Instability criterion of one-dimensional detonation wave with three-step chain branching reaction model

One-dimensional detonation waves are simulated with the three-step chain branching reaction model, and the instability criterion is studied. The ratio of the induction zone length and the reaction zone length may be used to decide the instability, and the detonation becomes unstable with the high ratio. However, the ratio is not invariable with different heat release values. The critical ratio, corresponding to the transition from the stable detonation to the unstable detonation, has a negative correlation with the heat release. An empirical relation of the Chapman - Jouguet Mach number and the length ratio is proposed as the instability criterion.