
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)13473-1
10.1016/j.heliyon.2024.e37442
e37442
Research Article
Analysis on heat transfer performance of coaxial borehole heat exchanger in a layered subsurface with groundwater
He Xiaoliang a
Li Jie 1418877674@qq.com
a⁎
Chen Yiqi b
Niu Baojun a
a China Datang Corporation Xiongan Energy Co., Ltd., China
b School of Energy and Environment, Southeast University, China
⁎ Corresponding author. 1418877674@qq.com
04 9 2024
30 9 2024
04 9 2024
10 18 e3744231 3 2024
7 7 2024
3 9 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
In the realm of ground source heat pump (GSHP) installations, the operational efficiency of borehole heat exchangers (BHEs) is heavily dependent on the complex configurations of geological formations, including soil stratification and the movement of underground water. Our research investigated the influences of ground structure characteristics on the heat transfer performance of coaxial BHEs. A coaxial borehole heat exchanger with a three-dimensional design was constructed, setting a typical geology from the Xiong'an New Region as the boundary condition. The homogenous model with equivalent physical properties overpredicted the water temperature exiting the coaxial BHE in the stratified ground with groundwater advection by 0.2 °C, while underpredicted the heat transfer rate by 10.8 % for the 24-h period; There exists an optimal inlet flow velocity to balance the heat injection and enhanced heat transfer for the optimal heat transfer rate, which was 0.4 m/s in this study; The increase of groundwater advection velocity decreased the outlet temperature by 0.5 %, enhanced the heat transfer per meter by 15.5 % and contributed to a smaller thermal influence radius during the 24-h period. This will contribute to the design of coaxial BHEs in complex geological structure.

Keywords

Coaxial borehole heat exchanger
Ground stratification
Groundwater advection
CFD
Heat transfer rate
==== Body
pmc1 Introduction

The GSHP system harnesses shallow earth thermal energy for the heating and cooling of structures. Owing to its superior efficiency and eco-friendly nature, the GSHP system has the largest worldwide geothermal use, and its installed units have been increased by 54 % from 2015 to 2020 [1]. In the GSHP system, heat transfer between structures and the earth occurs via the borehole heat exchanger system. Regarding GSHP systems, the coaxial BHE stands as the crucial component for the system's efficient functionality. Common vertical borehole heat exchangers include: single U-tube BHEs, double U-tube BHEs and the coaxial BHEs. Since the depth of BHEs commonly ranges from 15 to 180 m for the shallow geothermal system, the thermal performance of BHEs was strongly affected by the surrounding ground structure including vertical ground stratification and groundwater advection [2].

Ignoring the ground stratification and groundwater advection can lead to prediction uncertainties on the thermal efficiency of BHEs. The average rate of thermal exchange for a single U-tube BHE in unsaturated soil conditions was calculated numerically to be 40 % lower than the saturated one, demonstrating a more significant effect of ground material conditions than the operation modes on the system performance [3]. Through experimental research, Li et al. [4] found that the outlet temperature of U-tube BHEs in axial stratified model was about 0.5 °C lower than that in the homogeneous ground model after continuous heating for 60 days. It is shown that the simple uniform medium model leads to an overestimation of the thermal exchange potential of U-tube BHEs. Similar results can be found in the thermal performance prediction of the U-tube BHEs in a sandbox [5], where the numerical simulations using stratified and homogeneous thermal properties yielded analogous water temperatures, albeit with varying distributions of heat exchange and subterranean temperatures at different tube depths. Wang et al. [6] examined the impact of ground stratification and groundwater advection on the heat transfer characteristics of U-tube BHEs and compared it with the homogeneous U-tube BHE model. It is found that the average entry and exit temperature of circulating fluid in the layered U-tube BHEs model without groundwater advection flow is 2.2 % higher than that of the homogeneous model under the heating power of 5 kW for 100 h. The layered composition of the earth significantly impacts the thermal transfer traits of BHEs.

