Vibration induced flow in hoppers: DEM 2D polygon model

A two-dimensional discrete element model （DEM） simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle-particle interaction model used is based on a multi-contact principle. The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size （Bc） to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that Bc decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner. The second part of the study showed that vibration could enhance flow, effectively reducing Bc. The model demonstrated the importance of vibrator location （height）, consistent with previous continuum model results, and vibration amplitude in enhancing flow.     

Numerical simulation of polygonal particles moving in incompressible viscous fluids

A two-dimensional coupled lattice Boltzmann immersed boundary discrete element method is introduced for the simulation of polygonal particles moving in incompressible viscous fluids. A collision model of polygonal particles is used in the discrete element method. Instead of a collision model of circular particles, the collision model used in our method can deal with particles of more complex shape and efficiently simulate the effects of shape on particle–particle and particle–wall interactions. For two particles falling under gravity, because of the edges and corners, different collision patterns for circular and polygonal particles are found in our simulations. The complex vortexes generated near the corners of polygonal particles affect the flow field and lead to a difference in particle motions between circular and polygonal particles. For multiple particles falling under gravity, the polygonal particles easily become stuck owing to their corners and edges, while circular particles slip along contact areas. The present method provides an efficient approach for understanding the effects of particle shape on the dynamics of non-circular particles in fluids.     

Numerical simulation of the accumulation of heavy particles in a circular bounded vortex flow

In present work, an Eulerian–Lagrangian CFD model based on the discrete element method (DEM) and immersed boundary method (IBM) has been developed, validated and used to investigate the accumulation of heavy particles in a circular bounded viscous vortex flow. The inter-particle and particle-wall collisions are resolved by a hard-sphere model. Effects of one-way and two-way coupling, Reynolds number, and particle diameter are systematically explored. Results show that, in case of one-way coupling, the majority of particles will spiral into an accumulation point located near the stagnation point of the flow field. The accumulation point represents a stable equilibrium point as the drag created by the flow field balances the destabilizing centrifugal force on the particle. However, in case of two-way coupling, there does not exist a stable accumulation point due to the strong interaction between the particles and fluid dynamics. Instead most particles are expelled from the circular domain and accumulate on the confining wall. The percentage of accumulated particles on the wall increases with increasing Reynolds number and particle diameter. Moreover, influence of three well-known drag models is also studied and they give consistent results on the particle accumulation behavior, although small quantitative differences can still be discerned.     

离散颗粒流动堆积行为离散元模拟及实验研究

工程应用中存在许多颗粒流动堆积问题.首先设计了一系列测量方法,通过大量的实验和统计分析,得到了颗粒的多种物理参数.并以工程中高炉炉顶称量料罐为背景,采用离散元方法模拟不同物理条件下离散颗粒的流动堆积行为,得出料罐内颗粒系统中颗粒之间力的分布不均匀,而且强力链分布主要与料罐的左下壁方向平行.同时,设计并制作了具有多参数调节的离散颗粒料罐实验模型,进行了相应的物理实验,实测结果与数值模拟吻合良好.     

Simultaneous determination of position and mass of a particle by the vibration of a diaphragm-based nanomechanical resonator

We present a theoretical analysis of the vibration of a suspended circular diaphragm resonator with a particle at an arbitrary location when considering the effects of plate stiffness and membrane tension in the diaphragm. The analytical expression relating position and mass of a particle attached on a stretched diaphragm with varying residual stress to the resulting shifts in diaphragm resonant frequency is derived. It has been shown that the particle position and mass for the diaphragm configuration can be unambiguously resolved by combining resonant frequencies of the first three consecutive symmetric vibration modes. This finding is verified numerically in finite element modeling using a freestanding circular diaphragm with and without an added particle, and it proves that the method resolves the particle position and mass with high accuracy.     

