Propagation and extinction of an unsteady spherical spray flame front

Experimental evidence seems to indicate that the life of a laminar spherical flame front propagating through a fresh mixture of air and liquid fuel droplets can be roughly split into three stages: (1) ignition, (2) radial propagation with a smooth flame front and (3) propagation with flame front cellularization and/or pulsation. In this work, the second stage is analysed using the slowly varying flame approach, for a fuel rich flame. The droplets are presumed to vaporize in a sharp front ahead of the reaction front. Evolution equations for the flame and evaporation fronts are derived. For the former the combined effect of heat loss due to droplet vaporization and radiation plays a dominant explicit role. In addition, the structure of the evaporation front is deduced using asymptotics based on a large parameter associated with spray vaporization. Numerical calculations based on the analysis point to the way in which the spray modifies conditions for flame front extinction. Within the framework of the present simplified model the main relevant parameters turn out to be the initial liquid fuel load in the fresh mixture and/or the latent heat of vaporization of the fuel.