The ignition of fine iron particles in the Knudsen transition regime

A theoretical model is considered to predict the minimum ambient gas temperature at which fine iron particles can undergo thermal runaway--the ignition temperature. The model accounts for Knudsen transition transport effects, which become significant when the particle size is comparable to, or smaller than, the molecular mean free path of the surrounding gas. Two kinetic models for the high-temperature solid-phase oxidation of iron are analyzed. The first model (parabolic kinetics) considers the inhibiting effect of the iron oxide layers at the particle surface on the rate of oxidation, and a kinetic rate independent of the gaseous oxidizer concentration. The ignition temperature is solved as a function of particle size and initial oxide layer thickness with an unsteady analysis considering the growth of the oxide layers. In the small-particle limit, the thermal insulating effect of transition heat transport can lead to a decrease of ignition temperature with decreasing particle size. However, the presence of the oxide layer slows the reaction kinetics and its increasing proportion in the small-particle limit can lead to an increase of ignition temperature with decreasing particle size. This effect is observed for sufficiently large initial oxide layer thicknesses. The continuum transport model is shown to predict the ignition temperature of iron particles exceeding an initial diameter of 30 $\mu$m to a difference of 3% (30 K) or less when compared to the transition transport model. The second kinetic model (first-order kinetics) considers a porous, non-hindering oxide layer, and a linear dependence of the kinetic rate of oxidation on the gaseous oxidizer concentration. The ignition temperature is resolved as a function of particle size with the transition and continuum transport models, and the differences between the ignition characteristics predicted by the two models are discussed

Combustion behavior of single iron particles-part I:An experimental study in a drop-tube furnace under high heating rates and high temperatures

Micrometric spherical particles of iron in two narrow size ranges of (38–45) µm and (45–53) µm were injected in a bench scale, transparent drop-tube furnace (DTF), electrically heated to 1400 K. Upon experiencing high heating rates (104–105 K/s) the iron particles ignited and burned. Their combustion behavior was monitored pyrometrically and cinematographically at three different oxygen mole fractions (21%, 50% and 100%) in nitrogen. The results revealed that iron particles ignited readily and exhibited a bright stage of combustion followed by a dimmer stage. There was evidence of formation of envelope micro-flames around iron particles (nanometric particle mantles) during the bright stage of combustion. As the burning iron particles fell by gravity in the DTF, contrails of these fine particles formed in their wakes. Peak temperatures of the envelope flames were in the range of 2500 K in air, climbing to 2800 K in either 50% or 100% O2. Total luminous combustion durations of particles, in the aforesaid size ranges, were in the range of 40–65 ms. Combustion products were bimodal in size distribution, consisting of micrometric black magnetite particles (Fe3O4), of sizes similar to the iron particle precursors, and reddish nanometric iron oxide particles consisting mostly of hematite (Fe2O3).</p

A quantitative analysis of the ignition characteristics of fine iron particles

Ignition of iron particles in an oxidizing environment marks the onset of self-sustained combustion. The objective of the current study is to quantitatively examine the ignition characteristics of fine iron particles (i.e., 1µm- to 100µm-sized) governed by the kinetics of solid-phase iron oxidation. The oxidation rates are inversely proportional to the thickness of the oxide layer (i.e., following a parabolic rate law) and calibrated using the experimentally measured growth of iron-oxide layers over time. Steady-state (i.e., Semenov's analysis) and unsteady analysis have been performed to probe the dependence of the critical gas temperature required to trigger a thermal runaway (namely, the ignition temperature T ign) on particle size, initial thickness of oxide layer, inert gas species, radiative heat loss, and the collective heating effect in a suspension of particles. Both analyses indicate that T ign depends on δ 0, i.e., the ratio between the initial oxide layer thickness and particle size, regardless of the absolute size of the particle. The unsteady analysis predicts that, for δ 0≲0.003, T ign becomes independent of δ 0. Under standard conditions in air, T ign is approximately 1080 K for any particle size greater than 5µm. The ignition temperature decreases as the thermal conductivity of the oxidizing gas decreases. Radiative heat loss has a minor effect on T ign. The collective effect of a suspension of iron particles in reducing T ign is demonstrated. The transition behavior between kinetic-controlled and external-diffusion-controlled combustion regimes of an ignited iron particle is systematically examined. The influences of initial oxide-layer thickness and particle temperature on the ignition delay time, τ ign, of iron particles are parametrically probed. A d 2-law scaling between τ ign and particle size is identified. Possible sources of inaccuracy are discussed

Combustion behavior of single iron particles, Part II: A theoretical analysis based on a zero-dimensional model

Following the ignition and solid-to-liquid phase transition of a fine (on the order of 10–100µm in diameter) iron particle, the self-sustained combustion of a liquid-phase droplet of iron and its oxides takes place. The objective of the current work is to develop an interpretive and explanatory model for the liquid-phase combustion of a single fine iron particle. A zero-dimensional physicochemical model is developed assuming fast internal processes, such that the combustion rate is limited by the rate of external oxygen (O2) transport. The model considers a particle covered by a shell of liquid-phase FeO enclosing a core of liquid-phase Fe. Stefan flow and diffusion are considered for the gas-transport of O2, while the gas-transport of gas-phase Fe and FeO are calculated via diffusion only. The outward gas-phase Fe and FeO consume inward-transported O2 to stoichiometrically form hematite (Fe2O3), and the remaining oxygen that reaches the particle surface is entirely consumed to form liquid-phase FeO. The time history of simulated particle temperature shows consistent overprediction of the peak particle temperature when compared to experimental temperature measurements, indicating that the assumption of fast internal kinetics may be incorrect. The model is also unable to capture the apparent slow cooling rate observed in experiments. A further analysis is performed through a heuristic model with a calibrated reaction-rate law, where the internal diffusion of reactive Fe and O ions may become rate-limiting. The calibration of the pre-exponential factor in the Arrhenius term to match the experimental peak temperature yielded good agreement of time to peak temperature, as well as the slow cooling rate. The heuristic model considering internal diffusion predicts a plateau in peak temperature with increasing oxygen concentration. Possible uncertainties of the models, as well as future work, are discussed