Image processing for the study of bedload transport of two-size spherical particles in a supercritical flow

Bedload sediment transport of two-size coarse spherical particle mixtures in a turbulent supercritical flow was analyzed with image and particle tracking velocimetry algorithms in a two-dimensional flume. The image processing procedure is entirely presented. Experimental results, including the size, the position, the trajectory, the state of movement (rest, rolling, and saltation), and the neighborhood configuration of each bead, were compared with a previous one-size experiment. Analysis of the solid discharge along the vertical displayed only one peak of rolling in the two-size bed, whereas three peaks of rolling appeared in the one-size case due to a larger collective motion. The same contrast is evidenced in spatio-temporal diagrams where the two-size mixtures are characterized by the predominance of saltation and a smaller number of transitions between rest and rolling. The segregation of fine particles in a bed formed by larger particles was analyzed taking into account the neighborhood configurations.     

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.     

Effects of vibrations on particle motion near a wall: Existence of attraction force

The effects of small vibrations on a particle oscillating near a solid wall in a fluid cell, relevant to material processing such as crystal growth in space, have been investigated experimentally and theoretically. Assuming the boundary layer around the particle to be thin compared to the particle radius at high vibration frequencies, an inviscid fluid model was developed to predict the motion of a spherical particle placed near a wall of a rectangular liquid-filled cell subjected to a sinusoidal vibration. Under these conditions, a non-uniform pressure distribution around the particle results in an average pressure that gives rise to an attraction force. Theoretical expressions for the attraction force are derived for the particle vibrating normal to and parallel with the nearest cell wall. The magnitude of this attractive force has been verified experimentally by measuring the motion of a steel particle suspended in the fluid cell by a thin wire. Experiments performed at high frequencies showed that the mean particle position, when the particle is brought near a cell wall, shifts towards the same wall, and is dependent on the cell amplitude and frequency, particle and fluid densities.     

Sand particle dislodgement in windblown sand

The incipient motion of sand particle from sand bed plays a very important role in the prediction of windblown sand.In this paper,we proposed a new method for predicting the incipient motion of sand particle based on wind speed fluctuation as follows,when the wind speed is larger than the critical wind speed,if the total impulse on sand particle is larger than the critical impulse,incipient motion of sand particle would take place,otherwise if not.Furthermore,from the analysis of entrainment in the rolling and lifting modes,we come to the following conclusion.When the average wind speed is smaller than the critical wind speed,if the average wind speed is used to judge the incipient motion of sand particle,one will underestimate the number of sand particles jumping from the bed,if the instantaneous wind speed is used to judge incipient motion of sand particle,one will overestimate the number of sand particles jumping from the bed;When the average wind speed is larger than the critical wind speed,either the average or the instantaneous wind speeds is used to judge the incipientmotion of sand particles,one will overestimate the number of sand particles jumping from the bed.     

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.     

Rolling/sliding of a particle on a flat wall in a linear shear flow at finite Re

Recently Lee and Balachandar proposed analytically-based expressions for drag and lift coefficients for a spherical particle moving on a flat wall in a linear shear flow at finite Reynolds number. In order to evaluate the accuracy of these expressions, we have conducted direct numerical simulations of a rolling particle for shear Reynolds number up to 100. We assume that the particle rolls on a horizontal flat wall with a small gap separating the particle from the wall (L = 0.505) and thus avoiding the logarithmic singularity. The influence of the shear Reynolds number and the translational velocity of the particle on the hydrodynamic forces of the particle was investigated under both transient and the final drag-free and torque-free steady state. It is observed that the quasi-steady drag and lift expressions of Lee and Balachandar provide good approximation for the terminal state of the particle motion ranging from perfect sliding to perfect rolling. With regards to transient particle motion in a wall-bounded shear flow it is observed that the above validated quasi-steady drag and lift forces must be supplemented with appropriate wall-corrected added-mass and history forces in order to accurately predict the time-dependent approach to the terminal steady state. Quantitative comparison with the actual particle motion computed in the numerical simulations shows that the theoretical models quite effective in predicting rolling/sliding motion of a particle in a wall-bounded shear flow at moderate Re.     

Solid transport measurements through image processing

The paper describes a novel technique which enables evaluation of sediment fluxes on the upper layer of a granular bed by means of separate measurements of concentration and velocity of the moving particles. Specific elaboration techniques based on digital image processing were applied to films of the solid fluxes, allowing for automatic measurement. Sediment concentration was measured via a technique based on image subtraction and following proper filtering procedures, while grain velocity was measured by Particle Image Velocimetry. The method was applied in laboratory experiments of one dimensional bed load; the solid discharges measured by the proposed image processing technique were compared to those obtained by manual count of the grains passing over a fixed plate used as a sight. After calibration of the automatic technique, dimensionless solid discharges ranging from 1.0 × 10⁻³ to 1.2 × 10⁻¹ were measured with a maximum error as large as 25%. The technique proposed also enables measurement of the time variation of the quantities and the two dimensional direction of sediment motion, for a complete characterization of grain kinematics in solid transport processes.     

