## 4 Results and Discussion
### Effect of Cowl Lip Angle on the Starting Performance  
Figure 11 shows the starting Mach number distribution of the ICR = 1.9 inlet with different lip angles, where the abscissa and ordinate represent the cowl lip angle and starting Mach number, respectively. The blue and green dots represent the first and second types of starting processes, respectively. The inlet experiences the first type of starting process at a small cowl lip angle, and the second type at a large cowl lip angle. In addition, the cowl lip angle has a significant influence on the starting performance. When the cowl lip angle is small, the inlet starts at a high Mach number, showing a poor starting ability. With the increase in the cowl lip angle, the starting Mach number decreases gradually. The inlet with \(\delta\) = 9\({}^{\circ}\) enters the starting at Ma = 4.57, exhibiting the best starting performance. However, the starting ability deteriorates with the further increase in the cowl lip angle,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{\varphi}\) & \(\mathbf{\sigma}\) & \(\mathbf{Ma_{t}}\) & \(\mathbf{p_{t}/p_{\infty}}\) \\ \hline Flow field A & 0.725 & 0.4114 & 1.50 & 23.86 \\ Flow field B & 0.725 & 0.7753 & 2.30 & 13.33 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of main aerodynamic parameters at the throat under two types of flow fields.  
Figure 10: Structures of the two flow fields (\(\delta\) = 10\({}^{\circ}\)) at Ma = 4.3 for (**a**) Flow field A and (**b**) Flow field B.  
which implies that excessively small or large cowl lip angles will lead to unsatisfactory starting performances. There is an optimal cowl lip angle to achieve the lowest starting Mach number, which is denoted by \(\delta_{\text{opt}}\) in this study.  
To determine the underlying reason for the sharp rise of the starting Mach number at excessively small cowl lip angles, the wall pressure distributions during the starting process of the inlet with \(\delta=0^{\circ}\) are analyzed, as shown in Figure 12. When the inlet Mach number increases from 4.0 to 6.4, an opened separation zone appears in the flow field, and the separation point remains unchanged. However, owing to the increase in the incoming dynamic pressure, the wall pressure in the duct increases continuously, even exceeding \(70p_{\infty}\). This indicates that the inlet struggles to swallow the separation zone under the effect of the strong cowl lip shock, thereby resulting in a poor inlet starting performance [33].  
Excessively large cowl lip angles would also result in a poor starting performance. Figure 13 shows the wall pressure distribution during the starting process of the inlet with \(\delta=12^{\circ}\). At Ma = 4.0, the separation point is located near x/R = 3.7, with an opened separation zone in the flow field. However, when the inlet Mach number increases to 4.5, the separation zone enters the internal contraction section and forms a closed separation zone. In this flow field, with a further increase in the incoming Mach number, the separation zone keeps retreating, and the pressure in the duct keeps increasing to resist the increasing incoming dynamic pressure. The closed separation bubble is hard to be swallowed owing to the large contraction ratio of the duct, thereby leading to a high starting Mach number.  
Figure 11: Starting Mach number distribution of the inlet with different cowl lip angles.  
Figure 12: Wall pressure distributions during the starting process of the inlet with \(\delta=0^{\circ}\).