Heat Transfer Enhancement in Coaxial Downhole Heat Exchangers: Influence of Spiral Fins at the Bottom Section

Abstract

Coaxial downhole heat exchangers (CDHEs) extract heat directly from geothermal reservoirs through a closed loop, minimizing environmental impacts. However, the heat extraction efficiency is generally lower than that of groundwater harvesting technology. This study proposes integrating spiral fins on the CDHE outer tube’s inner surface to enhance heat transfer performance. Numerical simulations demonstrate that placing spiral fins on the inner wall of the outer tube significantly enhances rotational velocity and turbulence within the annular flow channel, outperforming configurations with fins on the outer wall of the inner tube. The intensified swirling flow extends to the bottom of the CDHE, promoting effective mixing of hot and cold fluids and consequently improving the heat transfer coefficient. This study also investigates the influence of fin pitch and height on heat transfer and flow characteristics. The results show that both the Nusselt number (Nu) and flow resistance increase as fin pitch decreases, causing the performance evaluation criteria (PEC) to initially increase and then decrease. Additionally, increased fin height enhances the heat transfer coefficient, but also leads to a greater pressure drop. The optimal performance was achieved with a fin pitch of 500 mm and a fin height of 10 mm, attaining a maximum PEC of 1.53, effectively balancing heat transfer enhancement and hydraulic resistance. These findings provide guidance for the structural optimization of coaxial downhole heat exchangers.

1. Introduction

Geothermal energy is a clean and sustainable resource with abundant reserves, widespread availability, and stable reliability [1,2]. Accelerating the exploitation and utilization of geothermal energy is essential for optimizing the energy structure, promoting energy conservation and reducing carbon emissions [3,4]. Recently, downhole heat exchangers (DHEs) have attracted considerable attention for their use of closed-loop systems to extract heat from deep geothermal reservoirs without groundwater withdrawal, thereby minimizing the environmental impacts typically associated with traditional drilling and water extraction methods [5,6]. A DHE installed in a single geothermal well can directly extract heat from the reservoir [7,8]. Due to the small footprint and lack of a need for reinjection, drilling costs are significantly reduced [9,10]. Moreover, it is not limited by geological conditions and can be applied to repurpose abandoned oil and gas wells for geothermal heat extraction, which has a broad application prospect [11,12]. DHEs can be categorized as coaxial, U-type, and extra-long gravity heat pipes [13,14]. Among them, the coaxial downhole heat exchanger (CDHE) is the most widely used because of its simple structure and convenient construction [15,16,17].

Numerous field tests and simulation studies have demonstrated the feasibility and potential of geothermal development using CDHE. Field tests conducted in China [18] and South Korea [19] confirmed that coaxial geothermal systems were applicable for exploiting geothermal resources in medium-depth to deep formations. These studies also revealed significant variations in heat extraction characteristics under different operating modes, well configurations, and geological conditions. Additionally, several numerical models have been developed to evaluate CDHE performance in medium-depth geothermal applications. The findings indicated that increasing the flow rate and decreasing the injection temperature can enhance total heat extraction [20,21]. Furthermore, improvements can be achieved by reducing the pipe diameter ratio, employing an insulated inner pipe, increasing the thermal conductivity of the pipe wall and backfill material, and extending the well depth [22,23]. Areas with higher rock thermal conductivity and a steeper geothermal gradient are also more favorable for geothermal exploitation [24]. Furthermore, the flow direction of the working fluid [25], intermittent operating modes [26], and the type of working fluid [27] also significantly affect both the heat extraction performance of the CDHE and the thermal recovery performance of the reservoir. In summary, the heat extraction performance of CDHEs is governed by a complex interplay of multiple factors.

The performance of CDHEs can be improved by optimizing the reinjection parameters, enhancing reservoir seepage and increasing the thermal conductivity of cementitious materials used in construction. However, the practical implementation of these adjustments is often limited by site-specific and equipment-related constraints. Consequently, structural modifications to the CDHE wall have emerged as a critical approach for enhancing heat transfer performance. The implementation of finned tubes represents a well-established and effective solution, widely applied in the metallurgy, chemical, and petroleum industries [28]. Finned tubes not only increase the effective heat exchange surface area, but also induce secondary flows, such as eddy currents and rotational motion, in the fluid adjacent to the wall. These effects reduce the boundary layer thickness, thereby enhancing the diffusion rate of heat across the fluid layers and improving the overall heat transfer coefficient [29,30].

