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. The evaporation completion front location considerably changes with flame radius. For larger droplet loading and a 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 the 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 a decreased Lewis number. The magnitude of the Markstein length is considerably reduced with increased droplet loading. Moreover, post-flame droplet burning behind the heterogeneous flame influences the flame propagation speed and Markstein length when the liquid fuel loading is relatively low.

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