Assumed Multivariate Beta-PDF Modeling for Turbulent Nonpremixed Flames

Numerical simulation based on a moment method is conducted to investigate the feasibility of an assumed probability density function (PDF) approach in the configuration of a turbulent jet nonpremixed flame. In this study, a multivariate β-PDF is employed to account for turbulence-chemistry interaction. The multivariate β-PDF approach has an advantage that only one additional transport equation of sum of composition variances is solved to determine the shape of species PDF to transport equations of mean compositions. The numerical simulation is carried out for H3 flame. Reaction mechanism is a single-step irreversible reaction including H₂, O₂ and H₂O species. The results are compared with those from measurements and a combined PDF/moment method that detailed reaction mechanism is applied. Velocity distributions obtained by the multivariate β-PDF approach show good agreement with measurements and combined PDF/moment results, which indicates that the present approach can predict the flow pattern of nonpremixed flames. The present approach also provides good predictions in terms of mean temperature and mass fraction. PDFs of mass fraction obtained by the present approach are similar to those by the combined PDF/moment method. On the other hand, the variance of temperature is underpredicted, which is attributed to an approximation of temperature variance. In order to achieve a good prediction of the reaction rate, a PDF approximation of enthalpy is proposed for the evaluation of mean reaction rate.