On flame bifurcation and multiplicity in consistently propagating spherical flame and droplet evaporation fronts

Abstract

The outwardly propagating spherical flames in premixed gas containing water droplets are theoretically studied in this work. The correlations between the flame propagation speed, droplet distribution and flame radius are derived, based on the large activation energy and quasi-planar flame assumptions. With this, flame bifurcation and multiplicity are analysed, focusing on the effects of initial droplet mass loading, evaporative heat loss and Lewis number. Meanwhile, the model can predict different gaseous flame types and liquid droplet distributions, as well as the bifurcations and transitions between them. It is shown that the spherical flame propagation is strongly affected by water droplet properties. When initial loading and/or heat loss coefficient are small, there is only one normal stable flame. Two stable flames arise when they increase, i.e. normal and weak flames. Increased droplet loading mainly affects the weak flame, resulting in decreased propagation speed, increased values of evaporation onset and completion fronts. However, increased heat loss affects both normal and weak flames, and flame bifurcation is observed for large heat loss. Droplet properties also greatly influence the weak flame transition between different regimes. Our results also show that Lewis number has significant influence on droplet-laden spherical flame propagation, in terms of flame bifurcation and regime transition. The Lewis number would affect the flame propagation jointly with the positive stretch rate and/or the evolving temperature gradients near the flame front through the interactions with the dispersed evaporating droplets. Furthermore, the magnitudes of Markstein length of the normal flames decrease when Lewis number approaches unity. However, those of the weak flames are mostly negative, indicating the enhancement over the shown Lewis number range. The larger magnitudes of Markstein length of weak flames show stronger sensitivity to stretch than those of normal flames. Finally, different flame types seen from our theoretical analysis are summarised.