| Abstract: | A basic understanding of the structure of the interactions between chemical and acoustic instabilities and the effects derived therefrom is sought for a medium undergoing one-step irreversible chemical reaction. Detailed examination of the acoustic-chemical system after the completion of the reaction shows the distinct presence of the chemical, acoustic, and mixed modes of instability. The chemical mode appears as a stationary yet spatially inhomogeneous entropy distribution, even though the medium initially (before reaction) is homogeneous throughout. The acoustic mode appears as a composite of both right- and left-travelling pressure or velocity waves, even though the initial acoustic wave is only right-travelling. The left-travelling wave is generated due to partial reflection or scattering as the right-travelling wave propagates in a spatially inhomogenous medium during the chemical reaction and is sustained even after the reaction is completed. The mixed modes of density and temperature fluctuations apparently retain to some degree the characteristics of both the acoustic and the chemical modes and may, under certain conditions, be dominated by either one of the modes of behavior. This is determined largely by the parameter Ω, the ratio of chemical to acoustic time scales.During reaction, it is found that the observed complicated behavior can be interpreted fruitfully in terms of the mode concept developed for the post-reaction behavior. It is observed that the temporal development of the physical fluctuating variables is dependent upon spatial position (the effect being stronger as Ω is reduced). Further, it is found that at specific values of Ω, the following effects are maximized: (a) acoustic amplification; (b) wave reflection; (c) reaction evolution enhancement.The energy contained in the fluctuations is found to be composed of an acoustic and a chemical part. The latter dominates during reaction. However, after reaction, the chemical part exactly balances any change in the acoustic part which occurs during reaction, thus resulting in no net change in the fluctuation energy. The chemical part seems to represent the loss (or gain) of mean thermal energy which was diverted by chemi-acoustic interactions into the increased (or decreased) acoustic energy of the system. |
