4. Results and discussion
4.1. Design optimization analysis of the electromagnetic pump
4.1.1. Design variables of the small electromagnetic pump
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(a) (b)
Figure 4.1.1. (a) Developed pressure versus inner core diameter and (b) efficiency versus inner core diameter for different number of pole pairs (πΊ = 0.013 m, πΌ = 140 A, πΏπ = 0.8 m, and Ξ± = 0.5)
(a) (b)
Figure 4.1.2. (a) Developed pressure versus inner core diameter and (b) efficiency versus inner core diameter for various core lengths (πΊ = 0.013 m, πΌ = 140 A, π = 3, and Ξ± = 0.5)
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(a) (b)
Figure 4.1.3. (a) Developed pressure versus inner core diameter and (b) efficiency versus inner core diameter for various core gaps (πΌ = 140 A, πΏπ = 0.8 m, π = 3, and Ξ± = 0.5)
As seen from Figure 4.1.4, a decrease in the slot width, or in other words, an increase in the slot tooth causes a uniform magnetic flux, which increases the developed pressure and decreases the efficiency owing to the increased impedance. Although the ratio of slot width to slot pitch affects the developed pressure and efficiency, this ratio is not changed significantly by changes in the other design variables. As a result, the ratio of the slot width to slot pitch is determined as 0.5 considering both the developed pressure and efficiency.
Figure 4.1.4. Developed pressure and efficiency versus slot width/slot pitch (π·o = 0.05 m, πΊ = 0.013 m, πΌ = 140 A, πΏπ = 0.8 m, π = 3, and Ξ± = 0.5)
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Based on an inner core diameter of 0.05 m, and a ratio of the slot width to slot pitch of 0.5, the core length, inter core gap and number of pole pairs, are optimized as seen in Figures 4.1.5 and 4.1.6.
These figures represent the developed pressure and efficiency of the ALIP based on the change in the core length and inter core gap corresponding to different number of pole pairs. Figure 4.1.5 shows that the maximum developed pressure appears at the longer pump core length when the number of pole pairs changes from two to four. The greater the number of pole pairs, the higher the maximum developed pressure.
When the number of pole pairs is greater than two, as seen in Figure 4.1.5 (b) and (c), the maximum developed pressure is higher than the required specification for the ALIP by 4.5 bar, while it is lower than the specification by 4.5 bar when the number of pole pairs is two at the same input current of 140 A.
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(a) (b)
(c)
Figure 4.1.5 Developed pressure versus inter-core gap and pump core length:
(a) π·o = 0.05 m, πΌ = 140 A, π = 2, Ξ± = 0.5; (b) π·o = 0.05 m, πΌ = 140 A, π = 3, Ξ± = 0.5;
(c) π·o = 0.05 m, πΌ = 140 A, π = 4, Ξ± = 0.5
In Figure 4.1.6, it is observed that the maximum value of the efficiency is also increased as the number of pole pairs is increased. It is understood that the increase in the number of pole pairs improves the pump performance. On the other hand, too small an inter-core gap causes a high hydraulic pressure owing to an increased flow velocity and too large an inter-core gap causes a low electromagnetic force owing to a reduced magnetic field. Therefore, the developed pressure and efficiency are optimized at an inter-core gap of 0.012 m, as depicted in Figures 4.1.5 and 4.1.6.
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(a) (b)
(c)
Figure 4.1.6. Efficiency versus inter-core gap and pump core length: (a) π·o = 0.05 m, πΌ = 140 A, π
= 2, Ξ± = 0.5; (b) π·o = 0.05 m, πΌ = 140 A, π = 3, Ξ± = 0.5; (c) π·o = 0.05 m, πΌ = 140 A, π = 4, Ξ± = 0.5
The pump core length, which is a product of the pole pitch and the number of poles, is increased as the number of pole pairs is increased at a fixed pole pitch. The electromagnetic force is proportional to square of the pole pitch when it is small; hence, the term of the pole pitch in the denominator is negligible. The electromagnetic force is approximately inversely proportional to the square of pole pitch when it is large. Furthermore, the hydraulic pressure loss is proportional to the core length.
Therefore, it is thought that the pump has the optimized number of pole pairs for the maximized developed pressure.
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As shown in Figure 4.1.7, the pump core length is increased in proportion to the number of pole pairs and the efficiency is increased as the number of pole pairs is increased for the ALIP of the required specification.
