4. Results and discussion
4.3. Development of the integrated nuclear electromagnetic pump
4.3.2. Performance and electromagnetic field analyses
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Table 4.3.1. Performance variations of the integrated nuclear electromagnetic pump with various design parameters
Variable Characteristics
Size of outer core
Increase • Leakage reactance increases
• Allowed turns of coils increases
Decrease • With a decrease in the leakage reactance, efficiency increases
• Allowed number of turns of the coil decreases
Duct width
Increase • For the same output, more current is needed and efficiency decreases
• Flow gap decreases
Decrease • Output and efficiency increase
• Flow gap increases
Pole pitch
Increase • Synchronous speed increases
• Length of inner core, weight, and size of the pump increase Decrease • Size of the pump decreases
• Body force increases with the same input Number of
poles
Increase • Dispersion of fluid thrust takes place
• Pump size increases
Decrease • Leakage reactance increases (in the secondary part)
Size of Inner core
Increase • Pump weight increases
• Area of duct increases (with the same duct width) Decrease • Pump weight decreases
• Area of duct decreases (with the same duct width) Number of
Coil turns
Increase • Input current decreases with the same output Decrease • Input current increases with the same output
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Table 4.3.2. Specifications of the small integrated nuclear electromagnetic pump model Design variable Unit Value Design variable Unit Value
Hydrodynamic
Flow rate [L/min] 252 Velocity [m/s] 0.204
Mass flow [kg/s] 21.37 Slip [%] 98.7
Developed pressure [Pa] 14815 Reynolds number [#] 90601
Temperature [C] 440 Head loss [Pa] 493
Geometric
Core length [mm] 800.0 Core thickness [mm] 25.00 Outer core diameter [mm] 444.1 Stacked coil thick [mm] 44.00 inner core diameter [mm] 178.4 Coil support ring [mm] 10.00 Inter core gap [mm] 47.35 Space in slot depth [mm] 6.50
Flow gap [mm] 29.35 Tooth width [mm] 17.39
Inner duct thickness [mm] 7.7 Slot pitch [mm] 43.48 Outer duct thickness [mm] 9.3 Conductor width [mm] 22.09
Slot width [mm] 26.09 Conductor
thickness [mm] 2.00
Slot depth [mm] 60.50 Insulator thickness [mm] 0.20
Core depth [mm] 85.50
Electrical
Input current [A] 100.0 Goodness factor [#] 0.5
Input voltage [V] 261.3 Pole pitch [cm] 13.33
Impedance [ohm] 2.6 Number of slots [#] 18
Input VA [kVA] 45.3 Turns/slot [#] 20
Input power [kW] 6.0 Number of pole
pairs [#] 3
Power factor [%] 13.3 Slot/phase/pole [#] 1
Figure 4.3.5 shows the distribution of the radial magnetic field along the coolant passage in the integrated nuclear electromagnetic pump. The results are depicted using a step size of approximately 1/60 s, which corresponds to one period of the 60-Hz AC current. Although the distribution differed between 0 and 0.0165 s, it changed very insignificantly after 0.0165 s. The reason for the difference between 0 and 0.0165 s is that the eddy current, which was induced by the magnetic field, could not be considered at 0 s. Consequently, there was no current density in Figure 4.3.6 or Lorentz force in Figure 4.3.7 at 0 s.
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Figure. 4.3.5. Radial component of the magnetic field distribution along the electromagnetic pump as a function of time
Figure. 4.3.6. component of the current density distribution along the electromagnetic pump as a function of time
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Figure 4.3.7. Lorentz force generated in the electromagnetic pump as a function of time
Figures 4.3.8–4.3.10 depict the Lorentz force distributions calculated with different numbers of pole pairs, flow gap widths, and pole pitches in the integrated nuclear electromagnetic pump model. The lines in Figure 4.3.8 represent the Lorentz force distributions of the integrated nuclear electromagnetic pump model with two, three, and four pole pairs, and the corresponding average Lorentz forces were found to be 4193, 3151, and 3146 N/m3, respectively, for the same input power. Thus, the integrated nuclear electromagnetic pump model with two pole pairs is approximately 30% more efficient than that with either three or four pole pairs.
