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).     

Interprétation de la double structure observée dans l'onde de détonation du nitrométhane gazeux

Calculations of the reaction zone of the detonation of gaseous nitromethane, either pure or diluted with oxygen, in the range of equivalence ratio Φ between 0.1 and 1.75, show that for 1.75⩾Φ⩾1.3 the chemical energy is released in two main successive reaction steps characterized by very different induction times. These results corroborate the experimental observations of two levels of cellular structures in the same range of equivalence ratios. To our knowledge this work is the first which deals with the problem of nonmonotonous chemical energy release behind the leading shock of a detonation wave.     

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).     

Structure and stability of one-dimensional detonationsin ethylene-air mixtures

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures ( 1.2$" align="middle" border="0"> ) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.Received: 13 September 2004, Revised: 1 November 2004, Published online: 3 March 2005[/PUBLISHED]Correspondence to: S. Yungster     

The structure and evolution of a two-dimensional H2/O2/Ar cellular detonation

This paper reports on two-dimensional numerical simulation of cellular detonation wave in a / / mixture with low initial pressure using a detailed chemical reaction model and high order WENO scheme. Before the final equilibrium structure is produced, a fairly regular but still non-equilibrium mode is observed during the early stage of structure formation process. The numerically tracked detonation cells show that the cell size always adapts to the channel height such that the cell ratio is fairly independent of the grid sizes and initial and boundary conditions. During the structural evolution in a detonation cell, even as the simulated detonation wave characteristics suggest the presence of an ordinary detonation, the evolving instantaneous detonation state indicates a mainly underdriven state. As a considerable region of the gas mixture in a cell is observed to be ignited by the incident wave and transverse wave, it is further suggested that these two said waves play an essential role in the detonation propagation.Received: 16 September 2003, Accepted: 14 June 2004, Published online: 20 August 2004[/PUBLISHED]PACS: 47.40.-x, 82.40.Fp, 82.33.Vx, 83.85.PtX.Y. Hu: Correspondence to Current address: Institut für Strömungsmechanik, Technische Universität Dresden, 01062 Dresden, Deutschland     

Parametric study of double cellular detonation structure

A parametric numerical study is performed of a detonation cellular structure in a model gaseous explosive mixture whose decomposition occurs in two successive exothermic reaction steps with markedly different characteristic times. Kinetic and energetic parameters of both reactions are varied in a wide range in the case of one-dimensional steady and two-dimensional (2D) quasi-steady self-supported detonations. The range of governing parameters of both exothermic steps is defined where a “marked” double cellular structure exists. It is shown that the two-level cellular structure is completely governed by the kinetic parameters and the local overdrive ratio of the detonation front propagating inside large cells. Furthermore, since it is quite cumbersome to use detailed chemical kinetics in unsteady 2D case, the proposed work should help to identify the mixtures and the domain of their equivalence ratio where double detonation structure could be observed.     

Direct initiation of detonation in cryogenic gaseous H2-O2 mixtures

Critical conditions for the direct initiation of self-sustained detonation in cryogenic hydrogen-oxygen mixtures are examined experimentally. These initial conditions are expected to depend mainly on four parameters: the equivalence ratio of the mixture, the amount of the initial energy deposition, the initial temperature and pressure of the mixture. These critical conditions are determined by fixing alternatively three of these parameters and varying the fourth one from subcritical to supercritical detonation conditions. Results are presented for initial pressuresP _o and equivalence ratios ranging from 0.3 to 1 bar and from 1 to 2 respectively, for the two initial temperaturesT _o, 123 K and 293 K. These results indicate that for the lowest values of the initial pressure, a decrease of initial temperature may favour the onset of detonation. Whatever the initial conditions, the measured detonation pressures and velocities are in reasonably good agreement with the corresponding Chapman-Jouguet values computed using the ideal-gas equation of state.     

