Aluminum Particles–air Detonation at Elevated Pressures

The effect of initial pressure on aluminum particles–air detonation was experimentally investigated in a 13 m long, 80 mm diameter tube for 100 nm and 2 μm spherical particles. While the 100 nm Al–air detonation propagates at 1 atm initial pressure in the tube, transition to the 2 μm aluminum–air detonation occurs only when the initial pressure is increased to 2.5 atm. The detonation wave manifests itself in a spinning wave structure. An increase in initial pressure increases the detonation sensitivity and reduces the detonation transition distance. Global analysis suggests that the tube diameter for single-head spinning detonation or characteristic detonation cell size would be proportional to (d ₀: aluminum particle size, p ₀: initial pressure). Its application to the experimental data results in m ~ O(1) and n ~ O(1) for 1 to 2 μm aluminum–air detonation, thus indicating a strong dependence on initial pressure and gas-phase kinetics for the aluminum reaction mechanism in detonation. Hence, combustion models based on the fuel droplet diffusion theory may not be adequate in describing micrometric aluminum–air detonation initiation, transition and propagation. For 2 μm aluminum–air mixtures at 2 atm initial pressure and below, experiments show a transition to a “dust quasi-detonation” that propagates quasi-steadily with a shock velocity deficit nearly 40% with respect to the theoretical C–J detonation value. The dust quasi- detonation wave can propagate in a tube with a diameter less than 0.4–0.5 times the diameter required for a spinning detonation wave.     

Numerical study of the detonation structure in rich H2?NO2/N2O4 and very lean H2?N2O mixtures

In some mixtures and under certain conditions, detonation soot records show substructures. In nitromethane and nitrogen tetroxide mixtures, particular cellular structures can be observed. This kind of structures has been reported as the so-called double cellular structure. One- and two-dimensional simulations of detonation have shown that the double cellular structure is related to a non-monotonous energy release. Two-step energy release is also observed in rich H₂−NO₂/N₂O₄ and in very lean H₂−N₂O mixtures. The present study aims at the investigation of the effect of the energy release profile on the detonation structure in these two mixtures through numerical simulations. The origin of the non-monotonous energy release is explained in both mixtures using one-dimensional simulations with detailed chemistry. Reduced kinetic schemes are obtained and used to perform two-dimensional simulations. It is shown that in rich H₂−NO₂/N₂O₄ mixtures, the double cellular structure appears, whereas in very lean H₂−N₂O mixtures, classical substructures are observed. Both behaviours are explained based on ZND calculations and previous stability results. Phenomenological considerations led the authors to link the formation of the double cellular structure with the appearance of a large scale instability mode (a super cellular structure).     

Two-cell detonation: losses effects on cellular structure and propagation in rich H2–NO2/N2O4–Ar mixtures

Detonation experiments in H₂–NO₂/N₂O₄–Ar mixtures (Equivalence ratio 1.2 and initial pressure lower than 0.1 MPa) confined in a tube of internal diameter 52 mm reveal two propagation regimes depending on initial pressure: (1) a quasi-CJ regime is observed along with a double cellular structure at high pressures; (2) at lower pressures, a low velocity detonation regime is observed with a single structure. Transition between this two regimes happens when the spinning detonation of the larger cell vanishes. Each detonation regime is characterized by velocity and pressure measurements and cellular structure records. Coherence between all experimental data for each experiment leads in assumption that losses are responsible for the transition between one regime to another. In a second part, we study such behaviour for a two-step mixture through numerical simulations using a global two-step chemical kinetics and a simple losses model. Numerical simulations qualitatively agree with experiments. Both detonation regimes with their own cellular structures are reproduced.     

