Transition of plane overdriven detonation wave to the Chapman-Jouguet regime

The asymptotic laws of behavior for plane, cylindrical, and spherical infinitely thin detonation waves were found in [1, 2] for increasing distance from an igniting source in those cases in which the waves changed into Chapman-Jouguet waves as they decayed. It was shown that the plane overdriven detonation wave approaches the Chapman-Jouguet regime asymptotically, while the transition of the cylindrical or spherical strong detonation wave into the Chapman-Jouguet wave may occur at a finite distance from the initiation source.Similar conclusions are valid for the propagation of stationary steadystate detonation waves which arise with flow of combustible gas mixtures past bodies.However, numerous experiments [3, 4] on firing bodies in a detonating gas show that the overdriven detonation wave which forms ahead of the body decays and decomposes into an ordinary compression shock and a slow combustion front. To establish why the wave does not make the transition to the Chapman-Jouguet regime, in the following we consider the propagation of a plane detonation wave and account for finite chemical reaction rates. We use the very simple two-front model (ordinary shock wave and following flame front). Conditions are found for which transition to the Chapman-Jouguet regime does not occur. We first consider the propagation of an unsteady plane wave and then the steady plane wave. It is found that for all the mixtures used in these experiments transition to the Chapman-Jouguet regime is not possible within the framework of the assumed model.     

Initiation of detonation regimes in hybrid two-phase mixtures

The problem of detonation initiation is studied in the case of hybrid two-phase mixtures consisting of a hydrogen-air gaseous mixture with suspended fine aluminium particles. In preceding works on this subject, investigation of the steady propagation regimes has shown that three main propagation regimes could exist: the Pseudo-Gas Detonation (PGD), the Single-Front Detonation (SFD), and the Double-Front Detonation (DFD). In the present study, a one-dimensional unsteady numerical code has been improved to study the build-up of the detonation in a heterogeneous solid particle gas mixture contained in a tube. The initiation is simulated by the deposition of a given energy in a point source explosion, and the formation of the detonation is observed over distances of 15 m to 30 m. As the code has been designed to run on a micro-computer, memory limitations preclude sufficient accuracy for quantitative results, however, good qualitative agreement has been found with the results of the steady analysis. In addition, it has been demonstrated that when both PGD and SFD could exist at the same particle concentration, the PGD regime was unstable and was able to exist only over a limited distance (a few meters): after some time, the reaction of aluminium particles in the unsteady flow perturbs the leading wave and accelerates it to the SFD regime. Influence of particle diameter and of initiation energy are examined.     

基于CE/SE方法模拟空气中RDX-Al悬浮粉尘的两相爆轰

通过CE/SE方法模拟了空气中炸药-铝粉尘的两相爆轰过程, 研究了双粉尘爆轰过程中粒子不同密度对爆轰波速度、压力的影响, 得到密度与波速、爆压间的线性关系。模拟得到悬浮粉尘在复杂通道中的爆轰波传播过程, 研究了双粉尘爆轰的流场演化过程, 选取流场中的一些点对该处流场的压力及温度随时间的变化进行重点研究, 对比了单铝粉尘在同种条件下的爆轰过程, 发现双粉尘爆轰明显提高了爆轰波波速和流场的压力及温度。模拟结果表明CE/SE方法可以成功模拟双粉尘的爆轰过程, 可为多粉尘爆轰的研究提供参考。     

Non-equilibrium model of steady detonations in aluminum particles - oxygen suspensions

Steady-state detonation regimes are studied on the basis of the mathematical model of detonation of aluminum particles in oxygen taking into account differences in velocities and temperatures of the mixture components. The final steady state is analyzed by determining the types of final singularities in the plane of relaxation parameters (the ratios of characteristic times of thermal and velocity relaxations and combustion). The regions of existence of steady-state regimes are found numerically, depending on the detonation wave velocity and relaxation parameters. Numerical illustrations of various flow types are presented, and the properties of the detonation wave structure caused by velocity nonequilibrium are examined. Qualitative agreement of data obtained with frozen relaxation parameters and their dependence on the flow parameters is shown. Received 5 July 1997 / Accepted 13 July 1998     

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.     

