Steady flamelet modelling of a turbulent non-premixed flame considering scalar dissipation rate fluctuations

A piloted turbulent methane/air jet flame (Sandia Flame D) is calculated by the combination of a multiple-time scale (MTS) k-ε turbulence model, the steady laminar flamlet model (SLFM), and the probability density function (PDF) transport equation approach. A joint PDF transport equation of mixture fraction and turbulent kinetic energy dissipation rate is computed by the node-based Monte Carlo particle method. The fluctuations of scalar dissipation rate at stoichiometric condition are deduced, in an ad hoc manner, from the distribution of turbulent kinetic energy dissipation rate based on their similar PDF distribution, viz. approximately lognormal. The SLFM is employed to decouple the interaction between turbulent fluctuations and chemistry through the instantaneous mixture fraction and the instantaneous stoichiometric scalar dissipation rate. The MTS k-ε turbulence model produces better prediction of the centerline profiles of mean velocity and mixture fraction than the standard k-ε model. Within the current modelling scope, the value of 1.5 for the ratio of mechanical to scalar timescales is better than the usual value of 2.0 since it gives better profiles of the root-means-square (rms) mixture fraction and mean CO, H2 mass fractions. Compared to the presumed-PDF for scalar dissipation rate, the present ad hoc model improves the predictions of flame structure to some extent, especially the conditional means of CO and H2 mass fractions in the fuel-rich region of the flame.