Detonability of THDCPD-exo–air mixtures

In the frame of industrial risk and propulsive application, the detonability study of JP10–air mixtures was performed. The simulation and measurements of detonation parameters were performed for THDCPD-exo/air mixtures at various initial pressure (1 bar < P ₀ < 3 bar) and equivalence ratio (0.8 < Φ < 1.6) in a heated tube (T ₀ ~ 375 K). Numerical simulations of the detonation were performed with the STANJAN code and a detailed kinetic scheme of the combustion of THDCPD. The experimental study deals with the measurements of detonation velocity and cell size λ. The measured velocity is in a good agreement with the calculated theoretical values. The cell size measurements show a minimum value for Φ ~ 1.2 at every level of initial pressure studied and the calculated induction length L _i corresponds to cell size value with a coefficient k = λ/L _i = 24 at P ₀ = 1 bar. Based on the comparison between the results obtained during this study and those available in the literature on the critical initiation energy E _c, critical tube diameter d _c and deflagration to detonation transition length L _DDT, we can conclude that the detonability of THDCPD–air mixtures corresponds to that of hydrocarbon–air mixtures.

---

This paper is based on the work presented at the 33rd International Pyrotechnics Seminar, IPS 2006, Fort Collins, July 16–21, 2006.     

Investigation of detonation initiation in aluminium suspensions

Detonation initiation is investigated in aluminium/oxygen and aluminium/air mixtures. Critical conditions for initiation of spherical detonations are examined in analogy with the criteria defined for gaseous mixtures, which correlate critical parameters of detonation initiation to the characteristic size of the cellular structure. However, experimental data on the detonation cell size in these two-phase mixtures are very scarce, on account of the difficulty to perform large-scale experiments. Therefore, 2D numerical simulations of the detonation cellular structure have been undertaken, with the same combustion model for Al/air and Al/O₂ mixtures. The cell size is found to be λ = 37.5 cm for a rich (r = 1.61) aluminium–air mixture, and λ = 7.5 cm for a stoichiometric aluminium-oxygen mixture, which is in reasonable agreement with available experimental data. Calculations performed in large-scale configurations (up to 25 m in length and 1.5 m in lateral direction) suggest that the critical initiation energy and predetonation radius for direct initiation of the unconfined detonation in the aluminium–air mixture are, respectively, 10 kg of TNT and 8 m. Moreover, numerical simulations reveal that the structure of the detonation wave behind the leading front is even more complicated than in pure gaseous mixtures, due to two-phase flow effects. This paper is based on work that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Measurement and scaling analysis of critical energy for direct initiation of gaseous detonations

In this paper, the critical energies required for direct initiation of spherical detonations in four gaseous fuels (C₂H₂, C₂H₄, C₃H₈ and H₂)–oxygen mixtures at different initial pressures, equivalence ratios and with different amounts of argon dilution are reported. Using these data, a scaling analysis is performed based on two main parameters of the problem: the explosion length R _o that characterizes the blast wave and a characteristic chemical length that characterizes the detonation. For all the undiluted mixtures considered in this study, it is found that the relationship is closely given by R_o ? 26 l{R_{\rm o} \approx 26 \lambda} , where λ is the characteristic detonation cell size of the explosive mixture. While for C₂H₂–2.5O₂ mixtures highly diluted with argon, in which cellular instabilities are shown to play a minor role on the detonation propagation, the proportionality factor increases to 37.3, 47 and 54.8 for 50, 65 and 70% argon dilution, respectively. Using the ZND induction length Δ _I as the characteristic chemical length scale for argon diluted or ‘stable’ mixtures, the explosion length is also found to scale adequately with R_o ? 2320 D_I{R_{\rm o} \approx 2320 \Delta_I} .     

