Internal Flow Field and Loss Analysis of a Magnetic Drive Pump’s Cooling Circuit

Abstract

The cooling circuit is an important component of the magnetic drive pump because it prevents demagnetization of the permanent magnet and damage to the containment shell owing to a high temperature increase. In this paper, the flow field and losses of the cooling circuit of the magnetic pump are discussed and experimentally verified based on numerical simulation methods. Five different lengths of magnetic couplings were designed, and the flow field distribution, cooling flow rate, and loss variation laws of the cooling circuit were analyzed. The results show that the pump flow rate and magnetic coupling length have a minimal effect on the velocity distribution in the cooling circuit. When the magnet length increases from 30 mm to 55 mm, the temperature rise of the cooling circuit and the pressure drop at the gap increase by 23.1% and 25.3%, respectively. When the length of the magnetic coupling remains constant, the cooling flow rate of the cooling circuit falls with an increasing pump flow rate, and it reduces by 8.4% when the pump flow rate increases from 0.7 Q to 1.3 Q. The water friction loss and eddy current loss of the cooling circuit increase with an increase in the magnetic coupling length, while the cooling flow rate decreases. When the magnet length increases from 30 mm to 55 mm, the eddy current losses in the coupling circuit and the water friction losses in the cooling circuit increase by 45% and 35%, respectively, while the cooling flow rate decreases by 13%.

1. Introduction

Magnetic drive pumps are commonly employed in the petrochemical and aerospace industries to convey flammable, explosive, poisonous, and hazardous media. Magnetic coupling is used to transmit torque in magnetic drive pumps. The pump is completely sealed thanks to the innovative contactless torque transmission mechanism. Magnetic coupling increases the loss in the pump; therefore, the efficiency of magnetic drive pumps is often low compared to conventional centrifugal pumps [1,2].

Many academics have undertaken studies on the internal flow field, and optimal design of magnetic drive pumps as CFD technology has matured and computer technology has advanced [3,4,5]. Kong et al. [6] investigated how rotational speed affects the internal flow field and performance of magnetic drive pumps. They explored the distribution of pressure and velocity in magnetic pumps at various speeds, as well as the head and efficiency of pumps at various speeds. They claimed that disk friction loss is the most significant of all power losses. Mitsuo et al. [7] created a magnetic drive pump with a noncontact floating impeller. The axial force of the impeller decreased as a result of the aileron blade and balancing hole, and the floating impeller was achieved. Zhao et al. [8] improved pump performance by optimizing the impeller of an ultra-low specific speed magnetic drive pump.

Bao and Sheng [9] used a numerical approach to investigate the water friction loss and temperature field distribution of a wet submersible motor. They declared that the magnetic coupling’s metal containment shell creates eddy current heat under the alternating magnetic field of the inner and outer magnetic rotors, raising the temperature of the magnetic coupling. The excessive temperature rise of the coupling can lead to failure of the permanent magnet due to demagnetization. Many investigations on the cooling circuit of magnetic drive pumps have been undertaken. Kim and Yun [10] compared the performance and internal flow characteristics of two types of balancing holes in a magnetic drive pump (in the impeller and in the shaft). They claimed that the magnetic drive pump with balance holes drilled in the shaft had a comparatively high efficiency. Zhou et al. [11] developed a cooling circuit for a multistage canned pump and investigated the canned sleeve’s convective heat transfer coefficient. Bai et al. [12] presented two types of variable-frequency motor cooling circuits (positive and reverse circuits) for a mine high-speed rescue pump. The internal flow fields and temperature fields of the two cooling circuits were compared. They adopted a reverse circuit to cool their work. Tan et al. [13] investigated the temperature distribution of a magnetic pump’s two cooling circuits (internal and external cooling circulations). The results demonstrated that the temperature distribution of the external circulation was uniform, but the temperature rise near the bottom of the internal circulation’s containment shell was the greatest. Gao et al. [14,15,16] used a numerical technique to investigate the internal flow, pressure fluctuation, and temperature distribution of a magnetic drive pump’s cooling circuit. They compared the temperature and pressure distribution of the cooling circuit of the magnetic pump at different flow rates. They claimed that the temperature of the medium at the outlet of the cooling circuit increases with an increase in flow rate. However, their maximum test speed was only 1450 rpm.