On the deposition of particles in liquid metals onto vertical ceramic walls

The deposition of non-metallic particles in liquid-metal flows is a serious industrial problem because the build-up of particles on ceramic walls clogs the flow path and interrupts the production, and this leads to large economic losses. This paper is an effort to extend the current state-of-the-art knowledge of particle deposition in air in order to predict particle deposition rates in liquid-metal flows using an improved Eulerian deposition model and considering Brownian and turbulent diffusion, turbophoresis and thermophoresis as transportation mechanisms. The model was used to predict the rate of deposition of particles in an air flow, and the predictions were compared to published measurements to demonstrate its performance. The model was then modified to take into account the differences in properties between air and liquid metals and thereafter applied to liquid-metal flows. Effects on the deposition rate of parameters such as steel flow rate, particle diameter, particle density, wall roughness and temperature gradient near the wall were investigated. It is shown that the steel flow rate has a very important influence on the rate of deposition of large particles, for which turbophoresis is the main deposition mechanism. For small particles, both wall roughness and thermophoresis have a significant influence on the particle deposition rate. Particle deposition rates under various conditions were successfully predicted.     

顶部重力加砂颗粒速度场及浓度场的实验研究

对砂尘环境试验设备顶部重力加砂气固两相流的颗粒速度场及浓度场进行了研究．利用中国科学院寒区旱区环境与工程研究所室内风沙环境风洞，采用激光数字式粒子成像测速技术(DPIV)，得到顺风向距加砂口不同水平距离截面位置颗粒相速度及空间分布规律．表明在顺风向距加砂口水平距离约3m左右处的位置，颗粒相速度才接近风洞风速，且粒子基本均匀扩散开，从而证明了国外砂尘实验设备的不合理性、为我国自行研制大型砂尘环境试验设备，确定加砂／尘方法及试验段参数等提供了依据．     

Effect of inertial particles with different specific heat capacities on heat transfer in particle-laden turbulent flow

The effect of inertial particles with different specific heat on heat transfer in particle-laden turbulent channel flows is studied using the direct numerical simulation(DNS) and the Lagrangian particle tracking method. The simulation uses a two-way coupling model to consider the momentum and thermal interactions between the particles and turbulence. The study shows that the temperature fields display differences between the particle-laden flow with different specific heat particles and the particle-free flow,indicating that the particle specific heat is an important factor that affects the heat transfer process in a particle-laden flow. It is found that the heat transfer capacity of the particle-laden flow gradually increases with the increase of the particle specific heat. This is due to the positive contribution of the particle increase to the heat transfer. In addition,the Nusselt number of a particle-laden flow is compared with that of a particle-free flow.It is found that particles with a large specific heat strengthen heat transfer of turbulent flow, while those with small specific heat weaken heat transfer of turbulent flow.     

NUMERICAL STUDY OF PARTICLE DISTRIBUTION IN WAKE OF LIQUID-PARTICLE FLOWS PAST A CIRCULAR CYLINDER USING DISCRETE VORTEX METHOD

Particle-laden water flows past a circular cylinder were numerically investigated. The discrete vortex method (DVM) was employed to evaluate the unsteady water flow fields and a Lagrangian approach was applied for tracking individual solid particles. A dispersion function was defined to represent the dispersion scale of the particle. The wake vortex patterns, the distributions and the time series of dispersion functions of particles with different Stokes numbers were obtained. Numerical results show that the particle distribution in the wake of the circular cylinder is closely related to the particle's Stokes number and the structure of wake vortices: (1) the intermediate sized particles with Stokes numbers, St, of 0.25, 1.0 and 4.0 can not enter the vortex cores and concentrate near the peripheries of the vortex structures, (2) in the circular cylinder wake, the dispersion intensity of particles decreases as St is increased from 0.25 to 4.0.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.     

Particle suspension in a simple shear flow

A hydrodynamic model describing the particle distribution over the cross-section of a finely dispersed flow is proposed. The model is constructed on the basis of notions concerning the diffusion of particles induced by their random displacements in the process of relative motion of neighboring layers at constant shear velocity. It is shown that the suspension capacity of the flow is large for small particles due to thermal fluctuations and for relatively large particles due to shear-induced particle pulsations. There are critical particle sizes for which the particles are suspended and transported by the flow less effectively than larger or smaller particles.Ekaterinburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 112–121, January–February, 1995.     

