## 4 Results and Discussion
### Comparison of Simulation and Experimental Results  
Figure 7 shows the piston speed versus the travel distances for the three cases, including the experimental and numerical results. The numerical results agree well with the corresponding experimental ones using the above models; and the differences are within \(\pm\) 10%, which is acceptable for the two-stage gas gun simulation. The numerical result without the piston-wall friction term for Case 1 is also shown in Figure 7. The results that include the piston friction are only 5% lower than \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & & **1** & **2** & **3** \\ \hline \multirow{2}{*}{Detonation tube} & Mixing molar ratio, \(\mathrm{H_{2}\mathcal{O}_{2}}\) & \multicolumn{3}{c}{3:1} \\  & Pressure (MPa) & 1.5 & 2.0 & 2.7 \\ \hline \multirow{3}{*}{Pump tube} & Gas & \multicolumn{3}{c}{\(\mathrm{H_{2}}\)} \\  & Pressure (MPa) & 0.8 & 0.8 & 0.45 \\ \cline{1-1}  & Piston mass (kg) & \multicolumn{3}{c}{10.44} \\ \cline{1-1}  & Rupture pressure (MPa) & 45 & 45 & 75 \\ \hline Launch tube & Projectile mass (g) & 19 & 100 & 31 \\ \hline \multirow{2}{*}{Exp. CFD} & \multirow{2}{*}{Projectile velocity (m/s)} & 2481 & 2260 & \multirow{2}{*}{4854} \\  & & 2839 & 2601 & & \\ \cline{1-1}  & Relative error (\%) & 14.4 & 15.1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Operating conditions in the experiments and simulation. Figure 6: Speed and pressure at the base of the piston for Case 1 and three grid resolutions. those that do not include the piston friction. Thus, the values of \(L_{f}\) and \(\Delta r\) (defined in Section 3.3) have only small influences on the piston speed in the simulation. Unlike a gas gun that is driven by high-pressure gases, which results in smooth changes in the piston speed, the detonation-drive gas gun produces fluctuations in the piston speed, as shown in Figure 7. This result is attributed to the complex interior ballistic process in the gas gun driven by detonation. The direct ignition at the upstream end in the detonation tube leads to a stable detonation wave traveling downstream. The detonation wave reflects from the base of the piston, generating a shock wave, and the motion of the piston generates compression waves. This shock wave then reflects several times between the end of the detonation tube and the base of the piston, which subjects the piston to a series of impulse loads, leading to fluctuations in the piston speed. The pressure at the base of the piston and projectile are shown in Figure 8; fluctuations also exist due to the shock wave reflections. The fluctuations are extensive in the initial stage and gradually weakened over time. However, it should be noted that the pressure at the base of the projectile was actually the pressure on diaphragm II before 82.8 ms. Since the projectile was placed close to diaphragm II, we use this pressure to monitor the pressure on diaphragm II or the pressure histories at the base of the projectile at the same time. In the simulation of Case 1, diaphragm II ruptures at 82.8 ms, and the projectile exits the launch tube at 88.2 ms; the corresponding times are 56.7 ms and 59.8 ms for Case 3, respectively. Thus, the pressure histories from 0 to 90 ms for Case 1 and 0 to 60 ms for Case 3 are chosen in the present discussion. Figures 9 and 10 show the experimentally measured and computed pressure histories at the monitoring points in the pump tube. In Figure 9, the pressure histories of P3  
Figure 8: Simulated pressure and temperature at the base and front of the projectile or piston for Case 1. Figure 7: Piston speed versus piston travel distance. and Case 3. The first significant pressure increase was due to the passing of the piston or the arrival of the high-pressure detonation gas. The pressure changes following the increase indicate the complicated gas-dynamic processes between the piston base and the left wall of the facility. The simulation results show a similar trend as the experimental results.