Detonation Cellular Structure Research Articles

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.

Detonation cellular structure in NO 2/N 2O 4–fuel gaseous mixtures

Experimental and numerical studies of the detonation in NO 2–N 2O 4/fuel (H 2, CH 4, and C 2H 6) gaseous mixtures show that for equivalence ratio Φ > 0.8 – 1 , (1) the detonation has a double cellular structure, the ratio between the cell size of each net being at least one order of magnitude; (2) inside the detonation reaction zone the chemical energy is released in two successive exothermic steps. Their chemical induction lengths, defined between the leading shock front and each local maximum heat release rate associated with each step, differ by at least one order of magnitude. The chemical reaction NO 2 + H → NO + OH is mainly responsible for the first exothermic step (fast kinetics), NO being the oxidizer on the second one (slow kinetics). Existence of correlations between calculated induction lengths and corresponding cell sizes strengthen the assumption that the cellular structure originates from local strong gradients of chemical heat release inside the detonation reaction zone.

The evolution and cellular structure of a detonation subsequent to a head-on interaction with a shock wave

This paper analyzes the results of a head-on collision between a detonation and a planar shock wave. The evolution of the detonation cellular structure subsequent to the frontal collision was examined through smoked foil experiments. It is shown that a large reduction in cell size is observed following the frontal collision, and that the detonation cell widths are correlated well with the chemical kinetic calculations from the ZND model. From chemical kinetic calculations, the density increase caused by shock compression appears to be the main factor leading to the significant reduction in cell size. It was found that depending on the initial conditions, the transition to the final cellular pattern can be either smooth or spotty. This phenomenon appears to be equivalent to Oppenheim's strong and mild reflected shock ignition experiments. The difference between these two transitions is, however, more related to the stability of the incident detonation and the strength of the perturbation generated by the incident shock.

Comments on explosion problems for hydrogen safety

The future widespread use of hydrogen as an energy carrier brings in safety issues that have to be addressed before public acceptance can be achieved. The prediction of the consequences of a major accident release of hydrogen into the atmosphere or the contamination of high-pressure hydrogen storage facilities by air entrainment requires a good knowledge of the explosion parameters of hydrogen–air mixtures. The present paper reviews and comments on the current knowledge of dynamic parameters of hydrogen detonation for hazard assessment. The major problem that remains to be resolved involves the understanding of the effect of turbulence on the cellular detonation structure, the propagation of high-speed deflagrations and the transition from deflagration to detonations. It is recommended that future research should be aimed towards experiments that permit the quantitative understanding of the mechanisms of high-speed turbulent combustion rather towards large-scale tests in complex geometries where minimal quantitative information of fundamental significance could be extracted. In spite of its wide flammability and sensitivity to ignition and detonation initiation, it is felt that hydrogen can be produced, stored and handled safely with the appropriate considerations in the design of the hydrogen facilities.

Simulation numérique des détonations à double structure cellulaire

We present the results of numerical two-dimensional simulations of detonation cellular structures under non-monotonous heat release provided by a chemical reaction comprising two successive exothermic steps. The influence of the rate of the second step of chemical reaction on the detonation cellular structure has been investigated. Our simulations are the first that reproduce a cellular structure composed of two clearly distinct sets of cells with different characteristic sizes where fine cells completely fill up larger ones, as has been observed experimentally. To cite this article: V. Guilly et al., C. R. Mecanique 334 (2006).

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 λCJ (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 λCJ≈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/λCJ 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/λCJ is.

Detonation in Mixtures of JP-10 Vapor and Air

An experimental study of the detonation properties of the high molecular weight aviation fuel JP-10 was performed. Detonation cell size measurements for mixtures of JP-10 vapor and air at elevated initial temperatures are reported. Experiments are preformed in a 6.2-m-long, 10-cm inner-diameter heated detonation tube at an initial mixture pressure of 2 atm and initial temperatures of 373, 473, and 528 K. The first half of the tube is equipped with turbulence producing orifice plates. Flame acceleration leads to detonation initiation within the first 2 m of the orifice-plate-laden part of the tube, and a detonation wave propagates in the smooth second half of the tube. The detonation cellular structure is recorded on a soot foil inserted into the end of the tube. The detonation velocity measured just before the foil is within 1 to 2% of the theoretical Chapman‐Jouget velocity. The detonation cellular structure for off-stoichiometric mixtures was found to contain substantial substructure. The average cell size is obtained by measuring the transverse distance between parallel diagonal tracks scoured onto the foil. It was found that to within the measurement uncertainty the cell size changed very little over the temperature range tested. The measured deflagration-to-detonation transition composition limits are found to correlate well with the classical detonation propagation criterion based on the detonation cell size λ and the orifice plate diameter d, that is, d/λ ≥ ≥ 1. The measured JP-10 vapor air mixture cell size is correlated with the calculated Zeldovich von Neumann Doring (ZND) induction length for propane air mixtures with similar stoichiometry.

