Pressure disturbances of Different Length Scales Interacting with Conventional Flames

The theory of large activation energy asymptotics is used to model the interaction of pressure disturbances characterised by different length scales with conventional flames. Byconventional flames it is understood that the deflagration Mach number is low and of the order of where 0 is the non dimensional activation energy and s is a positive power arising from the detail of a (global) kinetic scheme. By denoting the paper explores the coupling that exists between pressure disturbances and flames for medium to short wavelengths. that is with N in the range M −l to 1. The work complements that which has mainly been achieved assuming N ≫ M −1 (long wavelengths). As N becomes smaller the coupling from pre-heat and chemical zones becomes more pronounced. This work first deduces jump conditions across the flame zone for N ≈ M −1 with density variations included (up to now these have been ignored). The foundation is then laid for N ≈ 1/(02 M) (i.e. shorter wavelength) coupling and it is shown that a different unsteady flame structure equation is obeyed. This equation is solved for the special case of low amplitude. harmonic disturbances. and a maximum amplitude of oscillation is predicted.