3. Methods
3.2. Development and analysis of electromagnetic pump design program
3.2.2. P-Q characteristics analysis with change in electrical input
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For a turbulent flow, a theoretical calculation of the fluid flow is more involved; therefore, the analysis usually relies on the experimental data. Colebrook Equation (3.2.17) is deduced from the data analysis of accumulated experiment results. It takes the form of a negative function, in which the friction coefficient exists on both sides [80].
1
βπ= β2πππ(π/π·3.72β+π 2.51
πβπ) (3.2.17)
As an alternative to Colebrook equation, Haaland developed an equation that would approximate the Colebrook equation, and appears in the form of a positive function, as shown in Equation (3.2.18). A feature of Equation (3.2.18) is that if the Reynolds number is greater than 3,000, the result may be within 2% of that obtained by Colebrook equation without a recalculation [81].
1
βπ= β1.8πππ(π/π·β
3.72)1.11+6.9
π π (3.2.18)
The minor loss is usually calculated using Equation (3.2.19), or Equation (3.2.20), depending on the type of the device [78].
βππ= πΎπ
2
2 (3.2.19) βππ= ππΏπ
π· π2
2 (3.2.20) The loss coefficient of Equation (3.2.19) is determined experimentally for each case and expression πΏπ in Equation (3.2.20) is the equivalent length. There is a significant amount of experimental data for the minor loss; however, there are differences in the results depending on the source of the data even for the same flow geometry. Therefore, it is important to reduce the error in the results by considering the major and minor losses when conducting an analysis of the developed pressure and flow rate of an electromagnetic pump.
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Figures 3.2.5β3.2.8 and Tables 3.2.2β3.2.4 present the results of NASA's design and performance evaluation of electromagnetic pumps, center-return-type spiral linear induction electromagnetic pumps, no-center-return-type spiral linear induction electromagnetic pumps, FLIP, and ALIP [21].
Figure 3.2.5. Developed pressure and flow rate characteristics of NASAβs center-return-type spiral induction electromagnetic pump (Input frequency: 25 Hz)
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Figure 3.2.6. Developed pressure and flow rate characteristics of NASAβs no-center-return-type spiral linear induction electromagnetic pump (Input frequency: 60 Hz)
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Table 3.2.2. Design specifications of two types of spiral induction electromagnetic pumps from NASA
Center-return-type No-center-return-type
Frequency 25 Hz 60 Hz
Poles 2 2
Fluid velocity 25.3 ft/s 29.7 ft/s
Slip 0.49 0.58
Duct wall thickness 0.1 in. 0.075 in.
Duct cross section 8.6 in. OD 5.8 in. OD
Fluid passage 1.1 in. deep Γ 6.4 in. lead (4 passages in parallel)
1.4 in. deep Γ 4.4 in. lead (3 passages in parallel)
Slots/pole 18 12
Slot size 0.4 in. Γ 1.9 in.
approximate 0.5 in. Γ 2.1 in. approximate Stator size 14.8 in. OD Γ 15 in. long Γ
9 in. bore
12.4 in. OD Γ 18 in. long Γ 6.2 in. bore
Power input 28.3 kW 29 kW
Efficiency 15.8% 15.4%
Volt-amp input 42 kVA 63 kVA
Power factor 67% 46%
Winding temperature (Above 825 Β°F coolant)
200 Β°F (Average) 400 Β°F (Hot spot)
190 Β°F (average) 310 Β°F (hot spot)
Approximate total weight 970 lb 830 lb
Approximate overall
dimensions 16.1 in. OD Γ 50 in. long 13.7 in. OD Γ 52 in. long
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Figure 3.2.7. Developed pressure and flow rate characteristics of NASAβs FLIP (Input frequency: 60 Hz)
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Table 3.2.3. Design specifications of NASAβs FLIP
Frequency 60 Hz
Poles 4
Pole pitch 6 in.
Fluid velocity 31.5 ft/s
Slip 0.47
Duct wall thickness 0.04 in.
Duct cross section 0.58 in. Γ 11 in.
Fluid passage 0.5 in. Γ 10.5 in.
Slots/pole 9
Slot size 0.46 in. Γ 1.15 in. approx.
Stator size 10 in. stack Γ 30 in. long
Power input 27.8 kW
Efficiency 16.2 %
Volt-amp input 70 kVA
Power factor 39%
Winding temp.
