An application of fractals to modeling premixed turbulent flames

A fractal description of the geometry of rough surfaces is applied to flamelets in premixed turbulent combustion, and a model to predict the turbulent flame speed, ut, is developed and tested against experimental data. At low to moderate turbulence levels reaction is known to occur in thin flamelets which are rough with multiple scales of wrinkling. It is hypothesized that flamelets may be represented by fractal surfaces, and the results of Mandelbrot [11] are used to find an expression for flamelet surface area valid in the limit of large velocity fluctuations relative to the laminar flame speed. The expression is then corrected for conditions away from this limit, and a prediction for ut is obtained under the assumption that flamelets propagate at the unstrained laminar flame speed, u0: utu0={[1−(1−At−14R1−34) exp(−(AtR1)14u′u0)]At14R134}D−2. D is the fractal dimension and has a value of 2.32 to 2.4 as inferred from experiment [12, 28] and by analysis [13, 14]. At = 0.37, based on turbulent pipe flow data. Comparison of predictions with the data of Abdel-Gayed, Bradley, and coworkers obtained for several different mixtures and for a broad range of turbulence conditions shows good results. While predictions are generally low, absolute values are in most cases within 30% of experimental results. A correction for flame stretch effects is proposed and model predictions are improved thereby.