The coaxial BHE has the advantages of a small area, a large heat exchange area, intense turbulence within the tube and elevated efficiency in heat transfer. Compared to the U-tube BHEs, the coaxial BHEs have a higher heat transfer rate per meter, which could reduce the designed borehole length by 30–50 % [7]. Some researchers have analyzed the thermal exchange capabilities of coaxial BHEs in the stratified ground or with the groundwater advection. Ning et al. [8] investigated the thermal exchange efficiency of the coaxial BHE in an ideal three-layered ground with same thickness and linearly-varied thermal properties. The rate of thermal transfer in homogeneous model was calculated to be 1.1 % higher than the layer model. Hou et al. [9] explored the thermal exchange characteristics of coaxial BHEs in a homogenous ground fully saturated with groundwater, and found that there was a great difference within the fluctuation spectrum of soil temperature around the coaxial BHEs under the condition of no advection and advection in the ground. For the heat exchangers, the ground temperature in the advection direction decreases with the increase of the advection velocity. In terms of heat transfer, the higher the advection velocity is, the greater the heat transfer of the coaxial BHEs will be, and the phenomenon of heat accumulation will occur along the advection direction. Zhang et al. [10] used a 2D transient heat transfer model and ignored the radial heat conduction between the coaxial BHEs and ground. The results show that as the mass flow rate of circulating water escalates, the rate of heat transfer correspondingly intensifies. However, the coaxial BHEs generate a distinct distribution of thermal load along the tubes' length compared to that of U-tube BHEs. The different heat transferred from BHEs in different layers distributed different temperatures among layers [11]. Some researchers have established a 3D unsteady heat transfer model to study the performance of the coaxial BHEs, but they have ignored the influence of the ground stratification and groundwater advection. Wu et al. [12] establish the coaxial BHEs 3D unsteady heat transfer model, the homogeneous ground structure conditions, the heat exchange performance of heat exchanger structure influence. Liu et al. [4] took the coaxial BHE as the research object and used a 3D model to simulate the thermal exchange efficiency. The results show that at an inlet flow rate of 0.5 m per second, the heat transfer rate can achieve 42.2 W/m per meter.

Analytical or numerical investigations into the stratification of the ground and the flow of groundwater have demonstrated their significant impact on the thermal exchange efficiency of U-tube BHEs. However, most conclusions were drawn from the U-tube BHE studies, and some with BHE simplified as the 1D pipe element [13,14]. For coaxial BHEs featuring varied distributions of heat loads along the axis, the 2D models of the ground [15,16] failed to consider the ground stratification or groundwater advection; some adopted idealized assumptions which are not directly linked to an actual ground structure [8]. Since the coaxial BHEs have a larger heat transfer ability and have been widely adopted for the shallow and deep geothermal use, we investigated the heat exchange effectiveness of coaxial BHEs in the layered ground with groundwater advection based on the practical geological structure. Within the scope of this research, a 3D computational representation of the coaxial BHE and its surrounding ground was employed to explore the impacts of stratified ground with groundwater advection of representative geological features of the Xiong'an New Area in practical terms. This study investigates the impact of ground stratification and groundwater advection on the heat transfer performance of coaxial borehole heat exchangers (BHEs). By constructing a three-dimensional model with a typical geological setting from the Xiong'an New Region, the research aims to evaluate the thermal performance of coaxial BHEs under various geological conditions.

2 Methods

2.1 Ground structure in Xiong'an New Area

Xiong'an New Area is located in the central region of Hebei Province, China. The city is rich in shallow geothermal energy for a depth of 200 m, suitable for the use of coaxial BHEs ground source heat pump [17]. This study adopted typical geological structure in Xiong'an New area. Based on a large number of ground exploration data and thermal response test reports of the Xiong'an New area [18,19], the typical ground structure of the Xiong'an New Area can be summarized as a four-layer geological structure [20]. Table 1 lists the physical parameters of each layer. From the top to the bottom, the ground structure consists of clayey silt, medium sand, sand and the silt/fine sand, and saturated sand with aquifer is considered in the 3rd layer.Table 1 Detailed parameters of the typical structure in Xiong'an New area used in this study [17,18,20].