Figure 4.1.7. Pump core length and efficiency of the optimized ALIP versus number of pole pairs
Considering Figures 4.1.7β4.1.8, together, it can be seen that an increase in the number of pole pairs results in a higher efficiency and lower electrical input; however, it would result in a very long pump core. As a result, the ALIP of 5 pole pairs is thought to be suitable, when considering the geometrical constraints of the space, in which the loop is to be installed.
Figure 4.1.8. Input current and input power of the optimized ALIP versus number of pole pairs
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Table 4.1.1 summarizes the design data of the ALIP for the required specification with a flow rate of 900 L/min and a developed pressure of 4.5 bar, obtained from the results of the design variable analysis. In Figure 4.1.9, the characteristic curves of the developed pressure and efficiency are plotted against the flow rate.
Table 4.1.1. Optimized design specifications of the small ALIP
Design variable Unit Value Design variable Unit Value
Hydrodynamic
Flow rate [L/min] 900 Slip [%] 41.1
Developed pressure [bar] 4.49 Reynolds number [#] 378611
Temperature [ο°C] 550 Head loss [bar] 0.891
Velocity [m/s] 7.918
Geometric
Core length [mm] 1120.0 Core thickness [mm] 25.00 Outer core diameter [mm] 355.0 Stacked coil thick [mm] 96.00 inner core diameter [mm] 56.0 Coil support ring [mm] 10.00 Inter core gap [mm] 12.00 Space in slot depth [mm] 6.50
Flow gap [mm] 9.00 Tooth width [mm] 18.36
Inner duct thickness [mm] 1.0 Slot pitch [mm] 36.72 Outer duct thickness [mm] 1.0 Conductor width [mm] 14.36 Slot width [mm] 18.36 Conductor thickness [mm] 6.00 Slot depth [mm] 112.50 Insulator thickness [mm] 2.00 Core depth [mm] 137.50
Electrical
Input current [A] 96.0 Pole pitch [cm] 11.20
Input voltage [V] 502 Number of slots [#] 30
Impedance [ohm] 5.2 Turns/slot [#] 24
Input VA [kVA] 83.4 Number of pole pairs [#] 5 Input power [kW] 24.7 Slot/phase/pole [#] 1 Power factor [%] 29.6 Hydraulic efficiency [%] 27.33 Goodness factor [#] 1.4
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Figure 4.1.9. Developed pressure and efficiency of the optimized ALIP versus flow rate
The design variable analysis on the ALIP with a flow rate of 900 L/min and a developed pressure of 4.5 bar for an SFR thermal hydraulic experimental loop was carried out using the MHD method. It was shown that the developed pressure and efficiency reaches a maximum based on the change in the pump design variables, such as core length, number of pole pairs, inner core diameter, inter-core gap, and ratio of slot width to slot pitch.
It was understood conclusively that the variable analysis on the pump for the required specification yielded a core length of 1.1 m, an inner core diameter of 5.6 cm, five pole pairs, an inter-core gap of 1.2 cm, and an input VA of 83 kVA, considering the geometric limits, and electromagnetic and fluid flow effects.
4.1.2. Design variables of the large electromagnetic pump
The developed pressure and efficiency of the ALIP with changes in the number of poles for various outer core lengths are shown in Figures 4.1.10 and 4.1.11, respectively [89]. The number of poles is one of the main design variables that define the entire core length of the ALIP. It is the ratio of the outer core length to the pole pitch. The magnetic field in the flow gap is inversely proportional to the pole pitch at a constant magnetic flux. The developed pressure increases proportionally with the pole pitch. However, the decrease in the magnetic field in the flow gap decreases the developed pressure.
Therefore, a proper value of the pole pitch is determined to maximize the developed pressure and efficiency. As shown in the Figure 4.1.10, the efficiency is maximum with 12 poles and an outer core length of 3.5 m. However, the difference in the efficiency with eight poles and an outer core length of 2.5 m is only 1%.
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Figure 4.1.10. Efficiency versus number of poles for different outer core lengths
The difference between the synchronous and working fluid velocities is proportional to the developed pressure. The synchronous velocity corresponds to the velocity of the transverse magnetic field and is expressed through Equation (4.1.3) as a function of the pole pitch and input frequency.
Additionally, the velocity of the working fluid is calculated as the flow rate divided by the flow area as shown in Equation (4.1.3).
