1. Introduction
Presently, due to extreme environmental pollution and energy shortage around the world, the exploitation of renewable energies has become more vital. Geothermal energy is one of the renewable energies that can be used, specifically by means of coupling to ground source heat pump (GSHP) systems. GSHP system provides heating and cooling of buildings through the ground heat exchanger (GHE) which usually appears in horizontal and vertical configurations. Since the vertical GHE, also named borehole heat exchanger (BHE), needs less land for installation and has wide applicability and better performance than the horizontal GHE, it has been comprehensively investigated in recent years [
1].
To improve the thermal performance of the BHEs, various approaches have been taken such as geometry improvements [
2,
3], the use of new materials for pipe, backfill or grout, and working fluid [
1,
4]. Quaggiotto et al. [
5] studied two types of BHEs including coaxial BHE and double U-tube BHE. Based on the comparison made, heat transfer in the coaxial BHE was higher than the double U-tube BHE both in cooling and heating operating modes. Serageldin et al. [
6] investigated experimentally and numerically the use of oval cross-section pipes instead of the circular cross-section pipes used in the BHE in the presence of underground water. It was concluded that a BHE with oval cross-section pipes has the potential to decrease the installation costs and increase the thermal performance of the BHE. In a thermal response test (TRT) conducted by Sapinska-Sliwa et al. [
7] for three types of BHEs, for instance, single U-tube, double U-tube, and coaxial BHE, the last configuration was found to be the best one in achieving the effective thermal conductivity of the ground. In another study, carried out experimentally and numerically by Janiszewski et al. [
8], a single U-tube BHE was used to inject thermal energy into the surroundings. It was proven that a higher thermal conductivity of the pipe and backfill as well as a larger pipe distancing and pipe radius are essential for improving the borehole thermal energy storage (BTES) system efficiency. A review article concerning a variety of nanofluids that can be applied as working fluids in the BHE was conducted by Patil et al. [
9]. It was concluded that nanofluids can enhance the thermal performance of the BHE when it operates at higher temperatures, as the higher the temperature the better the thermal conductivity of nanofluids. In an experimental study done by Cao et al. [
10], it was shown that a BHE with a steel pipe can have superior thermal performance and lower thermal resistance compared to a BHE with a polyethylene pipe. Li et al. [
11] evaluated experimentally single U-tube and double U-tube BHEs at different depths and concluded that increasing the depth of the pipe results in greater thermal performance of BHEs in both summer and winter seasons.
One type of the backfill materials that is applied in the BHE is phase change material (PCM). The PCMs are generally categorized into organic, inorganic, hygroscopic, and solid-solid materials. The organic PCMs such as Paraffin have been widely used in the BTES systems to provide energy for the heat pumps because of their high TES capacity. In addition, organic PCMs are found to be beneficial for GSHP applications. To use such materials as backfill and to improve the thermal performance of the BHEs, their low thermal conductivity must increase, as the higher the thermal conductivity of the backfill the superior the heat transfer from the working fluid to the surrounding ground. Hence, a variety of methods are carried out to tackle this problem [
4]. Wang et al. [
12] studied numerically the use of a mixture of lauric acid and n-decanoic acid as backfill in a single U-tube BHE. The results showed that the thermal interference radius and the temperature difference between inlet and outlet could decrease and increase by 26% and 67% respectively, compared to the soil as backfill. Lei and Dai [
13] investigated theoretically the influence of using a mixture of lauric acid and capric acid as a backfill on the thermal performance of a coaxial BHE. The results indicated that the differences between the inlet and outlet temperatures of the working fluid are 0.24 °C when using soil backfill and 0.08 °C for the PCM backfill at the end of the cooling operation. A numerical study on applying shape-stabilized PCM (SSPCM), a mixture of lauric acid and decanoic acid, as backfill in a single U-tube BHE was carried out by Li et al. [
14,
15]. Based on their results, the heat exchange rate and thermal interference radius for the BHE backfilled with SSPCM could be 1.37 and 0.9 times of that for crushed stone concrete as a backfill. The effects of three types of PCM backfill including acid, enhanced acid, and Paraffin RT27 on the thermal performance of a single U-tube BHE is evaluated numerically by Qi et al. [
16]. The results demonstrated that PCM backfills have a smaller thermal interference radius than soil backfill. A numerical investigation of using SSPCM and microencapsulated Paraffin as backfill in a single U-tube BHE was conducted by Chen et al. [
