An extended flame index partitioning for partially premixed combustion
Résumé
Compared to partially premixed combustion (or combustion of non-homogeneous reactants in general), fully premixed and diffusion flames represent only two asymptotic limits of combustion modes. However, the deep knowledge accumulated over the years on these two elementary and archetypal flame prototypes is such that they remain the cornerstone and reference building blocks of most combustion modeling proposals. Therefore, from a general point of view, being able to distinguish between premixed and non-premixed modes of combustion thanks to a flame index appears as a quite appealing but challenging task that still concentrates many research efforts. Indeed, the availability of such an index is not only appealing to proceed with the analysis of either experimental or computational data issued from DNS (or highly resolved LES) databases. It is also an essential ingredient to elaborate advanced flamelet-based multiregime combustion models on the basis of single regime tabulated flamelet databases. In the present study, a new definition of the premixedness index ζPF is proposed for partially premixed combustion. It is based on a weighted form of the cross-scalar dissipation rate of the mixture fraction Yξ and progress variable Yc, i.e. quantities that have been previously identified as relevant parameters to describe partially premixed combustion regimes. The relevance of the corresponding index is assessed through a detailed computational procedure that includes three successive validation subsets: counterflow flames (including premixed, rich partially-premixed, and diffusion flames), (ii) stabilized triple flames for three distinct values of the inlet mixture fraction gradient, and finally (iii) unsteady flame kernel developments in non-homogeneous mixtures of fresh reactants, which are characterized by various initial levels of the segregation rate between the fuel and oxidizer. The proposed premixedness index ζPF and its counterpart ζDF=1−ζPF are used as the weighting coefficients between tabulated premixed flamelets (TPF) and tabulated diffusion flamelets (TDF) data, which have been parameterized as functions of Yξ and Yc. It is noteworthy that, in contrast to some previous proposals of the literature, the present flame index does not require the consideration of any other quantities in addition to those already used to parameterize the flamelets databases, i.e. Yξ and Yc. The validation procedure makes use of steady and unsteady processes with a priori and a posteriori analyses. In both cases, the comparisons between the results obtained with the proposed flame partitioning and detailed chemistry (DC) computations lead to a satisfactory level of agreement and, from a general viewpoint, the level of agreement is better than the one obtained with either premixed or diffusion flamelet-based models.
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