Inhibition of detonation wave with halogenated compounds

The influence of CF₃Br, CF₂HBr, CF₂HCl and CF₃H on a benchmark mixture composed of stoichiometric H₂−CO−O₂−Ar is experimentally investigated. Several ratios hydrogen/carbon monoxide are studied. For each benchmark mixture, the initial pressure is adjusted in such a way that the detonation cell sizes are quasi identical. The effect of the additives on the detonation velocity and the detonation cellular structure is analyzed. The experiments show that CF₃Br is the best inhibitor and CF₂HBr might be substituted for CF₃Br. CF₃H does not inhibit the detonation wave. Simple chemical kinetics analysis gives us a better understanding of the inhibiting and promoting effect of the halocarbons. 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     

气相爆轰波正反射激波加速研究

实验采用压力传感器测量了指定点压力时间曲线。数值模拟基于二维反应欧拉方程和基元反应模型,采用二阶附加半隐的龙格-库塔法和5阶WENO格式分别离散时间和空间导数项,获得了指定点数值压力时间曲线。理论分析基于爆轰理论和激波动力学,分析了气相爆轰波反射过程所涉及的复杂波系演变并获得了反射激波速度。结果表明:本文数值模拟和理论计算定性上重复并解释了实验现象。气相爆轰波在右壁面反射后,右行稀疏波加速反射激波。其加速原因是:尽管激波波前声速减小,但激波马赫数增大,波前气流速度减小。在低初压下,可能还由于爆轰波后未反应或部分反应气体的作用,导致反射激波加速幅度比高初压下大。     

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.     

Advances in the analytical study of the dynamics of gaseous detonation waves

Recent theoretical results on the dynamics of gaseous detonations are presented. An asymptotic analysis is performed, retaining the physical mechanisms controlling the modifications to the inner structure of the detonation. As a result, the system of hyperbolic equations for the compressible fluid mechanics coupled with a detailed chemical kinetics of heat release is reduced to a single integral equation for the propagation velocity of the combustion wave versus time. Concerning the direct initiation of spherical detonations by a blast wave, curvature effects are shown to be responsible for a critical condition of initiation. Near criticality, the role of the unsteadiness of the inner structure is pointed out. The whole complexity of the critical dynamics is reproduced and explained by the integral equation. The necessary background knowledge in gaseous detonation is recalled in the two first sections of the article in order to facilitate the reading by non-specialists.     

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.     

正向爆轰驱动高焓激波风洞的数值模拟

对充满氢氧可燃气体、带扩容腔的正向爆轰驱动的激波风洞进行了数值模拟。计算采用了欧拉方程,频散可控耗散差分格式（DCD）和改进的二阶段化学反应模型。在扩容腔附近采用二维轴对称计算模型,而在驱动段和被驱动段的直管道部分则采用一维计算模型。本文分析了爆轰波在管道中的传播、反射和绕射过程。计算结果表明扩容腔的尺寸对爆轰波的传播、反射、汇聚等起着决定性的作用;带扩容腔的正向爆轰驱动的激波风洞能够得到平稳的持续时间较长的气流,提高了实验的精确度和可重复性。     

The influence of cellular structure on detonation transmission

We present two-dimensional numerical simulations of the transmission of detonation from a rectangular channel into a larger volume. The simulations solve the Euler equations on a Cartesian grid using the method of Flux-Corrected Transport for the fluid equations and a two-step induction parameter model for the chemistry. We simulate detonation in a H₂/O₂/Ar mixture and use sufficient grid resolution to resolve the cellular structure of the detonation. When a planar detonation front without a resolved cellular structure expands into the larger volume, the reaction front separates from the shock front and the detonation fails. When the planar front is perturbed to induce a quasi-regular cellular structure in the detonation, it again initially begins to fail, but now the presence of the transverse waves leads to reignition of the detonation in the larger volume. The form of this reignition shows striking similarities to the reignition of detonation which has been seen experimentally in H₂/O₂ mixtures. We describe this reignition mechanism in detail, and also investigate the dependence of the reignition on the number of cells in the detonation front. 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     

Interpretation of wake instability at slip line in rotating detonation

ABSTRACT

In studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated with the 7-species-and-8-reaction finite-rate chemical reaction model of hydrogen/air mixtures, further studies are performed to simulate the 2-D rotating detonation, and the flow mechanism of instability at the slip line is investigated in depth. The results show that the distinct wake profile exists at the slip line, which is different from the typical mixing layer. Analysis indicates that the generation of wake is caused by the transition shock between the detonation wave and oblique shock. Because of the wake profile, the vorticity distribution therein appears in a double-layer layout, and different evolutions exist in different vorticity layers. Based on the velocity profile across the slip line, the analysis by the linear stability theory is made, and two main unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilised to analyse the numerical results, and similar shape profiles are obtained. A general coincidence in velocity of vortex movement is also attained between the theoretical predictions and simulations. Investigations show that the wake instability is responsible for the unstable mechanism, and corresponding unstable structures differ from the canonical ones in typical mixing layers.     

Influence of Molecular Characteristics of a Substance on Detonation Phenomena

In the present study, the molecular-dynamics method has been used to examine the influence of the thermal effect of the chemical reaction on processes in a detonating molecular crystal (propagation velocity and structure of the detonation wave, delay time of the chemical reaction, and energy macrocharacteristics of the crystal in the disturbed region). Molecular-dynamics data are compared with predictions of the continuum theory of detonation; in particular, fulfillment of the Chapman–Jouguet condition is verified.     