Figure 4.3.8. Lorentz force distributions corresponding to different numbers of pole pairs
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In Figure 4.3.9, the lines show the Lorentz force distributions of the integrated nuclear electromagnetic pump model, when the flow gap width was approximately 15.2, 30.4, and 45.6 mm, and the corresponding average Lorentz force was determined to be 8061, 3151, and 2497 N/m3, respectively, for the same input power. The force differences resulted from the magnetic field in the radial direction decreasing with an increase in the coolant passage width. Although too narrow a coolant passage would cause a high hydraulic pressure by increasing the flow velocity, this issue could be neglected in this model, as the flow velocity was very low. Therefore, decreasing the coolant passage width clearly increased the efficiency of the integrated nuclear electromagnetic pump model.
Figure 4.3.9. Lorentz force distribution corresponding to different coolant flow channel widths
From an analysis of the coolant circulation system design variables, the design specifications and conceptual design of the integrated nuclear electromagnetic pump for the SMLFR necessary to transport larger quantities of the LBE coolant were selected and are presented in Table 4.3.3 and Figure 4.3.10. The integrated nuclear electromagnetic pump described in Table 4 has been designed.
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Table 4.3.3. Specifications of the integrated nuclear electromagnetic pump
Design variable Unit Value
Requirements
Mass flow [kg/s] 4140
Developed pressure [Pa] 17634
Temperature [C] 350
Velocity [m/s] 0.458
Geometric
Core length [mm] 2000
Outer core diameter [mm] 2438 inner core diameter [mm] 1800
Flow gap [mm] 60
Inner duct thickness [mm] 20 Outer duct thickness [mm] 50
Electrical
Input current [A] 340
Input voltage [V] 610
Input VI [kVA] 359.3
Input power [kW] 220.9
Efficiency [%] 3.01
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Figure 4.3.10. Conceptual design of the integrated nuclear electromagnetic pump for the SMLFR
Figure 4.3.11 shows the Lorentz force distribution of the integrated nuclear electromagnetic pump for the SMLFR. There is a downward Lorentz force in the annular flow gap between the inner and outer cores, while there is no Lorentz force in the central coolant passage. Consequently, this coolant circulation system could transport twice as much LBE coolant, as natural circulation alone can. This is because of the assistance provided by the forced cooling system.
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Figure 4.3.11. Lorentz force distribution of the integrated nuclear electromagnetic pump for the SMLFR
Figure 4.3.12 shows the temperature of the circulation system for the SMLFR components [5]. The inlet plenum, where the LBE coolant enters has a temperature of approximately 300 °C, while the upper parts, where the heat exchange happens, has a temperature of approximately 450 °C. The range of temperatures from 300 to 450 °C is acceptable for the safe operation of the integrated nuclear electromagnetic pump for the SMLFR, considering the structural materials used, such as silicon steel, SUS 316, and copper. From a viewpoint of safety, the temperature of the cladding is kept below 550 °C.
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Figure 4.3.12. Temperature variation of the coolant circulation system for the SMLFR
Smaller reactors are smaller in scale, and shorter in construction time, resulting in a higher net present value of investment. The modular design allows the construction to be carried out by factory assembly of modules for shipment and assembly. Their factory production is also cheaper than the on- site production.
The main costs of this system include capital, fuel cycle, operation, and decommissioning costs. The percentages main costs in the total cost, as determined in some previous studies are shown in Table 4.3.4 [92–93]. Not only are the capital, operation, maintenance, and decommissioning costs lower for small plants than for the large plants, but also the processes involved are easier for small plants.
Table 4.3.4. Cost ranges for nuclear reactors
Cost type Capital Fuel Maintenance Decontaminations
Range 60% – 75% 5% – 10% 8% – 15% 1% – 5%
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