Optimised 0D model for the simulation of single iron particle combustion

Abstract

This paper proposes a 0D modelling strategy for the combustion of a single iron particle. The primary objective was to accurately represent the evolution of the particle temperature, including key parameters such as the peak temperature $T_{\max }$ and associated characteristic burn time ${\tau }_b$, and oxidation dynamics in a wide range of conditions. An optimisation approach, rather than a purely mechanistic model, was chosen to further close the current gap between numerical simulations and experimental observations. The model considers oxidation processes, heat transfer, solid–liquid phase changes and dissociative evaporation. Intra-particle reaction rates are controlled by external ${\text{O}}_2$ diffusion combined with an optimised ${\text{O}}_2$ absorption reduction quantity $\gamma$, but at the end of the combustion process by a more adequate empirical kinetic rate. A first combustion stage involving the reaction $2\text{Fe}+{\text{O}}_2\to 2\text{FeO}$ is followed by two successive stages with the respective reactions $6\text{FeO}+{\text{O}}_2\to 2{\text{Fe}}_3{\text{O}}_4$ and $4{\text{Fe}}_3{\text{O}}_4+{\text{O}}_2\to 6{\text{Fe}}_2{\text{O}}_3$. This oxidation strategy is based on the Fe-O phase diagram and experimental observations of oxidation beyond FeO. Mass and enthalpy balances for the particle gave its temperature evolution, which was compared with experimental data and state of the art modelling approaches. The numerical overestimation of $T_{\max }$ in environments with elevated ${\text{O}}_2$ concentration was addressed via the optimised quantity $\gamma$, which was modelled as piecewise constant, changing once at a predetermined burn time based on experimental measurements of the burn time ${\tau }_b$. Correlations for the moment of reduction of the quantity $\gamma$ and for its initial value were introduced, both related to the initial particle diameter and ${\text{O}}_2$ molar fraction in the gas. Further model refinement is required to enhance the accuracy of simulated cooling rates in high-temperature combustion environments, where experimental data are particularly scarce. In another scenario, characterised by reduced ${\text{O}}_2$ conditions and hitherto unexplored in the numerical modelling literature, an underestimation of $T_{\max }$ was found even assuming the maximum possible oxidation rate. This observation has prompted the authors to question the suitability of the correlations used in existing models to calculate the convection coefficient, which seems to be slightly overestimated. The proposed simple and efficient modelling framework has demonstrated its potential ability to accurately reproduce key combustion characteristics of a burning iron particle in a wide range of conditions. And it will thus serve as a good starting point for the simulation of heterogeneous particle-laden reactive flows.