Dense particle cloud dispersion by a shock wave

A dense particle flow is generated by the interaction of a shock wave with an initially stationary packed granular bed. High-speed particle dispersion research is motivated by the energy release enhancement of explosives containing solid particles. The initial packed granular bed is produced by compressing loose powder into a wafer with a particle volume fraction of $\phi _\mathrm{p} = 0.48$ . The wafer is positioned inside the shock tube, uniformly filling the entire cross-section. This results in a clean experiment where no flow obstructing support structures are present. Through high-speed shadowgraph imaging and pressure measurements along the length of the channel, detailed information about the particle shock interaction was obtained. Due to the limited strength of the incident shock wave, no transmitted shock wave is produced. The initial solid-like response of the particle wafer acceleration forms a series of compression waves that eventually coalesce to form a shock wave. Breakup is initiated along the periphery of the wafer as the result of shear that forms due to the fixed boundary condition. Particle breakup is initiated by local failure sites that result in the formation of particle jets that extend ahead of the accelerating, largely intact, wafer core. In a circular tube, the failure sites are uniformly distributed along the wafer circumference. In a square channel, the failure sites, and the subsequent particle jets, initially form at the corners due to the enhanced shear. The wafer breakup subsequently spreads to the edges forming a highly non-uniform particle cloud.     

A multiphase shock tube for shock wave interactions with dense particle fields

Currently there is a substantial lack of data for interactions of shock waves with particle fields having volume fractions residing between the dilute and granular regimes. To close this gap, a novel multiphase shock tube has been constructed to drive a planar shock wave into a dense gas–solid field of particles. A nearly spatially isotropic field of particles is generated in the test section by a gravity-fed method that results in a spanwise curtain of spherical 100-micron particles having a volume fraction of about 20%. Interactions with incident shock Mach numbers of 1.66, 1.92, and 2.02 are reported. High-speed schlieren imaging simultaneous with high-frequency wall pressure measurements are used to reveal the complex wave structure associated with the interaction. Following incident shock impingement, transmitted and reflected shocks are observed, which lead to differences in particle drag across the streamwise dimension of the curtain. Shortly thereafter, the particle field begins to propagate downstream and spread. For all three Mach numbers tested, the energy and momentum fluxes in the induced flow far downstream are reduced about 30–40% by the presence of the particle field.     

Formation of particle jetting in a cylindrical shock tube

A dense, solid particle flow is numerically studied at a mesoscale level for a cylindrical shock tube problem. The shock tube consists of a central high pressure gas driver section and an annular solid powder bed with air in void regions as a driven section with its far end adjacent to ambient air. Simulations are conducted to explore the fundamental phenomena, causing clustering of particles and formation of coherent particle jet structures in such a dense solid flow. The influence of a range of parameters is investigated, including driver pressure, particle morphology, particle distribution and powder bed configuration. The results indicate that the physical mechanism responsible for this phenomenon is twofold: the driver gas jet flow induced by the shock wave as it passes through the initial gaps between the particles in the innermost layer of the powder bed, and the chaining of solid particles by inelastic collision. The particle jet forming time is determined as the time when the motion of the outermost particle layer of the powder bed is first detected. The maximum number of particle jets is bounded by the total number of particles in the innermost layer of the powder bed. The number of particle jets is mainly a function of the number of particles in the innermost layer and the mass ratio of the powder bed to the gas in the driver section, or the ratio of powder bed mass (in dimensionless form) to the pressure ratio between the driver and driven sections.     

激波驱动的气固两相流的动态压力测量

利用水平圆柱形激波管对激波驱动的可压缩性气固两相流进行了试验研究.利用压电式压力传感器、电荷放大器、示波器及计算机组成的压力信号测试系统, 对激波与颗粒作用前后的气相参数进行测量及分析. 试验中测得了激波在管中的传播速度, 波后气流的压力, 反射激波、透射激波的压力和速度等. 分别考察颗粒、装载比、驱动气源以及入射激波马赫数等因素的差异对气相参数的影响.试验结果表明: 激波与颗粒群相互作用时, 会产生反射激波和透射激波,其强度与驱动气源、颗粒大小、颗粒装载比等参数有关;激波衰减率随着装载比、马赫数的增大而减小. 研究指出,在颗粒群被激波加速的初始阶段, 颗粒间的弹性碰撞起着重要的作用.      

Interaction of a shock wave with a loose dusty bulk layer

The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically. Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition, a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon. Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed numerically and agrees well with our corresponding experimental results.      

激波驱动下固体颗粒抛撒的实验研究

本文使用阴影照相技术、高速摄像技术及压力测试手段,实验记录和研究了激波与固体颗粒群的作用及激波作用后固体颗粒群的抛撒和云团的形成过程.结果表明:在激波与固体颗粒群作用过程中,存在着清晰的激波透射、反射及绕射现象,同时激波强度在作用后有明显的下降趋势;在固体颗粒抛撒及云团形成过程中,实验发现对同一粒径的颗粒抛撒来说,抛撒的颗粒群质量越大,云团形成的均匀性及稳定性越好,而对不同粒径的颗粒群来说,粒径越大,形成的云.团集中性越强.     

