A new blast wave scaling

Abstract

A new scaling is developed for both air and underwater blast waves based on dimensional analysis. The new length, time, velocity, and pressure scales are based on three control parameters: the energy release of the explosive $$E_{_\mathrm {HE}}$$ , the density of the undisturbed ambient medium $$\rho _{_0}$$ , and the speed of sound in the undisturbed ambient medium $$C_{_0}$$ . The shock wave propagation is divided into two regimes based on its decay characteristics, and the resulting control parameters are different in each regime. For strong shocks with Mach numbers $$M_{_\mathrm {SW}} \gtrsim 5$$ , the increase in the shock wave radius R with time t is approximated by a power law with an exponent of 2/5 as previously described by G. I. Taylor. Shock propagation in this regime is shown to not be a function of the ambient medium sound speed, but only the ambient medium density, explosive energy release, and time. For weak shock waves with Mach numbers $$M_{_\mathrm {SW}} \lesssim 5$$ , the shock wave radius increase with time can be approximated by a linear function plus a logarithmic-type correction which decays to a sound wave at sufficiently long time. Shock propagation in this regime is scaled according to the medium’s ambient density, sound speed, explosive energy release, and time. The new scaling is compared to, and agrees well with, published experimental data for air and underwater blasts, from milligram explosions to nuclear blasts. The new scaling improves upon traditional Hopkinson and Sachs scaling by relating shock propagation in liquid and gas environments, allowing them to be scaled to a single functional relationship. The functional scaling relationships developed here are dimensionless.