Fractal dimension of premixed flames in intermittent turbulence

Abstract

In turbulent premixed flames, the fractal dimension of flame iso-surface is argued to be D=7/3 for Damköhler’s large-scale limit (Da>>1) and D=8/3 for Damköhler’s small-scale limit (Da∼O(1)) based on heuristic scaling arguments. However, such scaling arguments do not consider the effect of the intermittent nature of turbulent kinetic energy dissipation on the flame surface. In this paper, we account for the effects of intermittent dissipation on the fractal dimension of low Da turbulent premixed flames. Intermittent dissipation leads to variability in the inner cut-off, which then affects the scalar flux and total interface area. We account for these variabilities through two approaches: coarse-grained approach based on the moments of the dissipation and fine-scale analysis by adopting the multifractal formalism. We derive two corrections to the upper-limit of fractal dimension – D=8/3+3/4(1−D1/4) and D=8/3+2/3(3−D1/3). We further show that the second correction leads to an explicit dependence of the fractal dimension (D) on the scaling exponent (ξ) of the velocity structure function through the relation: D=7/3+ξ. Thus, we explicitly quantify the effect of the intermittent nature of turbulence upon low Da premixed combustion.