Passive heat transfer enhancement techniques based on geometric perturbation have rarely been applied in the geothermal field, though preliminary studies have recently emerged, particularly in shallow geothermal applications. Zhao et al. [31] proposed a serpentine external finned backfill coupled heat exchanger (FBCHE) and constructed a 500 × 380 × 400 mm wooden test box to evaluate its performance. Their results showed that increasing both the fin thickness and height enhanced the inlet–outlet temperature difference, and the total amount of heat stored or released. Among various fin shapes, round fins achieved the highest energy efficiency factor of 51.45%, outperforming square, square-H, and round-H fin configurations. For horizontal U-shaped geothermal heat exchangers, Alnaqi et al. [32] implemented spiral fins on the outer surface of the pipe to improve heat transfer efficiency. Their findings indicated that increasing the fin diameter from 5 mm to 10 mm and the thickness from 2 mm to 4 mm improved the heat transfer rate by 15% and 10%, respectively. In the case of a vertical U-shaped heat exchanger, Roshani et al. [33] proposed and modeled a helical fin configuration over a 2 m length. With 24 h of continuous operation, the spiral fins reduced the outlet water temperature by 1 °C. In the optimal configuration, combining spiral fins with microencapsulated phase change material, the heat transfer coefficient was improved by up to 7.5%. Furthermore, Kim et al. [34] proposed a novel U-shaped geothermal heat exchanger with an offset strip fin (OSF) positioned in the lower section. Simulation results showed that the friction factor decreased with increasing fin length, while the pressure drop remained nearly independent of fin length. In addition, Al-Kbodi et al. [35,36] conducted a comparative numerical study of U-shaped borehole heat exchangers incorporating four fin shapes: rectangular, triangular, elliptical, and oval. Their results demonstrated that rectangular fins increased the average heat transfer rate by 13.9% and elliptical fins by 13.1% compared with conventional circular tubes.

The application of various fin types in shallow geothermal heat exchangers has proven effective in improving heat transfer performance. Similar strategies have been explored for mid-depth to deep geothermal systems. Chen et al. [37] designed and fabricated a coaxial heat exchanger equipped with interrupted spiral fins and conducted field tests to evaluate its performance. The measured steady-state heat extraction power reached 11.8 kW, which was approximately twice that of a conventional double-U heat exchanger. Zhu et al. [38] performed a series of tests on a coaxial heat exchanger with continuous spiral fins. Their results demonstrated that the heat transfer performance was strongly influenced by the well depth, flow rate, and physical properties of the surrounding rock. Notably, the heat extraction power was up to 1.61 times that of the double-U heat exchanger. Liu et al. [39] proposed a coaxial heat exchanger with continuous spiral fins on the outer wall of the inner tube. They found that the counterclockwise spiral fins effectively enhanced the mixing of cold and hot fluids, reduced the irreversible losses, and improved the heat transfer efficiency. Their results showed that the PEC reached up to 1.59. Sun et al. [40] proposed several structural enhancements to the outer wall of the inner tube in a coaxial heat exchanger, including spiral fins, bumps, and impellers. Spiral fins exhibited the best performance, with PEC 6.8% and 3.8% higher than those of bumps and impellers, respectively. The maximum PEC of 1.33 was obtained in the 5 m long model with a fin height of 20 mm, a pitch of 156.6 mm, and three fins.

An effective approach for enhancing the performance of heat exchangers is to modify the wall structure, with finned tubes emerging as a particularly promising solution. Finned structures have been extensively studied for their ability to increase the heat transfer surface area, promote turbulence, and reduce boundary layer thickness, thereby significantly improving heat transfer performance. Although finned tubes have been widely applied in shallow geothermal systems, their implementation and optimization in mid-depth to deep CDHEs remain underexplored. Previous studies have predominantly focused on fins mounted on the outer wall of the inner tube, demonstrating enhanced heat transfer performance [37,38,39,40]. However, limited attention has been paid to the use of fins on the inner wall of the outer tube in CDHE systems. This study addresses the research gap by numerically investigating the differences in turbulent kinetic energy and flow characteristics between CDHE configurations with fins located on the inner wall of the outer tube and the outer wall of the inner tube. This work reveals how fin placement influences flow dynamics and heat transfer performance. In particular, poor thermal mixing between the hot fluid at the bottom of the wellbore and the high-pressure descending fluid in the annulus is identified as a key factor limiting heat exchange efficiency. To address this issue, a finned structure at the bottom of CDHEs is proposed to enhance fluid mixing. Most of the current research on CDHEs focuses on evaluating overall heat transfer performance, while detailed investigations of local flow and heat transfer behavior within specific tube sections are still lacking. Computational fluid dynamics (CFD) offers a powerful tool for investigating complex flow and heat transfer phenomena in various engineering applications [41,42]. Supported by CFD techniques, this study analyzes the thermal and hydrodynamic behaviors between the descending fluid and the hot fluid at the wellbore bottom using various finned configurations. The effect of fin geometry on flow velocity, turbulence distribution, and temperature fields is systematically examined. While fins effectively enhance heat transfer, they also introduce additional flow resistance. To comprehensively evaluate this trade-off, the performance evaluation criterion (PEC) is used to assess thermal–hydraulic performance across a range of fin pitches and heights, and the structural parameters are optimized to achieve the maximum PEC.