ππ = π
πΏππ‘π, ππ = 2ππ =πΏππ
π (4.1.3)
Figure 4.1.11 shows the P-Q characteristics of the ALIP with the same power consumption, when its efficiency is maximized for each of the outer core lengths. The pole pitch affects the maximum flow rate because the synchronous velocity is proportional to the same. Furthermore, the developed pressure depends on the difference between the synchronous velocity and fluid velocity of the working fluid, whereas the synchronous velocity is related to the maximum flow rate. Thus, an increase in the pole pitch increases the maximum flow rate. The pole pitch affects the maximum flow rate and also the developed pressure in the low flow rate. The magnitude of the low flow rate depends on the magnetic field in the flow gap, outer core length, number of poles, and pole pitch as shown in Equation (4.1.3). The developed pressure with a low flow rate decreases when the pole pitch increases.
The developed pressure per pole is proportional to the outer core length, and an increase in the pole pitch of the ALIP decreases the developed pressure as shown in Figure 4.1.11.
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Figure 4.1.11. Developed pressure versus flow rate for different combinations of the number of poles and outer core lengths
An increase in the outer core length decreases the magnitude of the magnetic field in the flow gap.
Furthermore, the developed pressure is proportional to the square of the magnetic field. Additionally, the hydraulic loss in the ALIP is proportional to the outer core length. However, a longer outer core indicates that the working fluid exerts a Lorentz force over a longer path. Thus, the outer core length must not be excessively low. In Figure 4.1.12, the efficiencies obtained by changing the outer core length under different input frequencies are observed to be maximized in terms of the specific length values.
Figure 4.1.12. Efficiency versus outer core length under various frequencies
The flow velocity is proportional to the difference between the synchronous and working fluid velocities, and the developed pressure is also proportional to the same difference. The thickness of the flow gap is related to the velocity of the working fluid, and also to the major and minor pressure losses
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that are proportional to the square of the velocity of the working fluid. The inner core gap that is given by the sum of the thicknesses of the inner and outer ducts, and the flow gap is also an important factor that affects the developed pressure and efficiency of the ALIP. This is because the magnitude of the magnetic induction decreases as the gap increases. Conversely, the current is induced in the inner and outer ducts, and leads to Jouleβs dissipation. Thus, the inner and outer ducts should be designed to be as thin as possible, while ensuring an adequate mechanical strength of the ALIP.
In Figure 4.1.13, the efficiency is presented for variations in the flow gaps with different thicknesses of the inner and outer ducts. When the flow gap is 0.063 m, differences in the outer duct thicknesses between 0.004 and 0.014 m affect the efficiency by approximately 13%, while the differences in the inner duct thicknesses between 0.001 and 0.011 m affect it by approximately 7%. It is subsequently shown that the effect of the thickness of the outer duct on the efficiency exceeds that of the inner duct.
Figure 4.1.13. Efficiency versus flow gap for various duct thicknesses (f = 20 Hz, πΏπ= 3.5 m)
In Figure 4.1.14, the characteristic curves of the developed pressure on the flow rate are shown for different input voltages and frequencies. The slopes of the curves are similar at various input voltages, when the ratios of the voltage to frequency are identical. This is because the developed pressure and maximum flow rate are proportional to the input voltage and frequency, respectively. Therefore, the operating point corresponds to the intersection of the developed pressure and hydraulic pressure drop in the system and is considered convenient to control in the range of low flow rates.
In Figure 4.1.14, the efficiency of a 100% head flow under conditions of 1395 V and 15 Hz denotes the maximum for a nominal flow rate of 0.86 m3/s, and the operating point denotes the intersection of the developed pressure and hydraulic pressure drop of the system. Thus, the specifications for the ALIP with a flow rate of 0.86 m3/s and a developed pressure of 3.6 bar are given in Table 4.1.2. As shown in the table, the ALIP is optimized at an input frequency corresponding to a few tens of Hertz
83 as opposed to the commercially used frequency of 60 Hz.
