The role of separation of scales in the description of spray combustion

The present paper deals with the description of the interacting multiscale processes governing spray vaporization and combustion downstream from the near-injector atomization region in liquid-fueled burners. One of the main objectives is to emphasize the progress made in the mathematical description and understanding of reactive spray flows by incorporation of rationally derived simplifications based on the disparity of length and time scales present in the problem. In particular, we aim to show how the disparity of the scales that correspond - with increasing values of their orders of magnitude - to the droplet size, interdroplet spacing, and width of the spray jets, ensures the validity of their homogenized description. The two-way coupling associated with exchanges of mass, momentum, and energy between the gas and the liquid phases is dominated by the homogenized exchanges with the gas provided collectively by the droplets, and not by the direct interaction between neighboring droplets. The formulation is used as a basis to address nonpremixed spray diffusion flames in the Burke-Schumann limit of infinitely fast chemical reactions, with the conservation equations written in terms of chemistry-free coupling functions that allow for general nonunity Lewis numbers of the fuel vapor. Laminar canonical problems that have been used in the past to shed light on different aspects of spray-combustion phenomena are also discussed, including spherical spray clouds and structures of counterflow spray flames in mixing layers. The presentation ends with a brief account of some open problems and modeling challenges.