2. Methodology

2.1. Modeling

As shown in Figure 1, the coaxial heat exchanger (CDHE) with spiral fins primarily consists of an outer tube, spiral fins, and an insulated inner tube. Cold water is injected through the annulus between the inner and outer tubes, flowing downward along the guidance of the spiral fins and absorbing heat from the surrounding geothermal reservoir. Upon reaching the bottom of the well, the heated water is returned to the surface through the insulated inner tube, thereby enabling the extraction of geothermal energy.

The inclusion of spiral fins changes the flow characteristics within the annular channel. To accurately capture the effects of fins on velocity distribution and turbulent kinetic energy, two configurations are modeled separately: one with spiral fins on the inner wall of the outer tube and another with fins on the outer wall of the inner tube. An 8 m section at the bottom of the well, where the temperature is the highest and the heat transfer performance is most pronounced, is selected for detailed analysis. Additionally, a 1 m finless section is included at both the inlet and outlet ends of the model to eliminate potential distortions caused by inlet and backflow effects. The specific geometry and boundary parameters of the model are shown in Figure 2 and detailed in

Table 1. Main geometric and operating parameters of the CDHE section model.

Symbol	Parameters	Value and Unit
Dout	Outer diameter of outer tube	120 mm
dout	Inner diameter of outer tube	110 mm
Din	Outer diameter of inner tube	70 mm
din	Inner diameter of inner tube	60 mm
Ls	Length of the finned section	6 m
Lin	Length of the entrance section	1 m
Lout	Length of the export section	1 m
P	Spiral pitch	100–1000 mm
Hc	Height of the fins	10–15 mm
b	Width of the fins	5 mm

.

The heat transfer process in the model primarily involves thermal conduction through the reservoir and pipe wall, as well as convective heat transfer within the working fluid. Given the complexity of this heat transfer process, several reasonable simplifications are made to facilitate numerical modeling:

• The flow within the heat exchanger is assumed to be three-dimensional and incompressible;
• While groundwater flow can influence heat extraction in CDHE systems, it is not the focus of this work. Therefore, only the thermal conductivity of the reservoir is considered, and the influences of groundwater flow are ignored;
• The thermophysical properties of the reservoir surrounding the wellbore are assumed to be isotropic and uniformly distributed;
• The reservoir temperature at the boundary of the simulation domain is considered constant.

Under the assumption of continuous medium, fluid flow in the heat exchanger is governed by the conservation equations of mass, energy, and momentum:

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial \left(\rho u\right)}{\partial x_{\mathrm{i}}}}=0$$

(1)

$$\rho {\displaystyle \frac{\partial \mathrm{T}}{\partial t}}+\rho {\displaystyle \frac{\partial \left(u_i\mathrm{T}\right)}{\partial x_{\mathrm{i}}}}=-p{\displaystyle \frac{\partial u_i}{\partial x_i}}+\lambda {\displaystyle \frac{\partial }{\partial x_j}}\left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)$$

(2)

$$\rho {\displaystyle \frac{\partial u_i}{\partial t}}+\rho u_j{\displaystyle \frac{\partial u_i}{\partial x_j}}=-{\displaystyle \frac{\partial p}{\partial x_i}}+\mu {\displaystyle \frac{\partial }{\partial x_j}}\left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)$$

(3)

where u is the velocity, m·s⁻¹; ρ is the fluid density, kg·m⁻³; μ is the dynamic viscosity, Pa·s; and λ is the thermal conductivity, W·m⁻¹·K⁻¹.

The realizable k-ε turbulence model is well-suited for capturing a wind range of complex flow phenomena, including rotational flows, flow with strong curvature, and those influenced by intricate geometries. It achieves this by more accurately resolving two key turbulence parameters: the turbulent kinetic energy (k) and its dissipation rate (ε) [39]. Therefore, to accommodate the complex flow behavior within the CDHE equipped with spiral fins, the realizable k-ε model is employed in this study.

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho k{u}_j\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_b-\rho \epsilon -Y_M$$

(4)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho \epsilon u_j\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+\rho C_{1}S\epsilon -\rho C_2{\displaystyle \frac{{\epsilon }^2}{k+\sqrt{\nu \epsilon }}}-C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}{C}_{3\epsilon }{G}_b$$

(5)

where $C_1=\max \left[0.43,{\displaystyle \frac{\eta }{\eta +5}}\right]$; $\eta =S{\displaystyle \frac{k}{\epsilon }}$; $S=\sqrt{2S_{ij}{S}_{ij}}$; t is time; u_j is the velocity vector; and μ_t is the turbulent viscosity. G_k represents the generation of turbulence kinetic energy due to the mean velocity gradients, G_b is the generation of turbulence kinetic energy due to buoyancy, and Y_M represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C₂ is set to be 1.44 and C_1ε is set to be 1.9. σ_k and σ_ε are the turbulent Prandtl numbers for k and ε, respectively. σ_k is assumed to be 1.0 and σ_ε is assumed to be 1.2. S refers to the magnitude of the strain rate tensor.

