Modeling curvature effects in diffusion flames using a laminar flamelet model

Abstract

The goal of this paper is to investigate the effects of curvature of mixture fraction iso-surfaces on the transport of species in diffusion flames. A general flamelet formulation is derived mathematically considering both curvature effects and differential diffusion effects. These theoretical results suggest that curvature does not play a role in the transport process irrespective of the flame curvature if species transport is described with a unity Lewis number. On the other hand, a curvature-induced term becomes explicit when differential diffusion effects are considered, and it acts as a convective term in mixture fraction space. It is found that this term needs to be taken into account when the radius of curvature is comparable or smaller than the local flame thickness. For the proper integration of the flamelet equations, the scalar dissipation rate and curvature dependences on mixture fraction are modeled by considering two basic curved one-dimensional flame configurations. The flamelet equations accounting for curvature effects are solved with various prescribed curvature values. Results indicate that the mass fraction profiles of species with very small or large Lewis numbers are shifted significantly in mixture fraction space by the inclusion of curvature. Differential diffusion effects are enhanced by negative curvature values and suppressed by positive curvature values. In cases where flame curvature is not uniform, the curvature-induced convective term generates gradients along mixture fraction iso-surfaces, which enhance tangential diffusion effects. Budget analysis is performed on an axisymmetric laminar coflow diffusion flame to highlight the importance of the curvature-induced convective term compared to other terms in the full flamelet equation. A comparison is made between full chemistry simulation results and those obtained using planar and curved flamelet-based chemistry tabulation methods.