Filtered Reaction Rate Modelling in Moderate and High Karlovitz Number Flames: an a Priori Analysis

Direct numerical simulations (DNS) of statistically planar flames at moderate and high Karlovitz number (Ka) have been used to perform an a priori evaluation of a presumed-PDF model approach for filtered reaction rate in the framework of large eddy simulation (LES) for different LES filter sizes. The model is statistical and uses a presumed shape, based here on a beta-distribution, for the sub-grid probability density function (PDF) of a reaction progress variable. Flamelet tabulation is used for the unfiltered reaction rate. It is known that presumed PDF with flamelet tabulation may lead to over-prediction of the modelled reaction rate. This is assessed in a methodical way using DNS of varying complexity, including single-step chemistry and complex methane/air chemistry at equivalence ratio 0.6. It is shown that the error is strongly related to the filter size. A correction function is proposed in this work which can reduce the error on the reaction rate modelling at low turbulence intensities by up to 50%, and which is obtained by imposing that the consumption speed based on the modelled reaction rate matches the exact one in the flamelet limit. A second analysis is also conducted to assess the accuracy of the flamelet assumption itself. This analysis is conducted for a wide range of Ka, from 6 to 4100. It is found that at high Ka this assumption is weaker as expected, however results improve with larger filter sizes due to the reduction of the scatter produced by the fluctuations of the exact reaction rate.