# Launch Dynamic Simulation of a Compressed-Air Launcher for Fire Suppression
## 4 Results and Discussion  
A computational simulation program was developed on the Microsoft VC++ platform to solve the launching parameters of the compressed-air-driven projectile based on the dynamic model described above. The finite-difference method and Runge-Kuta method were employed to ensure the calculation accuracy of the time domain and space domain, respectively. The simulation parameters are provided in Table 1.  
Figure 3 shows the \(p\)-\(t\), \(v\)-\(t\), \(p\)-\(l\), and \(v\)-\(l\) curves when the nozzle diameter \(d\) is 10 mm, the gas cylinder volume \(V_{0}\) is 1.0 L, the initial pressure in the gas cylinder \(p_{0}\) is 10 MPa, the loading position \(l_{0}\) is 30 mm, and the launch angle \(\theta\) is 40\({}^{\circ}\). The bore pressure exhibits a similar trend to that of the traditional gunpowder launching process. However, despite the initial pressure in the gas cylinder being 10.0 MPa, the peak pressure in the chamber reaches only approximately 2.5 MPa. This limitation arises because the total amount of high-pressure gas entering the barrel is restricted by the size of the nozzle and gas flow restrictions. Initially, the bore pressure is lower than the friction between the projectile belt and the barrel wall. The projectile remains stationary, and as the high-pressure gas is injected, the bore pressure increases rapidly. Once the bore pressure reaches a certain threshold and surpasses the friction between the projectile belt and the barrel wall, the projectile starts to accelerate, and the space behind it continues to expand. However, due to limitations imposed by the size of the nozzle and the occurrence of choking phenomena in supersonic flow, the gas flow into the chamber cannot increase indefinitely. Additionally, the contribution of the gas inflow to the pressure rise is insufficient to compensate for the pressure drop resulting from the expansion of space behind the projectile. Consequently, the bore pressure exhibits a downward trend at this stage. The total barrel time is calculated to be 19.29 ms, and the resulting muzzle velocity is measured at 85.45 m/s.  
Figure 4 displays the density and mass increment curves of the gas in the barrel behind the projectile. It is evident that the nozzle back pressure is substantial, indicating a high-pressure region. The airflow at the nozzle consistently maintains a supersonic flow state. Additionally, the gas mass increment in the barrel behind the projectile exhibits a constant rate of increase over time, as depicted by the green curve in Figure 4a. The gas density curve follows a similar trend to that of the bore pressure. These simulation results align with the findings reported in reference [14]. The calculated pressure and velocity deviation are 1.5%  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Unit** & **Value** \\ \hline Caliber & \(D\) & mm & 50 \\ Projectile mass & \(m_{p}\) & kg & 0.5 \\ Projectile accelerating distance & \(L\) & mm & 1000 \\ Initial loading position & \(l_{0}\) & mm & 10-100 \\ Nozzle diameter & \(D\) & mm & 5-40 \\ Launch angle & \(\theta\) & \({}^{\circ}\) & 20–70 \\ Initial pressure in gas cylinder & \(p_{0}\) & MPa & 0–10 \\ Gas cylinder volume & \(V_{0}\) & L & 0.1–1.0 \\ Gas constant & \(R\) & J/(kg\(\cdot\)K) & 287.06 \\ Adiabatic exponent & \(\gamma\) & & 1.4 \\ Atmospheric pressure & \(p_{a}\) & Pa & 101,325 \\ Atmospheric temperature & \(T_{a}\) & K & 300 \\ Sliding friction coefficient & \(f\) & & 0.8 \\ Young’s elastic modulus of belt material & \(E\) & GPa & 0.0078 \\ Poisson’s ratio of belt material & \(\mu\) & & 0.47 \\ Interference of the belt & \(\delta\) & mm & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
and 1.2%, under the same calculation conditions, respectively. A series of simulations were executed to discuss the effects of different parameters on the launch process.