# The Effect of Shank-Space on the Thermal Performance of Shallow Vertical U-Tube Ground Heat Exchangers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Ground Source Heat Pump—A Short Review

## 3. Parameters Affecting the System Performance

#### 3.1. Effect of Shank-Space on System Performance

#### 3.2. Effect of Spatial Arrangement and Borehole Spacing

## 4. Scope of Research

## 5. Methodology

#### 5.1. Computational Domain of the Isolated Ground Heat Exchanger

^{−6}for both the flow and the energy equations (for the energy equation, the residuals were of the order of 10

^{−9}) and that the temperature at the two monitored points (Outlet 1 and Outlet 2) leveled to a constant value and did not change with further iterations.

_{g}, calculated on the basis of a radial one-dimensional analysis, which shows that resistance is an inverse function of the conductivity:

_{p}is the pipe radius. For this work, the relationship of Gu and O’Neal [45] is more appropriate since it includes the effect of shank spacing, s:

_{b}, gives the limiting value of zero for the logarithmic term giving negligible resistance.

#### 5.2. Establishing the Boundary Conditions

^{2}K and a free stream temperature of 27 °C. The bottom surfaces of the solid domains were specified as being adiabatic. The far-field ground surfaces were also set as adiabatic boundary surfaces.

#### 5.3. Computational Domain of the Ground Heat Exchanger Array

#### 5.4. Solution Methods

## 6. Results and Discussions

#### 6.1. Varying the Shank-Space for a 20 m Borehole

#### 6.2. Varying the Shank-Space for a 40 m Borehole

#### 6.3. Isolated Borehole Energetic Analysis

#### 6.4. Effect of Borehole Spacing

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

^{th}Sustainable Development of Energy, Water and Environment Systems (SDEWES) Conference held between the 1

^{st}and the 6

^{th}of October 2019 in Dubrovnik, Croatia. Compared to the Conference paper the introduction and the literature review has been extensively revised and expanded to better explain what research on the area is currently available, and how the paper tackles current existing research gaps. Also an additional section on insolated borehole energetic analysis was added.

## Conflicts of Interest

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**Figure 1.**A horizontal cross-section through a U-tube ground heat exchanger (GHE) illustrating the shank-space.

**Figure 5.**Variation of fluid temperature with depth for the five shank-spaces investigated for the 20 m borehole.

**Figure 6.**Temperature distributions at three different locations along the borehole depth (20 m) for the five different shank-spaces simulated.

**Figure 7.**Variation of fluid temperature with depth for the five shank-spaces investigated for the 40 m borehole.

Component | Material | Thermal Conductivity (W/mK) | Density (kg/m ^{3}) | Specific Heat Capacity (J/kgK) |
---|---|---|---|---|

Fluid | Water | 0.60 | 998 | 4182 |

Pipe | Low-density Polyethylene | 0.33 | 940 | 1900 |

Grout | Artificial High Conductivity Material | 6.5 | 2327 | 880 |

Ground | Calcium Carbonate | 2.25 | 2800 | 856 |

Shank-Space (mm) | Inlet 1 Temp. (°C) | Outlet 1 Temp. (°C) | Inlet 2 Temp. (°C) | Outlet 2Temp. (°C) | Temp. Drop (Inlet 1-Outlet 2) (°C) | Improvement over Previous Shank-Space (%) |
---|---|---|---|---|---|---|

40 | 40.00 | 39.58 | 39.53 | 39.24 | 0.76 | - |

95 | 40.00 | 39.58 | 39.48 | 39.18 | 0.82 | 7.9 |

150 | 40.00 | 39.58 | 39.47 | 39.16 | 0.84 | 2.4 |

205 | 40.00 | 39.58 | 39.47 | 39.15 | 0.85 | 1.2 |

260 | 40.00 | 39.59 | 39.47 | 39.15 | 0.85 | 0.0 |

Shank-Space (mm) | Inlet 1 Temp. (°C) | Outlet 1 Temp. (°C) | Inlet 2 Temp. (°C) | Outlet 2 Temp. (°C) | Temp. Drop (Inlet 1-Outlet 2) (°C) | Improvement over Previous Shank-Space (%) |
---|---|---|---|---|---|---|

40 | 40.00 | 39.22 | 39.18 | 38.78 | 1.22 | - |

95 | 40.00 | 39.23 | 39.16 | 38.72 | 1.28 | 4.92 |

150 | 40.00 | 39.24 | 39.16 | 38.70 | 1.30 | 1.56 |

205 | 40.00 | 39.25 | 39.16 | 38.69 | 1.31 | 0.77 |

260 | 40.00 | 39.27 | 39.16 | 38.68 | 1.32 | 0.77 |

Shank-Space (mm) | 20 m Deep Borehole Temp. Drop (Inlet 1 - Outlet 2) (°C) | 40 m Deep Borehole Temp. Drop (Inlet 1 - Outlet 2) (°C) | Depth Based Improvement (%) |
---|---|---|---|

40 | 0.76 | 1.22 | 60.53 |

95 | 0.82 | 1.28 | 56.10 |

150 | 0.84 | 1.30 | 54.76 |

205 | 0.85 | 1.31 | 54.12 |

260 | 0.85 | 1.32 | 55.29 |

Borehole Spacing (m) | Inlet 1 Temp. (°C) | Outlet 1 Temp. (°C) | Inlet 2 Temp. (°C) | Outlet 2Temp. (°C) | Temp. Drop (Inlet 1-Outlet 2) (°C) |
---|---|---|---|---|---|

5 | 40.00 | 39.89 | 39.89 | 39.81 | 0.19 |

10 | 40.00 | 39.79 | 39.76 | 39.60 | 0.40 |

15 | 40.00 | 39.71 | 39.65 | 39.43 | 0.57 |

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**MDPI and ACS Style**

Vella, C.; Borg, S.P.; Micallef, D.
The Effect of Shank-Space on the Thermal Performance of Shallow Vertical U-Tube Ground Heat Exchangers. *Energies* **2020**, *13*, 602.
https://doi.org/10.3390/en13030602

**AMA Style**

Vella C, Borg SP, Micallef D.
The Effect of Shank-Space on the Thermal Performance of Shallow Vertical U-Tube Ground Heat Exchangers. *Energies*. 2020; 13(3):602.
https://doi.org/10.3390/en13030602

**Chicago/Turabian Style**

Vella, Christopher, Simon Paul Borg, and Daniel Micallef.
2020. "The Effect of Shank-Space on the Thermal Performance of Shallow Vertical U-Tube Ground Heat Exchangers" *Energies* 13, no. 3: 602.
https://doi.org/10.3390/en13030602