## 4 Numerical Simulations
### Simulation Results  
A comparison of thrust coefficient \(C_{T}\) and power coefficient \(C_{P}\) both in experiment and simulation is shown in Figure 9 to validate the reliability of the CFD simulation. It can be seen that the results of the experiment and simulation are basically consistent, and the CFD simulation is capable to capture the flow details.  
As shown in Figure 10, the streamlines are symmetrically distributed where vortexes are formed below the blade tip when there is no wind disturbance. However, the regular vortexes below the blade tip disappear when the horizontal wind is introduced. Compared with the symmetrical streamlines without the effect of horizontal wind, the horizontal airflow directly acts on the rotor disk and flows to the lower right of rotors after being accelerated by the coaxial rotor pairs. Further, with the increase in wind speed, the slipstream moves more with the wind and the interaction between adjacent coaxial rotor pairs is also more intense. This may be the reason that the multi-rotor aircraft have larger power consumption with the effects of horizontal wind, which cause a decrease in hover efficiency.  
The pressure distribution of blade tip of a coaxial rotor pair with various wind speeds is shown in Figure 11.  
Figure 10: Streamline distribution: (**a**) 0 m/s; (**b**) 2.5 m/s; (**c**) 4.0 m/s.  
Figure 9: Comparison of \(C_{T}\) and \(C_{P}\) in experiment and simulation.  
As shown in Figure 11, the positive pressure is concentrated on the lower surface of the rotor, and the negative pressure is mainly concentrated on the upper surface of the rotor. Compared with 0 m/s, the area of positive pressure and negative pressure are enlarged to some extent with the effect of horizontal wind, which may result in an increase in the thrust of the rotor. In addition, the rotors have a larger pressure difference at 2.5 m/s than that at 4.0 m/s. Combined with experimental results, this may explain why that the multi-rotor aircraft has higher thrust coefficient and better aerodynamic performance at 2.5 m/s than those at 4.0 m/s.  
The velocity distribution of adjacent coaxial rotor pairs is shown in Figure 12.  
As shown in Figure 12, it is clear that the downwash flows are symmetrically distributed below the rotors when there is no wind disturbance. When the horizontal wind is introduced, the interaction between the downwash flows is strengthened and the downwash flow move with the wind, which may consume more power and reduce the aerodynamic performance of the multi-rotor aircraft. However, the interference between the rotors of a coaxial rotor pair is weakened with the horizontal wind, which may cause larger thrust on the rotors. Further, as the horizontal wind speed increases, the aerodynamic interaction between the adjacent coaxial rotor pairs will be more obvious and stronger.  
The vortices distributions of the multi-rotor aircraft with different wind speeds are shown in Figure 13.  
Figure 11: Pressure distribution of blade tip: (a) 0 m/s; (b) 2.5 m/s; (c) 4.0 m/s.  
Figure 12: Velocity distribution: (a) 0 m/s; (b) 2.5 m/s; (c) 4.0 m/s.  
It can be seen that vortices interference is much stronger with horizontal wind disturbance compared with no wind disturbance. It will eventually lead to vortex deformation. Additionally, the trailing vortex of the front rotors may be immersed with the inflow of the rear rotors, which will cause strong disturbance with the rear rotors. In the end, it may result in an increase in power consumption. With the increase in wind speed, the rotor interference is more intense, which may even interact with the inflow of upper rotor and waken the hover performance dramatically.