### Abstract

The average fluid temperature circulating through the ground loop is one of the main parameters required when choosing the most adequate heat pump for a ground source heat pump installation. Besides, the analysis of the fluid temperature over time will show the sustainability of the energy supply over the lifetime of the installation. The average fluid temperature is subjected to the type of ground heat exchangers and the thermal interactions between them, which also depend on the soil thermal properties. For the case of precast piles, the thermal interactions become significant as they are usually placed within short distances (0.5 to 4 metres). Fast models that can account for these interactions are required to enable feasibility studies and support the design phase. Besides, since pile heat exchangers have a main structural role, it is also relevant to develop models that can determine the temperature changes that the foundation might be subjected to, to assess thermo-mechanical implications.

3D finite element model (FEM) computation of the thermal behaviour of multiple pile heat exchanger foundations is not cost effective nor for feasibility studies, nor for most design applications. Therefore, this report describes a method to obtain simpler semi-empirical models based on 3D FEM simulations, called multiple pile g-functions.

The precast quadratic cross section pile heat exchangers analysed in this report have single-U and W-shape pipe heat exchangers and their aspect ratios (AR = Length/Diameter) are limited to 15, 30, 45 and 53. They are further described in [1] and [2]. The proposed g-functions account for the transient heat storage within the pile and are applicable over a range of timescales up to 20 years. This report builds on the methodology described in [3,4] and uses a similar notation. Different g-functions are used to describe the temperature responses of the ground surrounding the pile (ground G-functions Gg) and of the pile itself (concrete G-functions Gc).

The report first defines the g-functions, and then it explores each element required for the calculation of the average fluid temperature. After, some examples are studied, and an error analysis derived from using simplifications in the model is performed before the model is applied to analyse field thermal response test (TRT) data.

3D finite element model (FEM) computation of the thermal behaviour of multiple pile heat exchanger foundations is not cost effective nor for feasibility studies, nor for most design applications. Therefore, this report describes a method to obtain simpler semi-empirical models based on 3D FEM simulations, called multiple pile g-functions.

The precast quadratic cross section pile heat exchangers analysed in this report have single-U and W-shape pipe heat exchangers and their aspect ratios (AR = Length/Diameter) are limited to 15, 30, 45 and 53. They are further described in [1] and [2]. The proposed g-functions account for the transient heat storage within the pile and are applicable over a range of timescales up to 20 years. This report builds on the methodology described in [3,4] and uses a similar notation. Different g-functions are used to describe the temperature responses of the ground surrounding the pile (ground G-functions Gg) and of the pile itself (concrete G-functions Gc).

The report first defines the g-functions, and then it explores each element required for the calculation of the average fluid temperature. After, some examples are studied, and an error analysis derived from using simplifications in the model is performed before the model is applied to analyse field thermal response test (TRT) data.

Original language | English |
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Place of Publication | Aalborg |
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Publisher | Department of Civil Engineering, Aalborg University |

Number of pages | 34 |

Publication status | Published - 2018 |

Series | DCE Technical Reports |
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Number | 243 |

ISSN | 1901-726X |

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### Keywords

- Quadratic pile heat exchangers
- G-functions

### Cite this

Pagola, M. A., Jensen, R. L., Madsen, S., & Poulsen, S. E. (2018).

*Method to obtain g-functions for multiple precast quadratic pile heat exchangers*. Department of Civil Engineering, Aalborg University. DCE Technical Reports, No. 243