Critical diameter of liquid explosives as a function of powder content

The dependence of the critical diameter (d*) of nitromethane (NM) on the content of aluminum, aluminum oxide, tungsten powders, carbon black, and talc and the dependence of the d* of tetranitromethane (TNM) on aluminum and aluminum oxide content have been experimentally investigated. The powder content was varied over'a wide range (0–75% by weight), as was the particle size. It was found that for NM mixtures the variation of d* is quite different from that for TNM. For powder particle sizes of 1–50 the d* of the NM mixtures decreases with increase in powder concentration. The minimum value of d* is ten times less than the value for pure NM. In TNM mixtures d* increases monotonically with the amount of powder. It is assumed that this behavior of the NM mixtures is associated with the inhomogeneous structure of the detonation front in NM, a consequence of the particular reaction kinetics characteristic of nitromethane.     

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.     

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.     

Time-Asymptotic Limit of Solutions of a Combustion Problem

A combustion model which captures the interacting among nonlinear convection, chemical reaction and radiative heat transfer is studied. New phenomena are found with radiative heat transfer present. In particular, there is a detonation wave solution in which there is a sonic point inside the reaction zone. As a consequence, the traveling wave speed cannot be determined before the problem is solved. The shooting method is used to prove the existence of the traveling wave. The condition we shoot at is the compatibility condition at the sonic point. Furthermore, the speed of the detonation wave decreases as the heat loss coefficient increases, as expected physically. We study the time-asymptotic limit of solutions of initial value problem for the same problem. We prove that the solution exists globally and the solution converges uniformly, away from the shock, to a shifted traveling wave solution as t + for certain compact support initial data.     

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. 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     

液体燃料云雾爆轰参数实验

为深入了解液体燃料云雾爆轰机理,借助自行设计和建造的立式爆轰管,并采用升降法和烟迹技 术,对环氧丙烷等液体燃料云雾爆轰参数(爆速、爆压、临界起爆能和爆轰胞格尺寸)与当量比的关系进行了实 验研究。结果表明,环氧丙烷的爆速和爆压随当量比的增加先增大后平缓减小;碳氢液体燃料云雾爆轰的临 界起爆能与当量比呈U型关系,最佳值点偏向富燃料一侧;临界起爆能的大小与燃料的分子结构和挥发性 有密切关系,IPN和PO 临界起爆能相当,而烷烃类临界起爆能均较大。环氧丙烷在25和50 ℃时的爆轰胞 格宽度与当量比皆呈U型关系,最小值点偏向富燃料一侧;气相爆轰胞格宽度比云雾爆轰略小。常温下环 氧丙烷云雾爆轰主要由气相反应所控制。     

Simulation numérique des détonations à double structure cellulaireNumerical simulation of detonations with double cellular structure

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).     

