Effect of the chain initiation reaction rate on direct initiation of detonation

The effect of the initiation step of a reaction mechanism on direct initiation of a self-sustained detonation has been studied numerically. For this purpose, the reaction mechanism has been simulated with a three-step chemical kinetics model that consists sequentially of the chain-initiation and chain-branching steps, followed by chain termination. A characteristic time $\tau_I$ is defined for each step of the mechanism, which includes effects of different kinetics parameters. It is shown that $\tau_I$ is a determining factor of the minimum allowable shock pressure. It is observed that the minimum shock pressure in the decaying period of critical initiation tends to the von Neumann pressure when $\tau_I$ becomes large. As a result, at large $\tau_I$, the critical initiation becomes similar to the supercritical initiation. On the other hand, the amplification mechanism of the leading shock in the decaying period depends on $\tau_I$.