# Analysis of the Propulsion Performance and Internal Flow Field of an Underwater Launcher
## 3 Numerical Analysis
### Analysis of Pressure Distribution  
The corresponding pressure cloud maps of the internal flow field under the above three conditions are given in Figures 9-11 to further understand the influence of jet structure. As can be seen in Figure 9, due to less chamber gas being injected into the front of projectile A through the central nozzle (the diameter is 3 mm) at 1.0 ms, the pressure field is relatively straightforward, with the pressure decreasing down the axis. At 3.7 ms, the gas expands rapidly after exiting the nozzle outlet, causing the Taylor cavity's continuous expanding. Next, compression waves are then generated at the head of the Taylor cavity, producing several expansion-compression waves within the gas-curtain. Moreover, upstream of the Taylor cavity lies a high-pressure area with a maximum pressure of roughly 6.2 MPa. At 5.0 ms, the pressure is nearly 9.0 MPa at the nozzle exit. Afterward, the gas expands quickly, causing the pressure to rapidly fall to below 2.0 MPa. The pressure fluctuates at roughly 5.0 MPa due to the increasing expansion-compression effect within the Taylor cavity. The compression-expansion effect within the Taylor cavity reduced with the creation of the gas-curtain at 9.0 ms, despite the fact that the injection pressure continues to grow. Pressure decreases rapidly with certain oscillation after the nozzle outlet and fluctuates around 4.1 MPa downstream. At 15.0 ms, the gas-curtain further expands, and gas goes through two continuous compression-expansion processes after exiting the nozzle. The pressure downstream is kept within 4.0 MPa. The internal pressure is mildly more than 4.0 MPa, and there is a minor compression wave at the surface of the gas-liquid interface. The pressure is low overall at 29.3 ms, and it varies at the nozzle and drops along the way. Figure 8: The gas-curtain evolution process (projectile C). (**a**) The first stage; (**b**) the second stage; (**c**) the third stage. In Figure 10, while projectile B is used (the diameter of the central nozzle is 4 mm), maximum pressure at the Taylor cavity head reaches about 8 MPa and 14.3 MPa, respectively, at 1 ms and 2.5 ms. Pressure in the tube decreases along the way as a whole. From 4 to 7 ms, with the formation of Taylor cavity, there are multiple pressure waves reflected back and forth between the projectile head and the gas-liquid interface, which makes the pressure in the Taylor cavity fluctuate along the way. At 12 ms, the multiple pressure waves in the Taylor cavity are more obvious. At 17.8 ms, the gas expands and depressurizes rapidly after exiting the nozzle, forming a Mach plate structure downstream, and the pressure in the gas-curtain is within 5.7 MPa. In Figure 11, at 2 ms, the gas sprays to the projectile front are less while projectile C (with four \(2\times 2\) mm sidewall grooves) is used. Pressure near the projectile head is about 3.7 MPa and then decreases along the way. At 3.5 ms, the pressure in the central nozzle fluctuates at a high level and decreases after passing through the side nozzle, while pressure near the projectile head rises to about 5.6 MPa and then decreases along the way. From 5 ms to 6.5 ms, with the formation of the gas-curtain, the gas in the tube expands further, making pressure at the projectile head decrease to less than 5 MPa. At 13 ms, pressure at the projectile head decreases to about 3.3 MPa due to the further expansion of the gas-curtain. At 30.3 ms, pressure in most areas near the projectile head further decreases to less than 2.4 MPa, but the mean pressure on the surface begins to rise because the pressure at the bottom of sidewall grooves exceeds 9.9 MPa. Figure 9: Pressure distribution (projectile A). (**a**) The first stage; (**b**) the second stage; (**c**) the third stage. Figure 11: Pressure distribution (projectile C). (**a**) The first stage; (**b**) the second stage; (**c**) the third stage. Figure 10: Pressure distribution (projectile B). (**a**) The first stage; (**b**) the second stage; (**c**) the third stage.