Detonability of fuel-oxygen and fuel-air mixtures

An analysis of theoretical models and experimental investigations of the detonability of unconfined detonation in uniform gaseous mixtures shows a disparity in results. The present study is limited to propane, acetylene and methane diluted with oxygen or air in variable proportions and initial pressures at ambient temperature conditions. Because of the disparity in results, a simple and general formulation of critical initiation energy for gaseous detonations has been investigated. The problem has been formulated using the conservation equation of total energy enclosed by the shock. From this, a simple form for the critical energy has been deduced. This approach leads to a good simulation in uniform mixtures, regardless of initiation conditions. Some applications are presented in this paper. A new experimental study on the detonability of methane/oxygen mixtures diluted with propane and/or nitrogen is reported. The gaseous mixtures are confined in a cylindrical vessel. The initial conditions are various equivalence ratio and pressure under room temperature. In the case of methane/oxygen mixtures, the predetonation radius varies directly with the cell width. The constant ratio is in the order of 18, slightly different from the classical relation R _c= 20λ. For propane the slope variation of the critical energy versus initial pressure depends on the dilution. We have compared the critical energy obtained by several authors with the theoretical values. Fuel ratio and initial pressure are the chosen parameters. These comparisons show that the formulation allows for the prediction of the critical energy of detonation of uniform mixtures with a good estimation range. The correlation between the different geometries has been deduced and a test has been conducted as well in the case of stoichiometric methane/oxygen and acetylene/oxygen mixtures versus initial pressure for a cylindrical detonation. Received 9 January 1996 / Accepted 24 January 1997     

Influence of mixture sensitivity and pore size on detonation velocities in porous media

Experiments have been carried out to determine the dependence of the detonation velocity in porous media, on mixture sensitivity and pore size. A detonation is established at the top end of a vertical tube and allowed to propagate to the bottom section housing the porous bed, comprised of alumina spheres of equal diameter (1–32 mm). Several of the common detonable fuels were tested at atmospheric initial pressure. Results indicate the existence of a continuous range of velocities with change in Φ, spanning the lean and the rich propagation limits. For all fuels in a given porous bed, the velocity decreases from a maximum value at the most sensitive mixture near Φ≈1 (minimum induction length), toV/V _CJ≈0.3 at the limits. A decrease in pore size brings about a reduction inV/V _CJ and a narrowing of the detonability range for each fuel. For porous media comprised of spherical particles, it was possible to correlate the velocity data corresponding to a variety of different mixtures and for a broad range of particle sizes, using the following empirical expression:V/V _CJ=[1–0.35 log(d _c /d _p)]±0.1. The critical tube diameterd _c is used as a measure of mixture sensitivity andd _p denotes the pore diameter. An examination of the phenomenon at the composition limits, suggests that wave failure is controlled by a turbulent quenching mechanism.     

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.

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

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} .     

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.     

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 through different geometries

We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d _c  = k _c ·λ (with λ the detonation cell size and k _c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter (D/d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/λ. For ratios below k _c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k _lim (which depends on D/d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k _c by 50%. The results in configuration C show that the re-ignition process depends both on d/λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D _ch = 200 mm) at as small d/λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.

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This paper was based on work that was partly presented at the International Conference on Combustion and Detonation, Zel’dovich Memorial II, Moscow, Russia, 30 August–3 September 2004, and at the 20th International Colloquium on the Dynamics of Explosions and Reactive systems, Montreal, Canada, 31 July–5 August 2005.     

Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H ₂/O ₂ diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes. The English text was polished by Yumming Chen.     

高浓度氩气稀释气体爆轰波临界管径和临界间距关系

建立圆管及环形管道系统研究临近极限下爆轰波在管道内传播失效机理。选用C₂H₂+2.5O₂+70%Ar气体,采用光纤探针测量爆轰波在管道内传播速度,用烟迹法记录管道内爆轰波胞格结构。结果表明:初始压力远大于爆轰极限压力时,爆轰波在管道内以稳定速度传播;随着初始压力的减小,爆轰波速度逐渐降低;当初始压力一定时,爆轰波速度随着管道尺寸的减小而逐渐减小;当初始压力达到临界压力时,爆轰波在进入到管道内后其速度会逐渐衰减直至爆轰波完全失效。对于不同几何尺寸的圆管与环管,通过引入无量纲参数d/λ及w /λ(d为圆管管径,w为环管间距,λ为爆轰胞格尺寸)得出,爆轰波在管道内传播的临界圆管直径为环形间距的2倍,与理论模型结果相吻合,验证了稳态气体基于爆轰波波面曲率的失效机理。     

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.     