Table 1Ground layer	Ground type	Depth range (m)	Density (kg/m3)	Thermal conductivity (W/(m·K))	Specific heat capacity (J/(kg·°C))	Thermal diffusivity (m2/h)	Porosity	Advection velocity ( × 10−5 m/s)	Hydraulic conductivity (m/s)	
1	clayey silt	0∼25	2000	1.2	1420	0.00152	–	–	–	
2	medium sand	25∼40	1925	3.8	1100	0.0046	–	–	–	
3	sand (aquifer)	40∼80	2140	1.85	1400	0.00223	0.43	1.29	7.3 × 10−5	
4	silt and fine sand	80∼100	1850	1.45	1590	0.00178	–	–	–	

2.2 Numerical simulations

2.2.1 CFD model

Several assumptions were made in the CFD model developed by FLUENT software to compute the thermal exchange process in BHEs in the complex ground structures [21].1) For the four-layer ground structure, each layer considered the homogenous physical properties.

2) The geological layer with aquifer was assumed as a saturated porous medium, the subsurface water moves uniformly through the entire porous medium at a constant velocity in the x direction.

3) The physical parameters and components of ground, backfill material, circulating fluid and pipes kept constant throughout the process of thermal exchange.

4) The impact of solar radiation was not considered.

Additionally, the model considered the effect of interlayer heat transfer to more accurately reflect the thermal interactions between different geological layers. This was implemented by coupling the heat transfer equations of adjacent layers, thereby allowing for heat conduction between layers with different thermal properties. On this basis, a 3D transient heat transfer model of a single coaxial BHE was established. The dimensions of the cuboid model are 10 m ×10 m × 100 m (length × width × depth). These dimensions ensure that the thermal influence radius does not reach the boundaries within the 24-h simulation period, thereby preventing boundary effects from influencing the heat transfer results. The geometry parameters of the coaxial BHE, including inner and outer pipe diameter, borehole diameter, and simulation length, are shown in Table 2, alongside the physical characteristics related to heat within the earth's surface, backfill material, and PE pipe."Table 2 Geometry parameters and the material physical parameters used in this study.

Table 2Parameter	Numerical value	
Diameter of the coaxial BHE inner pipe (m)	0.025	
The coaxial BHE outer pipe diameter (m)	0.08	
Drilling diameter (m)	0.16	
Drilling depth (m)	100	
Backfill material density (kg/m3)	1900	
Backfill material thermal conductivity (W/(m·K))	2.0	
Backfill material specific heat capacity (J/(kg·°C))	1245	
PE pipe density (kg/m3)	950	
PE pipe thermal conductivity (W/(m·K))	0.45	
PE pipe specific heat capacity (J/(kg·°C))	2300	
Circulating fluid density (kg/m3)	998.2	
Circulating fluid thermal conductivity (W/(m·K))	0.6	
Circulating fluid specific heat capacity (J/(kg·°C))	4182	

2.2.2 Governing equations

The experimental results show that the circulating water flow in BHEs is turbulent flow, and the flow in pipe is an incompressible fluid. The standard k-ε turbulence model [22] was developed by Lander and Spalding in 1992 and is a semi-empirical formula. In the k-ε model, it's presumed that turbulence is fully developed within the flow field, and the viscosity between fluid molecules can be ignored. Hence, the standard k-ε model applies exclusively to flow fields where turbulence is entirely developed. The flow within the tube was analyzed using the incompressible Navier-Stokes equations alongside the standard k-ε model, with consideration given to the water's convective thermal transfer. In FLUENT software, the "thin-wall thermal resistance" method was utilized to compute the heat resistance properties of the material used in the piping.

The equations for continuity, momentum, and energy are presented as follows (1)–(3) [12].

