Mechanistic Model for Aluminum Particle Ignition and Combustion in Air

A mechanistic model for the ignition and combustion of an isolated aluminum particle burning in air is presented. The model consists of two stages, ignition and combustion. In the ignition stage, melting and heterogeneous surface reactions (HSR) are assumed to occur until a predefined transition temperature of the oxide is attained. In the combustion stage, a quasi-steady state diffusion flame is assumed, and a new conserved scalar formulation is presented that accounts for the deposition of metal oxide on the surface of the molten aluminum. A system of nonlinear ordinary differential equations that describes each stage self-consistently with the gas-phase analysis is developed. Representative results are presented for a range of ambient temperature conditions and compared to experimental measurements. Predictions of overall burn rates, particle velocity, and flame radius show good agreement with experimental data. Also discussed is the extension of the conserved scalar approach to include a more generalized oxidizing environment as well as HSR from nitride reactions during the quasi-steady burning stage. Nomenclature A = surface area A1 = preexponential constant B = transfer number Bi = Biot number C = specific heat CD = drag coefficient D = diameter Dl + s = particle diameter from liquid and solid phases Dm = diffusivity coefficient Ea = activation energy f = ratio of metal-oxide surface sink to total mass flux h = convection coefficient, total enthalpy (i.e., sensible plus chemical) hlg = heat of vaporization hr,gs = heat of reaction for homogeneous gas-phase reactions hr,ls = heat of reaction for heterogeneous surface reactions k = thermal conductivity m = mass m ̇ lg = mass evaporation rate of liquid aluminum from evaporation m ̇ ls = mass consumption rate of liquid aluminum to form solid aluminum oxide (Al2O3) ṁsl = mass transfer rate from solid to a liquid during melting Nu = Nusselt number P = pressur