Blast wave mitigation by dry aqueous foams

This paper presents results of experiments and numerical modeling on the mitigation of blast waves using dry aqueous foams. The multiphase formalism is used to model the dry aqueous foam as a dense non-equilibrium two-phase medium as well as its interaction with the high explosion detonation products. New experiments have been performed to study the mass scaling effects. The experimental as well as the numerical results, which are in good agreement, show that more than an order of magnitude reduction in the peak overpressure ratio can be achieved. The positive impulse reduction is less marked than the overpressures. The Hopkinson scaling is also found to hold particularly at larger scales for these two blast parameters. Furthermore, momentum and heat transfers, which have the main dominant role in the mitigation process, are shown to modify significantly the classical blast wave profile and thereafter to disperse the energy from the peak overpressure due to the induced relaxation zone. In addition, the velocity of the fireball, which acts as a piston on its environment, is smaller than in air. Moreover, the greater inertia of the liquid phase tends to project the aqueous foam far from the fireball. The created gap tempers the amplitude of the transmitted shock wave to the aqueous foam. As a consequence, this results in a lowering of blast wave parameters of the two-phase spherical decaying shock wave.     

Critical tube diameter for detonation transmission and critical initiation energy of spherical detonation

Two experimental setups are used to study propagation and attenuation of blast waves. In the first one, the blast wave is generated by a spherical detonation, and in the second one, the blast wave is created by the diffraction of a planar detonation propagating in a tube. The similarity of these phenomena appears clearly by means of dimensionless space-time and pressure-space diagrams of shock wave propagation. Dimensionless variables are expressed as a function of the supplied energy. Two energy formulations are proposed: a piston model and a bulk energy model. The established diagrams cover a wide range of industrial applications. Under critical conditions, the energy released by a planar detonation is correlated to the ignition source energy supply and a relationship which links the critical radius of detonation to the critical tube diameter. Received 5 July 1997 / Accepted 13 July 1998     

水及盛水容器对近距离爆炸载荷影响的实验研究

为研究用水包围炸药的方式对爆炸载荷的作用机理,在两端开口的钢筒内进行了水直接包覆炸药的爆炸实验,利用光纤位移干涉仪获取了钢筒外壁的径向速度和动态变形。结果表明:不同于无水爆炸,爆轰产物通过水的“裂缝”在空气中形成冲击波,造成该冲击波出现时间更晚、强度更低、持续时间更长,并要求相应的数值模拟采用二维以上的计算模型;盛水结构的材料密度越低、厚度越小对爆炸载荷的影响越小。     

Cinematographic investigations of the explosively driven dispersion and ignition of solid particles

We present results of an experimental study of blast wave propagation and particle dispersion induced by a free-field detonation of spherical charges made of a 125 g C-4 explosive surrounded by inert or reactive particles. Visualization of the flow was performed with a high-frame-rate video camera. Background oriented Schlieren (BOS) methods were adapted to process the images that allowed the detection of the shock waves. BOS analysis also revealed that particles form agglomerates, which may generate precursor perturbations on the recorded pressure signals. While inert glass particles notably delay the shock, the combustion of aluminium particles can accelerate it, especially if they are small atomized or flaked particles. When a mixture of inert glass particles with reactive particles is dispersed, the agglomerates are formed by coalescence of both materials.     

On the interaction and coalescence of spherical blast waves

The scaling and similarity laws concerning the propagation of isolated spherical blast waves are briefly reviewed. Both point source explosions and high pressure gas explosions are considered. Test data on blast overpressure from the interaction and coalescence of spherical blast waves emanating from explosives in the form of shaped charges of different strength placed in the vicinity of a solid propellant stack are presented. These data are discussed with regard to the scaling laws concerning the decay of blast overpressure. The results point out the possibility of detecting source explosions from far-field pressure measurements.      

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.      

