NO Prediction in Turbulent Diffusion Flame Using Multiple Unsteady Laminar Flamelet Modeling

The steady laminar flamelet model (SLFM) (Peters, 1984, “Laminar Diffusion Flamelet Models in Non-Premixed Turbulent Combustion,” Prog. Energy Combust. Sci., 10(3), pp. 319–339; Peters, 1986, “Laminar Flamelet Concepts in Turbulent Combustion,” Symp. (Int.) Combust., 21(1), pp. 1231–1250) has been shown to be reasonably good for the predictions of mean temperature and the major species in turbulent flames (Borghi, 1988, “Turbulent Combustion Modeling,” Prog. Energy Combust. Sci., 14(4), pp. 245–292; Veynante and Vervisch, 2002, “Turbulent Combustion Modeling,” Prog. Energy Combust. Sci., 28(3), pp. 193–266). However, the SLFM approach has limitations in the prediction of slow chemistry phenomena like NO formation (Benim and Syed, 1998, “Laminar Flamelet Modeling of Turbulent Premixed Combustion,” Appl. Math. Model., 22(1–2), pp. 113–136; Heyl and Bockhorn, 2001, “Flamelet Modeling of NO Formation in Laminar and Turbulent Diffusion Flames,” Chemosphere, 42(5–7), pp. 449–462). In the case of SLFM, the turbulence and chemistry are coupled through a single variable called scalar dissipation, which is representative of the strain inside the flow. The SLFM is not able to respond to the steep changes in the scalar dissipation values and generally tends to approach to the equilibrium solution as the strain relaxes (Haworth et al., 1989, “The Importance of Time-Dependent Flame Structures in Stretched Laminar Flamelet Models for Turbulent Jet Diffusion Flames,” Symp. (Int.) Combust., 22(1), pp. 589–597). A pollutant like NO is formed in the post flame zones and with a high residence time, where the scalar dissipation diminishes and hence the NO is overpredicted using the SLFM approach. In order to improve the prediction of slow forming species, a transient history of the scalar dissipation evolution is required. In this work, a multiple unsteady laminar flamelet approach is implemented and used to model the NO formation in two turbulent diffusion flames using detailed chemistry. In this approach, multiple unsteady flamelet equations are solved, where each flamelet is associated with its own scalar dissipation history. The time averaged mean variables are calculated from weighted average contributions from different flamelets. The unsteady laminar flamelet solution starts with a converged solution obtained from the steady laminar flamelet modeling approach. The unsteady flamelet equations are, therefore, solved as a post processing step with the frozen flow field. The domain averaged scalar dissipation for a flamelet at each time step is obtained by solving a scalar transport equation, which represents the probability of occurrence of the considered flamelet. The present work involves the study of the effect of the number of flamelets and also the different methods of probability initialization on the accuracy of NO prediction. The current model predictions are compared with the experimental data. It is seen that the NO predictions improves significantly even with a single unsteady flamelet and further improves marginally with an increase in number of unsteady flamelets.