椭圆颗粒在剪切流中旋转特性的数值研究

研究颗粒在流体剪切作用下的运动特性是理解和预测颗粒悬浮流流动行为的关键.当流体的惯性不能忽略时,颗粒的运动往往变得非常复杂.本文采用格子Boltzmann方法对中等雷诺数下椭圆颗粒在剪切流中的旋转运动进行了模拟.首先,研究了雷诺数(0Re 170)的影响,结果表明当雷诺数低于临界值时,颗粒以周期性的方式旋转,角速度最小时对应的长轴方向随着雷诺数的增大而逐渐远离水平方向,而且这一倾角与雷诺数呈分段线性关系;当雷诺数大于临界值时,椭圆形颗粒最终保持静止状态,且静止时的转角与雷诺数呈幂函数关系,雷诺数越大,转角越小,椭圆的长轴越远离水平位置.其次,研究了椭圆颗粒的长短轴之比α(1α10)的影响,结果表明颗粒旋转的周期与α呈幂函数关系,α越大,颗粒旋转周期越小.此外,当α超过临界值时,颗粒也在水平位置附近保持静止状态,此时的转角与α也呈幂函数关系,α越大,转角越小.研究还发现,当雷诺数较大时椭圆颗粒在旋转过程中会产生过冲现象.     

Self-organized domain microstructures in a plate-like particle suspension subjected to rapid simple shear

The evolution of the microstructure and rheological properties of plate-like particle suspensions subjected to rapid simple shear is studied numerically. In response to the shear-induced strain, particles in the suspensions rearrange to form a steady-state microstructure, and the suspension viscosity reaches a steady value. Under this condition, the microstructure is composed of two domains having different particle fractions and particle orientations. In the matrix (particle-poor) and cluster (particle-rich) domains, the particles’ long axes are oriented subparallel to the shear plane and normal to the maximum compressive principal direction, respectively. A higher particle concentration and friction coefficient enhance the development of cluster domains relative to matrix domains leading the intensity of the preferred particle orientation to decrease and the number of contacting particles, the aspect ratio of clusters, the inter-particle force, and the suspension viscosity to increase. The domain microstructure is governed by two factors: (1) geometric relations between the particle orientation and the maximum compressive axes and (2) the magnitude of particle–fluid and particle–particle interactions. The first factor results in the coupling of the particle orientation and the local fraction of particles, which is an important character of the domain microstructure. The second factor controls the relative development of the cluster and matrix domains through the change in the particles’ rotational behavior. Our results suggest that the microstructure of plate-like suspensions subjected to rapid shear is predictable in terms of the cluster stability, which has important implications for the kinematics of flow-related microstructures in nature and manufacturing.     

Void coalescence within periodic clusters of particles

The effect of particle clustering on void damage rates in a ductile material under triaxial loading conditions is examined using three-dimensional finite element analysis. An infinite material containing a regular distribution of clustered particles is modelled using a unit cell approach. Three discrete particles are introduced into each unit cell while a secondary population of small particles within the surrounding matrix is represented using the Gurson-Tvergaard-Needleman (GTN) constitutive equations. Deformation strain states characteristic of sheet metal forming are considered; that is, deep drawing, plane strain and biaxial stretching. Uniaxial tensile stress states with varying levels of superimposed hydrostatic tension are also examined.The orientation of a particle cluster with respect to the direction of major principal loading is shown to significantly influence failure strains. Coalescence of voids within a first-order particle cluster (consisting of three particles) is a stable event while collapse of inter-cluster ligaments leads to imminent material collapse through void-sheeting.     

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.     

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.     

A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements, the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.     

An enhanced treatment of boundary conditions in implicit smoothed particle hydrodynamics简

In this work, an enhanced treatment of the solid boundaries is proposed for smoothed particle hydrodynamics with implicit time integration scheme （Implicit SPH）. Three types of virtual particles, i.e., boundary particles, image particles and mirror particles, are used to impose boundary conditions. Boundary particles are fixed on the solid boundary, and each boundary particle is associated with two fixed image particles inside the fluid domain and two fixed mirror particles outside the fluid domain. The image particles take the flow properties through fluid particles with moving least squares （MLS） interpolation and the properties of mirror particles can be obtained by the corresponding image particles. A repulsive force is also applied for boundary particles to prevent fluid particles from unphysical penetra- tion through solid boundaries. The new boundary treatment method has been validated with five numerical examples. All the numerical results show that Implicit SPH with this new boundary-treatment method can obtain accurate results for non-Newtonian fluids as well as Newtonian fluids, and this method is suitable for complex solid boundaries and can be easily extended to 3D problems.     

