Supersonic H2-air combustions behind oblique shock waves

In order to study the mechanisms of initiation and stabilization of H₂-Air combustions (stoechiometric mixture initially atT ₀=293 K andp ₀=0.5 bar) in supersonic flow conditions behind an oblique shock wave (OSW), an original technique is used where OSW is generated in this mixture by the lateral expansion of the burnt gas behind a normal CJ gaseous detonation propagating into a bounding reactive mixture. Four Mach numberM of propagation of OSW are considered in the study, namelyM=7.7-6.1-4.4 and 3. Depending on the Mach numberM and inclinaison angle of OSW different regimes of combustion may occur in the driven mixture. For high values ofM (6.1 and 7.7) delayed steady overdriven oblique detonation waves (SODW) were obtained with a near CJ detonation wave as the critical regime. It was found that SODW obtained correspond quite well to prediction of the polar method. When thermal conditions behind the OSW are lower, either for high Mach number 6.1 and 7.7 for smaller angle than the previous case, or for lower Mach number, 4.4 and 3, the flame initiated at the apex is stabilized as a turbulent oblique flame behind the OSW. With much lower conditions, no combustion appears in the H₂-Air mixture.     

The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave

A simplified theoretic method and numerical simulations were carried out to investigate the characterization of propagation of transverse shock wave at wedge supported oblique detonation wave.After solution validation,a criterion which is associated with the ratio Φ (u 2 /u CJ) of existence or inexistence of the transverse shock wave at the region of the primary triple was deduced systematically by 38 cases.It is observed that for abrupt oblique shock wave (OSW)/oblique detonation wave (ODW) transition,a transverse shock wave is generated at the region of the primary triple when Φ < 1,however,such a transverse shock wave does not take place for the smooth OSW/ODW transition when Φ > 1.The parameter Φ can be expressed as the Mach number behind the ODW front for stable CJ detonation.When 0.9 < Φ < 1.0,the reflected shock wave can pass across the contact discontinuity and interact with transverse waves which are originating from the ODW front.When 0.8 < Φ < 0.9,the reflected shock wave can not pass across the contact discontinuity and only reflects at the contact discontinuity.The condition (0.8 < Φ < 0.9) agrees well with the ratio (D ave /D CJ) in the critical detonation.     

Initiation of gaseous detonation by a high speed body

The investigation of detonation initiated by the passage of a high speed body is presented. The following experiments are carried out for mixture of C₂H₂ + 2.5 O₂ passed by a hemispherical or blunt cylinder with velocity ranging from 800 to 1400 m/s. A new mechanism of the transformation of shock waves to detonation waves is observed at near-critical regimes. The analytical correlation between the aerodynamical characteristics of high speed body and the physico-chemical parameters of explosive mixture is proposed as the initiation criterion of gaseous detonation. Analytical and experimental data agree well with each other.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

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.     

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.     

Theory of the detonation of weak condensed explosives

The possibilities of detonation taking place in a material characterized by a shock adiabatic containing a sharp break (leading to a double shock-wave configuration) are examined. The range of possible velocities D of a self-sustaining detonation in the second shock wave is determined; D may be subsonic with respect to the original material. However, even for an arbitrarily low velocity of sound the range of subsonic D values above the break point on the adiabat is extremely limited: The minimum detonation velocity D_min coincides (apart from a factor of 0.5–0.8) with the velocity of a longitudinal sound wave in the original material below the break point. This limitation with regard to D is associated with the formation of a wave of rarefaction in the reaction products, For D < D_min the shock wave of rarefaction reaches the Jouguet point and breaks the steady-state complex of the detonation wave. The results obtained are valid not only for weak, but also for powerful, explosive substances, if (by virtue of any kind of losses) low-velocity forms of detonation are realized in these materials.     