Relaxation of overdriven detonation waves with finite reaction rate

A numerical study is made of the interaction of a detonation wave having finite reaction velocity with a rarefaction wave of different intensity which approaches it from the rear, for the Zeldovich-Neumann-Doring (ZND) model with a single irreversible reaction A B. It is found that, for a fixed value of the parameter characterizing the initial supercompression (depending on the activation energy and the heating value of the mixture), the considered interaction leads either to a gradual relaxation of the detonation wave and its transition to the Chapman-Jouguet (CJ) regime, or to the development of undamped oscillations.Interest in the problems of detonation and supersonic combustion has increased in recent years. This is associated with the appearance and development of new experimental and theoretical techniques; it is also associated with the further development of air-breathing reaction engines, and other practical requirements. The present state of detonation theory is reflected in the survey [1].It has been established [2] that the detonation wave in gases nearly always has a complex nonuniform structure. Transverse disturbances are observed under a wide range of conditions and differ both in amplitude and wavelength. At the same time, behind the detonation leading front there is a region of uncompletely burned gas corresponding to the effective ignition induction period [3]. In spinning detonation the induction period is significantly longer than the heat release period and transverse detonation waves traveling in the induction zone of the head wave appear [3, 4]. Such a secondary detonation wave is free of transverse disturbances. The same is true of the detonation waves observed in the wake behind a body moving at high speed in a combustible medium [5] or in a gas which has been preheated by a shock wave [6].Although it is possible, under favorable conditions, to study in detail the system of discontinuities accompanying detonation, information on the extensive zones in which heat release takes place is scarce, the mechanism of detonation wave autonomy (in particular, the role of the rarefaction zone behind the wave) is not entirely clear, and the fact that, in spite of the complex structure, an autonomous detonation propagates with the CJ velocity calculated on the basis of one-dimensional theory has not yet been explained.In studying the nonlinear phenomena associated with the finite reaction rate it is quite acceptable to investigate only the simple one-dimensional detonation model, with which it is convenient to restrict ourselves to a single effective chemical reaction. This model is particularly reasonable since, in certain cases, the real detonation is virtually one-dimensional.The question of the stability of the one-dimensional detonation wave to disturbances of its structure has been examined by several authors [7–13]. The use of computers makes possible the direct computation of flows with heat release and the study of their properties. This method has been used in [11–13] to study the stability problem for a detonation wave with respect to finite disturbances.In the present paper we present a numerical study of the interaction of a detonation wave having finite chemical reaction rate with a rarefaction wave of different intensity approaching it from the rear for the ZND model with a single irreversible reaction A B. It is found that for a fixed value of the parameter characterizing the difference between detonation and the CJ waves, depending on the activation energy E and the mixture heating value Q_m, the interaction in question leads either to a gradual relaxation of the detonation wave and its transition to the CJ regime (this relaxation may be accompanied by decaying oscillations) or to the appearance of undamped oscillations (the unstable regime). The parameters E and Q_m affect the wave stability differently: with increase of Q_m, the wave is stabilized; with increase of E, it is destabilized. The boundary between the stable and unstable detonation wave propagation regimes is found. This boundary has a weak dependence on the rarefaction wave intensity. Estimates and calculated examples show that the amplitude of the unstable wave oscillations is finite and that the average detonation propagation velocity is close to the CJ velocity computed for the given heating value Qm.The author wishes to thank G. G. Chernyi for his guidance and L. A. Chudov for advice on computational questions.     

周期性非均匀介质中气相爆轰波演变模式研究

气相爆轰波在周期性非均匀介质中的起爆, 稳态传播和失效机制都极为复杂, 很多物理机制尚不明确, 是当前爆轰物理领域研究的热点和难点. 本文使用反应欧拉方程和两步化学反应模型对爆轰波在非均匀介质中的传播机理进行了数值模拟研究, 非均匀性由横向周期性分布的温度扰动体现, 重点分析不同波长、不同幅度的温度扰动对波阵面波系结构的影响. 计算结果表明, ZND爆轰波在温度扰动下向胞格爆轰波的转变主要受制于两种竞争性因素: 一是爆轰波内在的不稳定性; 二是温度扰动的波长和幅度, 前者是内因, 后者是外因. 温度扰动的存在抑制横波的发展, 延迟了ZND爆轰波向胞格爆轰波的演化, 并且内在不稳定性的增加可以减慢这种延迟现象. 这说明, 温度扰动可以在一定的范围内抑制胞格不稳定性的发展, 但是不能够终止这一过程. 温度的不连续性使得爆轰波阵面更为扭曲, 并在横波附近存在较弱的三波点结构, 即温度扰动可增加爆轰波固有的不稳定性, 改变爆轰波阵面的传播机理. 幅值较大的人工温度扰动可抑制爆轰波的传播和爆轰波自身的不稳定性. 爆轰波阵面胞格结构的形成取决于温度扰动与其自身的不稳定性.      

