The structure of a steady high-speed deflagration with a finite origin

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Abstract
A theoretical study is made of the structure of a steady planar deflagration downstream of a specific origin location from which a compressible reactive gas flow emanates. The chemistry is modelled by a high-activation-energy Arrhenius reactionrate law without the introduction of an ignition temperature. Chemically derived heat addition is significant relative to the initial thermal energy of the flow. Perturbation methods, based on the limit of high activation energy, are used to construct solutions for sub- and supersonic values of the Mach number [ ] at the origin. With the exception of a thin layer adjacent to the origin in which very small changes occur, the structure of the deflagration is determined by a fundamental balance of convection, reaction and compressibility effects. Transport processes have an insignificant effect on the energetics of the flow. The upstream portion of the deflagration is dominated by an ignition event reminiscent of the induction period of an adiabatic thermal explosion. Subsequently in the neighbourhood of a well-defined ignition delay (or explosion) location a very rapid reaction takes place with order-unity changes in all the dependent variables. Compressibility effects are shown to be the source of basic limitations on the maximum temperature rise permitted in a flow with a particular value of [ ]. Chapman–Jouguet deflagrations are found to appear when the chemical heat addition is maximized for a given [ ]. Subsonic combustion is shown to exist for fairly general initial conditions at the origin. In contrast, a purely supersonic reaction is found to be possible only for specifically defined values of the initial strain rate and temperature gradient which would be difficult to control in the experimental environment.