T型管内流动气体中爆轰绕射过程的数值模拟

基于带化学反应的二维Euler方程,对H₂、O₂、Ar体积比为2:1:1的混合气体系统在T型管内的爆轰绕射进行了数值模拟。用二阶附加半隐的Runge-Kutta法和五阶WENO格式分别离散欧拉方程的时间和空间导数项,采用9组分48步基元反应简化模型描述爆轰波在静止系统和流动系统中的传播过程,得到了温度、压力、典型组元H质量分数的分布及数值胞格结构。结果表明:在流动系统中,迎风面上波阵面为斜爆轰结构,静止系统两侧和顺风面上的波阵面为完全解耦的前导激波;在水平管中,波阵面与上下壁面经历一系列马赫碰撞后,最终形成正爆轰;在流动系统中,胞格结构明显向下游偏移;横向爆轰波的产生对爆轰波的再生起到了关键作用。     

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.     

Population inversion behind a detonation wave propagating in a variable-density medium

The creation of an active medium by means of detonation has been investigated on a number of occasions. It was suggested that one could use the expansion of the detonation products of an acetylene-air mixture in vacuum [1] or the cooling of the detonation products of a mixture of hydrocarbons and air through a nozzle [2, 3]. In [4], the detonation of a solid high explosive was used to produce population inversion in the gas mixture CO₂-N₂-He(H₂O). Stimulated emission from HF molecules was observed in [5] behind the front of an overdriven detonation wave propagating in an F₂-H₂-Ar mixture in a shock tube. Population inversion behind a detonation wave was studied in H₂-F₂-He mixtures in [6–8] and in H₂-Cl₂-He mixtures in [9] with energy release on a plane and on a straight line in a medium with constant density. Similar problems were solved for shock waves propagating in both a homogeneous gaseous medium [7, 10] and in the supersonic part of an expanding nozzle. In the present paper, we study theoretically population inversion behind an overdriven detonation wave propagating in a mixture (fine carbon particles + acetylene + air) which flows through a hypersonic nozzle. The propagation of detonation in media with variable density and initial velocity was considered, for example, in [11, 12]. Analysis of the gas parameters behind a detonation wave propagating in a medium with constant density (for a given fuel) showed that the temperature difference across the detonation front is insufficient to produce population inversion of the vibrational levels of the CO₂ molecule.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 65–71, January–February, 1980.I am grateful to V. P. Korobeinikov for a helpful discussion of the results.     

Reinitiation process of detonation wave behind a slit-plate

The propagation phenomenon of a detonation wave is particularly interesting, because the detonation wave is composed of a 3D shock wave system accompanied by a reaction front. Thus, the passage of a detonation wave draws cellular patterns on a soot-covered plate. The pressure and temperature behind the detonation wave are extremely high and may cause serious damages around the wave. Therefore, it is of great significance from a safety-engineering point of view to decay the detonation wave with a short distance from the origin. In the present study, experiments using high-speed schlieren photography are conducted in order to investigate the behaviors of the detonation wave diffracting from two slits. The detonation wave produced in a stoichiometric mixture of hydrogen and oxygen is propagated through the slits, and the behaviors behind the slit-plate are investigated experimentally. When a detonation wave diffracts from the slits, a shock wave is decoupled with a reaction front. Since the two shock waves propagate from the slits interact with each other at the center behind the plate, the detonation wave is reinitiated by generating a hot-spot sufficient to cause local explosions. Furthermore, it is clarified that the shock wave reflected from a tube-wall is also capable of reinitiating the detonation wave. The reinitiation distance of the detonation wave from the slit-plate is correlated using a number of cells emerged from each slit.      

