Impact of Geometrical Misplacement of Heat Exchanger Pipe Parallel Configuration in Energy Piles

: Shallow geothermal or ground source heat pump (GSHP) energy systems offer efficient space heating and cooling, reducing greenhouse gas emissions and electrical consumption. Incorporating ground heat exchangers (GHEs) within pile foundations, as part of these GSHP systems, has gained significant attention as it can reduce capital costs. The design and optimisation of GHEs connected in parallel within energy piles have been researched widely, considering symmetrical placement, while the potential misplacement due to construction errors and the optimal placement remain mostly unexplored. This study utilises 3D finite element numerical methods, analysing energy piles with diameters from 0.5 m to 1.4 m, equipped with parallelly connected U-tube and W-tube GHEs. The impact of GHE loop placement is analysed, considering the influence of the ground and concrete thermal conductivities, pile length, fluid flow rate, GHE pipe diameter, and pile spacing. Results indicate a marginal impact, less than 3%, on the overall heat transfer when loops deviate from symmetry and less than 5% on the total heat transfer shared by each loop, except for highly non-symmetric configurations. Symmetrical and evenly spaced loop placement generally maintains favourable thermal performance and ease of installation. This study underscores the flexibility in GHE design and construction with a low risk of thermal yield variations due to uncertainties, particularly with a separation-to-shank distance ratio between 0.5 and 1.5 in a symmetrical distribution.


Introduction
Energy piles, or thermo-active piles [1], are a way to use the pile foundations as heat exchangers for ground source heat pump (GSHP) systems.Geothermal heat pumps use the heat stored in the ground to heat and cool buildings in the winter and in the summer, respectively.In recent years, and due to concerns about the energy crisis and environmental pollution, this technology has gained widespread use as a sustainable and green energy source that reduces greenhouse gas emissions [2].GSHP systems can significantly reduce electrical energy consumption used for space heating and cooling purposes by up to 75% compared to conventional electrical systems [1].Traditional geothermal heat pumps require drilling boreholes (or trenching) within the site, which take up space and can constitute the majority of the overall capital cost of the GSHP system [3].Heat transfer from energy piles can be more effective and efficient than that from boreholes (the traditional GSHP systems) at the same depth because energy piles are usually composed of concrete, which has a higher thermal conductivity than the grout surrounding heat exchanger pipes in boreholes [4].In addition, energy piles have a length-to-diameter ratio that ranges between 15 and 50 compared to 200 and 500 for boreholes, which increases the flexibility of the energy piles to accommodate longer ground heat exchanger pipes (GHEs) in different Energies 2024, 17, 2580 2 of 25 configurations, leading to higher energy production and reduced thermal interaction between nearby pipes [5,6].However, the design of the heat exchange component in energy piles is often restricted by the structural design of the pile foundation (i.e., the pile size and shape), which may restrict the length and the configuration of the heat exchanger pipes.
The arrangement of the pipes within the energy pile (e.g., loop shape, interconnection, and pipe spacing) is an important design and construction consideration, as it can affect the energy pile's heat exchange rate and ability to efficiently extract/inject heat from/to the ground [5,7].The efficiency of an energy pile can be improved by increasing the number of pipes, as it increases the surface area for thermal exchange.However, it is important to use the optimal number of ground heat exchangers with the appropriate spacing to prevent thermal interference that can occur when there are too many pipes with little space between them [8][9][10].In addition, increasing the pipe spacing generally leads to a higher energy pile thermal performance [11].Caulk et al. (2016), on the other hand, performed a sensitivity analysis study and showed a decrease in heat transfer rate after a certain threshold of the pipe spacing [12].A recommended typical pipe spacing in an energy pile is between 250 and 300 mm [13] to maximise the thermal exchange area, thus improving the efficiency of the energy pile while also avoiding thermal interference between the pipes.However, this may vary depending on the thermal load profile.
Among the various heat exchanger categories that exist according to their geometric construction for different engineering applications [14,15], ground heat exchangers incorporated, particularly within the energy piles application, generally involve the use of simple high-density polyethylene (HDPE) tubular pipes.There have been many studies in the literature on the different types of GHE pipes used in energy piles.The most common types include single or multiple U-tubes, W-tubes, spiral tubes, and helix tubes [5,7,16].Many experimental and numerical studies compared various GHE configurations to attest to the thermal performance of energy piles.For instance, Bezyan et al. (2017) conducted a numerical study on energy piles incorporated with U-tube, W-tube, and spiral-tube configurations and found that the spiral-tube yields the highest heat transfer rate of around 123 W/m compared to nearly 44.5 W/m and 54.3 W/m for U-tube and W-tube, respectively [17].Similarly, numerical results from Zhao et al. (2016) show that the short-term and the longterm thermal performance of an energy pile with a spiral tube outperforms that of piles with W-and U-tube ground heat exchangers due to the longer spiral tube length and its configuration that helps to maintain a uniform temperature distribution inside the energy pile [18].By conducting five thermal performance tests (TPT), Luo et al. (2016) experimentally investigated the thermal efficiency of energy piles with various GHE configurations, including double U-tube, triple U-tube, double W-tube, and spiral tube.According to their thermo-economic analysis, the triple U-tube was deemed as the best configuration among others.While the spiral tube showed nearly a similar thermal performance to the double W-tube, the double U-tube experienced an approximate decrease of 33% and 31% compared to the spiral and W-tube, respectively [19].More recently, a numerical study on optimising the GHE configuration in an energy pile presents a multi-U-tube composed of six branches (i.e., U6-tube) distributed around the pile's perimeter [20].Results indicate that, when compared to other configurations taken into consideration, such as single U-tube, W-tube, and spiral tube, the energy pile (with a 25 m length) integrated with the U6-tube configuration rendered the maximum heat transfer rate.Park et al. (2010) found that the most efficient configuration for heat exchanger pipes in large-diameter energy piles, which have more than five pairs of U-tubes, is in a helix shape, considering both economic feasibility and thermal performance [8].A numerical study compared eight new helical layouts of the GHEs and concluded that the triple-helix layout has the maximum thermal performance [21].However, there are difficulties with installing the helix shape, especially in piles with smaller diameters [22], and the installation cost of these types is a critical and challenging issue for their implementation [23].Despite all the results highlighted herein, over the past 30 years, the simple U-tube configuration has been chosen and extensively employed in the industry as the heat exchange element in both boreholes and energy pile, because of its design, transportation, and installation simplicity [5,24].
In addition to the loop shape and spacing design aspects, the connection of the loops within the energy pile is important.The series interconnection typically provides a longer path for the running fluid to exchange heat compared to the parallel connection, assuming performance is the same.On the other hand, the series interconnection may be riskier in terms of construction as if there was a defect after casting the concrete (such as leakage), the entire loop inside the energy pile would need to be abandoned.More importantly, pumping costs for the two can be significantly different, as in-series and in-parallel connections have different fluid flow rate requirements to ensure sufficient heat transfer [25].Figure 1 shows a schematic drawing of three U-tube pipes, as an example, comparing the parallel and series connection within the energy piles.
Energies 2024, 17, x FOR PEER REVIEW 3 of 25 employed in the industry as the heat exchange element in both boreholes and energy pile, because of its design, transportation, and installation simplicity [5,24].
In addition to the loop shape and spacing design aspects, the connection of the loops within the energy pile is important.The series interconnection typically provides a longer path for the running fluid to exchange heat compared to the parallel connection, assuming performance is the same.On the other hand, the series interconnection may be riskier in terms of construction as if there was a defect after casting the concrete (such as leakage), the entire loop inside the energy pile would need to be abandoned.More importantly, pumping costs for the two can be significantly different, as in-series and in-parallel connections have different fluid flow rate requirements to ensure sufficient heat transfer [25].Figure 1 shows a schematic drawing of three U-tube pipes, as an example, comparing the parallel and series connection within the energy piles.In addition, the GHEs connected in parallel within energy piles have been researched considering symmetrical placement, while potential misplacement due to construction errors and the optimal placement remain mostly unexplored.One of the handful studies incorporating in-parallel tube connection is from Park et al. (2019), who conducted six field tests on energy piles to examine how the configuration and density of GHEs affected the energy pile thermal performance, as well as a long-term thermal evaluation using numerical analysis [26].Three of the tests involved the use of the parallel connection between five, eight, and ten U-tube loops.The findings indicated that as the number of the heatexchanging loops, and consequently the total pipe length, is increased, the thermal interference becomes more noticeable.Additionally, while increasing the number of loops improved the pile's thermal performance over the short term, the performance fell off quickly over the long run due to a considerable rise in the ground temperature around the pile.
Another study was by Cui et al. (2020), who investigated the impact of various design parameters, including the number of heat-exchanging loops, on the heating effectiveness of multiple U-tubes connected in parallel in an energy pile of 1.0 m in diameter [27].According to the study, using four U-tube loops was found to be the optimum number of loops to have the highest thermal effectiveness.However, using more than four loops in parallel was found to decrease the heating effectiveness of the loops due to thermal interference.A more recent study [28] examined the impact of various design parameters on In addition, the GHEs connected in parallel within energy piles have been researched considering symmetrical placement, while potential misplacement due to construction errors and the optimal placement remain mostly unexplored.One of the handful studies incorporating in-parallel tube connection is from Park et al. (2019), who conducted six field tests on energy piles to examine how the configuration and density of GHEs affected the energy pile thermal performance, as well as a long-term thermal evaluation using numerical analysis [26].Three of the tests involved the use of the parallel connection between five, eight, and ten U-tube loops.The findings indicated that as the number of the heat-exchanging loops, and consequently the total pipe length, is increased, the thermal interference becomes more noticeable.Additionally, while increasing the number of loops improved the pile's thermal performance over the short term, the performance fell off quickly over the long run due to a considerable rise in the ground temperature around the pile.
Another study was by Cui et al. (2020), who investigated the impact of various design parameters, including the number of heat-exchanging loops, on the heating effectiveness of multiple U-tubes connected in parallel in an energy pile of 1.0 m in diameter [27].According to the study, using four U-tube loops was found to be the optimum number of loops to have the highest thermal effectiveness.However, using more than four loops in parallel was found to decrease the heating effectiveness of the loops due to thermal interference.A more recent study [28] examined the impact of various design parameters on the thermal resistance of the borehole, considering an energy pile with parallel U-tube heat-exchanging loops.The findings showed that the most important design factors were the number of Energies 2024, 17, 2580 4 of 25 loops and the concrete cover-to-diameter ratio.Moreover, the thermal performance of the energy pile was not proportional to the number of loops because of the rise in thermal interference between nearby loops.Ten parallel loops increased heat transfer compared to five parallel loops (i.e., half the length of the total loops) by only 21%.
Although the heat interference between the heat-exchanging legs in energy piles is generally considered minimal due to the wider space inside the piles compared to boreholes [13], and sometimes its effect is considered secondary [29], the previous studies show the importance of considering the thermal interference between adjacent energy pile loops connected in parallel.
However, most of the available studies on this subject consider an even number of parallel heat-exchanging loops, and all of the studies only consider a "symmetrical" parallel connection distribution.However, construction errors could deviate the parallelly connected loops from symmetry, and when an odd number of loops is placed, this deviation could cause a potential thermal interference between the adjacent legs forming each loop.
In addition, the most effective distribution in terms of the ratio of the shank spacing to the loop separation is rarely discussed in the literature.Furthermore, the available studies do not typically assess the effect that the layered nature of the ground with different thermal conductivities has on the pipe placement for moderate-to large-diameter energy piles, and instead, the simplified homogeneous ground conditions are typically used.Investigating these matters in the design of GHEs parallelly connected within energy piles can provide new insights into (i) the level of risk associated with the uncertainty in GHE placement on the potential degradation of the overall thermal performance of the system and (ii) the level of design flexibility, which may allow the designers to incorporate and distribute more GHEs within the energy piles, increasing the viability of this green technology.
This study aims to investigate and quantify the effect of the GHE distribution and the deviation from symmetry of in-parallel U-tube loops for a set of moderate-diameter piles and W-tube loops for a set of large-diameter piles, considering the shank spacing and the loop separation, focusing on the potential thermal interference between adjacent legs that form a loop due to shank spacing as well as between adjacent loops forming the entire parallel system inside the energy pile.This can become particularly important when using an odd number of pipe loops since, at least in one zone, thermal interference can occur when the inlet of one loop is adjacent to another loop's outlet.The study also covers different ranges of influencing parameters, including ground thermal conductivity, concrete thermal conductivity, pile length, fluid flow rate, pipe diameter, and pile spacing.A thorough examination of these factors is required to widen the collective knowledge around the practical design of energy piles as a promising sustainable technology.