2.2. Boundary Conditions

The boundary conditions are established based on parameters from a heat extraction test conducted at abandoned oil well ZK-1 in the Daqing oilfield, China [43]. The inlet is defined as a mass flow boundary with a flow rate of 5 kg·s⁻¹, while the outlet is set as a pressure boundary at 27.44 MPa. The wall surfaces are all assigned no-slip boundary conditions, and the contact surface between the water and the pipe wall is defined as a coupled wall surface to ensure accurate heat transfer simulation. The outer and bottom walls of the outer tube, which are in long-term direct contact with the geothermal reservoir, are treated as a fixed-temperature boundary at 70 °C. The material properties of the inner and outer tubes are listed in

Table 2. Physical properties of heat exchanger materials.

Parameters	Description	Inner Tube	Outer Tube
ρ	Density	2300 kg·m−3	8030 kg·m−3
cp	Heat capacity	133 J·kg−1·K−1	502.8 J·kg−1·K−1
λ	Thermal conductivity	0.02 W·m−1·K−1	16.27 W·m−1·K−1

. Water is used as the working fluid and is treated as an incompressible fluid. A UDF (user-defined function) is employed to specify its thermophysical properties, defining them as a single-valued function of temperature under wellbore pressure.

The realizable k-ε model, combined with a pressure-based solver and scalable wall functions, is employed for the simulation. The SIMPELIC and Coupled algorithms are used for pressure-velocity coupling to ensure numerical stability and accuracy. Convective terms are discretized using a second-order upwind scheme. The convergence criteria are set to a residual of 10⁻⁶ for the energy equation and 10⁻³ for other equations. Convergence is assessed based on the mass flux balance at the inlet and outlet, as well as by the average outlet temperature across the cross-section.

2.3. Definition of Parameters

The outlet temperature and heat extraction power are the main parameters for evaluating the performance of heat exchangers. The heat extraction power of the DHE can be defined as:

$$\dot{Q}=\dot{m}{c}_p(T_{out}-T_{in})$$

(6)

where $\dot{m}$ is the working fluid mass flow rate, kg·s⁻¹; c_p is the specific heat capacity at constant pressure, J·kg⁻¹·K⁻¹; and T_out and T_in are the outlet and inlet temperatures, °C.

The Nusselt number, Nu, is a key parameter for evaluating the heat transfer performance of a heat exchanger and is defined as:

$$Nu={\displaystyle \frac{h{D}_{he}}{\lambda }}$$

(7)

where λ is the thermal conductivity of the working fluid, W·m⁻¹·K⁻¹; h is the convective heat transfer coefficient, W·m⁻²·K⁻¹; D_he is the equivalent thermal circumference diameter of the pipeline, which is the ratio of four times the cross-sectional area to the circumference heated on the cross-section, m.

$$h={\displaystyle \frac{q}{T_w-T_m}}={\displaystyle \frac{\dot{Q}/A}{T_w-T_m}}={\displaystyle \frac{\dot{Q}}{\pi d_{out}L\cdot (T_w-T_m)}}$$

(8)

$$D_{he}={\displaystyle \frac{4A_{\mathrm{c}}}{P_{\mathrm{h}}}}$$

(9)

where q is the heat flux through the pipe wall, which is the ratio of the total heat transfer $\dot{Q}$ to the heat transfer area A, W·m⁻²; L is the tube length, m; T_w is the wall temperature of the outer tube, °C; T_m is the qualitative temperature of the working fluid, which is the average of the outlet temperature and inlet temperature, °C; A_c is the cross-sectional area of the pipeline, m²; and P_h is the circumference heated on the cross-section, m.

