Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium, and thus a constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatio-temporal averaged structure of the waves in these systems is analyzed via a Favre averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical non-equilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed

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

Numerical study of cellular detonation wave reflection over a cylindrical concave wedge

Numerical simulations were performed to study reflection of a stable detonation wave with regular cellular patterns over a cylindrical concave wedge. The dynamics of this reflection phenomenon was described by the two-dimensional reactive Euler equations with a two-step induction-reaction kinetic model and solved numerically using the adaptive mesh refinement code AMROC. The effects of various parameters on the reflection evolution were analyzed in detail. The results indicate that the reflection-type transition of a stable cellular detonation is similar to that of a planar shock wave over a concave wedge. The triple-point trajectory resulted from the Mach reflection when the cellular detonation first encounters the concave wedge coincides with that of the planar shock propagating for the case with the same incident Mach number. As the effective wedge angle continuously increases, the Mach reflection of cellular detonation deviates from that of a planar shock with a reduced Mach stem height, and the transition from Mach to regular reflection occurs at a smaller angle. This observation is further explored by adopting the length-scale (or “corner-signal”) concept, examining the velocity variation of corner signals generated by fluid particles around the wedge tip. The reflection dynamics is described qualitatively by the ratio of two length scales characterizing the detonation structure, namely, the induction-zone and reaction-zone lengths. The increase of these length scales raises the Mach stem height and transition angle. Apart from the detonation length scales, the wedge curvature radius is found to have an opposite effect since the increase of radius expands the region where the corner signals are generated by the particles behind the induction zone, and makes the corner signals persist in a state with attenuating velocity

Effect of Fe–O ReaxFF on Liquid Iron Oxide Properties Derived from Reactive Molecular Dynamics

As iron powder nowadays attracts research attention as a carbon-free, circular energy carrier, molecular dynamics (MD) simulations can be used to better understand the mechanisms of liquid iron oxidation at elevated temperatures. However, prudence must be practiced in the selection of a reactive force field. This work investigates the influence of currently available reactive force fields (ReaxFFs) on a number of properties of the liquid iron-oxygen (Fe-O) system derived (or resulting) from MD simulations. Liquid Fe-O systems are considered over a range of oxidation degrees Z O, which represents the molar ratio of O/(O + Fe), with 0 &lt; Z O &lt; 0.6 and at a constant temperature of 2000 K, which is representative of the combustion temperature of micrometric iron particles burning in air. The investigated properties include the minimum energy path, system structure, (im)miscibility, transport properties, and the mass and thermal accommodation coefficients. The properties are compared to experimental values and thermodynamic calculation results if available. Results show that there are significant differences in the properties obtained with MD using the various ReaxFF parameter sets. Based on the available experimental data and equilibrium calculation results, an improved ReaxFF is required to better capture the properties of a liquid Fe-O system. </p