The magnetic torque and magnetic eddy current losses of magnetic couplings have also been studied. Pan et al. [17] investigated two types of magnetic drive blood pumps using numerical modeling and tests. The magnetic force and torque of three different magnetic coupling arrangements were obtained numerically. Kong et al. [18] investigated the eddy current loss of two different containment shell materials. When all other parameters were held constant, the eddy current loss induced by 1Cr18Ni9Ti was 2.26 times more than that of TC4.

Although many scholars have conducted studies on magnetic drive pump cooling circuits, including cooling techniques, balancing hole kinds, and magnetic coupling temperature distribution, the cooling flow rate and cooling circuit losses are rarely explored. There are no published studies on the cooling circuits of high-speed magnetic drive pumps. Water friction losses at the inner magnetic rotor and containment shell walls, as well as magnetic eddy current losses in the containment shell, are the most significant losses in the cooling circuit. These losses are proportional to the rotating speed of the magnetic drive pump.

The higher the speed, the greater the losses in the cooling circuit, which should be paid attention to. This work examines the water friction loss in the cooling circuit and the eddy current loss in the metal containment shell of the magnetic coupling during the operation of a high-speed magnetic drive pump. In this study, commercial CFD software is utilized to simulate the flow field of a magnetic drive pump, and the pressure distribution, velocity distribution, temperature distribution, and water friction loss in the cooling circuit are obtained. Using Maxwell software, the eddy current loss in magnetic coupling is investigated. Five magnetic couplings of varying lengths are developed, and the effects of the magnet and pump flow rate on the cooling circuit’s loss and flow field are examined. The results indicate that the flow rate of the pump and the length of the magnet have minimal influence on the velocity distribution and cooling flow rate of the cooling circuit. The temperature and losses in the cooling circuit increase as the flow rate and magnet length grow.

2. Object of Study

This research investigates a compact high-speed magnetic drive pump. The shrouded impeller and inner magnetic rotor are integrated parts assembled in the pump chamber and are driven by the outer magnetic rotor mounted on the motor. The containment shell separates the inner and outer rotor and realizes the complete sealing of the pump. The structural diagram of the magnetic drive pump is demonstrated in Figure 1, and the design parameters of the pump are listed in

Table 1. Parameters of the magnetic drive pump.

Parameters	Value
Flow rate Q/m3/h	30
Head H/m	130
Rotational speed n/rpm	8000
Specific speed ns	69.2
Impeller diameter D2/mm	120
No. of blades	5

.

The cooling circuit is an important component of the magnetic drive pump. When the magnetic coupling functions, the inner and outer magnets create an alternating magnetic field, which generates eddy current heat in the containment shell and raises the magnetic coupling’s temperature. When the pump is running, the cooling circuit cools the magnetic coupling to prevent it from failing due to excessive temperatures. External circulation and internal circulation are the two most frequent cooling methods. The magnetic drive pump investigated in this research operates in internal circulation mode and cools the magnetic coupling with the working liquid. Figure 2 depicts the magnetic drive pump’s cooling circuit, with the flow channel of the cooling circuit indicated by red arrows. Through the gap between the containment shell and the inner magnetic rotor, the high-pressure fluid at the impeller output reaches the bottom of the containment shell. The fluid then returns to the impeller inlet via the gap between the sliding bearing and the containment shell.

Figure 3 depicts the magnetic coupling’s containment shell and inner and outer magnetic rotors.

Table 2. Geometric parameters of the magnetic coupling.

Parameters	Value
Outer magnet internal diameter	127 mm
Outer magnet external diameter	140 mm
Inner magnet internal diameter	106 mm
Inner magnet external diameter	117 mm
External diameter of inner magnetic rotor	120 mm
Magnet length	40 mm
No. of magnetic pole pairs	18

depicts the magnetic coupling’s geometric parameters. The magnetic coupling is made up of many materials. The inner and outer magnets are composed of S2mCo17, the containment shell is made of TC4, and the inner and outer magnetic rotors are made of 0Cr18Ni9.

