# Launch Dynamic Simulation of a Compressed-Air Launcher for Fire Suppression
## 4 Results and Discussion
### Influences of Structural Parameters  
#### 4.1.1 Nozzle Diameter  
Figure 5a shows the change in the peak pressure and muzzle velocity with different nozzle diameters when the gas cylinder volume \(V_{0}\) is 1.0 L, the initial pressure in the gas cylinder \(p_{0}\) is 10.0 MPa, the loading position \(l_{0}\) is 30 mm, and the launch angle \(\theta\) is 40\({}^{\circ}\). It is shown that the peak pressure increases with the increasing nozzle diameter, and it tends toward the initial pressure in the gas cylinder when the nozzle diameter is more than half of the launcher caliber. The muzzle velocity increases correspondingly. Figure 5b illustrates the variations in the total barrel time and gas mass increment in the barrel for different nozzle diameters under the same conditions. The graph demonstrates that the total barrel time exhibits an exponential decrease as the nozzle diameter increases. Additionally, the gas mass increment follows a similar trend to the peak pressure.  
Figure 4: Density and mass increment curves of gas in barrel behind the projectile: (**a**) \(\rho\)–\(t\) and \(\Delta m\)–\(t\) curves; (**b**) \(\rho\)–\(l\) and \(\Delta m\)–\(l\) curves.  
Figure 3: Barrel pressure and projectile velocity curves: (**a**) \(p\)–\(t\) and \(v\)–\(t\) curves; (**b**) \(p\)–\(l\) and \(v\)–\(l\) curves.  
Herein, the gas transfer efficiency \(\eta_{gas}\) and launch efficiency \(\eta_{total}\) are introduced to evaluate the launch process under different conditions. The gas transfer efficiency \(\eta_{gas}\) is defined as the ratio of the gas increment to the initial gas mass, which is written as  
\[\eta_{gas}=\frac{\Delta m}{m_{0}}, \tag{16}\]  
where \(\Delta m\) is the gas mass increment in the barrel behind the projectile. This variable reflects the extent to which the high-pressure gas actually enters the barrel from the gas cylinder.  
The launch efficiency \(\eta_{total}\) is defined as the ratio of the projectile kinetic energy to the high-pressure initial effective energy. It can be written as  
\[\eta_{total}=\frac{E_{k}}{Q}, \tag{17}\]  
where \(E_{k}\) is the muzzle kinetic energy of the projectile. The projectile is accelerated via the expansion of the compressed gas, and the kinetic energy obtained at the muzzle is  
\[E_{k}=\frac{1}{2}m_{p}{v_{0}}^{2}, \tag{18}\]  
where \(v_{0}\) is the muzzle velocity of the projectile.  
The initial effective energy of the compressed gas [15] in the gas cylinder is  
\[Q=p_{0}V_{0}\ln\left(\frac{p_{0}}{p_{a}}\right), \tag{19}\]  
where \(p_{a}\) is the atmospheric pressure.  
Hence, the energy conversion efficiency of the compressed gas during the whole launch process can be expressed as  
\[\eta_{total}=\frac{E_{k}}{Q}=\frac{m_{p}{v_{0}}^{2}}{2\left(p_{0}V_{0}\ln\frac {p_{0}}{p_{a}}\right)}. \tag{20}\]  
Figure 6 shows the changes in both the gas transfer efficiency \(\eta_{gas}\) and launch efficiency \(\eta_{total}\) with different nozzle diameters in the same conditions as above. It is shown that both the \(\eta_{gas}\) and \(\eta_{total}\) increase with the increasing nozzle diameter. When the nozzle diameter  
Figure 5: Changes in the peak pressure, muzzle velocity, total barrel time, and gas mass increment in barrel with different nozzle diameters: (**a**) \(p_{m}\)–\(d\) and \(v_{0}\)–\(d\) curves; (**b**) \(t_{g}\)–\(d\) and \(\Delta m\)–\(d\) curves. The blue dashed line is the value of the initial pressure in the gas cylinder \(p_{0}\).  
is more than half of the launcher caliber, the gas transfer efficiency is above 60.0% and increases slowly, and the launch efficiency is nearly 20.0% and also increases slowly. Hence, a larger nozzle size should be selected to ensure a higher efficiency of the launch system.