Formulation and importance of conservative transport in non-premixed flamelet models

Abstract

The flamelet approach is widely used to model non-premixed turbulent combustion. In this model, chemistry is solved in mixture fraction space and the mixture fraction field is solved in physical space. Transport of reactive scalars in mixture fraction space is governed by two flow parameters: the scalar dissipation rate and the curvature of the mixture fraction field. While these two flow parameters can be easily evaluated if all scales are resolved, models are required if turbulence modeling is applied. However, conventional flow parameter models, which presume the shape of the flow parameters in mixture fraction space, do not consider that mixing in physical and mixture fraction space need to be modeled consistently, which can cause leading order errors. In this study, a consistent formulation of the governing equations and the flow parameters is derived, which is then applied within the Representative Interactive Flamelet (RIF) model to an auto-igniting, sooting, temporal n-dodecane jet under engine-relevant conditions. A Direct Numerical Simulation (DNS) is carried out and serves as reference solution for model validation. It is shown that the revised flow parameters yield superior model predictions of all investigated quantities in comparison to conventional models. Although the auto-ignition process is captured reasonably well by the conventional model, the modeling error in soot quantities is not tolerable. The revised model shows much better agreement with the DNS data and demonstrates that the RIF model is generally able to predict pollutants under the considered conditions. An analysis of the temporal soot mass evolution shows that an accurate description of both species and particle transport in mixture fraction space is essential for predicting soot formation.