Research on Heat Transfer Characteristics Based on Thermal‐Fluid Coupling Analysis of the Magnetic Coupler

Abstract

ABSTRACT

Taking the magnetic coupler employed in the power generation device harnessing natural gas pressure energy as the research subject, the heat transfer characteristics of the magnetic coupler and the external flow field under the eddy current effect are exhaustively investigated to address the heating issue caused by that effect. A thermal‐fluid coupling model for the magnetic coupler and its flow field is established. With the eddy current loss on the isolation sleeve regarded as the heat source, the temperature distribution characteristics of each component of the magnetic coupler under the rated operating conditions are simulated. The flow state around the magnetic coupler and the heat transfer features on the outer wall of the isolation sleeve are further analyzed. To address the issues that the air in the gap has difficulty circulating along the axial direction and the temperature of the internal magnets is close to the maximum allowable working temperature, the heat dissipation structure of the magnetic coupler is enhanced by modifying the eccentric distance, increasing the quantity and the diameter of the heat dissipation holes on the external rotor. Eventually, the maximum convective heat transfer coefficient of the outer wall surface of the isolation sleeve is raised from 23.6 W/(m² °C) to 61.7 W/(m² °C), and the temperature of the internal magnet is kept below 50.9°C, attaining a favorable heat dissipation effect and meeting the usage requirements.

Introduction

In recent years, with the escalating research and application of the power generation technology utilizing natural gas pressure energy, magnetic couplers have been applied in those power generation devices on account of their advantages such as static sealing and zero leakage. Magnetic couplers are a novel type of coupler that have been widely used in recent years. Compared with traditional ones, they have no direct mechanical connection and belong to noncontact couplers. A magnetic coupler consists of an internal magnet, an external magnet, and an isolation sleeve. The internal and external magnets act as transmission components to drive magnetic rotors to rotate under the action of magnetic force. The internal and external magnets are separated by the isolation sleeve, thereby achieving contactless torque transmission. The isolation sleeve is designed to completely enclose the conveyed fluid inside the device, making the sealing form of the magnetic coupler become a static seal, greatly improving the reliability of mechanical operation and achieving absolute zero leakage [1]. Therefore, the application of magnetic couplers to power generation devices utilizing natural gas pressure energy can guarantee the sealing and safety of the system. However, the issue of eddy current loss needs to be taken into consideration when applying them.

During the utilization of magnetic couplers, eddy current loss may occur, which will exert a negative influence on the stable and reliable operation of magnetic couplers. The primary negative impact is that eddy current losses are dissipated in the form of heat. If the heat cannot be dissipated promptly, it will lead to an increase in the overall temperature of the magnetic coupler. The magnetism of permanent magnets is highly sensitive to temperature, and an increase in temperature will lead to a decrease in magnetism or even permanent demagnetization, seriously affecting the normal usage of the magnetic coupler. Therefore, it is crucial to understand the temperature conditions of the magnetic coupler during operation. When the temperature of the magnet exceeds the maximum allowable working temperature, cooling measures must be implemented to promptly dissipate the heat from the magnetic coupler, thereby stabilizing the magnet's temperature within the allowable working range and ensuring the proper functioning of the equipment. Consequently, the temperature field distribution of magnetic couplers, influenced by eddy current losses, has garnered significant attention from researchers. Fu Pan [2] developed two-dimensional and three-dimensional eddy current loss models and performed three-dimensional transient temperature field analyses for magnetic coupler transmission devices. Chen Zhipeng [3] and Wang Shuang [4] utilized the finite element analysis software ANSYS to conduct a three-dimensional temperature field analysis of a magnetic coupler, obtaining its overall temperature distribution, which provides valuable insights for studying the temperature field of high-power magnetic couplers. Zhao Bao [5] conducted transient temperature field analyses using the magnetic-thermal element coupling algorithm. Zhang [6] segmented the model into different temperature calculation zones using the finite element method and compared their approach with traditional synchronous magnetic-thermal coupling field analysis, demonstrating faster prediction of electromagnetic-thermal distributions. Jiang [7] identified electromagnetic power loss as the primary source of heat flux and conducted a new evaluation of material properties based on temperature distribution.

