Acoustic response of near-equilibrium diffusion flames with large activation energies*

This paper examines the interaction of a strained-reacting mixing layer separating two impinging streams with an acoustic pressure wave of characteristic wavelength large compared to the dimensions of the mixing layer. The exothermic reaction, confined to a thin layer within the mixing region, is described with use made of one-step Arrhenius chemistry and its interaction with the pressure wave is examined with both numerical integrations and asymptotic methods for systems with large activation energies. An asymptotic formulation is provided for arbitrary values of the ratio of the acoustic amplitude ε to the inverse of the Zeldovich number β; the acoustic limit βε ≪ 1 is then considered in detail. The results are used to investigate implications towards acoustic instabilities making use of the Rayleigh index whose frequency dependence is examined. Results indicate that finite-rate effects dominate the acoustic pressure response of strained flamelets near extinction. For robust, diffusion-controlled flames unsteady modifications to the outer chemical-equilibrium transport regions produce only moderate effects.