The influence of particle shape,volume fraction and distribution on post-necking deformation and fracture in uniaxial tension of AA5754 sheet materials

Finite element analysis was performed over a small particle field, edge constraint plane strain post-necking model. The aim is to understand the roles of particle shape, volume fraction and distribution over the post-necking deformation and fracture of AA5754-O sheet materials. For models containing one single particle, the post-necking deformation decreases when the particle varies from circular to elliptical. The inter-particle spacing, the major parameter of distribution to determine whether a pair of particles belongs to a stringer or not, was varied for models with two particles of circular or elliptical shape. The general trend is that the post-necking deformation and fracture strains decrease with decreasing spacing between particles. There is considerable difference in terms of both fracture topographies and strains for models containing 16 particles when distributions varied from random/uniform to stringer distributions. The post-necking deformation and fracture strains monotonically decrease with particle volume fractions for models with 4–64 particles of random or stringer distribution. This indicates that the post-necking behavior for AA5754-O alloys where the matrix material is rather ductile is not solely controlled by a single or pair of particles although they may become initiation places of damage. Multiple damaging sources such as stringers or large particles can act cooperatively and speed up the damaging propagation of the material, and therefore produce small post-necking deformation and early fracture. The center clustering of particles can be beneficial for post-necking behavior and bendability of sheet materials.     

Plasticity and ductile fracture of IF steels: experiments and micromechanical modeling

If one aims at the simulation of plasticity and failure of multiphase materials, the choice of an appropriate material law is of major importance. Plasticity models for porous metals contain, in addition to the yield surface and the flow potential, also functions describing the void nucleation, dependent on some macroscopically observable quantities, and the growth of these voids. In this paper, a micromechanically based method to develop a void nucleation function for porous plasticity models is proposed which is valid for all possible microstructures as long as the amount of second phase particles is low (i.e. the particles do not interact with respect to the stress and strain fields), and as long as the particles are large enough (above 0.1 μm) justifying a continuum mechanical approach. The method described consists of two stages: In the first stage, the microstructure is investigated via a finite element model. The FE model implicitly contains the effects of the shape of the precipitates, of the material parameters of both the matrix and the precipitates, of the void nucleation hypothesis (by the assumption of “nucleation limits” for characteristic damage-related quantities), and of the applied stress state. In the second stage, during postprocessing, the volume fraction of precipitates as well as the influences of the particle orientation distribution, size distribution, and size dependence of the damage-related quantities are taken into account. The model is applied to the microstructure of IF (Interstitially Free) steel, a material with a ductile matrix and rigid second phase particles of cubical shape. This microstructure is particularly suited for investigating shape and size effects. The model shows that either the size effect or the shape effect dominate the void nucleation behavior: in the case of particles of roughly the same size, the size distribution will hardly alter the nucleation strain distribution obtained by taking into account only the shape and orientation effects. For particles of very different sizes, the size effect will completely override the rather “sharp” original distribution regarding particle shape and orientation.     

Structural changes in granular materials: The case of irregular polygonal particles

This paper presents a series of numerical simulations of biaxial tests performed on assemblies of two-dimensional irregular polygonal particles. Each sample is prepared with a technique similar to dry pluviation. Different aspect ratios (1–3) are considered and the behavior of granular samples is analyzed from both a global and a local point of view. More precisely, the influence of the particle aspect ratio on both inherent (initial) and induced anisotropy is investigated. New internal variables which are related to the orientation of particles are proposed. They give new insight into the specific mechanisms that control the behavior of irregular polygonal materials. Associated to global variables, they demonstrate the existence of a critical state irrespective of the investigated aspect ratios. However, for materials with higher aspect ratios (2 and 3), their inherent anisotropy prevents any extensive reorganization, this means that, within the range of usual strains considered in civil engineering, the particle reorientation remains in progress and considerable deformations are required to reach the critical state.     

Rod-like particles matching algorithm based on SOM neural network in dispersed two-phase flow measurements

A matching algorithm based on self-organizing map (SOM) neural network is proposed for tracking rod-like particles in 2D optical measurements of dispersed two-phase flows. It is verified by both synthetic images of elongated particles mimicking 2D suspension flows and direct numerical simulations-based results of prolate particles dispersed in a turbulent channel flow. Furthermore, the potential benefit of this algorithm is evaluated by applying it to the experimental data of rod-like fibers tracking in wall turbulence. The study of the behavior of elongated particles suspended in turbulent flows has a practical importance and covers a wide range of applications in engineering and science. In experimental approach, particle tracking velocimetry of the dispersed phase has a key role together with particle image velocimetry of the carrier phase to obtain the velocities of both phases. The essential parts of particle tracking are to identify and match corresponding particles correctly in consecutive images. The present study is focused on the development of an algorithm for pairing non-spherical particles that have one major symmetry axis. The novel idea in the algorithm is to take the orientation of the particles into account for matching in addition to their positions. The method used is based on the SOM neural network that finds the most likely matching link in images on the basis of feature extraction and clustering. The fundamental concept is finding corresponding particles in the images with the nearest characteristics: position and orientation. The most effective aspect of this two-frame matching algorithm is that it does not require any preliminary knowledge of neither the flow field nor the particle behavior. Furthermore, using one additional characteristic of the non-spherical particles, namely their orientation, in addition to its coordinate vector, the pairing is improved both for more reliable matching at higher concentrations of dispersed particles and for higher robustness against loss of particle pairs between image frames.     

