# Research on the Aerodynamic-Propulsion Coupling Characteristics of a Distributed Propulsion System
## 4 Results and Discussion
### Intake Distortion of Ducted Fans  
In order to explore the impact of the flight Mach number on the inlet distortion of ducted fans, this paper conducts a quantitative evaluation on the degree of inlet distortion  
Figure 19: Axial velocity profile upstream of the inlet of the ducted fan at \(Ma=0.4\) and AOA = 26\({}^{\circ}\): (**a**) fan #3; (**b**) fan #4; (**c**) fan #5.  
of ducted fans by using two indicators, namely the total pressure distortion index \(DC_{60}\) and the swirl distortion index \(SC_{60}\)[27]. Their definitions formulas are as follows:  
\[DC_{60}=\frac{\overline{P_{\rm tot}}-\overline{P_{\rm tot,min}(60)}}{\overline{ q}} \tag{15}\]  
\[SC_{60}=\frac{\overline{V_{2,\rm max}(60)}-\overline{V_{2,\rm min}(60)}}{ \overline{\
abla}} \tag{16}\]  
where \(P_{\rm tot}\) denotes the total pressure, \(q\) denotes the dynamic pressure, and \(V_{2}\) denotes the secondary flow velocity. Figures 20 and 21, respectively, show the variation in the total pressure distortion and the swirl distortion at the inlet section (1.4 times the axial chord length from the leading edge of the fan rotor) with the flight Mach number at AOA = 21\({}^{\circ}\). And the swirl angle \(\alpha\) is defined as the ratio of the circumferential velocity component \(U_{\theta}\) of the airflow at the fan inlet to the axial velocity component \(U_{\rm x}\). A positive swirl angle indicates a positive pre-swirl, while a negative swirl angle represents a negative pre-swirl. The specific expression is as follows:  
\[\alpha=\arctan(\frac{U_{0}}{U_{\rm x}}) \tag{17}\]  
The perspective in the figures is from the fan inlet to the fan outlet, and clockwise is the positive direction. It can be seen from Figure 20 that as the flight Mach number increases, the intake uniformity of the ducted fan becomes worse. The total pressure loss at the inlet section becomes more severe, and the total pressure distortion area also expands accordingly. Taking fan #3 as an example, the \(DC_{60}\) value at a flight Mach number of 0.5 has increased by 867% compared with that at a flight Mach number of 0.2. When the flight Mach number ranges from 0.2 to 0.4, the angle of attack is far away from the stall angle of attack range, so the intake conditions among the ducted fans tend to be relatively consistent. Under the same Mach number, the \(DC_{60}\) values of each ducted fan are nearly equivalent, which means that the total pressure losses of each ducted fan are basically the same. Figure 20: Total pressure distortion at ducted fan inlet: (**a**) total pressure contours; (**b**) total pressure distortion index \(DC_{60}\). When \(Ma=0.5\), it can be clearly observed that fan #3 has the largest total pressure loss, followed by fans #2 and #4, and fans #1 and #5 have the smallest total pressure losses. Compared with fan #5, the \(DC_{60}\) value of fan #3 is 18% larger, indicating that the degree of total pressure distortion of fan #3 is the most severe. The reason for the differences in the degree of total pressure distortion among the ducted fan array lies in the fact that the angle of attack approaches the stall angle of attack corresponding to this flight Mach number. As elucidated in Section 4.2, under the influence of adverse pressure gradients and frictional resistance, the airflow first separates in the central area of the wing and even generates backflow, which leads to a significant reduction in the performance of fan #3, thereby making its total pressure loss reach the maximum. From Figure 21, it can be seen that as the flight Mach number increases, the swirl distortion at the inlet section of the ducted fans also increases. Taking fan #1 as an example, the \(SC_{60}\) value at a flight Mach number of 0.5 increases by 232% compared with that at a flight Mach number of 0.2. Meanwhile, the deviation of \(SC_{60}\) values among different ducted fans increases. The swirl distortion at the inlet sections of fans #1 and #5 grows most rapidly, followed by fans #2 and #4, and fan #3 is the slowest.