Numerical Study of Detonation Instability for a Two-Step Kinetics Model

The stability of CJ detonations has been investigated numerically with a two-step kinetics model. The reaction model consists of a non-heat release induction step, followed by an exothermic step. Both steps are governed by the Arrhenius kinetics model. The effect of activation energies associated with these steps on the detonation front behavior has been studied. This study was arranged in two stages. At each stage, one of the activation energies was kept constant and the other one was changed. In the steady detonation structure, the activation energies of the first and second steps (Ea_1, Ea_2) control the induction and reaction lengths, respectively. Increasing Ea_1 (for a fixed Ea_2) increases induction length and destabilizes a detonation, the same behavior as a one-step model. Increasing Ea_2 first increases reaction length and has a stabilizing effect (i.e., the amplitude of oscillation decreases). Further increasing Ea_2 has a destabilizing effect. The present study shows that the ratio of the reaction length to the induction length characterizes general features of detonation stability."