Analysis of acoustic wave interactions with turbulent premixed flames

Abstract

This paper analyzes acoustic wave interactions with turbulent, premixed flames. It generalizes a previousstudy that treated the flame as a passive temperature discontinuity by accounting for the effects of pressure disturbances upon the mass burning rate. Similar to the prior study the problem is posed with an integral formulation of the wave equation and assumes that the local flame front curvature is much larger than the acoustic wavelength. Thus, it is most appropriate for considering interactions between flames and short-wavelength (e.g., high-frequency) disturbances. The analysis 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 evolving, wrinkled front. Explicit solutions are derived for the coherent field, showing that its 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. These results suggest that several differences exist between the characteristics of waves scattered from laminar and turbulent flames. With increased flame front wrinkling, the coherent field becomes increasingly independent of the temperature jump across the flame and response of the mass burning rate. This result contrasts with the strong importance of these parameters in laminar-flame-acoustic-wave interaction problems. In addition, results show that the wrinkled characteristics of turbulent flames shift the phase and reduce the amplitude of the coherent field relative to its value if the flame front were smooth: that is, they serve as a source of damping of coherent acoustic energy. This damping source is particularly significant for disturbances whose wave-lengths are on the order of or smaller than the characteristic scales of flame wrinkling.