An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed

The dynamic behavior of individual particles during the mixing/segregation process of particle mixtures in a gas fluidized bed is analyzed. The analysis is based on the results generated from discrete particle simulation, with the focus on the trajectory of and forces acting on individual particles. Typical particles are selected representing three kinds of particle motion： a flotsam particle which is initially at the bottom part of the bed and finally fluidized at the top part of the bed; a jetsam particle which is initially at the top part of the bed and finally stays in the bottom de-fluidized layer of the bed; and a jetsam particle which is intermittently joining the top fluidized and bottom de-fluidized layers. The results show that the motion of a particle is chaotic at macroscopic or global scale, but can be well explained at a microscopic scale in terms of its interaction forces and contact conditions with other particles, particle-fluid interaction force, and local flow structure. They also highlight the need for establishing a suitable method to link the information generated and modeled at different time and length scales.     

End wall effect on particle motion in a chute flow

The influence of the end wall of a chute on the rotation of internal characteristic particles is mainly on the z-axis.A measurement device based on inertial measurement technology does not require the assistance of external information;hence,it is especially suitable for measuring the angular and translational velocities of internal characteristic particles.To study the influence of the end wall of the chute on the motions of the internal characteristic particles,the z-axis rotational and translational velocities of the internal characteristic particles in the chute were measured,and it was found that the rotational velocity about the z-axis differs according to the initial position.The z-axis angular velocity of a characteristic particle at the centre fluctuates near 0,and the average value approaches 0.The z-axis angular velocity of a characteristic particle at the left end wall is typically negative.This phenomenon is due to the influence of the end wall on the rotational motions of particles with initial positions that are near the end wall.In addition,the average translational velocity of the characteristic particles is also affected by the end wall.The distributions of the average z-axis angular velocity and the average translational velocity are quantitatively analysed,and the correlation between the tilt angle of the chute and the end wall effect is studied.     

PROPAGATION OF A LONG WAVE IN A CURVED DUCT (Ⅱ)APPLICATIONS OF MATCHED EXPANSION TO LONG WAVE PROPAGATION THROUGH A HOLE WITH VARIABLE CROSS-SECTION

Only the case in which the parameterε=ka《1 is considered in this paper,where k is the wave number and a is the characteris-tic radius of the cross-section of the hole.The general asymp-totic expansion of the complex velocity potential of a long wave propagating in the hole with variable cross-section is obtained by regular perturbation:The methods of matched asymptotic ex-pansion are employed to calculate the reflection coefficients,scattering coefficients and radiation coefficients at the open ends of the hole when a long wave propagates through it,which may be open at both ends or only at one end.Three examples of different kinds of holes are given to show the way to solve such two-dimensional or three-dimensional problems.     

Segregation behavior of a ternary mixture of titanium dioxide particles in a pseudo two-dimensional fluidized bed

The segregation behavior of a mixture of silica-coated titanium dioxide(TiO2)particles of three different sizes in a pseudo two-dimensional fluidized bed was studied experimentally by the freeze-sieving method and numerically by the multi-fluid model(MFM).Three-dimensional computational fluid dynamics(CFD)simulations were carried out to evaluate the effects of the solid wall boundary conditions on particle segregation in terms of specularity and particle-wall restitution coefficients.The quantitative indexes of segregation tendency and segregation degree were used to determine the axial segregation of the mixture in triangular coordinates.The simulation results revealed that the axial segregation increased with the specularity coefficient,whereas the particle-wall restitution coefficient had a minor effect on axial segregation.Comparison of the simulation results with experimental data showed that the appropriate value of the specularity coefficient used in the CFD model depended on superficial gas velocity.The study of the effects of superficial gas velocity on segregation behavior demonstrated that the greatest segregation was obtained at minimum fluidization velocity and the segregation decreased as the gas velocity gradually increased.     

Deformation of metallic single-walled carbon nanotubes in electric field based on elastic theory

The electromechanical properties of metallic single-walled carbon nanotubes (SWCNTs) in the electric field are demonstrated with a column shell model in this paper.A hemisphere model is introduced to determine the charge distribution and the local electric field in SWCNTs.By treating the SWCNT as an elastic column shell,the analytical solutions of the charged SWCNT’s axial strain and the radial strain are obtained.SWCNTs with a larger aspect ratio show greater deformation.The greatest radial deformation appears at the end of the tube.The significant axial strain can be induced in CNTs with a large length (around 100 nm) even though the applied electric field is not strong enough.When SWCNTs are fixed at both ends,the radius of SWCNTs becomes small along the axial position.     