Supersonic flow of combustible gas mixture past sphere with account for ignition delay time

Assume an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M₁, p₁, and T₁. A detached shock is formed ahead of the body and the mixture passing through the, shock is subjected to compression and heating. Various flow regimes behind the shock wave may be realized, depending on the freestream conditions. For low velocities, temperatures, or pressures in the free stream, the mixture heating may not be sufficient for its ignition, and the usual adiabatic flow about the body will take place. In the other limiting case the temperature behind the adiabatic shock and the degree of gas compression in the shock are so great that the mixture ignites instantaneously and burns directly behind the shock wave in an infinitesimally thin zone, i. e., a detonation wave is formed. The intermediate case corresponds to the regime in which the width of the reaction zone is comparable with the characteristic linear dimension of the problem, for example, the radius of curvature of the body at the stagnation point.The problem of supersonic flow of a combustible mixture past a body with the formation of a detonation front has been solved in [1, 2]. The initial mixture and the combustion products were considered perfect gases with various values of the adiabatic exponent .These studies investigated the effect of the magnitude of the reaction thermal effect and flow velocity on the flow pattern and the distribution of the gasdynamic functions behind the detonation wave.In particular, the calculations showed that the strong detonation wave which is formed ahead of the sphere gradually transforms into a Chapman-Jouguet wave at a finite distance from the axis of symmetry. For planar flow in the case of flow about a circular cylinder it is shown that the Chapman-Jouguet regime is established only asymptotically, i. e., at infinity.This result corresponds to the conclusions of [3, 4], in which a theoretical analysis is given of the asymptotic behavior of unsteady flows with planar, spherical, and cylindrical detonation waves.Available experimental data show that in many cases the detonation wave does not degenerate into a Chapman-Jouguet wave as it decays, bur rather at some distance from the body it splits into an adiabatic shock wave and a slow combustion front.The position of the bifurcation point cannot be determined within the framework of the zero thickness detonation front theory [1], and for the determination of the location of this point we must consider the structure of the combustion zone in the detonation wave. Such a study was made with very simple assumptions in [5].The present paper presents a numerical solution of the problem of combustible mixture flow about a sphere with a very simple model for the structure of the combustion zone, in which the entire flow behind the bow shock wave consists of two regions of adiabatic flow-an induction region and a region of equilibrium flow of products of combustion separated by the combustion front in which the mixture burns instantaneously. The solution is presented only for subsonic and transonic flow regions.     

Traveling Waves in Porous Media Combustion: Uniqueness of Waves for Small Thermal Diffusivity

We study traveling wave solutions arising in Sivashinsky’s model of subsonic detonation which describes combustion processes in inert porous media. Subsonic (shockless) detonation waves tend to assume the form of a reaction front propagating with a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity [5]. Moreover, it has been shown that, when the thermal diffusivity is neglected, the traveling wave is unique. The question of whether the wave is unique in the presence of thermal diffusivity has remained open. For the subsonic regime, the underlying physics might suggest that the effect of small thermal diffusivity is insignificant. We analytically prove the uniqueness of the wave in the presence of non-zero diffusivity through applying geometric singular perturbation theory. Dedicated to Mr. Brunovsky in honor of his 70th birthday.     

A generalized Zel’dovich-Neumann-Döring model of steady gaseous detonation

A model of N-component gas mixture detonation whose combustion zone is formed by n (1 ≤ n ≤ N − 1) independent reactions satisfying the kinetic formulation of the mass action law is studied. In the framework of this model, it is found that there exist two possible types of self-sustaining detonation waves with asymptotically stable combustion zones. It is shown that it is possible to observe only a strong wave propagating in the Chapman-Jouguet regime relative to the flow on the critical surface. It is also shown that, for a perfect gas mixture, this wave appears only when a combustion zone is formed by one or two reactions.     

