The influence of spatial dispersion on the steady-state characteristics and thermodynamic instability fluctuations of one-dimensional iron particle flames

Abstract

This study utilizes a simplified one-dimensional discrete model to analyze the characteristic parameters involved in the flame propagation of iron particles. It focuses on the influence of dispersive "micro flames" within these flames on propagation dynamics, investigating stable and unstable scenarios. The model adopts the form of particle suspension delineating alternant reaction intervals and inert intervals. The spatial dispersion rate (Γ) which describes the spatial extent of the "micro flames" is introduced, with Γ = 1 for the continuum model and Γ > 1 for the discrete model. Theoretical equations, combining kinetic and diffusion equations, are solved with the finite difference method. The solution is evaluated preliminarily to distinguish numerical instability and thermodynamic instability. Additionally, in the preset time and space range, conditions for different equivalence ratios, particle radius and spatial dispersion rates are analyzed emphatically, with a comparison of typical simulation results and experimental data. As shown in the numerical simulation, the flame maintains stable propagation when ϕ≥0.7. The flame front, where the particle temperature rises above the gas temperature, extends backward with the increase of particle radius. The increase of Γ tends to extend the flame front of the fuel-lean flame and constringe that of the fuel-rich flame. Thermodynamic instability occurs in fuel-lean suspension with its manifestation preliminarily classified to distinct fluctuation, faint fluctuation and the final cessation. The increase of Γ also extends the flame propagation time under the dominance of thermodynamic instability, indicating different temperature structure evolution from the continuum model.