Effects of global flame curvature on surface density function transport in turbulent premixed flame kernels in the thin reaction zones regime

Abstract

Three-dimensional simplified chemistry-based Direct Numerical Simulations (DNS) have been used to study the effects of global flame curvature (i.e. inverse of mean kernel radius) on the transport of the reaction progress variable gradient magnitude |∇c| which is alternatively known as the Surface Density Function (SDF). In order to understand the influences of global curvature on the statistical behaviour of SDF and the different terms of the SDF transport equation, turbulent premixed flame kernels with different initial radii have been simulated. In addition to this, a statistically planar flame has been simulated as a special case of the flame kernel with infinite radius. It has been found that the maximum mean value of the SDF decreases with decreasing kernel radius. The statistical behaviour of the different terms of the SDF transport equation has been studied in detail in order to understand the influence of curvature on the SDF transport. It has been observed that the tangential strain rate contribution to the SDF transport acts as a source term but its strength decreases with decreasing kernel radius. By contrast, the curvature contribution to the SDF transport acts to dissipate SDF in all the flames but the sink contribution becomes increasingly weak with decreasing kernel size. The SDF propagation term acts as a source term towards the fresh gas side and a sink term towards the burned gas side but the source contribution decreases with decreasing kernel size. The local curvature effects on the different terms of the SDF transport equation have been studied in terms of their joint pdfs with local curvature. It is shown that the local curvature dependence of displacement speed plays a key role in the statistics of the curvature and propagation terms of the SDF transport equation.