Sheath vaporization of a monodisperse fuel-spray jet

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 1, defined as the mass of liquid fuel per unit mass of gas in the spray stream, and the group vaporization parameter e, 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 e 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.

Regimes of spray vaporization and combustion in counterflow configurations

This article addresses the problem of spray vaporization and combustion in axisymmetric opposed-jet configurations involving a stream of hot air counterflowing against a stream of nitrogen carrying a spray of fuel droplets. The Reynolds numbers of the jets are assumed to be large, so that mixing of the two streams is restricted to a thin mixing layer that separates the counterflowing streams. The evolution of the droplets in their feed stream from the injection location is seen to depend fundamentally on the value of the droplet Stokes number, St, defined as the ratio of the droplet acceleration time to the mixing layer strain time close to the stagnation point. Two different regimes of spray vaporization and combustion can be identified depending on the value of St. For values of St below a critical value, equal to 1/4 for dilute sprays with small values of the spray liquid mass loading ratio, the droplets decelerate to approach the gas stagnation plane with a vanishing axial velocity. In this case, the droplets located initially near the axis reach the mixing layer, where they can vaporize due to the heat received from the hot air, producing fuel vapor that can burn with the oxygen in a diffusion flame located on the air side of the mixing layer. The character of the spray combustion is different for values of St of order unity, because the droplets cross the stagnation plane and move into the opposing air stream, reaching distances that are much larger than the mixing layer thickness before they turn around. The vaporization of these crossing droplets, and also the combustion of the fuel vapor generated by them, occur in the hot air stream, without significant effects of molecular diffusion, generating a vaporization-assisted nonpremixed flame that stands on the air side outside the mixing layer. Separate formulations will be given below for these two regimes of combustion, with attention restricted to the near-stagnation-point region, where the solution is self-similar and all variables are only dependent on the distance to the stagnation plane. The resulting formulations display a reduced number of controlling parameters that effectively embody dependences of the structure of the spray flame on spray dilution, droplet inertia, and fuel preferential diffusion. Sample solutions are given for the limiting cases of pure vaporization and of infinitely fast chemistry, with the latter limit formulated in terms of chemistry-free coupling functions that allow for general nonunity Lewis numbers of the fuel vapor.