Analysis of evaporation and autoignition of droplet clouds with a unit cell model considering transient evaporating boundary layer

Liquid clouds (sprays) are commonly encountered in nature and industrial applications, where droplets are subject to complex interactions. In this paper, an extended unit cell model is proposed to analyze the evaporation and autoignition of monodisperse, single-component, and quiescent droplet clouds. The extended model incorporates the transient development of the evaporating boundary layer attached to the droplet surface. Due to the inclusion of this gas-phase transient effect, the current theory can be applied to both dilute and dense clouds across a wide range of ambient pressures. In the absence of chemical reactions, the effects of multiple parameters, such as droplet spacing and ambient pressure, on the evaporation rate and lifetime of droplets are examined. The critical condition for fuel vapor saturation in the gas phase is re-obtained. Based on this, we further investigate the autoignition of droplet clouds exposed to hot oxidizing environments and derive the corresponding ignition criterion. Effects of various factors, including droplet size, droplet spacing, ambient pressure, initial oxygen concentration, and reaction order, on critical ignition temperatures are also considered. In comparison with transient numerical results, it is found that the current theoretical solutions predict well for a broad variety of parameters.