The effect on the timing of a detonator delay element due to detonation transmission tubin

We investigate the additional delay in the detonator delay element caused by a break in the detonation transmission tubing. In Chapter 1 we introduce the problem and give some background. In Chapter 2 we derive a system of model equations which describe the passage of a one-dimensional detonation wave along the detonation transmission tubing where the reaction is described by a single step kinetic equation. The resulting equations are a system of hyperbolic conservation laws. We then solve the equations by using TVD MacCormack method and modify these model equations by adding heat loss effect and the tube expansion effect. In Chapter 3 we consider the ignition chamber by treating it as a simple extension of the detonation transmission tubing. In Chapter 4 we derive a 1-D mathematical model for the delay element. Since the chemical kinetics of the sealer reactant is unknown to us, we then do a general study of ignition theory using the high activation energy assumption, with and without consumption of the reactant. In Chapter 5 we solve the delay element model equations by using the known kinetic of the main delay column. We discuss whether the additional delay observed in practice is a consequence of temperature variations in the ignition chamber, or of pressure variations there. In the Appendix we give a brief introduction to the hyperbolic conservation laws and their numerical methods of solution. Numerical experiments of several methods of solution of the hyperbolic conservation laws are also presented.