超音速来流中爆轰波衍射和二次起爆过程研究

预爆管技术被广泛地应用在爆轰波发动机的起爆过程中,但是在超音速来流中基于预爆管技术起始爆轰波的研究并未被广泛地开展。基于此,本文中数值研究了横向超音速来流对半自由空间内爆轰波的衍射和自发二次起爆、及管道内的衍射和壁面反射二次起爆两种现象的影响。数值模拟的控制方程为二维欧拉方程,空间上使用五阶WENO格式进行数值离散,采用带有诱导步的两步链分支化学反应模型。所模拟的爆轰波具有规则的胞格结构,对应于用惰性气体高度稀释过的可爆混合物中形成的爆轰波。结果表明:在半自由空间内,在本文所模拟的几何尺寸下,爆轰波并未成功发生二次起爆现象,但是爆轰波的自持传播距离随着横向超音速来流强度的增强而增加。在核心的三角形流动区域外,波面诱导产生了更多的横波结构;在管道内,横向的超音速来流在逆流侧对出口气流产生了压缩作用,能有效提高波面压力,因此反射后的激波压力也比较高。在同样的几何尺寸下,爆轰波在静止和超音速(Ma=2.0)气流中分别出现了二次起爆失败和成功两种现象,这是由于在超音速来流中化学反应面的褶皱诱导产生了横波结构,横波与管壁以及其他横波之间的碰撞提高了前导激波的强度,并最终促进了爆轰波在超声速流主管道内的成功起始。     

Nonstationary problems of the combustion of aerosuspensions in fuel that contains the oxidant

A study is made of one-dimensional nonstationary problems of the combustion and detonation of aerosuspensions of unitary fuels or propellants, which contain the oxidant as well as the combustible material (gunpowder, high explosives). A numerical analysis is made of the damping of the convective combustion which occurs at relatively low mass concentrations of the fuel; the critical concentration dividing the damped and the detonation regimes is determined. It is shown that the realization of the damped or detonation regime of convective combustion at a given concentration is completely determined by the gas dynamics of the relative motion of the gas and the particles (two-velocity effect), this being governed by the coefficient of friction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–27, January–February, 1981.     

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

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

A double-front structure of detonation wave as the result of phase transitions

Using thermochemical code calculations, we show that the nanographite–nanodiamond phase transition, which may occur in the detonation products of a number of carbon containing explosives, can affect the detonation properties and can cause a specific detonation regime with some unusual peculiarities. Among them, we first note the failure of the Chapman–Jouguet condition and the presence of the sonic plane, where the Mach number is equal to unity, in a detonation product expansion wave at a lower pressure than that at the Chapman–Jouguet point. The peculiarities of this detonation regime are demonstrated by the example of TNT, HNS, and RDX. The computed detonation velocities are in excellent agreement with experiments over a wide range of initial charge densities for all of the investigated explosives. The results of this work allow one to explain, e.g., contradictory experimental data on the detonation pressure and on the length of the reaction zone for TNT. We believe that some other solid–solid, solid–liquid, and liquid–liquid phase transformations in the detonation products may also cause a detonation regime with the same features as shown here for the nanographite–nanodiamond transition. We suggest a computational study that should facilitate proposing detonation experiments strongly arguing in favor of the model presented. PACS 47.40.-x; 47.40.Rs; 64.70.-p; 64.70.Kb; 05.70.-a; 05.70-.CeThis 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.     

Distinctive Features of the Dynamics of a Bubble Detonation Wave in Tubular Clusters

The distinctive features of the passage of a detonation wave from a tubular body of a bubbly liquid confined by a layer of a “pure” liquid into a region of a homogeneous bubbly liquid are investigated. It is shown that the detonation wave propagating in the tubular bubble cluster can break away on the passage through a region, where the cluster radius increases jumpwise, due to the two-dimensional wave scattering in the expansion zone, despite an increase in the system power-intensity.     

爆轰波在突扩通道中传播的数值模拟研究

建立了描述甲烷 空气混合物爆轰波传播的单步化学反应爆轰模型 ,通过数值模拟研究了在二维突扩通道中爆轰波的强度变化和各种波行为。结果表明 :爆轰波在进入突扩通道初始阶段的衍射使爆轰波局部向爆燃转变 ;爆炸波在壁面发生马赫反射形成的高温高压区域将直接诱导自持爆轰波的重新形成。     

Investigation of the detonation regimes in gaseous mixtures with suspended starch particles

