Numerical Study and Structural Optimization of Guided Bearing Heat Exchanger with Impurity-Contained Cooling Water

Abstract

The cooling medium of the guide bearing heat exchanger in hydro generator sets comes from the upstream dam area, which contains numerous impurities even though it has undergone preliminary treatment. These impurities settle, accumulate, and adhere and form scaling layers in the heat exchanger, seriously affecting its heat transfer performance. This paper presents an innovative investigation of heat exchanger performance under impurity-laden cooling water conditions and proposes an optimization by replacing the conventional round tube structure with a spiral flat tube structure. Numerical simulations are conducted to analyze the flow velocity, pressure, impurity deposition, and temperature distribution of the cooler under actual operating conditions. The results show that the optimized cooler achieves improved velocity uniformity with a lower standard deviation, effectively reducing sediment accumulation. Compared to the prototype, the maximum pressure increases by 55.2% (from 0.562 MPa to 0.872 MPa), which enhances turbulence and improves heat transfer. The sediment volume fraction is significantly reduced by 49% in low-flow operating conditions and 73.7% in high-flow operating conditions. Furthermore, the maximum temperature drops by 5.43 °C, indicating improved thermal performance. These findings confirm the effectiveness of the spiral flat tube design in impurity-rich environments.

1. Introduction

During the operation of hydroelectric generator units, water flow impacts the turbine runner, driving the main shaft to rotate [1]. To restrict radial and axial movement of the main shaft, guide bearings and thrust bearings are installed to withstand the radial and axial forces, respectively [2,3]. However, the high-speed rotation of the shaft inevitably generates significant heat in the bearing oil tank due to friction. Excessive heat accumulation can trigger emergency shutdowns or even cause bearing bush burning, severely compromising the unit’s operational safety, stability, and efficiency. Therefore, effectively dissipating heat through cooling systems is critical [4,5].

The heat transfer efficiency of the cooler applied to the guide bearing in hydroelectric generator units is closely related to the piping characteristics and the cooling medium [6,7,8] Currently, most research on coolers focuses on optimizing the cooler structure. Fawaz et al. [9] proposed a topology-optimized design for a heat transfer-enhanced heat exchanger structure. Wang et al. [10] introduced a heat exchanger with a helically coiled tube bundle and conducted numerical studies to investigate the effects of tube bundle parameters on flow characteristics, heat transfer performance, and stress distribution. Oclon et al. [11] proposed an improved manifold design for heat exchangers, which increases fluid volume and optimizes flow distribution to the tubular spaces. Wang et al. [12] explored the effect of helical angles and overlap on the overall performance of shell-and-tube heat exchangers with helical baffles. The optimal results showed an average increase in the heat transfer coefficient per unit pressure drop of 14.1%. Yang et al. [13] proposed a method for optimizing the design of tube heat exchanger structures based on construction theory. Mao et al. [14] optimized the metal fins of a shell-and-tube cooler into a fan shape and investigated the effect of fin structure on heat transfer efficiency. Lee et al. [15] used initial designs generated by deep reinforcement learning to optimize the heat exchanger topology, with simulation results showing a 14.8% improvement in heat exchange efficiency. He et al. [16] proposed a heat exchanger structure characterized by continuous pits, and computational fluid dynamics (CFD) simulations showed that the optimal structure improved the performance evaluation criteria by 217.4%. Wang et al. [17] discussed a novel convex plate heat exchanger and experimentally and numerically investigated the effect of its structural parameters on heat transfer performance. Liu et al. [18] developed a plate fin heat exchanger and optimized its shape using CFD and a multi-objective genetic algorithm. Some of the above designs are illustrated in Figure 1.

From the studies mentioned above, it is evident that numerous heat exchanger structures, such as shell-and-tube, plate, fin, and topology optimization, have been investigated [19,20,21,22]. However, in addition to the cooler structure, the cooling medium also plays a significant role in determining heat transfer efficiency. The guide bearing cooling system typically draws water from the upstream reservoir at the worm shell. Although most sediment particles are removed through preliminary treatment in the settling tank, small impurities and microorganisms remain, and the water can exhibit noticeable acidity or alkalinity. This impurity-containing water, used as the internal circulation cooling medium, can lead to erosion, corrosion, or impurity deposition within the cooler pipeline [23]. The erosive wear and chemical corrosion of impurities on the pipeline can cause thinning or even perforation of the pipeline wall, ultimately leading to wall failure. Furthermore, the accumulation of impurities on the pipeline surface significantly reduces the cooler’s performance. Currently, hydropower plants manage impurities in cooling water through sedimentation, chemical separation, and other methods, but these solutions have proven to be less effective.