受限颗粒体对制动系统非线性振动的影响

制动系统在工作时,往往受到沙粒、尘土以及磨屑等受限颗粒体的影响,这些受限颗粒体在摩擦副中的高度分布具有较强的随机性,一定程度诱发了制动系统的非线性振动. 本文中基于制动片切向振动模型,引入了新的受限颗粒体摩擦模型,提出了用波动系数来描述受限颗粒体高度分布随机性的强弱. 发现在特定参数下,当此系数为0时,制动片切向振动为周期运动;但是当此系数不为0时,制动片切向振动呈现拟周期或混沌运动,此时的切向振动分岔特性图的稳定轨道也会出现数量或分布的变化,甚至表现出混沌特性. 同一时变信号内,受限颗粒体引发制动片切向非线性振动包括发散、收敛以及拟周期运动等多种形式.      

垂直旋转流场中单颗粒运动状态判别及受力分析

为研究单颗粒在旋转流场中的运动状态及受力情况,以毫米级球形颗粒为例,利用旋转流场颗粒运动装置,通过使用摄像机记录颗粒在流场中的运动轨迹以获取其运动参数,分析了不同转速和颗粒直径条件下颗粒的运动轨迹,拟合得到了颗粒运动状态判别公式以及颗粒运动轨迹公式,分析了颗粒在旋转流场中的受力情况。结果表明,颗粒在旋转流场平衡状态下运动状态主要分为两类,一类是未离开壁面保持静止,另一类是离开壁面保持稳定周向运动;颗粒进行周向运动的轨迹为椭圆形,并且圆心随着转速的增大靠近旋转中心,而随着粒径的增大靠近壁面;颗粒在旋转流场的运动过程中主要受到离心力和旋转科式力作用。     

Agglomeration of inertial particles in a random rotating symmetric straining flow

This paper is concerned with the development and validation of a simple Lagrangian model for particle agglomeration in a turbulent flow involving the collision of particles in a sequence of correlated straining and vortical structures which simulate the Kolmogorov small scales of motion of the turbulence responsible for particle pair dispersion and collision. In this particular study we consider the collision rate of monodisperse spherical particles in a symmetric (pure) straining flow which is randomly rotated to create an isotropic flow. The model is similar to the classical model of Saffman and Turner (S&T) (1956) for the collision (agglomeration) of tracer particles suspended in a turbulent flow. However unlike S&T, the straining flow is not frozen in time persisting only for timescales ∼Kolmogorov timescale. Furthermore, we consider the collision of inertial particles as well as tracer particles, and study their behavior not only at the collision boundary but also in its vicinity. In the simulation, particles are injected continuously at the boundaries of the straining flow, the size of the straining region being typical of the Kolmogorov length scale η_K of the turbulence. For steady state conditions, we calculate the flux of particles colliding with a test particle at the centre of the straining flow and consider its dependence on the inertia of the colliding particles (characterized by the particle Stokes number, St). The model replicates the segregation and accumulation observed in DNS and in particular the maximum segregation for St ∼ 1 (where St is the ratio of the particle response time to the Kolmogorov timescale). We also calculate the contributions of the various turbulent forces in the momentum balance equation for satellite particles and show for instance that for small Stokes number, there is a balance between turbulent diffusion and turbophoresis (gradient of kinetic stresses) which in turn is responsible for the build-up of concentration at the collision boundary. As found in previous studies, for the case of inertialess tracer particles, the collision rate turns out to be significantly smaller than the S&T prediction due to a lowering of the concentration at the collision boundary compared to the fully mixed value. The increase in collision rate for St ∼ 0.5 is shown to be a combination of particle segregation (build-up of concentration near the collision boundary) and the decorrelation of the relative velocity between the local fluid and a colliding particle. The difference from the S&T value for the agglomeration kernel is shown to be a consequence of the choice of perfectly absorbing boundary conditions at collision and the influence of the time scale of the turbulence (eddy lifetime). We draw the analogy between turbulent agglomeration and particle deposition in a fully developed turbulent boundary layer.     