3. Numerical Method

The three-dimensional domain of the high-speed magnetic drive pump is constructed, which is divided into six computational domains: suction pipe, discharge pipe, impeller, volute, front pump chamber, and cooling circuit. The computational domain of the high-speed magnetic drive pump is shown in Figure 4. ICEM software meshes the computational domain, and all computational domains adopt a structured grid. In order to reduce the influence of the grid on calculation accuracy, grid independence verification is required. The pump head converges as the grid cells increase, according to previous work. When the high-speed magnetic drive pump’s grid cell number approaches 1.7 million, the variance of the pump head between numerical and experimental is less than 0.2% [2]. This research examines the flow field and losses in the cooling circuit, where the distance between the inner magnetic rotor and the containment shell is only 0.2 mm. In order to properly anticipate the flow information of the cooling circuit, the grid of the cooling circuit was verified to be irrelevant based on the previous work. Three different gap mesh schemes were designed, with 5, 10, and 15 nodes arranged at the gap, as shown in Figure 5. The grid numbers of the three schemes were 588,859, 765,115, and 831,744, respectively. The difference in the head and efficiency between the three schemes was 0.13 m and 0.03%, respectively. In this research, 10 nodes were arranged at the gap in the cooling circuit. Figure 6 depicts the mesh of the pump’s computational domain, and mesh information is presented in

Table 3. Mesh information of the computational domain.

Domain	No. of Grid	Min. Orthogonal Quality
Suction pipe	190,610	0.68
Front pump chamber	370,440	0.30
Impeller	653,660	0.31
Cooling circuit	765,115	0.32
Volute	385,007	0.22
Discharge pipe	86,720	0.74

. The y+ value of blade surfaces ranges from 0 to 10, and the maximum value is within 80.

In the simulation, the fluid is assumed to be incompressible and homogeneous. The governing equations based on the Newtonian fluid are as follows:

$$\frac{\partial \rho }{\partial t}+\frac{\partial }{\partial x_i}\left(\rho u_i\right)=0$$

(1)

$$\frac{\partial \left(\rho u_i\right)}{\partial t}+\frac{\partial \left(\rho u_i{u}_j\right)}{\partial x_j}=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}\left(\mu \frac{\partial u_i}{\partial x_j}\right)+\frac{\partial {\tau }_{ij}}{\partial x_j}$$

(2)

$$\frac{\partial \left(\rho T\right)}{\partial t}+\frac{\partial \left(\rho u_{i}T\right)}{\partial x_i}=\frac{\partial }{\partial x_j}\left(\frac{K}{C_p}\frac{\partial T}{\partial x_j}\right)+\varphi +S_T$$

(3)

where u is the velocity, p is the pressure, ρ is the mixture density, μ is the viscosity, ${\tau }_{ij}=-\rho \overline{u^{\prime }{}_i{u}^{\prime }{}_j}$ is the Reynolds stress, S_T is the heat source in the system, Cp is the specific heat capacity, T is the temperature, and Φ is the part of mechanical energy converted into heat energy due to viscosity.

When the magnetic coupling is working, the metal containment shell will transfer heat to the cooling medium, but this portion of energy cannot be accurately calculated. In this paper, the energy transmitted by the magnetic coupling to the cooling medium is estimated according to the following formula:

$$\Delta P=k\left(1-{\eta }_3\right)P_e{\eta }_1{\eta }_2$$

(4)

where ΔP is the energy transmitted by the magnetic coupling to the circulating medium, k is the coefficient, which is taken as 0.9, η₁, η₂, and η₃ are the efficiency of the frequency converter, motor, and magnetic coupling, respectively, and P_e is the input power of the pump unit. The inner surface of the containment shell was designated as the wall with constant heat flux, while the remaining walls were designated as the thermal insulation wall. The heat flux of the containment shell is calculated as follows:

$$\Delta P_{\mathrm{i}}=qS$$

(5)

where q is the heat flux and S is the area of the containment shell’s inner surface.

Since the shear stress transport (SST) model is well known to be suitable for pump analyses, the simulation results using the SST model are in good agreement with the experimental results [19,20,21]. The RANS equations are solved using the SST turbulence model in this study.

The total pressure and mass flow rate were set as the boundary conditions at the inlet and outlet, respectively. The temperature at the inlet was set to 300 K. The no-slip wall was applied to all solid walls. Wall roughness in the impeller and cooling circuit was set as 3.2 μm, whereas wall roughness in other domains was set as 25 μm. The calculation domain of the impeller was set as rotating domain, and the speed was 8000 rpm; other calculation domains were set as stationary domain. The interface between the rotating and stationary domains was designated as a frozen rotor type, and the association between interface grids was set to GGI mode. The convergence criteria in the calculations were that the residuals of the continuity equation and momentum equation was less than 1 × 10⁻⁴, and the residual error of the energy equation was less than 5 × 10⁻⁴.

