The effects of heat loss on the burning velocity of cellular premixed flames generated by hydrodynamic and diffusive-thermal instabilities

The effects of heat loss on the burning velocity of cellular premixed flames are investigated by two-dimensional unsteady calculations of reactive flows based on the compressible Navier-Stokes equation and on the diffusive-thermal model equation. Hydrodynamic and diffusive-thermal instabilities are taken into account as contributing to the intrinsic instability of premixed flames. A sufficiently small disturbance is superimposed on a planar flame to obtain the relation between the growth rate and the wavenumber, i.e., the dispersion relation. As the heat loss becomes larger, the growth rate decreases and the unstable range narrows. This is because hydrodynamic instability caused by thermal expansion weakens for nonadiabatic flames. To investigate the characteristics of cellular flames, the disturbance with the linearly most unstable wavenumber, i.e., the critical wavenumber, is superimposed. As the superimposed disturbance evolves, the cellular-flame front forms due to the intrinsic instability. The lateral movement of cellular flames is observed at low Lewis numbers, and the behavior of cellular-flame fronts becomes more unstable for nonadiabatic flames. As the heat-loss parameter increases, the burning velocity of a cellular flame normalized by that of a planar flame increases at Lewis numbers lower than unity. By contrast, when the Lewis number is not less than unity, the burning-velocity increment decreases by increasing the heat loss. Diffusive-thermal instability thus has a pronounced influence on the unstable behavior and burning velocity of nonadiabatic cellular flames.