An Extended Flamelet-based Presumed Probability Density Function for Predicting Mean Concentrations of Various Species in Premixed Turbulent Flames

Direct Numerical Simulation (DNS) data obtained by Dave and Chaudhuri (2020) from a lean, complex-chemistry, hydrogen-air flame associated with the thin-reaction-zone regime of premixed turbulent burning are analyzed to perform a priori assessment of predictive capabilities of the flamelet approach for evaluating mean species concentrations. For this purpose, dependencies of mole fractions and rates of production of various species on a combustion progress variable c, obtained from the laminar flame, are averaged adopting either the actual Probability Density Function (PDF) P (c)  extracted from the DNS data or a common presumed β-function PDF. On the one hand, the results quantitatively validate the flamelet approach for the mean mole fractions of all species, including radicals, but only if the actual PDF P (c) is adopted. The use of the β-function PDF yields substantially worse results for the radicals’ concentrations. These findings put modeling the PDF P (c) on the forefront of the research agenda. On the other hand, the mean rate of product creation and turbulent burning velocity are poorly predicted even adopting the actual PDF. These results imply that, in order to evaluate the mean species concentrations, the flamelet approach could be coupled with another model that predicts the mean rate and turbulent burning velocity better. Accordingly, the flamelet approach could be implemented as post-processing of numerical data yielded by that model. Based on the aforementioned findings and implications, a new approach to building a presumed PDF is developed. The key features of the approach consist in (i) adopting a re-normalized flamelet PDF for intermediate values of c and (ii) directly using the mean rate of product creation to calibrate the presumed PDF. Capabilities of the newly developed PDF for predicting mean species concentrations are quantitively validated for all species, including radicals.