Overview
In this study, a detailed three-dimensional model of an energy pile surrounded by a layered ground is implemented within the finite element package COMSOL Multiphysics.The three-dimensional finite element modelling allows for capturing potential thermal interference among the HDPE pipes in the pile (and with the ground), more realistic conditions, and other details such as ground layering and, indeed, the whole components of the energy pile system (including GHEs), avoiding inaccuracies related to simplified considerations used in the available analytical methods [16].The methodology and the governing equations to build the model are presented.Next, the input parameters associated with the geological, thermal, and operational characteristics are discussed.After that, a mesh sensitivity study for the numerical model is presented.Finally, the numerical simulations conducted in this study based on the numerical model specifications and boundary conditions are explained.

Governing Equations
The three-dimensional numerical model of the energy pile buried in the ground and equipped with HDPE heat exchanger loops combines heat conduction and heat convection physics.The heat conduction occurs within the solid parts of the system (HDPE wall, concrete body of the pile, and the soil mass), while the heat transport in the carrier fluid (water in this case) flowing inside the heat-exchanging loops is dominated by heat convection.The methodology used to build the thermal numerical model that combines and solves for the heat conduction-convection multiphysics has been used in the literature to build different geo-structure models, including energy piles [30,31], and has been previously validated by the authors in their past study on energy piles [32].
The developed numerical model represents the heat exchange pipes as one-dimensional elements, i.e., a line heat source, while the remaining components, the body of the energy pile and the surrounding ground, are comprised of three-dimensional elements.
The governing equations mainly link the heat convicted by the carrier fluid flowing inside the GHE pipes as a line heat source (due to the small diameter-to-length ratio) with the heat conducted mainly by the solids (i.e., the concrete of the energy pile and the ground components).First, to solve for the fluid temperature field, the fluid velocity and pressure fields are obtained from numerically solving the momentum and continuity equations for a one-dimensional incompressible fluid, as shown in Equation (1) and Equation (2), respectively [33]: where ρ w [kg/m 3 ] and v w [m/s] represent the fluid density and velocity, respectively.A [m 2 ] is the heat exchanger's internal area, t [s] is the time, p w [Pa] is the pressure of the running fluid, f D represents the Darcy friction factor, and d h [m] corresponds to the hydraulic diameter of the heat exchanger.The velocity and pressure fields are then used to solve the energy equations, Equations (3) and (4), for the convective fluid temperature and the corresponding conduction heat transfer via the wall of the GHEs (Q wall ): where C p,w [J/(kg•K)] and λ w [W/(m•K)] are the specific heat capacity and thermal conductivity of the carrier fluid, respectively.T [K] is the running fluid temperature, T s,pipe wall [K] is the temperature of the GHE external wall, and Q wall [W/m] is the heat exchange per length within the GHE wall.Finally, Equation ( 5) solves for the heat conducted from the GHEs' wall through all solid elements (i.e., the concrete in the pile and the surrounding soil mass): where ρ s [kg/m 3 ], C p,s [J/(kg•K)], and λ s [W/(m•K)] represent the solid material density, specific heat capacity, and thermal conductivity, respectively.T s [K] is the temperature of the solid.

Geological, Thermal, and Operation Parameters
Geological parameters: This study first considers a realistic geological setting located in Melbourne (Australia).The data are based on in situ thermal conductivity (TRT) and laboratory measurements conducted to determine the thermal conductivities of the layers on soil and rock samples in the Arden site located in North Melbourne by authors in [34].Figure 2a shows the Arden site geological setting and the corresponding layers' thermal conductivities, density, and heat capacity based on the measurements in [34] and data from [35,36].The pile length considered for this site is 40 m, as shallower piles are more suitable for in-series interconnections due to the loops requiring sufficient length for a temperature difference between the inlet and outlet that can run the heat pump effectively.The layers' thermal properties have been measured under the presence of a water table at a depth of 3 m from the surface.However, groundwater flow has not been reported.Therefore, groundwater flow is not considered in this work, which is a conservative approach as it would enhance the thermal performance of the energy piles [32,37,38].

