Limiting regimes of self-similar gas flows with account for finite chemical-reaction rate

One-dimensional unsteady flows of a combustible gas mixture with account for the finite chemical-reaction rate were studied in [1]. The conditions for self-similarity of such flows were indicated, mathematical formulation of the problem was given, and several numerical calculations were carried out.The authors pointed out the necessity for conducting additional studies, since they were not able to obtain numerically, by means of passages to the limit, self-sustaining detonation waves propagating with the Chapman-Jouguet (CJ) velocity.In this article we point out the reason why it was not possible to reach the CJ regime in [1], and a qualitative analysis is made, by means of the results of [2], of the system of equations describing the self-similar flows of a gas with finite chemical-reaction rate, and the passage to the limit is made to the self-sustaining CJ detonation waves in the presence of chemical reactions. It is also shown that the problem of unsteady flows of a combustible mixture of gases with finite chemical-reaction rate is analogous to the problem of the flow of a gas heated by radiation, examined in [3].In conclusion the authors wish to thank I. V. Nemchinov and A. G. Kulikovskii for discussions of this study.     

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.      

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。     

爆轰波与激波对撞的实验研究

对乙炔氧气混合气体中爆轰波与激波的正面对撞现象的实验研究是以高速摄影获取两波对撞的x-t纹影图,以烟迹板记录对撞中的爆轰胞格图案,并基于激波理论和经典CJ爆轰理论求解了两波对撞的稳态解并探寻其规律. 研究发现透射波系包括一道激波和爆轰波,以及紧随爆轰波后的稀疏波区,这一结果对应于一维理论分析中的CJ解. 透射波系基本不受初始压强影响;初始温度也只成比例地改变流场整体速度,温度越高,速度越快;对波系起实质影响作用的是入射激波强度,激波越强,则整个透射流场呈现偏向激波的趋势;理论分析还指出,稀疏波区的出现不可避免,当激波强度趋于声波稀疏波区趋于消失,激波越强则疏波区趋于扩大. 两波对撞存在一个有限的转变阶段,透射爆轰首先减缓,接着迅速迸发为过驱爆轰,然后再逐渐平衡为CJ爆轰. 对于强不稳定的燃气,对撞后爆轰波在空间上的发展极不均衡,一些区域发生火焰面与诱导激波的严重脱离,随后的火焰面失稳发展为诱导激波区内的爆轰波,实验观察到了这种爆轰在烟迹板上留下的极为精细的迹线.      

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.     

可燃气体中激波与障碍物作用在下游形成爆轰波的数值研究

对平面激波和单个矩形障碍物作用的过程进行了数值模拟,研究了反射产生的上行爆轰波在下游可燃气体中形成爆轰波的过程。数值结果表明,下游爆轰波形成过程主要有2种模式:爆轰波直接绕射和绕射波在上壁面反射,这和已有的实验结果是一致的。通过研究下游爆轰波的形成过程受入射激波马赫数、混合气体的压力和管道尺度的影响,分析了上游爆轰波向下游传播的波动力学过程,讨论了2种形成过程的作用规律和控制因素,阐明了下游爆轰波的形成规律。     

Detonation driver for enhancing shock tube performance

The development of a shock-induced detonation driver for enhancing the performance of a shock tube is described. The detonation wave is induced by the expansion of helium or air. Various gaseous fuel-oxidizer combinations are examined. This method produces a detonation wave which propagates downstream that transitions into a shock wave in the driven section. High-enthalpy flows with a maximum total temperature of 4200 K and a maximum total pressure of 34 atm in the driven tube are achieved. The problems of achieving the so-called perfectly-driven mode as well as those of inadequate fuel-oxidizer mixing are discussed.Received: 26 April 2002, Accepted: 23 December 2002, Published online: 28 April 2003     

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。     

On the propagation mechanism of a detonation wave in a round tube with orifice plates

This study deals with the investigation of the detonation propagation mechanism in a circular tube with orifice plates. Experiments were performed with hydrogen air in a 10-cm-inner-diameter tube with the second half of the tube filled with equally spaced orifice plates. A self-sustained Chapman–Jouguet (CJ) detonation wave was initiated in the smooth first half of the tube and transmitted into the orifice-plate-laden second half of the tube. The details of the propagation were obtained using the soot-foil technique. Two types of foils were used between obstacles, a wall-foil placed on the tube wall, and a flat-foil (sooted on both sides) placed horizontally across the diameter of the tube. When placed after the first orifice plate, the flat foil shows symmetric detonation wave diffraction and failure, while the wall foil shows re-initiation via multiple local hot spots created when the decoupled shock wave interacts with the tube wall. At the end of the tube, where the detonation propagated at an average velocity much lower than the theoretical CJ value, the detonation propagation is much more asymmetric with only a few hot spots on the tube wall leading to local detonation initiation. Consecutive foils also show that the detonation structure changes after each obstacle interaction. For a mixture near the detonation propagation limit, detonation re-initiation occurs at a single wall hot spot producing a patch of small detonation cells. The local overdriven detonation wave is short lived, but is sufficient to keep the global explosion front propagating. Results associated with the effect of orifice plate blockage and spacing on the detonation propagation mechanism are also presented.     

Head-on Collision of a Detonation with a Planar Shock Wave

The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave.     

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.     

