## 4 Results and Discussion
### Flow Field Analysis of Case 1  
Figure 5 shows the Mach number streamline (a) of the whole flow field and the velocity streamline (b) around the rotor. It can be seen from Figure 5a that the whole flow field is very complex and consists of multiple vortex rings. After the downstream airflow passes through the rotor disc, it is divided by the test bench and forms two large vortex rings up and down. The vortex rings shrink into smaller vortex rings and disappear as time passes by. The upper one is stronger because the blades create a low-pressure area over the rotor, drawing more air flows. Small vortexes also generate along the edge of the test bench. Notably, although the rotor only reaches maximum Mach number of 0.42 at 5259 RPM rotational speed, the airspeed within the flow reaches 220.9 m/s (_Ma_ = 0.9847), indicating that the low-density Martian air is highly compressible and may exhibit complex flow characteristics. From Figure 5b, we can see that vortexes generate at the leading edge from the tip side of the blade due to high pressure and move along the blade span-wise fast and chord-wise slowly, creating low pressure zones that generate lift. Airflow from a high-pressure zone below the lower surface passes the leading edge and joins the acceleration of airflow on the upper surface.  
As for the influence of the bench, it can be seen from Figure 5a that the maximum Mach number of the flow nearly reaches 1; however, the flow speed quickly decreases along the streamline and becomes close to zero at the far corner below the bench. After passing the rotor disk, the airflow impacts the bench by a Mach number of approximately 0.2. Part of the flow passes the edge of the bench and down, joining into the circulation. The other part bounces back due to the impact and curls between the rotor and the bench, creating a high-pressure zone in between--this is the reason why case 1 has a 5% higher lift. This indicates that the bench does have some influence on the lift performance of the rotor. Further research can be made to reveal how the height and bench width affect the results.  
Figure 6 shows the slice contours of the pressure and Mach number on the upper surface of a blade. It can be seen that there is a large low-pressure zone created by vortexes over the outer half of the upper surface of the blade. From the Mach number contours, we can see clearly that the vortex generates at the leading edge close to the blade root, attached on the blade and moves along the blade span-wise. The airspeed within the vortex accelerates to maximally 0.985 Mach during the movement and a large vortex grows  
Figure 4: Calculation results of lift (a) and torque (b).  
and begins to detach at 70% of the blade span-wise from the root. It may also split into some smaller vortexes and move along the blade to the root. This reveals that, under the low-density Martian air conditions, the flow is more complex, and the airflow is much easier to increase to a high Mach number. Therefore, air compressibility must be taken into account during CFD research.  
Figure 7 shows the pressure contour of one blade of the rotor. It can be seen that, under such low-density air, even for the air flows at a trans-sonic speed, the difference between maximum and minimum pressure is only about 360 Pascal, which is extremely small compared with the case in Earth's air conditions. This is the reason why the rotor only generates a lift of less than 2 N. The high-pressure zone mainly lies around the blade tip at the leading edge, while the low-pressure zones cover more of the middle part of the blade. Nearly 30% part of the blade close to the root of the blade contributes hardly any lift, and this reveals that blade topology can be made to reduce rotor weight in the actual design of a Mars helicopter. Furthermore, it also indicates that simplifying the model by removing the fixtures has little influence on the research.