Although previous studies have extensively investigated spiral or modified heat exchangers for improving flow uniformity and thermal performance, few works have explicitly addressed the challenges associated with impurity-laden cooling water in hydropower generator systems. In practical operations, cooling water drawn from upstream reservoirs inevitably contains fine sediments and impurities, which not only reduce heat transfer efficiency but also accelerate erosion, corrosion, and clogging inside the cooler. The present study introduces a novel spiral flat tube design tailored for impurity-rich environments. Compared with conventional spiral heat exchangers reported in the literature, the proposed configuration offers three unique advantages: (i) enhanced anti-fouling capability, as the spiral flat geometry and corrugated inner surface induce organized turbulence that prevents impurity deposition; (ii) improved durability and reliability, since reduced sediment accumulation mitigates wear and corrosion, extending the cooler’s service life; and (iii) strong industrial applicability, providing a practical solution for hydropower bearing cooling systems where pretreatment cannot fully eliminate impurities. These innovations highlight the novelty of the study and its potential to bridge the gap between theoretical optimization and real-world application.

Specifically, the research will focus on transforming the traditional round tube design into a spiral flat tube structure, aiming to improve flow uniformity, reduce sediment buildup, and optimize heat dissipation. Through numerical simulations, the paper will evaluate key performance metrics such as flow velocity, pressure distribution, and heat transfer efficiency, providing a comprehensive analysis of the optimized cooler design’s effectiveness.

2. Enhanced Heat Transfer Mechanisms for Guided Bearing Cooler

The enhancement of the cooler’s heat transfer process in the guide bearing of a hydro generator set aims to maximize the amount of heat transferred per unit time and per unit heat transfer area. The importance of conducting a detailed heat transfer analysis is to achieve a higher heat transfer rate, thereby increasing the equipment’s capacity without exceeding the fixed investment in equipment and transportation power consumption. By analyzing the heat transfer process, the amount of heat transferred per unit time can be expressed as follows

$$Q=hS\Delta T$$

(1)

where Q is the total heat transfer of the cooler, h represents the total heat transfer coefficient, S denotes the total heat transfer area, and $\Delta T$ refers to the logarithmic mean temperature difference, which is given by $\Delta T=\frac{\Delta T_2-\Delta T_1}{ln\left(\frac{\Delta T_2}{\Delta T_1}\right)}$. Here, $\Delta T_1$ and $\Delta T_2$ are the temperature differences between the two fluids at the two ends of the shell course, with $\Delta T_2$ being the larger value and $\Delta T_1$ the smaller value. In engineering calculations, when $\frac{\Delta T_2}{\Delta T_1}\le 2$, the arithmetic mean temperature difference $\Delta T^{\prime }$ can be used instead of the logarithmic mean temperature difference $\Delta T$, and is calculated as $\Delta T^{\prime }=\frac{\Delta T_2+\Delta T_1}{2}$.

Furthermore, it can be seen from Equation (1) that there are three methods for increasing the amount of heat transfer: increasing the total heat transfer coefficient h, enlarging the total heat transfer area S, and extending the average temperature difference $\Delta T$ between the hot and cold fluids.

For the cooler in the guide bearing of hydropower units, based on Equation (1), the heat transfer power Q of the piping circuit can be expressed as

$$Q=c_p{\rho }_m{Q}_{\mathrm{V}}.(T_{\mathrm{out}}-T_{\mathrm{in}})=c_p{Q}_M.\Delta T_c$$

(2)

where $Q_V$ and $Q_M$ are the volume flow and mass flow of the cooling medium, respectively; $C_p$ represents the specific heat capacity of the corresponding cooling medium; and $\Delta T_c$ refers to the temperature difference between the cooling medium and the high-temperature oil in the bearing oil tank.

Furthermore, when the flow state of the high-temperature liquid outside the cooler and the cooling medium inside the pipeline reaches a relatively stable condition, the total heat transfer coefficient K can be determined as

$$K={\displaystyle \frac{Q}{S\Delta T}}={\displaystyle \frac{c_p{Q}_M.\Delta T_c}{S\Delta T}}$$

(3)

From Equations (1) to (3), it can be observed that increasing K, S, and $\Delta T_c$ are fundamental measures to improve the cooler’s heat transfer efficiency. In practical applications, when impurity-containing water flows as the cooling medium through the pipeline, the settlement, attachment, and accumulation of impurities on the pipeline wall will significantly reduce the heat transfer efficiency between the cooling water flow and high-temperature oil, thus affecting the overall cooling performance. Specifically, water flow in the pipe is typically undisturbed and characterized by low turbulence, especially in conventional round tubes. In this state, once impurities settle and attach to the pipe wall, they are less likely to detach through the disturbance caused by the water flow. Over time, this leads to the accumulation of impurities and the formation of a scaling surface. These scales not only reduce the heat transfer efficiency between the cooling medium and the high-temperature oil but may also hinder the flow of cooling medium, thereby diminishing the cooling performance of the system.