Figure 4.1.14. PβQ curves for 100%, 70%, and 40% flow rates and efficiency curve for a 100% flow rate
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Table 4.1.2. Optimized design specifications of the large ALIP
Design variable Unit Value Design variable Unit Value
Hydrodynamic
Flow rate [m3/s] 0.860 Slip [%] 0.165
Developed pressure [bar] 3.60 Reynolds number [#] 3.08 E+06 Temperature [K] 595 Pressure loss [bar] 0.417
Velocity [m/s] 9.39
Geometric
Core length [m] 3 Slot width [mm] 43.0
Outer core diameter [m] 1 Slot depth [mm] 159 inner core diameter [mm] 0.415 Stacked coil thick [mm] 216 Inter-core gap [mm] 66.6 Tooth width [mm] 19.5
Flow gap [mm] 60.9 Slot pitch [mm] 62.5
Inner duct thickness [mm] 0.75 Conductor width [mm] 26.6 Outer duct thickness [mm] 1 Conductor thickness [mm] 6
Electrical
Input current [A] 184 Frequency [Hz] 15
Input voltage [V] 1395 Pole pitch [cm] 37.5 Impedance [ohm] 7.58 Number of slots [#] 48
Input VA [kVA] 1070 Turns/slot [#] 36
Input power [kW] 648 Number of poles [#] 8 Power factor [%] 60.6 Slot/phase/poles [#] 1 Magnetic Reynolds
number [#] 0.9312 Hydraulic efficiency [%] 47.57
The ALIP is designed according to the magnetohydrodynamic stability criterion, which is based on the magnetic Reynolds number. When the magnetic Reynolds number exceeds one, the pressure and flow rate pulsations with a relatively low frequency may appear in the sodium flow and they are often accompanied by the vibrations of pumps and pipes [64β66]. The magnetic Reynolds number of the optimized ALIP, i.e., 0.9312, as obtained by the calculations is considered to suggest flow stability.
Table 4.1.3 shows the main specifications of the reference ALIP that has been designed to investigate the adequacy of the ALIP system for a large-sized (1,500 MWe) sodium-cooled fast reactor [45], and Figure 4.1.15 shows the ALIP characteristics controlled by the constant voltage/frequency method. To verify the accuracy of the results from the ALIP design code, the PβQ curves of the reference ALIP using the data from Table 4.1.3 are illustrated in Figure 4.1.16. Although the data in both Figs. 4.1.15 and 4.1.16 have been calculated based on the results of the ALIP model by using different computational methods, the overall slopes of the developed pressure under various
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frequencies exhibit a small relative error (less than 15%), ignoring the instability region. In the region, in which the flow rate is proportional to the developed pressure, an increase in the flow rate increases the developed pressure, and this suggests the possibility of a positive feedback. Thus, its disadvantage is that the operating point does not converge when a flow perturbation occurs.
The voltages of the listed conditions correspond to 1230, 1110, 888, 666, 444, and 222 V while the voltage/frequency ratio was constant at 44. As shown in Figures 4.1.15 and 4.1.16, there is a difference between the two, in terms of the developed pressure in the low-flow-rate region. However, both the developed pressure and flow rate near the operating condition exhibit good agreement with a relative error of 5 %.
Table 4.1.3. Design specifications of the reference ALIP
Design variable Unit Value
Flow rate m3/s 2.1
m3/min 126
Developed pressure bar 5.5
Supply frequency Hz 27.7
Phase voltage V 1,230
Phase current A 3,400
Velocity m/s 15.1
RemΓS β 0.99
Stator length m 11.3
Pole pitch m 0.312
Channel diameter m 0.64
Channel width m 0.068
Number of winding poles
β
32
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Figure 4.1.15. PβQ curves of the reference ALIP at different supply frequencies
Figure 4.1.16. Predictive PβQ curves of the reference ALIP
The results indicate that the geometric variables, including the outer core length and flow gap, and the electromagnetic variables, including the number of poles, input frequency, and pole pitch are the dominant factors that affect the ALIPβs efficiency. The results reveal that an input frequency corresponding to a few tens of Hertz maximizes the ALIP efficiency, as opposed to the commercially employed frequency of 60 Hz, and thereby, leads to an effective flow control of the geometrically fixed ALIP during its operation.
It is confirmed that the optimized ALIP can be fabricated by considering the behavior of the materials under a high-temperature environment. The PβQ characteristics of the designed ALIP have been verified by comparing the existing design of a large ALIP that exhibits a relative error of less than 5% near the operating condition.
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4.2. Estimation of the performance and measurement of electromagnetic field
4.2.1. Fabrication of the electromagnetic pump and test bed
An ALIP for the estimation of the performance and measurement of the electromagnetic field with a flow rate of 100 L/min and a developed pressure of 0.76 bar was designed in-house and manufactured.
Its design specifications are presented in Table 4.2.1 and Figures 4.2.1β4.2.3 [90].
