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Remarks on diffusionless combustion

Classical studies of the dynamics of compressible media incorporate the possibility of exothermic actions in the field via the use of model combustion waves treated as discontinuous, and hence quasi–steady, phenomena. The latter are familiar under their broad titles of plane detonation waves, which travel at supersonic speeds, and deflagrations, which travel subsonically. Such deflagrations are not like conventional premixed flames insofar as laminar heat conduction and mass diffusion have no part to play in them; it is convenient to categorize these combustion waves as diffusionless. With the inclusion of adiabatic shock waves and contact discontinuities, a whole range of formally unsteady phenomena can be analysed with the aid of these discontinuous combustion–wave models. Such skeletal theoretical ideas can be instructive, but they do suffer from a serious difficulty since they do not relate speeds of propagation of the combustion waves to the local environments that they inhabit, and it is necessary to call on empirical evidence to close the theory. The present paper shows that these difficulties can be overcome by adopting an asymptotic parameter–perturbation approach to the construction of a self–contained rational theory of diffusionless combustion. It is demonstrated that asymptotic ideas are intrinsic to the classical studies of gas dynamics. Then logical pursuit of asymptotic thinking helps to consolidate the theory into a complete and consistent form, banishes the need for empiricism and sheds light on the physics of compressible reacting flows. The latter is exemplified here with an examination of the ephemeral character of weak detonations and their role in the birth of strong detonation waves.