The influence of hydrodynamic instability on the structure of cellular flames

The influence of hydrodynamic instability on the structure of two-dimension al (2D) and three-dimensional (3D) cellular flames is numerically investiga ted. 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 t he 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 becom es stronger. The unstable range normalized by the preheat zone thickness ha rdly changes, even though the flame temperature increases. The critical wav e number, which corresponds to the maximum growth rate, is almost constant. Therefore, the normalized spacing between cells of the cellular flame is i ndependent of the flame temperature. Moreover, we superimpose the disturban ce with the critical wave number to investigate the structure of cellular f lames. The stationary cellular flame is obtained when the inlet-flow veloci ty 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 add ition, 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. (C) 1999 American Institute of Physics. [S1070-6631(99)00911-3].