t*is time (s).

The equation (2) is derived from the experimental data provided by the Tianjin Geothermal Exploration and Development-Design Institute, China. All contact surfaces are set as temperature-coupled walls, and the upper surfaces are set as adiabatic surfaces. Water is employed as a heat carrier in GHEs.

The heat exchange rate was used to analyze the heat transfer performance of vertical U-tube GHEs. An equation of heat exchange rate, as given in Javadi et al. [6], is as follows:

*Q*is the heat exchange rate (W),

*m*is the mass flow rate (kg/s),

*C*

_{p}is the specific heat capacity (J/kg K),

*T*

_{i}is the water temperature at the inlet (K), and

*T*

_{o}is the water temperature at the outlet (K). The heat exchange rate per meter of borehole depth (

*Q*

_{L}) is calculated as follows:

*L*is the depth of a GHE (m).

As shown in Figure 3, model validation and grid independence tests are conducted using cases with four grid meshes from 3 to 24 M. It is found that simulated results are consistent with experimental data tested in summer.

### Figure 3

Figure 3 shows the temperature differences between experimental data and simulated results at different grid numbers. Outlet experimental temperature is 298.42 K. It is found that when the grid number is above 12 M, the outlet temperature is almost constant. Compared to the tested data, temperature variations from the cases with 12 and 24 M grid cells are 3.24 and 3.23%, respectively. The results from 12 M cell case are acceptable and finally used for all the simulations in this research.

## 3 Results and discussion

The heat transfer performance of a vertical U-tube GHE is investigated under eight operation conditions. Figure 4 shows heat exchange rates with different inlet velocities. It is found that heat exchange rates increase with the increase of the inlet velocity. It is also found that the *Q* is 3.42 kW at an inlet velocity of 0.4 m/s. An increase of 123.3% is observed when the velocity changes from 0.4 to 1.0 m/s.

### Figure 4

Heat exchange rates increase with the increase of buried depth, as shown in Figure 5. The heat exchange rate increases by 57% with the increase of the buried depth from 80 to 140 m. Heat exchange rate per meter of borehole depth is directly proportional to the inlet velocity and inversely proportional to the buried depth. Comparing with 28.47 W/m at inlet velocity of 0.4 m/s, *Q* _{L} increases by 123.34% at 1.0 m/s. *Q* _{L} decreases by 9.72% with a buried depth increasing from 80 to 140 m. The growth rates of *Q* are 20.5, 18.4, and 18.1%, when the buried depth changes from 80 to 100 m, 100 to 120 m, and 120 to 140 m, respectively. The growth rate of *Q* tends to be constant when the buried depth is above 120 m. It is concluded that 120 m is the optimal buried depth, considering thermal performance.

### Figure 5

The construction costs consist of expenses of drilling and grouting. Supplied heat produced by GHEs can be equivalent to electricity power based on ladder electricity price in China. Table 2 shows costs of GHE construction and 70-day electricity saving. Although the construction costs increase with the increase of the borehole depth, the electricity saving using GHEs increases. The recommended borehole depth depends on service time every year and cost recovery time as planned.

Buried depth (m) | GHE length (m) | Construction cost (USD) | 70-day saving bill (USD) |
---|---|---|---|

80 | 160.2 | 833.9 | 695.2 |

100 | 200.2 | 1042.1 | 841.0 |

120 | 240.2 | 1250.3 | 971.9 |

140 | 280.2 | 1458.5 | 1100.6 |

## 4 Conclusion

In this research, the heat transfer performance of a vertical U-tube GHE was studied numerically. *Q* increases with the increases of both the inlet velocity and the buried depth. *Q* _{L} is proportional to inlet velocity and inversely proportional to buried depth. The buried depth of 120 m is optimal in this study. The heat diffusion of turbulent is considered as the main factor affecting the heat transfer performance of the vertical U-tube heat exchanger.

# Acknowledgements

This work is supported by the Project of Innovation Ability Training for Postgraduate Students of Education Department of Hebei Province [Grant number CXZZSS2021046] and the Foundation of Key Laboratory of Thermo-Fluid Science and Engineering (Xi’an Jiaotong University), Ministry of Education, Xi’an 710049, P. R. China (Grant No. KLTFSE2018KFJJ01).

**Funding information:** The authors acknowledge the funding and support by the EU project Sustainable Process Integration Laboratory – SPIL, funded as project No. CZ.02.1.01/0.0/0.0/15_003/0000456, by Czech Republic Operational Programme Research and Development, Education, Priority 1: Strengthening capacity for quality research operated by the Czech Ministry of Education, Youth and Sport under a collaboration agreement with Hebei University of Technology.

**Conflict of interest:** Authors state no conflict of interest.

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**Received:**2021-02-01

**Revised:**2021-04-15

**Accepted:**2021-04-21

**Published Online:**2021-06-08

© 2021 Li Yang *et al*., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.