Geological, Thermal, and Operation Parameters
Geological parameters: This study first considers a realistic geological setting loca Melbourne (Australia).The data are based on in situ thermal conductivity (TRT) a boratory measurements conducted to determine the thermal conductivities of the on soil and rock samples in the Arden site located in North Melbourne by authors i Figure 2a shows the Arden site geological setting and the corresponding layers' th conductivities, density, and heat capacity based on the measurements in [34] an from [35,36].The pile length considered for this site is 40 m, as shallower piles are suitable for in-series interconnections due to the loops requiring sufficient length temperature difference between the inlet and outlet that can run the heat pump effec The layers' thermal properties have been measured under the presence of a water t a depth of 3 m from the surface.However, groundwater flow has not been rep Therefore, groundwater flow is not considered in this work, which is a conservati proach as it would enhance the thermal performance of the energy piles [32,37,38].In addition to the geology based on the Arden site, a more generalised geo profile is also used as part of the presented analyses, extending the work to cover di influential parameters in heat transfer.For this purpose, the geological paramete the pile length are modified, as explained later in Section 2.6.
Ground temperature: The undisturbed ground temperature is estimated followi method described in [39].The method states that the undisturbed ground tempe can be estimated as the average annual air temperature plus 2 °C.According to th tralian Government Bureau of Meteorology [40], the annual minimum and max mean temperature over nearly the past 30 years in Melbourne is 11.6 °C and 20.8 spectively.Therefore, the undisturbed ground temperature in the considered loca around 18.2 °C, which agrees with measurements from 12 different sites in Melb reported in [34], ranging from 17.8 °C to 19.5 °C.
Operational parameters: For commercial building applications (where piles ar cally found), the American Society of Heating, Refrigerating and Air-Conditioning neers (ASHRAE) standard suggests for the heat pump entering water temperature higher than the undisturbed ground temperature by 11 °C to 17 °C in cooling mod In addition to the geology based on the Arden site, a more generalised geological profile is also used as part of the presented analyses, extending the work to cover different influential parameters in heat transfer.For this purpose, the geological parameters and the pile length are modified, as explained later in Section 2.6.
Ground temperature: The undisturbed ground temperature is estimated following the method described in [39].The method states that the undisturbed ground temperature can be estimated as the average annual air temperature plus 2 • C. According to the Australian Government Bureau of Meteorology [40], the annual minimum and maximum mean temperature over nearly the past 30 years in Melbourne is 11.6 • C and 20.8 • C, respectively.Therefore, the undisturbed ground temperature in the considered location is around 18.2 • C, which agrees with measurements from 12 different sites in Melbourne reported in [34], ranging from 17.8 • C to 19.5 • C.
Operational parameters: For commercial building applications (where piles are typically found), the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) standard suggests for the heat pump entering water temperature to be higher than the undisturbed ground temperature by 11 • C to 17 • C in cooling mode, and lower than the undisturbed ground temperature by 6 • C to 9 • C in heating mode [41].These are the extreme limits of inlet temperatures to ensure the heat pump works efficiently.They have been used in this study to have the maximum possible heat transfer, thus depicting the worst-case scenario for any potential thermal interference between the GHE loops.Therefore, considering average values, the inlet temperature entering the GSHP in cooling and heating modes is taken as 32.2 • C and 10.7 • C, respectively.
In addition, according to the data by the Bureau of Meteorology in Australia [40], the mean maximum air temperature is above 25 • C from January through March (summer in the southern hemisphere), and the mean minimum air temperature is below 10 • C from July through September (winter).Therefore, the system is assumed to operate during these hottest and coldest periods (three months of building cooling from January through March and three months of building heating mode from July through September) and turned off during the other six months of the year.Given that the mean monthly air temperature is approximately similar (±1 • C) between the three hot months and between the three cold ones, the inlet temperature entering the ground heat exchangers is assumed to be the same through the three months of the cooling mode (i.e., 32.2 • C from January through March) and the three months of the heating mode (i.e., 10.7 • C from July through September).The three months of continuous operation without interruption during the day allows us to consider the worst-case scenario of any potential thermal interaction between the GHE loops in the energy piles in both modes of operation.
A flow rate of 5.5 L/min is used for the Arden side, as listed in Table 1, and based on the heat exchanger pipe and fluid characteristics.This value is found to be the minimum flow rate that can be used for each heat exchanger loop connected in parallel inside the energy pile to keep the flow in transient-turbulent condition (the calculated Reynold number ~4300) and fulfil the fluid flow requirement to keep the heat pump run efficiently [25].The study is then extended to cover a range of flow rate values, as detailed in Section 2.6.

Modelling Specifications and Boundary Conditions
Typically, a group of piles is thermally activated to meet the thermal demand of the building.For simplicity and to isolate the effects of pile-to-pile thermal interaction and reduce the computational cost, a single energy pile is modelled and analysed herein, with outer boundaries prescribed with symmetry boundary conditions considering a typical separation distance of 5 m between two adjacent energy piles.Thermally activated piles with a separation distance of less than 5 m show a drop in their thermal performance due to the thermal interference between them (refer to Figure A1 in Appendix A.1), and therefore, this study assumes that only piles with sufficient spacing between them will be thermally activated.The parameters in Table 1 are assumed to be constant over time.
A zero-heat flux condition through the top surface is used to represent thermal insulation due to the building supported by the pile(s).The bottom surface of the model (10 m below the pile's toe) is subjected to an undisturbed ground temperature of 18.2 • C, assuming no boundary effect at this depth.Further details of the boundary conditions are presented in Figure 2b.Table 1 lists the numerical model input parameters for the Arden site case, in which the material parameters are within the range commonly used in the literature.

Mesh Sensitivity Study
A mesh sensitivity study of the built numerical model is undertaken to ensure the independence of the grid partitioning on the results.The energy pile with a 0.5 m diameter has been chosen as a critical case, as it has the smallest diameter compared to the surrounding ground, raising the potential of convergence issues.The mesh uses free tetrahedral elements with two different sizes, such that the assigned mesh to the energy pile is finer than that for the surrounding ground.The amount of heat transfer within the GHEs over the annual cooling and heating periods is chosen as a decisive parameter, as it is used throughout the discussion in this study.The results of the mesh sensitivity study listed in Table 2 suggest using mesh (C) to perform the study, balancing both accuracy and computational time.The computational time is based on high-performance computing that utilises a 64-core processor.