Regular reflection of plane detonation waves from an elastic half-space

An effective method for the approximate solution of the Eq. [1] for the intensity of a reflected shock wave in the case of oblique incidence of a detonation wave on an elastic half-space is described; the elastic half-space is described by a certain specific form of the equation of state. Formulas relating the front and particle velocities behind the transmitted wave front to physical parameters are derived. Values of the wave intensity and other quantities determined with the aid of a Ural-2 computer are cited.The author of [1, 2] investigated the regular reflection of shock waves from the boundary between two bodies. In the present paper we solve the analogous problem in the case of oblique incidence of a detonation wave on an elastic half-space. The detonation wave deforms the elastic half-space, which assumes the position OK₁ (Fig. 1) forming the angle to the initial direction KO of the halfspace boundary. We assume that the acoustic stiffness of the halfspace is larger than the acoustic stiffness of the explosive. In this case, both reflected wave 2 and transmitted wave 3 are shock waves [3]. Let us denote the velocities of propagation of the detonation, reflected, and transmitted waves by U_i(i=1, 2, 3), respectively; let the pressure be p_i and let the density bep _i(i=0, 1, 2, 3, 4). The quantities U₁, ₁, ₀, and ₄ are given. We determine the intensities of waves 2 and 3, their velocities of propagation, and the angles ₂, ₃ and . The parameters are constant within each of the domains a, b, c, d, and e. In domains a and e the medium is stationary, i.e., u₀=u₄ =0. The basic equations of the problem express the conditions at the wave fronts and the dynamic and kinematic relationships.     

Fundamentals of rotating detonations

A rotating detonation propagating at nearly Chapman–Jouguet velocity is numerically stabilized on a two-dimensional simple chemistry flow model. Under purely axial injection of a combustible mixture from the head end of a toroidal section of coaxial cylinders, the rotating detonation is proven to give no average angular momentum at any cross section, giving an axial flow. The detonation wavelet connected with an oblique shock wave ensuing to the downstream has a feature of unconfined detonation, causing a deficit in its propagation velocity. Due to Kelvin–Helmholtz instability existing on the interface of an injected combustible, unburnt gas pockets are formed to enter the junction between the detonation and oblique shock waves, generating strong explosions propagating to both directions. Calculated specific impulse is as high as 4,700 s.      

Interaction of a shock wave with a two-phase interface

The acceleration by an incident shock of a planar interface between a gas and a particle-gas mixture has been investigated experimentally and numerically. The experiments were conducted in a newly developed vertical shock tube in which the planar interface of the particle-gas mixture was generated and its particle concentration history was measured. Polydisperse corn starch particles with a mean diameter of 10m were used. We recorded the motion of the interface, as well as of the incident and reflected shock by using a 4 channel spark shadowgraph. The experimental conditions were Mach numberM _s=5.15 and initial pressurep ₁=50kPa for various particle concentrations in nitrogen. The reflected shock appears with a delay after the incident shock enters the particle-gas mixture. Numerical methods were employed to solve the two-phase governing equations. Experiments and numerical solutions are in good agreement.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

高速弹丸诱导斜爆轰激波结构实验研究

斜爆轰推进系统在高超声速推进领域具有广阔的应用前景,其释热迅速、比冲高、燃烧室结构简单的优点吸引研究人员的持续关注.然而,斜爆轰的地面试验同时涉及到高速试验环境模拟、燃料与氧化剂混合、高温燃烧流场结构测量等技术难点,当前国内外系统的试验研究仍然十分有限,难以支撑斜爆轰发动机的研制.为了研究自持传播的斜爆轰激波结构与波面流动特性,基于爆轰驱动二级轻气炮开展了高速弹丸诱导斜爆轰实验研究,使用直径30 mm球头圆柱形弹丸发射进入充满氢/氧可燃混合气体的实验舱中以起爆斜爆轰波,并采用两种阴影技术对实验流动结构进行测量.实验中在不同速度、不同充气压力下观察到三种弹丸诱导激波结构,即激波诱导燃烧、弹丸起爆爆轰波和相对弹丸驻定的斜爆轰波,实验舱充气压力下降则会造成爆轰横波尺度增加与波面流动失稳.实验中,斜爆轰激波角与理论分析结果吻合较好,弹丸气动不稳定带来较大的弹丸攻角会对激波角测量带来一定偏差.通过对斜爆轰波波面法向传播速度的测量发现,随着远离弹丸,斜爆轰传播速度由弹丸飞行速度衰减至接近实验气体CJ速度,弹丸速度的降低会加速斜爆轰波传播速度的衰减.     