The critical tube diameter in a two reaction steps detonation: the H2/NO2 mixture case

We present experimental results on the detonability of the H₂/NO₂ mixture whose detonation exhibits a single cellular structure (λ₁) for the lean mixtures and a double cellular structure (fine cells of size λ₁ inside larger cells of size λ₂) for stoichiometric and rich mixtures. Whatever the equivalence ratio ${\phi}$ , the chemical energy is released in two successive exothermic steps of heat of reaction Q ₁ and Q ₂ (Q ₁ + Q ₂ = Q, the total heat release) and characterised (for ${\phi > 1}$ ) by two chemical lengths. The detonability is evaluated on the basis of critical conditions of self-sustained detonations transmission from a cylindrical tube of i.d. d to free space. Results show that for the critical tube diameter relationship d/λ₁ = k, with respect to the equivalence ratio ${\phi}$ ranging from 0.5 to 1.3 at ambient temperature, k is higher than the classical value 13 and its variation is rather complex. Indeed, d/λ₁ increases with ${\phi}$ from 17–18 for ${\phi = 0.5}$ to 45–50 for ${\phi = 1}$ and to 90–100 for ${\phi = 1.3}$ . The highest detonability obtained for ${\phi = 0.6}$ is explained on the basis of the highest relative contribution of the first exothermic step to the total energy Q. We conclude that, as d/λ₁ drops with Q ₂ decreasing, it should tend to 13 with the vanishing second exothermic reaction.     

Ethylene–air detonation in water spray

Detonation experiments are conducted in a 52 \(\hbox {mm}\) square channel with an ethylene–air gaseous mixture with dispersed liquid water droplets. The tests were conducted with a fuel–air equivalence ratio ranging from 0.9 to 1.1 at atmospheric pressure. An ultrasonic atomizer generates a polydisperse liquid water spray with droplet diameters of 8.5–12 \(\upmu \hbox {m}\), yielding an effective density of 100–120 \(\hbox {g}/\hbox {m}^{3}\). Pressure signals from seven transducers and cellular structure are recorded for each test. The detonation structure in the two-phase mixture exhibits a gaseous-like behaviour. The pressure profile in the expansion fan is not affected by the addition of water. A small detonation velocity deficit of up to 5 % was measured. However, the investigation highlights a dramatic increase in the cell size (\(\lambda \)) associated with the increase in the liquid water mass fraction in the two-phase mixture. The detonation structure evolves from a multi-cell to a half-cell mode. The analysis of the decay of the post-shock pressure fluctuations reveals that the ratio of the hydrodynamic thickness over the cell size (\(x_{{\mathrm {HT}}}/{\lambda }\)) remains quite constant, between 5 and 7. A slight decrease of this ratio is observed as the liquid water mass fraction is increased, or the ethylene–air mixture is made leaner.     

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.     

Influence of upstream properties on detonation wave structure. Irreversible, unimolecular reaction with small rate parameter

Summary Wood's analysis of detonation wave structure for an irreversible, unimolecular reaction with small rate parameter is used to study the influence of upstream properties on the coupling between pressure rise and reaction zones. The variation of a reduced distance due to adiabatic upstream burning, upstream heat addition, and variation of heat release per unit mass of reactant is considered. is the reduced distance between the point of minimum velocity (essentially the point of maximum pressure) and the point where the temperature is some chosen fraction of the final temperature, i.e., is a measure of the coupling between pressure rise and reaction zones.The wave structure immediately downstream of the pressure rise zone is found to be most sensitive to adiabatic upstream burning but much less sensitive to upstream heat addition and variation of heat release per unit mass of reactant. The first two processes cause to decrease because the temperature and reaction rate at the pressure maximum are increased. The last process causes to increase slightly because in this case the temperature and reaction rate at the pressure maximum is decreased. The wave structure far downstream of the pressure rise zone is not altered by adiabatic upstream burning but is influenced by upstream heat addition and variation of heat release per unit mass of reactant. The latter two processes cause to decrease. It is also shown that the wave structure immediately downstream of the pressure rise zone, for detonation waves which initially consist of widely separated pressure rise and reaction zones, is very sharply altered by the three processes of upstream variation here considered. Upstream burning and upstream heat addition cause rapid reductions in || while an increase in heat release per unit mass of reactant increases || for the same reasons as noted in the case of more closely coupled waves.Available experimental data are not directly applicable to the present results. However there is sufficient similarity between theory and experiment to support the qualitative trends predicted by this idealized analysis.