颗粒材料中致密波结构研究

采用一维两相流模型与相应颗粒构形应力函数,研究了致密波的形成及其结构．用简化两相流模型系统地讨论致密波对有关因素的依赖关系．分析指出：小于基体材料音速的致密波仅能在非理想颗粒材料中存在,从波前到波后,所有状态物理量光滑过渡．大于基体材料音速的致密波,波头可能存在间断．应力函数与致密粘性确定后,致密波速度决定致密波结构、宽度、终态压实度．采用一维两相流模型模拟了活塞驱动颗粒床形成致密波这一动态过程．用线方法（MOL）对该方程组求数值解．计算表明,经过短暂的非稳态过程,颗粒床中形成一稳态致密波．分析了活塞速度与初始孔隙率对致密波结构的影响,并对简化两相流模型与两相流模型的计算结果进行了对比．     

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     

Numerical study of the lift force influence on two-phase shock tube boundary layer characteristics

The importance of the lift force acting on the dispersed phase in the boundary layer of a laminar gas-particle dilute mixture flow generated by a shock wave is investigated numerically. The particle phase is supposed to form a continuum and is described by an Eulerian approach. The ability of the Eulerian model to simulate particle flows and the importance of the two-way coupling are proven by comparison with experimental data as well as with the numerical results from schemes based on a Lagrangian approach. The models used for the lift force are discussed through comparisons between numerical and experimental results found in the literature. Some results about the formation of a dust cloud are numerically reproduced and show the major role of the lift force. Simulations of two-dimensional two-phase shock tube flows are also performed including the lift force effects. Although the wave propagation is weakly influenced by the lift force, the force modifies substantially the dynamics of the flow near the wall. Received 17 February 2000 / Accepted 30 November 2000     

An Eulerian model for the motion of granular material with a large Stokes number in fluid flow

This study introduced a novel Euler–Euler approach for modeling granular multiphase flow. The motion of particles with a large Stokes number was investigated assuming that granular material has unilateral compressibility. Solid pressure in the momentum equations for granular multiphase flow was determined so that the unilateral incompressibility condition was satisfied. Using the continuity condition of the granular phase, the equation was rewritten in the optimal form to calculate the solid pressure. A discrete formulation of smoothed particle hydrodynamics was applied for the convective terms so that the discrete matrix was positive semidefinite for the convergence and the discretization for an unstructured mesh was allowed. Frictional stress was then determined from solid pressure and, by using the solid pressure and frictional stress, momentum equations for the granular phase were solved. The method was incorporated into ANSYS FLUENT by a UDF (user defined function). Model validation was performed through a comparison with two previous results, and efficacy of the proposed model was confirmed.     

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.     

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.     

The effect of an unsteady drag force on the structure of a non-equilibrium region behind a shock wave in a gas-particle mixture

For numerical analysis of shock wave propagation in gas-particle mixtures, drag coefficients of a sphere in steady flows are generally used. However, it is shown both experimentally and numerically that a shock loaded solid sphere experiences unsteady drag forces. The paper describes a model of unsteady drag force and its effect on the structure of the non-equilibrium region behind a shock front traveling in a dusty gas. The results are compared with those obtained by using a steady drag coefficient and are discussed. It is demonstrated that the large drag force at the early stage of the interaction between shock-wave induced flow and a solid particle affects the flow structure that is obtained with a steady drag force.      

Droplet break-up through an oblique shock wave

The interaction of a two-phase flow with a wedge where a stationary shock wave is initially settled is studied in a two-dimensional configuration. Before the introduction of the dispersed phase, the flow around the wedge is a supersonic one phase flow such as an attached stationary shock wave is present. Then, the dispersed phase is introduced upstream the initial position of the stationary shock wave. The purpose of this study is to point out two-phase and droplets break-up effects on the oblique shock wave. The two-dimensional equations are solved by a TVD scheme where fluxes are computed by using Riemann solver for the gas phase equations and also for the dispersed phase equations wich is an original approach due to the authors (Saurel et al. 1994). In addition to drag forces and heat and mass transfers, the process of droplets fragmentation based on the particle oscillation is considered. Accepted April 28, 1995     

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study, a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed. Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop. One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore, and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations. Predictions are compared with experimental data measured by Lali et al., where the computed porosities from model B are closer to the measured data than other models. Furthermore, the predicted pressure drop rises as liquid velocity increases, while it decreases with the increase of particle size. Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient, and particle concentration, granular temperature, granular pressure, and granular viscosity go down accordingly.     

FLAT-PLATE BOUNDARY-LAYER FLOWS INDUCED BY DUSTY SHOCK WAVE

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爆轰波通过扩张喷管的双曝光全息实验和数值研究

结合实验和数值模拟方法,对以脉冲爆轰发动机为背景的爆轰波通过扩张喷管的流动进行了系列研究。实验采用双曝光全息干涉方法对爆轰波绕射流场进行测量,得到了比传统的纹影法更清晰和可定量化的照片。发展了基于非结构四边形网格自适应有限体积程序,结合基元化学反应模型对扩张喷管中爆轰化学反应流场进行了数值模拟,模拟结果与实验照片吻合较好。实验和数值模拟结果表明,爆轰波绕射具有许多和激波绕射不同的流场特征,其中包括二次起爆现象、化学反应面与前导激波相脱离而引起的复杂流场等,同时初始压力和扩张角度变化也对爆轰波绕射过程产生较大影响,初始压力越低,化学反应区和前导激波分离现象越明显,且前导激波的曲率越大。     

Shock wave diffraction by a square cavity filled with dusty gas

A simple two-dimensional square cavity model is used to study shock attenuating effects of dust suspension in air. The GRP scheme for compressible flows was extended to simulate the fluid dynamics of dilute dust suspensions, employing the conventional two-phase approximation. A planar shock of constant intensity propagated in pure air over flat ground and diffracted into a square cavity filled with a dusty quiescent suspension. Shock intensities were and , dust loading ratios were and , and particle diameters were and {\rm \mu}$m. It was found that the diffraction patterns in the cavity were decisively attenuated by the dust suspension, particularly for the higher loading ratio. The particle size has a pronounced effect on the flow and wave pattern developed inside the cavity. Wall pressure histories were recorded for each of the three cavity walls, showing a clear attenuating effect of the dust suspension. Received 15 November 1999 / Accepted 25 October 2000     

Numerical simulation of 1-D unsteady two-phase flows with shocks

In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the fiow parameters for the gas antiparticle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.     