Sediment-discharge vector in a turbulent flow above an eroded bottom

The problem of determination of sediment discharge by a turbulent flow of a fluid above an eroded surface of an arbitrary relief with a finite slope of the bottom is considered. The surface of the bottom separates a stationary granular medium (sand) from a moving two-phase mixture of a fluid and solid particles. The medium is set into motion under the action of shear stress of the fluid. The medium obeys Coulomb's friction law for a granular medium and Prandtl's law of turbulent friction of the fluid. As a result of solving the boundary-value problem for the motion of a two-phase mixture of a fluid and solid particles, a generic formula for sediment discharges is derived. The sediment-discharge vector is expressed through the vector of shear stress on the bottom, the vector of the slope of the bottom, and the distribution function of the solid particles in the bottom layer for an arbitrary relief of the bottom with a finite slope. It is shown that the sediment discharge depends weakly on the detailed distribution of particles in the bottom layer. Conditions of failure of the bottom surface are obtained. The sediment-discharge formula allows one to derive a closed system of equations that determines the process of bottom erosion in the river or channel bed. Institute Problems of Mechanics, Russian Academy of Sciences, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 102–112, March–April, 2000.     

Solids behavior in dilute zone of a CFB riser under turbulent conditions

The behavior of the solid phase in the upper zone of a circulating fluidized bed riser was studied using a phase Doppler anemometer. Glass particles of mean diameter 107 μm and superficial gas velocities U_g covering the turbulent and the beginning of the fast fluidization regime were investigated. Three static bed heights were tested. Ascending and descending particles were found co-existing under all operating conditions tested, and at all measurement locations. Superficial gas velocity proved/happened to have a larger effect on descending particles at the wall and on ascending particles in the central region. Transversal particle velocities in both directions (toward the center and toward the wall) behaved relatively equivalently, with only slight difference observed at the wall. However, observation of the number of particles moving in either transversal direction showed a change in bed structure when increasing U_g. Furthermore, a balance was constantly observed between the core zone and the annulus zone where the mutual mass transfer between these two zones occurred continuously. Transition from a slow to a fast particle motion was accompanied by a transition to high levels of velocity fluctuations, and was found corresponding to the appearance of significant solid particle flow rate.     

A finite difference self-adaptive mesh solution of flow in a sedimentation tank

A new numerical model has been developed to evaluate the removal efficiency of primary sedimentation clarifiers operating at neutral density condition. The velocity and concentration fields as well as the development in time and space of the settled particle bed thickness are simulated. The main difficulties in simulation of velocity and concentration fields are related to (1) numerical instabilities produced by the prevalence of convective terms in the unknown variable high-gradient regions and (2) turbulence effects on the suspension of solid particles from the settled bed. The need to overcome the numerical instabilities without the upwind difference approximation, which introduces high numerical viscosity, suggests the use of non-uniform grids of calculation. The velocity field is obtained by solving the motion equations in the vorticity and streamfunction formulation by means of a new numerical method based upon a dynamically self-adjusting calculation grid. These grids allow for a finer mesh following the evolution of the unknown quantities. A k–? model is used to simulate turbulence phenomena. The sedimentation field is found by solving the diffusion and transport equation of the solid particle concentration. Boundary conditions on the bottom line are imposed relating the amount of turbulence flux and sedimentation flux to the actual concentration and the reference concentration. Such an approach makes it possible to represent the solid particle suspension from the bottom, taking into account its dependence on (1) the characteristics and the evolution in time of the settled bed, (2) the velocity component parallel to the bottom line and (3) the turbulence structure.     

基于碰撞模型的斜坡滚石颗粒速度预测

滑坡滚石灾害是西部山区常见的地质灾害类型,具有突发性和随机性强的特点,是山区地质灾害预测和防治工作的重点和难点. 本文基于颗粒接触理论,考虑影响斜坡滚石碰撞过程中的随机因素,建立了用于预测斜坡滚石颗粒碰撞后速度的理论模型. 根据冲量及冲量矩定理建立滚石颗粒碰撞基本方程,得到斜坡滚石颗粒碰撞后反弹速度的解析解. 结果表明:斜坡滚石碰撞后反弹速度的解析解包含了坡角、坡体上被碰颗粒速度以及角度、入射速度和角度以及撞击角度等随机因素;当考虑入射滚石颗粒与坡体上被碰颗粒的撞击角度变化时,模型预测结果与试验结果吻合较好;本文进一步预测了滚石颗粒碰撞后颗粒反弹线速度和角度以及反弹旋转角速度的概率分布情况. 结果显示,反弹颗粒速度和角度以及反弹旋转角速度的概率分布均服从高斯分布;当坡体上被碰颗粒速度和坡角发生变化时,其对反弹颗粒速度和角度以及反弹旋转角速度概率分布定性上没有影响,但是对概率分布的中心参数有显著影响.      

