The Hydrodynamic Stability of Flame Fronts

The hydrodynamic stability of a plane flame of finite thickness is treated by investigating the temporal behavior of first-order infinitesimal disturbances. This work is a generalization of earlier studies and takes into account the effect of distortion on burning velocity. The general equations of motion for the disturbance in a viscous gas under the influence of gravity are derived and solved. Horizontal and upward propagating plane flames are always unstable and those propagating downward are unstable under most conditions, so their measured transformation velocity under such conditions does not equal the stationary burning velocity. The calculated maximum cell size for downward propagation (λmax=32UuUb×10−4 cm) and the cell size for a flame propagated by thermal conduction (λthermal=22k/CpρuUu ) are in good agreement with existing experimental observations. The variation of cell size with pressure yields the pressure dependence of the burning velocity. The sudden appearance of cells in slow hydrocarbon flames (Uu≈10 cm/sec) observed at stoichiometric in going from lean to rich mixtures, indicating a corresponding decrease in flame thickness, is advanced as provisional evidence of a shift in the dominant propagation mechanism in these flames—from diffusion by atomic radicals for lean flames to thermal conduction for rich ones.