17]. It was concluded that SSPCM improves the thermal performance of the BHE compared to microencapsulated Paraffin, thanks to its higher thermal conductivity. It was also found that the use of the SSPCM backfill is beneficial where the effect of underground water is negligible. Besides, Chen et al. [
18] examined the impact of different melting temperatures of PCM backfill on the BHE thermal performance and selected 20.4 °C as the best melting temperature which led to improving the cooling operation of the system. A study on the thermal performance of a single U-tube BHE when it is backfilled with salt hydrate PCM was done by Zhang et al. [
19]. The numerical results showed that when the PCM was used as a backfill in the BHE, the temperature differences of the working fluid at the inlet and outlet after 6 h of cooling operation increased compared to the corresponding temperature differences in the BHE containing a conventional backfill which led to enhancing the heat transfer rate and system efficiency in the summer. Yang et al. [
20] studied both numerically and experimentally the use of a mixture of lauric acid and decyl acid for cooling operating and oleic acid for heating operating as backfill material in a single U-tube BHE. According to the results, PCM backfills reduce almost 88% and 86% of the thermal interference radius for heating operating and cooling operating compared to soil backfill, respectively. An increase of 28% and 9.4% are found in the heat exchange rate per meter of borehole depth for heating and cooling operating, respectively, when using PCM backfills instead of soil backfill.
Please note that there have been also a few articles regarding the use of PCM (microencapsulated PCM) as backfill in the Horizontal GHE [
21,
22,
23]. Moreover, PCM has had other applications in GSHP systems. Zhang et al. [
19] presented a new type of BHE named underground thermal battery in which both BHE and PCM (forming a ring inside the borehole) were immersed in a water tank. In a theoretical study of Rabin and Korin [
24], Paraffin was used in the form of a ring as TES inside/outside the borehole. Benli and Durmus [
25,
26] experimentally investigated the integration of a Horizontal GHE with a TES system containing salt hydrate PCM for heating of a greenhouse. A mixture of microencapsulated Paraffin and soil was examined as TES combined with a Horizontal GHE both experimentally and numerically [
27]. Eslami-Nejad and Bernier [
28] evaluated numerically the use of a PCM-sand mixture as a ring inside the borehole. In a numerical investigation conducted by Zhu et al. [
29], hydrate sodium sulfate was applied as TES which was integrated with a BHE. Jeon et al. [
30] studied numerically the incorporation of a panel form of PCM as TES with a Horizontal GHE. In a numerical study carried out by Alkhwildi et al. [
31], a BHE combined with a TES system containing salt hydrate PCM. The application of microencapsulated PCM slurry as a working fluid in a tree-shaped BHE was evaluated numerically by Pu et al. [
32].
Furthermore, there is another type of PCM called nano-enhanced PCM (NEPCM) that is created by dispersing the nanoparticle into a pure PCM. Khodadadi and Hosseinizadeh [
33] were the first scholars who investigated the addition of nanoparticles into PCM and proved that the created NEPCM has better thermal conductivity and higher TES capacity than the conventional PCMs. NPCM has brought many benefits to buildings [
34], heat exchangers [
35], TES [
36], solar systems [
37], and electronic devices [
38]. Kalaiselvam et al. [
34] dispersed experimentally Al
2O
3 and Al nanoparticles to a PCM comprised of n-hexadecane and n-tetradecane which were applied in an advanced building for cooling operation. Their results indicated 4.97% and 12.97% reductions in the solidification time when using Al and Al
2O
3 nanoparticles, respectively, in comparison with the pure PCM. The impact of adding CuO nanoparticles to RT50 PCM placed inside a shell and tube heat exchanger was carried out numerically by Pahamli et al. [
35]. It was concluded that the melting time decreases by 11.6% and 4.56% provided that the volume fractions of the nanoparticles are 4% and 2%, respectively, resulting in superior thermal performance of the heat exchanger. Ramakrishnan et al. [
36] added experimentally graphene nanoparticles to a PCM consisted of expanded perlite and RT27 which were used as TES. According to the results, both melting and solidification time decrease by 33% compared to the pure PCM, due to an increase of 49% in the thermal conductivity of the PCM when applying graphene with 1% by weight. An experimental investigation of adding graphene oxide, TiO
2, and CuO nanoparticles to the Paraffin used in a solar still was conducted by Rufuss et al. [
37]. The results showed the increments of 101%, 25%, and 29% in the thermal conductivity of the PCM at the presence of graphene oxide, TiO
2, and CuO nanoparticles, respectively, which led to the higher production of freshwater. In another study, the use of NEPCM made of Paraffin wax as PCM and multi-wall carbon nanotube (MWCNT) as nanoparticles in an electronic chipset was examined experimentally by Farzanehnia et al. [
38]. The studied NEPCM was found to extend the time of electronic board operation and decrease the time of the cooling process by 6%.
