Acoustic nearfield characteristics of a wrinkled premixed flame

Nearly all combustion systems are prone to exhibit self-excited oscillations. These oscillations are driven by means of acoustic interactions between the flame and it's acoustic near-field. This acoustic nearfield is sensitive to the shape of the flame surface. This paper analyzes the near-field acoustic characteristics of premixed wrinkled, flame fronts subjected to acoustic excitation. The flame thickness is assumed to be very small compared to the length scale of the acoustic oscillations. The values of acoustic pressure and velocity on the wrinkled flame surface are transferred to a mean reference surface by means of a Taylor's expansion. A Boundary Integral Equation describing the expectation value of the coherent acoustic pressure field in the domain of interest is derived. The flame surface wrinkling is modeled by a Weierstrass-Mandelbrot fractal function. Numerical results for 2-D dump and rod stabilized flame configurations using the Boundary Element Method (BEM) are presented. The acoustic pressure field is seen to be highly two-dimensional in the case of the wrinkled flame. The difference between the acoustic pressure on the flame surface and the wall is shown to be significant in the case of a wrinkled flame subjected to acoustic excitation from downstream for the case of the dump stabilized flame. The same is observed under upstream excitation in the case of the rod stabilized flame. The normalized flame surface acoustic impedance is found to vary monotonically from the base of the flame to the tip of the flame in the case of smooth flames (i.e., flame front with no wrinkling). The wrinkled flame however, is seen to have a nearly constant impedance variation along its surface.