The Fractal Nature of Premixed Turbulent Flames

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Abstract
Two-dimensional flame structure measurements of a freely propagating premixed turbulent flame were examined for fractal character over a range of turbulent Reynolds numbers from 52 to 1431 and Damkohler numbers from 10 to 889. The fractal dimension was found to increase with u'/SL, from 2.13 at u'/SL of 0.25 to 2.32 at u'/SL of 11.9. An inner cutoff was not identified due to limited spatial resolution, however, it was shown that the inner cutoff was smaller than the Gibson scale for the conditions studied. The outer cutoff was found to occur at scales comparable to the integral scale, however, the cutoff was a gradual, rather than sharp, transition from fractal behavior. A heuristic relationship between the turbulent flame surface fractal dimension and u'/SL was developed which agrees well with the fractal dimension measurements made in this study, as well as those made in a number of different flame configurations.