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.     

Measurement of effective blast energy for direct initiation of spherical gaseous detonations from high-voltage spark discharge

In this study, effective energy from spark discharge for direct blast initiation of spherical gaseous detonations is investigated. In the experiment, direct initiation of detonation is achieved via a spark discharge from a high-voltage and low-inductance capacitor bank and the spark energy is estimated from the analysis of the current output. To determine the blast wave energy from the powerful spark, the time-of-arrival of the blast wave in air is measured at different radii using a piezoelectric pressure transducer. Good agreement is found in the scaled blast trajectories, i.e., scaled time c _o·t/R _o where c _o is the ambient sound speed, as a function of blast radius R _s/R _o between the numerical simulation of a spherical blast wave from a point energy source and the experimental results where the explosion length scale R _o is computed using the equivalent spark energy from the first 1/4 current discharge cycle. Alternatively, by fitting the experimental trajectories data, the blast energy estimated from the numerical simulation appears also in good agreement with that obtained experimentally using the 1/4 cycle criterion. Using the 1/4 cycle of spark discharge for the effective energy, direct initiation experiments of spherical gaseous detonations are carried out to determine the critical initiation energy in C₂H₂–2.5O₂ mixtures with 70 and 0% argon dilution. The experimental results obtained from the 1/4 cycle of spark discharge agree well with the prediction from two initiation models, namely, the Lee’s surface energy model and a simplified work done model. The main source of discrepancy in the comparison can be explained by the uncertainty of cell size measurement which is needed for both the semi-empirical models.     

Generation and stabilization of detonation in a plane elbowed channel

The problem of detonation initiation in a supersonic flow of a stoichiometric propane-air mixture in a plane elbowed channel of constant width is considered. In the bend zone the channel walls are made in the shape of circles of given radii, whose lengths are determined by the given angle of the channel turn. An investigation is performed within the framework of the single-stage combustion kinetics using a numerical method based on the Godunov scheme and included in an original program complex, or a “virtual experimental setup”, developed for performing multiparameter calculations and flow visualization. The critical conditions of detonation generation are determined as functions of the oncoming flow velocity, the channel turn angle and width, and the radii of curvature of the walls.     

Experimental study on detonation parameters and cellular structures of fuel cloud

In this paper,detonation parameters of fuel cloud,such as propylene oxide(PO),isopropyl nitrate(IPN),hexane,90 # oil and decane were measured in a self-designed and constructed vertical shock tube.Results show that the detonation pressure and velocity of PO increase to a peak value and then decrease smoothly with increasing equivalence ratio.Several nitrate sensitizers were added into PO to make fuel mixtures,and test results indicated that the additives can efficiently enhance detonation velocity and pressure of fuel cloud and one type of additive n-propyl nitrate(NPN) played the best in the improvement.The critical initiation energy that directly initiated detonation of all the test liquid fuel clouds showed a U-shape curve relationship with equivalence ratios.The optimum concentration lies on the rich-fuel side(φ > 1).The critical initiation energy is closely related to molecular structure and volatility of fuels.IPN and PO have similar critical values while that of alkanes are larger.Detonation cell sizes of PO were respectively investigated at 25 C,35 C and 50 C with smoked foil technique.The cell width shows a U-shape curve relationship with equivalence ratios at all temperatures.The minimal cell width also lies on the rich-fuel side(φ > 1).The cell width of PO vapor is slightly larger than that of PO cloud.Therefore,the detonation reaction of PO at normal temperature is controlled by gas phase reaction.     

