Numerical investigation on unstable behaviors of cellular premixed flames at low Lewis numbers based on the diffusive-thermal model and compressible Navier-Stokes equations

Two dimensional unsteady calculations of reactive flows were performed in large domain to investigate the unstable behaviors of cellular premixed flames at low Lewis numbers based on the diffusive-thermal (D-T) model and compressible Navier-Stokes (N-S) equations including one-step irreversible chemical reaction. The relations between the growth rate and wave number, i.e. the dispersion relations, were obtained. The growth rates obtained by the compressible N-S equations were large and the unstable ranges were wide compared with those obtained by the D-T model equations. This was because both hydrodynamic and diffusive-thermal effects were taken into account in the compressible N-S equations. A disturbance with the maximum growth rate was superimposed on a stationary planar flame to generate the cellular flame. The cellular flame formed, and the overshoot of temperature evolved. When the length of computational domain increased, the number of small cells separated from large cells of the cellular flame increased drastically. As the results, flame surface area and average burning velocity increased. The stronger unstable behaviors and the larger average burning velocities were observed especially in the numerical results based on the compressible N-S equations. In addition, the fractal dimension obtained by the compressible N-S equations was larger than that by the D-T model equations. Moreover, we confirmed that the radiative heat loss promoted the instability of premixed flames at low Lewis numbers. (author)