On the origin of the double cellular structure of the detonation in gaseous nitromethane and its mixtures with oxygen

An experimental study of the detonation in gaseous nitromethane (NM) and nitromethane-oxygen mixtures has exhibited unambiguously the existence of a double cellular structure in the range of equivalence ratio from 1.3 to 1.75 (NM). Calculations of the reaction zone of the detonation in the same range of equivalence ratio, using a detailed chemical scheme in the ZND model, demonstrate that the chemical energy is released in two main successive distinct exothermic reaction steps characterized by their own induction length which justifies the existence of a two levels detonation cellular structure. This result strengthens the idea that the cellular detonation structure finds its origin in instabilities amplified by delayed local high energy release rate inside the reaction zone.Received: 2 February 2002, Accepted: 27 May 2004, Published online: 7 December 2004[/PUBLISHED]H.-N. Presles: Correspondence to     

Structure cellulaire de la détonation des mélanges H2–NO2/N2O4Cellular structure of the detonation of gaseous mixtures H2–NO2/N2O4

Calculations of the detonation reaction zone of gaseous reactive mixtures of NO₂/N₂O₄ as oxidizer and H₂, CH₄ or C₂H₆ as fuel, in the range of equivalence ratio Φ between 0.5 and 2, show that, for Φ?1, the chemical energy is released in two distinct and successive exothermic steps with different chemical induction times. The first exothermic stage is mainly due to the reaction NO₂+H→NO+OH, NO being the main oxidizer of the second one.The experimental study conducted on the same range of equivalence ratio (0.5?Φ?2) shows that, for Φ?1, the detonation wave of these mixtures contains a double set of cellular structures. A similar result had already been obtained with the detonation of gaseous Nitromethane, the NO₂ group being here included in the molecule. Consequently, the oxidizer NO₂ being either initially separated from the fuel or included inside the molecule of a monopropellant (Nitromethane) is responsible, because of its specific chemical kinetics, of a chemical energy release in two main steps and of the existence of a double cellular structure in the detonation wave for the same range of equivalence ratio. These results reinforce the assumption that the cellular structure of the detonation finds its origin in the strong rates of chemical energy release inside the reaction zone. To cite this article: F. Joubert et al., C. R. Mecanique 331 (2003).     

Inhibition of detonation wave with halogenated compounds

The influence of CF₃Br, CF₂HBr, CF₂HCl and CF₃H on a benchmark mixture composed of stoichiometric H₂−CO−O₂−Ar is experimentally investigated. Several ratios hydrogen/carbon monoxide are studied. For each benchmark mixture, the initial pressure is adjusted in such a way that the detonation cell sizes are quasi identical. The effect of the additives on the detonation velocity and the detonation cellular structure is analyzed. The experiments show that CF₃Br is the best inhibitor and CF₂HBr might be substituted for CF₃Br. CF₃H does not inhibit the detonation wave. Simple chemical kinetics analysis gives us a better understanding of the inhibiting and promoting effect of the halocarbons. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995     

Etude de la détonation de mélanges pauvres H2NO2/N2O4

Calculations of the detonation reaction zone of gaseous H₂NO₂/N₂O₄ mixtures in the range of equivalence ratio Φ between 0.25 and 0.7 show that for 0.25Φ0.4 the chemical energy is released in two distinct and successive exothermic steps characterised by different chemical characteristic times. As for rich mixtures, the first exothermic step is mainly due to the reaction NO₂ + H → NO + OH, but the second one is different since it results from the exothermic decomposition of NO into N₂ and O₂. For Φ=0.3 the measured detonation velocity in a tube of 52 mm internal diameter is very much smaller than the calculated value and the mean size of the cellular structure is very much larger than the value extrapolated from data obtained with mixtures of higher but close equivalence ratio. All these results show that the detonation, though self-sustained and steady, is ‘non-ideal’, i.e. it is supported only by a part of the available chemical energy, that provided mainly by the first exothermic step. To cite this article: D. Desbordes et al., C. R. Mecanique 332 (2004).     

