A priori analysis of the curvature and propagation terms of the flame surface density transport equation for large eddy simulation

The statistical behavior of the propagation and curvature terms in the transport equation for flame surface density (FSD) is studied in the context of large eddy simulation (LES) of premixed combustion in the thin reaction zones regime. It is found that the propagation term is strongly influenced by curvature effects on displacement speed, and it is shown that the propagation term can be closed exactly without any additional modelling provided that the surface averaged displacement speed is accurately represented. The FSD curvature term is decomposed into resolved and subgrid contributions and three different model expressions for the resolved curvature term are studied. It is shown that the choice of expression for the resolved curvature term affects the modelling of the subgrid curvature term. This is important since the treatment of the subgrid curvature term involves the largest modelling uncertainties. Following this, it is argued that the most preferable expression for the resolved curvature term is the one which allows for the smallest subgrid contribution and which captures the correct trend of the complete LES-filtered curvature term. Predictions of existing models for the subgrid curvature term are assessed in comparison to values obtained from filtered direct numerical simulation data. It is demonstrated that the local curvature dependence of the LES surface averaged displacement speed plays a significant role in the modelling of both the curvature and propagation terms. A model is proposed which explicitly accounts for this dependence.