Optimal systems of Lie subalgebras for a two-phase mass flow

We apply the Lie symmetry method to a two-phase mass flow model (Pudasaini, 2012 [18]) and construct one-, two- and three-dimensional optimal systems of Lie subalgebras corresponding to the non-linear PDEs. As an optimal system contains structurally important information about different types of invariant solutions, it provides precise insights into all possible invariant solutions emerging from infinitesimal symmetries. We use the optimal system of one-dimensional Lie subalgebras to reduce the two-phase mass flow model to other systems of PDEs. Using the fact that the Lie bracket contains information about further reduction, we further reduce to systems of ODEs and PDEs. We solve a system numerically and present results for different physical and Lie parameters. Simulations reveal fluid and solid dynamics are distinctly sensitive to different Lie parameters, whereas both phases are influenced by the solid and the fluid pressure parameters. Higher pressure gradients result in higher flow velocities and lower flow heights. Fluid velocities dominate solid velocities, but the solid heights are higher than the fluid heights. Results provide an overall picture of the physical process, and the coupled dynamics of the solid and fluid phase velocities and the flow heights. These are physically meaningful results in sheared inclined channel flow of coupled two-phase mixture. This confirms the consistency of the obtained similarity solutions and potential applicability of the models and the constructed optimal systems.     

Non-conservative pressure-based compressible formulation for multiphase flows with heat and mass transfer

A pressure-based compressible multiphase flow solver has been developed based on non-conservative discretization of the mixture continuity equation. The formulation is an extension of the single phase incompressible pressure-correction approach, such that it can be applied to both two-phase flows using interface resolving methods and general n-phase ensemble-averaged mixture flows. The formulation is currently presented with the single pressure and single temperature assumption, but extension to multiple temperatures is straightforward. A robust treatment of phase change allows the method to model conditions with rapid phase change such as expansion through nozzles and valves. The method has been validated thoroughly using canonical single phase problems such as the shock tube, tank filling and sudden valve closure problems. Multiphase flow validation has been carried out for sound propagation in mixtures using the ensemble-averaged model and pressure wave transmission and reflection across an air-water interface, using the level set interface tracking method. The method has been used to study sound propagation in saturated steam-water systems under thermodynamic non-equilibrium, where the expected drastic reduction in the speed of sound is reproduced. Finally the method is applied to the problem of critical (choked) flow in a nozzle for a saturated steam-water system.     

The flow structure of dilute gas-particle suspensions behind a shock wave moving along a flat surface

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented.The Saffman lift force acting on a particle in a shear flow istaken into account.It is shown that particle migration across the boundary layer leads tointersections of particle trajectories.The corresponding modification of dusty gas model isproposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at aconstant speed are obtained by using the method of matched asymptotic expansions.Themethod of the calculation of particle phase parameters in Lagrangian coordinates isdescribed in detail.Some numerical results for the case of small particle concentration aregiven.     

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.     

收敛柱激波在粉尘气体中的传播

取稀颗粒群气固两相耦合的双流体简化模型,采用高解数值方法研究了收敛柱激波在粉尘气体中的传播和波后流场特性。通过与纯气体情况比较,揭示了固体颗粒出现对收敛柱激波传播特性的影响。     

Numerical and experimental study of an innovative pipeline design in a granular pneumatic-conveying system

During gas–solid mixture conveying in a dense phase, material is conveyed in dunes on the bottom of the pipeline, or as a pulsating moving bed. This phenomenon increases the pressure drop and power consumption. We introduce a new technique to reduce the pressure drop, which is termed the perforated double tube. To validate this new model, the gas–solid flow pattern and pressure drop were studied numerically and experimentally. The power consumption was also studied experimentally. Numerical studies were performed by the Eulerian–Lagrangian approach to predict gas and particle movement in the pipeline. Comparisons between the numerical predictions and the experimental results for the gas–solid flow patterns and pressure drop show good agreement.     

A numerical investigation of transient detonation in granulated material

A two-phase model based upon principles of continuum mixture theory is numerically solved to predict the evolution of detonation in a granulated reactive material. Shock to detonation transition (SDT) is considered whereby combustion is initiated due to compression of the material by a moving piston. In particular, this study demonstrates the existence of a SDT event which gives rise to a steady two-phase Chapman-Jouguet (CJ) detonation structure consisting of a single lead shock in the gas and an unshocked solid; this structure has previously been independently predicted by a steady-state theory. The unsteady model equations, which constitute a non-strictly hyperbolic system, are numerically solved using a modern high-resolution method. The numerical method is based on Godunov's method, and utilizes an approximate solution for the two-phase Riemann problem. Comparisons are made between numerical predictions and known theoretical results for 1) an inert two-phase shock tube problem, 2) an inert compaction wave structure, and 3) a reactive two-phase detonation structure; in all cases, good agreement exists. Received 4 August 1995 / Accepted 17 February 1996