Numerical Simulations
Two sets of analyses are performed using the Arden site configuration to investigate (i) the influence of GHE pipe parallel configuration (i.e., the separation distance between adjacent U-and W-shape loops) inside the energy pile, and (ii) the optimal ratio between GHE shank spacings (i.e., the distance between the legs forming each loop) and the adjacent loops separation distance, to maximise the thermal performance of the energy pile in terms of the heat injected/extracted to/from the ground through the incorporated GHEs.
Both sets of analyses consider different energy pile diameters: moderate energy pile diameters (0.5, 0.6, and 0.7 m) with three loops of single U each connected in parallel, and large pile diameters (1.0, 1.2, and 1.4 m) with three loops of single W, considering the larger available internal space of the piles in this case to host such W-shape loops, each connected in parallel.The reason to choose three loops of single W instead of, for instance, six U in the large-diameter piles in this study is to avoid dividing the flow rate between a large number of loops (keeping a consistent header pipe flow for comparison purposes), which might lead to an unfavourable flow condition (laminar flow) and affect the pumping and heat transfer efficiency.Meanwhile, a single W-loop proves a higher thermal performance by nearly 54% of the heat exchange rate per metre pile compared to the single U at the same flow rate conditions [42].Although the analyses are performed on different energy Energies 2024, 17, 2580 9 of 25 pile diameters, a 40 m length of the energy pile is used and kept the same for all analyses.This is because the maximum GHE length for the considered configurations (i.e., three loops of single U and three loops of single W for moderate and large energy pile diameter, respectively) is constrained by the structural pile length, while the GHE distribution and spacings can be adjusted for a certain energy pile's diameter.Figure 3 shows further details of the modelled energy pile and the ground heat exchanger loops used in the simulations.
Following the site-specific analyses, to extend and generalise these findings, another set of numerical analyses is undertaken, considering key influential parameters on heat transfer.The investigation includes extreme values of influential parameters that are likely to affect the thermal performance of the energy pile, which is related to (i) ground thermal conductivity (equivalent homogeneous ground thermal conductivity of 1 W/(m•K) and 4 W/(m•K)), (ii) concrete thermal conductivity (1 W/(m•K) and 3 W/(m•K)), (iii) pile length (15 m and 25 m), (iv) fluid flow rate (7.5 l/min and 10 l/min), (v) inner pipe diameter (12.7 mm and 38.1 mm, all with SDR 11), and (vi) spacing between energy piles (2 m and 3.5 m).Two values for the pile diameter from the previous studies on the Arden site are adopted in this second set of analysis: 0.5 m diameter with three loops of single U and 1.0 m diameter with three loops of single W, as these diameters accommodate the loops such that the separation distances between them are small, which increase the likelihood of thermal interference showcasing the effect of the other parameters.The results from the two investigations, site-specific and generalised, are then discussed.
large number of loops (keeping a consistent header pipe flow for comparison purposes), which might lead to an unfavourable flow condition (laminar flow) and affect the pumping and heat transfer efficiency.Meanwhile, a single W-loop proves a higher thermal performance by nearly 54% of the heat exchange rate per metre pile compared to the single U at the same flow rate conditions [42].Although the analyses are performed on different energy pile diameters, a 40 m length of the energy pile is used and kept the same for all analyses.This is because the maximum GHE length for the considered configurations (i.e., three loops of single U and three loops of single W for moderate and large energy pile diameter, respectively) is constrained by the structural pile length, while the GHE distribution and spacings can be adjusted for a certain energy pile's diameter.Figure 3 shows further details of the modelled energy pile and the ground heat exchanger loops used in the simulations.
Following the site-specific analyses, to extend and generalise these findings, another set of numerical analyses is undertaken, considering key influential parameters on heat transfer.The investigation includes extreme values of influential parameters that are likely to affect the thermal performance of the energy pile, which is related to (i) ground thermal conductivity (equivalent homogeneous ground thermal conductivity of 1 W/(m•K) and 4 W/(m•K)), (ii) concrete thermal conductivity (1 W/(m•K) and 3 W/(m•K)), (iii) pile length (15 m and 25 m), (iv) fluid flow rate (7.5 l/min and 10 l/min), (v) inner pipe diameter (12.7 mm and 38.1 mm, all with SDR 11), and (vi) spacing between energy piles (2 m and 3.5 m).Two values for the pile diameter from the previous studies on the Arden site are adopted in this second set of analysis: 0.5 m diameter with three loops of single U and 1.0 m diameter with three loops of single W, as these diameters accommodate the loops such that the separation distances between them are small, which increase the likelihood of thermal interference showcasing the effect of the other parameters.The results from the two investigations, site-specific and generalised, are then discussed.three single U parallel loops, while three single W parallel loops are incorporated in the large-diameter piles (Figure 3).
As Figure 4 depicts, different distributions/locations of the loops around the pile's perimeter are considered by moving one of the loops and keeping the other two loops fixed to investigate the geometrical configuration that yields the highest thermal performance for the thermal load and geological conditions prescribed, and to study the thermal interference effect between adjacent loops.The first case, as shown in Figure 4a, is to move the position of loop-2 (L2) clockwise to increase the separation of the inlet of loop-2 from the outlet of loop-3 (L3), such that the outlets of both L2 and L1 become closer to each other.The second case in Figure 4b is to move the location of L3 counter-clockwise to keep its outlet away from the inlet of L2, but now such that both L3 and L1 inlets become closer to each other.Loop-1 (L1) is considered fixed in all cases as its inlet is adjacent to the inlet of L3, and its outlet is adjacent to the outlet of L2; therefore, there is a low potential for thermal mismatch and interference to occur.To simulate different loops' positions around the pile's perimeter, the angle (β) is introduced as the angle that separates the three loops in a symmetrical distribution.The separation angle between L2 and L3 (α) is then altered by a specific portion called a "Rotation Factor" depending on the location of the moving loop.This Rotation Factor is then defined as the ratio of angles α and β depicted in the figure .For instance, a rotation factor of 1/6 when L2 is moving means that L2 moves from its symmetrical location (i.e., rotation factor = 1) towards L3 such that the separation angle between them is α = β/6.The larger the Rotation Factor, the larger the separation between L2 and L3 herein, the smaller the separation between the moving loop and L1.

Effect of GHE Distribution
This section investigates the effects of distribution and spacing of the three loops connected in parallel and distributed around the perimeter of both moderate-diameter pile set (0.5, 0.6, and 0.7 m) and large-diameter pile set (1.0, 1.2, and 1.4 m), with the aim to produce the maximum heat exchange rate.The moderate-diameter piles are equipped with three single U parallel loops, while three single W parallel loops are incorporated in the large-diameter piles (Figure 3).
As Figure 4 depicts, different distributions/locations of the loops around the pile's perimeter are considered by moving one of the loops and keeping the other two loops fixed to investigate the geometrical configuration that yields the highest thermal performance for the thermal load and geological conditions prescribed, and to study the thermal interference effect between adjacent loops.The first case, as shown in Figure 4a, is to move the position of loop-2 (L2) clockwise to increase the separation of the inlet of loop-2 from the outlet of loop-3 (L3), such that the outlets of both L2 and L1 become closer to each other.The second case in Figure 4b is to move the location of L3 counter-clockwise to keep its outlet away from the inlet of L2, but now such that both L3 and L1 inlets become closer to each other.Loop-1 (L1) is considered fixed in all cases as its inlet is adjacent to the inlet of L3, and its outlet is adjacent to the outlet of L2; therefore, there is a low potential for thermal mismatch and interference to occur.To simulate different loops' positions around the pile's perimeter, the angle (β) is introduced as the angle that separates the three loops in a symmetrical distribution.The separation angle between L2 and L3 (α) is then altered by a specific portion called a "Rotation Factor" depending on the location of the moving loop.This Rotation Factor is then defined as the ratio of angles α and β depicted in the figure .For instance, a rotation factor of 1/6 when L2 is moving means that L2 moves from its symmetrical location (i.e., rotation factor = 1) towards L3 such that the separation angle between them is α = β/6.The larger the Rotation Factor, the larger the separation between L2 and L3 herein, the smaller the separation between the moving loop and L1. Figure 5 shows the total heat transfer from all loops over the annual building cooling and heating periods (i.e., three months of heating and three months of cooling for each year over a 20-year design period as shown in Figures A2 and A3 in Appendix A.1) for the Figure 5 shows the total heat transfer from all loops over the annual building cooling and heating periods (i.e., three months of heating and three months of cooling for each year over a 20-year design period as shown in Figures A2 and A3 in Appendix A.1) for the three energy piles with moderate diameters (P 0.5m , P 0.6m , and P 0.7m ) and the other three energy piles with large diameters (P 1.0m , P 1.2m , and P 1.4m ) by considering two cases of loop movements for each pile's diameter.These thermal load profiles are found to be typical for temperate climates.
three energy piles with moderate diameters (P0.5m,P0.6m, and P0.7m) and the other th ergy piles with large diameters (P1.0m,P1.2m, and P1.4m) by considering two cases movements for each pile's diameter.These thermal load profiles are found to be for temperate climates.The first case is when L2 is moving from a separation angle of β/6 from L3 t L1.The second case is when L3 is moving from a separation angle of β/6 from L2 t L1.Results in Figure 5 show that the total heat transfer for each certain pile diame P0.7m in moderate-diameter pile set or P1.4m in large-diameter pile set) is similar w inlets or outlets between L1 and L3 come closer.It is also evident from the results maximum total heat transfer for each of the pile diameters set occurs when the GH are symmetrically distributed around the pile's perimeter (i.e., rotation factor = 1 over, differences in terms of the total heat transfer between different rotation facto to be minimal compared to the symmetrical distribution.For instance, the worst-c nario when the rotation factor is β/6 in the case of P0.7m produces ~ 133 kW h (i.e. less heat transfer compared to the symmetrical distribution over the annual b The first case is when L2 is moving from a separation angle of β/6 from L3 towards L1.The second case is when L3 is moving from a separation angle of β/6 from L2 towards L1.Results in Figure 5 show that the total heat transfer for each certain pile diameter (e.g., P 0.7m in moderate-diameter pile set or P 1.4m in large-diameter pile set) is similar whether inlets or outlets between L1 and L3 come closer.It is also evident from the results that the maximum total heat transfer for each of the pile diameters set occurs when the GHE loops are symmetrically distributed around the pile's perimeter (i.e., rotation factor = 1).Moreover, differences in terms of the total heat transfer between different rotation factors seem to be minimal compared to the symmetrical distribution.For instance, the worstcase scenario when the rotation factor is β/6 in the case of P 0.7m produces ~133 kW h (i.e., ~2.7%) less heat transfer compared to the symmetrical distribution over the annual building cooling period of three months (Figure 5a).The same observation can be seen for large-diameter pile set.The total heat transfer of the P 1.4m pile, for example, decreases by ~144 kW h (i.e., ~2.0%) when moving away from the symmetrical distribution to a position where the rotation factor is β/6 over the annual building cooling period (Figure 5c).The reasons behind these differences are related to the heat transfer interplays.For adjacent loops where the inlet and outlet are close together, a thermal short-circuit is likely to occur.On the other hand, where inlet and inlet or outlet and outlet are close together, thermal accumulation will likely occur.Since both of these can be detrimental to the system performance, a maximum distance between all loops, in symmetrical distribution, seems to be the least interference.For the same reason, the case when both loops (L2 and L3) are moving towards loop-1 (L1) has not been considered in this study, as the total heat transfer will likely be less than in the other cases.
Furthermore, the results show that increasing the pile diameter generally increases the heat transfer capacity for the same GHE design (i.e., same total length, distribution, diameter, material, inlet flow rate, inlet temperature, etc.).For instance, the total heat transfer over the annual building cooling period increased by nearly 6.7% for the pile with a 0.6 m diameter (P 0.6m ) and by nearly 11.7% for P 0.7m compared to the pile with a 0.5 m diameter (P 0.5m ).For the large-diameter piles, the total heat transfer over the annual building cooling period of three months increased by nearly 8.4% for the pile with a 1.2 m diameter (P 1.2m ) and by nearly 14.9% for P 1.4m compared to the pile with a 1.0 m diameter (P 1.0m ).This is because of the increase in the separation distance between loops and herein decrease the thermal interaction, as shown in Figure 6, which depicts the computed temperature distribution at the mid-depth of the moderate-and large-diameter energy piles, considering the GHEs are symmetrically distributed, as an example, at the end of the annual building cooling period.As the diameter increases for moderate and large pile sets, the potential of thermal interference decreases, considering the same GHE design, and the temperature becomes evenly distributed around the GHEs, which positively affects the heat transfer rate.
cooling period of three months (Figure 5a).The same observation can be seen for largediameter pile set.The total heat transfer of the P1.4m pile, for example, decreases by ~144 kW h (i.e., ~2.0%) when moving away from the symmetrical distribution to a position where the rotation factor is β/6 over the annual building cooling period (Figure 5c).The reasons behind these differences are related to the heat transfer interplays.For adjacent loops where the inlet and outlet are close together, a thermal short-circuit is likely to occur.On the other hand, where inlet and inlet or outlet and outlet are close together, thermal accumulation will likely occur.Since both of these can be detrimental to the system performance, a maximum distance between all loops, in symmetrical distribution, seems to be the least interference.For the same reason, the case when both loops (L2 and L3) are moving towards loop-1 (L1) has not been considered in this study, as the total heat transfer will likely be less than in the other cases.
Furthermore, the results show that increasing the pile diameter generally increases the heat transfer capacity for the same GHE design (i.e., same total length, distribution, diameter, material, inlet flow rate, inlet temperature, etc.).For instance, the total heat transfer over the annual building cooling period increased by nearly 6.7% for the pile with a 0.6 m diameter (P0.6m) and by nearly 11.7% for P0.7m compared to the pile with a 0.5 m diameter (P0.5m).For the large-diameter piles, the total heat transfer over the annual building cooling period of three months increased by nearly 8.4% for the pile with a 1.2 m diameter (P1.2m) and by nearly 14.9% for P1.4m compared to the pile with a 1.0 m diameter (P1.0m).This is because of the increase in the separation distance between loops and herein decrease the thermal interaction, as shown in Figure 6, which depicts the computed temperature distribution at the mid-depth of the moderate-and large-diameter energy piles, considering the GHEs are symmetrically distributed, as an example, at the end of the annual building cooling period.As the diameter increases for moderate and large pile sets, the potential of thermal interference decreases, considering the same GHE design, and the temperature becomes evenly distributed around the GHEs, which positively affects the heat transfer rate.

