# Research on the Aerodynamic-Propulsion Coupling Characteristics of a Distributed Propulsion System
## 4 Results and Discussion
### Influence of the Internal and External Flow Coupling Effect on the Performance of Ducted Fans  
The variations in the mass flow rate and thrust of each ducted fan with the flight Mach number at an angle of attack of 26\({}^{\circ}\) are presented in Figure 12. The normalization of the mass flow rate and thrust is carried out with reference to the corresponding values of the middle fan (#3) when the angle of attack is 0\({}^{\circ}\) and the Mach number is 0.2. It can be found that both the mass flow rate and thrust of the #1 and #5 fans increase with the increase in the flight Mach number at AOA = 26\({}^{\circ}\). Taking the #5 fan as an example, the mass flow rate and thrust at a Mach number of 0.4 increase by 10% and 23%, respectively, compared with those at a Mach number of 0.2. However, when the Mach number is 0.4, the mass flow rate and thrust of fans #2, #3, and #4 are all smaller than those at a Mach number  
Figure 12: Mass flow rate and thrust of each fan at different Mach numbers: (**a**) variation in the mass flow rate of each fan with the flight Mach number; (**b**) variation in the thrust of each fan with the flight Mach number. of 0.3. Among them, the mass flow rate and thrust of fan #3 are even smaller than those at a Mach number of 0.2, decreasing by 16% and 28%, respectively. The results indicate that as the Mach number increases, the inlet flow tube area of the fan is reduced. This reduction then triggers the stagnation of the airflow, which consequently brings about a substantial decrease in both the mass flow rate and thrust of the fan. From the perspective of improving this situation, further explorations of the layout strategies of ducted fans can be carried out in follow-up studies. For example, considering increasing the spacing between fans or installing the fans on a lower surface of the wing, with the expectation of alleviating the adverse effects caused by the increase in Mach number, may achieve the optimization and improvement of the fan performance. Figures 13-15, respectively, present the flow characteristics of the NACA 643-618 clean airfoil and the coupled configuration without the fan suction effect under the conditions of a Mach number of 0.2 and an angle of attack of 26\({}^{\circ}\) from different perspectives. Figure 13 shows the static pressure coefficient contours and limiting streamlines on the upper surface of the wing, Figure 14 presents the streamline distribution at the middle section of the wingspan (as shown in the red section of Figure 7), and Figure 15 shows the axial velocity contours at the \(x=-0.15\) m section (corresponding to the red dashed line in Figure 14). The static pressure coefficient \(C_{P}\) is defined as follows in Equation (14):  
\[C_{p}=\frac{p-p_{\infty}}{0.5\rho_{\infty}V_  
A comprehensive analysis reveals that when the Mach number is 0.2 and the angle of attack is \(26^{\circ}\), the airflow undergoes severe separation on the upper surface of the clean wing, with the separation region nearly covering the entire upper surface. Meanwhile, a large-scale separation vortex forms near the trailing edge of the wing, and there is a distinct backflow close to the wing surface. For the coupled configuration without the fan suction effect, although airflow separation also occurs in the upstream region of the duct inlet, the separation degree is significantly lower than that of the clean wing. In this coupled configuration, the separation is the most severe in the upstream region of fan #3, while it is relatively less severe in the wingtip region. Moreover, a saddle node-type separation structure is observed, where the saddle point \(S\) and the two separation nodes \(N1\) and \(N2\) jointly form the separation line. There are two main aspects contributing to the changes in the separation characteristics of these two configurations. On one hand, for the coupled configuration, when the airflow passes through the duct, the flow area suddenly decreases compared to the far field, leading to an increase in the flow velocity.