A general flamelet transformation useful for distinguishing between premixed and non-premixed modes of combustion

The flame index was originally proposed by Yamashita et al. as a method of locally distinguishing between premixed and non-premixed combustion. Although this index has been applied both passively in the analysis of direct numerical simulation data, and actively using single step combustion models, certain limitations restrict its use in more detailed combustion models. In this work a general flamelet transformation that holds in the limits of both premixed and non-premixed combustion is developed. This transformation makes use of two statistically independent variables: a mixture fraction and a reaction progress parameter. The transformation is used to produce a model for distinguishing between premixed and non-premixed combustion regimes. The new model locally examines the term budget of the general flamelet transformation. The magnitudes of each of the terms in the budget are calculated and compared to the chemical source term. Determining whether a flame burns in a premixed or a non-premixed regime then amounts to determining which sets of these terms most significantly contribute to balancing the source term. The model is tested in a numerical simulation of a laminar triple flame, and is compared to a recent manifestation of the flame index approach. Additionally, the model is applied in a presumed probability density function (PDF) large eddy simulation (LES) of a lean premixed swirl burner. The model is used to locally select whether tabulated premixed or tabulated non-premixed chemistry should be referenced in the LES. Results from the LES are compared to experiments.