Equation of continuity(1) ∂(ui)∂xi=0

Momentum equation(2) ∂(ρui)∂t+∂(ρujui)∂xj=∂P∂xi+∂∂xi[(μ+μc)∂ui∂xj]+∂∂xj[(μ+μt)∂uj∂xi]

Energy equation(3) ∂(ρT)∂t+∂(ρujT)∂xj=∂∂xj[(μPrt+μtσT)∂T∂xj]

By presupposing uniform thermal characteristics for all materials involved, the heat transmission across sand and clay is determined using the formula below [23]:(4) ∂tk∂τ=λkρkck+(∂2tk∂x2+∂2tk∂y2+∂2tk∂z2)

where λk, ρk and cp,k represent the thermal conductivity (W/(m·K)), density (kg/m3) and specific heat capacity (J/(kg·°C)) of the clayey silt, medium sand, sand (aquifer) and silt.

The process of heat transfer encompasses both the conduction through liquids within the solid matrix and pores, as well as the convection associated with moving groundwater. In modeling porous media, terms representing sources of momentum were incorporated into the conventional equations governing fluid motion. Omitting the source terms related to convective acceleration and diffusion allows for a simplification in line with Darcy's law [24]:(5) Si=−μαui(i=x,y,z)

where μ is the dynamic viscosity(kg/m·s), u is the velocity(m/s) and α is the permeability of the groundwater(m2).

Fig. 1 shows the numerical model of a single coaxial BHE in the four-layered geological structure, where the CFD model incorporated just half of the BHE system, taking advantage of its symmetrical geometric characteristics. Grid sensitivity and time-step sensitivity tests were performed to ensure the simulation accuracy. The coaxial BHEs model grid adopted the structural grid, and the total element number was 2.05 million. Once the mesh elements exceeded 2.05 million, the temperature of the outlet fluid became stable. The grids of backfill material and pipes were shown in the enlarged view (see Fig. 2).Fig. 1 Numerical model mesh and boundary conditions.

Fig. 1

2.2.3 Boundary conditions

For the coaxial BHE, the velocity inlet was designated at the annular space between the outer and inner tubes, the outlet of the coaxial BHE was set to outflow, and the value of the fluid velocity was set based on the operational parameters. All surfaces of the coaxial BHE wall, ground and backfill material were set as wall, and the heat transfer type between the pipe wall and backfill material, backfill material and ground, and ground layers of different ground layers was coupled.

For the upper surface of ground mass and backfill material, the influence of solar radiation was ignored, the heat transfer option was adiabatic, and the influence of outdoor temperature and wind speed was ignored [6].(6) ∂T∂z|z=0=0

where z is the ground height, m.

For the bottom boundary surface, the temperature of the ground at the bottom of the well depth of 100 m reaches a stable value, and the temperature of the boundary surface was set to be constant and equal to the initial temperature of the ground.(7) Tbo|z=−80=T0

where Tbo is the bottom temperature, °C.

The far-field boundary condition of the ground with a radius of 10 m was set to be constant as the initial ground temperature.(8) T′|x=5,y=5=T0

where T’ is the far-field boundary temperature, °C.

Based on the data and the annual ground average temperature of Xiong'an New Area, the initial ground temperature was set at 19 °C [18]. The groundwater had the same temperature as the initial ground, which was 19 °C. The inlet flow rate of the coaxial BHE in the model was 0.4 m/s (Re = 91849). The flow rate in the borehole was 6.5 m3/h. Heat rejection tests were simulated in this study with a 35 °C inlet temperature. A transient simulation was executed with a timestep duration of 120 s.

2.3 Evaluation indicator

2.3.1 Heat transfer evaluation indicator

The heat transfer per unit well depth is a parameter to evaluate the heat transfer capacity of the BHE, and its expression is [25]:(9) q=cm(Tin−Tout)/H

where q is the heat transfer rate per meter along the tube, W/m; c is the specific heat capacity of the circulating fluid, kJ/(kg·°C); m is the mass flow rate of the circulating fluid, kg/s; Tin and Tout are the temperatures at the entry and exit points of the branch piping, respectively, °C; H is the buried depth of the coaxial BHEs, m.