CFD-DEM simulation of spouting of corn-shaped particles

Three dimensionally coupled computational fluid dynamics (CFD) and discrete element method (DEM) were used to investigate the flow of corn-shaped particles in a cylindrical spouted bed with a conical base. The particle motion was modeled by the DEM, and the gas motion by the k-? two-equation turbulent model. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas–particle interactions in terms of momentum exchange. The corn-shaped particles were constructed by a multi-sphere method. Drag force, contact force, Saffman lift force, Magnus lift force, and gravitational force acting on each individual particle were considered in establishing the mathematical modeling. Calculations were carried out in a cylindrical spouted bed with an inside diameter of 200 mm, a height of 700 mm, and a conical base of 60°. Comparison of simulations with experiments showed the availability of the multi-sphere method in simulating spouting action with corn-shaped particles, but it depended strongly on the number and the arrangement of the spherical elements. Gas–solid flow patterns, pressure drop, particle velocity and particle concentration at various spouting gas velocity were discussed. The results showed that particle velocity reaches a maximum at the axis and then decreases gradually along the radial direction in the whole bed. Particle concentration increases along the radial direction in the spout region but decreases in the fountain region, while it is nearly constant in the annulus region. Increasing spouting gas velocity leads to larger pressure drop, remarkably increased speed of particle moving upward or downward, but decreased particle concentration.     

Experimental analysis of volatile liquid injection into a fluidized bed

Experiments were conducted on a lab-scale fluidized bed to study the distribution of liquid ethanol injected into fluidized catalyst particles. Electrical capacitance measurements were used to study the liquid distribution inside the bed, and a new method was developed to determine the liquid content inside fluidized beds of fluid catalytic cracking particles. The results shed light on the complex liquid injection region and reveal the strong effect of superficial gas velocity on liquid distribution inside the fluidized bed, which is also affected by the imbibition of liquid inside particle pores. Particle internal porosity was found to play a major role when the changing mass of liquid in the bed was monitored. The results also showed that the duration of liquid injection affected liquid–solid contact inside the bed and that liquid–solid mixing was not homogeneous during the limited liquid injection time.     

Nondestructive evaluation of plastic deformation in AA6061 aluminum alloy by electromagnetic discharge image

The electromagnetic discharge imaging (EDI) technique is combined with image analysis methods and used as a nondestructive method to evaluate the amount of plastic deformation of AA6061 aluminum alloy. Various amounts of plastic deformation was introduced mechanically by cold rolling on specimens having identical surface conditions to the specimen. Since the EDI discharge characteristics and intensity are affected by plastic deformation, the results can be used as a correlation. It is shown that the EDI discharge intensity increases with increasing rolling ratio up to 25% and reaches a saturation limit, beyond which the discharge intensity is inversely proportional to the rolling ratio. Since the changes of the internal energy and the electrical properties of the specimen caused by cold rolling has opposing effects on the EDI discharge intensity. That would eventually be saturated. Further analysis shows that the high intensity region of EDI discharge pattern is increased from 0–10% rolling ratio and then from 30% and up. As the AC frequency increased, the discharge intensity becomes proportional to the increase rolling ratio.     

Drying of suspensions and solutions on inert particle surface in mechanically spouted bed dryer

To eliminate some disadvantages of the conventional spouted bed dryers the mechanically spouted bed （MSB） system was developed. This dryer type is convenient to use inert particles providing an increased surface area for drying of materials of high-moisture content and heat sensitive materials. On three different drying tasks are demonstrated the experimental optimization of process parameters to obtain products of demanded quality. The main object was at drying of AIO（OH） suspension to preserve the particle size under 2.5μm and to obtain product with a moisture content of about 0.05 kg/kg （d.b.）. For this reason a very thin particle coating and intensive abrasion had to be assured. At drying of tomato concentrates the thermoplasticity makes the process very difficult. To jump over the deliquescent and sticky state developed at the critical temperature-moisture content values a very short drying time （8-10 s） must be provided. The third task was to form powder-like product from bovine serum albumin （BSA） solution having very low solid content （2-4%）. The selected process parameters given in this paper resulted in a mean particle size of less than 20 μm while the soluble oreserved orotein content was higher than 90%.     

