Assessment of various models of scalar dissipation rate by use of DNS of a counterflow flame

The basic idea of the flamelet model is to represent turbulent flames as an ensemble of laminar flamelets, which are described by one-dimensional transport equation. The key parameter appearing in the flamelet equation is the conditional scalar dissipation rate, which is usually modeled as a function of the mixture fraction variable in various forms. In this study, the accuracy and validity of the existing models are assessed by using direct numerical simulation data for turbulent counterflow flames. Post-processing and filtering of the data allowed a comparison of four models for the scalar dissipation rate. It was found that neither model gives satisfactory accuracy in predicting the mean scalar dissipation rate. Once the analysis was limited to points close to stoichiometric compositions, the correlation remained qualitatively the same with significant scatter. We can assume therefore, that the errors are not coupled with the flame. On the other hand, the turbulence parameters used in the models seem to be the main source of discrepancies. Further analysis of the results showed that the best correlation can be found for mean scalar dissipation rate and for gradient of mean mixture fraction Z. It is especially apparent for smaller filter sizes. One can expect such behavior, because downsizing the filter leads to DNS-type model, when filter size is smaller that the smallest turbulence scale. The presented study provides a good background for building sub-model of the mean scalar dissipation rate for LES schemes.