(Above 825 Β°F coolant)
180 Β°F (average) 250 Β°F (hot spot)
Approximate total weight 960 lb.
Approximate overall dimensions 15 in. Γ 37 in. Γ 41 in.
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Figure 3.2.8. Developed pressure and flow rate characteristics of NASAβs ALIP (Input frequency: 60 Hz)
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Table 3.2.4. Design specifications of NASAβs ALIP
Frequency 60 Hz
Poles 4
Pole pitch 6 in.
Fluid velocity 28.7 ft/s
Slip 0.52
Duct wall thickness 0.062 in.
Duct cross section 4.3 in. OD
Fluid passage Annulus 4.18 in. OD Γ 3.18 in. ID
Slots/pole 6
Slot size 0.55 in. Γ 2 in. approx.
Stator size 10.7 in. OD Γ 30 in. long
Power input 29.9 kW
Efficiency 15%
Volt-amp input 80 kVA
Power factor 37.6%
Winding temp.
(Above 825 Β°F coolant)
200 Β°F (average) 300 Β°F (hot spot)
Approximate total weight 720 lb.
Approximate overall dimensions 12 in. OD Γ 56 in. long
The flow rate is directly proportional to the velocity of the fluid, as the electromagnetic pump always has a certain cross-sectional area in flow gap. In other words, an increase in the flow rate means that if the velocity of the fluid is increased, the major and minor losses are also increased, as they are proportional to the velocity. The developed pressure is computed considering the pressure loss at the driving pressure of the electromagnetic pump; therefore, the resulting developed pressure is gradually reduced as the flow rate increases. Figures 3.2.5β3.2.8 show that overall, regardless of the type of the electromagnetic pump, the resulting developed pressure tends to gradually decrease as the flow rate increases, as the theory suggests. In the case of electromagnetic pumps with this type of developed pressure and flow rate characteristics, even if the flow rate is temporarily increased or decreased owing to a flow instability or unforeseen reasons, it can naturally return to the operating point of the electromagnetic pump owing to the changes in the developed pressure to ensure the drive stability. It is, therefore essential to assess the flow stability as shown in Figure 3.2.9 [75].
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Figure 3.2.9. Classification of flow stability
The efficiency characteristics with a change of flow rate are observed in Figures 3.2.5β3.2.8, which show that the maximum efficiency is at a point where the multiplication of the developed pressure and flow rate is maximized, as is also indicated by the equation for efficiency derived in Section 3.1.
Therefore, the basic operating point of an electromagnetic pump is formed at the part shown by a slashed line in Figures 3.2.5β3.2.8.
Figure 3.2.10 shows the distribution of the developed pressure and flow rate characteristics when the input current is changed to 20, 30, 40, and 50 A for an ALIP with a rated flow rate of 100 L/min and developed pressure of 2.57 bar developed using the electromagnetic pump design program. The hydrodynamic, geometric, and electrical design variables of the ALIP are summarized in Table 3.2.5.
Additionally, the pressure drop curve of the loop is also shown. Because the major and minor losses are proportional to the square of the flow rate, the loop pressure drop curve is shown to be a quadratic function. Therefore, the designed ALIP is operated at the point where the developed pressure is equal to the loop pressure drop at the same flow rate.
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Figure 3.2.10. Developed pressure and flow rate characteristics of the ALIP corresponding to input power changes (600 Β°C, 60 Hz)
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Table 3.2.5. Design specifications of the ALIP with a flow rate of 100 L/min
Design variable Unit Value Design variable Unit Value
Hydrodynamic
Flow rate [L/min] 100 Slip [%] 91.7
Developed pressure [bar] 2.57 Reynolds number [#] 32766
Temperature [ο°C] 600 Head loss [Pa] 15817
Velocity [m/s] 1.850
Geometric
Core length [mm] 372.0 Core thickness [mm] 25.00 Outer core diameter [mm] 240.5 Stacked coil thick [mm] 45.00 inner core diameter [mm] 38.7 Coil support ring [mm] 10.00 Inter core gap [mm] 10.90 Space in slot depth [mm] 10.00
Flow gap [mm] 5.90 Tooth width [mm] 12.00
Inner duct thickness [mm] 2.0 Slot pitch [mm] 30.00 Outer duct thickness [mm] 3.0 Conductor width [mm] 14.00 Slot width [mm] 16.00 Conductor thickness [mm] 1.30 Slot depth [mm] 65.00 Insulator thickness [mm] 0.20 Core depth [mm] 90.00
Electrical
Input current [A] 50.0 Pole pitch [cm] 18.60
Input voltage [V] 344 Number of slots [#] 12
Impedance [ohm] 6.9 Turns/slot [#] 60
Input VA [kVA] 29.8 Number of pole pairs [#] 1 Input power [kW] 21.9 Slot/phase/pole [#] 2 Power factor [%] 73.5 Hydraulic efficiency [%] 6.23 Goodness factor [#] 2.6
B. Evaluation of the electromagnetic pump performance by change of frequency
An analysis of the input frequency was conducted as the main design variables of the ALIP.