Intensification of a detonation wave in the zone of secondary reactions in a two-phase medium

A method is proposed for the numerical calculation of one-dimensional nonsteady-state flows of a mixture of a gas with particles, based on the separation of a system of differential equations for a two-phase medium into two subsystems. The problem is solved concerning the propagation of a plane detonation wave in a mixture of a detonating gas with particles, behind the front of which secondary chemical reactions are taking place between the vapors of the particle material and the detonation products. The velocity profiles of the gas and of the thermodynamic functions behind the detonation wave front are determined, and also the dependence of the detonation velocity on the distance to the point of initiation. The conditions for intensification of the detonation wave are obtained in the zone of secondary reactions.Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 92–96, September–October, 1972.     

Numerical study on the performance of a twin-raft wave energy dissipator in a stilling basin

In this paper, a raft-typed wave energy dissipator is proposed, and a mathematical model for the hydrodynamics of such a dissipator is presented, based on Reynolds-averaged Navier–Stokes equations. The model is validated by a comparison of the numerical results with the results of other investigators. The validated model is then utilized to examine the effect of wave height, wave frequency, damping coefficient, flow velocity on wave energy dissipation ratio and wave transmission coefficient for a hinged twin-raft wave energy dissipator. Our results reveal that the differences in behaviour exhibited by an inviscid fluid and a viscous fluid can be large and vary considerably, depending on the flow velocity.     

Numerical simulation of H2/air detonation using unstructured mesh

To explore the capability of unstructured mesh to simulate detonation wave propagation phenomena, numerical simulation of H₂/air detonation using unstructured mesh was conducted. The unstructured mesh has several adv- antages such as easy mesh adaptation and flexibility to the complicated configurations. To examine the resolution dependency of the unstructured mesh, several simulations varying the mesh size were conducted and compared with a computed result using a structured mesh. The results show that the unstructured mesh solution captures the detailed structure of detonation wave, as well as the structured mesh solution. To capture the detailed detonation cell structure, the unstructured mesh simulations required at least twice, ideally 5times the resolution of structured mesh solution.      

爆震室壁面条件对脉冲爆震发动机爆震性能的影响

在爆震室内快速形成稳定传播的爆轰波是脉冲爆震发动机的关键．本文利用有限速率化学反应模型,考虑粘性、热对流,基于N-S方程对氢气与空气/氧气为反应混合物的爆震发动机爆震室内流场进行计算．从流场压力、速度、涡量、湍流动能等方面研究爆震室壁面条件对燃烧爆轰性能的影响,分析流场爆轰波压力与流场湍动能的关系,讨论可燃气体燃烧转爆轰的机理．结果表明：爆震室内燃烧爆轰机理受到化学反应能量释放、壁面摩擦效应、壁面与外界热交换的影响．在文中讨论的范围内,相比于半圆形和三角形的爆震室装置,矩形的爆震室增强装置能在更短的时间内得到较高的爆轰波压力和湍动能峰值．壁面粗糙层高度（粗糙度）影响爆震室的燃烧爆轰性质．当壁面粗糙度为0.15mm时,粗糙度对爆轰的激励作用大于抑制作用,能较快形成稳定的爆轰波,且推力为35.5N;随着壁面对流换热系数的增大,爆震室壁面的散热加剧．当壁面对流换热系数大于临界值2.6W/(m2·K)时,爆震室内不能形成稳定的爆震波．     

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.     

气体-燃料液滴两相系统爆轰的数值模拟

用两相流体力学模型对气体 燃料液滴系统进行了研究。数值模拟了点火后两相系统爆轰波的发展过程，得到爆轰波的结构和参数。数值模拟结果表明气体 燃料液滴系统爆轰波有较宽的反应区，因而两相爆轰波的曲率对爆速的影响效应十分明显。进行了燃料液滴尺寸对爆轰波的结构和参数的影响的数值模拟。除了很小的液滴外，燃料液滴在爆轰波前导激波面和ＣＪ面间不能完全气化。随着液滴尺寸的增加，燃料液滴在爆轰波前导激波面和ＣＪ面间释放出的能量随之减少，爆轰参数也随之下降。     

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.     

The evolution of a detonation wave in a variable cross-sectional chamber

A two-dimensional numerical simulation has been performed to study the interaction of a gaseous detonation wave with obliquely inclined surfaces in a variable cross-sectional chamber. The weighted essentially non-oscillatory (WENO) numerical scheme with a relatively low resolution grid is employed. A detailed elementary chemical reaction model with 9 species and 19 elementary reactions is used for a stoichiometric oxy-hydrogen mixture diluted with argon. In this work, we study the effect of area expansion and contraction on the main/gross features of the detonation cellular structures in the presence of detonation reflection, diffraction and localized explosion. The result shows that there exists a transition region as the detonation wave propagates through the converging/diverging chamber. Within the transition region, the initial regular detonation cells become distorted and irregular before they re-obtain their regularity. While the ultimate regular cell size and the length of the transition region are strongly affected by the converging/diverging angle, the width/length ratio of the cells is fairly independent of it. A localized explosion near the wall is found as the detonation wave propagates in the diverging chamber.      

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.     

激波管双爆轰驱动段性能的数值模拟研究

采用频散可控的耗散格式(DCD),求解Euler方程和一种改进的二阶段化学反应模型, 对氢氧反向-正向双爆轰驱动段激波管进行了数值模拟. 计算结果表明：当辅驱动段与主驱动 段初始压力比小于临界值时,Taylor波仍会出现,但波扇夹角较单一前向爆轰驱动段小,入 射激波马赫数衰减率变小;当初始压力比等于临界值时,主驱动段中的Taylor波完全被消除, 入射激波马赫数不再衰减. 当初始压力比大于临界值时,在主驱动段中能产生过驱动爆轰波, 不仅Taylor波被完全消除,而且驱动能力较单一前向爆轰驱动段强.