Researchers are actively studying cooling methods to address the issue of temperature rise caused by eddy current loss in magnetic couplers [8]. The cooling forms of magnetic couplers are generally divided into three types. The first is to introduce the fluid into the isolation sleeve by means of internal or external circulation and flush the inner wall of the isolation sleeve to take away the heat. The second is to open air holes on the external rotor component outside the isolation sleeve, so that the external airflow enters from the holes and blows towards the outer wall of the isolation sleeve, achieving air cooling and heat dissipation. The third is to install a fin radiator on the magnetic coupler to dissipate the heat generated on the isolation sleeve through the fins. Internal or external circulation is the most common cooling form of magnetic couplers, which is mainly used for the conveying conditions of liquids. Due to the large pressure and temperature variations of the high-pressure gas as it passes through the guide hole, it is difficult for the gas to flow unidirectionally in the cooling channel like a liquid, and it also forms an unbalanced axial force when passing through the guide hole. For magnetic couplers used in high-pressure natural gas transportation environments, this internal/external circulation cooling method is not suitable for magnetic couplers in gas conveying.

There is limited research on the application of the latter two cooling methods to magnetic couplers, whereas there is more extensive research on these cooling techniques in magnetic couplers used for speed and torque regulation without an isolation sleeve structure. By incorporating additional features such as heat dissipation holes and fins into the original design of the magnetic coupler, the cooling efficiency has been enhanced, thereby further optimizing the external cooling structure. Based on this body of research, empirical references can be derived for improving the cooling and heat dissipation of magnetic couplers utilized in power generation devices that harness natural gas pressure energy.

This study focuses on optimizing the eddy current-induced heating in the magnetic coupler. A thermal-fluid coupling model is established to investigate the temperature and flow fields of the magnetic coupler. Simulations are conducted to determine the overall temperature distribution and airflow field of the magnetic coupler. Improvements are made to the heat dissipation structure to ensure that the operating temperatures of both the internal and external magnets stay below the maximum allowable working temperature of the permanent magnet [9–14]. Finally, the effectiveness of the enhanced structural design is assessed.

Mathematical Model of the Thermal-Fluid Field for the Magnetic Coupler

Mathematical Model of the External Flow Field of the Magnetic Coupler

The external flow field of a magnetic coupler should meet three conservation laws, i.e. mass conservation, momentum conservation, and energy conservation.

(1) Mass conservation of fluid

Continuity equation is a mathematical description of the mass conservation law, and the flow of any fluid shall meet the continuity equation. Here, it is considered that the air in the external flow field of the magnetic coupler is a homogeneous fluid with no change in density. The difference between the mass flowing into and out of the microelement per unit time is zero. The continuity equation at this point is: 1$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$where:

$u$, $v$, and $w$—flow velocity in $x$, $y$ and $z$ directions, in m/s.

(2) Momentum conservation of fluid

The N-S equation is a mathematical description of the momentum conservation law. For viscous incompressible fluids, the sum of all external force vectors on a microelement is equal to the change rate of momentum over time within the microelement. Its expression is as follows: 2$\begin{array}{l}\rho \left({\displaystyle \frac{\partial u}{\partial t}}+u{\displaystyle \frac{\partial u}{\partial x}}+v{\displaystyle \frac{\partial u}{\partial y}}+w{\displaystyle \frac{\partial u}{\partial z}}\right)=\rho f_x-{\displaystyle \frac{\partial p}{\partial x}}+\mu \left({\displaystyle \frac{\partial {\tau }_{xx}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yx}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{zx}}{\partial z}}\right)\\ \rho \left({\displaystyle \frac{\partial v}{\partial t}}+u{\displaystyle \frac{\partial v}{\partial x}}+v{\displaystyle \frac{\partial v}{\partial y}}+w{\displaystyle \frac{\partial v}{\partial z}}\right)=\rho f_y-{\displaystyle \frac{\partial p}{\partial y}}+\mu \left({\displaystyle \frac{\partial {\tau }_{xy}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yy}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{zy}}{\partial z}}\right)\\ \rho \left({\displaystyle \frac{\partial w}{\partial t}}+u{\displaystyle \frac{\partial w}{\partial x}}+v{\displaystyle \frac{\partial w}{\partial y}}+w{\displaystyle \frac{\partial w}{\partial z}}\right)=\rho f_z-{\displaystyle \frac{\partial p}{\partial z}}+\mu \left({\displaystyle \frac{\partial {\tau }_{xz}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yz}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{zz}}{\partial z}}\right)\end{array}$where:

$f_x,f_y\text{and}{f}_z$ - Unit mass force of microelement in x, y and z directions, in m/s²;

${\tau }_{xx},{\tau }_{yx},{\tau }_{zx},{\tau }_{xy},{\tau }_{yy},{\tau }_{zy},{\tau }_{xz},{\tau }_{yz},and{\tau }_{zz}$ - Shear stress component within the microelement, in Pa;

ρ - Fluid density, in kg/m³;

p - Pressure in the microelement, in Pa.

(3) Energy conservation of fluid

The external flow field of the magnetic coupler follows the law of energy conservation, which means that the increase in total energy inside the microelement is equal to the sum of the net heat flux entering the microelement and the work done by the external force on the microelement. Its expression is: 3$\frac{\partial \left(\rho T\right)}{\partial t}+\text{div}\left(\rho uT\right)=\text{div}\left(\frac{k}{c_p}gradT\right)+S_T$where:

$T$ - thermodynamic temperature, ⁱⁿ K;

$k$ - thermal conductivity of fluid, ⁱⁿ W/(m·K);

$c_p$ - specific heat capacity of fluid, ⁱⁿ J/(kg·K);

$S_T$ - the portion of internal heat source and loss converted into internal energy.

Mathematical Model of Temperature Field for the Magnetic Coupler

Before analyzing the mathematical model of the temperature field for the magnetic coupler, the following assumptions are made to simplify the calculations [15]:

(1) The eddy current loss on the isolation sleeve is the only heat source in this temperature field, and all that loss is converted into heat dissipation.

(2) The material properties of each part of the magnetic coupler are isotropic, and the physical properties do not change with temperature.

(3) Only the temperature changes due to heat conduction and convection are considered, and the effects of heat radiation are ignored.

The heat exchange inside the various components of a magnetic coupler and between the components in contact with each other is mainly carried out in the form of heat conduction. The process meets the energy conservation law: The heat transferred into the microelement in the form of thermal conduction + the heat generated by the heat source inside the microelement = the increment of internal energy in the microelement, that is 4$d{Q}_c+d{Q}_g=dQ$

According to Fourier's law, the above equation can be expressed in the Cartesian coordinate system as 5$\frac{\lambda }{\rho c}\left(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}+\frac{{\partial }^{2}T}{\partial z^2}\right)+\frac{q_v}{\rho c}=\frac{\partial T}{\partial t}$

This paper primarily investigates the temperature distribution of the magnetic coupler in a steady state. For steady-state heat transfer, the change rate of temperature T with respect to time t is zero. Therefore, the steady-state temperature field of the magnetic coupler is governed by the thermal conductivity differential equation as follows: 6$\left(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}+\frac{{\partial }^{2}T}{\partial z^2}\right)+\frac{q_v}{\lambda }=0$where:

$T$ - temperature at any point within the solution domain, in K;

$q_v$ - heating power of the internal heat source per unit volume, which is the eddy current loss on the isolation sleeve, in W/m³;

$\lambda$ - Thermal conductivity, measured in W/(m K).

Convection heat exchange is mainly carried out between the wall and the air for each part of the magnetic coupler. Due to the rotating state of the magnetic rotors, it causes disturbance to the surrounding air, and the convection form is forced convection. Under steady-state conditions, the heat transfer at the wall surface satisfies the following relationship: 7${-\lambda \frac{\partial T}{\partial n}∣}_w=h\left(T_W-T_f\right)$where:

$h$ - convective heat transfer coefficient at the wall, W/(m² K);

$T_W$ - temperature at the wall surface, K;

$T_f$ - temperature of the fluid, K.