The influence of cellular structure on detonation transmission

We present two-dimensional numerical simulations of the transmission of detonation from a rectangular channel into a larger volume. The simulations solve the Euler equations on a Cartesian grid using the method of Flux-Corrected Transport for the fluid equations and a two-step induction parameter model for the chemistry. We simulate detonation in a H₂/O₂/Ar mixture and use sufficient grid resolution to resolve the cellular structure of the detonation. When a planar detonation front without a resolved cellular structure expands into the larger volume, the reaction front separates from the shock front and the detonation fails. When the planar front is perturbed to induce a quasi-regular cellular structure in the detonation, it again initially begins to fail, but now the presence of the transverse waves leads to reignition of the detonation in the larger volume. The form of this reignition shows striking similarities to the reignition of detonation which has been seen experimentally in H₂/O₂ mixtures. We describe this reignition mechanism in detail, and also investigate the dependence of the reignition on the number of cells in the detonation front. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995     

Optimization of the deflagration to detonation transition: reduction of length and time of transition

The aim of this experimental investigation is the study of Deflagration to Detonation Transition (DDT) in tubes in order to (i) reduce both run-up distance and time of transition (L _DDT and t _DDT) in connection with Pulsed Detonation Engine applications and to (ii) attempt to scale L _DDT with λ_CJ (the detonation cellular structure width). In DDT, the production of turbulence during the long flame run-up can lead to L _DDT values of several meters. To shorten L _DDT, an experimental set-up is designed to quickly induce highly turbulent initial flow. It consists of a double chamber terminated with a perforated plate of high Blockage Ratio (BR) positioned at the beginning of a 26 mm inner diameter tube containing a “Shchelkin spiral” of BR ≈ 0.5. The study involves stoichiometric reactive mixtures of H₂, CH₄, C₃H₈, and C₂H₄ with oxygen and diluted with N₂ in order to obtain the same cell width λ_CJ≈10 mm at standard conditions. The results show that a shock-flame system propagating with nearly the isobaric speed of sound of combustion products, called the choking regime, is rapidly obtained. This experimental set-up allows a L _DDT below 40 cm for the mixtures used and a ratio L _DDT/λ_CJ ranging from 23 to 37. The transition distance seems to depend on the reduced activation energy (E _a/RT _c) and on the normalized heat of reaction (Q/a ₀ ²). The higher these quantities are, the shorter the ratio L _DDT/λ_CJ is. PACS 47.40.Rs · 47.60.+i · 47.70.Pq · 47.80.CbThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

Two-dimensional numerical simulations of multi-headed detonations in oxygen-aluminum mixtures using an adaptive mesh refinement

Abstract. Two-dimensional numerical simulations of detonations in two-phase lean mixtures of aluminum particles and pure oxygen have been performed. The computational procedure adopts an adaptive mesh refinement methodology in order to increase spatial resolution in the most interesting parts of the flow field. A one-step heterogeneous reaction describes the evaporation and combustion of aluminum. Depending on the gas-phase temperature, the combustion product is aluminum oxide or aluminum monoxide. The results show that the heterogeneous detonations resemble gaseous single-phase ones although the scale of the phenomena is very different. The detonation of aluminum dust evolves into the 2-headed mode of propagation with the characteristic detonation cell width equal to cm. For aluminum dust the cellular structure is much finer. The detonation initially propagates in the 11-headed mode with the characteristic cell width equal to cm and evolves into the 8.5-headed mode with the characteristic cell size $\lambda_{\rm cell}$ equal to cm. Received 7 May 2001 / Accepted 25 March 2002 Published online 23 January 2003 Correspondence to: K. Benkiewicz (e-mail: kbenk@cow.me.aoyama.ac.jp)     

