The influence of hydrodynamic instability on the structure of cellular flames

Abstract

The influence of hydrodynamic instability on the structure of two-dimensional (2D) and three-dimensional (3D) cellular flames is numerically investigated. The equation used is the compressible Navier–Stokes equation including a one-step irreversible chemical reaction. We superimpose an infinitesimal disturbance on the stationary plane flame and calculate the evolution of the disturbed flame front to obtain the relation between the growth rate and the wave number, i.e., the dispersion relation. With an increase in flame temperature, the growth rate increases since hydrodynamic instability becomes stronger. The unstable range normalized by the preheat zone thickness hardly changes, even though the flame temperature increases. The critical wave number, which corresponds to the maximum growth rate, is almost constant. Therefore, the normalized spacing between cells of the cellular flame is independent of the flame temperature. Moreover, we superimpose the disturbance with the critical wave number to investigate the structure of cellular flames. The stationary cellular flame is obtained when the inlet-flow velocity is set to the flame velocity of the cellular flame. The higher the flame temperature, the deeper the cell and the broader the flame surface. In addition, the cell depth and the surface area of the 3D flame are larger than those of the 2D flame. This is caused by the difference in the disposition of cells.