Numerical calculations!of the bubble pulsation forces of underwater explosions

Near-field underwater explosions can be divided into three phases: explosion of charges;generation and propagation of blast waves;formation and pulsation of bubbles.Although the peak value of the bubble pulsation pressures is relatively small compared to that of the shock waves,the attenuation of the bubble energies is very slow compared with the shock waves.Because of this,their influences on a structure cannot be neglected.We derived an improved equation for bubble pulsation and pressure distribution in an underwater explosion,considering energy losses and the effects of virtual forces and bubble energies on the characteristics of air bubble pulsation.Then the diameter,period,and velocity of bubble pulsations were calculated using the Runge-Kutta numerical method.The calculated results are in good agreement with those obtained in experiments,indicating that the suggested method accurately describes the real situation of bubble pulsation.Our research results show that both the blast wave and the bubble pulsation pressures contribute to near field structural damage.