## 4 Results and Discussion
### Comparison of Simulation and Experimental Results
Additionally, the pressure value of the experiment agrees well with that of the simulation in the initial stage. However, the differences increase over time. It is believed that this result is attributable to a transducer problem rather than a code problem and is related to the influence of the high-temperature gas on the piezoelectric pressure transducers, which are supposed to operate at a temperature of 353 K. However, the temperature of the detonation gas is higher than 3000 K, and the temperature of the light gas also increases as it is compressed, as shown in Figure 8. The temperature of the light gas at the front of the piston exceeds 400 K at 60 ms for Case 1, and the maximum temperature exceeds 800 K. The temperatures are even higher for Case 2 and Case 3 because of higher piston speeds. Thus, the pressure transducer is exposed to high-temperature gases. Pressure differences occur and increase after a specific time. This phenomenon is also observed in Figure 10. More suitable high-temperature pressure sensors will be used in the future to validate the numerical results. The pressure changes due to the geometric variation in the longitudinal direction of the piston (see Figure 3b) are difficult to simulate. Thus, the pressure between the period of piston front and piston rear in the simulation is set equal to the initial pressure in the pump tube, i.e., 0.8 MPa for Case 1, as shown in Figure 10a between the time moment of 68.8 ms to 70.7 ms. However, they do not participate in the calculation and have no influence to the simulated results. Additionally, it can be found that there are larger discrepancy between CFD and Exp for P6 and P9 sensor after the passing of the piston. The reason may attribute to the inaccurate estimation of the energy exchange between the high temperature detonation gas (exceeds 3000 K) and the tube wall. This influence may go greater as time increases. Figure 10: Pressure histories for Case 1. (**a**) P6 sensor; (**b**) P9 sensor. Figure 9: Pressure histories of the P3 sensor. (**a**) Case 1; (**b**) Case 3. The launch tube has a relatively small diameter, and it would be complicated to measure the projectile velocity along the tube wall. Thus, only the muzzle velocity value is measured in the experiments; the results for Case 1 and 2 are listed in Table 1. However, in the simulation, we can obtain the projectile speed versus the projectile travel distance, as shown in Figure 6:0 The friction between the projectile and the wall is considered to be similar to that between the piston and the wall, as described in Section 3.3. The simulated projectile velocities at the exit of the launch tube are 2481 m/s, 2260 m/s, and 4854 m/s for Case 1, Case 2, and Case 3, respectively. The measured projectile velocities (Table 1) are 2481 m/s and 2260 m/s for Case 1 and Case 2, respectively. These values are about 14% lower than the numerical results. One reason for the difference is the rough estimate of the rupture pressure of diaphragm II. Scored diaphragms are used, and their rupture pressures are challenging to obtain experimentally under such a high pressure. The influence of the high-temperature light gas on the rupture pressure is also difficult to determine. Thus, only a semi-empirical formula is used to estimate the rupture pressure. The rupture pressure is 45 MPa for Case 1 and Case 2 and 75 MPa for Case 3. The influence of the rupture pressure on the projectile velocity is shown in Figure 6:1 Rupture pressures of 30 MPa, 45 MPa, and 75 MPa are considered for diaphragm II, and the other parameters are the same as in Case 1. A higher rupture pressure delays the rupture of diaphragm II, resulting in higher gas compression of the light gas; hence, the light gas provides a higher driving capability. The muzzle projectile velocities are 2553 m/s, 2601 m/s, and 2742 m/s for the three cases, respectively. In a future study, we will use simulations to model the rupture process of the diaphragm and improve the present method.