The existence of a secondary discontinuity at the rear of a detonation front shown in experiments by Peraldi and Veyssiere (1986) in stoichiometric hydrogen-oxygen mixtures with suspended 20-m starch particles has not been explained satisfactorily. Recently Veyssiere et al. (1997) analyzed these results using a one-dimensional (1-D) numerical model, and concluded that the heat release rate provided by the burning of starch particles in gaseous detonation products is too weak to support a double-front detonation (DFD), in contrast to the case of hybrid mixtures of hydrogen-air with suspended aluminium particles in which a double-front detonation structure was observed by Veyssiere (1986). A two-dimensional (2-D) numerical model was used in the present work to investigate abovementioned experimental results for hybrid mixtures with starch particles. The formation and propagation of the detonation has been examined in the geometry similar to the experimental tube of Peraldi and Veyssiere (1986), which has an area change after 2 m of propagation from the ignition point from a 69 mm dia. section to a 53 mm 53 mm square cross section corresponding to a 33% area contraction. It is shown that the detonation propagation regime in these experiments has a different nature from the double-front detonation observed in hybrid mixtures with aluminium particles. The detonation propagates as a pseudo-gas detonation (PGD) because starch particles release their heat downstream of the CJ plane giving rise to a non-stationary compression wave. The discontinuity wave at the rear of the detonation front is due to the interaction of the leading detonation front with the tube contraction, and is detected at the farthest pressure gauge location because the tube length is insufficient for the perturbation generated by the tube contraction to decay. Thus, numerical simulations explain experimental observations made by Peraldi and Veyssiere (1986). Received 5 July 1997 / Accepted 13 July 1998     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Effect of chemical reactivity on the detonation initiation in shock accelerated flow in a confined space

The interactions of a spherical flame with an in- cident shock wave and its reflected shock wave in a confined space were investigated using the three-dimensional reactive Navier-Stokes equations, with emphasis placed on the effect of chemical reactivity of mixture on the flame distortion and detonation initiation after the passage of the reflected shock wave. It is shown that the spatio-temporal characteristics of detonation initiation depend highly on the chemical reactivity of the mixture. When the chemical reactivity enhances, the flame can be severely distorted to form a reactive shock bifurcation structure with detonations initiating at different three-dimensional spatial locations. Moreover, the detonation initiation would occur earlier in a mixture of more enhanced reactivity. The results reveal that the detonations arise from hot spots in the unburned region which are initiated by the shock-detonation-transition mechanism.     

甲烷-空气爆轰波传播的数值模拟

研究了甲烷-空气混合物爆轰波在二维突扩通道中传播的各种复杂行为。结果表明：爆轰波在进入突扩通道的初始阶段有局部向爆燃转变的现象；爆炸波在壁面发生马赫反射形成的高温高压区域将直接驱动自持爆轰波的重新形成。     

Global modelling of heat release during initiation and propagation of detonation and deflagration waves in methane-air-particle systems

In the present paper the direct initiation of a self supporting detonation and propagation of a low-speed combustion in methane-air-coal particles mixtures are solved. For particles, a heterogeneous regime of combustion is used, for methane one overall chemical reaction is taken into account: CH + 2O = CO + 2HO. The heat release rate is assumed to be defined as a delay time based on the well-known thermal theory of Frank-Kamenetsky (1967). The proposed model allows one to investigate the influence inert particles or coal dust on the explosion limits of methane-air mixtures. It is shown that the addition of a limited quantity of particles leads to detonation stability. In low speed combustion problems this method allows one to get a good correlation between theoretical and experimental velocities of steady flame propagation in carbon-hydrogen gaseous mixtures. Coal dust influence on gasdynamics of a methane-air mixture combustion is investigated in an unsteady problem by using of the global modelling. It is shown that limited coal dust concentration increases the flame wave intensity in lean methane-air mixtures in contrast to inert particles. In stoichiometric gas mixtures, sand and coal dusts decrease a flame velocity. Far from the ignition point flame, the velocity is largely defined by the dust mass concentration and not by the size of particles. Received 5 July 1997 / Accepted 13 July 1998     

Investigation of the Process of Compression of a Magnetic Field by a Strong Ionizing Shock Wave in a CsI Single Crystal

A mathematical model is proposed for the process of compression of a magnetic field by a strong ionizing shock wave in a single crystal when a compressible electroconducting medium is formed behind the shock. The detailed physical pattern of the process is obtained numerically. It is shown that in the final stage different magnetic field compression regimes are possible: cumulation on the axis, an oscillatory regime in which the magnetic field and gas dynamic quantities change sharply, and a quasi-steady regime with smooth slow variation of all the parameters. In previous studies the possibility of this regime was not noted. For the dimensionless parameters characterizing the process of compression of the magnetic field as a whole domains corresponding to different compression regimes are obtained.