Effects of water droplet evaporation on initiation, propagation and extinction of premixed spherical flames

In this study, we develop a simplified theoretical model for flame initiation, propagation and extinction in premixed gas mixture containing water droplets, by considering water droplet evaporation in pre-flame or/and post-flame zones. The Eulerian droplet model with simplified evaporation sub-model is employed, while for gas phase the assumptions of constant-density, quasi-steady and large activation energy are made. Analytical correlations describing different flame regimes and transitions among flame balls, propagating spherical flames and planar flames are then derived to investigate the spherical flame initiation, propagation and extinction, with emphasis on the effects of water droplet evaporation on spherical flames at different Lewis numbers. Five different flame regimes are observed and discussed for droplets evaporation in pre-flame or/and post-flame zones. It is found that the droplets with larger heat exchange coefficient are more effective in reducing flame propagation speed and temperature but increasing the vaporization front. Moreover, the cooling effect of evaporation heat loss plays an important role on flame regimes and their transitions. At the relatively large heat exchange coefficient, the total evaporation heat loss from pre-flame and post-flame zones reaches its maximum at an intermediate flame radius. The cooling effect is strong enough to quench the flame and results in the self-extinguishing flame. In addition, the combined effects of stretch rate and Lewis number compete with the evaporation heat loss from droplet evaporation. For small Lewis number, the flammability limits can be achieved through self extinguishing flames, whereas for large Lewis number the flames approach their flammability limits in their evolution into planar flames. For ignition of spherical flames, if the droplet-laden mixture is intrinsically non-flammable, although a propagating flame kernel can be initiated, however it would still be quenched due to evaporation heat loss at a critical radius. The minimum ignition energy increases with heat exchange coefficient and Lewis number. (C) 2019 Elsevier Ltd. All rights reserved.