Acoustic-kinetic interactions in an irreversibly reacting medium

Abstract

Acoustic-kinetic coupling in a gaseous medium undergoing an exothermic irreversible reaction with Arrhenius kinetics is studied in both the quasi-steady and non-quasi-steady regimes. For the quasi-steady limit (high acoustic frequency or slow reaction) an approximate analytical solution employing a Sylvester expansion is obtained in terms of four normal modes which permits critical examination of the acoustic-kinetic coupling. The amplification or attenuation behaviors and the propagation speeds are characterized by analytical expressions for density, entropy, and concentration fluctuations. It is shown that non-acoustic oscillations are possible; the existence of a sound wave reflection effect is indicated; and acoustic wave instigation of chemical instability is predicted. The instantaneous amplitudes, phases, and speeds of propagation of density, velocity, and pressure fluctuations are studied numerically by means of a transformation for both the quasisteady and non-quasi-steady cases. In the quasi-steady case, all fluctuations have nearly equal phase and propagate at nearly the frozen isentropic speed of sound. However, their amplification characteristics are, in general, different due to the temporal variation in acoustic frequency and acoustic-kinetic interaction. In the non-quasi-steady case, the instantaneous amplitudes, phases, and speeds of propagation oscillate about base lines very close to their respective quasi-steady limit curves; an indication that frequency-dependent selective amplification and dispersion effects in wave packets are small. Furthermore, the instantaneous phases and speeds of propagation are different for the different fluctuating variables. The instantaneous amplification or attentuation of density fluctuations is shown to be dependent upon the velocity-density fluctuation phase difference. From an acoustic-energy study, the chemical reaction is accelerated by the presence of fluctuations for all exothermic reactions considered. Energy transport during reaction between mean sensible internal energy and mean kinetic energy is discussed.