However, based on the previous works concerning NEPCMs [
39,
40,
41] and to the best of the authors’ knowledge, to this day, no scholar has studied the application of NEPCMs as backfill in the BHE which indicates the significance of this study. Therefore, the novelty of the present article is the numerical simulation of NEPCMs in a single U-tube BHE. Accordingly, in the first section of the present study, seven types of NEPCMs are considered and numerical results are compared. Afterward, the selected NEPCM (from the first section) is evaluated in terms of volume fraction and shape of its nanoparticles.
2. Computational Fluid Dynamics Model and Simulation Conditions
In this work, an unsteady 3D model of a BHE is simulated numerically by ANSYS Fluent 18.2 software (see
Figure 1). The BHE comprises a single U-tube (copper tube), working fluid (water), backfill (NEPCM), and the surrounding ground. The whole domain is considered to be a cube with a side length of 1.2 m while the length of the U-tube is 1.1 m. The borehole depth and borehole diameter are 1.2 m and 0.06 m, respectively. The distance between centers of two legs of U-tube is 0.0365 m and the outer and inner diameters of U-tube are 0.0065 m and 0.005 m, respectively. The thermo-physical properties of the BHE components are shown in
Table 1 and
Table 2. Based on a review article conducted by Yang et al. [
39], mostly dispersed nanoparticles into the PCMs, such as Cu, CuO, Al
2O
3, TiO
2, SiO
2, MWCNT, and graphene, are used as nanoparticles in this study to be added to the Paraffin (n-Octadecane) as the base fluid.
As illustrated in
Figure 2, the meshing of the model is provided with high accuracy, especially in the regions near the center of the model as in view of their great influence in the performance of the BHE.
Table 3 indicates the grid independence test performed by analyzing four different numbers of elements in terms of outlet temperature of working fluid and liquid fraction after 10 h of BHE operation. Taking into account the balance between precision and calculation speed, a total number of 2,244,671 elements with maximum skewness of 0.79 and minimum orthogonal quality of 0.25 is selected for the numerical simulations. We have applied structured meshing methods for the fluid and the U-tube, and unstructured methods for the backfill and the ground. The BHE works in the summer season for 12 h daily and the inlet temperature of working fluid is considered to be 308.15 K. At the inlet of the model (see
Figure 1b), we used a Velocity Inlet boundary condition with a constant value of 0.6 m/s and at the outlet, a Pressure Outlet boundary condition is chosen which can minimize the reverse flows when a backflow condition occurs. The interfaces between the regions are supposed to be temperature-coupled walls and the BHE components are homogeneous, isotropic, and temperature independent. Since the heat transfer fluid inside U-tube is in turbulent regime, we implemented the standard k-epsilon as a turbulence model and the SIMPLE scheme for the velocity-pressure condition. The energy and momentum equations that are discretized spatially by Second-Order Upwind have the Under Relaxation Factors of 1 and 0.7, respectively. The numerical simulation converged once the residuals for momentum, continuity, k, and epsilon were less than 10
−3 while the corresponding value for energy was 10
−6 (see
Table 4).
