On the Relationship Between the Statistics of the Resolved and True Rate of Dissipation of Mixture Fraction

Abstract

The relationship between the one-point probability-density-function (PDF) of the dissipation rate of mixture fraction fluctuations and the corresponding resolved quantity available in large eddy simulation (LES) is analyzed. The investigation pursues two fronts: an a priori study using direct numerical simulation (DNS), and an analytic development that, using common turbulence physics simplifications, relates the one-point statistics of the resolved and true scalar dissipations. Particularly, the analysis reveals the connection between the multi-point correlations of the mixture fraction gradient and the one-point PDF of the resolved scalar dissipation. A DNS of a temporally evolving shear layer with and without heat release is used to quantify the accuracy of the analytical result. It is verified, both by filtering the DNS and from the theory, that increasing the filter cutoff width reduces the magnitude of the resolved scalar dissipation fluctuations, as expected and observed experimentally. Comparison with DNS indicates that the analytical relationship predicts the behavior of the resolved scalar dissipation PDF well at the center planes of the shear layer, where turbulence is locally more isotropic and homogeneous. Large-scale anisotropy and inhomogeneities in the DNS degrade the accuracy of the approximate analytical result close to the edges of the shear layer. These results may be improved with future investigations to account fully for the missing statistics in LES, which have the potential to allow a more accurate quantification of finite-rate chemistry effects in reacting flows.

Statistical Analysis of the Reaction Progress Variable and Mixture Fraction Gradients in Flames Propagating into Droplet Mist: A Direct Numerical Simulation Analysis

“…The only exception takes place at high values of Ñ j j and Ñc j j where there is insufficient data in the DNS dataset to accurately predict the value of the PDF and the regions with high probability of finding Ñc j j % 0, which log-normal distribution fails to predict. The discrepancy between the log-normal distribution and the tail of the scalar gradient PDFs is consistent with several experimental (Geyer et al, 2005;Karpetis and Barlow, 2002;Markides and Mastorakos, 2006;Sreenivasan and Antonia, 1997;Su and Clemens, 2003) and computational (Hawkes et al, 2007;Knaus et al, 2012;Malkeson et al, 2013;Pantano, 2004;Ruan et al, 2012) findings in the context of passive scalar mixing, non-premixed, and partially-premixed combustion. Despite some inaccuracies, the log-normal distribution appears to do a reasonable job for the purpose of parameterising Ñ j j and Ñc j j, which in turn could be used for modeling the scalar dissipation rates and cc .…”

Statistics of reaction progress variable and mixture fraction gradients of a pulverised coal jet flame using Direct Numerical Simulation data

“…that the PDFs of |∇c| and |∇ξ| are well approximated by the lognormal distribution, but considerable discrepancies between the log-normal distribution and PDFs obtained from DNS data can been observed for small values of |∇c| and |∇ξ|. This behaviour is consistent with the earlier experimental[40,41] and numerical investigations[8,42,43] of non-premixed and stratified combustion and also for passive scalar mixing. In the specific case of coal combustion it is argued here that this discrepancy can be attributed to the small fluctuations caused by the interaction of the coal particles in the centre of the jet.…”