As the fluid flows through the heat exchanger, it is obstructed by the spiral fins, resulting in resistance loss along the flow path. The resistance losses can be characterized by the Darcy friction factor, f:

$$f={\displaystyle \frac{2D_h}{L}}{\displaystyle \frac{\Delta p}{\rho u^2}}$$

(10)

where $∆$p is the pressure drop of fluid in the heat exchanger; u is the velocity of fluid; and D_h is the hydraulic diameter that characterizes the average flow state inside the heat exchanger, which can be calculated from the cross-sectional area A_c and the wetting circumference of the cross-section P_w:

$$D_{\mathrm{h}}={\displaystyle \frac{4A_{\mathrm{c}}}{P_{\mathrm{w}}}}$$

(11)

Nu and f evaluate the heat exchanger performance from the perspectives of heat transfer and flow resistance, respectively. However, each metric alone is insufficient to comprehensively assess the combined effects of enhanced heat transfer and increased frictional resistance losses. To address this limitation, the performance evaluation criteria (PEC) [44] has been introduced. PEC provides a more holistic assessment by quantifying the trade-off between heat transfer improvement and flow resistance, typically through the ratio of Nu to f, with and without heat transfer enhancement structures.

$$PEC={\displaystyle \frac{\left(Nu/{Nu}_s\right)}{{\left(f/f_s\right)}^{1/3}}}$$

(12)

where the subscripts represent the case of the plain tube without fins.

2.4. Grid Independence Test

The number and quality of computational meshes directly affect the convergence and accuracy of the numerical calculations. As shown in Figure 3, a hybrid meshing strategy combining structured and unstructured meshes is employed to balance mesh quality and computational efficiency. Specifically, unstructured meshes are generated using a free-mesh method for the spiral fins and adjacent regions near the tube wall and fluid interface, where complex geometries require greater flexibility. In contrast, structured meshes are applied to the remaining pipe wall regions using a sweeping method to ensure mesh regularity and numerical stability.

Due to the presence of a boundary layer near the wall, where sharp velocity and temperature gradients occur, a locally refined mesh is necessary to accurately capture the turbulent behavior within the region. However, high mesh refinement significantly increases the total mesh count, leading to longer computation times and high aspect ratios that may hinder convergence. To address this challenge, wall functions are employed to model the near-wall flow behavior, enabling accurate representation of the boundary layer without excessive computational cost.

To eliminate the influence of mesh density on the simulation results, a mesh independence study was conducted. The variations in Nu and f with respect to grid size are shown in Figure 4. Based on the results, mesh sizes of 580,000 (for the smooth tube), 1,590,000 (for the inner tube with fins), and 1,860,000 (for the outer tube with fins) were selected for subsequent simulations. These mesh densities were chosen because further refinement resulted in negligible changes in Nu and f, indicating convergence and mesh independence.

2.5. Validation of Computational Model

Based on the experimental study by Jensen et al. [45], a model of an eight-headed helical inner-finned tube was constructed, and numerical simulations were conducted under identical conditions to validate the modeling approach. As shown in Figure 5, the maximum deviation between the numerical results and the experimental data was less than 10%; it may have come from the experimental environment, measurements, or necessary simplifications of the turbulence model, numerical discretization errors, etc. It demonstrated that the present model reliably captured both the flow characteristics within the complex channel and the heat transfer behavior inside the spiral inner-finned tube.

3. Results and Analysis

3.1. Flow and Heat Transfer Characteristics of Fins on the Outer Tube vs. the Inner Tube

Spiral fins with a height of 15 mm and a pitch of 200 mm were installed on the outer and inner tubes of the CDHE, respectively. To evaluate the impact of these fins, the flow and heat transfer characteristics of configurations with and without spiral fins were compared. The analysis focuses on the middle section of the model to illustrate representative flow and thermal behaviors. Figure 6 shows the streamlines for configurations with spiral fins on the inner and outer tubes. In these cases, the spiral fins guide the fluid to generate a radial velocity component and induce rotational motion around the tube axis. Unlike the straight streamlines observed in the smooth tube, the flow in the finned configuration became clearly spiral, indicating enhanced turbulent and intensified heat and mass transfer.

Figure 7 shows the turbulent kinetic energy for the same cases. The turbulent kinetic energy of the fluid in the smooth tube was relatively low and uniformly distributed, with an average value of 2.37 × 10⁻³ m²·s⁻². In contrast, the presence of spiral fins significantly disrupted the flow, increasing both the velocity magnitude and directional variability, thereby intensifying turbulence. The average turbulent kinetic energy increased by 38% with inner tube fins and by 59% with outer tube fins, compared with the smooth tube. This difference was primarily attributed to the larger spiral diameter of the outer tube fins, which resulted in a smaller helix angle at the same pitch, leading to a radial velocity component and a longer total spiral length, which induced stronger flow disturbances.

Figure 8 shows the velocity distribution for the various configurations. In the smooth tube, the velocity distribution was relatively uniform, with an average velocity of 0.26 m·s⁻¹. The addition of fins reduced the effective cross-sectional area of the channel, thereby increasing the average flow rate. Compared with the smooth tube, the average velocity of the water increased to 0.31 m·s⁻¹ for the inner tube with fins, which was a relative increase of 19%, while the outer tube with fins increased the average velocity to 0.34 m·s⁻¹, representing a 31% increase.