4. Test Setup

To validate the numerical results, the magnetic drive pump’s performance was tested on a closed-loop test rig, which included a water tank, pipes, valves, sensors, and a control cabinet, as illustrated in Figure 7 [22]. The pump flow rate was regulated by the outlet valve and monitored with a turbine flowmeter, with a ±0.5% accuracy. The pump head was computed by measuring the pump’s inlet and outlet pressures. The ranges of pressure sensors were −0.1 MPa to 0.1 MPa at the inlet and 0 MPa to 2.5 MPa at the outlet, and the measurement accuracy was ±0.5% [2].

Figure 8 depicts the validation results of the numerical computation and experimentation. When the pump flow rate was between 18 and 39 m³/h, the numerical results corresponded well with the experimental data. The high-speed magnetic drive pump’s test head at rated flow is 130.79 m, and the simulated result is 127.13 m, with an error of 2.2%. The highest error is 4.76% at off-design conditions.

5. Results and Discussions

5.1. Discussion of the Initial Pump Flow Field

CFX software is used to simulate the steady-state flow field of the magnetic drive pump under varied flow conditions in order to get information about the flow field in the magnetic drive pump, including the water friction loss and the cooling flow rate of the cooling circuit. Figure 9 depicts the pressure distribution and streamlines at the rated flow rate. According to the pressure distribution shown in Figure 9a, the blade has a substantial influence on fluid pressurization. The pump’s lowest pressure zone is at the impeller inlet, but the pressure is substantially greater than the vaporization pressure; therefore, cavitation does not occur. The pressure inside the blade channel progressively rises. The cooling circuit is depicted in Figure 9a by the dashed box. The pressure at the inlet of the cooling circuit is the same as the impeller outlet, and the pressure at the outlet of the cooling circuit is the same as the impeller inlet. The streamline in Figure 9b shows that the fluid flows smoothly from the impeller inlet to the volute outlet, but there is also a local flow separation in the blade channel. Simultaneously, a local low-speed zone exists at the volute outlet impacted by the partition.

Figure 10 is a schematic diagram of the cooling circuit’s calculation domain that shows the inlet (in green) and outlet (in red) of the cooling circuit, as well as the placement of the two sections of the cooling circuit (XY plane and YZ plane). Figure 11 depicts the pressure distribution of the two sections under various flow conditions. The cooling circuit’s inlet is at “a” in Figure 11, which is linked to the impeller outlet, and the cooling circuit’s outlet is at “e” in Figure 11, which is connected to the impeller inlet. The medium flows in the cooling circuit in the a→b→c→d→e direction. Figure 11 shows how the pressure in the cooling circuit steadily lowers from the inlet to the outlet. The pressure drop is caused by the loss along the cooling circuit, as well as the local loss. The most substantial local pressure loss occurs at the bottom of the containment shell (b→c), where the gap size quickly reduces from 5.5 mm to 0.2 mm, resulting in a major local pressure loss. The sliding bearing (c→d) causes the most loss throughout the path because the gap between the sliding bearing and the containment shell is just 0.2 mm, resulting in a high-pressure drop. The pressure drop from the cooling circuit’s inlet to the bottom of the containment shell (a→b) is negligible, and the gap between the containment shell and the inner magnetic rotor is 1.5 mm in this portion. The findings of the varied flow conditions in Figure 11 demonstrate that as the flow rate increases, the pressure in the cooling circuit gradually lowers. This is because the fluid in the cooling circuit originates from the impeller outlet, and as the pump flow rate increases, the pressure at the impeller outlet lowers.

Figure 12 illustrates the temperature distribution of the cooling circuit at various flow rates. The inlet temperature of the cooling circuit is the lowest, and the temperature rises steadily from the cooling circuit’s inlet to the bottom of the containment shell (a→b). The outside edge of the bottom of the containment shell is where the cooling circuit reaches its maximum temperature (b). From “c” to “e,” the temperature changes little because it is far away from the heat source. Comparing the results of various flow rates reveals that the temperature rise in the cooling circuit decreases as the flow rate drops. As the flow rate grows, the pump power increases, the eddy current loss in the containment shell increases, and the heat generated by the containment shell increases accordingly, leading to an increase in the temperature rise of the cooling circuit. In addition, since the gap size of the cooling circuit is very small and the velocity is high, viscous dispersion has a great effect on heat transfer here [23,24,25]. Combining Figure 11 and Figure 12, despite the varying degrees of temperature rise generated in the cooling circuit, the pressures in the cooling circuit are all greater than the vaporization pressure, preventing cavitation from occurring.