Experimental and numerical investigations on PDE performance augmentation by means of an ejector

To improve the performance of pulse detonation engines, a 48 cm long cylindrical combustion chamber of 5cm internal diameter (i.d.) is fitted with an ejector of constant section. The role of the ejector is (i) to provide partial confinement of the detonation products escaping from the chamber and (ii) to suck in fresh air and then to increase the mass ejected compared to the ejection of burned gases alone.The combustion chamber is fully filled with a stoichiometric ethylene/oxygen mixture at ambient conditions. Three parameters of the ejector are varied: the i.d. D, the length L, and the position d relative to the thrust wall of the combustion chamber. For various configurations, the specific impulse (I _sp) is determined in single shot experiments. The maximum operating frequency (f _max) and the maximum thrust are then deduced. I _sp is measured by means of the ballistic pendulum method, and f _max is derived from the pressure signal recorded on the combustion chamber thrust wall.The addition of an ejector increases the specific impulse up to 60% in the best configuration tested, from 164s without ejector to 260s with ejector. The specific impulse can be represented by a single curve using suitable dimensionless parameters. The thrust results for the main ejector studied (D = 80mm) indicate an optimal (L, d) configuration that provides a 28% thrust gain. For the same ejector, f _max remains constant and equal to the frequency obtained without ejector in a large range of (L, d) values, before decreasing.Two-dimensional unsteady numerical computations agree reasonably with the experiments, slightly overestimating the experimental values. The results indicate that 80% of the I _sp gain comes from the action of the expanding detonation products on the annular end surface of the combustion chamber, governed by the tube wall thickness.This 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 PACS 47.40.Rs     

Effect of scale on the onset of detonations

Critical conditions for onset of detonations are compared at (1) two significantly different scales, (2) for a range of -air mixtures diluted with C, O, and (3) for two types of geometry – one a long obstructed channel and the other a room with a relatively small aspect ratios. For the range of scales, mixtures, and initial conditions tested, the detonation cell size was shown to be a reliable scaling parameter for characterization of detonation onset conditions. An experimental correlation is suggested for the critical detonation onset conditions. This correlation is based on a wide variety of available experimental data on DDT in mixtures of hydrogen and hydrocarbon fuels with air and on the use of detonation cell size as a scaling parameter characterizing the mixture. Received 14 November 1999 / Accepted 16 February 2000     

DDT in methane-air mixtures

Experimental results from a study on the critical condition for deflagration-to-detonation transition (DDT) in methane-air mixtures are presented. Experiments were carried out at 293 K and 1 atm using methane-air mixtures with methane concentrations ranging from 5.5 to 17% vol. The tests were performed in detonation tubes with inner-diameters of 174 mm and 520 mm. Detonation cell widths l\lambda were determined in the tests for a range of methane concentrations. The results of DDT tests indicate that for a tube cross-sectional area blockage ratio (BR) of 0.3 the critical condition for DDT can be characterized by the d/l = 1d/\lambda = 1 criterion. However, for a BR = 0.6 the critical value d/ld/\lambda was significantly higher. The data also show that the critical condition for DDT can be described by L/l = 7L/\lambda = 7, where L is the characteristic length-scale of the channel volume between orifice plates. This length-scale is defined by a grouping of the orifice plate dimensions (inner and outer-diameter) and plate spacing.     

Detonation combustion of hydrogen in an axisymmetric channel with a central body

The problem of initiation and stabilization of detonation combustion of a hydrogen–air mixture injected into an axisymmetric channel with a finite-length central body in a flow with a Mach number M₀ = 5–9 is solved. It is numerically demonstrated that the presence of the central body both in a convergent–divergent nozzle and in an expanding channel leads to stabilization of detonation combustion of a stoichiometric hydrogen–air mixture at free-stream Mach numbers M₀ > 7. Various channel configurations that ensure different values of thrust generated by detonation combustion of a stoichiometric hydrogen–air mixture are compared.     

Experiments on the effect of acceleration on the drag of tapwater bubbles

Three-dimensional (3D) trajectories of spherical air bubbles passing through a converging part of a rectangular channel have been measured. Bubble diameters, d _b, were less than 1 mm and the Reynolds numbers, Re _b, for stagnant tapwater and for mean liquid velocity vˉ _L=0.25 m/s were in about same range. Received: 15 January 2001 / Accepted: 12 June 2001