Heat Transfer Share between Loops
In addition to the total heat transfer from all loops, this section investigates the contribution of each loop (i.e., the loop share) to the total heat transfer for the different loop placements.The aim is to investigate the impact on each loop when changing the loop

Heat Transfer Share between Loops
In addition to the total heat transfer from all loops, this section investigates the contribution of each loop (i.e., the loop share) to the total heat transfer for the different loop placements.The aim is to investigate the impact on each loop when changing the loop distribution from symmetrical to another placement, which might happen for design reasons or due to some uncertainties associated with the installation process.
The percentage share of each loop (L1, L2, and L3) from the total heat transfer for the moderate-diameter piles is shown in Figure 7, and for large-diameter piles, in Figure 8.As shown in Figure 7, for P 0.7m and to a lesser extent for P 0.6m , the share of the total heat transfer between loops L1, L2, and L3 is nearly equal when loops are symmetrically distributed.However, a small movement from the symmetrical distribution (for instance, from a rotation factor = 1 to 5/6 β or from a rotation factor = 1 to 7/6 β), which can be due to a human error during construction, can affect the total heat transfer share between Energies 2024, 17, 2580 13 of 25 loops by up to 1.5% for P 0.7m (~24 kW h over the annual building cooling period), and up to 2.0% for P 0.6m (~31 kW h over the annual building cooling period).These marginal differences due to the small movement increase as the loops' distribution becomes far from the symmetric distribution.Therefore, although the differences in the total heat transfer from all loops (Figure 5) seem to be minimal for some highly non-symmetrical locations (for example, at rotation factor <3/6 β or >10/6 β) compared to the symmetrical position, the total heat transfer shared by each loop can be highly different, which might imply operational consequences for the GSHP system depending on the header pipe arrangements and proximity to the GSHP plant.Importantly, the uneven temperature distribution within the pile may induce some thermo-mechanical strains.
In the case of the 0.5 m pile's diameter (P 0.5m ), the difference between loop shares, even at the symmetrical distribution, reaches up to 2.0% (which is, in this case, equal to ~30 kW h per pile over the annual building cooling period).This might be because the smaller the pile's diameter is, the smaller the separation distance becomes between individual loops (considering a 25 cm shank spacing between the individual loop's legs), and therefore, the potential of thermal interference between adjacent loops increases.However, even for the small pile diameter, the differences continue to be in an acceptable range (less than 5%) as long as the loop distribution is not highly non-symmetric.
The percentage share of each loop (L1, L2, and L3) from the total heat transfer fo moderate-diameter piles is shown in Figure 7, and for large-diameter piles, in Figure shown in Figure 7, for P0.7m and to a lesser extent for P0.6m, the share of the total heat tra between loops L1, L2, and L3 is nearly equal when loops are symmetrically distrib However, a small movement from the symmetrical distribution (for instance, from a tion factor = 1 to 5/6 β or from a rotation factor = 1 to 7/6 β), which can be due to a hu error during construction, can affect the total heat transfer share between loops by 1.5% for P0.7m (~24 kW h over the annual building cooling period), and up to 2.0% fo (~31 kW h over the annual building cooling period).These marginal differences due small movement increase as the loops' distribution becomes far from the symmetri tribution.Therefore, although the differences in the total heat transfer from all loops ure 5) seem to be minimal for some highly non-symmetrical locations (for examp rotation factor <3/6 β or >10/6 β) compared to the symmetrical position, the total transfer shared by each loop can be highly different, which might imply operationa sequences for the GSHP system depending on the header pipe arrangements and pro ity to the GSHP plant.Importantly, the uneven temperature distribution within th may induce some thermo-mechanical strains.
In the case of the 0.5 m pile's diameter (P0.5m), the difference between loop sh even at the symmetrical distribution, reaches up to 2.0% (which is, in this case, equ ~30 kW h per pile over the annual building cooling period).This might be becaus smaller the pile's diameter is, the smaller the separation distance becomes between vidual loops (considering a 25 cm shank spacing between the individual loop's legs therefore, the potential of thermal interference between adjacent loops increases.ever, even for the small pile diameter, the differences continue to be in an acceptable (less than 5%) as long as the loop distribution is not highly non-symmetric.Looking at the large-diameter pile set in Figure 8, the loop heat transfer share d ences at symmetry reaches up to 1.6%, 1.8%, and 3.7% for P1.4m, P1.2m, and P1.0m, re tively.These slightly higher differences, compared to the moderate-diameter pil might be because of the higher heat transfer due to the use of the W-loop shape fo Looking at the large-diameter pile set in Figure 8, the loop heat transfer share differences at symmetry reaches up to 1.6%, 1.8%, and 3.7% for P 1.4m , P 1.2m , and P 1.0m , respectively.These slightly higher differences, compared to the moderate-diameter pile set, might be because of the higher heat transfer due to the use of the W-loop shape for the individual loops of the large-diameter piles compared to the U-loop shape for the moderate-diameter piles, which increases the thermal interaction potential.While these differences increase as the loops' distribution becomes highly non-symmetric (for example, at rotation factor <3/6 β or >10/6 β) in the case of P 1.4m and P 1.2m , the behaviour is different for P 1.0m .When L2 is the moving loop (Figure 8a), the loop heat transfer share becomes more similar as the outlet of L2 gets closer to the outlet of L1.However, when L3 is the moving loop (Figure 8b), the difference in loop heat transfer share becomes larger as the inlet of L3 gets closer to the inlet of L1.This means that the thermal performance of the loops becomes more critical when inlets become adjacent to each other compared to the case when outlets become near to each other.P1.0m.When L2 is the moving loop (Figure 8a), the loop heat transfer share becomes similar as the outlet of L2 gets closer to the outlet of L1.However, when L3 is the m loop (Figure 8b), the difference in loop heat transfer share becomes larger as the in L3 gets closer to the inlet of L1.This means that the thermal performance of the becomes more critical when inlets become adjacent to each other compared to the when outlets become near to each other.It is also evident that, as discussed earlier in Figure 5, the total heat transfer for pile diameter is similar whether L2 or L3 is moving.However, for the same rotation f the heat transfer share between L2 and L3 is different for each pile diameter case, de ing on which loop is moving.To simplify this, by looking at P0.7m when L2 moves fro symmetrical location towards L3 in Figure 7a, L3 shows a faster decrement in its transfer share compared to the case when L3 is moving towards L2 in Figure 7b.M ver, regardless of which loop is moving, L3 continues to have the minimum heat tra share between all loops when L2 and L3 become closer to each other (from rotation = 1 to 1/6 β) because the thermal interference between L2 and L3 has a higher impa the outlet leg of L3 than the inlet leg of L2 as typically the inlet leg contributes m heat exchange than other legs forming a heat-exchanging loop.This is why the heat fer share of L2 when it moves towards L3 appears to be stable in Figure 7a.And f same reason, the heat transfer share decrement of L2 when L3 moves towards it in F 7b is less than the decrement that occurs for L3 when L2 moves towards it in Figu Similar observations can be seen for P0.6m and P0.5m, as well as for the large-diamete set in Figure 8.
From the previous discussion, except for the highly non-symmetric distributio example, at rotation factor < 3/6 β or >10/6 β), we can gain a benefit from the ma differences in the thermal performance of the parallel loops at different relative ments from each other within the energy pile to increase the flexibility in design distributing the loops.It also benefits to a certain extent from decreasing the risk of h It is also evident that, as discussed earlier in Figure 5, the total heat transfer for each pile diameter is similar whether L2 or L3 is moving.However, for the same rotation factor, the heat transfer share between L2 and L3 is different for each pile diameter case, depending on which loop is moving.To simplify this, by looking at P 0.7m when L2 moves from the symmetrical location towards L3 in Figure 7a, L3 shows a faster decrement in its heat transfer share compared to the case when L3 is moving towards L2 in Figure 7b.Moreover, regardless of which loop is moving, L3 continues to have the minimum heat transfer share between all loops when L2 and L3 become closer to each other (from rotation factor = 1 to 1/6 β) because the thermal interference between L2 and L3 has a higher impact on the outlet leg of L3 than the inlet leg of L2 as typically the inlet leg contributes more in heat exchange than other legs forming a heat-exchanging loop.This is why the heat transfer share of L2 when it moves towards L3 appears to be stable in Figure 7a.And for the same reason, the heat transfer share decrement of L2 when L3 moves towards it in Figure 7b is less than the decrement that occurs for L3 when L2 moves towards it in Figure 7a.Similar observations can be seen for P 0.6m and P 0.5m , as well as for the large-diameter pile set in Figure 8.
From the previous discussion, except for the highly non-symmetric distribution (for example, at rotation factor < 3/6 β or >10/6 β), we can gain a benefit from the marginal differences in the thermal performance of the parallel loops at different relative placements from each other within the energy pile to increase the flexibility in design when distributing the loops.It also benefits to a certain extent from decreasing the risk of having a significant decline in the energy pile thermal performance due to installation uncertainties.Nevertheless, it might be advisable that practitioners distribute the loops symmetrically during installation.However, the separation distance between loops in symmetrical distribution for the same diameter of the pile depends on the shank spacing between the legs of individual loops.Therefore, understanding the effects of the loops' shank spacing in symmetrical distribution allows us to design the best thermal performance for each pile diameter.This is investigated next.