Aerodynamic characteristics of solid particles�� acceleration by shock waves

In this study, the interaction of a planar shock wave with a group of particles has been investigated using high-speed photography and dynamic pressure measurements. Experiments were carried out in a horizontal circular shock tube. The influence of the particle loading ratio, particle diameter, driving gas and shock wave Mach number on the acceleration was studied. It was found that the higher the particle loading ratio, the greater was the particle velocity. This is due to the higher driving pressure. Helium and nitrogen gases play quite different roles in acceleration. Pressure multiplication during shock wave interaction with particles also appears. Based on the experimental results, the discussion regarding partial quantitative velocities and accelerations of particle groups, as well as the attenuation factors when shock waves pass through the particles, is given.     

The erosion of dust by a shock wave in air: initial stages with laminar flow

The erosion of dust by a shock wave in air and by the subsequent air flow was investigated theoretically and experimentally. The paths of single particles were calculated for the initial state of erosion when the flow in the shock tube boundary layer was still laminar. High-speed cinematographic experiments performed with a shock tube yielded mapping of the development of the dust cloud. From the agreement between the measured height of the cloud and the calculated height of flight of the particles one can conclude that the assumed model for the motion of the particles adequately describes the removal of particles from the wall.     

Interaction of a high-speed combustion front with a closely packed bed of spheres

The head-on collision of a combustion front with a closely packed bed of ceramic-oxide spheres was investigated in a vertical 76.2 mm diameter tube containing a nitrogen diluted stoichiometric ethylene–oxygen mixture. A layer of spherical beads in the diameter range of 3–12.7 mm was placed at the bottom of the tube and a flame was ignited at the top endplate. Four orifice plates spaced at one tube diameter were placed at the ignition end of the tube in order to accelerate the flame to either a “fast-flame” or a detonation wave before the bead layer face. The mixture reactivity was adjusted by varying the initial mixture pressure between 10 and 100 kPa absolute. The pressure before and within the bead layer was measured by flush wall-mounted pressure transducers. For initial pressures where a fast-flame interacts with the bead layer peak pressures recorded at the bead layer face were as high as five times the reflected Chapman–Jouget detonation pressure. The explosion resulting from the interaction developed by two distinct mechanisms; one due to the shock reflection off the bead layer face, and the other due to shock transmission and mixing of burned and unburned gas inside the bead layer. The measured explosion delay time (time after shock reflection from the bead layer face) was found to be independent of the incident shock velocity. As a result, the explosion initiation is not the direct result of the shock reflection process but instead is more likely due to the interaction of the reflected shock wave and the trailing flame. The bead layer was found to be very effective in attenuating the explosion front transmitted through the bead layer and thus isolating the tube endplate. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Advances in detonation driving techniques for a shock tube/tunnel

Early works on the detonation driven shock tube are reviewed briefly. High initial pressure detonable mixture can be used in backward-detonation driver when the buffer tube is attached to the end of the driver for eliminating the excessive reflected peak pressure. Experimental data showed that an improvement on attenuation of the incident shock wave generated by the forward driver can be obtained, provided the diameter of the driver is larger than that of the driven section and an abrupt reduction of cross-section area is placed just beyond the diaphragm. Also, it is clearly verified by a numerical analysis. An additional backward-detonation driver is proposed to attach to the primary detonation driver and on condition that the ratios of initial pressure in the additional driver to that in the primary driver exceed the threshold value, the Taylor wave behind detonation wave in the primary detonation driver can be eliminated completely.     

平面激波加载下砂墙结构的冲击响应特性

砂墙结构在爆炸安全防护领域具有广泛应用，为了研究激波加载下砂墙结构的冲击响应特性，基于水平激波管实验装置，开展平面激波冲击砂墙结构系列实验，采用高速纹影摄像系统捕捉流场中激波波系的演化过程和砂墙结构的运动过程。入射激波马赫数为1.827～2.413，相应入射激波载荷强度为0.378～0.724 MPa。砂墙结构利用铁砂、矾土、石英砂3种实验用砂制备，所制备砂墙结构孔隙度分别为56.6%、69.3%、56.6%。高速纹影照片显示:平面激波冲击砂墙结构发生反射和透射，伴随入射激波和透射激波的传播，在百微秒内，砂墙未产生显著运动，表现出显著的类固体动力学响应特性。基于冲击理论，确定了铁砂墙、矾土砂墙、石英砂墙的线性冲击关系，冲击关系中线性常数λ值量级为100，根据凝聚介质实用状态方程推断:较低强度载荷冲击作用下，砂墙主要产生体积变形，而由冲击引起的热能效应则可以忽略。     

Investigation of the acceleration of aluminum particles behind a shock wave using instantaneous Laser Doppler Velocimetry