Finite Element Model of Thermal-Fluid Field for the Magnetic Coupler

In this paper, the cylindrical magnetic coupler is selected, whose structure is shown in Figure 1, consisting of an internal rotor, an external rotor, and an isolation sleeve among other components. The internal rotor of the cylindrical magnetic coupler is slightly smaller in diameter with a shaft shape, while the external rotor is slightly larger with a cylindrical shape. Magnets are installed on the inner ring side of the external rotor and the outer ring side of the internal rotor, arranged in pairs with alternating magnetization directions. The cylindrical magnetic coupler enhances torque transmission by increasing the coupling length of the internal and external magnetic rotors. This magnetic coupler is designed for use in a power generation device that harnesses natural gas pressure energy under the following operating conditions: a rated speed of 900 rpm, a power generation capacity of 2.2 kW, and a maximum internal pressure within the isolation sleeve of 1.0 MPa.

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The three-dimensional model of the magnetic coupler is divided into a solid domain and fluid domain. The solid domain primarily comprises the three main components of the magnetic coupler, including the external rotor, the internal rotor and the isolation sleeve. For the purpose of calculation, only the key feature dimensions of the magnetic coupler are retained, and some structures that have little influence on the calculation results are simplified. The tile-type magnets on the internal and external rotors are approximated as complete cylindrical magnets. The fluid domain consists of two parts: the high-pressure natural gas inside the isolation sleeve and the ambient air outside it. The gas inside mainly affected by the pressure difference enters the isolation sleeve through the dynamic sealing gap between the shaft and the bearing. Upon reaching a steady operating condition, the gas on both sides of the bearing gap reaches a pressure balance. Due to the very small size of the bearing gap, the gas exchange inside the isolation sleeve with the external fluid is very weak after reaching the pressure equilibrium state. Therefore, it can be assumed that the gas within the isolation sleeve remains in a closed state with no material exchange with the external fluid. To simulate the ambient airflow induced by the rotation of the external rotor, a rotating air domain surrounding the external rotor is established. The models of solid and fluid domains are shown in Figure 2.

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The built-in mesh partitioning software Mesh in Workbench is used to partition the mesh. Due to the small air gap size between the outer rotor and the isolation sleeve, only the boundary layer mesh is divided for the outer wall surface of the isolation sleeve. Numerical calculations were performed using a mesh model with a global partition size of 3 mm, an isolation sleeve mesh refinement size of 1 mm, and a total mesh count of 3569852. The cross-sectional view of the mesh model and the mesh division of the three major components of the magnetic coupling are shown in Figures 3 and 4. The relevant material properties of the magnetic coupling are shown in Table 1.

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Table 1 Material properties of magnetic couplings.

Component	Material	Density (kg/m³)	Specific heat capacity (J/kg·°C)	Thermal conductivity (W/m·°C)
Inner and external magnet	ND-FE-B(N45)	7400	502	9
Isolation sleeve	TC4	4400	611	7.6
Inner and external rotor	Q235A	7800	460	50

The outlet pressure is atmospheric pressure, and the reflux temperature is 26°C. Take one point each on the outer rotor, inner rotor, and isolation sleeve as a temperature monitoring point, while monitoring the highest and lowest temperatures of the magnetic coupling. When the temperature changes at these points with the increase of iteration steps by less than 0.1°C, the energy residual is less than 10⁻⁶, and the remaining residuals are all less than 10⁻³, and the size of each residual tends to flatten out with the increase of iteration steps, the solution is considered complete by default.

Analysis of Calculation Results

Temperature Distribution Characteristics

The isolation sleeve, from which heat starts to generate and transfer, is a component that generates eddy current loss. As shown in Figure 5, the isolation sleeve experiences the highest temperature increase with a pronounced temperature gradient. A high-temperature region exceeding 80°C forms in the projection area of the permanent magnets onto the isolation sleeve. The temperature on the isolation sleeve is evenly distributed along the circumference, while the axial temperature gradually decreases from the high-temperature section towards the bottom and top ends. The maximum temperature of the isolation sleeve is 88.7°C. The minimum temperature is 59.2°C, which occurs at the bottom of the isolation sleeve. The maximum temperature difference is 29.5°C. This significant temperature variation can be attributed to the concentration of eddy current losses in specific areas of the isolation sleeve. Outside these concentrated regions, there is minimal eddy current loss and no additional heat sources. Heat transfer primarily occurs via conduction from the high-loss areas; however, the poor thermal conductivity of the isolation sleeve material limits heat propagation to the bottom. Additionally, higher airflow velocity in the air gap at the bottom of the isolation sleeve enhances convective cooling, leading to lower temperatures at this location. Consequently, the temperature difference across the isolation sleeve is substantial.

