Resonance in a granular system

The dynamics of a 3D vibrated granular system is investigated. A new effect of resonant behaviour in the granular system is reported. The resonant frequencies can cause vibro-induced segregation in a granular system.     

Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis

The information of a hopper flow at a particle scale, obtained from discrete particle simulation, is used to investigate the macroscopic dynamic behaviour of granular flow in a cylindrical hopper with flat bottom by means of an averaging technique. The macroscopic properties including velocity, mass density, stress and couple stress are quantified under the cylindrical coordinate framework, and an effort is made to link these variables to the microscopic variables considered. The velocity and density distributions are first illustrated to match qualitatively the experimental and numerical results, confirming the validity of the proposed averaging method. Four components of stress, T_zz, T_rr, T_rz and T_zr, and two dominant components of couple stress, M_{r θ} and M_{z θ}, are then investigated in detail. It is shown that large vertical normal stress is mainly observed in the region close to the bottom corner, large radial normal stress is observed within the particle bed as well as the bottom corner, and large shear stresses in the region adjacent to the vertical wall. The four stresses are relatively small in a region close to the orifice. Their magnitudes are mainly contributed by the interaction forces between particles and between particles and walls. However, the transport of particles also plays a significant role at the orifice, especially, in the vertical normal stress. The couple stress can be ignored except for the regions close to the vertical and bottom walls, where the most dominant components are M_{r θ} adjacent to the vertical wall and M_{z θ} close to the bottom wall. The magnitudes of these macroscopic variables depend on the geometric and physical parameters of the hopper and particles such as the orifice size and wall roughness of the hopper, and the friction and damping coefficients between particles although their spatial distributions are similar.     

DEM study of monodisperse granular flow in a pipe

Flow of granular material through a pipe has several industrial applications but maintaining a uniform mass flux is quite challenging. In this work, monodisperse granular flow (non-turbulent and non-dense phase particle transport) through a vertical pipe was simulated using discrete element method (DEM). Effects of different geometric and granular parameters on mass flux of cohesive and non-cohesive solids were analyzed and evaluated. Several important parameters and their effects on mass flux were studied like: L/D ratio, pipe diameter to particle diameter ratio (D/D_p), Poisson ratio, and pipe inclination angle. Furthermore, effects of moisture content and Bond number on mass flux were also investigated. These parameters influenced mass flux except Poisson ratio which showed no significant improvement in mass flux upon increasing the value of this ratio.     

Regimes of segregation and mixing in combined size and density granular systems: an experimental study

Granular segregation in a rotating tumbler occurs due to differences in either particle size or density, which are often varied individually while the other is held constant. Both cases present theoretical challenges; even more challenging, however, is the case where density and size segregation may compete or reinforce each other. The number of studies addressing this situation is small. Here we present an experimental study of how the combination of size and density of the granular material affects mixing and segregation. Digital images are obtained of experiments performed in a half-filled quasi-2D circular tumbler using a bi-disperse mixture of equal volumes of different sizes of steel and glass beads. For particle size and density combinations where percolation and buoyancy both contribute to segregation, either radial streaks or a “classical” core can occur, depending on the particle size ratio. For particle combinations where percolation and buoyancy oppose one another, there is a transition between a core composed of denser beads to a core composed of smaller beads. Mixing can be achieved instead of segregation if the denser beads are also bigger and if the ratio of particle size is greater than the ratio of particle density. Temporal evolution of these segregated patterns is quantified in terms of a “segregation index” (based on the area of the segregated pattern) and a “shape index” (based on the area and perimeter of the segregated pattern).     

Dynamics of a gas bubble rising through a thin immersed layer of granular material: an experimental study

 Packings of non-cohesive grains, immersed in a fluid, differ significantly from classical porous media as the grains, subjected to stresses and flows, can move within the sample, changing then the local properties of the material. We study experimentally the conditions for a gas to pass through a layer of immersed granular material. Above a threshold pressure, which depends mainly on the grains size and on the surface free energy of the liquid-gas interface, the gas creates a channel within the whole thickness of the layer. Received: 23 January 2002     

Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment

This paper investigates the interaction between rapid granular flow and an obstacle. The distinct element method (DEM) is used to simulate the flow regimes observed in laboratory experiments. The relationship between the particle properties and the overall flow behaviour is obtained by using the DEM with a simple linear contact model. The flow regime is primarily controlled by the particle friction, viscous normal damping and particle rotation rather than the contact stiffness. Rolling constriction is introduced to account for dispersive flow. The velocity depth-profiles around the obstacles are not uniform but varying over the depth. The numerical results are compared with laboratory experiments of chute flow with dry granular material. Some important model parameters are obtained, which can be used to optimize defense structures in alpine regions.     