DDT and detonation waves in dust-air mixtures

This paper summarizes the studies of DDT and stable detonation waves in dust-air mixtures at the Stosswellenlabor of RWTH Aachen. The DDT process and propagation mechanism for stable heterogeneous dust detonations in air are essentially the same as in the oxygen environment studied previously. The dust DDT process in tubes is composed of a reaction compression stage followed by a reaction shock stage as the pre-detonation process. The transverse waves that couple the shock wave and the chemical energy release are responsible for the propagation of a stable dust-air detonation. However, the transverse wave spacing of dust-air mixtures is much larger. Therefore, DDT and propagation of a stable detonation in most industrial and agricultural, combustible dust-air mixtures require a tube that has a large diameter between 0.1 m and 1 m and a sufficient length-diameter ratio beyond 100, when an appropriately strong initiation energy is used. Two dust detonation tubes, 0.14 m and 0.3 m in diameter, were used for observation of the above-mentioned results in cornstarch, anthraquinone and aluminum dust suspended in air. Smoked-foil technique was also used to measure the cellular structure of dust detonations in the 0.3 m detonation tube. Received 11 February 2000 / Accepted 1 August 2000     

中心引爆破片战斗部产生的近区空气爆炸波的计算

本文提出一种计算中心起爆有限装药尺寸破片战斗部产生的近区空气爆炸波超压的近似方法。战斗部壳体碎片除受爆轰产物的推力及空气反压外,还考虑了碎片形状等因素引起的形阻修正。适当选取形阻修正系数及修正项引入时刻,计算数据与数十公斤装药战斗部近区实验结果十分接近。本文结果表明,爆破战斗部近区空气爆炸波的计算不能采用强爆炸波理论,应当考虑飞片驱动冲击波的模型。     

气相爆轰波传播过程中的自点火效应

基于基元反应模型和单步反应模型,对直管道中H₂-air混合气体中爆轰波的传播过程进行了数值模拟,揭示了气相爆轰波传播过程中的自点火效应。利用数值模拟方法计算了不同爆轰模型的点火延迟时间,并得到了爆轰波三波点的传播过程以及所形成胞格结构的尺寸。结果表明,胞格宽度与点火延迟时间成正比;爆轰波诱导区内气体的点火延迟时间与三波点的运动周期基本一致。进一步对结果分析可知,爆轰波的自维持传播取决于点火延迟时间(表征化学反应的特征时间)和三波点的运动周期(表征流动的特征时间)的匹配;当二者相匹配时,经过前导激波压缩后形成的高温高压爆轰气体,在短时间内实现了自点火,同时释放出大量的能量推动了爆轰波的前进,即爆轰波的稳定自维持传播依靠其自点火机制。     

近距离爆炸比例爆距的界定标准及荷载模型

如何准确界定“近距离爆炸（close-in explosion）”一直是防护工程研究领域的热点。本文中基于已被充分验证的精细化有限元模型,研究了TNT球形装药自由场爆炸冲击波传播与爆轰产物高速膨胀共同作用的特点和规律,发现在比例爆距小于0.80 m/kg1/3的范围内,爆轰产物对刚性壁面的爆炸荷载影响显著,提出球形装药近距离爆炸的比例爆距界定标准为0.30～0.80 m/kg1/3。研究发现,在近距离爆炸下,爆炸波在入射角为0°～5°范围内的刚性壁面反射荷载峰值会出现急剧下降的现象,这是由爆轰产物喷射的不均匀性和随机性导致的;近距离爆炸下,刚性壁面反射超压出现了两个峰值的现象,这是由冲击波和爆轰产物分别与刚性壁面相互作用导致的。提出了近距离爆炸情况下两个荷载峰值的计算公式,以及适合工程结构响应计算的简化荷载模型;揭示了近距离爆炸下刚性壁面反射超压的分布规律。     

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.     

Dynamic characteristics of spherically converging detonation waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure. Zonglin Jiang is presently a visiting professor at McGill University, Canada.     

