Unstable behavior of premixed flames generated by hydrodynamic and diffusive-thermal effects is studied by two-dimensional unsteady calculations of reactive flows. In the present numerical simulation, the compressible Navier-Stokes equation including a one-step irreversible chemical reaction is employed. We consider two basic types of phenomena to account for the intrinsic instability of premixed flames, i.e., hydrodynamic and diffusive-thermal effects. The hydrodynamic effect is caused by the thermal expansion through flame fronts; the diffusive-thermal effect is caused by the preferential diffusion of mass and heat. A disturbance with several wavelengths is superimposed on a stationary planar flame, and the formation of cellular flames generated by hydrodynamic and diffusive-thermal effects is numerically simulated. After the cellular-flame formation, the division and combine of cells are observed at low Lewis numbers. The cell size changes with time, and its mean value is greater than the critical wavelength. At the Lewis number unity, on the other hand, the division of cells is not observed but the combine is. Thus, the diffusive-thermal effect has an important role in the appearance of unstable behavior of premixed flames. The flame velocity of a cellular flame depends on the length of computational domain. As the domain length increases, the flame velocity becomes larger. This is because the long-wavelength components of disturbances have a great influence on the unstable behavior of cellular flames.
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.