Effect of GHE Pipe Leg Spacing
In the previous section, the shank spacing (K) between the legs of individual loops was fixed to 0.25 m, and the separation distance (S) between loops was changed considering different rotation factors.The symmetrical distribution of the loops has been found to be a suitable choice considering both the thermal performance and the practical installations.
This section aims at finding the optimised shank spacing while all loops are in symmetric distribution, in which the total thermal exchange is maximised for the moderate and large-diameter pile sets.In this situation, the higher the shank spacing, the lower the separation distance between loops; therefore, the shank spacing should be carefully designed to avoid any potential decrement in the thermal performance due to the thermal interference between the legs forming each loop when K is small, or between the legs of the adjacent loops when K is large.For this aim, a parametric analysis was performed for each pile's diameter, considering different separation-to-shank distance ratios (S/K) from 0.1 to 3. Results for moderate-and large-diameter pile sets over the annual building cooling (Figures 9a and 10a, respectively) as well as over the annual building heating period (Figures 9b and 10b) show that the total heat transfer is approximately similar for a separation-to-shank distance ratio between 0.5 and 1.5.These results suggest that there is great flexibility in designing the GHE distribution inside energy piles without losing a significant amount of their thermal performance.However, even though when S/K is between 0.5 and 1.5 and has negligible differences in total heat transfer compared to the equally spaced distribution (i.e., S/K = 1), it may be more practically convenient and easier to install the entire loops' distribution in an equally spaced configuration.
diameter.This is investigated next.

Effect of GHE Pipe Leg Spacing
In the previous section, the shank spacing (K) between the legs of individual loops was fixed to 0.25 m, and the separation distance (S) between loops was changed considering different rotation factors.The symmetrical distribution of the loops has been found to be a suitable choice considering both the thermal performance and the practical installations.
This section aims at finding the optimised shank spacing while all loops are in symmetric distribution, in which the total thermal exchange is maximised for the moderate and large-diameter pile sets.In this situation, the higher the shank spacing, the lower the separation distance between loops; therefore, the shank spacing should be carefully designed to avoid any potential decrement in the thermal performance due to the thermal interference between the legs forming each loop when K is small, or between the legs of the adjacent loops when K is large.For this aim, a parametric analysis was performed for each pile's diameter, considering different separation-to-shank distance ratios (S/K) from 0.1 to 3. Results for moderate-and large-diameter pile sets over the annual building cooling (Figures 9a and 10a, respectively) as well as over the annual building heating period (Figures 9b and 10b) show that the total heat transfer is approximately similar for a separation-to-shank distance ratio between 0.5 and 1.5.These results suggest that there is great flexibility in designing the GHE distribution inside energy piles without losing a significant amount of their thermal performance.However, even though when S/K is between 0.5 and 1.5 and has negligible differences in total heat transfer compared to the equally spaced distribution (i.e., S/K = 1), it may be more practically convenient and easier to install the entire loops' distribution in an equally spaced configuration.Total heat transfer from all loops for moderate-diameter energy piles (P 0.5m , P 0.6m , and P 0.7m ) for different separation-to-shank distance ratios (S/K) over the annual building cooling period (a) and the annual building heating period (b).

Generalised Case and Influencing Parameters
This section aims to investigate six other cases besides the study performed for the Arden site (Section 3.1), where each case covers a range of one of the influencing parameters on energy pile thermal performance, as listed in Table 3.Each case includes three

Generalised Case and Influencing Parameters
This section aims to investigate six other cases besides the study performed for the Arden site (Section 3.1), where each case covers a range of one of the influencing parameters on energy pile thermal performance, as listed in Table 3.Each case includes three subcases: subcase (a) represents the parameter value used for the Arden site, and subcases (b) and (c) represent two other chosen parameter values (smaller or greater than the Arden site subcase (a)).For each case, all other parameters used are those corresponding to the base case of the Arden site, and the thermal capacity for each pile varies such that the average fluid temperature of the energy piles is within the GSHP typical optimal operation range (i.e., between 8 and 32 • C) as before.The smallest pile diameter from each of the moderateand large-diameter sets (i.e., P 0.5m and P 1.0m , respectively) has been chosen to run the parametric analyses, as their pile diameter is small to accommodate the three parallel loops; therefore, they represent critical cases in terms of thermal interference between adjacent loops.Table 3. Parametric analysis cases for more critical pile diameters of 0.5 m (U-loops) and 1.0 m (W-loops).The first case is related to variations in the ground thermal conductivity and adopts an isotropic homogeneous soil assumption for subcases b and c.The equivalent weighted average thermal conductivity to the Arden site setting is 2.5 W/(m•K), and it has been found to have similar behaviour (although different magnitude) compared to the realistic layered ground of the Arden site, as shown in Appendix A.2 (Figures A4 and A5).The second case considers a lower value of the concrete thermal conductivity of 1 W/(m•K) and a higher value of 3 W/(m•K) compared to the 2.1 W/(m•K) in the Arden site.The third case covers two pile lengths of 15 m and 25 m beside the 40 m used for the Arden site.For case four, fluid flow rates of 7.5 l/min and 10 l/min were chosen, besides the 5.5 l/min, in the Arden site condition.The fifth case is related to the pipe diameter, where smaller and larger commercial diameters, compared to 25.4 mm for the Arden site, have been investigated.Finally, thermoactivated pile spacing in the Arden site has been altered in the sixth case to have a value of 2 m and 3.5 m.