Hydrodynamics of gas-solid fluidization of a homogeneous ternary mixture in a conical bed： Prediction of bed expansion and bed fluctuation ratios

Hydrodynamic characteristics of fluidization in a conical or tapered bed differ from those in a columnar bed because the superficial velocity in the bed varies in the axial direction. Fixed and fluidized regions could coexist and sharp variations in pressure drop could occur, thereby giving rise to a noticeable pressure drop-flow rate hysteresis loop under incipient fluidization conditions. To explore these unique properties, several experiments were carried out using homogeneous, well-mixed, ternary mixtures with three dif- ferent particle sizes at varying composition in gas-solid conical fluidized beds with varying cone angles. The hydrodynamic characteristics determined include the minimum fluidization velocity, bed fluctuation, and bed expansion ratios. The dependence of these quantities on average particle diameter, mass fraction of the fines in the mixture, initial static bed height, and cone angle is discussed. Based on dimensional analysis and factorial design, correlations are developed using the system parameters, i.e. geometry of the bed （cone angle）, particle diameter, initial static bed height, density of the solid, and superficial velocity of the fluidizing medium. Experimental values of minimum fluidization velocity, bed fluctuation, and bed expansion ratios were found to agree well with the developed correlations.     

Capillary effects on a particle rolling on a plane surface in the presence of a thin liquid film

An experimental study has been performed of the effects of a liquid film on a particle rolling on a planar surface using a combination of laser-induced fluorescence and particle-image velocimetry. Contact angle hysteresis leads to asymmetry of the liquid meniscus, resulting in a difference in contact angle between the front and rear sections of the meniscus relative to the rolling particle. This asymmetry results in a capillary torque that resists the rolling motion of the particle. The particle rolling motion also induces a viscous transport of fluid from the front to the rear of the particle, which acts to shift the location of the contact point. The laser-induced fluorescence method is used to characterize the meniscus asymmetry and the resulting change in contact angle on the two sides of the particle. Particle-image velocimetry in various horizontal and vertical cross-sectional planes is used to examine the flow trajectories and velocity magnitude within the meniscus in the presence of rolling. All experiments are conducted at small capillary number, so that the meniscus is approximately circular in shape.     

The effect of column tilt on flow homogeneity and particle agitation in a liquid fluidized bed

The motion of particles in a solid-liquid fluidized bed was experimentally studied by video tracking of marked particles in a matched refractive index medium. In this study, two fluidized states are compared, one carefully aligned in the vertical direction ensuring a homogeneous fluidisation and another one with a non-homogeneous fluidisation regime that results from a slight tilt of the fluidisation column of 0.3° with respect to the vertical. As a result of the misalignment, large recirculation loops develop within the bed in a well-defined spatial region. It is found that in that range of solid fraction (between 0.3 and 0.4), the inhomogeneous motion of the particles leads to significant differences in velocity fluctuations as well as in self-diffusion coefficient of the particles in the vertical direction, whereas the fluidisation height remains unaffected. At lower (less than 0.2) or higher (higher than 0.5) concentration, particle agitation characteristics are almost unchanged in the vertical direction.     

Stability of the rectilinear motion of a railway Wheelset

A railway wheelset rolling on rails without slip is studied with consideration of the creep hypothesis. The wheelset is represented by two cones having a common base; the rails are represented by two circular cylinders with parallel axes. The kinematic characteristics of undisturbed rolling for the wheelset are determined when its center of mass moves along a straight line; these characteristics are also determined in the case of disturbed motion when the mass center of the wheelset moves along a sinusoidal trajectory. For these modes of motion, the constraint reactions are found with an accuracy up to the second order of smallness with respect to the values of disturbed variables. When the absolutely rigid point contact is replaced by the elastic contact, the creep hypothesis is used, the method of averaging with respect to the fast variables is applied, and a critical velocity above which the rectilinear rolling becomes unstable is determined on the basis of the averaged equations.     

Effect of rolling friction on wall pressure,discharge velocity and outflow of granular material from a flat-bottomed bin

The present paper provides both experimental and DEM analyses of the filling and discharge of pea grains from a 3D flat-bottomed bin. In the DEM model, the fixed mean values of the experimentally determined single particle data, such as the particle density, Young's modulus, Poisson's ratio as well as the sliding and rolling friction coefficients were incorporated to analyse their effects on the macroscale indicators, such as the wall pressure, discharge velocities and material outflow parameters. The effect of rolling friction was studied based on the experimentally measured single particle rolling friction coefficient. This analysis is aimed at the quantitative prediction of flow parameters as related to the identification of material parameters.