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Figure 6 shows the temperature distribution nephogram of the external rotor. It can be seen that the overall temperature on the external rotor is relatively low. This phenomenon can be attributed to the poor thermal conductivity of air, which results in heat transferred by the isolation sleeve primarily entering the air gap between the isolation sleeve and the external rotor, making it difficult for this heat to propagate to the external rotor. As a whole, the temperature on the external rotor is uniformly distributed in the circumferential direction and exhibits a gradual decrease in the radial direction [16–20]. The highest temperature point on the external rotor is located on the external magnet, reaching 42.8°C, which is significantly lower than the allowable operating temperature of NdFeB magnets.

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Figure 7 shows the temperature distribution of the internal rotor. The temperature of the internal rotor is higher than that of the external rotor. This can be attributed to the internal rotor being housed within a closed isolation sleeve, where the fluid inside has minimal heat exchange with the external environment. Consequently, heat entering the isolation sleeve continuously raises the temperature of the internal fluid and subsequently transfers this heat to the internal rotor via convective heat exchange. The maximum temperature of the internal rotor reaches 76.1°C on the internal magnets, and the lowest temperature is 75.4°C at the bottom of the internal rotor. Overall, the temperature difference across the internal rotor is minimal, with a maximum temperature difference of less than 1°C. This uniformity in temperature distribution is due to the rotational disturbance of the internal rotor, which facilitates efficient heat exchange between the fluid and the rotor wall, leading to thermal equilibrium between the internal rotor and its surrounding fluid. Finally, the temperature on the internal rotor is uniformly distributed circumferentially and gradually increases along the radial direction.

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The temperature distribution characteristics within the air gap warrant particular attention. From Figure 8, it can be seen that the maximum temperature in the air gap between the isolation sleeve and the external rotor is observed near the wall surface of the eddy current concentration area of the isolation sleeve, reaching 80.4°C, and the minimum temperature is recorded at the bottom of the external rotor, at 33.5°C. Within the narrow gap between the external magnet and the isolation sleeve wall, the fluid exhibits an extremely high temperature gradient, with a temperature difference exceeding 30°C over a mere 3 mm distance. The air inside the gap between the external rotor and the isolation sleeve has a higher temperature compared to the external air, and the convective heat transfer effect with the outer wall of the isolation sleeve is poor. There is still room for improvement in the heat dissipation structure of the magnetic coupler.

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Flow Characteristics of the Flow Field in the Air Gap

Figure 9 shows the air trace distribution of the air gap flow field between the isolation sleeve and the external rotor when the magnetic coupler reaches a steady state under rated operating conditions. It is evident that the air in the gap at both the side wall surface and the bottom surface of the isolation sleeve moves in the same direction with the rotation of the external rotor. The airflow velocity is minimal at the center of the isolation sleeve's bottom surface, increasing progressively toward the edge of the external rotor. The axial airflow in the gap is weak, with most air remaining confined to a fixed axial plane during rotation. The air inside and outside the gap is difficult to circulate, and only a small amount of air near the edge of the gap can flow in or out by rotational inertia. The characteristics of airflow in the gap result in high air temperature, making it difficult to achieve good convective heat transfer.

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Convective Heat Transfer Characteristics on the Isolation Sleeve

Figures 10 and 11 show the axial variation trend of the heat flux and convective heat transfer coefficient on the isolation sleeve wall when the magnetic coupler reaches steady-state temperature under the rated conditions. As the external rotor rotates, it drives the air within the gap, resulting in high airflow velocity and forced convective heat transfer on the outer wall of the isolation sleeve within the air gap. In addition, the convective heat transfer coefficient near the edge of the air gap exhibits a clear trend of initially decreasing and then increasing. This phenomenon is attributed to changes in the axial flow section of the air at the gap's edge. As the air flows out from the gap, its flow channel becomes wider, which results in the reduction of the flow velocity and the decrease of the convective heat transfer coefficient. At the edge of the air gap, enhanced convective heat exchange occurs due to increased heat and mass exchange between the air near the wall surface and the external air, ultimately presenting a saddle-shaped trend. The air outside the gap flows very weakly without the disturbance of the rotation of the external rotor, resulting in natural convection being the primary heat transfer mode on the outer wall of the isolation sleeve outside the air gap, with a convective heat transfer coefficient less than 10 W/(m² °C). The heat transmitted from the eddy current concentration area is difficult to be dissipated into the air and is mostly converted into internal energy, which increases the wall temperature at this place. However, overall, the convective heat transfer coefficient on the isolation sleeve is not high, with a maximum value of only 23.6 W/(m² °C). This suggests that despite the high airflow velocity within the gap, the weak axial flow makes it challenging to effectively carry away the heat from the isolation sleeve, thus failing to achieve optimal convective heat transfer. Therefore, there is potential for improving the heat dissipation structure of the magnetic coupler.

