ACCUMULATING SEQUENCE OF IGNITIONS FROM A PROPAGATING PULSE

Some surprising effects are seen in studying numerically the evolution of a propagating pulse of pressure in a medium reacting via a one-step exothermic Arrhenius reaction. The length and amplitude of the pulse are taken to be large enough for steepening effects to be important and for enhanced reaction to lead to a substantial reduction in ignition time. The evolution proceeds through a repeated sequence of similar stages involving: shock-formation and growth; ignition behind the shock; and the generation of another propagating pressure pulse. Substantial unsteady behavior is seen to be engendered by the entropy released through shock formation. A number of unsteady reignitions are seen to culminate in a pressure-peak, substantially higher than the von Neumann spike of a Chapman-Jouget wave, during the formation of a transient overdriven detonation; this decays subsequently towards a Chapman-Jouget state. It is conjectured that this sort of evolution may well be generic to ignition via a range of pressure-pulses in state-sensitive systems. A saturation of, or relative reduction in, the reaction's thermal sensitivity ultimately prevents the reignition process after shock-formation from happening quickly enough to continue its repetition. As such, the behavior should be strongly dependent on the nature of the chemical model and is likely to be modified significantly by changes in the chemical mechanism.