DISCRETE PARTICLE SIMULATION OF SIZE SEGREGATION OF PARTICLE MIXTURES IN A GAS FLUIDIZED BED

This paper presents a study of the mixing/segregation behaviour of particle mixtures in a gas fluidized bed by use of the discrete particle simulation. Spherical particles with diameters 2 mm （jetsam） and 1 mm （flotsam） and density 2 500 kg.m^-3 are used as solid mixtures with different volume fractions. The particles are initially packed uniformly in a rectangular bed and then fluidized by gas uniformly injected at the bottom of the bed. The gas injection velocities vary to cover fixed, partially and fully fluidized bed conditions. Segregation/mixing behaviour is discussed in terms of flow patterns, solid concentration profile and mixing kinetics. The results show that segregation, as a transient fluidization process, is strongly affected by gas injection velocities for a given particle mixture. With the increase of the volume fraction of flotsam, size segregation appears at lower velocities.     

A NUMERICAL STUDY OF THE STRESS DISTRIBUTION IN HOPPER FLOW

The stress distributions of granular flow in a cylindrical hopper with fiat bottom are investigated by means of a combined approach of discrete element method (DEM) and averaging method. The filling and discharge of the hopper flow are first simulated at a particle level by means of a modified DEM. The results are then used to determine the velocity and stress profiles of the hopper flow by means of an averaging method. The analysis is focused on a central section plane of the hopper due to the relatively perfect axial symmetry. The velocity profiles are illustrated to be consistent with those obtained by the previous experiments, confirming the validity of the proposed approach. The distributions of four components of the planar stress tensor at different heights are quantified. It is shown that the vertical normal stress increases with increasing the height near the central axis, the horizontal normal stress varies more slowly at a higher level and is almost constant when the height is equal to or greater than about 12 particle diameter, and the magnitudes of two shear stresses are equal at the central zone of the hopper but not so at the points near the walls. The dependence of stress distributions on the wall mechanical properties such as sliding resistance and rolling resistance is also discussed.     

Forced vibration and special effects of revolution shells in turning point range

The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions: either the membrane drive or the bending drive causes motions of both the membrane type and bending type.Three interesting effects characteristic of the forced vibration emerge from the coupling nature:the non-bending effect,the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect.These effects may have potential applications in engineering.     

Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

The electric band energy variation in a bent piezoelectric semiconductor(PSC) nanowire of circular cross-section induced by the mechanical force is analyzed based on a six-band k · p method. The electric-mechanical fields are first obtained analytically in a cantilever bent PSC nanowire by solving the fully-coupled electro-mechanical equations. Then, the band energy is acquired numerically via the six-band Hamiltonian.By considering further the nonlinear coupling between the piezoelectric and semiconducting quantities, the contribution of the redistribution carriers to the electric field is analyzed from the Gauss' s law. Numerical examples are carried out for an n-type Zn O nanowire in different locations induced by an applied concentrated end force. They include the electric potential, heavy hole(HH), light hole(LH), spin-orbit split-off(SO),and conduction band(CB) edges along the axial and thickness directions. Our results show that the applied force has a significant effect on the band energies. For instance, on the bottom surface along the axial direction, the bandgaps near the fixed end are greater than those near the loading end, and this trend is reversed on the top surface. Moreover,at a fixed axial location, the energy level of the lower side can be enhanced by applying a bending force at the end. The present results could be of significant guidance to the electronic devices and piezotronics.     

Adjacent mode resonance of a hydraulic pipe system consisting of parallel pipes coupled at middle points

The coupling vibration of a hydraulic pipe system consisting of two pipes is studied. The pipes are installed in parallel and fixed at their ends, and are restrained by clips to one bracket at their middle points. The pipe subjected to the basement excitation at the left end is named as the active pipe, while the pipe without excitation is called the passive pipe. The clips between the two pipes are the bridge for the vibration energy.The adjacent natural frequencies will enhance the vibration c...     

Particle–wall interaction in entrained-flow slagging coal gasifiers: Granular flow simulation and experiments in a cold flow model reactor

Entrained-flow slagging coal gasifiers display large conversion efficiencies and small levels of unconverted carbon at the exhaust. Both features are apparently at odds with the fairly small “space-time” of the particle-laden gas feeding, as compared with the time scale of heterogeneous gasification of carbon. This apparent inconsistency can be explained by considering that fuel residence times are longer than the “space-time” due to segregation of fuel particles in the near-wall region of the gasifier. Segregation is promoted by swirl flow, by particle–wall interaction as the wall is covered by a molten layer of slag and by the establishment of a dense-dispersed flow of granular solids in the proximity of the wall.This study presents results of granular flow simulations of the interaction of a dense-dispersed particle flow with the confining wall. Simulations consider that both the particles and the wall may be either “sticky” or “non sticky”, based on the prevailing elastic vs plastic behaviour upon collision. The effect of drag forces exerted on particles by swirled gas flow is simulated in a simplified manner. Particle–particle collisions are modelled with a Hertzian approach that includes torque and cohesion. The extent and time scale of segregation of a lump of particles loaded into a cylindrical vessel are assessed. Results clearly indicate the different structure of the layer of particles establishing at the wall surface in the different interaction regimes.Results of simulations are qualitatively compared with results of an experimental campaign performed in a reactor representing a cold flow model of the entrained-flow gasifier, where solid, molten or semi-molten particles have been simulated by atomized wax as surrogate material. Altogether, the results confirm the importance of the particle–particle and particle–wall micromechanical interactions for a correct prevision of the segregation of fuel particles in entrained-flow slagging gasifiers.     

