FAST DEFLAGRATION WAVES.

The analysis of steady plane deflagration waves invariably starts from the combustion approximation, i. e. , equations for the leading nonconstant terms in Mach-number expansions. Even then, explicit formulas can only be obtained in the limit of large activation energy. There are circumstances, however, notably the transition from deflagration to detonation, when the Mach number is not vanishingly small; this paper gives a description, again using activation-energy asymptotics, of such fast deflagrations. The principal result is not limited to Arrhenius kinetics, being a formula for the Mach number as a function of an ignition temperature near which the reaction is supposed to go very rapidly to completion. Such behavior can be exhibited by Arrhenius kinetics for large activation energy, the model for which the structure of the thin reaction zone and its associated perturbations outside are calculated. The calculations reveal a leakage of reactant through the zone, with its ultimate consumption over exponentially large distances downstream (exponential tail), and a 'Mach layer' behind the reaction zone for small Mach numbers, in which a velocity adjustment takes place; both of these are missed by the combustion approximation.