Experimental and numerical investigation of the shock-induced fluidization of a particles bed

An experimental study on unsteady two phase flow is conducted in a vertical shock tube. Shock Mach numbers range from 1.3 to 1.5 in 1 bar. The particles are initially positioned in horizontal beds of various thicknesses. Our research covers a large domain of void fraction from 1 (single particles) to 0.35 (compact beds). The experiments provide shadowgraph images for the recording of particle trajectories (effect of the gas on the particles) and side-wall pressures (action of the particles on the gas). A dense two phase flow model has been elaborated and numerically solved using a finite difference scheme with pseudoviscosity. The simulated shock-induced fluidization of a 2 cm thick bed of 1.5 mm diameter glass particles is compared to the experiment. Received 10 September 1996 / Accepted 4 January 1997     

Supersonic low-concentration dusty-gas flow past a plane cylinder in the presence of an oblique shock wave interacting with the bow shock

The motion of an inertial dispersed admixture near a plane cylinder immersed in a steady-state hypersonic dusty flow in the presence of an oblique shock wave interacting with the bow shock is considered. It is assumed that the free-stream particle mass concentration is small and the particles do not affect the carrier flow. The III and IV shock wave interaction regimes are considered. The gas flow parameters in the shock layer are calculated from the numerical solution of the full Navier-Stokes equations for the perfect gas. A TVD second-order finite-difference scheme constructed on the basis of a finite volume method is used. For calculating the dispersed-phase parameters, including the concentration, the full Lagrangian method is used. On a wide range of variation of the particle inertia parameters, the patterns of the particle trajectories, velocity, concentration, and temperature in the shock layer are studied. The possibility of aerodynamic focusing of the particles behind the shock wave intersection point and the formation of narrow beams with a high particle concentration is revealed. These beams impinge on the cylinder surface and result in a sharp increase in the local heat fluxes. The maximal possible increase in the heat fluxes caused by the particles colliding with the cylinder surface is estimated for the flows with and without the incident oblique shock wave.     

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.      

Non-stationary effects in hypersonic nonuniform dusty-gas flow past a blunt body

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found. The project supported by the Russian Foundation for Basic Research (project No. 96-01-00313) and the National Natural Science Foundation of China (joint RFBR-NSFC grant No. 96-01-00017c)     

Micromechanics of breakage in sharp-edge particles using combined DEM and FEM

By combining DEM （Discrete Element Method） and FEM （Finite Element Method）, a model is established to simulate the breakage of twodimensional sharp-edge particles, in which the simulated particles are assumed to have no cracks. Particles can, however, crush during different stages of the numerical analysis, if stress-based breakage criteria are fulfilled inside the particles. With this model, it is possible to study the influence of particle breakage on macro- and micro-mechanical behavior of simulated angular materials. Two series of tests, with and without breakable particles, are simulated under different confining pressures based on conditions of biaxial tests. The results, presented in terms of micromechanical behavior for different confining pressures, are compared with macroparameters. The influence of particle breakage on microstructure of sharp-edge materials is discussed and the related confining pressure effects are investigated. Breakage of particles in rockfill materials are shown to reduce the anisotropy coefficients of the samples and therefore their strength and dilation behaviors.     

Micromechanics of breakage in sharp-edge particles using combined DEM and FEM

By combining DEM (Discrete Element Method) and FEM (Finite Element Method),a model is established to simulate the breakage of two-dimensional sharp-edge particles,in which the simulated particles are assumed to have no cracks.Particles can,however,crush during different stages of the numerical analysis,if stress-based breakage criteria are fulfilled inside the particles.With this model,it is possible to study the influence of particle breakage on macro- and micro-mechanical behavior of simulated angular materials.Two series of tests,with and without breakable particles,are simulated under different confining pressures based on conditions of biaxial tests.The results,presented in terms of micromechanical behavior for different confining pressures,are compared with macroparameters.The influence of particle breakage on microstructure of sharp-edge materials is discussed and the related confining pressure effects are investigated.Breakage of particles in rockfill materials are shown to reduce the anisotropy coefficients of the samples and therefore their strength and dilation behaviors.     

含RDX四组元HTPB固体推进剂的冲击起爆特性研究

为了研究含RDX四组元HTPB固体推进剂的冲击起爆行为和在低温条件下的适应性,在常温和低温条件下,对该固体推进剂进行了冲击加载拉氏分析实验。采用锰铜压力计测量了推进剂中不同位置处的压力变化历程,采用电离探针测量了固体推进剂的爆速。分析了固体推进剂的爆轰成长规律,获得了推进剂的临界起爆压力、爆速、爆压和爆轰成长距离等爆轰特征参量。通过对比不同条件下的特征参量发现,低温对固体推进剂的冲击起爆特性影响较小。此外,还对固体推进剂的冲击起爆过程进行了数值模拟,标定了固体推进剂点火增长模型的反应速率方程参数和推进剂的未反应JWL状态方程参数。     

Transient phenomena in one-dimensional compressible gas–particle flows

The transient behavior of compressible gas– particle flows produced in shock tubes with particle-laden driver section is studied. Particular attention is focused on the time scales with which the solution approaches the equilibrium state. Theoretical estimates indicate that the gas and particle contact surfaces equilibrate first, followed by the shock wave, and finally by the expansion fan. The estimates are in good agreement with numerical simulations. The simulations also show that the approach to equilibrium condition of the shock speed is non-monotonic (monotonic) if the mass fraction of particles initially located in the driver section is below (above) a particle-diameter dependent critical value. For the speed of the particle contact surface, the reverse trends are observed.      

Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.     

Numerical simulation of a supersonic gas–solid flow over a blunt body: The role of inter-particle collisions and two-way coupling effects

A supersonic dusty gas flow over a blunt body is considered. The mathematical model of the two-phase gas–particle flow takes into account the inter-particle collisions and the two-way coupling effects. The carrier gas is treated as a continuum, the averaged flow field of which is described by the complete Navier–Stokes equations with additional source terms modeling the reverse action of the dispersed phase. The dispersed phase is treated as a discrete set of solid particles, and its behavior is described by a kinetic Boltzmann-type equation. Particles impinging on the body surface are assumed to bounce from it. Numerical analysis is carried out for the cross-wise flow over a cylinder. The method of computational simulation represents a combination of a CFD-method for the carrier gas and a Monte Carlo method for the “gas” of particles. The dependence of the fine flow structure of the continuous and dispersed phases upon the free stream particle volume fraction α_p∞ and the particle radius r_p is investigated, particularly in the shock layer and in the boundary layer at the body surface. The particle volume fraction α_p∞ is varied from a negligibly low value to the value α_p∞ = 3 × 10⁵ at which inter-particle collisions and two-way coupling effects are simultaneously essential. Particular attention has been given to the particles of radii close to the critical value r_p1, because in this range of particle size the behavior of the particles and their effect on the carrier gas flow are not yet completely understood. An estimate of the turbulent kinetic energy produced by the particles in the shock layer is obtained.     

Fracture of a burning solid propellant attenuated by a crack-type cavity

A plane steady problem of fracture mechanics for a burning deformable solid propellant attenuated by a crack-type cavity with a burning surface is considered. The crack-type cavity is assumed to have tip zones with bonds between the faces, and mixed boundary conditions are imposed on the propellant charge boundary. The problem of equilibrium of a propellant charge containing a crack-type cavity reduces to solving a system of nonlinear singular integrodifferential equations with a Cauchy-type kernel. Based on the solution obtained, the normal and tangential forces in the tip zones of the crack-type cavity are found. Local conditions determining stability (safety) of the solid propellant burning regime are found.     

Analysis of elastoplastic deformation in metal-matrix composites with particulate reinforcements

In this paper, elastoplastic stress-strain behavior during tensile deformation of an aluminum alloy matrix composite containing alumina circular and non-circular particles is analyzed. In terms of cell models in conjunction with continuum plasticity theory, various periodic arrays of particles are assumed in a three-dimensional finite element simulation. The geometrical effects of particle volume fraction, shape, aspect ratio, array and distribution, as well as non-circular particle orientation on the overall elastoplastic stress-strain behavior are examined in view to design optimum microstructures of the composites. The project supported by the National Natural Science Foundation of China and the State Education Commission of China     

Particle fracture in high-volume-fraction ceramic-reinforced metals: Governing parameters and implications for composite failure

Weibull parameters of angular alumina particles are determined from experimental tensile test data on high-ceramic-content metal matrix composites using a micromechanical model that accounts for internal damage in the form of particle cracking, the dominant damage mode in these composites. The fraction of broken particles is assessed from the drop of Young's modulus and particle fracture is assumed to be stress controlled. Two extreme load-sharing modes, namely a purely local and a global load-sharing mode, are considered to account for the load redistribution due to particle fracture. Consistent powder strength parameters can be thus “back-calculated” for particles that are embedded in different Al-Cu matrices. On the other hand, this calculation fails for pure Al matrix composites, which exhibit a much larger strain to failure than Al-Cu matrix composites. It is shown that for Al matrix composites, the role of plastic (composite) strain on particle fracture constitutes a second parameter governing particle damage. This finding is rationalized by particle-particle interactions in these tightly packed ceramic particle-reinforced composites, and by the increase of matrix stress heterogeneity that is brought with increasing plastic strain. Failure of the alloyed matrix composites is well described by the (lower bound) local load-sharing micromechanical model, which predicts a catastrophic failure due to an avalanche of damage. The same model predicts failure of pure aluminium matrix composites to occur at the onset of tensile instability, also in agreement with experimental results once the role of plastic strain on damage accumulation is accounted for.     

