Theory of High Frequency Acoustic Wave Scattering by Turbulent Flames

This paper describes an analysis of acoustic wave scattering by turbulent premixed flames with moving, convoluted fronts that have random and possibly fractal characteristics. Such interactions play a role in the characteristic unsteadiness observed in turbulent combustion processes. The problem is posed with an integral formulation of the wave equation and assumes that the smallest scales of flame wrinkling are much larger than the acoustic wavelength. Thus, these results apply to high frequency (short wavelength) wave scattering. Explicit solutions for the spatial and temporal characteristics of the scattered field are derived for cases where the characteristics of the flame surface are Gaussian. These characteristics are investigated for flames with single, multiple, and continuous (e.g., fractal) scales of wrinkling. It is shown that the spectral characteristics of the waves scattered from weakly corrugated flames are the same as those of the incident frequency shifted spectrum of the flame front position. Thus, these results suggest that scattering measurements can provide information about the spectrum of the flame front position. It is also shown, however, that as the flame roughness increases, the spectral characteristics of the scattered waves become increasingly scrambled relative to those of the flame itself, and thus, provide less information about the temporal characteristics of the flame’s movement. The paper closes with a discussion of additional possibilities for using the integral equation approach used in this paper to assess other characteristics of acoustic wave—turbulent flame interactions. © 2001 by The Combustion Institute