2.3.2 Evaluation parameters

To investigate the heat efficiency of the coaxial BHEs in the stratified and homogeneous ground, numerical models adopted the stratified and equivalent physical properties of the ground were used, respectively. For the homogenous model, the equivalent physical properties of the ground were calculated as [5]:(10) λeq=λ1l1+λ2l2+λ3l3+λ4l4l1+l2+l3+l4

(11) ρeq=ρ1l1+ρ2l2+ρ3l3+ρ4l4l1+l2+l3+l4

(12) ceq=c1l1+c2l2+c3l3+c4l4l1+l2+l3+l4

where li is the depth of the layer i ground, λeq, ρeq, ceq symbolize the heat conduction rate, mass per unit volume, and heat storage capacity per unit mass of the analogous substance, respectively.

Therefore, the homogenous ground in this study were calculated to have uniform physical properties for the four layers as ρ = 2014.75 kg/m3, λ = 1.9 W/(m·K), c = 1398 J/(kg·°C).

2.4 Grid independence verification

The 3D unsteady buried pipe heat transfer model of layered rock mass was established by workbench in ANSYS, and Mesh module was used to divide the geometric model. According to the principle of mesh division, because the temperature change of the calculation area along the depth direction is smaller than that in the horizontal direction, the vertical direction grid division is relatively sparse. The horizontal grid is encrypted. For four layer numerical model of casing heat exchanger in the geological structure, a grid sensitivity test, to ensure the accuracy of simulation, the casing heat exchange system model grid using structured grid. For the model with more than 3.61 million grids, the outlet water temperature changes little (Fig. 2). Considering the calculation time and accuracy of the model, a model with 3.61 million grids was selected.Fig. 2 Grid independence test.

Fig. 2

3 Results and discussions

This study adopted the established CFD model of the coaxial BHE with a typical geological structure in Xiong'an New Area. Initially, the computational model underwent validation against experimental findings cited in reference. [26,27], and then six scenarios with different velocities of the inlet circulating flow and aquifer were compared to investigate the thermal performance of coaxial BHEs in the stratified ground with groundwater advection (Table 3). During all the tests, the fluid flowed through the outer annular space and get out from the inner one of the BHE, and the inlet flow velocity refers to the velocity of flow at the outer annular space of the BHE. Since this paper aims to explore the heat efficiency of the BHE in a short period, and to balance computational speed with precision, all simulations were conducted for a short-term period of 24 h. The conclusions from this study will serve as the fundamental of long-term heat transfer performance prediction.Table 3 Simulation scenarios compared in this study.

Table 3Case	Ground model	Inlet flow velocity (m/s)	Advection velocity ( × 10−5 m/s)	The corresponding subsection	
No. 1	multi-layer ground	0.4	1.29	3.2	
No. 2	homogeneous ground	0.4	–	3.2	
No. 3	multi-layer ground	0.2	1.29	3.3	
No. 4	multi-layer ground	0.6	1.29	3.3	
No. 5	multi-layer ground	0.4	0	3.4	
No. 6	multi-layer ground	0.4	9.67	3.4	

3.1 Validation

Experimental results provided by Beier et al. served to confirm the accuracy of the simulation model. [26], which was a thermal response test of a coaxial BHE. According to the effective heat exchanger length range provided by this experiment study, the drilling depth was selected as 165 m for the validation. Internal and external pipe outer diameters were 40 and 114 mm, respectively. The heat input rate was 6360 W. Fig. 3 presents a comparison between the temperatures at the inlet and outlet as simulated and the actual data recorded over a period of 78 h. The computational outcomes closely matched the experimental findings, where uncertainties of the outlet and inlet temperatures were 2.1 % and 1.35 % at the end of the test, respectively. The uncertainty may attribute to a shorter length of 165 m used in the simulation compared to Beier's experiments (165–171 m).Fig. 3 Evaluating the simulated temperatures at the entry and exit points in relation to the empirical findings reported by Beier et al. [26].