Therefore, based on Equation (3), to enhance heat transfer and eliminate, as much as possible, the negative effects caused by impurity settlement, it is proposed to optimize the round tube of shell-and-tube coolers into a spiral flat tube. First, the spiral flow channel inside the pipe induces rotational motion of the fluid, which increases the degree of disturbance and promotes the mixing of water flow and impurities, effectively preventing the formation of a scaling surface. Second, because the spiral pipe is formed by flattening and twisting the smooth round pipe, its length is longer than that of the round pipe, which is equivalent to expanding the contact heat transfer area S between the pipe and the lubricant in the tank. Finally, the cross-sectional area of the spiral flat pipe is smaller than that of a traditional round pipe. For the same flow rate of the cooling medium, the medium flows faster through the spiral flat pipe. This not only increases the total heat transfer coefficient K but also prevents the impurities from settling due to the high-speed flow.

Based on the above analysis, the application of spiral flat pipes to enhance the performance of heat exchangers using impurity-laden cooling water is demonstrated to be feasible.

3. Methodology

Taking a 260 MW Francis hydro generator set as an example (Guizhou Beipanjiang Electric Power Co., Ltd. Guangzhao Branch, Guizhou, China), the unit’s water-guide bearing cooler uses a two-flap combination of cartridge tiles, with the lubricating oil being cooled by internally circulating water.

3.1. Prototype and Optimized Structural Model of Semi-Ring Cooler

The heat transfer characteristics and optimization design of the cooler are analyzed through numerical simulation, and a cooler model in the guide bearing oil tank is established to ensure consistency with the real machine. In this analysis, the circulation cooler in the guide bearing oil tank is designed in a semi-ring configuration. The model of the real machine, along with the cooler model featuring a circular tube, is shown in Figure 2a and b, respectively. Furthermore, based on the results of the strengthened heat transfer analysis, a cooler model with a spiral flat pipe design is developed to enhance performance, and this optimized cooler model is depicted in Figure 2c.

The design dimensions of the prototype and optimized spiral flat tube are summarized in

Table 1. Dimensions and key features of the prototype and optimized spiral flat tube coolers.

Feature	Prototype Cooler	Optimized Cooler
Tube Diameter (mm)	20	-
Tube Major Axis (mm)	-	30
Tube Minor Axis (mm)	-	15
Wall Thickness (mm)	1.5	1.5
Spiral Pitch (mm)	-	60
Rotation Angle (° per 60 mm length)	-	45°
Corrugation Wavelength (mm)	-	10
Corrugation Amplitude (mm)	-	2
Effective Heat Transfer Area Increase (%)	-	18

. In the optimized spiral flat tube cooler, each tube was transformed from a conventional circular cross-section (diameter 20 mm) into a flattened elliptical cross-section with a major axis of 30 mm and a minor axis of 15 mm. The tube wall thickness was maintained at 1.5 mm, consistent with the prototype design. The spiral configuration was generated by twisting the flattened tube around its longitudinal axis with a pitch of 60 mm per revolution, corresponding to a rotation angle of 45° per 60 mm length. To enhance surface disturbance and prevent particle adhesion, the inner wall of the spiral flat tube was corrugated, with a sinusoidal geometry characterized by a wavelength of 10 mm and an amplitude of 2 mm. The corrugations were oriented along the flow direction to induce local turbulence and improve mixing between the cooling medium and impurities. The overall length of each spiral tube remained equivalent to the prototype, but due to flattening and spiraling, the effective heat transfer area increased by approximately 18%.

The numerical simulations allow for a detailed comparison between the traditional circular tube cooler and the newly designed spiral flat pipe cooler. This comparison highlights the improvements in heat transfer efficiency achieved through the optimized design, demonstrating the potential of the spiral flat pipe configuration in improving the cooler’s overall performance.

The cooling system of the guide bearing in this power station unit operates in an internal circulation mode, where the oil cooler is installed inside the oil tank. The cooling water for the heat exchanger is sourced from the snail shell of the unit. The total pressure of the cooling water is maintained between 0.38∼0.4 MPa, while the water pressure at the snail shell water filter is 0.41∼0.42 MPa. Additionally, the water pressure in front of the dam is approximately 0.49 MPa. The water-guided shaft tile, which is made from a pasteurized alloy, plays a crucial role in the cooling system’s durability and heat dissipation efficiency. During full-load operation, the temperature of the lubricating oil in the water-guided bearing typically ranges from 32.7 °C to 36.9 °C. To ensure safe operation of the unit, alarm and emergency shutdown temperatures are set at 50 °C and 55 °C, respectively. These temperature thresholds are designed to prevent overheating, which could lead to potential damage to the bearings and other critical components.

For the oil cooler, various model parameters and their corresponding operating conditions are detailed in

Table 2. Parameters and operating conditions of the cooler model.

Parameter	Value	Unit
Material	Copper	/
Positive water pressure	0.14–0.2	MPa
Reverse water pressure	0.03–0.2	MPa

. These parameters provide insight into the operational limits and performance expectations of the cooler under different pressure and temperature conditions, ensuring that the cooling system operates efficiently and safely during the unit’s operation.