Simulations for dynamics of granular mixtures in a rotating drum

We present a simple model and carry out simulations to investigate the dynamics of mixtures of granular material within a rotating drum. On the basis of the commonly held belief (supported by considerable experimental evidence) that segregation is due to motion of particles on the active layer, the bulk playing little or no role, we introduce a 2d lattice gas model which takes into account the rotational frequency, frictional forces, and the gravitational field, and represents segregation tendencies via activated effective grain-grain interactions. Our results include the onset of segregation perpendicular to the drum axis, the appearance and subsequent coarsening of bands and peculiarities of the effects of periodic modulation of the drum. Observed effects such as the segregation of rougher (smoother) particles into the bellies (necks) of the modulation are reproduced by our simulation. Received: 30 March 2000     

Dynamic and perturbative system analysis of granular material in a vibrating screen

In most particulate classification systems, feed rates in excess of 80% of the designed capacity leads to inefficiency and conversely feed rates below this value significantly diminishes the operational efficiencies. It therefore implies that maximum efficiency is only attainable at the expense of low capacity, and vice versa. This problem is caused by transience in granular flow due to start-ups and fluctuating feed-rates, in addition to fluctuations in feed material properties. If these variations are not checked, they cause instabilities, resulting in chaotic saddles responsible for in-process systemic error generation. These errors produce intermittent disruptions in production process and control. We have applied perturbation theory to study the effects of infinitesimal changes on the material balance analysis of the unit operation. The problem was identified as one of the highly multi-stable dynamic systems, characterized by ‘predator-prey’ phenomenon in dynamical systems theory. The study allowed formulation of optimal state equations, whose numerical solutions resulted in establishment of optimal operating conditions required to sustain stability, and consistently high tonnages and efficiency up to 99% simultaneously. The study also led to development of an optimization algorithm, which upon validation with experimental data showed a close relationship, with a minimal absolute error of 0.8 and a relative error of 6%. Finally, a representative case study was conducted on screen dimensioning, based on the determined parameters. Successful evolution of this methodology may be applied for up-scaling of real systems in future.     

Construction and characterization of a sputter deposition system for coating granular materials

In many modern ceramic or metal matrix composites the interface between the matrix and the reinforcements (particles or fibres) plays an important role. Either no or only weak mechanical bonding is observed or severe reactions between the matrix and the filler during the manufacturing process take place. A method to promote adhesion or to avoid severe reactions is to use coated reinforcements. A uniform film can act as an adhesion promoter, a compliant layer, a reaction inhibitor or a promoter of thermal transport across the interface.The aim of this work was to construct a particle coating system based on magnetron sputter deposition which allows to keep the particles or the granular material in motion during the deposition process to guarantee a homogenous coating on every single particle. As particles to be coated diamond granulates and carbon fibres were investigated. For transparent diamond particles the uniformity of a metallic coating could be evaluated by transmission optical methods and was found to be quite high. Carbon fibres, on the other hand, could only partially be coated due to agglomeration and shadowing effects. The system presented here can be considered as suitable for coating spherical or close to spherical granular matter.     

A discrete element study of settlement in vibrated granular layers: role of contact loss and acceleration

This paper deals with the vibration of granular materials due to cyclic external excitation. It highlights the effect of the acceleration on the settlement speed and proves the existence of a relationship between settlement and loss of contacts in partially confined granular materials under vibration. The numerical simulations are carried out using the Molecular Dynamics method, where the discrete elements consist of polygonal grains. The data analyses are conducted based on multivariate autoregressive models to describe the settlement and permanent contacts number with respect to the number of loading cycles.     

Velocity depth profile of granular matter in a horizontal rotating drum

Using MRI velocimetry, we verify that the velocity depth profile of the flowing layer near the axial center of a half-filled 3D drum has the form V _m[1 − (r/r ₀)²]-Ω r, where r is the depth measured from the cylinder center, except very close to the free surface where it lies below the quadratic form. We confirm that this deviation is due in part to particles reaching the surface with large components of their velocity in the azimuthal direction. We used a 3D cylinder with a radial “paddle” placed at approximately the dynamic angle of repose, covering the top third of the flow, so as to null any azimuthal velocity. It was found that the deviation from the quadratic form was reduced by the presence of the paddle when the comparison is made at the same solid body rotation rate, at the same free surface velocity, and with the paddle placed at different positions, so long as it makes good contact with the surface. Thus, we conclude that a quadratic velocity depth profile may be a fundamental property of granular shear flows in this geometry, when the sole effect of the cylinder rotation is to transport the particles from the end of the flow to the beginning without imparting velocity perpendicular to the flow.     

