# Research on the Aerodynamic-Propulsion Coupling Characteristics of a Distributed Propulsion System
## 4 Results and Discussion
### Wing Aerodynamic Performance  
Under the condition that the physical rotational speed of the fan remains constant, Figure 11 presents the variation laws of the wing lift coefficient \(C_{L}\) with the incoming angle of attack, the variation relationship between the lift coefficient and the drag coefficient \(C_{D}\), the lift-to-drag ratio, and the variation relationship of the pitching moment coefficient \(C_{M}\) with the lift coefficient in the Mach number range from 0.2 to 0.5. These coefficients are defined as follows:  
\[C_{L}=\frac{L}{\frac{1}{2}\rho_{\infty}V_{\infty}^{2}S} \tag{11}\]  
\[C_{D}=\frac{D}{\frac{1}{2}\rho_{\infty}V_{\infty}^{2}S} \tag{12}\]  
\[C_{M}=\frac{M}{\frac{1}{2}\rho_{\infty}V_{\infty}^{2}Sl} \tag{13}\]  
where \(L\) denotes the lift, \(D\) denotes the drag, and \(M\) denotes the pitching moment. \(\rho_{\infty}\) and \(V_{\infty}\) denote the density and velocity of the air at infinity when \(Ma=0.2\). \(S\) denotes the equivalent wing reference area, which is defined as \(S=bc\). The reference point of the pitching moment is taken as the quarter chord length from the leading edge of the wing, as shown in the projection of point \(C_{g}\) on the spanwise center plane of the wing in Figure 7.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Number of Grids \(\times\) 104** & \(C_{L}\) & \(C_{D}\) & \(C_{M}\) \\ \hline
836 & 0.314541 & 0.035984 & \(-\)0.103817 \\
1065 & 0.309606 & 0.035231 & \(-\)0.100242 \\
1392 & 0.310634 & 0.035205 & \(-\)0.100418 \\
1612 & 0.30906 It can be observed that the lift/drag characteristic curves of the wing are generally in agreement with the results predicted by the classical subsonic airfoil theory. In the distributed propulsion system, the suction and exhaust effects of the fans alter the local flow field around the wing. At small angles of attack, the fan suction accelerates the airflow on the upper surface of the wing, reducing the pressure and thereby increasing the lift coefficient. Meanwhile, the increase in the drag coefficient is relatively slow, leading to an increase in the lift-to-drag ratio. As the angle of attack continues to increase to the stall angle of attack, due to the increase in the adverse pressure gradient, the suction effect of the ducted fans on the airflow weakens. The airflow on the upper surface of the wing starts to separate, and even backflow occurs. The growth of the lift coefficient stagnates and then decreases, while the drag coefficient rises sharply. This causes the variation in the lift coefficient with the angle of attack, the variation in the lift-to-drag ratio with the lift coefficient, and the polar curve to exhibit a bell-shaped trend. As the flight Mach number increases, the lift and drag coefficients of the wing also increase. The maximum lift coefficients corresponding to the Mach numbers from 0.2 to 0.5 are 1.96, 3.81, 6.02, and 7.96, respectively. The maximum lift coefficient at a Mach number of 0.5 has increased by 306% compared with that at a Mach number of 0.2, and the drag coefficient corresponding to the maximum lift coefficient has increased by 97%. However, the stall angle of attack of the wing during flight decreases as the flight Mach number increases. The stall angles of attack corresponding to the flight Mach numbers from 0.2 to 0.5 are 38\({}^{\circ}\), 32\({}^{\circ}\), 26\({}^{\circ}\), and 23\({}^{\circ}\), respectively. The stall angle of attack at a Mach  
Figure 11: Aerodynamic performance characteristics of the wing. (**a**) Variation in lift coefficient with angle of attack; (**b**) polar curve; (**c**) variation in lift-to-drag ratio with lift coefficient; (**d**) variation in pitch moment coefficient with lift coefficient. number of 0.2 is 15\({}^{\circ}\) larger than that at a Mach number of 0.5. This is because the increase in the flight Mach number leads to a reduction in the inlet flow tube area of the fan, which in turn weakens the suction effect of the ducted fan on the airflow on the upper surface of the wing and enhances the drag effect of the fan casing.