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

摘要

The interaction of nonpremixed flamelets with acoustic pressure waves of large characteristic wavelength, central to the development of acoustic instabilities in liquid-propellant rocket engines, is investigated by evaluating the periodic response of a counterflow diffusion flame subject to a harmonic pressure variation. An irreversible step with an Arrhenius rate having a large activation energy is used to model the exothermic reaction between the fuel and the oxidizer. The interactions of the chemistry with the prescribed time-dependent pressure variations are analyzed by numerical and asymptotic methods for large values of the Zel'dovich number β » 1 measuring the temperature dependence of the heat-release rate and small values of the relative amplitude ∈ « 1 of the pressure fluctuation, with the the product β∈ assumed to be of order unity in the distinguished limit addressed. Evaluations of the local Rayleigh index for β∈« 1 indicate that finite-rate chemical-kinetic effects dominate the acoustic pressure response of strained flamelets under conditions near diffusion-flame extinction. For robust, diffusion-controlled flames, on the other hand, unsteady modifications to the outer chemical-equilibrium transport regions flanking the reaction layer are more important but produce only moderate effects on acoustic instabilities.