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

Abstract

The steady laminar flamelet model (SLFM) [1, 2] has been shown to be reasonably good for the predictions of mean temperature and the major species in turbulent flames [3, 4]. However, the SLFM approach has limitations in the prediction of the slow chemistry phenomena like NO formation [5, 6]. In 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 model is not able to respond to the steep changes in the scalar dissipation values and generally tend to approach to the equilibrium solution as the strain relaxes [7]. The 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 over predicted using 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 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 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.

Investigation of NOx in piloted stabilized methane-air diffusion flames using finite-rate and infinitely-fast chemistry based combustion models

“…They studied the effect of different methods of initialization of the probability of finding particles and initialization region extended to fuel rich regions provided better results. [4] conducted a study on Sandia flame D and Delft flame III using multiple unsteady flamelet method and observed similar trends in NO predictions as in [12]. They also found that increasing the number of flamelets increased the accuracy of prediction in the Delft flame III whereas the results hardly improved for Sandia flame D. The present study extends the analysis on Sandia flames E and F that have not been studied before on these aspects while comparing with the finite rate chemistry-based approaches.…”

“…The steady laminar flamelet model (LFM) is used to model the turbulent-chemistry interaction to obtain a converged steady flow solution and then the Eulerian unsteady laminar flamelet model is used to model the slow kinetic species as a post processing on the steady-state, steady flamelet solution. The detailed description of the approach can be found in [13,4].…”

“…[15] used a reduced mechanism derived from GRI 1.2 (ARM 2) for methane oxidation in the PDF calculations of flames D -F and a very good agreement between the predicted results and experimental data for NOx were observed. [16] used a skeletal mechanism for methane, GRI 2.11 and Miller -Bowman mechanism to perform Conditional Moment Closure (CMC) prediction on flame D and [4] used GRI 2.11 in the unsteady flamelet modeling of pollutants in Delft Flame III and Sandia flame D and observed that GRI mechanism produces very good agreement with the experimental results for NO.…”

“…Hence the kinetics of formation of species like NOx is slow and it forms in the regions of high residence times where steady diffusion flamelet model (SDFM) approaches equilibrium solution and could over-predict NOx by orders of magnitude. Scalar dissipation rate, the parameter that represents the state of non-equilibrium of the flamelet decays strongly along the jet axis due to relaxation of strain and steady flamelet cannot follow the rapid changes of the scalar dissipation rate instantaneously [4][5][6][7] and hence it slowly tends to approach the state of equilibrium as the strain relaxes. In the present study, we resort to an unsteady flamelet modeling approach in order to accurately represent the influence of transient effects in the formation of slow kinetic species and to represent the transient history of scalar dissipation of individual flames.…”

“…Flamelet modeling is one of the most commonly used approaches for modeling turbulent combustion due to its computational efficiency [2 & 3]. Steady flamelet model can simulate local chemical nonequilibrium due to aerodynamic straining of the flame by the turbulent flow field whereas, slow kinetic species like NOx that don't respond quickly to the turbulent straining have to be modeled using unsteady flamelet model for accurate prediction since their formation depends w t on the history of molecular mixing and reactions and its formulation is extensively studied by [4]. [1] performed laminar flamelet modeling of turbulent jet flame and predicted NOx by solving another transport equation for NO mass fraction.…”