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From the perspective of heat flux, the axial variation trend of heat flux on the outer wall of the isolation sleeve is consistent with that of the convective heat transfer coefficient. The heat exchange on the outer wall of the isolation sleeve mainly occurs in the eddy current concentration area, where the eddy current losses are the main source of heat generation. Since the heat exchange on the isolation sleeve originates from this region, the heat flux here is significantly higher compared to other locations.

When the temperature of the magnetic coupler reaches a steady state underrated working conditions, the maximum temperature of the internal magnet is 76.1°C, which approaches the maximum allowable working temperature of 80°C for NdFeB magnet. The residual magnetism of the internal magnet is about 94.2% of its room-temperature value, and the intrinsic coercivity drops to only 69.2% of its room-temperature value. This indicates that under rated operating conditions when the magnetic coupler reaches a stable temperature, the temperature rise has a relatively minor impact on the magnetic flux density but a significant effect on the permanent magnet's ability to resist demagnetization. If the internal magnet works under the maximum allowable temperature for a long time, the magnetism of the permanent magnet will be irreversibly degraded, which will affect the transmission performance of the magnetic coupler. To ensure the normal operation of the magnetic coupler, the heat dissipation structure of the magnetic coupler should be improved.

Improvement of Heat Dissipation Structure for the Magnetic Coupler

The hot air between the external rotor and the isolation sleeve of the magnetic coupler can only follow the rotation of the external rotor in a limited space, with minimal axial circulation, making it difficult to form effective convection. To enhance the heat transfer in the air gap between the external rotor and the isolation sleeve, improvements are made to the heat dissipation structure on the external rotor. Specifically, these improvements involve repositioning the center of the heat dissipation holes and increasing both the number and diameter of the holes. This increases the contact area between the hot air inside the gap and the cold air outside, promoting axial airflow within the gap and facilitating more efficient heat removal from the isolation sleeve.

The external rotor used in this study originally had two circular heat dissipation holes with a diameter of 10 mm, positioned at the bottom of the external rotor with an eccentricity of 45 mm. To investigate the effect of varying the eccentric distance on temperature changes, while keeping the setting parameters and boundary conditions of the temperature field model unchanged, the number and diameter of the heat dissipation holes were kept constant. The eccentric distance was varied between 30 and 60 mm in equal intervals of 5 mm. Temperature changes in the magnetic coupler were then calculated for different eccentric distances of the heat dissipation holes.

Figure 12 shows the variations of the maximum temperatures of the magnetic coupler and the internal magnet under different eccentric distances of the heat dissipation holes. It can be seen that the changing trends of both are consistent. When the eccentric distance changes from 30 to 40 mm, the maximum temperatures exhibit a slight downward trend, but the variation amplitude remains minimal. Conversely, as the eccentric distance increases from 40 to 60 mm, the maximum temperatures rise correspondingly. This is because the fluid flow state between the isolation sleeve and the external rotor is changed by varying eccentric distances. The fluid around the external rotor rotates with it, and the closer the fluid is to the edge of the external rotor, the higher its rotational speed and dynamic pressure. When the eccentric distance is small, the fluid flow velocity around the external rotor is smaller and the dynamic pressure is lower, forming a pressure difference with that from the edge of the external rotor. This facilitates the introduction of external fluid into the heat dissipation holes, promoting convection with the outer wall of the isolation sleeve. From the perspective of cooling effect, an eccentric distance of 30 to 40 mm for the holes can achieve better heat dissipation. However, considering that a too small eccentric distance may limit the subsequent increase of the number and diameter of the holes, an eccentric distance of 40 mm is more suitable for optimal heat dissipation.