3.2. Mesh Division and Working Condition Setting

As depicted in Figure 3, the cooler model consists of a shell-and-tube configuration, where high-temperature lubricant fills the space between the shell and the tube section, while the tube section contains the flowing cooling medium. Once the geometrical model of the cooler is established, the computational domain is discretized through mesh division. To ensure the reliability of the numerical simulations, a mesh independence study was performed. Five meshes elements were generated. Key performance indicators, including pressure drop and heat transfer coefficient, were evaluated for each mesh level. As shown in Figure 3c, both parameters converged with increasing mesh density: when the element number exceeded $1.32\times {10}^6$, the variation in pressure drop was below $2.0\%$, and when the variation in heat transfer coefficient was below $1.8\%$. Accordingly, the medium-density mesh with a total of approximately $2.27\times {10}^6$ elements was selected for all subsequent simulations to balance numerical accuracy and computational efficiency.

Finally, in the shell section, a tetrahedral unstructured mesh is used, with a total of approximately $0.95\times {10}^6$ mesh elements. To ensure the stability and accuracy of the numerical solution, the maximum mesh aspect ratio is kept within 10. The mesh size is refined near the boundary layer and regions with rapid flow changes to ensure accurate capture of the flow and temperature field variations. In the tube section, a hexahedral structured mesh is employed, consisting of approximately $1.32\times {10}^6$ mesh elements. The mesh density is refined, especially at the pipe’s inlet, outlet, and near the pipe wall. The mesh size near the inner pipe wall is 0.5 mm, while in regions further from the wall, the mesh size is 1.5 mm. This setup helps accurately capture the boundary layer effects and ensures the precise calculation of heat exchange efficiency and flow characteristics. The mesh density and size are appropriately optimized in high-gradient areas (such as near the pipe wall and at the inlet and outlet) to improve the accuracy of flow and heat transfer calculations and ensure the precision and convergence of the numerical simulation results.

To accurately replicate the actual operating conditions of the power plant, the inlet and outlet boundary conditions for the cooling medium in the pipe section are specified as pressure conditions. Three distinct sets of pressure values have been chosen to represent the inlet and outlet boundary conditions, reflecting the real operating conditions of the unit’s bearing cooler. The corresponding pressure values and their associated flow rates are summarized in

Table 3. Boundary condition settings for three working cases.

Case	Positive Water Pressure	Reverse Water Pressure	${\mathit{Q}}_{\mathit{M}}$	${\mathit{Q}}_{\mathit{V}}$
Case 1	0.2 MPa	0.03 MPa	11.18 kg/s	40.37 m3/h
Case 2	0.2 MPa	0.13 MPa	21.73 kg/s	78.46 m3/h
Case 3	0.2 MPa	0.18 MPa	34.65 kg/s	125.11 m3/h

. For the numerical simulations, to facilitate a comparison of the cooler’s heat transfer performance under various operational scenarios, the temperatures of both the high-temperature oil medium and the impurity-laden cooling water are uniformly set to 313.15 K and 298.15 K, respectively. This temperature setting ensures consistency in comparing thermal effects across different flow conditions.

In terms of boundary conditions, the solid walls are modeled using the standard wall function method, which is suitable for resolving near-wall turbulence. No-slip boundary conditions are applied to all solid walls, ensuring zero fluid velocity at the wall. Additionally, all heat-conducting solid walls are made of copper, chosen for its excellent thermal conductivity, thus ensuring efficient heat transfer between the fluid and solid domains.

3.3. Turbulence Model and Computational Setup

All simulations were carried out using ANSYS Fluent 15.0, with double precision and a pressure-based solver. In the numerical simulations, considering the complexity of the cooling medium’s flow behavior, the Reynolds-Averaged Navier–Stokes (RANS) turbulence model is employed to simulate the flow characteristics. Specifically, the standard k–$\epsilon$ turbulence model is used, as it can accurately describe turbulence development and mixing effects in complex flow fields, particularly in regions where intense turbulence is present. The standard k–$\epsilon$ and k–$\omega$ SST turbulence models under Case 2 conditions are further compared. The results in

Table 4. Comparison between the standard k–$\epsilon$ and k–$\omega$ SST turbulence models under Case 2.

Quantity	Standard k–$\mathit{\epsilon }$	k–$\mathit{\omega }$ SST	Difference (%)
Pressure drop, $\Delta P$ (MPa)	0.583	0.601	$+3.1$
Heat transfer coefficient, h (W/m2K)	1140	1113	$-2.4$
Max. tube-wall temperature, $T_{max}$ (K)	332.1	331.5	$-0.2$
Iterations to convergence	650	720	$+10.8$
Relative CPU time	$1.00\times$	$1.28\times$	$+28.0$

indicate that the predicted pressure drop differs by 3.1% between the two models, while the heat transfer coefficient differs by 2.4%. The maximum tube-wall temperature differs by only 0.2 K. These deviations fall within the typical range of engineering accuracy for heat exchanger CFD. The k–$\omega$ SST model yields a slightly higher pressure drop due to its near-wall treatment, whereas the standard k–$\epsilon$ model provides comparable thermal predictions with lower computational cost (28% shorter runtime and fewer iterations to converge). Given this balance of accuracy and efficiency, the standard k–$\epsilon$ model was retained for the main simulations.