Table 4.2.1. Design specifications of the ALIP for estimation
Design variable Unit Value Design variable Unit Value
Hydrodynamic
Flow rate [L/min] 100 Velocity [m/s] 7.152
Mass flow [kg/s] 1.45 Slip [%] 38.8
Developed pressure [bar] 0.76 Reynolds number [#] 64778
Temperature [ο°C] 165 Head loss [bar] 0.116
Geometric
Core length [mm] 389.7 Core thickness [mm] 25.00 Outer core diameter [mm] 185.0 Stacked coil thick [mm] 33.00 inner core diameter [mm] 17.1 Coil support ring [mm] 5.00
Inter-core gap [mm] 7.45 Space in slot depth [mm] 13.48
Flow gap [mm] 3.15 Tooth width [mm] 12.57
Inner duct thickness [mm] 1.65 Slot pitch [mm] 31.43 Outer duct thickness [mm] 1.65 Conductor width [mm] 7.50
Slot width [mm] 18.86 Conductor thickness [mm] 1.70 Slot depth [mm] 51.48 Insulator thickness [mm] 0.50 Core depth [mm] 76.48
Electrical
Input current [A] 30.0 Goodness factor [#] 1.3
Input voltage [V] 39 Pole pitch [cm] 9.74
Impedance [ohm] 1.3 Number of slots [#] 12
Input VA [kVA] 2.0 Turns/slot [#] 30
Input power [kW] 0.9 Number of pole
pairs [#] 2
Power factor [%] 44.1 Slot/phase/pole [#] 1
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Figure 4.2.1. Sectional view of the ALIP for estimation
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Figure 4.2.2. Detailed design of the ALIP (Parts 1β8)
90 Figure 4.2.3. Detailed design of the ALIP (Part 9β13)
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The experimental loop was designed and constructed as shown in Figures 4.2.4β4.2.8 for testing the preliminary characteristics of the ALIP. Drive ability and performance of the ALIP was checked within a temperature range of 145 to 200 Β°C.
Figure 4.2.4. Test bed design drawing plan
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Figure 4.2.5. Support design drawings
Figure 4.2.6. Storage tank design drawing
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Figure 4.2.7. Expansion tank design drawing
Figure 4.2.8. Test bed for the experimentation on the preliminary properties of the electromagnetic pump
4.2.2. Comparison of performance results between the experiments and program
Experiments for P-Q characteristics were conducted under temperatures of 145, 165, 185, and 205
ο°C. The input voltage values investigated include 10, 15, 20, 25, and 30 V. The theoretical and
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experimental errors of the electronic pump drive pressure based on the flow rates are shown in Figure 4.2.9, which shows the characteristics decreasing with an increasing flow rate within a maximum of 10% at 15 V or below and up to 16% at 20 V or above.
Figure 4.2.9. Preliminary characteristics of the ALIP from the test results (145 Β°C)
Figure 4.2.10. Preliminary characteristics of the ALIP from the test results (165 Β°C)
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Figure 4.2.11. Preliminary characteristics of the ALIP from the test results (185 Β°C)
Figure 4.2.12. Preliminary characteristics of the ALIP from the test results (205 Β°C)
Figures 4.2.13β4.2.18 show the results of the ALIP, which was optimized to reduce the end effects by linear grading methods, which consequently, would decrease the turns of the winding at both ends of the ALIP. In that case, the amount of the distorted magnetic field was decreased that caused a decrease or elimination of the Lorenz electromagnetic force of the reverse direction. The input voltage and current conditions were different for the same conditions of input power while the linear grading of the winding rendered the resistance of the ALIP insignificant.
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Unlike the data calculated and measured from the same input power values of the normal ALIP design, it was found that in the case of the ALIP with the linear grading, there was no reverse Lorenz electromagnetic force from the flow path near the entrance and exit owing to a magnetic field distortion.
The theoretical and experimental values of the Lorenz electromagnetic force distribution about the ALIP were compared and analyzed, as shown in Figures 4.2.13β4.2.15. The theoretical calculation confirmed the Lorenz electromagnetic force to be about 30% stronger near the tooth of the outer core owing to an increase in the local magnetic field. However, the magnitude of the Lorenz force near the tooth of the outer core did not appear clearly through the experimental measurement results. The distortion of the magnetic field near both ends of the ALIP caused a significant reduction in the Lorenz electromagnetic force, especially near the inlet. Theoretically, it was expected that the overall loss in the Lorenz electromagnetic force owing to the linear grading would be 20% or less; however, the data from the experiments in Figures 4.2.13β4.2.15 show that the loss of the Lorenz electromagnetic force on the flow path could be up to 10%, with an average of 6% over the complete data. On the other hand, it was found that the reverse Lorenz electromagnetic force, which occurred at the entrance and was considered to be 2% of the total Lorenz electromagnetic force, was converted into a forward Lorenz electromagnetic force of a similar size by a reduced design, which could be calculated by increasing the efficiency by approximately 4%.
Figure 4.2.13. Lorenz force distribution of the ALIP near 222 VA