LINEAR-STABILITY OF A DETONATION-WAVE WITH A MODEL 3-STEP CHAIN-BRANCHING REACTION

The linear stability of a planar detonation wave with a three-step cha in-branching reaction is studied by a normal mode approach. The reacti on model consists of a chain-initiation step and a chain-branching ste p governed by Arrhenius kinetics, with a chain-termination step which is independent of temperature. It mimics the essential reaction dynami cs of a real chain-branching chemical system. The linear stability of the steady detonation wave to tww-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 b ifurcation parameter. This parameter determines the ratio of the lengt h of the chain-branching induction zone to the chain-termination zone within the steady detonation wave. The effect of linear transverse dis turbances is considered for two values of the chain-branching crossove r temperature: in one the planar steady detonation wave is stable to o ne-dimensional disturbances, while in the other it is unstable to such disturbances.