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Keeping the parameters and boundary conditions of the temperature field model unchanged, the heat dissipation holes have a diameter of 10 mm, and the previously calculated optimal eccentric distance of 40 mm is selected. The number of heat dissipation holes is varied from 0 to 16 in intervals of 2, arranged uniformly along the circumference. Temperature changes on the magnetic coupler are then calculated for different numbers of heat dissipation holes.

Figure 13 shows the maximum temperature variations of the magnetic coupler and the internal magnet for different numbers of heat dissipation holes. It can be seen that the maximum temperatures decrease continuously with the increase of the number of heat dissipation holes, indicating that a greater number of heat dissipation holes facilitates more effective entry of external air into the air gap for heat transfer. However, with the increase of the number of heat dissipation holes, the magnitude of temperature decrease also changes. As the number of heat dissipation holes gradually increases from 0 to 8, for every 2 more heat dissipation holes, the maximum temperatures of the magnetic coupler and internal magnet can decrease by 3°–4°C. When the number of heat dissipation holes exceeds 8, the cooling effect begins to weaken. For every two more heat dissipation holes added, the resulting temperature drop is less than 2°C. This phenomenon can be attributed to two factors: first, as the temperature of the magnetic coupler decreases, achieving further significant temperature reductions becomes more challenging. Second, the area of the holes increased by increasing the number of those is limited. Therefore, expanding the diameter of the heat dissipation holes is necessary. To allow for future expansion of the aperture, the number of heat dissipation holes should not be excessively large. Considering the overall heat dissipation performance and spatial layout, using 8 heat dissipation holes is appropriate.

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Keeping the parameters and boundary conditions of the temperature field model unchanged, using the optimal eccentric distance of 40 mm selected in the previous section, with 8 heat dissipation holes, we varied the diameter of these holes from 10 mm to 24 mm in 2 mm increments and calculated the corresponding temperature changes on the magnetic coupler.

Figure 14 shows the maximum temperature variations of the magnetic coupler and the internal magnet at different heat dissipation diameters. As shown in the figure, with the increase of the heat dissipation diameter, the maximum temperatures of the magnetic coupler and the internal magnet both show a decreasing trend, but the magnitude of the decrease becomes smaller and smaller. This phenomenon can be attributed to the quadratic relationship between diameter and area; each 2 mm increase in diameter leads to a progressively larger heat dissipation area, but the resulting temperature drop becomes incrementally smaller. When the diameter is larger than 20 mm, the maximum temperature of the internal magnet is basically stable at about 50°C. Increasing the diameter further does not significantly improve the heat dissipation effect, and may greatly damage the structural strength of the external rotor. Therefore, the optimal heat dissipation hole diameter is selected as 20 mm.

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Based on the research on the influence of eccentricity, number, and diameter of heat dissipation holes on the cooling effect in the previous section, the final optimized heat dissipation structure of the external rotor is as follows: the eccentricity of heat dissipation holes is 40 mm, the number of holes is 8, and the diameter of each hole is 20 mm. The temperature distribution of the magnetic coupler with improved heat dissipation structure under rated operating conditions is shown in Figures 15–17. It can be observed that the overall temperature distribution remains symmetrically aligned with the structural design, but the temperature values have significantly decreased. The temperature comparison before and after the improvement of heat dissipation structure is shown in Table 2. The maximum temperature of the magnetic coupler still appears on the isolation sleeve, which is 63.2°C. Compared with that of the original structure, this represents a decrease of 23.5°C, with a maximum temperature difference on the isolation sleeve of 29.9°C. The maximum temperature of the external rotor is 30.1°C, which is 12.7°C lower than before the improvement. Similarly, the maximum temperature of the internal rotor has decreased to 50.8°C, representing a reduction of 25.3°C compared to the original structure. These results demonstrate that the optimized heat dissipation structure effectively enhances the cooling performance of the magnetic coupler.

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Table 2 Maximum temperature comparison of various components for the magnetic coupler before and after Improvement of heat dissipation structure.