The use of Hugoniot analysis for the propagation of vapor explosion waves

Experimental studies have shown that a mixture of molten metal and water can support the propagation of a quasi-steady vapor explosion wave. Analysis of steadily propagating vapor explosion waves has been carried out by applying the one-dimensional conservation laws of mass, momentum and energy and appropriate equations of state to a homogeneous mixture of molten tin, water and steam. The effects of void fraction, melt/water volume fraction and melt temperature on the Hugoniot curves have been considered. For low temperature melts, the Hugoniot curve lies partially inside the saturation dome and a Chapman-Jouguet (CJ) detonation point occurs only for low void fractions. For high melt temperatures, the downstream states lie entirely outside the saturation region. Increasing the volatility of the coolant or the addition of chemical reactions increases the predicted CJ detonation pressure and velocity. CJ deflagration solutions were obtained in all cases. The existence of a CJ detonation or CJ deflagration for a multiphase fuel-coolant mixture has yet to be substantiated experimentally and nonequilibrium effects may play a role in the divergence between theory and experiments.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

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} .     

A numerical study of the mechanisms of self-reignition in low-overdrive detonations

Below a threshold in overdrive, both stability analysis and numerical simulations predict that one-dimensional detonations in high activation energy mixtures behave as a chaotic sequence of failures followed by reignition. Instead, less chaotic, cellular detonations almost invariably occur in experiments. Numerical simulation, based on the Euler equations with single step chemistry, shows that a ZND detonation initially fails in that regime. The detonation splits into a weaker shock, a surface discontinuity separating reacted from unreacted fluid, and a rarefaction wave. However, the detonation is eventually reignited by the explosion of a small gas pocket, in a process reminiscent of deflagration to detonation transition. In the fluid heated by the leading shock, the chemical reaction occurs slowly at first, but becomes faster as heat is released, until the pocket explodes. Small differences in initial temperature result in large enough differences in reaction time sufficient for one pocket of fluid to explode. In two dimensions, the explosion occurs earlier because an oblique shock structure develops which unevenly heats the fluid that passes through the leading shock. Hence, pockets that underwent more heating will explode sooner. As it moves upstream, the two-dimensional explosion, meets the leading shock and the detonation quickly develops a transverse wave structure. 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.     

Flow between parallel walls containing the lines of neutrally buoyant circular cylinders

The motions of a single and two lines of neutrally buoyant circular cylinders in fluid between flat parallel walls are numerically investigated over the range of the Reynolds number of 12 < Re < 96, the ratio of the diameter of the cylinder D_s to the channel width D of 0.25≤D_s/D≤0.5, and the ratio of the streamwise spacing of the cylinders L to the channel width of 0.75≤L/D≤2. The lattice Boltzmann method is used for computations of the fluid phase and the cylinders are moved according to Newton’s law of motion. The Segré–Silberberg effect is found for both a single and two lines of cylinders. It is also found that for two lines of cylinders with D_s/D=0.25 and L/D=1, the equilibrium positions of the two lines are arranged to be staggered with respect to each other in the flow direction. The effects of the Reynolds number Re, D_s/D, and L/D on the equilibrium position of the lines of cylinders and on the friction factor of the cylinder–fluid mixture are presented and discussed.     

可燃介质中飞行圆球诱导斜爆轰的流场结构

基于带化学反应的二维轴对称Euler方程,利用带有Superbee限制函数的波传播算法,对氢/氧/ 氮预混气中飞行圆球诱导斜爆轰进行了数值模拟。结果表明,在达姆科勒数Da略大于临界情形时,圆球诱导 的驻定爆轰是一个由强过驱斜爆轰、弱过驱斜爆轰、反应激波和惰性激波组合而成的复合结构。波后的圆球 绕流流场内存在2个亚音速区和1个超音速区。在圆球背风表面,还形成了第2道斜激波。