Direct Numerical Simulations for the Effects of Small Perturbation on the Intrinsic Instabilities of Two-dimensional Hydrogen/air Premixed Flames

Abstract

Direct numerical simulations were implemented and studied for the intrinsic instabilities of two-dimensional hydrogen/air premixed planar flames. The 6th-order compact finite difference scheme was used for the spatial discretization, and the 3rd-order Runge-Kutta method for the time advancement. The boundary conditions were based on the Navier-Stokes characteristic boundary conditions. The hydrogen/air detailed kinetics, which contains 9 species and 35 elementary reactions, was used. Small perturbation was imposed at the upstream boundary of the calculation domain (a rectangle), and then the perturbation grew up when it reached a planar flame. The flame became unstable due to the intrinsic instabilities. Afterwards, a cusp, which was a concave part towards the unburned gas, appeared, and developed rapidly. It is considered to be due to the diffusive-thermal instability. And then, the cusp was closing, while a convex part towards the unburned gas appeared. This is considered as a cellular structure. The dispersion relation between the wave number and the growth rate of the perturbation was obtained and compared with a theoretical prediction. The behaviour of the flame was qualitatively similar to one obtained in past experiments. Furthermore the results with the perturbation imposed continuously and in a limited time were compared.