An a priori DNS subgrid analysis of the presumed β-PDF model

A common way of carrying out LES or RANS of premixed and partially premixed turbulent flames with tabulated combustion chemistry consists of using a presumed shape for the probability density function (PDF) of progress variable and mixture fraction in order to compute the reaction rates. Commonly utilized for this purpose is the β-function PDF. To the aim of clarifying the applicability of the presumed β-PDF approach to the modeling of methane and hydrogen turbulent premixed flames, in this paper an investigation of the probability density distribution is performed by processing three-dimensional DNS computational results performed with detailed chemistry. This analysis is performed by means of a detailed comparison between the DNS data and the corresponding a priori LES obtained with top-hat filters of various sizes. The analysis is conducted for hydrogen and methane turbulent flames, for comparison. In particular, it is assessed whether a lean premixed turbulent hydrogen-air flame can be well-represented in LES by a β-PDF approach as traditionally applied for methane in literature. It is shown that the presumed β-PDF model performs rather well for both hydrogen and methane. The total error between the real distribution and the presumed β-PDF is of comparable amount for the two fuels. However, the error shows a more consistent profile in methane flames. In addition, it is shown that mean and variance are not sufficient as control parameters for an improved modeling of hydrogen flames by means of presumed PDF, plausibly because of its strong differentially diffusive effects.