Evaluation of scalar mixing and time scale models in PDF simulations of a turbulent premixed flame

Numerical simulation results obtained with a transported scalar probability density function (PDF) method are presented for a piloted turbulent premixed flame. The accuracy of the PDF method depends on the scalar mixing model and the scalar time scale model. Three widely used scalar mixing models are evaluated: the interaction by exchange with the mean (IEM) model, the modified Curl’s coalescence/dispersion (CD) model and the Euclidean minimum spanning tree (EMST) model. The three scalar mixing models are combined with a simple model for the scalar time scale which assumes a constant C ϕ = 12 value. A comparison of the simulation results with available measurements shows that only the EMST model calculates accurately the mean and variance of the reaction progress variable. An evaluation of the structure of the PDF’s of the reaction progress variable predicted by the three scalar mixing models confirms this conclusion: the IEM and CD models predict an unrealistic shape of the PDF. Simulations using various C ϕ values ranging from 2 to 50 combined with the three scalar mixing models have been performed. The observed deficiencies of the IEM and CD models persisted for all C ϕ values considered. The value C ϕ = 12 combined with the EMST model was found to be an optimal choice. To avoid the ad hoc choice for C ϕ , more sophisticated models for the scalar time scale have been used in simulations using the EMST model. A new model for the scalar time scale which is based on a linear blending between a model for flamelet combustion and a model for distributed combustion is developed. The new model has proven to be very promising as a scalar time scale model which can be applied from flamelet to distributed combustion.