# Aerodynamic Performance Assessment of Distributed Electric Propulsion after the Wing Trailing Edge
## 4 Numerical Simulations
### Simulation Result  
To figure out the increased lift for a higher AoA, as presented in the experiments, as shown in Figure 6, we selected the velocity distribution at the 43% span section of pusher structures for an AoA ranging from \(20^{\circ}\) to \(30^{\circ}\). \begin{table}
\begin{tabular}{c c c} \hline
**Part** & **Parameter** & **Numerical Value** \\ \hline Simulation calculation domain & - & 600 mm \(\times\) 600 mm \\ \hline \multirow{3}{*}{NACA4415 airfoil used for the wing} & Span & 300 mm \\  & Chord & 150 mm \\  & Aspect Ratio & 2 \\ \hline \multirow{3}{*}{Four propellers} & Diameter & 76.2 mm \\  & Pitch & 76.2 mm \\  & No. of blades & 4 \\ \hline \multirow{2}{*}{Boundary conditions} & Speed inlet & 18 m/s (typical) \\  & Rotation domain RPM & 18,000 rpm \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 5: The mesh distribution: (a) face mesh; (b) side view of cell. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Rotated Region Grid (\(\times 10^{5}\))** & **Total Grid (\(\times 10^{5}\))** & **Cl** & **Cl Error (\%)** & **Cd** & **Cd Error (\%)** \\ \hline
1.89 & 85.47 & 0.95 & \(-10.2\) & 0.44822 & +5.8 \\
2.14 & 107.51 & 0.987 & \(-7.9\) & 0.43678 & +3.1 \\
2.55 & 133.64 & 1.013 & \(-5.5\) & 0.43466 & +2.6 \\
2.83 & 167.29 & 1.014 & \(-5.4\) & 0.43424 &Figure 6: Cont. Figure 6: Velocity distribution at 43% spanwise. (a) \(Xr=0,D_{p}=0.1c\), AoA = 20\({}^{\circ}\); (b) \(Xr=0,D_{p}=0.1c\), AoA = 24\({}^{\circ}\); (c) \(Xr=0,D_{p}=0.1c\), AoA = 30\({}^{\circ}\); (d) \(Xr=0,D_{p}=0.1c\), AoA = 20\({}^{\circ}\); (e) \(Xr=0.5,D_{p}=0.1c\), AoA = 20\({}^{\circ}\); (f) \(Xr=0.5,D_{p}=0.1c\), AoA = 20\({}^{\circ}\); (g) \(Xr=0.5,D_{p}=0.1c\), AoA = 24\({}^{\circ}\); (h) \(Xr=-0.5,D_{p}=0.1c\), AoA = 24\({}^{\circ}\); (i) \(Xr=0.5,D_{p}=0.1c\), AoA = 30\({}^{\circ}\); (j) \(Xr=1,D_{p}=0.1c\), AoA = 30\({}^{\circ}\);  
For the horizontal position at \(D_{rp}=0.1c\), by changing the vertical offset of the propeller, it can be found that there is a significant difference in the inflow of the propeller where the upper inflow is mixed with the outflow of the wing. For the flow field near the trailing edge of the propeller, a deflection was found in the inflow direction of the propeller at \(Xr=0.5\) with the increasing velocity. It was more obvious for the propeller mounted above the paddle. On the contrary, the interaction with the lower wing was weak. For the two pusher structures at a \(30^{\circ}\) AoA with a distance of \(0.1c\) from the trailing edge and a vertical offset of \(Xr=0.5\) and \(Xr=1\), the airflow through the wing interacted with the rotor flow field, creating a stabilized leading edge vortex [28]. The vortex at \(Xr=0.5\) interacted with the inflow of the propeller, and the vortex at \(Xr=1\) began to affect the propeller's tip vortex and down wash flow, forming another smaller vortex behind the paddle. Therefore, when the trailing edge of the wing approached the tip of the blade, the eddy current action was more intense, and the \(Xr=1\) with a large vertical offset weakened the eddy current intensity above the wing, thereby increasing the lift. Figure 7 shows a pressure contour for DEP structures ranging from \(20^{\circ}\) to \(30^{\circ}\). The pressure difference in the leading edge of the wing increased slightly with the positions for a lower AoA. Thus, the lift of the DEP system did not increase significantly. For AoA = \(30^{\circ}\), the negative pressure area increased significantly, which directly increased wing lift and drag. In Figure 7c, it can be seen that the increment for the negative pressure on the wing reached the maximum when the distance from the propeller center to the rear edge was \(0.1c\) to \(0.15c\). Within a certain range, the small change in the flow direction of the propeller in the DEP has no significant effect on the aerodynamic performance. Similarly, the vertical installation position of the propeller significantly changes the DEP flow field distribution.