圆球诱发斜爆轰波的数值研究

斜爆轰发动机是飞行器在高马赫数飞行条件下的一种新型发动机,具有结构简单、成本低和比冲高等优点.但是斜爆轰发动机的来流马赫数范围广,来流条件复杂,为实现斜爆轰波的迅速、可靠引发,采用钝头体来诱发.利用Euler方程和氢氧基元反应模型,对超声速氢气/空气混合气体中圆球诱导的斜爆轰流场进行了数值研究.不同于楔面诱发的斜爆轰波,球体首先会在驻点附近诱发正激波/爆轰波,然后在稀疏波作用下发展为斜激波/爆轰波.模拟结果显示,经过钝头体压缩的预混气体达到自燃温度后,会出现两种流场:当马赫数较低时,由于稀疏波的影响,燃烧熄灭,钝头体下游不会出现燃烧情况;而当马赫数较高时,燃烧阵面能传到下游.分析表明,当钝头体的尺度较小时,驻点附近的能量不足以诱发爆轰波,只会形成明显的燃烧带与激波非耦合结构;当钝头体的尺度较大时,流场中不会出现燃烧带与激波的非耦合现象,且这一特征与马赫数无关.通过调整球体直径,获得了激波和燃烧带部分耦合的燃烧流场结构,这一流场结构在楔面诱发的斜爆轰波中并不存在,说明稀疏波与爆轰波面的相互作用是决定圆球诱发斜爆轰波的关键.     

氢氧燃烧及爆轰驱动激波管

分析并观察了沿驱动段轴向分布多火塞燃烧驱动段的性能．提出主膜处同一管截面均匀分布三火花塞引燃的点火方法．用这种点火方法驱动产生的入射激波强度重复性较高,激波后气流速度、温度和压力的定常性亦大大改善,可满足气动试验实际要求．提出在驱动段尾端串接卸爆段来消除爆轰波反射高压,从而可使反向爆轰驱动段用来产生高焓高密度试验气流．这种反向爆轰驱动产生的入射激波重复性高,激波衰减弱．在主膜处的收缩段产生的反射波可缓解爆轰波后跟随的稀疏波的不利影响,从而使前向爆轰驱动具有实用性．在产生的入射激波强度相同条件下,前向爆轰驱动所需的爆轰驱动段可爆混合气初始压力可较反向爆轰低近一个量级．     

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.     

Reignition of detonations by reflected shocks

Numerical simulations are used to study the diffraction, decay, and reignition that occurs when a detonation propagates past an increase in cross-sectional area in a rectangular tube. The computations solve the time-dependent two-dimensional equations describing a reactive flow in an argon-diluted stoichiometric hydrogen-oxygen mixture at atmospheric pressure. Previous studies have shown that soon after transmission to a larger area, the reaction front decouples from the leading shock and forms a decaying blast wave (“bubble”) in the larger tube. Then, depending on the initial conditions, the detonation either continues to decay or is reignited as the bubble reflects off confining surfaces. For a strongly overdriven initiating detonation, reignition occurs through an interaction between the bubble and the original contact surface. For a more weakly driven system, reignition can occur in two ways: either in the slip line and Mach stem of the Mach reflection formed when the bubble reflects off the bottom surface of the tube, or by multiple shock interactions that occur when the reflected bubble overtakes the initial detonation front. The computations show the evolution and development of the cellular structure of the steady detonation front. Submitted to the 14th International Colloquium on the Dynamics of Energetic and Reactive Systems, Coimbra, Portugal, August, 1993     

On some conditions for detonation initiation downstream of a perforated plate

An experimental study is presented of the influence of detonation wave parameters and detonation product composition upstream of a perforated plate on the onset of detonation downstream. Experiments were performed in detonation tube 106 mm in diameter, separated into two sections by a perforated plate combined with a diaphragm. The tube was equipped with pressure sensors and a semi-cylindrical smoked foil. Hydrogen–air mixtures with different hydrogen concentrations were used upstream and downstream of the perforated plate. It is shown for mixtures containing 25 and 34 % of hydrogen in air that the onset of detonation downstream depends on detonation parameters upstream of the perforated plate. An increase in the initial pressure upstream of the plate leads to detonation initiation immediately downstream. The variation of mixture composition upstream of a perforated plate does not affect on detonation initiation downstream under the present experimental conditions.     

Strong explosion in a combustible gas mixture

Assume that a planar, cylindrical, or spherical point explosion takes place in a combustible mixture of gases. As a result of the explosion a strong shock wave develops and triggers chemical reactions with the release of heat. The solution of the problem for the case in which the thickness of the heat release zone is neglected (the infinitely thin detonation wave model) was obtained in [1–3].It was emphasized in [4] that these solutions can be considered only as asymptotic solutions for time and distance scales which are large in comparison with the scales which are characteristic for the chemical reactions, and under the assumption that as the overdriven detonation wave which is formed in the explosion is weakened by the rarefaction waves it does not degenerate into an ordinary compression shock. Here the question remains open of the possibility of obtaining such asymptotic solutions with account for finite chemical-reaction rates.In conclusion the authors wish to thank E. Bishimov for carrying out most of the computations for this study.     

引射器位置对脉冲爆震发动机性能影响

以氢气和氧气混合物为例,通过对加装收敛扩张型引射器,采用数值计算方法对脉冲爆震发动机性能进行模拟,获得了爆震管出口相对引射器喉部处于上游、中间和下游三种引射器位置对脉冲爆震发动机性能的影响规律.计算结果表明,爆震管出口相对引射器喉部处于下游时的增推效果最好,处于中间时次之,上游时效果最差.将二次流率与增推比进行比较,发现引射器的冲量增推比随引射的二次流率增加而增大.