## 4 Results and Discussion  
### Two Types of Starting Processes under Different Lip Angles  
The numerical method is utilized to calculate the starting process of inlets with different cow lip angles. The results show that there are two different starting processes depending on the cow lip angle. In this paper, the inlets with \(\delta\) = 3\({}^{\circ}\) and 10\({}^{\circ}\) are considered to analyze the two starting processes. First, the inlet with \(\delta\) = 3\({}^{\circ}\) is used to introduce the first type of starting process. Figure 6 shows the Mach contours of the flow fields under typical freestream Mach numbers during the starting process. When the incoming Mach number is 3.0, the airflow chokes at the throat. Subsequently, a high-pressure signal propagates upstream, which leads to a large-scale separation bubble at the entrance. The separation shock makes the incoming flow deflect in advance, and forms a supersonic spillage above the cow lip, thus easing the choke at the throat. In addition, complex shock systems, such as the cow lip shock and the reattached shock, leads to significant flow loss. Note that the inlet is in the unstarting state. Since the separation shock induced by the separation bubble is upstream of the cow lip and results in spillage, the separation zone is called the opened separation bubble. When the incoming Mach number increases from 3.0 to 5.9, the separation shock approaches the cow lip gradually, and the spillage decreases accordingly. However, the opened separation zone continues to exist in this process, and the separation point remains almost unchanged. In particular, at Ma = 5.9, the separation shock intersects the cow lip, and the spillage almost disappears. As the Mach number increases to 6.0, the separation bubble suddenly disappears, and an unblocked supersonic flow is formed in the duct. Obviously, the inlet enters the starting state. Figure 4: Inlet computational domain and grid. Figure 5: Schlierens of the flow fields obtained by the current numerical method and experimental result. Figure 7 shows the mass flow ratio and total pressure recovery coefficient at the throat during the first type of starting process. The definition of mass flow ratio is expressed in Equation (4), where \(\dot{m}\) is the mass flow at the throat, \(\rho_{\infty}\) and \(v_{\infty}\) represent the density and velocity of the freestream, \(A\) is the inlet capture area. The total pressure recovery coefficient is the ratio of the total pressure at the throat (\(TP_{t}\)) to the total pressure of the freestream (\(TP_{\infty}\)), which is expressed in Equation (5). At Ma = 3.0, the inlet shows poor flow capture capability because of the spillage induced by the separation bubble. In addition, because of the large-scale separation zone, the total pressure recovery coefficient is also low. Moreover, the mass flow rises gradually with the increasing Mach number; however, owing to the increase in the shock intensity, the total pressure recovery coefficient decreases further. When the Mach number increases from 5.9 to 6.0, the two parameters increase significantly (as denoted by the arrows in Figure 7), and the inlet enters the starting state. In summary, the first type of starting process can be described as follows. Owing to the low incoming Mach number, an opened large-scale separation bubble is formed in the entrance and a supersonic spillage is generated. When the Mach number increases till the separation shock reaches the cow lip, even a marginal increase in the incoming Mach number would enable the inlet to enter starting state. During this starting process, the mass flow and total pressure recovery coefficient rise sharply as the inlet enters the starting state.