Spherical combustion clouds in explosions

This study explores the properties of spherical combustion clouds in explosions. Two cases are investigated: (1) detonation of a TNT charge and combustion of its detonation products with air, and (2) shock dispersion of aluminum powder and its combustion with air. The evolution of the blast wave and ensuing combustion cloud dynamics are studied via numerical simulations with our adaptive mesh refinement combustion code. The code solves the multi-phase conservation laws for a dilute heterogeneous continuum as formulated by Nigmatulin. Single-phase combustion (e.g., TNT with air) is modeled in the fast-chemistry limit. Two-phase combustion (e.g., Al powder with air) uses an induction time model based on Arrhenius fits to Boiko’s shock tube data, along with an ignition temperature criterion based on fits to Gurevich’s data, and an ignition probability model that accounts for multi-particle effects on cloud ignition. Equations of state are based on polynomial fits to thermodynamic calculations with the Cheetah code, assuming frozen reactants and equilibrium products. Adaptive mesh refinement is used to resolve thin reaction zones and capture the energy-bearing scales of turbulence on the computational mesh (ILES approach). Taking advantage of the symmetry of the problem, azimuthal averaging was used to extract the mean and rms fluctuations from the numerical solution, including: thermodynamic profiles, kinematic profiles, and reaction-zone profiles across the combustion cloud. Fuel consumption was limited to $\sim $ 60–70 %, due to the limited amount of air a spherical combustion cloud can entrain before the turbulent velocity field decays away. Turbulent kinetic energy spectra of the solution were found to have both rotational and dilatational components, due to compressibility effects. The dilatational component was typically about 1 % of the rotational component; both seemed to preserve their spectra as they decayed. Kinetic energy of the blast wave decayed due to the pressure field. Turbulent kinetic energy of the combustion cloud decayed due to enstrophy $\overline{\omega ^{2}} $ and dilatation $\overline{\Delta ^{2}} $ .     

Detonation in heterogeneous mixtures of liquids and particles

The mechanisms of detonation propagation in heterogeneous systems comprising closely packed particles and a liquid explosive are not fully understood. Recent experimental work has suggested the presence of two distinct modes of detonation propagation. One mode is valid for small particles (which is the regime we will address in this paper) with another mode for large particles. In this work we model numerically the detail of the wave interactions between the detonating liquid and the solid particles. The generic system of interest in our work is nitromethane and aluminium but our methodology can be applied to other liquids and particles. We have exercised our numerical models on the experiments described above. Our models can now qualitatively explain the observed variation in critical diameter with particle size. We also report some initial discrepancies in our predictions of wave speeds in nominally one dimensional experiments which can be explained by detailed modelling. We find that the complex wave interaction in the flow behind the leading shock in the detonating system of liquid and particles is characterised by at least two sonic points. The first is the standard CJ point in the reacting liquid. The second is a sonic point with respect to the sound speed in the inert material. This leads to a steady state zone in the flow behind the leading shock which is much longer than the reaction zone in the liquid alone. The width of this region scales linearly with particle size. Since the width of the subsonic region strongly influences the failure diameter we believe that this property of the flow is the origin of the observed increase in failure diameter with particle size for small inert particles. Received 3 December 1999 / Accepted 5 July 2000     

Blast wave propagation in air from a gaseous charge

In the point explosion problem it is assumed that an instantaneous release of finite energy causing shock wave propagation in the ambient gas occurs at a space point. The results of the solution of the problem of such blasts are contained in [1–4]. This point model is applied for the determination of shock wave parameters when the initial pressure in a sphere of finite radius exceeds the ambient air pressure by 2–3 orders of magnitude. The possibility of such a flow simulation at a certain distance from the charge is shown in papers [4, 5] as applied to the blast of a charge of condensed explosive and in [6, 8] as applied to the expansion of a finite volume of strongly compressed hot gas. In certain practical problems the initial pressure in a volume of finite dimensions exceeds atmospheric pressure by a factor 10–15 only. Such cases arise, for example, in the detonation of gaseous fuel-air mixtures. The present paper considers the problem of shock wave propagation in air, caused by explosion of gaseous charge of spherical or cylindrical shape. A numerical solution is obtained in a range of values of the specific energy of the charge characteristic for fuel-air detonation mixtures by means of the method of characteristics without secondary shock wave separation. The influence of the initial conditions of the gas charge explosion (specific energy, nature of initiation, and others) is investigated and compared with the point case with respect to the pressure difference across the shock wave and the positive overpressure pulse.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–118, May–June, 1986.     

