The dynamics of the combustion products behind plane and spherical detonation fronts in explosives

TLDR

Detonation dynamics in confined geometries have a three‑dimensional analogue. The study analyzes the dynamics of spherical detonation from a point source in an explosive. The authors apply the derived results to TNT detonations in both linear and spherical geometries using Jones & Miller (1948) data. The study finds that detonation fronts generate a progressive wave with linear velocity profiles, a fixed proportion of the burnt gas remains at rest, and radial gradients of velocity, pressure, and density diverge at the front, mirroring one‑dimensional behavior.

Abstract

The flow behind the detonation front of an explosive contained in a tube strong enough to confine the motion to one dimension is shown to be a progressive wave of finite amplitude of the type studied by Riemann. The wave is similar at all stages of its progress if the initiation of the explosion is instantaneous, the linear scale of the whole field of flow increasing at a uniform rate. If the products of combustion obey the law Pρ ¯γ = constant the distribution of gas velocity along the tube is linear. If the initiation end of the tube is closed a fixed pro­portion of the whole detonating column is at rest. This last case has an analogy in three dimensions. The dynamics of spherical detonation from a point in an explosive is analyzed. As in the one-dimensional case, a fixed proportion of the whole volume of burnt gas is at rest. The radial rate of change of the variables, velocity, pressure and density become infinite at the detonation front, but it is unlikely that this result would be true in a real explosive where the time of reaction is not zero. The results are applied in both linear and spherical cases to the detonation of T. N. T., using data given by Jones & Miller (1948).