Case
Parametric analyses have been conducted by changing the influencing parameter value associated with each case over the annual heating and cooling loads.For each case, the symmetrical distribution of the three single U-loops and the three single W-loops for P 0.5m and P 1.0m , respectively, continue to have the highest total heat transfer among other rotation factors.However, the differences between symmetrical and non-symmetrical placements for each case appear to be as marginal as the investigations for the Arden site case.These are listed in Table 4, which shows the maximum differences in the total heat transfer over the annual cooling period, as an example, for P 0.5m and P 1.0m when the loops are symmetrically distributed (i.e., rotation factor = 1) compared to when L2 or L3, which was found to be nearly similar, is moved and placed at rotation factor = 1/6 β.Refer to Appendix A.3 for more details regarding the total heat transfer over the annual cooling and heating periods for P 0.5m and P 1.0m at all the considered rotation factors.Finally, the total heat transfer share between the three loops (L1, L2, and L3) inside P 0.5m and P 1.0m at different locations (rotation factors) has been investigated for all the cases.Figure 11 summarises the maximum differences between the total heat transfer share of the three loops for each case at placements near the symmetry condition and in highly non-symmetric conditions (i.e., at rotation factor < 3/6 β or >10/6 β).It is evident that the various distributions of the loops, except the highly non-symmetric, keep the share of the total heat transfer between the loops in an acceptable margin for all cases.
P0.5m and P1.0m at different locations (rotation factors) has been investigated for all the cases.Figure 11 summarises the maximum differences between the total heat transfer share of the three loops for each case at placements near the symmetry condition and in highly non-symmetric conditions (i.e., at rotation factor < 3/6 β or >10/6 β).It is evident that the various distributions of the loops, except the highly non-symmetric, keep the share of the total heat transfer between the loops in an acceptable margin for all cases.

Conclusions
A three-dimensional finite element model has been used to perform numerical analyses and parametric studies to examine the effect of altering the location and separations of ground heat-exchanging loops connected in parallel within energy piles on their thermal performance.The study has been conducted considering a real layered site setting located in Melbourne, Australia (Arden site).Two main sets of energy piles have been investigated.The first set consists of moderate-diameter piles with diameters between 0.5 m and 0.7 m equipped with three U-tube loops.The second set includes large-diameter piles with diameters ranging from 1 m to 1.4 m, containing three W-tube loops.The loops are connected in parallel and distributed around the pile's perimeter with a 75 mm cover, with varying separation between each loop.In addition to the site-specific investigations on the Arden site and to generalise the results, different cases have also been considered with various ranges of influencing (isotropic) parameters on the thermal performance of the energy pile, including ground thermal conductivity, concrete thermal conductivity, pile length, fluid flow rate, pipe diameter, and pile spacing.The study reveals the following:

•
A drop of less than 3% in the total heat transfer is observed considering a worst-case scenario (highly non-symmetrical placement) of the GHE distribution connected in parallel within the energy pile compared to the symmetrical case.This means that the effect of altering the loops' distribution is minimal from the thermal yield point of view;

•
The share of the total heat transfer between the parallel loops generally varies within a range of less than 5%, except for highly non-symmetric configurations.These results allow ample flexibility in distributing the loops during the design stages.In

Conclusions
A three-dimensional finite element model has been used to perform numerical analyses and parametric studies to examine the effect of altering the location and separations of ground heat-exchanging loops connected in parallel within energy piles on their thermal performance.The study has been conducted considering a real layered site setting located in Melbourne, Australia (Arden site).Two main sets of energy piles have been investigated.The first set consists of moderate-diameter piles with diameters between 0.5 m and 0.7 m equipped with three U-tube loops.The second set includes large-diameter piles with diameters ranging from 1 m to 1.4 m, containing three W-tube loops.The loops are connected in parallel and distributed around the pile's perimeter with a 75 mm cover, with varying separation between each loop.In addition to the site-specific investigations on the Arden site and to generalise the results, different cases have also been considered with various ranges of influencing (isotropic) parameters on the thermal performance of the energy pile, including ground thermal conductivity, concrete thermal conductivity, pile length, fluid flow rate, pipe diameter, and pile spacing.The study reveals the following: • A drop of less than 3% in the total heat transfer is observed considering a worst-case scenario (highly non-symmetrical placement) of the GHE distribution connected in parallel within the energy pile compared to the symmetrical case.This means that the effect of altering the loops' distribution is minimal from the thermal yield point of view; • The share of the total heat transfer between the parallel loops generally varies within a range of less than 5%, except for highly non-symmetric configurations.These results allow ample flexibility in distributing the loops during the design stages.In addition, the results suggest low risks associated with deviations from design during installation with regard to thermal performance; • The heat transfer share between loops might be different as two adjacent inlets become closer to each other compared to two adjacent outlets in the pile.This becomes more important as the internal space of the pile becomes smaller and equipped with higher thermally efficient GHE loops such as W-tube compared to U-tube loops, and may be a consideration for structural integrity given the thermal gradients within the horizontal cross-section of the pile induced during operation of the GSHP system; • The insignificant decrease in thermal performance when the separation-to-shank distance ratios range from 0.5 to 1.5 in the symmetrical distribution allows for more flexibility in designing and installing the GHE loops as well as the possibility of increasing the number of loops, which increases the total energy pile thermal yield.
However, installing the loops in symmetrical and evenly spaced distribution (i.e., separation-to-shank distance ratio equal to 1) results in the best overall performance and is thus recommended; • Regardless of variations in the considered cases of the influencing parameters (i.e., ground thermal conductivity, concrete thermal conductivity, pile length, fluid flow rate, pipe diameter, and pile spacing), when the loops stay near a symmetric distribution, they are within 5% of difference in sharing the load.However, if one loop is not carefully placed and becomes loose, it could result in up to a 12% difference in the load share among the loops.This may impose inter-pile thermal strains; • Anisotropic material conditions were not evaluated but are suspected to render sim- ilar trends, albeit different absolute values in results.This may be the subject of future work.

Figure A1.
Total heat transfer over the heating period for P1.0m considering a range of pile spacing.
In addition, a long-term analysis (20 years) has been conducted for two critical cases when the inlet of loop-2 is adjacent to the outlet of loop-3 for the smallest diameter of the moderate-diameter pile set (i.e., P0.5m) and the large-diameter pile set (i.e., P1.0m).Figures A2 and A3 show that the outlet fluid temperature from each loop is typical at each thermal cycle over 20 years.Therefore, performing analysis over one year is sufficient to generalise  In addition, a long-term analysis (20 years) has been conducted for two critical cases when the inlet of loop-2 is adjacent to the outlet of loop-3 for the smallest diameter of the moderate-diameter pile set (i.e., P 0.5m ) and the large-diameter pile set (i.e., P 1.0m ).Figures A2 and A3 show that the outlet fluid temperature from each loop is typical at each thermal cycle over 20 years.Therefore, performing analysis over one year is sufficient to generalise it over the total design period (i.e., 20 years) with a dramatic decrease in the computational cost.In addition, a long-term analysis (20 years) has been conducted for two critical c when the inlet of loop-2 is adjacent to the outlet of loop-3 for the smallest diameter o moderate-diameter pile set (i.e., P0.5m) and the large-diameter pile set (i.e., P1.0m).Fig A2 and A3 show that the outlet fluid temperature from each loop is typical at each the cycle over 20 years.Therefore, performing analysis over one year is sufficient to gener it over the total design period (i.e., 20 years) with a dramatic decrease in the computat cost.For the layered ground in the Arden site and its equivalent homogeneous val 2.5 W/(m•K), Figures A4 and A5 show the total heat transfer over the annual buil cooling period, as an example, and its associated shares between the loops for P0.5m P1.0m, respectively.The total heat transfer differences, independent of which loop is m ing, between different rotation factors considering the homogeneous ground are as m mal as that of the Arden site condition, in addition to the marginal shares of the heat t fer between the loops around symmetry.This justifies, in this study, the us homogeneous thermal conductivity values for subcases b and c in the first case (Se 3.2).

