## 3 Simulation Results and Analysis
### Simulation Results and Analysis on Coriolis Effect in C-MHD Ars  
Before we begin the sensing part of the simulation using the magnetic approach in the fluid domain as shown in Figure 3b, it is critical to test the transmission of the radial velocity distribution in the bottom sensing channel. The comparison of the radial velocity along the \(x\)-axis between the two solving methods is made. The results are plotted in Figure 8, respectively, under \(I_{1}=1.5\) A and \(I_{2}=3\) A. Obviously, the uniformity strongly confirms the previous assumption on the interactive method between the two approaches, as illustrated in Section 2.2. Thus, the next sensing effect analysis using the magnetic approach can be given based on the radial velocity under the current setting in the MHD pump, obtained by the electric method. It is known that the Coriolis effect could be induced as the driven radial flow when the case is rotating. The simulation with angular velocity \(\Omega=\sin(2\pi\cdot 0.01\cdot\mathrm{t})\), under energized current \(I=0\) A, and \(I=1.5\) A are made to provide an analysis of the Coriolis effect. In Figure 9, we compare the radial  
Figure 8: The radial velocity along the axis \(x\), respectively, on the plane \(z=-0.001\) m using the electric and magnetic method under energized current \(I_{1}=1.5\) A and \(I_{2}=3\) A.  
Figure 7: The velocity \(u_{z}\) in the center of the MHD pump with different imposed current \(I\). velocity \(u_{r}\) and the relative circumferential velocity \(u_{\theta}\) of the test point \(P(0.010,\,0,\,-0.001)\) in the sensing bottom channel. The velocity curve of the boundary point \(P(0.010,\,0,\,-0.002)\) is plotted as a reference for comparison. When without energized current, the radial velocity with the order of a few \(10^{-4}\) m/s is negligible. As the energized current is set at 1.5 A, the radial flow along the centripetal direction is induced and its magnitude is about 0.008 m/s. It is apparent that the radial velocity is mainly determined by the MHD pump and is unaffected by angular motion. At the same time, the amplitude of relative circumferential velocity \(u_{\theta}\) is increased from 0.0002 m/s to 0.004 m/s. The phase difference between the relative circumferential velocity and the reference signal is about 170\({}^{\circ}\) under energized current \(I=1.5\) A, while nearly 90\({}^{\circ}\) without energized current. It seems that the relative circumferential motion is accelerated by the energized radial velocity. Thus, the poor performance of the MHD effect at low frequency may be compensated by the Coriolis effect. The vector graph of the velocity when the angular velocity reaches the peak and valley on the middle plane \(z=-0.001\) m of the bottom fluid are presented in Figure 10 with energized current \(I=1.5\) A. The streamline is obviously controlled by the Coriolis effect irrespective of the direction of the rotation. The results provide compelling evidence that the Coriolis effect can be generated especially at low frequency in the C-MHD ARS, which is quite different from the laminar flow characteristics without energized current. Figure 10: The vector graphs of velocity on the middle plane \(z=-0.001\) m with the energized current \(I=1.5\) A at the peak and valley when rotating with \(\Omega=\sin(2\pi\cdot 0.01\cdot\)t). Figure 9: The radial velocity \(u_{r}\) and relative circumferential velocity \(u_{\theta}\) of test point \(P(0.010,\,0,\,-0.001)\) under energized current \(I=0\) A and \(I=1.5\) A when rotating with \(\Omega=\sin(2\pi\cdot 0.01\cdot\)t). In order to analyze the Coriolis effect varying with the rotating frequency, the simulation results at the frequency \(f=10\) Hz are shown in Figure 11. The radial velocity \(u_{r}\) under energized current \(I=0\) is more negligible in contract to the results at low frequency in Figure 10, while the amplitude is also stable at 0.008 m/s under \(I=1.5\). The relative circumferential velocity \(u_{\theta}\) under \(I=0\) A and 1.5 A are almost and identical and both reverse to the reference signal.