The dynamical limit of one-dimensional detonations

The stability problem of one-dimensional piston supported gaseous detonations has been examined via both linear stability analysis and direct numerical simulation. It has been demonstrated that for other parameters being fixed, there are two critical values of the reduced activation energy, Ec1 and Ec2, according to which the propagation of planar detonation may be classified into three regimes: (i) when the reduced activation energy Ea is smaller than the first critical value, Ea<Ec1, the propagating detonation is stable: (ii) when Ec1<Ea<Ec2, the galloping oscillations appear in the propagation of detonations; (iii) when Ec2<Ea, the period of oscillations becomes infinitely large, the planar detonation cannot propagate via autoignition mechanism. Regime (iii) has never been pointed out in previous works. This regime occurs since the strong hydrodynamical instability effect makes the leading shock decay to a very low level which is too weak to cause a rapid autoignition.