Turbulent premixed combustion modelling using fractal geometry

The fractal geometry concept has been applied to the problem of turbulent premixed flame propagation. This approach has been based on the fact that turbulent surfaces are wrinkled over a wide range of scales, and experimental evidence shows that the scales are self-similar. Self-similarity of the scales over a wide range is the distinctive characteristics of fractal objects. A new model, derived using the fractal geometry, for the wrinkled flames (or flames-sheets) regime has been proposed. The distinct feature of the present formulation is the adoption of a variable inner cutoff scale as a function of turbulent and molecular diffusivities. With a fractal dimension of 7/3 and an outer cutoff approximating the integral length scale of turbulence, our analysis has yielded u t /u 1 ∞(u′/u 1 ) 1/2 Re L 1/4 . This model suggests a wrinkled flame structure influenced by a turbulent length scale as well as the turbulence intensity. Comparison of the predictions of the model and the experimental data from a variety of rigs shows excellent agreement despite the uncertainties involved in the measurement of the turbulence parameters, propagation velocities, and the intuitive assumptions made in the theories.