Combining a population balance approach with detailed chemistry to model the condensation of oxide smoke during aluminum combustion in spatially homogeneous reactors

Abstract

At high temperatures, aluminum particles can be burned exothermally in oxidizing atmospheres in a similar way to carbon-based particulate fuels. The main reaction product, aluminum oxide (Al2O3, alumina), is solid under ambient conditions and may form through two distinct chemical pathways. On the one hand, vapourized aluminum burns in the gas phase, leading to the condensation of aluminum oxide into very fine smoke droplets that are thought to be nano-sized. On the other hand, heterogeneous reactions at the particle surface cause a direct conversion of aluminum into aluminum oxide and result in the transformation into a bi-phasic aluminum/alumina particle. As aluminum powder is being investigated as a potential carbon-free, recyclable energy carrier, we face unanswered questions about the droplet sizes within the oxide smoke and the techniques required for extraction from flue gases. This article constitutes a first step towards a detailed modelling framework for predicting alumina smoke size distributions.Physically, the oxide droplet size distribution is influenced by the ambient gas phase composition and shaped by the mutual competition of nucleation, condensational surface growth, evaporation, dissociation and coagulation. The heat release and dispersion temperature, on the other hand, are affected by chemical reactions, the gas-to-liquid phase change and radiation. In this article, we present a complete set of droplet formation and interaction kinetics for alumina droplets and analyze the interaction, competition and mutual reinforcement of the relevant physical processes in a perfectly stirred reactor and a partially stirred reactor. These simplified model formulations are representative of the dynamics that characterize the changes in gas phase composition and droplet size distribution in a single grid cell during the reaction and droplet formation fractional steps of a spatially inhomogeneous laminar reactive flow solver or a one-point, one-time probability density function (PDF) description. The partially stirred reactor model is extended to account for the presence of a reactive surface with small-scale variability in terms of surface composition. Detailed chemical and heterogeneous surface kinetics, also including NOx formation, are taken into account. Finally, we point out open challenges and incomplete kinetic or constitutive information.