Theoretically, a lower frequency causes a higher electrical resistance, but lower end effects of the electromagnetic pump. Furthermore, it decreases the flow rate, which is caused by a lower synchronous velocity related with the slip. Figures 3.2.11β3.2.14 depict the developed pressure, flow rate, and efficiency characteristics as a function of frequency options built on the design specifications in Tables 3.2.2β3.2.4 [21].
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Figure 3.2.11. Developed pressure and flow rate characteristics of the center-return-type spiral induction electromagnetic pump under various frequencies (input voltage: 160 V)
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Figure 3.2.12. Developed pressure and flow rate characteristics of the no-center-return-type spiral induction electromagnetic pump under various frequencies (input voltage: 140 V)
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Figure 3.2.13. Developed pressure and flow rate characteristics of the FLIP under various frequencies (input voltage: 145 V)
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Figure 3.2.14. Developed pressure and flow rate characteristics of the ALIP under various frequencies (input voltage: 135 V)
Although the effects of the input frequency on developed pressure cannot be defined in simple terms, an analysis of Figures 3.2.11β3.2.14 confirm that the reduction of end effects at low frequencies is very significant for electromagnetic pumps. Therefore, it is seen that the low frequency conditions demonstrate a high developed pressure at the same input voltage in the low flow rate region, including the operating point. However, the converse is true in the high flow rate region. The results suggest that
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the higher frequency has caused high synchronous velocity in the magnetic field, which was advantageous for the high flow rate, considering the same slip conditions. The efficiency is also spread without having the maximum value at a constant flow rate owing to these changes in the developed pressure [82β83].
Figure 3.2.15 shows the developed pressure in the frequency range from 10 to 100 Hz, for flow rates of 50, 100, 150, and 200 L/min, respectively. The ALIP is designed with a flow rate of 100 L/min and a developed pressure of 2.57 bar. The overall curve is similar, indicating that the input current of 50 A represents the maximum developed pressure near a frequency in the range of 20β30 Hz.
Figure 3.2.15. Developed pressure and frequency characteristics of the ALIP under various flow rate (600 Β°C, 50 A)
Figure 3.2.16 shows the distribution of developed pressure and flow rate characteristics in commercial and low frequency ranges. The low frequency is relatively high for the normal flow rate of 100 L/min. However, the developed pressure is decreased at 15 Hz, which is smaller than its maximum value at 25 Hz.
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Figure 3.2.16. Developed pressure and flow rate characteristics of the ALIP under various frequencies (600 Β°C, 50 A)
In Figure 3.2.17, the design code was applied to Novatome's commercial electromagnetic pump IA 21 model (developed pressure of 1.3 bar and flow rate of 67 L/min) to derive the distribution of developed pressure and flow rate characteristics [84]. In the same input power conditions, input frequencies in the range of 25 to 35 Hz represented the maximum developed pressure. Therefore, the electromagnetic pump can be operated efficiently in a lower frequency range than the commercial frequencies, which range from 50 to 60 Hz.
The developed pressure and flow rate distribution in Figure 3.2.18 indicate that the developed pressure is maximized when frequency is close to 25 Hz. However, as shown in Figure 3.2.16, a frequency of 15 Hz shows a rapid decrease in the developed pressure. On the other hand, the developed pressure is decreased while the flow rate is increased, indicating that the flow is stable and free from problems, such as external fluctuations.
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Figure 3.2.17. Developed pressure and frequency characteristics of the ALIP under various flow rates (600 Β°C, 16.5 A)
Figure 3.2.18. Developed pressure and flow rate characteristics of the ALIP under various frequencies (600 Β°C, 16.5 A)
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