Figure 13 depicts a comparison of the magnetic drive pump’s cooling flow rate and water friction loss at various flow rates. If the cooling flow rate of the cooling circuit is too high, the pump’s efficiency will suffer. If the cooling flow rate is too low, the temperature rise of the magnetic coupling will increase, lowering the efficiency of the magnetic coupling. In severe conditions, the magnetic coupling will fail to function correctly. As shown in Figure 13, as the pump flow rate increases, the cooling flow rate gradually decreases. When the magnetic pump flow rate is 0.7 Q (Q is the rated flow rate), the cooling flow rate is 1.07 m³/h, and it drops to 0.98 m³/h when the pump flow rate is increased to 1.3 Q, which is 8.4% less than 0.7 Q. The change in the cooling flow rate for different pump flow conditions is caused by a drop in pressure at the impeller outlet as the pump flow rate increases, resulting in a reduction in the cooling circuit’s inlet and outlet pressure differential. The inlet pressure of the cooling circuit is 1.104 MPa and 1.044 MPa at 0.7 Q and 1.3 Q, respectively, and the pressure at the outlet of the cooling circuit is the same for different flow conditions.

The losses of ordinary centrifugal pumps mainly comprise hydraulic loss, mechanical loss, and disk friction loss. The magnetic drive pump contains the magnetic coupling and the cooling circuit. Compared with the ordinary centrifugal pump, the loss within the magnetic drive pump is greater, and the pump efficiency is lower. Magnetic drive pump losses include not just disk friction and hydraulic loss but also water friction loss in the cooling circuit and magnetic eddy current loss generated in the containment shell. The cooling circuit’s water friction loss and magnetic eddy current loss account for a significant amount of the pump’s losses, which cannot be disregarded [6,23]. The water friction loss in the cooling circuit is mostly determined by the cooling circuit’s structural dimensions and has minimal relationship with the pump flow rate. The calculation results also reveal that the water friction loss of the cooling circuit varies relatively little when the pump flow rate increases, as illustrated in Figure 13. The cooling circuit’s water friction loss is the minimum, 5.39 kW, at the magnetic drive pump flow rate of 0.7 Q. The water friction loss of 1.2Q is the greatest, at 5.61 kW, yet it is only 3.9% greater than that of 0.7 Q.

5.2. Discussion of Cooling Circuit for Different Schemes

Because the losses in the cooling circuit are mostly determined by the structural sizes of the magnetic couplings, this research examines the losses in couplings of various lengths in order to decrease the cooling circuit’s water friction loss and the magnetic eddy current loss caused by the containment shell. In this paper, five magnetic coupling schemes with varying magnet lengths were constructed, the water friction loss and magnetic eddy current loss analyses for each scheme were explored, and two schemes were chosen for experimental verification.

Table 4. Different design schemes of the magnetic coupling.

Scheme	Magnet Length (mm)	Containment Shell Length (mm)
1	30	43
2	35	48
3	40	53
4	45	58
5	55	68

shows the magnet lengths for the five schemes. The axial length of the sliding bearing and containment shell was adjusted when the magnet length was changed. Other magnet characteristics, such as the number of block pairs, magnet thickness, inner and outer magnet gaps, material, and so on, remain unaltered. It should be noted that altering the magnet length only affects the cooling circuit and has a minimal influence on the pump’s head and hydraulic efficiency.

Figure 14 depicts the pressure distribution in the cooling circuit for every scheme at the design flow rate. There is a noticeable pressure loss from the inlet to the outlet of the cooling circuit, and the pressure drop is most pronounced at the cooling circuit’s gap. Figure 14 does not intuitively illustrate the distinction between different schemes. For this reason, four sections are taken at the gap of the cooling circuit, which are, respectively, designated as L1, L2, L3, and L4. The locations are depicted in Figure 15. By comparing the average pressure of the four sections, the pressure drop at the cooling circuit gap of different schemes is examined. The results are shown in Figure 15. Compared with L3 to L4, the pressure drop from L1 to L2 is minimal, since the clearance between L1 and L2 is 1.5 mm, but the clearance between L3 and L4 is 0.2 mm. With increasing magnet length, the pressure drop at the gap steadily increases. When the length of the magnet is 55 mm, the pressure drop from L3 to L4 is 321369 Pa, which is 25.3% more than when the length is 30 mm.

