The convergence of combustion models and compliance with the Kolmogorov scaling of turbulence

Development of turbulent combustion models has resulted in the convergence of some of the probability density function models with models based on the effective use of the mixture fraction. These new models are global but implement localized mixing and are compliant with the laws of the inertial interval of turbulence and, consequently, are consistent with the fast chemistry and flamelet limits. This consistency can be extended to distributed premixed flames but, generally, not to premixed flamesheets. We show that turbulent scaling of premixed flamesheets is not exactly the same as the Kolmogorov scaling of turbulence and, to some extent, still remains unknown. The proposed interpretation for the scaling of turbulent premixed flames in flamesheet regimes is consistent with experiments, upholds principal elements of Kolmogorov's theory of turbulence, and can serve as a possible explanation and/or a guiding constraint for practical modeling.