Additionally, cross-sectional velocity profiles revealed that the water was obstructed near the fin roots, forming a thicker velocity boundary layer in those regions. However, a distinct high-velocity zone emerged near the fin tips due to the constricted flow path. Meanwhile, the boundary layer adjacent to the walls became significantly thinner as a result of the increased flow velocity and turbulence intensity.

Figure 9 shows the temperature distribution for the configurations with spiral fins on the inner and outer tubes. In the heat exchanger section equipped with spiral fins, the increased turbulence and flow velocity led to a thinning of the thermal and velocity boundary layers, enhancing the mixing between hot and cold fluids. As a result, the heat transfer coefficient was improved and the average fluid temperature was increased. In a CDHE, heat was primarily transferred from the geothermal reservoir to the working fluid through conduction across the outer tube, while the inner tube did not participate in external heat exchange. Consequently, the temperature within the cross-section of the heat exchanger decreased radially inward from the outer tube to the inner tube. When spiral fins were applied to the outer tube, the flow near the fin roots was obstructed, reducing the local velocity. This extended residence time allowed for more effective heat absorption from the reservoir, resulting in a higher fluid temperature in those regions. However, when the fins were installed on the inner tube, the changes in velocity near the fin surfaces had a limited impact on the overall heat transfer process, since this region is not in contact with the reservoir. As a result, the temperature distribution near the fin surfaces remained relatively unchanged and was similar to that of the smooth tube configuration. Overall, the use of spiral fins on the outer tube yielded superior heat transfer performance. Compared with the smooth tube, the outlet temperature of the fluid increased by 0.96 °C with inner tube fins, and by 1.13 °C with outer tube fins, indicating a more effective enhancement in heat transfer when the fins were placed on the outer tube.

Under the same outlet pressure condition, the presence of spiral fins increased flow resistance within the heat exchanger section, resulting in a higher inlet pressure and a significant increase in the average pressure inside the tube. The water velocity was higher and the local pressure was lower in the regions near the fin surfaces. Compared with the smooth tube, the pressure losses between the inlet and outlet increased from 59.5 Pa to 250.4 Pa for the inner tube with fins, and further to 348.3 Pa for the outer tube with fins. Correspondingly, the Darcy friction factor, f, increased from 0.024 (smooth tube) to 0.073 (inner tube with fins) and 0.081 (outer tube with fins).

In summary, the incorporation of spiral fins in the CDHE section effectively enhanced the heat transfer coefficient, but also led to a notable increase in pressure drop. For the inner tube with fins, the Nusselt number, Nu, increased by 33.5%; however, the Darcy friction factor, f, increased more than twice, resulting in a PEC of only 0.93, which indicates a net reduction in overall thermal–hydraulic performance. In contrast, Nu increased by 58.7% and f increased by a factor of 2.4 for the outer tube with fins, yielding a PEC of approximately 1.06. At the same pitch and fin height, the spiral fins on the outer tube more effectively intensified the heat transfer process, resulting in higher heat extraction efficiency and better overall performance of the heat exchanger section.

Additionally, as illustrated in Figure 10 and Figure 11, a localized high-velocity zone formed as water entered the inner tube from the outer tube, caused by changes in the flow direction and the pipe’s cross-sectional area. Conversely, the structural configuration of the heat exchanger promoted the formation of a low-velocity region near the bottom. In this region, the water remained in prolonged contact with the heated wall at the well bottom, resulting in a pronounced temperature gradient in the lower section of the CDHE.

However, the introduction of fins on the outer tube helped to mitigate this issue. The spiral fins guided the water into a circumferential flow pattern, which extended into the stagnant zone at the bottom, increasing both velocity and turbulence. This promoted better mixing between the fluid in the low-velocity region and that in the high-velocity core, reducing fluid and heat buildup at the bottom and improving overall heat extraction efficiency. In contrast, the fins on the inner tube yielded the opposite effect. While the fins on the inner tube enhanced the heat transfer efficiency due to increased velocity and turbulence, the disturbance did not sufficiently extend to the bottom of the well. As a result, the water near the bottom remained at a higher temperature than that in the smooth tube case, and the temperature gradient at the bottom section of CDHE became even more pronounced, as shown in Figure 11.

3.2. Influence of Fin Pitch on Heat Transfer Performance

As demonstrated in the previous section, the CDHE configuration with fins on the outer tube exhibited superior flow and heat transfer performance compared with the other configurations. Therefore, the following parametric study focuses on this configuration to evaluate the influence of fin pitch on heat transfer characteristics. A series of models with varying fin pitches were developed while maintaining a constant fin height (H_c) of 15 mm. Simulations were conducted under consistent operating conditions: an injection mass flow rate of 5 kg·s⁻¹ and an inlet water temperature of 40 °C.

