Effects of pressure and heat loss on the unstable motion of cellular-flame fronts caused by intrinsic instability in hydrogen-air lean premixed flames

Abstract

Effects of pressure and heat loss on the unstable motion of cellular-flame fronts in hydrogen-air lean premixed flames were numerically investigated. We adopted the reaction mechanism for hydrogen-oxygen combustion, modeled with seventeen reversible reactions of eight reactive species and a diluent. Two-dimensional unsteady reactive flow was treated, and the compressibility, viscosity, heat conduction, molecular diffusion and heat loss were taken into account. A sufficiently small disturbance was superimposed on a planar flame to obtain the relation between the growth rate and wave number, i.e. the dispersion relation, and the linearly most unstable wavelength, i.e. the critical wavelength. As the pressure became higher, the maximum growth rate increased and the unstable range widened. These were due mainly to the decrease of flame thickness. As the heat loss became larger, the former decreased and the latter narrowed, which were due mainly to the decrease of burning velocity. To investigate the characteristics of cellular-flame fronts, a disturbance with the critical wavelength was superimposed. The superimposed disturbance developed owing to intrinsic instability, and then the cellular shape of flame fronts appeared. The burning velocity of a cellular flame normalized by that of a planar flame increased as the pressure became higher and the heat loss became larger. This indicated that the pressure and heat loss affected strongly the unstable motion of cellular-flame fronts. The burning velocity of a cellular flame increased monotonically with an increase in the space size. This was attributed to long-wavelength components of disturbances. Moreover, we estimated the fractal dimension of flame fronts through the box counting method. As the pressure and heat loss increased, the fractal dimension became larger, which denoted that the flame shape became more complicated.