The tempering behavior of granular structure in a Mn-series low carbon steel

The granular structure in a Mn-series low carbon steel composed of ferrite matrix and martensite-austenite islands does not exhibit temper brittleness which is quite different from common microstructures in steels. This characteristic facilitates the performance optimization through adjusting tempering temperature. A good combination of tensile strength (750-1000 MPa) and impact toughness (Aku, 138-154 J) can be obtained after quenching and tempering at 400 °C for a round billet with 250 mm in diameter.     

Experimental study of a miniature vapor compression refrigeration system with two heat sink evaporators connected in series or in parallel

A miniature vapor compression refrigeration system included two heat sinks connected in series (indicated as series system) or in parallel (indicated as parallel system) was built. The performance of the series system was studied and compared with that of the parallel system. The results indicate that the largest cooling capacity of the two systems is about 160 W and the optimal refrigerant charge is about 0.6 M_total in the miniature vapor compress refrigeration (VCR) system. There is no relation between the optimal refrigerant charge and the arrangement of the heat sinks. The coefficient of performance (COP) of the series system ranged from 1.81 to 3.22, while the COP of the parallel system was in the range of 1.51–2.92 under the cooling capacity of 100 W. The cooling of the heat sink 2 lag behind that of the heat sink 1 in the serial system, while the refrigerant is difficult to equally distribute in the parallel system.     

Application of a cellular automaton to simulations of granular flow in silos

A cellular automaton based on a gas model of hydrodynamics was used to calculate the kinematics of non-cohesive granular materials during confined flow in a mass flow and funnel flow model silo. In the model, collisions of particles were taken into account during granular flow. In addition, a simplified automaton was used wherein granular flow was assumed as an upward propagation of holes through a lattice composed of cells representing single particles. The advantages and disadvantages of both cellular automata were outlined.     

Effect of energy nonequipartition on the transport properties in a granular mixture

The Boltzmann kinetic theory is used to analyze the effect of energy nonequipartition on the pressure and the shear viscosity of a granular binary mixture under simple shear flow. Theory and Monte Carlo simulations show that both quantities exhibit a non–monotonic behaviour with the mass ratio in contrast to the predictions made from previous theories based on the equipartition assumption. Our results agree qualitatively well with recent molecular dynamics simulations performed by Alam and Luding [Granular Matter 4, 139 (2002)]. The authors acknowledge partial support from the MCYT (Spain) through Grants No. BFM2001-0718 and ESP2003-02859.     

调节阀-管道-流体系统流固耦合动态特性研究

针对调节阀-管道-流体系统的流固耦合问题,建立了考虑阀门定位器作用的系统动态仿真模型,给出了求解调节阀阀芯-阀杆系统响应的预估-校正算法和求解调节阀-管道-流体系统响应的流固耦合有限元方法,利用ANSYS软件对系统在固定开度与变开度情况和流开型与流闭型情况下振动响应进行了定性分析。研究表明:在给定压差下,管道以及流体流向对调节阀阀芯-阀杆系统的位移响应以及阀芯受到的流体不平衡力响应都有较大影响。     

FE-investigations of a deterministic and statistical size effect in granular bodies within a micro-polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during shearing of an infinite layer under plane strain conditions and free dilatancy. For a simulation of the mechanical behavior of a cohesionless granular material during a monotonous deformation path, a micro-polar hypoplastic constitutive was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. To describe a deterministic size effect, the calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2,000 mm. To investigate a statistical size effect, the distribution of the initial void ratio in infinite granular layers was assumed to be spatially correlated. As only primary stochastic calculations were performed, single examples of different random fields of the initial void ratio were generated. For this purpose a conditional rejection method was used.     

基于复模态的空间锥螺旋管管内流固耦合振动特性的有限元分析*

空间锥螺旋管束作为一种新型流体诱导弹性传热元件,由于其锥型螺旋结构,管内流动产生的非比例阻尼对其固有振动特性影响明显.基于此,采用有限元法研究螺旋管束管内流固耦合振动特性,通过螺旋升角变换、螺旋单元坐标变换以及对连接体的简化处理,建立了管束振动状态方程,依据复模态理论分析了科氏力所致阻尼对空间锥螺旋管的频率的影响.结果表明:管内流动对锥螺旋管束基频影响很大;由于科氏力所致阻尼阵的存在,螺旋管束在管内流固耦合作用下呈现复模态;随着螺旋节距及流速的变化,管束的基频及阻尼比发生变化.     

Comparative study of electron beam-gas interaction in an SEM operating at pressures up to 300 Pa

The effects of three different gas environments formed by pure argon, helium and nitrogen with variable pressures up to 300 Pa inside the specimen chamber of a scanning electron microscope on the electron beam parameters were investigated and compared using Monte Carlo calculations. The calculations show that the skirt of the electron beam probe is nearly independent of pressure in the case of helium, which is also supported by experimental evidence. Both theoretical simulation and experimental facts indicate helium as the environment of choice in specimen chambers for minimizing the effect of beam-gas interactions.