多孔颗粒火药床燃烧转爆轰的敏感性研究

本文以不同粒度硝胺火药RDU-4,硝胺火药RPB,3/1-S为研究对象,探讨了多孔颗粒火药床燃烧转爆轰的敏感性。研究结果表明,火药颗粒尺寸越小,硝胺火药燃烧转爆轰越易实现:硝基胍组分具有抑制燃烧转冲击的作用,就同一装填条件下燃烧转冲击的难易而言,以RPB最易,3/1-S次之,RDU-4最难     

Self-similar solution of cylindrical shock wave propagation in a rotational axisymmetric mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for one- dimensional isothermal and adiabatic unsteady flow behind a strong cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has a variable azimuthal fluid velocity together with a variable axial fluid velocity. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. The shock Mach number is not infinite, but has a finite value. The azimuthal and axial component of the fluid velocity in the ambient medium are assumed to be vary and obey power laws, and the density of the ambient medium is taken to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. Effects of the variation of the parameter of non-idealness of the gas in the mixture, the mass concentration of solid particles and the ratio of the density of solid particles to the initial density of the gas are investigated.     

Shock-induced Near-wall Two-phase Flow Structure Over a Micron-sized Particles Bed

The present paper studies numerical modelling of near-wall two-phase flows induced by a normal shock wave moving at a constant speed, over a micron-sized particles bed. In this two-fluid model, the possibility of particle trajectory intersection is considered and a full Lagrangian formulation of the dispersed phase is introduced. The finiteness of the Reynolds and Mach numbers of the flow around a particle as well as the fineness of the particle sizes are taken into account in describing the interactions between the carrier- and dispersed-phases. For the small mass-loading ratio case, the numerical simulation of flow structure of the two phases is implemented and the profiles of the particle number density are obtained under the constant-flux condition on the wall. The effects of the shock Mach number and the particle size and material density on particle entrainment motion are discussed in detail. The obtained results indicate that interphase non-equilibrium in the velocity and temperature is a common feature for this type of flows and a local particle accumulation zone may form near the envelope of the particle trajectory family.     

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.     

Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms

A viscoplastic approach using the Fast Fourier Transform (FFT) method for obtaining local mechanical response is utilized to study microstructure-property relationships in composite materials. Specifically, three-dimensional, two-phase digital materials containing isotropically coarsened particles surrounded by a matrix phase, generated through a Kinetic Monte Carlo Potts model for Ostwald ripening, are used as instantiations in order to calculate the stress and strain-rate fields under uniaxial tension. The effects of the morphology of the matrix phase, the volume fraction and the contiguity of particles, and the polycrystallinity of matrix phase, on the stress and strain-rate fields under uniaxial tension are examined. It is found that the first moments of the stress and strain-rate fields have a different dependence on the particle volume fraction and the particle contiguity from their second moments. The average stresses and average strain-rates of both phases and of the overall composite have rather simple relationships with the particle volume fraction whereas their standard deviations vary strongly, especially when the particle volume fraction is high, and the contiguity of particles has a noticeable effect on the mechanical response. It is also found that the shape of stress distribution in the BCC hard particle phase evolves as the volume fraction of particles in the composite varies, such that it agrees with the stress field in the BCC polycrystal as the volume of particles approaches unity. Finally, it is observed that the stress and strain-rate fields in the microstructures with a polycrystalline matrix are less sensitive to changes in volume fraction and contiguity of particles.     

Shear-induced changes of electrical conductivity in suspensions

The effect of shear on electrical conductivity (rheo-conduction) is studied to give information about particle behaviour in suspensions. Past work is reviewed, and expressions are derived for the rheo-conduction of a suspension of nonconducting spheroids in a conducting matrix for current flow, parallel and normal to the suspension flow direction. A simple apparatus to study rheo-conduction in pipe flow is described, and measurements of steady and time-dependent effects are reported for various suspensions of colloidal particles. Suspensions of anisometric rod- and platelike particles at low concentrations showed rheo-conductive changes of sign, magnitude and relaxation that were consistent with the particle shape, concentration and interactions. The rheo-conductive response decreased with increasing volume fraction for platelike kaolinite particles, attributed to orientational jamming. Spherical latex particles gave unexpected rheo-conductive changes consistent with shear disruption of a conductive network of particles. It is concluded that rheo-conduction measurements are a useful adjunct to conventional rheometry.     

Ductile-to-brittle transition in tensile failure of particle-reinforced metals

We present an analytical micromechanical model designed to simulate the tensile stress-strain behaviour and failure of damaging composites containing a high volume fraction of reinforcing particles. One internal damage micromechanism is considered, namely particle fracture, which is assumed to obey a Weibull distribution. Final composite tensile failure occurs when one of two possible failure criteria is reached, given by (i) the onset of tensile instability, or (ii) an “avalanche-like” propagation of particle breaks to neighbouring particles. We show that an experimentally observed transition from failure by tensile instability to abrupt failure resulting from an increase of matrix strength can be mimicked by the model because local load-sharing (i.e. load transfer from a broken particle to its immediate neighbours) is accounted for.