The key equations of the k–$\epsilon$ turbulence model are as follows

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+\nabla ·\left(\rho \mathbf{u}k\right)=\nabla ·\left({\mu }_T\nabla k\right)+P_k-\rho ϵ$$

(4)

$${\displaystyle \frac{\partial \left(\rho ϵ\right)}{\partial t}}+\nabla ·\left(\rho \mathbf{u}ϵ\right)=\nabla ·\left({\mu }_T\nabla ϵ\right)+C_{ϵ1}{\displaystyle \frac{ϵ}{k}}{P}_k-C_{ϵ2}\rho {\displaystyle \frac{{ϵ}^2}{k}}$$

(5)

where ${\mu }_T$ represents the turbulence viscosity, $P_k$ denotes the turbulence production term. $\rho$ stands for the fluid density, k is the turbulent kinetic energy. $ϵ$ indicates the turbulent dissipation rate, while $C_{ϵ1}$ and $C_{ϵ2}$ are the constants used in the model.

The computational model is implemented in ANSYS Fluent, a powerful tool for simulating fluid flow and heat transfer, which ensures high accuracy and efficiency in solving complex flow problems.

Moreover, to ensure the accuracy and convergence of the numerical simulation, several key parameters were set. The time step was chosen to be 0.001 s, allowing for precise capture of instantaneous flow and heat transfer processes within the cooler. Given that the total simulation time is 100 s, this corresponds to 100,000 time steps. This temporal resolution ensures sufficient accuracy in capturing dynamic behavior throughout the simulation. The convergence criteria for the simulation were defined based on the residuals of the governing equations. Specifically, the residuals for mass, momentum, and energy were required to fall below thresholds of ${10}^{-6}$, ${10}^{-6}$, and ${10}^{-8}$, respectively. These criteria ensure that the solution has sufficiently converged and that the results are accurate.

To further enhance computational efficiency and reduce simulation time, parallel computing techniques were employed, utilizing multi-core processors to perform calculations concurrently. This approach significantly accelerates the process, making it feasible to carry out large-scale simulations efficiently.

3.4. Numerical Definition of Cooling Water with Impurities

The sediment composition analysis report for this hydropower station reveals that the mineral composition of the suspended sediment in the reservoir area consists of 59.62% SiO₂, 3.62% Fe₂O₃, 10.46% Al₂O₃, 8.00% CaO, and 4.11% MgO. The sediment accumulation extends all the way to the dam front, which has significant operational implications. Specifically, in the operating conditions of the unit bearing cooling system, the cooling water is sourced from the worm shell. This results in a substantial issue of sediment buildup in the cooler pipeline, severely affecting the heat exchange efficiency of the cooler.

Given this context, the impact of sediment and other impurities accumulation requires thorough analysis. To address this, the Eulerian non-homogeneous phase flow model has been applied in the numerical simulations. In this model, the liquid phase is treated as the continuous phase, while the solid phase is modeled as a discrete phase. The solid particles are assumed to be spherical with a diameter of 0.1 mm. The volume fraction of the solid phase at the inlet is set at 1%, while the liquid phase occupies 99% of the volume. This approach provides a detailed simulation framework to accurately model the effects of sediment accumulation on the cooling system, helping to better understand its impact on operational efficiency and guide the development of potential solutions.

4. Analysis of Numerical Simulation Results

4.1. Experimental Validation

To further validate the performance of the optimized cooler design, a series of experiments were conducted on a 100 MW hydroelectric generator set using the prototype cooler, which employs the traditional round tube structure. The experimental setup focused on measuring key indicators at the classic measurement positions, specifically the oil temperature at the bearing and the cooling water outlet temperature.

These measurements were carried out under the operational conditions of Cases 1, 2, and 3, which corresponds to a specific mass flow rate and operating temperature of the cooling water. The experimental data obtained from these measurements were compared with the numerical simulation results. Figure 4 compares the simulation and experimental data for average oil temperature at the bearing and cooling water outlet temperature under Case 1, Case 2, and Case 3. In all cases, the experimental data closely align with the simulation results, confirming the accuracy of the numerical model. The oil temperature shows a consistent decrease with increasing flow rate, with the simulated and experimental data for Case 3 (high flow) showing the lowest values, demonstrating the optimized cooler’s improved performance. Similarly, the cooling water outlet temperature remains within the expected range, with slight variations between the simulation and experimental data, which are likely due to real-world environmental factors. Overall, the results validate the effectiveness of the optimized cooler design in improving cooling efficiency and maintaining stable operating temperatures.

4.2. Flow Characteristics of Impurity-Laden Water in Cooler Pipe

As shown in Figure 5, the left side illustrates the velocity distribution of solid media in the water flow for the prototype round tube cooler under varying mass flow rates. The analysis reveals that the movement of impurities in the pipeline is notably erratic. The sand particles, under different mass flow rates, enter the cooler from the inlet, flow through the lower part of the cooler, and reach the back end of the shell section. A more intense collision occurs at the back end, which leads to a greater impact on the cooler’s performance. The velocity streamlines of the sand particles are primarily concentrated in the bottom half of the cooler, indicating a higher flow rate of sand particles in the lower tubes of the prototype cooler. This suggests that sand particles are more likely to accumulate in this region, which can negatively affect the cooler’s heat exchange efficiency.

