Formulation and analyses of vaporization and diffusion-controlled combustion of fuel sprays

Abstract

This dissertation focuses on the modelling of vaporization and combustion of sprays. A general two-continua formulation is given for the numerical computation of spray flows, including the treatment of the droplets as homogenized sources. Group combustion is considered, with the reaction between the fuel coming from the vaporizing droplets and the oxygen of the air modeled in the Burke-Schumann limit of infinitely fast chemical reaction, with nonunity Lewis numbers allowed for the different reactants. Linear combinations of the conservation equations for species and energy are used to formulate the gas-phase problem in terms of coupling functions satisfying chemistry-free conservation equations that contain sources associated with the vaporizing droplets. The resulting set of gas-phase conservations equations are accompanied by a Eulerian description of the liquid phase, with appropriate conservation equations written for the number density, velocity, temperature, and radius of the droplets. The formulation, which can be used in general in direct numerical simulations of spray diffusion flames and may also serve as starting point in modelling strategies of turbulent flows, is employed for the analysis of two different spray problems. First, the two-continua formulation is used to investigate by numerical and asymptotic methods the group vaporization of a monodisperse fuel-spray jet discharging into a hot coflowing gaseous stream for steady flow. 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 ?c, defined as the mass of liquid fuel per unit mass of gas in the spray stream, and the group vaporization parameter ?, 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 ? 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 ?, 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 quasisteady vaporization front. Separate consideration of dilute and dense sprays, corresponding, respectively, to the asymptotic limits ?c <<1 and ?c>> 1, enables simplified descriptions to be obtained for the different flow variables, including explicit analytic expressions for the spray penetration distance. Second, the general formulation is employed for the analysis of the combustion of a typical hollow cone spray issuing from a pressure swirl atomizer for injection conditions such that the breakup length from the injector is comparable to the vaporization length. The characteristic Reynolds number is large enough for the resulting flow to be slender, thereby enabling the boundary-layer approximation to be employed. Numerical computations are used to investigate the dependence of the solution on the two parameters mainly controlling the flow, namely, the characteristic dilution parameter,?c, and the ratio of the atomization-to-vaporization lengths, lBU, both assumed to be or oder unity. The highly simplified flow configurations investigated here facilitate understanding of the underlying physical phenomena involved in the vaporization and combustion of sprays. Despite the associated simplifications, it is expected that many of the results obtained, such as influences of dilution, apply qualitatively also to realistic configurations. Besides, by replacing the molecular diffusivity by an appropriately selected turbulent diffusivity, quantitative information, including for instance penetration distances, could also be extracted for direct use in evaluating overall combustion properties of spray flames. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------