Axial distribution of fragment velocities from cylindrical casing with air parts at two ends

In practical applications of cylindrical explosive-filled casing, non-explosive materials or structures need to be filled at two ends, which make the ends of the casing have no corresponding explosive charge drive. If the non-explosive materials or structures are regarded as air, it is called cylindrical casing with air parts at two ends. The casing of air parts at two ends will be accelerated by the shock waves and detonation products generated from explosive charge, which cannot be predicted by Gurney formula because the mass ratio of explosive charge to metal casing is 0. In the present work, according to theoretical analysis and simulation, it was found that the existence of air parts at two ends would have no effect on the velocity distribution of fragments generated from the casing with explosive charge. In addition, the fragment velocities generated from air parts decreased exponentially with the increase of the distance from two ends, and the fragment velocities generated from air part at non-detonation end would also present an exponential decay with the increase of the length of air part at non-detonation end. A new formula was proposed to predict the axial distribution of fragment velocities of cylindrical casing with different length of air parts at two ends, which was detonated at one end. The proposed formula was further validated by experimentally verified numerical simulations, and the results showed that the average relative error was no more than 6.28%, RMSE was no more than 60.23 m/s, and R_adj ² was more than 0.958, which indicated that the new formula could predict the axial distribution of fragment velocities very well. This work could provide reference for the theoretical analysis and the design of similar warhead.