Abstract
The investigation of idealized detonations in a two-reaction A⇄B, A⇄C medium is extended to consideration of the one-dimensional piston problem for cases in which strictly steady flows are not possible. On easing the steady-state assumption so as to allow two (steady) waves of different velocity, the weak detonation can no longer be excluded on the basis of ``structural stability''. For the parallel-reaction case in which both reactions are exothermic but the first is at least twice as energetic as the second, the weak detonation solution is proposed when the second reaction is sufficiently slow. Slight overdrive is shown to yield two-wave detonations involving either a diffuse shock or a second detonation wave following the weak detonation. At sufficient overdrive the two waves merge into a strong detonation. The regimes of relative rate and piston velocity appropriate to the various situations are given numerically for several values of the other parameters.
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