Appendix A.2
For the layered ground in the Arden site and its equivalent homogeneous value of 2.5 W/(m•K), Figures A4 and A5 show the total heat transfer over the annual building cooling period, as an example, and its associated shares between the loops for P 0.5m and P 1.0m , respectively.The total heat transfer differences, independent of which loop is moving, between different rotation factors considering the homogeneous ground are as minimal as that of the Arden site condition, in addition to the marginal shares of the heat transfer between the loops around symmetry.This justifies, in this study, the use of homogeneous thermal conductivity values for subcases b and c in the first case (Section 3.2).
P1.0m, respectively.The total heat transfer differences, independent of which loop is moving, between different rotation factors considering the homogeneous ground are as minimal as that of the Arden site condition, in addition to the marginal shares of the heat transfer between the loops around symmetry.This justifies, in this study, the use of homogeneous thermal conductivity values for subcases b and c in the first case (Section 3.2).

Appendix A.3
The following tables list the total heat transfer over the annual cooling and heating periods for P0.5m and P1.0m at all the considered rotation factors for the considered generalised cases in (Section 3.2).Appendix A.3 The following tables list the total heat transfer over the annual cooling and heating periods for P 0.5m and P 1.0m at all the considered rotation factors for the considered generalised cases in (Section 3.2).

Figure 1 .
Figure 1.Schematic drawing showing an example of three U-tube loops connected in parallel (a) and in series (b) in an energy pile.

Figure 1 .
Figure 1.Schematic drawing showing an example of three U-tube loops connected in parallel (a) and in series (b) in an energy pile.

Figure 2 .
Figure 2. Schematic drawings (not to scale) for the adopted geological setting and propertie Arden site (Melbourne, Australia) after [36] (a) and the vertical cross-section passing throu centre of the energy pile and the ground showing the details of the model set up and key bo conditions (b).

Figure 2 .
Figure 2. Schematic drawings (not to scale) for the adopted geological setting and properties of the Arden site (Melbourne, Australia) after [36] (a) and the vertical cross-section passing through the centre of the energy pile and the ground showing the details of the model set up and key boundary conditions (b).

Figure 3 .
Figure 3. Schematic drawings showing an example of an energy pile equipped with three single Uloops and details of the GHEs used in the simulations.

Figure 3 .
Figure 3. Schematic drawings showing an example of an energy pile equipped with three single U-loops and details of the GHEs used in the simulations.

3 .
Results and Discussion 3.1.The Arden Site-Specific Case 3.1.1.Effect of GHE Distribution This section investigates the effects of distribution and spacing of the three loops connected in parallel and distributed around the perimeter of both moderate-diameter pile set (0.5, 0.6, and 0.7 m) and large-diameter pile set (1.0, 1.2, and 1.4 m), with the aim to produce the maximum heat exchange rate.The moderate-diameter piles are equipped with Energies 2024, 17, 2580 10 of 25

Figure 4 .
Figure 4. Distribution of GHE loops inside the energy pile when L2 is moving (a) and when L3 is moving (b) considering different rotation factors.

Figure 4 .
Figure 4. Distribution of GHE loops inside the energy pile when L2 is moving (a) and when L3 is moving (b) considering different rotation factors.

Figure 5 .
Figure 5.Total heat transfer from all loops for moderate-diameter (P 0.5m , P 0.6m , and P 0.7m ) (top: (a,b)-with parallel U-loops) and large-diameter (P 1.0m , P 1.2m , and P 1.4m ) (bottom: (c,d)-with parallel W-loops) energy piles at different rotation factors, for the three months of the annual building cooling period (left: (a,c)) and the annual building heating period (right: (b,d)).

Figure 6 .
Figure 6.Horizontal cross-sections at the mid-depth of the energy piles showing the resulting temperature distributions at the end of the annual building cooling period when GHEs are symmetrically distributed for moderate-diameter piles (a) and large-diameter piles (b).

Figure 6 .
Figure 6.Horizontal cross-sections at the mid-depth of the energy piles showing the resulting temperature distributions at the end of the annual building cooling period when GHEs are symmetrically distributed for moderate-diameter piles (a) and large-diameter piles (b).

Figure 7 .
Figure 7. Loop heat transfer share from the total heat transfer for moderate-diameter pile set ferent locations when L2 is moving (a) and when L3 is moving (b).

Figure 7 .
Figure 7. Loop heat transfer share from the total heat transfer for moderate-diameter pile set at different locations when L2 is moving (a) and when L3 is moving (b).

Figure 8 .
Figure 8. Loop heat transfer shares from the total heat transfer for large-diameter pile set at di locations when L2 is moving (a) and when L3 is moving (b).

Figure 8 .
Figure 8. Loop heat transfer shares from the total heat transfer for large-diameter pile set at different locations when L2 is moving (a) and when L3 is moving (b).

Figure 9 .
Figure 9.Total heat transfer from all loops for moderate-diameter energy piles (P0.5m,P0.6m, and P0.7m) for different separation-to-shank distance ratios (S/K) over the annual building cooling period (a) and the annual building heating period (b).

Figure 9 .
Figure 9.Total heat transfer from all loops for moderate-diameter energy piles (P 0.5m , P 0.6m , and P 0.7m ) for different separation-to-shank distance ratios (S/K) over the annual building cooling period (a) and the annual building heating period (b).

Energies 2024 , 25 Figure 10 .
Figure 10.Total heat transfer from all loops for large-diameter energy piles (P1.0m,P1.2m, and P1.4m) for different separation-to-shank distance ratios (S/K) over the annual building cooling period (a) and the annual building heating period (b).

Figure 10 .
Figure10.Total heat transfer from all loops for large-diameter energy piles (P 1.0m , P 1.2m , and P 1.4m ) for different separation-to-shank distance ratios (S/K) over the annual building cooling period (a) and the annual building heating period (b).

Figure 11 .
Figure 11.Maximum difference in total heat transfer shares between loops near symmetrical and highly non-symmetrical distributions considering all cases in Table 3 for 0.5 m pile diameter with three single U-loops (a) and 1.0 m pile diameter with three single W-loops (b).

Figure 11 .
Figure 11.Maximum difference in total heat transfer shares between loops near symmetrical and highly non-symmetrical distributions considering all cases in Table 3 for 0.5 m pile diameter with three single U-loops (a) and 1.0 m pile diameter with three single W-loops (b).

Figure A1 .
Figure A1.Total heat transfer over the heating period for P 1.0m considering a range of pile spacing.

Figure A1 .
Figure A1.Total heat transfer over the heating period for P1.0m considering a range of pile spac

Figure A2 .
Figure A2.Outlet fluid temperature in each GHE loop for P0.5m at a rotation factor of 1/6 β ov years of operation.

Figure A2 .Figure A3 .
Figure A2.Outlet fluid temperature in each GHE loop for P 0.5m at a rotation factor of 1/6 β over 20 years of operation.Energies 2024, 17, x FOR PEER REVIEW 21

Figure A3 .
Figure A3.Outlet fluid temperature in each GHE loop for P 1.0m at a rotation factor of 1/6 β over 20 years of operation.

Figure A4 .
Figure A4.Total heat transfer from all loops for moderate-diameter energy pile P0.5m for different rotation factors when L2 or L3 is moving over the annual building cooling period for homogeneous (2.5 W/m•K) and layered (Arden site) ground conditions (a) and their associated loop heat transfer share (b).

Figure A4 . 25 Figure A5 .
Figure A4.Total heat transfer from all loops for moderate-diameter energy pile P 0.5m for different rotation factors when L2 or L3 is moving over the annual building cooling period for homogeneous (2.5 W/m•K) and layered (Arden site) ground conditions (a) and their associated loop heat transfer share (b).Energies 2024, 17, x FOR PEER REVIEW 22 of 25

Figure A5 .
Figure A5.Total heat transfer from all loops for large-diameter energy pile P 1.0m when L2 or L3 is moving around the pile circumference over the annual building cooling period for homogeneous (2.5 W/m•K) and layered (Arden site) ground conditions (a) and their associated loop heat transfer share (b).

Table 1 .
Energy pile model parameters (Arden site case).

Table 2 .
Mesh sensitivity analysis (on a 64-core processor computer).

Table 4 .
Total heat transfer over the annual cooling period for P 0.5m and P 1.0m at rotation factors: 1 (symmetry) and β/6.Design average fluid temperature kept between 8 and 32 • C.

Table A1 .
Total heat transfer over the annual cooling period for P0.5m at all rotation factors.

Table A1 .
Total heat transfer over the annual cooling period for P 0.5m at all rotation factors.

Table A2 .
Total heat transfer over the annual heating period for P0.5m at all rotation factors.

Table A3 .
Total heat transfer over the annual cooling period for P 1.0m at all rotation factors.

Table A4 .
Total heat transfer over the annual heating period for P1.0m at all rotation factors.