The system of equations describing the effects of heating, evaporation, and combustion of fuel droplets in a monodisperse spray is simplified assuming that the Nusselt and Sherwood numbers are equal to 2. The radiative energy exchange between fuel droplets surface and gas is described by using the P-1 model with Marshak boundary conditions. The chemical term is presented in the Arrhenius form with the pre-exponential factor calculated from the enthalpy equation, using the Shell autoignition model. The resultant, singularly perturbed system of ordinary differential equations is analyzed, based on the geometrical version of the integral manifold method. The ignition process is subdivided into two stages: droplet evaporation and ignition of the gaseous mixture. Results predicted by the analytical solutions are compared with those predicted by the CFD package VECTIS. It is suggested that the analytical solution underpredicts the evaporation time. A considerably better agreement between the evaporation times predicted by VECTIS and the proposed theory is achieved when the gas temperature is assumed to be equal to the local temperature in the vicinity of droplets. The effects of thermal radiation are significant, especially at high temperatures and with large droplets, and cannot be ignored.
Sazhin, S., Feng, G., Heikal, M., Goldfarb, I., Gol'dshtein, V., & Kuzmenko, G. (2001). Thermal ignition analysis of a monodisperse spray with radiation. Combustion and Flame, 124(4), 684-701. https://doi.org/10.1016/S0010-2180(00)00237-6