Sheath vaporization of a monodisperse fuel-spray jet

Abstract

The group vaporization of a monodisperse fuel-spray jet discharging into a hot coflowing gaseous stream is investigated for steady flow by numerical and asymptotic methods with a two-continua formulation used for the description of the gas and liquid phases. The jet is assumed to be slender and laminar, as occurs when the Reynolds number is moderately large, so that the boundary-layer form of the conservation equations can be employed in the analysis. Two dimensionless parameters are found to control the flow structure, namely the spray dilution parameter λ, defined as the mass of liquid fuel per unit mass of gas in the spray stream, and the group vaporization parameter ϵ, defined as the ratio of the characteristic time of spray evolution due to droplet vaporization to the characteristic diffusion time across the jet. It is observed that, for the small values of ϵ often encountered in applications, vaporization occurs only in a thin layer separating the spray from the outer droplet-free stream. This regime of sheath vaporization, which is controlled by heat conduction, is amenable to a simplified asymptotic description, independent of ϵ, in which the location of the vaporization layer is determined numerically as a free boundary in a parabolic problem involving matching of the separate solutions in the external streams, with appropriate jump conditions obtained from analysis of the quasi-steady vaporization front. Separate consideration of dilute and dense sprays, corresponding, respectively, to the asymptotic limits λ ≪ 1 and λ ≫ 1, enables simplified descriptions to be obtained for the different flow variables, including explicit analytic expressions for the spray penetration distance.