Coherent acoustic wave amplification/damping by wrinkled flames

The objective of this paper is to determine the conditions under which a monochromatic acoustic wave incident upon a wrinkled flame is amplified or damped. Recent experiments and analysis have demonstrated that the wrinkled characteristics of the flame act as a source of damping of coherent acoustic energy. This coherent energy is fed into spectrally broadened, incoherent acoustic oscillations. It is also known, however, that acoustic disturbances generate fluctuations in the flame burning velocity and surface area that amplify the acoustic field. Thus, the overall energy in the coherent field depends upon the relative balance between these competing amplification and damping processes. This paper describes an analysis that incorporates these competing processes to determine the conditions under which either dominates. alysis includes such factors as the response of the mass burning rate to acoustic perturbations, the temperature change across the flame, and the geometric complexities of the temporally evolving, wrinkled front. Solutions show that acoustic wave amplification/damping characteristics are controlled by the wavelength of the disturbance, the probability density function of the flame front position and orientation, the incident wave angle, the temperature jump across the flame, and the response of the mass burning rate to acoustic perturbations.