## 3 Computational Modeling
### Simulation Results
#### 3.3.2 Comparison between Experimental and Numerical Results  
To further verify the reliability of the FE model, a comparison between the experimental and the numerical results is performed. Four variables are compared: the peak incident pressure, the blast arrival time, the projectile velocity at the tube's exit, and \(\Delta t\). Figure 18 shows a comparison between experimental and numerical data of the TNT equivalent peak pressures and blast arrival times at 1180 mm from the center of detonation for 10, 20, and 30 g spherical explosive charges. The solid and dashed curves represent the experimental and numerical pressure-time history curves, respectively. The relative error in the peak overpressures obtained by FE model and the tests ranges between \(-23.11\%\) and \(-4.72\%\) while for the blast arrival time it ranges between \(+6.25\%\) and \(+8.33\%\). The largest differences between the experiments and the simulations in blast arrival time and peak pressure are 60 \(\upmu\)s and 0.46 MPa, respectively. Figure 18 shows that the simulation tends to under-estimate the peak pressure and over-predict the blast arrival time. This is not surprising knowing that the physics of the simulation is not fully able to capture the irregularity of the fire ball development inside the tube. The numerical pressure-time histories show a less sharp decay during the positive phase duration when compared to the experimentally recorded pressure profiles. Figure 19 shows a comparison between experimental and numerical simulation results of the projectiles velocities at the tube's exit (1200 mm) for the detonation of 10, 20, and 30 g explosive charges. The solid and dashed curves represent the simulated projectile velocities as a function of time for 5 and 7 mm diameter projectiles, respectively. Each curve tip-end corresponds to the projectile arrival time to the tube's exit. Corresponding experimental results for the projectile velocities are given for 5 and 7 mm projectile diameter in terms of square and circle error bars, respectively. The relative error in projectile velocities obtained by the physical blast tests and the corresponding simulations ranges between \(+11.63\%\) and \(+27.39\%\). This error margin is not surprising knowing that the parameters in the physical detonation such as projectile position in the charge, exact detonator position, charge surface irregularities and imperfect sphericity of the explosive charge are all ideally represented in the computational model. Figure 17: A graph of a typical projectile velocity evolution from the moment of detonation until its arrival at the tube’s exit (case of 30 g of C4 and 7 mm projectile diameter). Figure 20 shows the experimental and numerical simulation results of the time interval at the tube's exit. The mean \(\Delta t\) underestimation for the 5 and 7 mm diameter projectiles amounts to 17.04% and 16.64%, respectively. This error margin could be due to the limited capability of the simulation to reproduce the exact projectile's deformation resulting from the explosion. In the physical blast tests, it is found that some of the recovered steel spheres exhibited a mass reduction due to deformation and partial fragmentation. This means that the blasted samples gained additional velocity as compared to their numerical counterparts. The change in the projectile's velocity alters the projectile's arrival time to the tube's exit and consequently the time interval \(\Delta t\). In conclusion, a good agreement between the simulation results and the experimental data is found. The numerical model is able to reproduce the peak pressures, the blast and projectile arrival times, the projectile velocity, and the time interval. Figure 19: Comparison between experimental and numerical simulation results of the projectiles velocities at the tube’s exit (1200 mm) for detonation of 10, 20, and 30 g spherical explosive charges and 5 and 7 mm projectile diameters.