Lagrangian Intermittent Modelling of a Turbulent Lifted Methane-Air Jet Flame Stabilized in a Vitiated Air Coflow

The present manuscript reports results of numerical simulations of turbulent lifted jet flames of methane with special emphasis placed on the autoignition effects. The impact of dilution with burned gases on the flame stabilization is analyzed under the conditions of a laboratory jet flame surrounded by a vitiated air coflow. In this geometry, mass flow rates, temperature levels and exact chemical composition of hot products mixed with air are fully determined. The effects of both finite rate chemistry and partially premixed combustion are taken into account within a Lagrangian intermittent framework. Detailed chemistry effects are incorporated through the use of chemical time scales, which are tabulated as functions of the mixture fraction. The concept of residence time (or particle age) and the transport equation for the mean scalar dissipation rate of the mixture fraction fluctuations, i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\widetilde{\varepsilon}_Z=\overline{\rho \mathcal{D} (\partial Z'' / \partial x_i) (\partial Z'' / \partial x_i) }/\overline{\rho}$\end{document}, are also considered. This allows to improve the description of turbulent mixing including both the large scales engulfment processes through the consideration of the residence time scale, as well as the small scales molecular mixing processes the intensity of which is set by the integral scalar (mixing) time scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau_Z=\widetilde{Z''^2}/\widetilde{\varepsilon}_Z$\end{document}. Numerical simulations of the turbulent diluted jet flame of methane studied by Cabra and his co-workers are performed. The flame liftoff height is reasonably well-captured and the computational results display a fairly satisfactory level of agreement with experimental data. They also confirm that the consideration of an additional transport equation for the mean scalar dissipation rate may significantly improve the computational results. The investigation is supplemented by a sensitivity analysis of the scalar to turbulence time scale ratio Cmix = τZ/τt often referred to as the mixing constant. Finally, the manuscript ends with the application of the proposed closure to experimental conditions which are characterized by variations of (i) the jet exit velocity, (ii) coflow velocity and (ii) coflow temperature.