# Improvement of Hexacopter UAVs Attitude Parameters Employing Control and Decision Support Systems
## 5 FEM Decision Support
### CFD Approach  
The proposed study consists of three main steps: geometry modelling and defeaturing, followed by the CFD computations to extract the lift and drag forces on each propeller and then the evaluation of the displacements on the mechanical structure of the hexacopter for the worst-case scenario. The results were compared with the analytical ones. The workflow is represented in Figure 35a, encompassing the five environmental settings: lateral wind speed of 0 m/s, 4 m/s, 10 m/s, 15 m/s and 20 m/s (Figure 36a) and the CFD enclosure (Figure 35b). For all cases, the maximum rotational velocity of the propellers of 6500 rpm was considered. The final step is the fluid-structure interaction to evaluate the effect of the air fillets on the hexacopter structure. Figure 35: Fluid dynamics simulation. (**a**) CFD approach; (**b**) Enclosure. Figure 36: Velocity profile and dissipated turbulences for no wind and lateral wind scenarios. The CFD simulation model explored a transient regime, and a corresponding mesh size was determined considering the Curant number. To avoid the numerical instability, this number must be 1 [87]. \[Co=v_{max}.\frac{dt}{dx}=1 \tag{1}\]  
where vmax is the maximum velocity in the flow domain, dt is the time increment and dx is the finite element size. The CFD model comprises nearly 2,900,000 elements with controlled inflation layers, named selections and multiple sizing options. The quality of the mesh was controlled, taking into account the skewness criterion, and the flow regime was based on the realizable k- \(\varepsilon\) flow model, employing advanced scalable wall functions and near-wall treatment interfaces. In Figure 36, the contours of the velocities and pressures in the vertical plane are plotted, and the streamlines at rotor level for all the turbulent flows are processed. The influence of the wind on the fluid flow of the propellers occurring in the vertical plane can be observed, and the dissipation of the central turbulence is significant. The turbulence is deflected by the crosswind progressively for the cases v = 4 m/s, v = 10 m/s, v = 15 m/s and v = 20 m/s, respectively. The reaction thrust forces of the six propellers were between 0 and 38 N in absolute values. The lift forces were exported in a static analysis, and the spatial orientation of the hexacopter structure was evaluated as a function of the air pressure caused by the created turbulences, the rotational speed of the six rotors and the acceleration of the hexacopter. The velocity streamlines were processed in Figure 37, as well as the contour plot of the air pressure on the six drone rotors for the case of 10 m/s side wind speed. The maximum air pressure of 383 Pa on the rotors is low, but the influence on the hover flight attitude is further investigated in this paper in a fluid-structure interaction approach. The vortices and joint interferences at the small rotor spaces are compressed by the side wind, increasing the power consumption. The wind produces the movement of the coupled turbulences in the same direction, and this may cause the vibration of the rotors. The consequence is that a power increase and changes of the attack angle are necessary in order to maintain the desired hover flight. The aerodynamic efficiency is also ensured by high trust forces and small power consumption. These parameters were also reported by the CFD analysis. Figure 38 depicts the graph of the drag force on propeller 1 (0.552486 N) computed in the CFD simulation and the same force calculated analytically (0.5605 N). The difference is lower than 1.5%. The same comparison is performed for the lift force on propeller 3 (29.6611 N) as the output of the CFD simulation and by means of hand calculations  
Figure 37: Streamlines and pressure contours on the rotors. (29.1486 N) employing the same analytical model. The difference remains low, of approximately 1.72% between the two methods. This validates the CFD computational model and the accuracy of the simulation results.