Existence of the detonation cellular structure in two-phase hybrid mixtures

The cellular detonation structure has been recorded for hybrid hydrogen/air/aluminium mixtures on 1.0 m 0.110 m soot plates. Addition of aluminium particles to the gaseous mixture changes its detonation velocity. For very fine particles and flakes, the detonation velocity is augmented and, in the same time, the cell width diminishes as compared with the characteristic cell size of the mixture without particles. On the contrary, for large particles, the detonation velocity decreases and the cell size becomes larger than . It appears that the correlation law between the cell size and the detonation velocity in the hybrid mixture is similar to the correlation between the cell size and the rate of detonation overdrive displayed for homogeneous gaseous mixtures. Moreover, this correlation law remains valid in hybrid mixtures for detonation velocities smaller than the value D of the mixture without particles. Received 10 May 2001 / Accepted 12 August 2002 Published online 19 December 2002 Correspondence to: B. Veyssiere (e-mail: veyssiere@lcd.ensma.fr)     

DDT in fuel–air mixtures at elevated temperatures and pressures

An experimental study was carried out to investigate flame acceleration and deflagration-to-detonation transition (DDT) in fuel–air mixtures at initial temperatures up to 573 K and pressures up to 2 atm. The fuels investigated include hydrogen, ethylene, acetylene and JP-10 aviation fuel. The experiments were performed in a 3.1-m long, 10-cm inner-diameter heated detonation tube equipped with equally spaced orifice plates. Ionization probes were used to measure the flame time-of-arrival from which the average flame velocity versus propagation distance could be obtained. The DDT composition limits and the distance required for the flame to transition to detonation were obtained from this flame velocity data. The correlation developed by Veser et al. (run-up distance to supersonic flames in obstacle-laden tubes. In the proceedings of the 4th International Symposium on Hazards, Prevention and Mitigation of Industrial Explosions, France (2002)) for the flame choking distance proved to work very well for correlating the detonation run-up distance measured in the present study. The only exception was for the hydrogen–air data at elevated initial temperatures which tended to fall outside the scatter of the hydrocarbon mixture data. The DDT limits obtained at room temperature were found to follow the classical d/λ = 1 correlation, where d is the orifice plate diameter and λ is the detonation cell size. Deviations found for the high-temperature data could be attributed to the one-dimensional ZND detonation structure model used to predict the detonation cell size for the DDT limit mixtures. This simple model was used in place of actual experimental data not currently available. PACS 47.40.-x; 47.70.Fw This paper was based on work that was presented at the 19th Interna-tional Colloquium on the Dynamics of Explosions and Reactive Sys-tems, Hakone, Japan, July 27 - August 1, 2003     

Dynamics study of detonation-wave cellular structure 1. Statistical properties of detonation wave front

We have investigated the evolution of cellular detonation-wave structure as a gaseous detonation travels along a round tube and measured cell lengths as a function of the initial pressure of the gas. We have tested acetylene-containing combustible gas mixtures with different degrees of regularity. Along with the smoked-foil technique, an emission method has been used to the measure current and average values of the detonation cell length. The method is based on the detection of an emission spectrum behind the detonation front in the spectral range corresponding to local gas temperatures that are much higher than those for the Chapman-Jouguet equilibrium condition. This technique provides quasi-continuous cell-length measurements along the normal to the detonation front over the length of several factors of ten times the tube. Our study has experimentally identified the steady states of detonation structure in round tubes, referred to here as the single detonation modes. When the state of a single mode is fully established, then both the flow structure and the energy release at detonation front develop strictly periodically along the tube at a constant frequency inversely proportional to the cell length of the mixture. The mixture regularity has had no influence on the occurrence of the detonation mode, which is defined by the value of initial pressure or the total energy release of the mixture. Outside of the pressure range where a detonation mode was most likely to occur, the detonation front is unstable and may exhibit an irregular cellular pattern. Monitoring the evolution of cells over a long distance revealed that the local gas emissivity, which is time dependent and corresponds to axial pulsations of the detonation structure, has the appearance of a superposition of separate harmonics describing the states of emissivity oscillations and cell structure of single detonation modes. Received 18 October 1999 / Accepted 10 June 2001     

Experimental observation of the onset of detonation downstream of a perforated plate

