Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model: 1. A priori study and presumed PDF closure

Abstract

Previously conducted studies of the flamelet/progress variable model for the prediction of nonpremixed turbulent combustion processes identified two areas for model improvements: the modeling of the presumed probability density function (PDF) for the reaction progress parameter and the consideration of unsteady effects [Ihme et al., Proc. Combust. Inst. 30 (2005) 793]. These effects are of particular importance during local flame extinction and subsequent reignition. Here, the models for the presumed PDFs for conserved and reactive scalars are re-examined and a statistically most likely distribution (SMLD) is employed and tested in a priori studies using direct numerical simulation (DNS) data and experimental results from the Sandia flame series. In the first part of the paper, the SMLD model is employed for a reactive scalar distribution. Modeling aspects of the a priori PDF, accounting for the bias in composition space, are discussed. The convergence of the SMLD with increasing number of enforced moments is demonstrated. It is concluded that information about more than two moments is beneficial to accurately represent the reactive scalar distribution in turbulent flames with strong extinction and reignition. In addition to the reactive scalar analysis, the potential of the SMLD for the representation of conserved scalar distributions is also analyzed. In the a priori study using DNS data it is found that the conventionally employed beta distribution provides a better representation for the scalar distribution. This is attributed to the fact that the beta-PDF implicitly enforces higher moment information that is in excellent agreement with the DNS data. However, the SMLD outperforms the beta distribution in free shear flow applications, which are typically characterized by strongly skewed scalar distributions, in the case where higher moment information can be enforced.