多相燃料空气炸药爆炸压力场研究

采用高速运动分析系统对固态燃料FAE（Fuel Air Explosive）分散、爆轰过程进行光学测量,用压电传感器等组成的压力测试系统对FAE爆炸压力场进行测量,对固态燃料FAE燃料分散、爆轰波及冲击波进行了研究。分析了气-固-液多相爆轰的特征和压力波形的特点,研究了其冲击波峰值超压及比冲量随传播距离变化的规律。在云雾区内,多相爆轰波压力波形具有多峰结构,爆炸波峰值超压及冲量为一恒定值;爆轰区外,爆轰波转变成爆炸冲击波,峰值压力和比冲量迅速衰减,得到了峰值超压、比冲量随传播距离的变化规律。     

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.      

Explosive dispersal of solid particles

Abstract. The rapid dispersal of inert solid particles due to the detonation of a heterogeneous explosive, consisting of a packed bed of steel beads saturated with a liquid explosive, has been investigated experimentally and numerically. Detonation of the spherical charge generates a blast wave followed by a complex supersonic gas-solid flow in which, in some cases, the beads catch up to and penetrate the leading shock front. The interplay between the particle dynamics and the blast wave propagation was investigated experimentally as a function of the particle size (100–925 m) and charge diameter (8.9–21.2 cm) with flash X-ray radiography and blast wave instrumentation. The flow topology during the dispersal process ranges from a dense granular flow to a dilute gas-solid flow. Difficulties in the modeling of the high-speed gas-solid flow are discussed, and a heuristic model for the equation of state for the solid flow is developed. This model is incorporated into the Eulerian two-phase fluid model of Baer and Nunziato (1986) and simulations are carried out. The results of this investigation indicate that the crossing of the particles through the shock front strongly depends on the charge geometry, the charge size and the material density of the particles. Moreover, there exists a particle size limit below which the particles cannot penetrate the shock for the range of charge sizes considered. Above this limit, the distance required for the particles to overtake the shock is not very sensitive to the particle size but remains sensitive to the particle material density. Overall, excellent agreement was observed between the experimental and computational results. Received 16 August 1999 / Accepted 26 June 2000     

以DSD理论和LS方法为基础的程序燃烧法

给出了二维弯曲爆轰波后产物流场计算方法。爆轰波阵面传播规律满足Detonation Shock Dynamics (DSD)理论并用level set (LS)方法计算,波阵面传播规律与波后流场的耦合通过程序燃烧法实现,反应进程变量可作为LS函数的函数给出。爆轰波从刚性细管道向粗管道传播产生绕射的二维计算结果表明,化学反应速率不影响波后流场分布,只影响反应区结构。此方法可用于钝感炸药的驱动计算问题。     

激波与爆轰波对撞的数值模拟研究

用二阶精度NND差分格式和改进的二阶段化学反应模型模拟了爆轰波与激波的对撞过程,研究了不同强度入射激波对爆轰过渡区域的影响. 当对撞激波较弱时,透射爆轰波演变主要受流动膨胀作用的影响,可划分为对撞影响区、爆轰恢复区和稳定发展区3个阶段. 在爆轰恢复区和稳定发展区,前导激波压力经历一个过冲、然后向稳定爆轰过渡的过程,表现了爆轰波熄爆和再起爆的物理特征. 当对撞激波较强时,可燃混合气体的高热力学参数导致了更高的化学反应活化程度,形成了弱爆轰向稳定爆轰的直接转变.