	Isolation sleeve	Internal rotor	External rotor
Maximum temperature before improvement (°C)	88.7	76.1	42.8
Maximum temperature after improvement (°C)	63.2	50.8	30.1

Figure 18 shows the air trace distribution of the gap flow field between the isolation sleeve and the external rotor when the magnetic coupler reaches a steady state under rated operating conditions. Due to the increase in the number and diameter of heat dissipation holes, a greater volume of external air enters these holes. Under the disturbance of the rotation of the external rotor, the air traces in the gap at the bottom of the isolation sleeve are relatively chaotic and disordered. In contrast, the air traces in the gap along the side wall of the isolation sleeve form a mesh-like crossing pattern. This is because the air entering the gap comes from two directions. One part enters through the heat dissipation holes at the bottom of the external rotor. As the external rotor rotates, the air rotates clockwise around the external wall of the isolation sleeve from bottom to top. The other part enters through the air gap at the end of the external rotor. Due to the higher rotational speed and dynamic pressure at the edge of the external rotor compared to the fluid in the air gap, the air at the edge of the external rotor flows into the air gap in a rotating state due to the pressure difference. It rotates clockwise from top to bottom around the outer wall of the isolation sleeve at the top air gap of the external rotor. The intersection of these two air streams within the gap results in a complex cross-network pattern of air traces. Compared to the air trace distribution before the improvement of the heat dissipation structure, the axial movement of air traces in the gap has been significantly enhanced. This leads to better circulation of air within the gap and more efficient convective heat transfer on the isolation sleeve.

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Figure 19 shows the comparison of heat flux on the outer wall of the isolation sleeve before and after improving the heat dissipation structure. After improving, the heat flux in the eddy current concentration area on the isolation sleeve has significantly increased, while that in other regions has slightly decreased relative to that before improving. This is because the heat on the isolation sleeve mainly comes from the eddy current loss generated in the eddy current concentration area, which is also the most intense region for heat exchange. The improved design facilitates better air circulation within the gap, thereby enhancing heat transfer in the eddy current concentration area and increasing the heat flux. However, the continuous heat generation from eddy current losses on the isolation sleeve leads to an increase in convective heat transfer. This results in a reduction of the heat conducted to other areas of the isolation sleeve, thereby decreasing the heat flux at other positions on the outer wall.

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Figure 20 shows the comparison of convective heat transfer coefficients on the outer wall of the isolation sleeve before and after improving the heat dissipation structure. The improved design facilitates better air circulation, leading to an overall enhancement in the convective heat transfer coefficient on the outer wall. This enhancement is particularly evident in the air gap region. Specifically, the maximum convective heat transfer coefficient reaches 61.7 W/(m² °C) at the edge of the vortex concentration area, corresponding to the position of the outer magnet. This peak value is attributed to the reduced air gap size, which increases the air velocity in the bottom air gap, thereby maximizing the convective heat transfer coefficient in this critical region.

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Conclusions

A thermal-fluid coupling model was developed to simulate the temperature and flow fields of the magnetic coupler. This model integrates the eddy current losses in the isolation sleeve as a heat source, enabling the simulation of the flow dynamics and temperature distribution characteristics of the magnetic coupler under rated operating conditions. Upon reaching steady-state temperature, the temperature distribution is symmetrical with respect to the structure, with the highest temperature (88.7°C) observed at the isolation sleeve. The maximum temperature of the internal magnet reaches 76.1°C, approaching the maximum allowable temperature for the permanent magnet. To address the issue of poor axial air circulation in the gap between the external rotor and the isolation sleeve, which results in inadequate heat exchange and temperature rise in the magnetic coupler, the heat dissipation structure was optimized. The effects of the eccentric distance, number, and diameter of the bottom heat dissipation holes in the external rotor on the heat dissipation performance were analyzed. Consequently, the eccentric distance of the heat dissipation holes was adjusted to 40 mm, the number of holes was set to 8, and the diameter was increased to 20 mm. These modifications led to a significant increase in the maximum convective heat transfer coefficient on the outer wall of the isolation sleeve, from 23.6 W/(m² °C) to 61.7 W/(m² °C). As a result, the overall temperature of the magnetic coupler decreased substantially, and the maximum temperature of the internal magnet dropped to 50.9°C, well below the maximum allowable working temperature of the permanent magnet.

Acknowledgements

Funded by the Open Foundation of Industrial Perception and Intelligent Manufacturing Equipment Engineering Research Center of Jiangsu Province (No. ZK21-05-08).

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