Shock-induced chain-branched ignition

Shock-induced ignition is considered for a three-step chain-branching mechanism at large activation energies. The nature of the ignition process depends critically on the magnitude of the initial post-shock temperature relative to the chain-branching cross-over temperature. For the limits examined, the induction region is preceded by an exponentially weak initiation zone that provides relevant initial conditions for the induction phase. When the initial post-shock temperature is sufficiently close to the chain-branching temperature, ignition is characterized by logarithmic singular behaviors in the pressure and temperature perturbations and the structure has some similarities with the one-step chemistry problem. However, for larger initial post-shock temperatures, the logarithmic singularities are replaced by linear temporal growth. Suitable non-linear Clarke equations are deduced for both of these cases and numerical solutions are presented.