Acoustic Response of Near-Equilibrium Diffusion Flames with Large Activation Energies

Abstract

The interaction of non-premixed 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 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 measuring the temperature dependence of the heat-release rate and small values of the relative amplitude of the pressure fluctuation, with the product assumed to be of order unity in the distinguished limit addressed. Evaluations of the local Rayleigh index for 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.