Figure 12 shows the velocity distributions within the CDHE for different fin pitches. In general, for a fixed exchanger length, smaller pitches corresponded to a greater number of helical turns. This intensified flow disturbance, as the fins more actively redirected the fluid motion. Moreover, a smaller pitch resulted in a decreased spiral rise angle and an increased effective fin cross-section, which constrained the flow passage and accelerated the average fluid velocity. As shown in Figure 13, reducing the pitch from 1000 mm to 500 mm increased the average velocity from 0.23 m·s⁻¹ to 0.26 m·s⁻¹, representing an 11.5% increase. Further decreasing the pitch to 100 mm resulted in a 21.2% increase in average velocity. The velocity profiles also revealed that, in the CDHE section with spiral fins, the fluid flowed in a clockwise helical path and was locally obstructed near the fin roots, where velocity decreased significantly. In contrast, at the fin tips, particularly near the inner tube side, the flow accelerated due to the reduced cross-sectional area, resulting in higher velocity and enhanced turbulence. Between the fins, where the fluid was less influenced by structural elements, the flow pattern resembled that in a smooth tube with relatively uniform radial velocity distribution. However, when the pitch was reduced to 100 mm, the fin spacing was insufficient for the velocity profile to fully redevelop between turns. As a result, the velocity remained uneven, with consistently lower values near the fin roots and high values near the fin tips.

Figure 14 and Figure 15 show the streamlines and turbulent kinetic energy distributions within the CDHE for different fin pitches. In the smooth tube configuration, the flow remained stable and the streamlines were relatively straight and uniform. In contrast, the flow lines inside the CDHE section with fins showed a clear spiral shape, and turbulence intensity increased significantly as the pitch decreased. Specifically, as the pitch decreased from 1000 mm to 500 mm, the average turbulent kinetic energy increased from 1.91 × 10⁻³ m²·s⁻² to 2.26 × 10⁻³ m²·s⁻², representing an 18% increase. With a further decrease in pitch to 100 mm, the average turbulent kinetic energy reached 6.59 × 10⁻³ m²·s⁻², corresponding to a 192% increase relative to the smooth tube case.

Figure 16 shows the temperature distribution within the CDHE section for various fin pitches. The helical fins changed the flow structure in the annular channel, which in turn altered the temperature field. As a result, the temperature distribution exhibited a trend similar to that of the velocity field. As the pitch decreased, the fins induced stronger flow disturbances, enhancing the mixing between the hot fluid near the outer tube wall with the cooler fluid near the center. This led to a higher average fluid temperature. Moreover, the increase in flow velocity and turbulence at smaller pitches resulted in a thinner thermal boundary layer, further enhancing the heat transfer performance of the heat exchanger section. Specifically, decreasing the pitch from 1000 mm to 500 mm increased the outlet temperature by 0.3 °C and increased the heat extraction power by approximately 5%. Further decreasing the pitch to 100 mm results in a 0.7 °C increase in outlet temperature and an 11% increase in heat extraction power.

At a constant outlet pressure, reducing the fin pitch resulted in increased flow resistance within the annular channel. As the pitch decreased from 1000 mm to 500 mm, the pressure drop increased by approximately 73%. Further decreasing the pitch to 100 mm led to a dramatic 614% increase in pressure drop.

In summary, the helical rise angle decreased and the total length of the fins increased as the pitch decreased. This enhanced turbulence and reduced the thermal boundary layer thickness, thereby improving the heat transfer performance of the heat exchanger section. However, the denser fin configuration also significantly increased flow resistance, leading to a substantial increase in pressure drop.

As shown in Figure 17, the Nusselt number, Nu, increased by 17% as the fin pitch decreased from 1000 mm to 500 mm. However, the increase in heat transfer was accompanied by a 100% increase in pressure loss and a 40% increase in the Darcy friction factor. As a result, the PEC of the heat exchanger section increased moderately from 1.40 to 1.47. When the pitch was further decreased to 100 mm, Nu increased to 534, representing a 22% increase compared with that in the 1000 mm pitch case. However, the pressure loss increased by nearly six times and f grew significantly to 0.289, a relative increase of 382%. In this case, the excessive flow resistance introduced by the fins outweighed the benefits of heat transfer enhancement, causing the PEC to decrease sharply to 1.07. These results highlight the importance of balancing heat transfer improvement with the associated increase in flow resistance when selecting the optimal fin pitch. An overly dense fin arrangement may lead to diminishing returns or even reduced overall performance.

3.3. Influence of Fin Height on Heat Transfer Performance

To investigate the effect of fin height on flow and heat transfer characteristics, simulations were conducted for CDHE configurations with fin heights of 10 mm, 15 mm, and 20 mm while keeping the pitch (P) constant at 500 mm. The inlet water temperature was set to 40 °C and the mass flow rate was 5 kg·s⁻¹.

