On the fractal characteristics of low DamkAPGhler number flames

• Published in: Combustion and flame Vol. 160; no. 11; pp. 2422 - 2433
• Main Authors: Chatakonda, Obulesu, Hawkes, Evatt, Aspden, Andrew, Kerstein, Alan, Kolla, Hemanth, Chen, Jacqueline
• Format: Journal Article
• Language: English
• Published: 01-11-2013
• Subjects: Combustion; Fractal analysis; Fractals; Mathematical models; Premixed flames; Similarity; Supernovae; Three dimensional
• ISSN: 0010-2180
• DOI: 10.1016/j.combustflame.2013.05.007

Knowledge of the fractal properties of premixed flame surfaces can potentially be used to help develop turbulent combustion models. Here, direct numerical simulations of low DamkAPGhler number flames are used to analyse the fractal nature of the flames. Two sets of data are considered: (i) thermochemical hydrogen-air turbulent premixed plane-jet flames with detailed chemistry and (ii) thermonuclear flames in type Ia supernovae. A three-dimensional box counting method is used to investigate fractal dimension of the flame surface, characterising the self similarity of flame fronts. In the premixed flames, the fractal dimension is found to vary in time between 2.1 and 2.7. The supernovae flames in distributed combustion regimes yield fractal dimension about 2.7. The results for the maximum fractal dimensions are higher than previously reported. They are explained theoretically by a Reynolds number similarity argument which posits that the high Reynolds number, low DamkAPGhler number limiting value of the fractal dimension is 8/3. Also tested is Mandelbrotas fractal additive law which relates the fractal dimension determined in two dimensions, which is typical of experimental measurements, to that in three dimensions. The comparison of the fractal dimension in both two-dimensional and three-dimensional spaces supports the additive law, even though the flames considered do not formally satisfy isotropy. Finally, the inner-cut off is extracted from the hydrogen flames and found to be consistent in order of magnitude with Kolmogorov scaling.