Statistical analysis of the fractal nature of turbulent premixed flames

Abstract

Since the introduction of fractal geometry, it has been widely accepted that naturally arising geometries governed by a nonlinear process exhibit fractal aspects. Numerous measurements on interfaces subject to turbulent motion demonstrated that those surfaces indeed display a fractal nature. Turbulent premixed flame surface is an example of such an interface. Past fractal analyses of turbulent flames emphasized fractal dimensions that were retrieved from tomographic images of the flames. Aside from confirming that the turbulent flame is indeed fractal-like, the use of the fractal dimension was relatively limited. Attempts were made to incorporate the fractal dimension into the modeling of turbulent premixed flames but the results were inconclusive. In the present study, we attempted a statistical approach in the fractal analysis of turbulent flames in the hope of retrieving additional information that can correlate the fractal dimension and flame properties. The present investigation was partly triggered by the finding that a wide variation of fractal dimension existed among measurements. Using previous measurements on turbulent flames, the statistical analysis resulted in clear indication of Damkohler number effect on fractal dimension on top of the turbulent intensity and laminar burning velocities which were regarded as two major parameters determining the fractal dimension of turbulent flames. The statistical analysis also explicitly showed the effect of intermittency on the distribution of fractal dimension. The proposed method was applied for analyses of four existing measurements.