Figure 16 depicts the velocity distribution of several cooling circuit schemes at the rated flow rate. The cooling circuit has a high velocity on the outside and a low velocity at the center. This is because the magnetic drive pump in this study has a high rotational speed. The circumferential velocity component in the cooling circuit is greater, whereas the axial velocity component is smaller. The magnitude of the fluid’s velocity in the cooling circuit is mostly determined by the circumferential velocity. When the velocity distribution in the cooling circuit of different schemes is compared, it is discovered that changing the magnetic coupling length has no influence on the cooling circuit’s velocity distribution. Because just the magnet’s length is modified, the radial dimension of the magnetic coupling remains unchanged; hence, the velocity in the cooling circuit does not vary much. However, due to the influence of the inlet flow of the impeller, the velocity distribution at the center of the cooling circuit varies slightly with different magnet lengths. The low-speed region at the center of the cooling circuit increases slightly as the magnet length increases.

The temperature distribution of the cooling circuits of different schemes at the rated flow rate is shown in Figure 17. The pattern of temperature change in the cooling circuit of various schemes is the same. When the flow rate remains constant, the temperature at the corresponding location rises as the magnet length grows. The highest temperature in the cooling circuit is 312.23 K when the magnet length is 55 mm, and the temperature rise is 23.1% more than when the magnet length is 30 mm.

Figure 18 compares the cooling flow rate and water friction loss for various schemes at the rated flow rate. The cooling flow rate does not alter considerably when the magnet length is smaller than 35 mm, 1.1 m³/h and 1.11 m³/h, respectively. When the magnet length exceeds 35 mm, the cooling circulation flow rate steadily reduces as the magnet length increases. The cooling flow rate for the 55 mm scheme is 0.94 m³/h, which is 14.5% lower than the cooling flow rate for the 30 mm scheme. The difference in cooling flow rate is caused by the fact that the differential pressure between the inlet and outlet of the cooling circuit is essentially the same for all systems. In contrast, as the length of the magnetic coupling rises, the resistance in the cooling circuit increases, and therefore the cooling flow rate falls. The water friction loss grows linearly as the magnet length increases. The water friction loss is 4.99 kW for the 30 mm scheme and 6.67 kW for the 55 mm scheme, representing a 33.67% increase over the 30 mm scheme.

5.3. Magnetic Eddy Current Loss in Various Schemes

This work uses Maxwell software to perform two-dimensional transient magnetic field simulation for magnetic couplings of various schemes in order to investigate the magnetic eddy current losses in the containment shell of different schemes. The magnetic coupling’s magnetic eddy current losses and maximum magnetic torque are calculated. The magnetic coupling investigated in this study has 18 pairs of inner and outer magnets, with a maximum rotational angle variation of 10° between the inner and outer blocks. Figure 19 depicts the configuration of the inner and outer magnetic blocks in a 2D model of the magnetic coupling created in Maxwell software. The inner and outer magnetic rotors covered with an air layer were set as the rotating domain, while the other domains were set as the stationary domain. Domain depths were 30 mm, 35 mm, 40 mm, 45 mm, and 55 mm, respectively. The containment shell was configured as a single coil conductor, with an initial current of 0 A supplied to it.

Figure 20 depicts the predicted maximum magnetic torque and eddy current loss for different schemes. It can be seen that the maximum magnetic torque and eddy current loss of the magnetic coupling increase linearly with the increase of the axial length of the magnet, and the increase of the eddy current loss leads to a decrease in the transmission efficiency of the magnetic coupling [26]. The highest magnetic torque is 49.7 N·m, and the eddy current loss is 4.67 kW when the magnet length is 30 mm. The highest magnetic torque is 91.1 N·m and the eddy current loss is 8.56 kW when the magnet length is 55 mm. The eddy current loss and magnetic torque rise by 0.79 kW and 8.28 N·m for every 5 mm increase in magnet length, respectively.

