A numerical study of internal transport in oxidizing liquid core–shell iron particles

Abstract

In an effort to improve the understanding of the rate-limiting mechanisms in liquid iron particle combustion, this study investigates the impact of internal transport within a core–shell structure. The two-dimensional axisymmetric transient continuum model as presented in previous publication (Thijs et al., 2023) is extended, such that the boundary layer between the particle and the gas, surface processes at the particle–gas interface, as well as the internal oxide layer within the particle, considering the transport of reactive O and Fe ions, are resolved. Information from the equilibrium phase diagram, which is included as supplementary data, is used to determine oxidation rate of the particle. The study reveals that finite-rate internal transport significantly alters the temperature evolution compared to models assuming infinitely fast transport. At elevated oxygen concentrations, internal transport becomes rate-limiting, restricting the maximum particle temperature. The core–shell assumption leads to a higher local oxidation degree at the particle–gas interface than the average in the particle, reducing the overall oxygen consumption rate. The maximum particle temperature is reached when heat loss exceeds heat release. Although internal transport limits the maximum temperature, the initial heating rate remains overestimated, suggesting that the initial phase is not solely limited by external oxygen diffusion, and the L2-gas surface is not at thermodynamic equilibrium. The model does not account for the particle size effect on maximum temperature as observed in some experiments. A hypothetical explanation is that internal convection, more pronounced in larger particles, may reduce the internal transport limitation, leading to higher maximum temperatures in larger particles.

Novelty and significance

This study advances the understanding of oxidation rate-limiting mechanisms in liquid iron particle combustion by numerically investigating the impact of internal transport within a core–shell structure. By using a two-dimensional axisymmetric transient continuum model, the research reveals that finite-rate internal transport significantly affects temperature evolution of an oxidizing micron-sized iron particle, particularly at elevated oxygen concentrations where it becomes rate-limiting. The findings demonstrate that a finite-rate internal transport leads to a higher local oxidation degree at the particle–gas interface, reducing the oxygen consumption rates. The study highlights that finite-rate internal transport limits the maximum particle temperature at elevated oxygen concentrations, a trend observed in isolated iron particle combustion experiments. Furthermore, this study provides a hypothetical explanation for the experimentally observed particle size effects on the maximum particle temperature, emphasizing the role of internal convection in larger particles