Expanding of Fire-Ball and Subsequent Shock Wave Propagation by Explosives Detonation in Underwater

A well known problem in hydrodynamics involves the sudden release of explosion energy, concentrated in a finite volume, to surroundings with uniform density. However, only similarity solutions which have no detailed information on the behavior of the fire-ball are available on this problem. In this study, we obtain a set of analytical solutions for the time dependent radius of expanding fire-ball after explosives detonation by solving continuity, Euler and energy equations with a “polytope” assumption for the fire-ball center. Subsequent spherical shock waves developed from the fire-ball in underwater are obtained by Kirkwood-Bethe hypothesis with Tait’s equation of state for water. The pressure waves emanating from the oscillating bubble in underwater, which has a notably different time scale from the shock wave generation, are obtained using the Rayleigh equation. The calculated results of period and the maximum radius of bubble developed from the fire-ball and the pressure wave from the oscillating bubble are similar to those observed.