3. Mathematical Formulation
The nanoparticles and PCM that form NEPCM are in thermal equilibrium and the no-slip condition is considered between them. Other key assumption for this study is to consider the thermo-physical properties of the NEPCM as temperature independent. The density of NEPCM (
ρNEPCM) is written as [
33]:
where
ϕ is the volume fraction of the nanoparticles. The specific heat of NEPCM ((
Cp)
NEPCM) is given by [
33]:
The latent heat of NEPCM (
LNEPCM) can be expressed as [
33]:
The dynamic viscosity of NEPCM (
μNEPCM) is defined as [
33]:
The thermal conductivity of NEPCM (
kNEPCM) can be calculated by means of the Hamilton–Crosser formula [
47], in which in addition to including the thermal conductivities of nanoparticles and PCM as well as the nanoparticle volume fraction, the shape of nanoparticles has also been taken into account, which is as follows:
where
n represents the shape factor of the nanoparticles as shown in
Table 5.
To model the phase change process of NEPCM, we used the Enthalpy-Porosity method. The Boussinesq approximation is applied to account for buoyancy effects [
33]:
The continuity, momentum, and energy equations are as follows [
50,
51,
52]:
where
hsens and
hlat are the sensible heat enthalpy and latent heat enthalpy, respectively. The total enthalpy is obtained by summation of the enthalpies:
The sensible heat and latent heat enthalpies can be obtained by Equations (11) and (12) [
53,
54,
55]:
where
λ is the liquid fraction which varies from 0 to 1.
λ = 0 indicates that the material is in solid phase, while for
λ = 1, the NEPCM is full of liquid. The region where 0 <
λ < 1 is considered to be the mushy zone, which acts as a porous region. This parameter is defined as:
In Equation (8),
which is a source term named Darcy’s law damping term is added to the momentum equation:
where
indicates the slow increase of the velocities from zero value in the full solid phase to a finite value in the liquid phase throughout the computational cells at the phase transition occurrence.
Cmush is the mushy zone constant fixed at 10
5 and
ε is a small positive quantity (here 0.001) called computational constant which prevents a division by zero [
53,
54,
55].
6. Conclusions and Future Scope
In this study, a 3D numerical model of a single U-tube borehole heat exchanger is investigated by means of commercial computational fluid dynamics code, ANSYS Fluent 18.2, to simulate ground source heat pump cooling operation. The objectives of the research are first to analyze the application of seven kinds of nano-enhanced phase change material made from the addition of Cu, CuO, Al2O3, TiO2, SiO2, multi-wall carbon nanotube, and graphene nanoparticles to the Paraffin as backfill in the borehole heat exchanger; then, to study the effects of volume fraction of nanoparticles which varies from 0.05 to 0.20 on the thermal performance of the borehole heat exchanger; and finally, to evaluate the role of nanoparticles’ shape such as the sphere, brick, cylinder, platelet, and the blade on the melting rate of nano-enhanced phase change material. The obtained results are as follows:
The nano-enhanced phase change materials with Cu and SiO2 nanoparticles demonstrated to be the best and worst nanoparticles in improving the thermal performance of the single U-tube borehole heat exchanger, respectively. Therefore, Cu nano-enhanced phase change material was selected for further investigation.
In terms of volume fraction, it was founded that the increase in the volume fraction of Cu nanoparticles enhanced considerably the melting rate of nano-enhanced phase change material, being 0.20 the most suitable volume fraction which increased up to 55% the thermal conductivity of the nano-enhanced phase change material in comparison with the pure phase change material.
Concerning the shape of nanoparticles, the blade shape was by far the best shape of the Cu nanoparticles which resulted in about 85% melting of the nano-enhanced phase change material.
To sum up, the nano-enhanced phase change material with Cu nanoparticles in the blade shape at 20% of volume fraction showed to have notable potential to absorb thermal energy from the heat transfer fluid and decrease the outlet water temperature compared to the other nanoparticles which were used as the addition to the Paraffin.
It is worth mentioning that this is the first time that a nano-enhanced phase change material is implemented in a borehole heat exchanger; therefore, more numerical studies are necessary to extend the flow solver to model the melting and solidification processes in the proposed borehole heat exchanger. Also, performing experimental tests for both the charging/discharging process are required to see how the borehole heat exchanger equipped with nano-enhanced phase change material works in a real project.