Figure 18 shows the velocity distribution inside the CDHE section for different fin heights. The average water velocity increased as the fin height increased due to the reduced cross-sectional area of the annular flow channel. When the fin height increased from 10 mm to 15 mm, the cross-sectional area of the annular channel decreased by 0.31 cm², resulting in an increase in average velocity from 0.24 m·s⁻¹ to 0.26 m·s⁻¹, representing an 8% improvement. Further increasing the fin height to 20 mm decreased the cross-sectional area by 0.28 cm² and increased the average velocity by 6%. Notably, taller fins resulted in a more pronounced velocity increase near the inner tube wall.

As shown in Figure 19, higher fins more effectively guided the fluid along the spiral path, intensifying turbulence within the heat exchanger section. The increased flow disturbance led to higher peak velocities. When the fin height was increased from 10 mm to 20 mm, the maximum velocity at a depth of 4 m increased from 0.29 m·s⁻¹ to 0.35 m·s⁻¹, indicating stronger local acceleration due to the fin geometry.

Figure 20 and Figure 21 show the temperature distribution inside the CDHEs for various fin heights. In the low-velocity region near the fin roots, the fluid remained in longer contact with the outer tube wall, allowing more complete heat exchange and resulting in higher local temperatures. The obstruction to fluid flow became more pronounced as fin height increased, leading to an expanded region of elevated temperature near the outer wall. When the fin height was increased from 10 mm to 20 mm, both the velocity and turbulent kinetic energy increased. This thinned the thermal boundary layer and enhanced mixing between hot- and cold-fluid regions, thereby improving the overall heat transfer performance. As a result, the outlet temperature increased by 0.1 °C, and the heat extraction power was increased by 3% accordingly.

The fluid was obstructed near the fin surface, resulting in localized increase in velocity and a corresponding decrease in pressure. As the fin height increased, the flow passage narrowed further, causing an additional increase in flow velocity and a progressive increase in frictional resistance, which resulted in a more pronounced pressure drop. Specifically, when the fin height increased from 10 mm to 15 mm, the pressure drop increased from 139 Pa to 204 Pa, representing a relative increase of 47%. Further increasing the fin height to 20 mm increased the pressure drop to 273 Pa, representing an additional 34% increase.

In summary, taller fins enhance turbulence and promote more effective mixing between fluid regions, thereby improving the heat transfer coefficient. However, due to the thermal resistance of the pipe wall and the increased fluid velocity, improvements in the outlet temperature and overall heat extraction power are limited. Meanwhile, the increase in the pressure drop becomes more significant. For example, increasing the fin height from 10 mm to 20 mm results in only a 1% improvement in Nu, while the pressure drop between the inlet and outlet nearly doubles. The Darcy friction factor increases from 0.047 to 0.073, a relative increase of 55.2%, causing the PEC of the heat exchanger section to decrease from 1.53 to 1.34.

While spiral fins effectively enhance heat transfer in a CDHE, they also substantially increase flow resistance. Therefore, in selecting fin parameters and designing the heat exchanger, both the heat extraction power and the associated pumping power should be carefully considered. Excessively tall fins may lead to increased flow resistance and decreased overall performance.

4. Conclusions

To enhance the heat transfer efficiency of a single-well closed-loop geothermal system, this study proposed a CDHE design incorporating spiral fins near the bottom section. Numerical simulations were conducted to investigate the effects of spiral fins on flow behavior and heat transfer characteristics within the CDHE section. The key findings of this study are summarized as follows.

• Spiral fins induce circumferential flow within the annular channel, promoting enhanced fluid mixing and a more uniform velocity distribution near the bottom section of the CDHE. This significantly improves the heat transfer performance in the low-flow region;
• Spiral fins installed on the outer tube outperform those on the inner tube due to a larger spiral diameter and smaller rise angle. This configuration results in a 15% increase in turbulence intensity and a 9.7% increase in average velocity compared with fins mounted on the inner tube;
• The performance evaluation criteria (PEC) of the CDHE section first increases and then decreases with decreasing fin pitch, while it shows a slight decline with increasing fin height. The optimal performance is achieved with a fin height of 10 mm and a pitch of 500 mm, yielding a maximum PEC of 1.53.

Overall, the application of spiral fins within the CDHE effectively enhances heat transfer efficiency. However, the associated increase in flow resistance must be carefully considered during design optimization to ensure balanced system performance. Future research should focus on further optimizing fin geometries to achieve a better trade-off between heat transfer enhancement and flow resistance. In addition, experimental studies under various geological and operating conditions are recommended to validate the numerical findings and to explore the long-term reliability and durability of spiral-fin CDHE designs.