## 4 Calculation Results and Discussion
### Case 3: Flat-Nosed Projectile
Therefore, a detached BSW with high intensity is formed in front of the projectile nose. The SSW diffracts at the corner of the projectile, causing a drastic change in the flow field near the corner and producing a vortex. The vortex moves backwards along the projectile wall under the effect of the detached boundary layer flow induced by the BSW and drives the backward movement of the SSW. Additionally, the CS becomes rarefied during its propagation prior to reaching the BSW. Figure 7d represents the muzzle flow field characteristics at \(t=0.671\) ms when the BSW is about to encounter the PSW. At this point, the second blast continues to expand. Since its axial velocity is greater than that of the projectile, the gas stream surpasses the projectile base. From Figure 7c the rightward movement of the second blast and leftward movement of the SSW of the first-blast exist along the sidewall of the projectile. These two shock waves encounter and interact with each other in Figure 7d, causing the deformation of the LSW. The CS of the first blast is distorted under the effect of the BSW. Figure 7e shows the muzzle flow-field characteristics at \(t=0.736\) ms. From the principle of wave superposition, the SSW of the first-blast and that of the second blast move towards each other and maintain their respective characteristics. A disturbance is created at the point of intersection that then propagates radially. The first triple-point is caused at the point of intersection by the BSW catching up with the PSW. The velocity of the gas jet flow is far greater than that of the projectile. Therefore, the airstream behind the projectile is compressed, and the projectile base shock wave is formed. When the separated flow encounters the LSW, the wavefront is distorted. Due to the high velocity of the projectile, the intensity of the BSW is high, and the velocity and pressure of the separated flow behind the wave are also high. After the separated flow of the boundary layer is formed, a positive pressure gradient is formed on the side of the projectile. This pressure gradient drives the separation point upstream until a balance is reached. A concave reversed flow occurs at the separation point, and a separation shock wave is produced at the reversed point and intersects the LSW. Figure 7f shows the muzzle flow field characteristics at \(t=0.989\) ms when the LSW is about to catch up with the PSW. At this moment, the SSWs formed in the two blasts are combined and form a new shock wave. The disturbance causes the upper edge of the SL of the second-blast to twist. With the attenuation of the wave and the decline of the powder gas ejected from the bore, the velocity of the wave reduces. The SSW of the second blast is gradually separated from the projectile. When the projectile exits the shock cell, the shock wave diffracts at the tail of the projectile. This leads to the absorption of the CS of the second blast on the rear of the diffraction waves. After the LSW sweeps through the non-uniform region behind the PSW, the Richtmyer-Meshkov instability (RMI) phenomenon is induced and evolves with the movement of the LSW. Figure 7g shows the muzzle flow field characteristics at \(t\) = 1.091 ms when the LSW merges with the PSW and interacts with the BSW to form the second triple-point. At this moment, the first triple-point vanishes. The diffraction shock waves at the projectile base gradually converge at the axis of symmetry and form a cylindrical shock focusing effect at the projectile base. The shock waves then detach from the projectile base, gradually vanish, and eventually form a stable bottle shock wave in the muzzle region at \(t\) = 1.371 ms, as shown in Figure 7h. Moreover, the separation shock wave settles at the middle of the sidewall of the projectile. Figure 7f-h show the development of what appears to be a RMI. The RMI occurs when an interface separating two different fluids is impulsively accelerated. After the shock impact, the interface is hydrodynamically unstable and eventually turbulent mixing dominates the flow [23].