Near-Field Thermal and Momentum Effects in Counterflow Spray Diffusion Flames

A new mathematical analysis is presented of certain aspects of near-field thermal and momentum effects of opposed flow polydisperse spray diffusion flames within the framework of a model in which mild slip is permitted between the droplets and their host surroundings. A solution strategy is outlined under circumstances in which the Stokes number of the droplets in the spray is a small parameter that can be exploited for developing a perturbation solution. It is shown that analytical solutions up to the 2nd order of approximation reveal phenomena described by previous numerical and experimental works. The analytical formulation enables a closed-form recursive solution for the leading orders of the physical properties and demonstrates the possibility of finding a separate solution for the host gas temperature field that can be exploited to extract the thermal field of the liquid phase. Computed results based on the new analysis illustrate the influence the heat transfer between phases (through the Stokes and Nusselt numbers) has on the flame structure and the consequent modification of conditions for flame extinction