Stretch rate effects on displacement speed in turbulent premixed flame kernels in the thin reaction zones regime

Direct numerical simulation (DNS) of three-dimensional turbulent premixed flame kernels is carried out in order to study correlations of displacement speed with stretch rate for a range of different flame kernel radii. A statistically planar back-to-back flame is also simulated as a special case of a flame kernel with infinite radius of curvature. In all the cases the joint pdf of displacement speed with stretch rate shows two distinct branches, whose relative strength is found to be dependent on the mean flame curvature. A positive (negative) correlation is prevalent when the flame is curved in a convex (concave) sense towards the reactants. The observed non-linearity of the displacement speed-stretch rate correlation, qualitatively consistent with previous two-dimensional DNS with complex chemistry, is shown to exist purely due to fluid-dynamical interactions even in the absence of detailed chemistry. It is demonstrated that the combined contribution of reaction and normal diffusion is important in the response of flame propagation to stretch rate, and the effect is found to increase with decreasing mean kernel radius. The implications of the stretch rate dependence of displacement speed are discussed in detail in the context of the flame surface density (FSD) approach to turbulent combustion modelling. (C) 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.