Linear stability of a detonation wave with a model three-step chain-branching reaction

The linear stability of a planar detonation wave with a three-step chain-branching reaction is studied by a normal mode approach. The reaction model consists of a chain-initiation step and a chain-branching step governed by Arrhenius kinetics, with a chain-termination step which is independent of temperature. It mimics the essential reaction dynamics of a real chain-branching chemical system. The linear stability of the steady detonation wave to two-dimensional disturbances is studied with the chain-branching crossover temperature, i.e., the temperature at which chain-branching and chain-termination rates are equal, as a bifurcation parameter. This parameter determines the ratio of the length of the chain-branching induction zone to the chain-termination zone within the steady detonation wave. The effect of linear transverse disturbances is considered for two values of the chain-branching crossover temperature: in one the planar steady detonation wave is stable to one-dimensional disturbances, while in the other it is unstable to such disturbances.