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 \(\phi\) 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.

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 $\times$ 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 $\lambda $ diminishes as compared with the characteristic cell size $\lambda _0 $ of the mixture without particles. On the contrary, for large particles, the detonation velocity decreases and the cell size becomes larger than $\lambda _0$ . 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 $_{\rm CJ}$ of the mixture without particles.

On the shock-induced explosion resulting from an impact by a planar detonation

We analyse the processes which occur when a planar detonation propagating from the fixed end of a donor explosive charge impacts on an acceptor homogeneous explosive. We propose a model for estimating the minimal length of the donor charge for which an explosion can be generated in the acceptor. We show that the self-similarity of the donor flow imposes a minimal length on the donor charge so its piston effect be capable of keeping the volumetric-expansion rate of the shocked acceptor to small-enough values and, thereby, of triggering explosion in a finite time. The donor detonation is represented as a Chapman-Jouguet discontinuity; the chemical decomposition in the acceptor is described by the Arrhenius global rate law. The model reproduces the experimental trend according to which the smaller minimal lengths are obtained with donor explosives that have larger heats of reaction and initial pressures. The minimal lengths predicted by the model agree well with those obtained by means of one-dimensional numerical simulations. Additional simulations show that the minimal length for generating an explosion is smaller than, but perhaps of the same order as, the minimal length for generating a transition to detonation. Further work is necessary to (i) analyse the case of donor explosives with finite reaction rates, and to (ii) account for the detonation cellular structure in the simulations of shock-to-detonation transitions.

Structure and stability of weak–heat–release detonations for finite Mach numbers

The stability of an overdriven detonation wave for a one–step Arrhenius reaction in an ideal gas is examined in the limits of a finite detonation Mach number, small modified heat release γ−1)β and large activation energy θ, limits that are relevant to the generation of the regular cellular detonation structures observed experimentally in highly diluted mixtures. Here, γ is the specific heat ratio and β is the formation energy. The limiting case, β = 0, corresponds to a finite Mach number reactionless shock, which in an ideal gas is always stable. Nevertheless, for small but finite values of (γ−1)β, we will show that detonation instabilities can arise when perturbations in the reaction rate generated by a small disturbance at the shock front are sufficient in magnitude to balance the corresponding acoustic fluctuations that are also generated. These acoustic disturbances are also those that govern the stability of a reactionless shock (β = 0). Such reaction–rate perturbations are only generated for sufficiently large activation energies, and it is the precise magnitude of the activation energy that leads to detonation instability that we identify here for various choices of β and γ. In particular, subject to the restriction on the modified heat release (γ−1)β ≪ 1, three new weakly exothermic ordered limits are identified that are relevant to detonation instability: (1) θ(γ−1) = O (1) and (γ−1) = O (1); (2) θ(γ−1) = O (1) and (γ−1) = o (1); and (3) θ(γ−1) ≫ 1 and (γ−1) = o (1).

Critical tube measurements at elevated initial mixture temperatures

Experimental results obtained on the transmission of a planar detonation wave from a cylindrical tube into an unconfined volume are reported. Experiments are performed using a 9.1 mm long tube connected to an 88.9 cm inner diameter receiver vessel. Both the detonation tube and receiver vessel can be heated. Tests are performed using 10, 20, and 27.3 cm tubes. The minimum, or critical, hydrogen concentration in air that results in detonation transmission into the receiver vessel is measured at an initial pressure of 1 atm and initial temperatures of 300, 500, and 650 K. The value of the ratio of the tube diameter, d, and the critical mixture detonation cell size, u c , is found to be between 18 and 24. The data show no correlation between the value of d/ u c and the initial mixture temperature and there is no observable effect of temperature on the regularity of the soot foil line spacing. The uncertainty in the average cell size measurement of - 25% is not sufficient to explain the significant departure from the classical empirical correlation d/ u c =13. It is proposed that the d/ u c =13 is neither a unique nor adequate correlation for describing detonation diffraction in mixtures considered to have a regular or irregular detonation cellular structure.

DDT and detonation waves in dust-air mixtures

This paper summarizes the studies of DDT and stable detonation waves in dust-air mixtures at the Stosswellenlabor of RWTH Aachen. The DDT process and propagation mechanism for stable heterogeneous dust detonations in air are essentially the same as in the oxygen environment studied previously. The dust DDT process in tubes is composed of a reaction compression stage followed by a reaction shock stage as the pre-detonation process. The transverse waves that couple the shock wave and the chemical energy release are responsible for the propagation of a stable dust-air detonation. However, the transverse wave spacing of dust-air mixtures is much larger. Therefore, DDT and propagation of a stable detonation in most industrial and agricultural, combustible dust-air mixtures require a tube that has a large diameter between 0.1 m and 1 m and a sufficient length-diameter ratio beyond 100, when an appropriately strong initiation energy is used. Two dust detonation tubes, 0.14 m and 0.3 m in diameter, were used for observation of the above-mentioned results in cornstarch, anthraquinone and aluminum dust suspended in air. Smoked-foil technique was also used to measure the cellular structure of dust detonations in the 0.3 m detonation tube.