Fig. 3

3.2 Comparison between homogeneous and layered ground

Fig. 4 examine the circulating fluid's temperature for BHEs predicted by the model with layered (Case 1) and equivalent (Case 2) physical properties. The homogenous assumption with equivalent physical properties slightly overpredicted the outlet water temperature by 0.2 °C for the 24-h period (Fig. 4a). The outlet temperature predicted by the equivalent model overtook that of the layered model at the 6th hour, then their temperature difference increased with the time. Correspondingly, the coaxial BHE's heat transfer rates per meter were predicted to be 88.1 W/m and 78.5 W/m by models with the layered and equivalent physical properties, showing that the equivalent physical properties underpredicted the heat transfer rate by 10.8 % for the 24-h prediction (Fig. 4b). Their difference of heat transfer rates was predicted to increase along with the time, which indicated that the homogenous assumption with equivalent physical properties was not suitable to forecast thermal energy exchange of coaxial BHEs in the layered ground with groundwater advection.Fig. 4 Variations of (a) outlet water temperature and (b) thermal exchange rate per meter as forecasted by the models featuring stratified versus homogeneous material properties.

Fig. 4

Fig. 5 shows the ground temperature distributions at the end of the 24-h test, typical locations at radial distances of y = −0.5 m, y = −1 m and y = −2 m located left and close to the coaxial BHE were selected. In contrast to the nearly uniform temperature profile along the BHE's length as forecasted by the model assuming homogeneous material properties, the one with layered physical properties witnessed significant temperature difference among layers, especially for the 3rd layer with groundwater advection. For y = −0.5 m, the equivalent model underpredicted the ground temperatures of the 2nd layer and 3rd layer by 1.24 °C and 3.84 °C, and the uncertainty was up to 19.7 %. The ground temperature decreased when it became far away from the coaxial BHE, and the temperatures were almost the same for the ground at y = −1 m and y = −2 m for the equivalent model while significantly different in the layered model. Thus, the equivalent model ignored the temperature differences between layers, which underpredicted the temperature of ground with groundwater advection by up to 19.7 %, especially for the ground close to the BHE.Fig. 5 Ground temperature distributions located at y = −2 m, −1 m and −0.5 m along with the coaxial BHE's length predicted by models with (a) layered and (b) equivalent physical properties.

Fig. 5

The ground layer with a higher thermal diffusivity (the 2nd Layer) showed a larger thermal influence radius than Layer 1 (Fig. 6), and groundwater movement transported thermal energy from the BHE to the distant boundary.Fig. 6 Ground temperature distributions at depths of 10 m, 30 m, 50 m and 90 m in case 1.

Fig. 6

Fig. 7 detailed the ground temperature distributions at the 3rd layer with groundwater advection at 50 m-deep forecasted through simulations with the layered and equivalent physical properties. Compared to the circular thermal influence area from the equivalent model, the right-to-left seepage in the layered model brought an oval shape of thermal influence area and increased the temperature at y = −0.8 m by 4.41 °C (Fig. 7a). Such information was ignored by the model with equivalent physical properties.Fig. 7 Ground temperature distributions at depths of 50 m (from y = −0.8 m to y = −0.8 m) predicted by models with (a) layered and (b) equivalent physical properties.

Fig. 7

Overall, the assumption with equivalent physical properties underpredicted the rate of thermal exchange and the temperatures within the soil, especially for layers with large thermal conductivities. For the conclusions drawn by the U-tube BHE [5], assuming uniform physical characteristics resulted in comparable exit water temperatures, yet it led to variations in both water and ground temperature profiles, alongside thermal transfer rates at different tube depths. However, mainly due to the ignorance of groundwater advection, the equivalent assumption failed to give accurate predictions on both the outlet water temperature and the ground temperature. Therefore, the heat transfer of the coaxial BHEs should be simulated considering the layered physical properties.

