Displacement Speed Statistics for Stratified Mixture Combustion in an Igniting Turbulent Planar Jet

The statistics of the density-weighted displacement speed of the reaction progress variable $c$ isosurfaces for stratified mixture combustion arising from localized ignition in a turbulent planar coflowing jet have been studied based on 3D Direct Numerical Simulation data where the jet is considered to be fuel-rich and the coflow is taken to be fuel-lean. The resulting flame following successful ignition shows the premixed mode of combustion in fuel-rich and fuel-lean zones although an additional diffusion flame branch was also observed on the stoichiometric mixture isosurface at early times of flame evolution. The flame propagation characteristics have been analyzed in terms of the reaction, normal diffusion and tangential diffusion components of the density-weighted displacement speed for different values of reaction progress variables across the flame brush. It has been found that the reaction, normal diffusion and tangential diffusion components of density-weighted displacement speed, remain the major contributors to the density-weighted displacement speed at all stages of flame evolution as the magnitude of the component which originates due to mixture inhomogeneity remains negligible in comparison to the magnitudes of other components in accordance with previous experimental studies. It has been demonstrated that curvature and tangential strain rate dependences of the reaction progress variable gradient play key roles in determining strain rate dependences of the reaction and normal diffusion components of the density-weighted displacement speed. It has been shown that the interrelation between tangential strain rate and curvature affects the strain rate dependence of tangential diffusion component of the density-weighted displacement speed. The density-weighted displacement speed and curvature are found to be predominantly negatively correlated throughout the flame brush at all stages of the flame evolution. The relative strengths of the tangential strain rate dependence of the reaction, normal diffusion and tangential diffusion components of the density-weighted displacement speed ultimately determine the nature of correlation between the density-weighted displacement speed and the tangential strain rate. The strain rate and curvature dependences of the density-weighted displacement speed in stratified mixtures are found to be qualitatively similar to the statistics previously obtained for turbulent premixed flames.