5.4. Experimental Confirmation

The simulation results reveal that altering the length of the magnetic coupling’s inner and outer magnets has no influence on pump performance. However, the magnet length has a higher impact on cooling circuit loss, which lowers the pump’s efficiency. Scheme 1 and Scheme 3 were chosen to validate the simulation results, and magnetic couplings with magnet lengths of 30 mm and 40 mm, respectively, were constructed. Figure 21 and Figure 22 illustrate the pump performance results for the two schemes. Figure 21 shows that the magnet length has minimal influence on the pump head. At low flow rates, there is essentially no difference in the head of the magnetic drive pump between the two schemes, and the pump head fluctuates a little from 0.9 Q to 1.2 Q with a maximum variance of only 1.9%. In contrast, as shown in Figure 21, the magnetic coupling length has a considerable influence on pump efficiency. Pump efficiency rises with increasing pump flow rate and decreasing magnet length. At the rated flow rate, the pump efficiency of Scheme 1 and Scheme 3 is 42.58% and 31.59%, respectively.

Figure 22 depicts a comparison of the magnetic drive pump power curves for Scheme 1 and Scheme 3. Because the power of the magnetic drive pump cannot be measured directly, the power measured in the experiment is the input power of the pump unit. The experimental power of Scheme 1 and 3 units is 29.27 kW and 34.15 kW, respectively, with a 4.88 kW difference between the two schemes. The total water friction loss and magnetic eddy current loss estimated by simulation in Scheme 1 and Scheme 3 is 9.67 kW and 11.73 kW, respectively, with a 2.07 kW difference between the two schemes. The experimental and simulation losses grow linearly with magnet length; however, the disparity between the experimental and simulation results is substantially bigger.

The simulation in this research only analyzed water friction loss and magnetic eddy current loss and ignored all other factors. The power measured in the experiment is the magnetic drive pump supporting the inverter’s input power, which comprises the power consumption of the motor, inverter, and magnetic coupling. This is the main reason for the large difference between the simulation results and experimental values. Furthermore, the discrepancy between the experimental and simulation results might be caused by the following factors.

• In the simulation, the surface roughness of the cooling circuit is set to 3.2 μm, and the manufacturing error of the experimental inner magnetic rotor and containment shell may deviate from this value. The other two designs’ inner magnetic rotors are made individually, and the surface roughness of the cooling circuit may also differ. These factors may increase the differential in water friction loss.
• The increases in the magnet length will lead to an increase in the mass of the inner magnetic rotor. When the magnetic drive pump is operating at a high speed, its power consumption increases. Furthermore, in the simulation, the inner and outer walls of the cooling circuit are specified as perfect cylindrical surfaces, but the magnetic drive pump may work with an eccentric inner magnetic rotor, thus increasing the difference between the simulation findings and the actual values.

6. Conclusions

The current study employed a centrifugal high-speed magnetic drive pump to investigate the internal flow field and cooling circuit loss. Five magnetic coupling length schemes were devised to investigate the influence of axial length on the flow field and losses in the cooling circuit, and the following findings were reached.

• The pressure and velocity distribution in the magnetic drive pump’s cooling circuit is less impacted by the pump flow rate. The cooling flow rate falls as the pump flow rate increases, and the cooling flow rate of 1.3 Q reduces by 8.4% compared to 0.7 Q. The water friction loss in the circuit varies little, depending on the flow conditions.
• Changing the length of the magnetic coupling has little effect on the pressure and velocity distribution of the cooling circuit. However, as the magnetic coupling length rises, the cooling flow rate steadily drops, and the water friction loss increases linearly. When compared to the 30 mm scheme, the cooling flow rate of the magnet length 55 mm scheme reduced by 14.5%, while the water friction loss rose by 33.67%.
• The maximum temperature in the cooling circuit occurs at the bottom of the containment shell. The temperature rise in the cooling circuit increases as the pump flow rate and magnet length increase. At the rated flow rate, the cooling circuit temperature rise with a 50 mm magnet length is 23.1% more than with a 30 mm magnet length.
• As the magnet length increases, the maximum magnetic torque and eddy current losses of the magnetic coupling grow linearly. Compared to the 30 mm scheme, the maximum magnetic torque and eddy current losses of the 55 mm scheme rise by 45%.

In the current study, only the effect of magnet length on the flow field and loss of cooling circuit is investigated, without considering the effect of magnet diameter. In the future, the radial and axial dimensions will be merged to eliminate cooling circuit losses while maintaining magnetic torque and significantly enhancing the efficiency of magnetic drive pumps.