Linear stability analysis of laminar premixed spray flames

Abstract

We present an analysis of instability to transverse perturbations of laminar premixed plane spray flames. To this end, a thermal‐diffusional model of a flame front propagating through an overall fuel‐rich or fuel‐lean droplet‐vapour‐air mixture is presented. The fuel droplets are permitted to vaporize at a finite rate so that their interaction with, and possible traversal of, the flame front is accounted for. After establishing steady‐state solutions by means of high activation energy asymptotics, a detailed linear stability analysis is carried out in order to determine neutral stability boundaries. For the fuel‐rich case, it is demonstrated that under certain circumstances a spray flame may be cellular even though its equivalent non‐spray flame is completely stable. In addition, even when the non‐spray flame is itself cellular, the equivalent spray flame will have a finer cellular structure. To our knowledge, these results are the first theoretical qualitative verification of sparse but compelling experimental evidence from the literature. The main effect of the spray on the stability of these flames is due to heat loss from the absorption of heat by the droplets for vaporization. The influence of the initial liquid fuel loading, the latent heat of vaporization and the vaporization coefficient on the critical wavenumber associated with cellularity provides strong evidence of the major role of the heat‐loss mechanism in these sprayrelated phenomena. For fuel‐lean spray flames, it is found that the heat‐loss mechanism manifests itself prominently via the pulsating stability boundary which penetrates into the region of realistic Lewis numbers, thus verifying recent experimental observations of pulsating cellular spray flames. Finally, the cellularity of the spray flames, with their attendant increase in flame front area, suggests a plausible rationale for those circumstances in which burning velocity enhancement, induced by the use of a spray of droplets, was observed experimentally.