Flame Fractal Dimension Induced by Hydrodynamic Instability

Premixed flames self-turbulized due to hydrodynamic instability have self-similar, fractal-like structures as evidenced by the acceleration of spherically-propagating flames. The fractal dimension of a self-turbulized premixed flame needs to be known if its apparent flame speed is to be estimated. CFD simulations of outwardly-propagating flames have been conducted to predict their fractal dimensions. There are, however, difficulties in accurately determining fractal dimension based on the flame-propagation behavior of such an outwardly-propagating flame. This paper demonstrates a newly proposed method to determine the fractal dimension based on the CFD simulation of a planar flame. The fractal dimension is computed from the dependency of apparent flame speed on the computational domain size. The computed fractal dimension well agrees with the experimental value. The box-counting method is also applied to calculate the flame’s fractal dimension. The fractal dimensions obtained by these two methods agree well, confirming the fractal nature of the self-turbulized flame.