## 4 Results and Discussions
### The Influence of the Initial Pressure on Nozzle Startup
Moreover, the second shock wave and expansion wave decelerate faster, which lengthens the unstable region, resulting in an increase in the center instability duration. When the initial pressure is lower than the critical pressure, the starting shock wave and the second shock wave accelerate, but at this time, the velocity of the left-traveling expansion waves is no longer dependent on the initial pressure, which is related to the profile of the center. Figure 8: Nozzle center startup and instability duration under different initial pressure. Figure 7: Velocity distribution of nozzle axis (**left**) and Ma contour (**right**) in different initial pressure at 0.5 ms.  
the nozzle and the parameters of the reservoir region. As a result, the velocity of the left-traveling expansion waves remains unchanged, so the center startup duration remains unchanged. However, due to the acceleration of the starting shock wave and the second shock wave, the unstable region is prolonged, which leads to an increase in the center instability duration. The second shock wave curves inward under the influence of the boundary layer during its movement, forming a low-velocity zone and an oblique shock wave on the wall surface, as shown in Figure 9. Only when all the low-velocity zone and oblique shock waves move outside the nozzle can the flow field be stabilized in the entire outlet section (complete startup). Under the conditions of \(P_{5}\) = 1.333 MPa, \(T_{5}\) = 4120 K, and \(P_{e}\) = 100 Pa, the pressure distribution at the nozzle outlet changes with time, as shown in Figure 10. At 1.8 ms, the flow field reaches stability at the center of the nozzle outlet, but it is not until 2.6 ms that the flow field reaches a stable state at the whole outlet. It takes 1.8 ms to start the nozzle from the center to the complete startup. It can be seen that the low-velocity zone significantly prolonged the startup duration of the nozzle and resulted in a huge loss to the effective test time. Increasing the initial pressure changes not only the velocity of the waves in the nozzle but also the shape of the waves. When the initial pressure rises, the second shock wave contracts inward and the low-velocity zone expands, as shown in Figure 11. In the above-mentioned reservoir region conditions, when the initial pressure is 20 Pa, the second shock wave curves slightly inward and still occupies most of the exit area. However, when the  
Figure 10: Pressure distribution at different moments of the nozzle outlet. Figure 9: Low velocity zone and oblique shock. initial pressure increases to 50 Pa, the degree of bending of the second shock wave increases significantly, and the second shock wave can only occupy about half of the exit section. When the backpressure continues to increase to 150 Pa, there is only an oblique shock wave at the nozzle exit. The curve of the complete startup duration with the initial pressure is shown in Figure 8.0  
Additionally, Figure 12 also compares the center startup and the complete startup duration of the nozzle under different initial pressures. For the complete startup, there is no critical pressure, and the startup duration increases linearly with an increase in the  
Figure 8.1 Schematic diagram of the low-velocity flow zone under different initial pressure values. (a) \(P_{e}=20\) Pa, (b) \(P_{e}=50\) Pa, (c) \(P_{e}=100\) Pa, (d) \(P_{e}=150\) Pa.  
Figure 8.2 Center startup time and complete startup time. initial pressure. In addition, it can be seen from Figure 12 that, at a very low initial pressure (about 0.1 times the pressure at the outlet of the nozzle when the flow field is stable), the complete startup duration is equal to the center startup duration. In other words, the low-velocity zone is very small, and the flow field can be stable in the entire nozzle outlet at the same time.