Modelling the combustion of metal powders in laminar and turbulent flames

Besides their ubiquitous use in load-bearing structures, metals also possess qualities of energetic materials. Lithium, for example, is a common fuel in batteries, while aluminum is frequently added to solid rocket propellants and used in pyrotechnics. At high temperatures, metal powders can be burned in air in a similar way to hydrocarbon fuels, releasing chemically stored energy as sensible heat. Contrary to hydrocarbon combustion, however, the main reaction products are solid oxide particles that can, in principle, be retrieved from the exhaust fumes. This amenability to oxide sequestration has stimulated the idea of harnessing metal powders as recyclable energy carriers which are burned, retrieved and, subsequently, recharged by a reduction process based on clean primary energy. Conceptually, the metal powders are akin to high-temperature batteries, serving as a means to buffer the large spatial and temporal intermittency associated with renewable energy sources.

Motivated by the potential use of metal powders as recyclable fuels, we qualitatively discuss the physical and chemical processes involved in the combustion of a single metal particle and of metal dusts, respectively. Subsequently, a population balance model for predicting the size distribution of the oxide smoke precipitating in the vicinity of a single burning aluminum particle is presented. Here, we specifically focus on the kinetic rates that control the phase transitions and smoke dynamics, integrating recently developed detailed kinetics for gas phase and heterogeneous surface reactions. The population balance equation governing the oxide size distribution is solved with the aid of a tailored adaptive grid method. An alternative, potentially more economical solution approach we propose is based on an embedded reduced order representation of the particle size distribution that is informed by a training step. The accuracy and convergence properties of this method are investigated for a simplified test case involving particle growth and dispersion in a laminar plane jet.

In the final part of the seminar, the physical description, from an Eulerian viewpoint, of metal powders is discussed with a particular emphasis on the ramifications of carrier flow turbulence. In order to account for the small-scale interactions between dispersed particles and the ambient gas phase, the population balance equation governing the metal powder or oxide smoke is integrated into a probabilistic description that naturally accounts for the variability among independent realizations of a turbulent, particle-laden flow. Owing to the high dimensionality of the resulting transport equations, a stochastic solution approach based on Eulerian stochastic fields is proposed for which we show preliminary accuracy and convergence analyses.

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