# Asymmetric Magnetohydrodynamic Propulsion for Oil-Water Core Annular Flow Through Elbow
## 4 Discussion
### Flow Field  
Differential MHD heavy oil flow stabilization accelerator model flow field analysis is based on the electromagnetic field simulation analysis, still using COMSOL Multiphysics(r) [30] software for the calculation and analysis of the coupling between the electromagnetic field and the flow field, including the flow pattern of the oil-water annular flow in the elbow, the flow velocity distribution, and other content. Research on the fluid velocity inside the pipe is of great significance for the practical application of the device, so this paper uses two methods, particle tracking and probe analysis, based on the simulation analysis to better study the flow process of the oil-water ring inside the pipe. First of all, the analysis of the fluid velocity cloud inside the pipe is shown in Figure 5. Since the initial velocity of the oil phase is higher than that of the water phase, the red portion in the center of the pipe (oil phase) has a greater velocity than the blue portion at the edge of the pipe (water phase). Figure 5a shows that when the device is opened, there is  
Figure 4: Mechanism of differential MHD heavy oil flow stabilization accelerator. (**a**) Electric field effect diagram, where red flow lines and arrows indicate electric field direction, and bottom color shows current density in A\(\cdot\)m\({}^{-2}\). (**b**) Magnetic field effect diagram, where black flow lines and arrows indicate magnetic induction direction, and bottom color shows magnetic flux density in T. (**c**) Lorentz force effect diagram, where bottom color shows force field in N\(\cdot\)m\({}^{-3}\). a significant change in the velocity of the oil-water ring in the pipe by the electromagnetic force (Lorentz forces) provided by the device, with a higher amount of change in the speed on the side affected by the electromagnetic forces. Meanwhile, the A-A' section at the acceleration region (region of device action) in Figure 5a shows that the device accelerates the outer water ring. The B-B' section shows the red area (oil phase) distributed in the central region of the pipeline and the blue area (water phase) wrapped around the red area, neither of which breaks through the border of the oil-water ring. The velocity cloud of the pipeline when the device is not turned on is shown in Figure 5b. From the left side of the pipeline velocity cloud, the red area (oil phase) and blue area (water phase) at the entrance of the pipeline are in a normal distribution, indicating that the oil-water ring has not ruptured at this stage, which corresponds to the fluctuating state of the oil-water ring in Figure 3b. However, the red region at the pipe outlet has an insignificant offset, and the right D-D' cross-section reveals this phenomenon. The D-D' section clearly shows that the red region (oil phase) breaks through the oil-water ring boundary and shifts towards the pipe wall, implying that the rupture phenomenon is generated. By a comparative analysis of Figure 5a,b, the above results indicate that the acceleration of the outer water ring affected by the magnetohydrodynamic acceleration device plays a positive role in stabilizing the passage of the oil-water ring through the elbow. Secondly, particle tracking analyses and probes are used to analyze the velocity change process of the oil-water ring inside the pipe. Figure 5c,d show the particle tracking velocity cloud, while Figure 5e,f show the probe position and the variation in fluid velocity inside the probe recording pipe. The tracking of particles in the pipe water ring before and after opening the device is shown in Figure 5, and by comparing Figure 5c,d, the velocity change in the oil-water ring in the elbow section is revealed. When the device is opened, the marked part in the middle and lower parts of Figure 5c evidently indicates that the device has an acceleration effect on the particles in the outer water ring of the pipeline, and the velocity of particles inside and outside the pipe tends to be the same at the elbow.