In this study, the onset of detonation downstream of a perforated plate subsequent to the reflection of a Chapman–Jouguet detonation upstream is investigated. The experiments were performed with C₃H₈ + 5O₂ and C₂H₂+2.5O₂+70%Ar. The former has a much more irregular transverse wave pattern whereas the latter is known to have a piecewise laminar structure with a regular cellular structure. The onset of detonation phenomenon was found to be significantly different for the two mixtures. For the high argon diluted mixtures, the onset of detonation occurs in the vicinity downstream of the perforated plate. However, if the onset of detonation does not occur close to the plate, the precursor shock decouples from the reaction zone and a deflagration results. For the propane–oxygen mixtures, the onset of detonation is found to occur relatively far from the perforated plate at critical conditions. The major difference between these two mixtures is that the metastable turbulent reaction front can be maintained for relatively long distances for the propane–oxygen mixture. This turbulent metastable regime is also observed to be able to maintain a relatively constant propagation velocity for many channel widths prior to the onset of detonation. For the propane–oxygen mixtures, the onset is caused by a strong local explosion within the turbulent reaction zone.     

Comparison of critical conditions for DDT in regular and irregular cellular detonation systems

Abstract. The results of an experimental study of DDT in mixtures with regular and irregular detonation cellular structures are presented. Experiments were carried out in a tube 174 mm i. d. with obstacles (blockage ratios were 0.1, 0.3, and 0.6). Mixtures used were hydrogen–air and stoichiometric hydrogen–oxygen diluted with , Ar, and He. The critical conditions for DDT are shown to depend on the regularity of the cellular structure of test mixtures. The critical values of the cell sizes in Ar- and He-diluted mixtures are shown to be significantly smaller than those in -diluted mixtures. This means that systems with a highly regular detonation cellular structure have far less capacity for undergoing DDT compared to irregular ones with the same values of detonation cell sizes. Received 18 November 1999 / Accepted 15 May 2000     

Detonation diffraction from an annular channel

In this study, gaseous detonation diffraction from an annular channel was investigated with a streak camera and the critical pressure for transmission of the detonation wave was obtained. The annular channel was used to approximate an infinite slot resulting in cylindrically expanding detonation waves. Two mixtures, stoichiometric acetylene–oxygen and stoichiometric acetylene–oxygen with 70% Ar dilution, were tested in a 4.3 and 14.3 mm channel width (W). The undiluted and diluted mixtures were found to have values of the critical channel width over the cell size around 3 and 12 respectively. Comparing these results to values of the critical diameter (d _c ), in which a spherical detonation occurs, a value of critical d _c /W _c near 2 is observed for the highly diluted mixture. This value corresponds to the geometrical factor of the curvature term between a spherical and cylindrical diverging wave. Hence, the result is in support of Lee’s proposed mechanism [Lee in Dynamics of Exothermicity, pp. 321, Gordon and Breach, Amsterdam, 1996] for failure due to diffraction based on curvature in stable mixtures such as those highly argon diluted with very regular detonation cellular patterns.     

Reconsideration on the role of the specific heat ratio in Arrhenius law applications

Arrhenius law implicates that only those molecules which possess the internal energy greater than the activation energy Ea can react. However, the internal energy will not be proportional to the gas temperature if the specific heat ratio y and the gas constant R vary during chemical reaction processes. The varying y may affect significantly the chemical reaction rate calculated with the Arrhenius law under the constant γ assumption, which has been widely accepted in detonation and combustion simulations for many years. In this paper, the roles of variable γ and R in Arrhenius law applications are reconsidered, and their effects on the chemical reaction rate are demonstrated by simulating one- dimensional C-J and two-dimensional cellular detonations. A new overall one-step detonation model with variable γ and R is proposed to improve the Arrhenius law. Numerical experiments demonstrate that this improved Arrhenius law works well in predicting detonation phenomena with the numerical results being in good agreement with experimental data.