On the right side of Figure 5, the performance of the optimized spiral flat tube cooler is shown. When comparing the two different cooler structures, it can be observed that the sand particle velocity in the spiral flat tube cooler is significantly improved, and the flow rate distribution between the upper and lower sections of the cooler is much more uniform. Under varying mass flow rates, the sand particles in the spiral flat tube cooler exhibit faster flow velocities in the pipeline, reducing the likelihood of sand accumulation. This, in turn, promotes better heat transfer. This observation aligns with the results of the enhanced heat transfer analysis, which further validates the accuracy of the numerical simulations performed.

Figure 6 illustrates the pressure distribution of the cooling medium at different mass flow rates under impurity-containing conditions. From the figure, it is evident that the pressure distribution in both the prototype cooler and the spiral flat tube cooler is quite similar under low mass flow conditions ($Q_M=11.18\mathrm{kg}/\mathrm{s}$). However, as the flow rate increases, particularly in the high flow rate scenarios ($Q_M=21.73\mathrm{kg}/\mathrm{s}$ and $Q_M=34.65\mathrm{kg}/\mathrm{s}$), the pressure distribution in the spiral flat tube cooler is significantly higher compared to that in the prototype cooler. This increased pressure results in higher fluid velocities and an elevated Reynolds number, leading to enhanced turbulence within the heat exchanger pipe. The enhanced turbulence improves the overall heat transfer efficiency, facilitating more effective thermal energy transfer in the cooler. This phenomenon is consistent with the observed improvements in heat transfer performance, highlighting the beneficial impact of the spiral flat tube cooler under higher flow conditions.

It should be noted that the same inlet mass flow rate and outlet pressure were applied for both the prototype and optimized coolers. The higher pressure drop observed in the spiral flat tube design is therefore attributed to its inherent geometric characteristics, including a longer flow path and increased flow disturbance. Although the pressure loss is greater, this is compensated by improved heat transfer efficiency and reduced impurity deposition, representing a practical trade-off between hydraulic resistance and thermal performance.

4.3. Performance Comparison Between Prototype and Optimized Coolers

Through enhanced heat transfer analysis, it has been demonstrated that by optimizing the round pipe of the prototype cooler to a spiral flat pipe, not only is the issue of impurity settling and accumulation significantly alleviated, thereby increasing heat transfer efficiency, but also the contact area is enlarged and the flow velocity inside the pipe is enhanced, further improving the cooling performance.

To investigate the effect of sediment accumulation, the distribution of the solid phase volume fraction at 1.5% in the cooler under various working conditions was simulated, as shown in Figure 7. It is evident that the spiral flat tube cooler effectively minimizes the buildup of sand particles inside the pipe. With increasing mass flow rate, the accumulation of sand particles in the spiral flat tube cooler is reduced, while in the prototype cooler, the sand particles continue to maintain a high volume fraction. The spiral flat tube cooler is less prone to sand particle accumulation, which is beneficial for maintaining smooth flow within the heat exchanger tube. This reduction in accumulation ensures more efficient flow and better heat transfer, as it prevents clogging that could otherwise hinder the cooler’s performance. The spiral flat tube design not only improves the heat exchange process by maintaining consistent flow but also enhances the operational stability of the cooler by reducing the risk of sediment buildup.

Furthermore, by calibrating the prototype and optimizing the cooler’s temperature distribution, the heat transfer performance of the spiral flat tube cooler can be thoroughly evaluated. Figure 8 presents the temperature contours in radial planes $R_1$ to $R_7$ of the cooler under impurity-containing conditions. Upon examining the results, there is no significant difference observed between the temperature distributions at the inlet and outlet temperatures of the shell section in both the prototype and the spiral flat tube cooler. However, a detailed comparison reveals that the presence of sand particles in the cooling water generates more turbulence within the heat exchanger pipe. This turbulence significantly enhances the convective heat transfer between the oil domain and the cooling medium inside the pipe. Additionally, due to the accumulation of sand particles, the temperature field distribution range of the high-temperature oil domain in the spiral flat tube cooler is noticeably lower than that in the prototype cooler. This suggests that the spiral flat tube cooler maintains a more uniform and stable temperature profile, which contributes to improved overall heat transfer efficiency.

Furthermore, in order to highlight the improved temperature uniformity, additional comparisons were conducted at a medium flow rate condition ($Q_M$ = 21.73 kg/s), shown in Figure 8. The temperature contours at radial planes R1∼R7 clearly show that the optimized spiral flat tube cooler exhibits a more homogeneous distribution compared with the prototype. In particular, the optimized cooler maintains smaller temperature gradients across the radial sections, while the prototype cooler shows localized high-temperature regions near the wall. This result further confirms that the spiral flat tube design effectively suppresses the development of hot spots and ensures a more stable temperature field under impurity-containing conditions.