On the Cellular Structure of Carbon Detonations

We present the results of a numerical study on two-dimensional carbon detonations. For an upstream density of 107 g cm-3 the length-to-width ratio of the detonation cells is about 1.6 and is not strongly dependent on the spatial resolution of the simulation. However, the curvature of the weak incident shocks, strength of the triple points and transverse waves, and sizes of the underreacted and overreacted regions all depend strongly on the spatial resolution of the calculation. These resolution studies help define the minimum resolution required by multidimensional Type Ia supernovae models where the cellular structure of a detonation front is a key feature of the model.

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 $\rm N_2$ , 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 $\rm N_2$ -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.

Calculation of the Cellular Structure of Detonation of Sprays in an H2—O2 System

On the basis of the mathematical model of a two–phase two–velocity medium, detonation of a cryogenic mixture (gaseous hydrogen—drops of liquid oxygen) was studied numerically. The dynamics of formation and the special features of the structure of the two–dimensional reaction zone of the detonation wave are discussed. The cellular structure of detonation is modeled for the first time for a cryogenic hydrogen—oxygen spray.

Inhibition of detonation wave with halogenated compounds

The influence of CF3Br, CF2HBr, CF2HCl and CF3H on a benchmark mixture composed of stoichiometric H-2-CO-O-2-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.

Gaseous nitromethane and nitromethane-oxygen mixtures: A new detonation structure

Detonation in gaseous nitromethane (NM) and mixed with O2 has been studied. Experiments were performed in a preheated steel tube at an initial temperatureT 0∼=390 K for different initial pressuresP 0 (1.7≥P 0≥5 10−2 bar). Different selfsustained detonation regimes were obtained, from multiheaded mode to spinning and galloping mode in marginal conditions. These chemical systems were characterized by a specific detonation cellular structure very different from that currently observed with classical gaseous C n H m /O2/N2 mixtures. All modes of detonation propagation in rich NM/O2 mixtures exhibit a double scale cellular structure. The pattern of this double scale structure is particularly clear in the case of spinning mode.

The effect of energy release on the regularity of detonation cells in liquid nitromethane

We have used time-dependent two-dimensional numerical simulations to study the effect of the rate of energy release on the regularity of the cellular structure of detonations in liquid nitromethane. Chemical decomposition of nitromethane is descrbed by a two-step model composed of an induction time followed by energy release. The same expression is used for the induction time throughout the calculations. The energy release rate and its dependence on temperature were varied. A simplified equation of state based on the Walsh and Christian technique for condensed phases and the BKW equation of state for gas phases is used. When mixtures of both phases are present, pressure and temperature equilibrium is assumed. In the model, the walls of the detonation chamber are assumed to heavily confine the liquid explosive. Boundary layer effects are neglected. The solution thus simulates the detonation structure near the center of a wide channel. The simulations show that the energy release process controls whether the detonation dies, becomes one-dimensional, or becomes multidimensional. Once the multidimensional structure is established, its regularity is mainly controlled by the temperature dependence of the induction time, and to a lesser extent by the energy release rate. Increasing the energy release time and decreasing the activation energy generally improve the regularity. The simulations also show a correlation between the regularity of the cellular structure and both the change in induction zone thickness across the transverse waves and, the shock front curvature. When the change in the width of the induction zone is larger, the shock has more curvature and the structure is more regular.

Analyses of the cellular structure of detonations

We have investigated the effects of chemical composition and dilution on the regularity of gaseous detonation cellular structure at a fixed critical tube diameter of 52 mm. Three fueloxygen mixtures were studied as function of argon dilution (0% to 80% by volume); the fuels were acetylene, hydrogen and ethane. Smoked foil records were analyzed by digital image processingto obtain a quantitative spectrum of the spatial wavelengths present in the cellular structures. With increasing argon dilution, the number of cells across the tube diameter increases from 4–10 at 0% Ar to 20–30 at 80% Ar at critical transmission conditions for acetylene-oxygen detonations, and the spectra of the cellular structures show a dramatic narrowing in spectral content. A smaller decrease in the dominant spectral wavelength and less increase in regularity with increasing argon dilution are observed for hydrogen-oxygen detonations. Ethane-oxygen detonations have a much more irregular cellular structure and the spectrum is characterized by a broad band of features with the dominant spectral wavelengths independent of argon dilution. Reaction zone lengths and sensitivity parameters have been computed using the steady-state ZND model of detonation structure. The results of these computations show that these parameters cannot account for the systematic variations in cell regularity and the differences in macroscopic behavior. A partial explanation is offered based on the response of the chemistry to large amplitude variations in shock strength, i.e., degree of overdrive. The amount of overdrive at which the reaction zone becomes endothermic is proposed as a figure of merit for instability and is shown to correlate with present observations.