Tracer particle generation in superfluid helium through cryogenic liquid injection for particle image velocimetry (PIV) applications

This paper reports the first experimental study of liquid neon injection into superfluid helium (He II) through a plain orifice atomizer to explore different means of introducing micron-size tracer particles into a He II bath for particle image velocimetry (PIV) applications. The obtained results verify that the direct injection of liquid neon into He II introduces seed particles into the He II bath. It is also demonstrated that the particle sizes can be controlled by changing the pressure above the injected liquid. Additionally, the size distribution of the particles is calculated from the PIV results through the use of the correlations to the standard drag curve.     

Heat transfer effects on particle motion under rarefied conditions

Gas–solid flows occurring on very small spatial scales (of the order of micro and nanometres) are of great relevance in a number of industrial applications. It is currently not well established how particle motion and filtration are affected by non-isothermal conditions at such scales. Furthermore, when the particle size is comparable to the mean free path of the gas, rarefaction effects become important. In the present work we investigate the effects of heat transfer and non-isothermal conditions on the motion of small particles in rarefied flow. For that purpose, a suitable framework is developed here as a generic multiphase DNS method for rarefied flows. The resulting model is valid for low particle Reynolds number flows, irrespective of the Biot number, and for particle Knudsen numbers up to unity in unbounded flow. Using this model, we show that there is different settling behaviour of particles with an internal heat source in rarefied and continuum cases of the carrier gas respectively. It is shown that the chances for thermal levitation and/or lifting up of a particle due to buoyancy effects are significantly reduced under rarefied conditions.     

Particle deposition in channels with permeablewalls

The filling of a channel with solid particles is considered in connection with the problem of preserving the geometry of a slot produced by hydraulic fracturing in a petroleum reservoir. The channel walls are permeable for the fluid. In the study, an experimental model of the channel (slot) in a permeable porous medium is used, on the periphery of which a constant pressure is sustained. The conditions of particle deposition on the permeable channel walls are determined. It is shown that in the case considered the initial stage of the particle deposition is independent of the viscosity and velocity of the fluid and is determined by the particle size and the specific permeability of the channel walls. It is found that the particles moving in the fluid stop at a certain distance and fill the fracture closely, forming a slug which loses stability as the pressure difference on its edges increases. The loss of the stability of the slug is accompanied by the appearance of a wavy channel, devoid of the particles and propagating in the flow direction.     

Limiting self-similar motion of a solid particle in a free-molecular gas flow escaping from an orifice

A problem of motion of a single spherical solid particle in the far wake of a free-molecular gas flow escaping from an orifice is considered. It is shown that the spatial distributions of macroscopic parameters of the gas are completely determined by functions of one variable: coordinate along an arbitrary straight line normal to the axis of symmetry. Based on this property, a dimensionless equation of particle motion is derived, which has self-similar solutions: trajectories of motion and particle coordinates (traces) on the target for different initial conditions. Conditions of determining the gas flow behavior on the basis of particle traces on the target are considered.     

双滑移转动率模型对椭圆散粒体的适用性

首先基于椭圆颗粒接触点的运动关系推导出新的平均纯转动率（APR）表达式,并将其引入到已有的描述圆形散粒体流动特性的双滑移转动率模型（DSR²模型）中;而后采用改进的NS2D离散元程序对长短轴比例分别为1.4和1.7的椭圆颗粒堆积体进行一系列不排水单剪试验,验证以椭圆颗粒为基础的离散元方法模拟砂土流动特性的可行性及DSR²模型的合理性。数值试验及已有成果表明,以椭圆颗粒为基础的NS2D程序能够模拟砂土的流动特性,对圆形和椭圆形颗粒体系,DSR²模型均能很好地预测运动模型中转动率参量的变化情况;APR是联系连续介质力学和离散介质力学的重要参数,它将二者有机结合成一个整体。