Impact of mixture fraction field curvature on chemical species transport in diffusion flames

This study investigates the effects of curvature of mixture fraction iso-surfaces on the non-unity Lewis number transport of species in diffusion flames. A general flamelet formulation is derived mathematically for both unity and non-unity Lewis number transport and for different contours of mixture fraction iso-surfaces (i.e. non-zero curvature with varying magnitude.). These theoretical results suggest that curvature does not play a role in the transport process for unity Lewis number irrespective of the flame curvature, which was varied between highly curved and perfectly flat. On the other hand, for nonunity Lewis numbers, a curvature-related term becomes explicit for perfectly spherical flames, and this term acts as a convective term in mixture fraction space. Finally, in cases where flame curvature is not uniform, this convective term induces a non-zero diffusion flux in the direction normal to the mixture fraction gradient, which is inconsistent with the 1D flamelet assumptions. The flamelet equations accounting for curvature effects are solved considering first laminar spherical diffusion flames with different prescribed curvature at the stoichiometric mixture fraction. The results indicate that the magnitude of the curvature-induced convection term can become much larger than that of the convective term in the traditional flamelet formulation. Furthermore, the mass fraction profiles of heavy hydrocarbons, such as PAHs, are shifted significantly by the inclusion of curvature. The current work suggests a possible means to account for curvature effects via a new a priori chemistry tabulation which includes curvature for laminar and mildly turbulent diffusion flames.