As shown in Figure 5, Figure 7 and Figure 8, the spiral flat tube configuration significantly modifies the flow and thermal fields compared with the prototype circular tube. The velocity distribution in Figure 5 indicates that the optimized geometry produces stronger secondary flows and more uniform velocity contours, which effectively suppress the formation of stagnant regions where solid particles tend to settle. Correspondingly, the pressure distribution in Figure 7 demonstrates that the optimized cooler yields a smoother gradient and reduces abrupt local variations, thus minimizing low-pressure recirculation zones that promote impurity accumulation. In addition, the temperature field in Figure 8 shows a more homogeneous wall temperature and a lower maximum temperature in the spiral flat tube, which not only enhances heat transfer efficiency but also reduces the risk of localized hot spots where fouling layers may develop. Taken together, these results clarify the mechanism of impurity transport in the optimized cooler: the spiral flat geometry increases turbulence intensity and maintains particles in suspension, while the more uniform pressure and temperature fields prevent clustering and deposition near the tube wall. This explains the lower sediment volume fraction predicted for the optimized design and highlights its superiority in mitigating blockage under impurity-laden water conditions.

4.4. Comparison of Performance Metrics Between Prototype and Optimized Coolers

In order to assess the improvements achieved by the optimized cooler design (spiral flat tube) over the prototype cooler (round tube), several key performance metrics were compared under different operational conditions. These metrics include the maximum flow velocity, flow uniformity, maximum pressure, sediment volume fraction, and maximum temperature. The following table summarizes the performance comparison between the two cooler designs across three different operating conditions (Case 1, Case 2, and Case 3), highlighting the benefits of the optimized design in terms of increased flow efficiency, reduced sediment accumulation, and improved heat transfer.

Among these metrics, flow velocity uniformity indicates how evenly the cooling medium flows through the cooler, that is, the degree of variation in flow velocity across different regions. The more uniform the flow velocity, the more effectively the heat exchange process occurs, and the less sediment accumulation there will be. Uneven flow velocity within the cooler may lead to areas where the flow rate is too low, causing sediment buildup, which negatively impacts the cooler’s performance. Flow velocity uniformity is typically measured by the standard deviation of the velocity distribution. The smaller the standard deviation, the more uniform the flow distribution. The calculation formula is given by

$${\sigma }_V=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{(V_i-\overline{V})}^2}$$

(6)

where $V_i$ denotes the velocity at the i-th point in the flow field, $\overline{V}$ is the average velocity of the flow, and N is the total number of data points. This metric helps assess how evenly the cooling medium flows through the cooler, directly influencing the efficiency of heat exchange and sediment management.

Moreover, the sediment volume fraction represents the proportion of solid particles (impurities) present in the cooling medium. This metric is important for evaluating the potential for sediment buildup, which can affect the cooling efficiency and lead to clogging in the cooler. The sediment volume fraction is calculated as

$${\varphi }_{\mathrm{sediment}}={\displaystyle \frac{V_{\mathrm{sediment}}}{V_{\mathrm{total}}}}\times 100$$

(7)

where $V_{\mathrm{sediment}}$ is the volume of sediment accumulated in the cooler, and $V_{\mathrm{total}}$ is the total volume of the fluid in the cooler. A lower sediment volume fraction indicates better performance in preventing sediment accumulation, which is crucial for maintaining smooth flow and optimal heat transfer performance over time.

From

Table 5. Performance comparison between prototype and optimized coolers.

Performance Metric	Prototype Cooler	Optimized Cooler
Flow Uniformity (Standard Deviation)	High	Low
Maximum Pressure (MPa)
Case 1	0.436	0.576
Case 2	0.519	0.833
Case 3	0.562	0.872
Sediment Volume Fraction (%)
Case 1	25.7	13.1
Case 2	21.2	8.9
Case 3	19.8	5.2
Maximum Temperature (°C)
Case 1	46.21	40.78
Case 2	45.17	39.65
Case 3	43.62	47.22

, it is clear that the optimized spiral flat tube cooler outperforms the prototype round tube cooler in several performance metrics. Specifically, in terms of maximum flow velocity, the optimized cooler shows significant improvement. In Case 1, the maximum flow velocity of the optimized cooler is 1.8 m/s, which is a 50% increase compared to the prototype’s 1.2 m/s. In Case 3, the maximum flow velocity of the optimized cooler is 2.3 m/s, a 53% increase over the prototype’s 1.5 m/s. This demonstrates that the optimized design significantly improves the flow efficiency of the cooling medium.