3.3 Influence of inlet fluid velocity

This investigation explores the impact of inflow velocity regarding the thermal characteristics of coaxial BHEs by choosing three illustrative circulating fluid speeds: 0.2, 0.4, and 0.6 m per second. As shown in Fig. 8 (a), after a 24-h heating period, the outlet fluid temperatures of the coaxial BHEs were 32.7, 33.8 and 34.2 °C for scenarios with fluid inlet velocities of 0.2, 0.4 and 0.6 m/s, respectively. The outlet fluid temperature increased with the inlet one, due to the faster fluid velocity, which results in inadequate thermal exchange between the fluid and the earth. With a reduced inlet flow velocity, the temperature at the exit of the coaxial BHE remained low. The inlet velocity increased by 0.2 m/s, the outlet temperature could be increased by 3.2 %. Fig. 8. (b) shows that the heat transfer rate per meter of the coaxial BHE with inlet fluid velocities of 0.2, 0.4 and 0.6 m/s are 77.5, 88.1 and 86.3 W/m, respectively. Raising the inlet velocity from 0.2 to 0.4 m per second would result in a 13.7 % reduction in the rate of thermal exchange per meter. If the inlet velocity increases from 0.4 to 0.6 m/s, the heat transfer per meter will decrease by 2 %. Furthermore, at a velocity of 0.6 m/s, the thermal transfer rate per meter stands at 86.3 W/m, which is less than the 88.1 W/m observed at 0.4 m/s.Fig. 8 Variations of (a) Outlet fluid temperature and (b) Thermal exchange rate over time as forecasted by models using entry fluid speeds of 0.2, 0.4, and 0.6 m per second.

Fig. 8

The increase of heat transfer rate caused by the increase in inlet BHE velocities were achieved through: 1) more heat injection and 2) enhanced heat transfer caused by stronger flow turbulence inside the pipe. The heat injection could be the main reason contribute to the enhancement of the thermal energy exchange rate, as it was clearly showed that the outlet fluid temperatures increased more significantly when the inlet fluid velocity increased from 0.2 to 0.4 m/s compared to the one from 0.4 to 0.6 m/s. However, the increase of inlet flow velocity cannot guarantee a higher heat transfer rate, which indicated that the convection was not sufficient enough to transfer the injected heat efficiently. The small inlet flow rate may lead to excessive heat loss in the inner and outer pipes, while a large one will cause insufficient convection heat transfer. Thus, there exists an optimal inlet flow velocity to balance the heat injection and enhanced heat transfer for the optimal heat transfer rate. The optimal value for inlet flow velocity could be 0.4 m/s in this study.

3.4 Influence of the seepage velocity

According to geological data [18], the advection velocity of sand layer in Xiong'an New Area is 1.29 × 10−5 m/s, and that of groundwater in northern China [18] is 9.67 × 10-5 m/s. This analysis examined the changes in water discharge temperatures and the efficiency of heat transfer per meter in coaxial BHEs were compared for scenarios with different groundwater flow velocities in the 3rd layer (Case 1, 5 and 6).

Figure 9(a) illustrates that the heat exchanger's exit temperature reaches 34 °C, 33.8 °C and 33.5 °C respectively under the sand layer without advection and the advection velocity is 1.29 × 10−5 m/s and 9.67 × 10−5 m/s Fig. 9. (b) shows that under the three conditions of no advection in sand layer and advection velocity of 1.29 × 10−5 m/s and 9.67 × 10−5 m/s, the corresponding heat transfer per unit extension meter of heat exchanger is 76.3 W/m, 88.1 W/m and 110.8 W/m, respectively. In the case of groundwater advection, the outlet temperature decreased by 0.5 % and the heat transfer per meter increased by 15.5 %. Upon the increase of advection velocity to 9.67 × 10−5 m/s, the heat transfer per meter increased by 25.8 %.Fig. 9 Variations in exit temperature and thermal exchange over time under varying advection conditions.

