  Propagation of weakly stretched spherical flames in partially pre-vaporized
fuel sprays is theoretically investigated in this work. A general theory is
developed to describe flame propagation speed, flame temperature, droplet
evaporation onset and completion locations. The influences of liquid fuel and
gas mixture properties on spherical spray flame propagation are studied. The
results indicate that the spray flame propagation speed is enhanced with
increased droplet mass loading and/or evaporation heat exchange coefficient (or
evaporation rate). Opposite trends are found when the latent heat is high, due
to strong evaporation heat absorption. Fuel vapor and temperature gradients are
observed in the post-flame evaporation zone of heterogeneous flames.
Evaporation completion front location considerably changes with flame radius,
but the evaporation onset location varies little relative to the flame front
when the flame propagates. For larger droplet loading and smaller evaporation
rate, the fuel droplet tends to complete evaporation behind the flame front.
Flame bifurcation occurs with high droplet mass loading under large latent
heat, leading to multiplicity of flame propagation speed, droplet evaporation
onset and completion fronts. The flame enhancement or weakening effects by the
fuel droplet sprays are revealed by enhanced or suppressed heat and mass
diffusion process in the pre-flame zone. Besides, for heterogeneous flames,
heat and mass diffusion in the post-flame zone also exists. The mass diffusion
for both homogeneous and heterogeneous flames is enhanced with decreased Lewis
number. The magnitude of Markstein length is considerably reduced with
increased droplet loading. Moreover, post-flame droplet burning behind
heterogeneous flame influences the flame propagation speed and Markstein length
when the liquid fuel loading is relatively low.
