Two-Reaction Steady Detonations

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Abstract
Steady, one‐dimensional detonations in an idealized, three‐component, gaseous medium with reactions A ⇋ B, A ⇋ C, proceeding with Arrhenius unimolecular kinetics are investigated by way of exemplification of the Wood‐Salsburg analysis as well as delineation of the behavior at the trouble‐some ``pathological'' locus for this special case. The analysis is detailed for the exothermic parallel‐reaction case with large disparity in the heats of reaction but results for other cases are mentioned. Stability conditions for a pathological detonation are reformulated as conditions on the parameters of the system which, though necessary, are by no means sufficient. For both the exothermic parallel‐reaction case and the consecutive‐reaction case, with the second reaction endothermic, it appears that the stability conditions are not inconsistent with the existence of a pathological solution. Numerical results for several systems at the equilibrium Chapman‐Jouguet detonation velocity are presented, including one in which the equilibrium CJ condition is inapplicable.

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