The acceleration of aluminum particles with a 5μm diameter in the flow field behind an incident shock wave was investigated experimentally in a 10-m long and 70 mm inner diameter shock tube. By means of instantaneous Laser Doppler Velocimetry (LDV) the velocity of the particles was observed directly. The light scattered by the moving particles is Doppler shifted and sent to the laser Doppler velocimeter. The velocimeter essentially consists of a phase-stabilized Michelson interferometer used as a sensitive spectrometer. An electro-optical circuit ensures the phase stabilization that results in a voltage signal independent of the scattered light intensity and proportional to the mean velocity of the particles at the measurement point. Because of the very short response time (1μs) of the LDV system used here, the latter gives a continuous real-time signal of the particle acceleration. To avoid particle oxidation the particles were accelerated by a high-speed nitrogen gas flow. From the measured velocity the dimensionless drag coefficient was calculated. The drag coefficient is related to the fluid dynamic force exerted by the gas on the particles. The experimental data were compared to theoretical models from the literature. A significant deviation between the model and the experimental data was observed. This deviation is supposed to be induced by the shock wave, which hits the particles and breaks them into pieces of a smaller diameter. Further experiments will be carried out in the future to check the size distribution of the particles after the shock has gone past them.      

爆燃波在含内构件管道中传播现象的实验研究

为了评估高温气冷核反应堆热交换器H2泄漏、爆炸的安全性,研究含内构件管道的H2/空气爆燃传播现象,建造了几何相似、尺寸相同的实验管道（真空筒）。分别充入不同初压和当量比H2/空气混合物,在真空筒顶部点火并引发爆燃,利用多通道瞬态压力测量和数据采集系统,记录各测点压力时间曲线。结果表明:对化学计量比H2/空气混合物,在慢化剂室和真空筒顶部空间产生爆燃,邻近测点的压力时间曲线显示了冲击波特征。该冲击波通过慢化剂室和真空筒侧壁的狭缝（2.5 mm）,进入含内构件的扩张管道并形成爆燃。冲击波在真空筒端部反射、向后传播并与火焰相互作用,爆炸流场波系复杂。对富油和低初压化学计量比混合物,在慢化剂室和真空筒顶部空间产生燃烧,高温富油燃气的压力上升速率较慢。当燃气通过上述狭缝时,在真空筒突扩空间内再次点火并形成较强爆燃,压力时间曲线显示了冲击波特征及其在端面的反射。     

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     

激波诱导含灰气体边界层中的粒子分布

本文研究当激波沿着一个固体表面等速地穿越含灰气体运动时所诱导的层流边界层特性。考虑了作用在气体边界层中球形粒子的 Saffman 升力,建议了一种计算近壁区中弥散相密度剖面的方法,并给出了数值计算结果。本文结果表明:在激波后方存在着一个弯曲的薄层区域,其中的粒子密度可以比其波前原始值增加许多倍。这种粒子聚集效应对于工业中粉尘爆炸等实际问题具有重要意义。     

激波诱导两相流中影响阻力系数的特性参数研究

基于双流体模型 ,利用Euler Lagrange组合方法 ,对激波诱导的气固两相流场进行了数值计算 ,系统研究了影响颗粒群阻力系数的几个重要特性参数。结果表明 :目前采用激波管技术研究非定常条件下颗粒群阻力系数时界定这些因素的影响程度是必要的。     

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     

Microscale Numerical Simulation of the Permeability Reduction due to Trapping of Suspended Fine Particles Within Sand Sediments

The reduction in permeability of sediments due to blockages caused by the trapping of suspended particles is a common concern for the extraction processes of oil or natural gas. In this study, the effect of trapped fine particles in sand sediments is studied numerically using a three-dimensional lattice Boltzmann method. The geometrical properties of larger, immobile, sand grains are digitally extracted by the spherical harmonics series expansions of CT scans of real sand grains. The migrating fine particles are assumed to be spherical in shape with their volumes following a log-normal distribution. These fine particles, together with larger frame sands, are positioned, without overlapping, within a microscopic, cubic, domain with periodic boundaries. The remaining empty volume is filled with water and imposing a pressure gradient simulates the flow of fluid through the sediment. As a result of fine particles becoming trapped by the frame sand, the initial porosity of which is 0.589, the absolute permeability of the system is reduced by approximately 60?C90?%, corresponding to fine particle saturations of 0.15?C0.29, respectively. The permeability change due to the trapping of fine particles is also modelled theoretically using not only volume saturations but also specific surface areas of both the frame sands and the fine particles with a coefficient of proportionality.     

Shock wave attenuation by grids and orifice plates

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.     

On shock wave propagation in a branched channel with particles

The problem of wave propagation in a dust–air mixture inside a branched channel has not been studied widely in literature, even though this topic has many important applications especially in process safety (dust explosions). In this paper, a shock wave interaction with a cloud of solid particles, and the further behaviour of both gas and particulate phases were studied using numerical techniques. The geometry mimicked a real channel where bends or branches are common. Two numerical approaches were used: Eulerian–Eulerian and Eulerian–Lagrangian. Using Eulerian-Lagrangian simulation, it was possible to include the effects of particle–particle and particle–wall collisions in a realistic and direct manner. Results are mainly shown as snap-shots of particle positions during the simulations and statistics for the particle displacement. The results show that collisions significantly influence the process of particle cloud formation. PACS47.40.Nm, 02.60.Cb, 47.55.kf