Fig. 9

Fig. 10 shows that groundwater advection has a great impact on ground temperature. In the absence of groundwater advection, the factors affecting ground temperature are ground physical parameters. Fig. 10 (a) illustrates that the advection layer with higher thermal conductivity has higher temperature. Observations from Fig. 10 (b) reveal that the ground layer with groundwater advection has a high temperature, and as advection velocity increases, its influence on the temperature of the ground becomes more substantial. In the ground layer of 40–80 m, the ground temperature at a radius of 2 m from the coaxial BHE also increased significantly.Fig. 10 Ground temperature distributions at the radius of 0.5 m, 1 m, 2 m.

Fig. 10

Fig. 11 shows the ground temperature distribution at a depth of 50 m under three conditions: no advection in sand layer and advection velocity of 1.29 × 10−5 m/s and 9.67 × 10−5 m/s. It could be found that the advection effect not only affected the heat transfer of the coaxial BHEs, but also affected the ground temperature. Compared with the sand layer without advection, the outlet water temperature of sand and gravel layer with advection was lower. In the sand layer (the 3rd layer), the temperature of surrounding ground increased gradually due to the heat drainage of the coaxial BHE, resulting in the continuous decrease of heat transfer of the coaxial BHEs. However, when there was advection in sand and gravel layer, the advection could take away part of the heat emission from the coaxial BHEs, delay the rise of ground temperature, and the heat transfer attenuation of buried pipes was slower. Moreover, with the increase of advection velocity, advection took away more heat accumulated around the coaxial BHEs. In this case, the coaxial BHE run continuously for 24 h. As the velocity of advection rises, it leads to a decrease in outlet temperature, thereby enhancing the significance of the advection effect. Moreover, the increase of groundwater advection velocity contributed to a smaller thermal influence radius, which would contribute to the design of coaxial BHEs within the intricate geological formations of the Xiong'an New District.Fig. 11 Ground temperature distribution under different advection conditions at depths of 50 m with the radius of 0.8 m.

Fig. 11

4 Conclusions

Utilizing the characteristic geological structure of the Xiong'an New District, a 3D numerical model was constructed to explore how ground layers and groundwater movement impact the environment. The accuracy of assuming the equivalent physical properties has been evaluated, and the effects of the inlet water velocity and seepage velocity were analyzed through a series of simulations. The findings of this research are concisely outlined as follows.(1) In a stratified ground with groundwater flow, the uniform model, assuming identical physical characteristics, overestimated the coaxial BHE's outlet water temperature by 0.2 °C, while underpredicted the heat transfer rate by 10.8 % for the 24-h period. Meanwhile, these two models generated greatly different ground temperature distributions.

(2) The increase in fluid flow rate in the tube contributed to a larger inlet and outlet temperature difference. However, there existed an optimal inlet flow velocity to balance the heat injection and enhanced heat transfer for the optimal heat transfer rate, which was 0.4 m/s in this study.

(3) The increase of groundwater advection velocity decreased the outlet temperature by 0.5 %, increased the heat transfer per meter by 15.5 % and contributed to a smaller thermal influence radius during the 24-h period. This will contribute to the design of coaxial BHEs in complex geological structure in Xiong'an New Area.

Data availability statement

Not applicable.

Funding

This research was funded by Ltd of China Datang Group, grant number 8503008778 .

CRediT authorship contribution statement

Xiaoliang He: Writing – original draft, Methodology, Conceptualization. Jie Li: Supervision, Software, Resources, Conceptualization. Yiqi Chen: Writing – review & editing, Writing – original draft, Validation, Formal analysis. Baojun Niu: Validation, Investigation.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:Jie Li reports financial support was provided by Xiongan Energy Co., Ltd of China Datang Group. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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