The initial behaviour of a spherical explosion. I. Theoretical analysis

Abstract

The analysis of the disturbance near the source of spherical blast from a polytropic explosive in which γ = 3, given in Berry Sc Holt (1954), is generalized to apply to an explosive gas and a surrounding medium governed by any equations of state. Most of the properties established in the special case are found to be generally true. In particular, a second blast wave is shown to be a consequence of the breakdow of continuous gas flow in the neighbourhood of a singular characteristic. The complete field near the origin of b last can be determined from series expansions similar in type to those in Berry & Holt (1954). Except in the gas expansion zone the coefficients in these expansions can be expressed in simple terms. The quantity defining the first departure of the second shock from the singular characteristic is given by an expression as simple as that in the polytropic case, although its derivation presents new difficulties. The analysis shows that, for all types of explosive, the second shock is a second-order effect in term s of the square root of the time from the end of detonation. This contradicts the conclusion reached earlier by Wecken (1951) on the basis of less detailed analysis. Application to actual explosions is described in the second part of this paper.