An improved Kirkwood–Bethe model for calculating near-field shockwave propagation of underwater explosions

To calculate the near-field shockwave propagation of underwater explosions for different explosives quickly and accurately, an improved calculation model, based on the Kirkwood–Bethe theory, is proposed. Based on the detonation theory and shock jump conditions, the model establishes initial equilibrium conditions and an initial shockwave-front state of the explosion bubble interface. By incorporating a second-order Mach-precision bubble dynamics equation, the model determines the physical parameters and enthalpy change functions at the initial expanding stage in real time. By solving the isentropic flow of the enthalpy change function G at varying delay times, a functional relation was established between the enthalpy change function and the pressure at arbitrary flow points and times. The model obtained the near-field shockwave-front peak-pressure spatial distributions of underwater explosions and the pressure decay time constants at arbitrary flow points. The results indicated that the proposed method can quickly and accurately determine the near-field shockwave propagation of underwater explosions for different explosives, with satisfactory agreement with experimental data. The proposed method relates the explosive detonation, explosion bubble expansion, and shockwave propagation, thus connecting the explosive parameters with the shockwave front state parameters.