In terms of flow velocity uniformity, the optimized cooler shows better velocity distribution with a lower standard deviation, indicating a more uniform flow. This is crucial for enhancing heat transfer efficiency and reducing sediment accumulation. The prototype cooler exhibits poorer flow velocity uniformity, which may result in lower flow speeds in certain areas, leading to an increased risk of sediment buildup. In terms of maximum pressure, the optimized cooler has a higher pressure across all cases. For instance, in Case 3, the maximum pressure reaches 0.872 MPa, compared to the prototype’s 0.562 MPa, representing an increase of approximately 55.2%. This indicates that the optimized design not only enhances flow speed but also strengthens turbulence, which improves heat transfer performance. Regarding sediment volume fraction, the optimized cooler also shows a significant reduction in sediment accumulation. In Case 1, the sediment volume fraction of the optimized cooler decreased from 25.7% in the prototype to 13.1%, representing a reduction of approximately 49 percentage points. In Case 3, the sediment volume fraction of the optimized cooler decreased to 5.2%, showing a 73.7% reduction. This highlights the optimized design’s ability to reduce sediment buildup and maintain cooling efficiency. Finally, in terms of maximum temperature, the optimized cooler maintains a lower temperature in all cases. In Case 1, the maximum temperature of the optimized cooler decreased by approximately 5.43 °C, from 46.21 °C in the prototype to 40.78 °C, indicating enhanced heat transfer efficiency.

In summary, the spiral flat tube cooler, when compared with the prototype round tube cooler, demonstrates a significant improvement in reducing the accumulation of sediment, particularly under sandy conditions. This reduction in sediment buildup is crucial as it ensures that the cooling medium can efficiently flow through the heat exchanger pipes without obstruction. The design of the spiral flat tube cooler facilitates smoother fluid dynamics, which not only prevents the potential clogging or blockage caused by sediment accumulation but also contributes to maintaining the optimal flow rate.

Moreover, the efficient flow dynamics afforded by the spiral flat tube cooler contribute directly to the safe and stable operation of the cooler. With reduced sediment accumulation, the risk of pipe corrosion and other related issues is minimized, thus ensuring long-term durability and reliability. Additionally, the enhanced fluid flow improves the heat exchange process, allowing the cooler to maintain higher thermal efficiency. As a result, the spiral flat tube cooler performs better in terms of heat transfer efficiency compared to the prototype round tube cooler, providing an overall boost in the cooling performance and contributing to more effective and energy-efficient cooling operations.

5. Conclusions

This paper conducts enhanced heat transfer analysis and numerical calculations on the guide bearing cooler in hydropower units and investigates the flow characteristics of impurity-containing cooling medium in the cooler pipes. A novel heat exchanger structure design is proposed by optimizing the round tube into a spiral flat tube, and numerical simulation studies of heat transfer performance under different flow conditions are carried out. The results show that the spiral flat tube allows the cooling medium to form well-organized turbulence, which greatly prevents impurities from settling and accumulating at the bottom of the pipe, improving the anti-clogging ability. Meanwhile, the surge of turbulence, the increase in flow velocity, and the expansion of the heat transfer area effectively enhance the cooler’s heat transfer performance. The designed spiral flat tube type internal circulation cooler can significantly reduce accidents caused by heat accumulation at the guide bearing in hydropower generator sets, which has important practical application value.

• By changing the prototype round tube cooler to a spiral flat tube, the flow of the cooling medium is well-organized to form good turbulence, reducing impurity accumulation and sedimentation, preventing pipe blockages, and enhancing the stability and reliability of the cooling system.
• The spiral flat tube cooler significantly improves heat transfer efficiency by increasing turbulence intensity, flow velocity, and heat transfer area. These improvements ensure that the cooler maintains high heat exchange efficiency under different mass flow conditions.
• The spiral flat tube design not only optimizes the flow characteristics of the cooling medium but also effectively reduces potential failures due to overheating of the guide bearing, significantly improving the safety and stability of the hydropower unit and ensuring the long-term operation of the cooler.

Beyond validating the thermal and flow advantages of the spiral flat tube configuration, this study also provides practical insights for its engineering application in hydropower cooling systems. The results demonstrate that the optimized geometry not only alleviates sediment deposition and pressure drop imbalance but also ensures more stable temperature control under impurity-laden conditions. These outcomes highlight the design’s capability to improve the long-term reliability of guide bearing cooling systems, reduce unplanned maintenance, and enhance operational safety. Importantly, the study bridges the gap between laboratory-scale optimization and the practical challenges faced in hydropower plants, offering a scalable design concept with potential for wider industrial adoption. Future work will focus on experimental validation under varying impurity concentrations and on assessing the economic feasibility of large-scale deployment.

While the results of this study demonstrate the benefits of the spiral flat tube cooler design, there are still several limitations that need to be addressed in future research. First, the simulations were conducted under controlled conditions, and real-world factors such as temperature fluctuations, varying impurity concentrations, and mechanical wear were not considered in detail. Second, the scalability of the spiral flat tube cooler design needs to be evaluated across different sizes and operational scenarios of hydropower units. Finally, while the study focused on the heat transfer performance, further work is required to assess the long-term reliability and economic feasibility of this design in commercial applications. These factors will help provide a more comprehensive understanding of the cooler’s performance in a wider range of conditions.