动力应变局部化传播及尺寸效应数值模拟

采用 FLAC-3 D模拟了应变软化岩土材料局部化剪切带的发展、扩容对剪切带倾角的影响及试件的宽度效应。随着加载时步的增加 ,彼此孤立的两个应变场逐渐靠近、叠加 ,最终形成了剪切带网络。无论端面约束强或弱 ,剪切带的倾角的数值模拟结果都与罗斯科倾角比较接近。增加试样宽度 ,剪切带的宽度增加 ,剪切带变得不平直 ;宽度越大 ,岩样上端面中点的压应力 -加载时步曲线的峰值强度越大 ,宽度对弹性阶段没有大的影响     

回转窑多粒径颗粒流动与偏析的DEM模拟与实验研究

为明晰回转窑内颗粒的运动行为及偏析机理,以绿豆、黄豆和黑豆为颗粒介质,依次对3种装填顺序下的颗粒流动过程进行离散元模拟与实验研究,以颗粒质量分数和平均粒度为判据,对颗粒偏析进行评价。结果表明,回转窑内颗粒流动区可分为自由滚落区、渗流呆滞区以及窑壁携带区,自由滚落区颗粒流速最大,而渗流呆滞区流速最小。窑内颗粒沿轴向输运过程发生径向偏析,形成夹层结构,小颗粒受渗流作用在渗流呆滞区中心形成内核,大粒径和中等粒径颗粒集中在自由滚落区和窑壁携带区。窑内颗粒力链分布不均匀,强力链分布于近窑壁区,弱力链分布于自由滚落区和渗流呆滞区,且渗流呆滞区力链细而密集。当窑头附近不同粒径颗粒存在轴向速度差时,颗粒在轴向发生掺混,并产生径向偏析。     

Deformations of a clamped–clamped elastica inside a circular channel with clearance

In this paper, we study the planar deformations of an elastica inside a circular channel with clearance. One end of the elastica is fully clamped, while the other end is partially clamped in the lateral direction and is subject to a pushing force longitudinally. In the experiment we first observe various deformation patterns after pushing the elastica through the partial clamp. Both symmetric and asymmetric deformations are recorded. Special attention is focused on the contact conditions between the elastica and the circular channel. In order to analyze the elastica deformation theoretically, we first divide the elastica into several elementary sub-domains depending on the contact condition between the elastica and the circular channel. In each sub-domain the elastica is either loaded only at the ends or in full contact with the outer wall. Armed with these basic equilibrium analyses, we proceed to calculate and classify the loaded elastica into several deformation patterns. Finally, we present the load-deflection curves, both theoretically and experimentally, which relate the longitudinal forces at both ends to the elastica length increase inside the channel. The branching phenomena predicted theoretically agree fairly well quantitatively with the experimental measurements.     

岩石试件端面摩擦效应数值模拟研究

试件端面摩擦效应直接影响试件内的塑性等效应变、侧向位移的分布和单元应力应变曲线。本文运用ANSYS中的接触单元模拟了平面应变状态下端面摩擦效应对塑性等效应变、侧向位移和单元应力应变曲线的影响,得到了不同摩擦系数时塑性等效应变及侧向位移的渐进变化形式。当接触面摩擦较小时,塑性等效应变图案为上下两个X形网络,侧向位移上下分布均匀;当接触面摩擦增大时,塑性等效应变网络向中部靠拢并且明显增大,侧向位移上下分布不均匀,中部较上下端面位移大;当试件端面侧向位移被限制,即摩擦力很大时,塑性等效应变网络变为一个X形局部化带,侧向位移分布更加不均匀,中部明显隆起。     

Multi-fluid modeling of density segregation in a dense binary fluidized bed

This paper presents simulation results of the density segregation in a dense binary gas fluidized bed using a multi-fluid model from Chao et al. (2011). The segregation behavior of two types of particles with approximately same particle diameters and different particle densities was studied and validated using the experimental data from Formisani et al. (2008). Some detailed information regarding the gas, particle velocity profiles, the distributions of the particle volume fractions and the flotsam-to-total particle volume fraction ratios is presented. The simulation results show that the simulated axial average flotsam-to-total particle volume fraction ratio distribution agrees reasonably with the experimental data of Formisani et al. (2008). The binary particle velocities are closely coupled though the segregation exists. The segregation behavior and the particle velocity profiles are superficial gas velocity dependent. The number and distribution of particle velocity vortices change dramatically with superficial gas velocity: at a comparatively low superficial gas velocity, the particles mainly segregate axially, and at a comparatively high superficial gas velocity, the particles segregate both axially and radially.     