Rheology of SiO 2 /(acrylic polymer/epoxy) suspensions. III. Uniaxial elongational viscosity

Uniaxial elongational viscosity of SiO₂/(acrylic polymer/epoxy (AP/EP)) suspensions with various SiO₂ volume fractions (?) in a blend of acrylic polymer and epoxy was investigated at various temperatures (T). The matrix polymer ((AP/EP) blend) contained 70?vol.% of EP. At ?????35?vol.% at T????80°C, where the suspensions were in sol state, strain-hardening behavior was observed. This strain hardening of the suspensions is attributable to the elongational flow properties of (AP/EP) medium. At critical gel state (??=?35?vol.% and T?=?100°C) and in gel state (?????40?vol.%), the elongational viscosity exhibited the strain-softening behavior. These results strongly suggest that the strain softening results from the strain-induced disruption of the network structure of the SiO₂ particles therein.     

Using S-statistic for investigating the effect of temperature on hydrodynamics of gas–solid fluidization

The influence of temperature on fluidization was investigated by a statistical chaotic attractor comparison test known as S-statistic. After calibration of the variables used in this method, the S-test was applied to the radioactive particle tracking (RPT) data obtained from a lab-scale fluidized bed. Experiments were performed with sand as fluidized particles and in temperatures from ambient up to 600 °C with superficial gas velocities of 0.29, 0.38 and 0.52 m/s. Considering the behavior of bubbles and comparing with frequency domain analysis, it was concluded that S-statistic is a reliable method for characterization of fluidization process behavior at different temperatures.     

Bifurcation and chaos of a flag in an inviscid flow

A two-dimensional model is developed to study the flutter instability of a flag immersed in an inviscid flow. Two dimensionless parameters governing the system are the structure-to-fluid mass ratio M^⁎ and the dimensionless incoming flow velocity U^⁎. A transition from a static steady state to a chaotic state is investigated at a fixed M^⁎=1 with increasing U^⁎. Five single-frequency periodic flapping states are identified along the route, including four symmetrical oscillation states and one asymmetrical oscillation state. For the symmetrical states, the oscillation frequency increases with the increase of U^⁎, and the drag force on the flag changes linearly with the Strouhal number. Chaotic states are observed when U^⁎ is relatively large. Three chaotic windows are observed along the route. In addition, the system transitions from one periodic state to another through either period-doubling bifurcations or quasi-periodic bifurcations, and it transitions from a periodic state to a chaotic state through quasi-periodic bifurcations.     

非球形颗粒两相流的数值模拟研究进展

非球形颗粒两相流是多相流的重要研究方向之一, 常见于自然界及工业生产过程中. 不同于球形颗粒, 由于非球形颗粒形状的各向异性, 除了颗粒平动行为, 还需要考虑颗粒的转动与取向行为, 颗粒的取向与转动行为会影响颗粒所受的力和力矩. 为了准确模拟非球形颗粒的运动行为, 目前非球形颗粒两相流的数值模拟研究主要基于欧拉?拉格朗日的求解框架展开, 常见的非球形颗粒两相流数值模拟方法主要包括点颗粒法与全分辨颗粒法. 本文将对这两类方法进行介绍, 同时会全面介绍非球形颗粒两相流研究的基础理论模型, 并系统总结非球形颗粒在简单基本流和复杂湍流中的研究进展, 包括对于非球形颗粒在湍流中的取向与转动行为机理, 以及颗粒对湍流减阻调制作用的研究. 最后, 本文提出了非球形颗粒两相流研究存在的问题及未来研究方向.      

Introducing the theory of successful settling in order to evaluate and optimize the sedimentation tanks

A rectangular settling tank in full scale is investigated using the Fluent software to increase its efficiency. First, the pure water is simulated in the absence of particles. Then particles are injected into the flow field and tracked by means of the discrete phase model. Three methods are presented to optimize the settling tank: (1) adding a baffle which is mounted in the bottom and is extended up to the near of free surface, (2) adding a baffle which is mounted in the free surface and is extended up to the near of the tank bottom and (3) install a bi-directional baffle which is mounted in the free surface and is extended up to the near of the bottom. These three suggestions are checked using the short-circuiting phenomenon and the successful settling theory. The successful settling theory states that a particle can be accounted as a “trapped” particle if (1) settled particle stays static and stable in the tank bottom and (2) settled particle doesn’t return to purified sewage. Although the second method provided higher efficiency, the third method was selected as the most appropriate method in order to optimize the settling tank.     

