Comparison of Presumed PDF Models of Turbulent Flames

Over the past years, the use of a presumed probability density function (PDF) for combustion progress variable or/and mixture fraction has been becoming more and more popular approach to average reaction rates in premixed and partially premixed turbulent flames. Commonly invoked for this purpose is a beta-function PDF or a combination of Dirac delta functions, with the parameters of the two PDFs being determined based on the values of their first and second moments computed by integrating proper balance equations. Because the choice of any of the above PDFs appears to be totally arbitrary as far as underlying physics of turbulent combustion is concerned, the use of such PDFs implies weak sensitivity of the key averaged quantities to the PDF shape. The present work is aimed at testing this implicit assumption by comparing mean heat release rates, burning velocities, and so forth, averaged by invoking the aforementioned PDFs, with all other things being equal. Results calculated in the premixed case show substantial sensitivity of the mean heat release rate to the shape of presumed combustion-progress-variable PDF, thus, putting the approach into question. To the contrary, the use of a presumed mixture-fraction PDF appears to be a sufficiently reasonable simplification for modeling the influence of fluctuations in the mixture fraction on the mean burning velocity provided that the mixture composition varies within flammability limits.