Mixing and segregation of solid particles in a conical spouted bed: Effect of particle size and density

In this work, the mixing and segregation of binary mixtures of particles with different sizes and densities in a pseudo-2D spouted bed were studied experimentally. A binary mixture of solid particles including sand, gypsum, and polyurethane was used. To determine the particles mass fraction, and their mixing and segregation in the bed, an image-processing technique was developed and used. Important hydrodynamic parameters, such as the axial and radial segregation profiles of the solid particles, were measured. The effects of air velocity, particle size, and particle mass fraction were also evaluated. The flow regime in the spouted bed and the time required for reaching the equilibrium state of the solid particles were discussed. The results showed that the segregation of solid particles and the time to equilibrium both decreased when the air velocity increased to much larger than the minimum spouting velocity. The axial segregation increased with the diameter ratio of the particles. Upon completion of the test, coarse particles were concentrated mainly in the spout region, while fine particles were aggregated in the annulus region. Examination of the flow pattern in the spouted bed showed that the particles near the wall had longer flow paths, while those near the spout region had shorter flow paths.     

Experiments on the dynamic behavior of fluid-coupled concentric cylinders

This paper describes an experimental vibration study of fluid-coupled coaxial cylinders that simulates the vibration of a reactor vessel with a thermal liner. The model cylinders are made of acrylic. Thickness and gap-size parameter studies are performed by a series of different compinations of three outside cylinders and nine inside cylinders that have variable thicknesses and diameters. Damping ratios are measured on a mode-by-mode basis for several combinations of cylinders. The vibrated cylinders are mounted to a rigid stand, with the cuter cylinder supported at both ends and the inner cylinder supported at either one end (pendulum mode) or both ends, as the case may be. The natural frequencies are obtained first in air and then with coaxial cylinders coupled by water. The mode shapes are obtained by circumferential (shell modes) and axial (shell/beam modes) mapping of the response with two diametrically opposite ‘roving’ Dymac eddy probes. In general, the natural vibration of the system has two distinct responses in-phase and/or out-of-phase modes, i.e., the radial displacement phase relationship between inner and outer cylinders. In the out-of-phase modes the frequency is shown to decrease to either zero or a very low limiting value as the gap size cecreases. The opposite occurs for in-phase modes. Damping ratios are found to be much higher for out-of-phase modes and for relatively rigid cylinders than for in-phase modes and flexible cylinders, respectively.     

End-grip configurations for axial loading of composite tubes

Testing of high-strength, tubular, composite specimens in uniaxial and biaxial tension require end-grip fixturing to transfer large axial loads into the specimen. Two gripping configurations were analytically and experimentally evaluated to determine their affect on stress distribution within the specimen test section. The first was a bonded grip in which the tubular specimen is adhesively bonded in a deep-slotted aluminum end tab. The second was a threaded grip with glass cloth/epoxy overwrap on the specimen ends that thread into an aluminum, split-collar end tab. Large axial loads can be transmitted to the specimen with either design; however, each introduces axial-stress concentrations into the composite sample. The magnitude and distribution of stresses (strains) with axial position, which are a function of biaxial-stress ratio, were computed by finite-element analyses and verified experimentally with surface-strain measurements. This study illustrates the importance of utilizing analytical tools to examine the effect of end grip/specimen interaction on stress distribution within the gage section and on test data.     

基于电子万能试验机的新型压杆稳定实验装置

本文介绍了一种基于电子万能试验机开发的新型压杆稳定实验装置。该装置利用电子万能试验机自身传感设备,通过测量压杆两端受力与绘制端部轴向位移曲线来确定压杆失稳荷载。装置包括上、中、下三个约束部分与压杆试样部分,可实现两端固支、两端铰支、一端固支一端铰支和一端固支一端自由等4种不同端部约束型式,并且能够施加中部固支约束与压杆初始偏心。本文同时讨论了两种铰支型式,即刀刃铰支与轴承铰支对测试精度的影响。实验表明,轴承铰支测量精度比刀刃铰支高。该套装置的整体测量精度高,与理论值的相对误差最高为2%。