IV. Results and discussion
4.1. MHD circulator
4.1.1. Feature analysis
The z-direction magnetization permanent magnet was included next to the r-direction magnetization magnet to increase the high magnetic flux density in the r-direction as shown in Fig. 4.1.2. To determine the efficiency of a z-direction magnetization permanent magnet, Fig. 4.1.3 shows a schematic of the magnetic flux density distribution depending on the presence of the z-direction magnetization magnet.
When shielding the magnetic field with ferromagnetic material, the magnetic flux density has the characteristic of a high value in the center but a low value in the outer angle. The magnetic flux density is constantly maintained and increased when a z-direction magnetization magnet is added due to the perpendicular direction of the magnetic flux in the z-direction magnetization magnet. The average value of the magnetic flux density was increased from 0.885 T to 0.908 T, showing a 2.5% increase.
Consequently, the layout with a z-direction permanent magnet was adopted.
Figure 4.1.3. Magnetic flux density distribution according to height depending on the presence of a z- direction magnetization permanent magnet in the analysis region
The ferromagnet has high permeability, which leads to magnetic flux inside the geometry. The degree of magnetic shielding differs according to the thickness of the ferromagnet. Generally, large thickness provides high magnetic shielding but this is limited due to the weight problem from the high specific gravity of a ferromagnet (7.9 g/cm3). In the case of an inner ferromagnet, the increase of the magnetic flux density was less than 110 mm as shown in Fig. 4.1.4. However, its decrease was recorded after 110 mm due to the increase of the distance with magnets. The magnetic flux density according to the thickness and height of the outer ferromagnet converged at 40 mm and 440 mm, respectively, due to the limited magnet shielding as shown in Figs. 4.1.5 and 4.1.6. Consequently, the magnetic flux density was 0.91 T when the inner ferromagnet thickness was 100 mm, the outer ferromagnet thickness was 40 mm, and the outer ferromagnet height was 440 mm.
Figure 4.1.4. Magnetic flux density according to the inner ferromagnet thickness
Figure 4.1.6. Magnetic flux density according to the inner ferromagnet height
The two-dimensional arrangement of the magnet and ferromagnet was represented in Fig. 4.1.7. The flow path was located in a range of 150 mm with a high magnetic flux density as shown in Fig. 4.1.3.
Fig. 4.1.8 represents the magnetic flux density distribution at the duct part where the actual flow path exists. The magnetic field has the highest value when it is near a permanent magnet, with a value of 0.95 T. The minimum value was 0.87 T with a difference from the maximum at 9.5% and average magnetic flux density was 0.91 T.
Figure 4.1.7. 2D arrangement design of a permanent magnet and ferromagnet.
Fig. 4.1.9 shows the current density distribution in the duct part. The brazing was considered as half size compared with the outer diameter of the flow channel. In that condition, most of the current flows through the liquid lithium, 88.6% of the current density was distributed in liquid lithium.
Figure 4.1.9. Current density distribution at the duct part
The developed pressure was calculated using the electromagnetic variables and derived Eq. (3.1.55).
There are three pressure mechanisms of MHD circulation that generate pressure due to the Lorentz force and pressure loss of the electromotive force and hydraulic friction. As the input current increased, the developed pressure was linearly increased as shown in Fig. 4.1.10. The pressure caused by the Lorentz force (∆PEM) was almost same as the total developed pressure (∆Ptotal). This implies that the pressure loss was relatively small compared to the pressure due to the Lorentz force. The input current of 872 A was required to achieve 10.5 bar of developed pressure, which is our maximum object pressure.
At that point, the pressure loss was 0.31 bar, which is only 3% compared to the developed pressure.
Figure 4.1.10. Developed pressure due to the Lorentz force and total developed pressure according to the input current
Fig. 4.1.11 shows the pressure-flowrate curve of the MHD circulator. The black line representing the loop system pressure drop and operating point had a developed pressure of 10.5 bar and flowrate of 6 cm3/s at an input current of 872 A. The negative pressure-flowrate slope attains a stable flow when the flowrate changes.
Figure 4.1.11. Pressure-flowrate curve of the MHD circulator according to the input current change
Table 4.1.1. Design variables of the MHD circulator
Variables Units Values
Flowrate [cm3/s] 6
Developed pressure [bar] 10.5
Temperature [K] 473
Velocity [m/s] 0.94
Pressure loss [bar] 0.3
Outer diameter of duct [mm] 10
Inner diameter of duct [mm] 9
Inner ferromagnet thickness [mm] 110
Outer ferromagnet thickness [mm] 40
Outer ferromagnet height [mm] 440
Number of turns # 14
Magnetic flux density [T] 0.91
Input current [A] 872
Weight [kg] 340
Figure 4.1.12. Overall design of the MHD circulator
Figure 4.1.14. Design of an MHD circulator – duct
Figure 4.1.15. Design of an MHD circulator – brazing
Figure 4.1.16. Design of an MHD circulator – electrode stub
Figure 4.1.18. Design of an MHD circulator – r-direction magnetization magnet
Figure 4.1.19. Design of an MHD circulator – z-direction magnetization magnet
Figure 4.1.20. Design of an MHD circulator – inner ferromagnet
Figure 4.1.22. Design of an MHD circulator – component of the outer ferromagnet
The MHD circulator was fabricated based on the proposed design shown in Fig. 4.1.23. There was a weakness in a manufactured MHD circulator due to its strong magnetic flux and heavy weight. It is difficult to change a duct when the vacuum in the duct breaks or when lithium oxidation or thermal deformation occur. The ferromagnet was stuck by strong magnet. Therefore, Chapter 4.1.2 considers the newly designed MHD circulator.
Figure 4.1.23. Manufactured MHD circulator