Numerical investigation on motion of an ellipsoidal particle inside confined microcavity flow

The behaviors of a neutrally buoyant ellipsoidal particle in vortical flow confined by a microcavity are numerically studied using the Lattice-Boltzmann method. For specific initial position, an isolated ellipsoid may develop a stable limit cycle orbit inside microcavity due to the interaction between particle and the carrier flow. It is observed that ellipsoidal particles of different shapes exhibit two different stable rotational modes depending on the initial orientation and lateral position. A prolate spheroid tends to enter a tumbling mode whereas an oblate spheroid is apt to achieve a rolling mode. The evolution of rotational velocities along the stable orbit is also analyzed for particles of different shapes.     

Measurements and model predictions of transient elongational rheology of polymeric nanocomposites

Transient elongational rheology of two commercial-grade polypropylene (PP) and the organoclay thermoplastic nanocomposites is investigated. A specifically designed fixture consisting of two drums (SER Universal Testing Platform) mounted on a TA Instruments ARES rotational rheometer was used to measure the transient uniaxial extensional viscosity of both polypropylene and nanoclay/PP melts. The Hencky strain rate was varied from 0.001 to 2 s^− 1, and the temperature was fixed at 180°C. The measurements show that the steady-state elongational viscosity was reached at the measured Hencky strains for the polymer and for the nanocomposites. The addition of nanoclay particles to the polymer melt was found to increase the elongation viscosity principally at low strain rates. For example, at a deformation rate of 0.3 s^− 1, the steady-state elongation viscosity for polypropylene was 1.4 × 10⁴ Pa s which was raised to 2.8 × 10⁴ and 4.5 × 10⁴ Pa s after addition of 0.5 and 1.5 vol.% nanoclay, respectively. A mesoscopic rheological model originally developed to predict the motion of ellipsoid particles in viscoelastic media was modified based on the recent developments by Eslami and Grmela (Rheol Acta 47:399–415, 2008) to take into account the polymer chain reptation. We show that the orientation states of the particles and the rheological behavior of the layered particles/thermoplastic hybrids can be quantitatively explained by the proposed model.     

Rational approximation for fractional-order system by particle swarm optimization

In this paper, a rational approximation me-thod is proposed for the fractional-order system using the particle swarm optimization (PSO). Firstly, the approximation method for the fractional-order operator is studied, because a fractional-order system consists of many fractional-order operators. The coefficients of the transfer function are calculated using PSO with a fitness function under the continued fraction expansion (CFE) framework in the frequency domain. The average velocity of the particle swarm is defined to reflect the real state of particle swarm. To improve the global optimization and achieve a more satisfactory fitting result, comparing with the linear PSO, the chaotic optimization is combined with PSO. The numerical examples of fractional-order systems demonstrate the effectiveness of this method.     

A moving particle semi‐implicit method for free surface flow: Improvement in inter‐particle force stabilization and consistency restoring

The moving particle semi‐implicit (MPS) method has been widely applied in free surface flows. However, the implementation of MPS remains limited because of compressive instability occurred when the particles are under compressive stress states. This study proposed an inter‐particle force stabilization and consistency restoring MPS (IFS‐CR‐MPS) method to overcome this numerical instability. For inter‐particle force stabilization, a hyperbolic‐shaped quintic kernel function is developed with a non‐negative and smooth second order derivative to satisfy the stability criterion under compressive stress state. Then, a contrastive study is conducted on the contradiction between the common understanding of the conventional MPS hyperbolic‐shaped kernel function and its performance. The result shows that the conventional MPS hyperbolic‐shaped kernel function can easily cause violent repulsive inter‐particle force and then lead to the compressive instability. Therefore, the first order derivative of the modified hyperbolic‐shaped quintic kernel function is recommended as the form of the contribution of the neighbor particles to achieve a more stable inter‐particle repulsive force. For consistency restoring, the Taylor series expansion and the hyperbolic‐shaped quintic kernel are combined to improve the accuracy of the viscosity and pressure calculation. The IFS‐CR‐MPS algorithm is subsequently verified by the inviscid hydrostatic pressure, jet impacting, and viscous droplet impacting problems. These results can be used for choosing kernel function and the contribution of neighbor particles in particle methods. Copyright © 2016 John Wiley & Sons, Ltd.