Effects of Axial Heat Conduction in the Metal Wall of a Detonator Delay Element

Abstract

We investigate the effect of axial heat conduction in the metal wall of a detonator delay element on the speed of a deflagration wave. An axisymmetric time dependent model is formulated in which the reaction rate is described by a single step kinetic equation. Numerical solutions are obtained and it is found that the flame speed is reduced below its one-dimensional adiabatic value at early times due to heat loss into the cold wall, but exceeds the adiabatic value at later times because the unreacted pyrotechnic ahead of the flame is preheated by radial conduction. These effects happen to almost cancel out for a typical 8s delay element. It is also shown that the wall temperature can exceed the decomposition temperature of the pyrotechnic leading to the onset of a radial flame. A simplified analytical model is presented which allows the wall temperature to be estimated.