Film flow of a suspension down an inclined plane

A method is developed for simulating the film flow of a suspension of rigid particles with arbitrary shapes down an inclined plane in the limit of vanishing Reynolds number. The problem is formulated in terms of a system of integral equations of the first and second kind for the free-surface velocity and the traction distribution along the particle surfaces involving the a priori unknown particle linear velocity of translation and angular velocity of rotation about designated centres. The problem statement is completed by introducing scalar constraints that specify the force and torque exerted on the individual particles. A boundary-element method is implemented for solving the governing equations for the case of a two-dimensional periodic suspension. The system of linear equations arising from numerical discretization is solved using a preconditioner based on a particle-cluster iterative method recently developed by Pozrikidis (2000 Engng Analysis Bound. Elem. 25, 19-30). Numerical investigations show that the generalized minimal residual (GMRES) method with this preconditioner is significantly more efficient than the plain GMRES method used routinely in boundary-element implementations. Extensive numerical simulations for solitary particles and random suspensions illustrate the effect of the particle shape, size and aspect ratio in semi-finite shear flow, and the effect of free-surface deformability in film flow.     

Capillary attraction of floating rods

The capillary attraction of two parallel cylinders with circular cross-section representing slender particles floating at the interface between two immiscible fluids is considered. Given the particle separation, the elevation of the particle centers in hydrostatics is computed to satisfy the vertical force balance involving the buoyancy force, the capillary force, and the particle weight. A numerical procedure is developed for calculating the horizontal force exerted on a pair of cylinders in solitary or periodic arrangement. The results confirm that the particles attract each other under the conditions considered. The particle motion and transient flow due to the particle attraction are computed using a boundary-integral method for Stokes flow. In the algorithm, the particle center velocity of translation and angular velocity of rotation are calculated to satisfy force and torque balances. Numerical simulations using a boundary-element method subject to an initial state provided by hydrostatics illustrate the nature of the motion and furnish estimates for the particle velocity induced by capillarity.     

喷涂工艺条件对超音速火焰喷涂Cr3C2-NiCr粒子速度的影响

运用热辐射法测定了超音速火焰喷涂Cr3C2-NiCr粒子速度,研究了燃气流量、氧气流量和喷涂距离对粒子速度的影响规律,结果表明,燃气流量、氧气流量对粒子速度具有显著影响,当燃气流量在37～46L/min范围内增加,氧气流量在368～447L/min范围内增加时,粒子速度上升显著.适中的氧气流量有利于获得较高的粒子速度.粒子速度随喷涂距离呈现先增加后减小的变化规律,粒子的加速过程主要在距枪口160mm的范围内进行.     

The movement law and orientation control of rectangular particles in the viscous fluid domain based on IS-FEM

Understanding the movement law and orientation control mechanism of non-spherical particles are significant for industrial applications. In this work, the flow characteristics of rectangular particles, in the uniform and wedge viscous fluid domain, are simulated by the immersed smoothed finite element method (IS-FEM). The influences of mesh resolution and time-step on particle velocity are analyzed, and the numerical procedure is validated by the published model and sedimentation experiments. The operating parameters that affect the particle flow are systematically studied, including Reynolds number, initial angle, channel offset distance, and aspect ratio. Moreover, the particle angles are adjusted by the velocity gradient of fluid domains. The result indicates that the velocities, angle, and drag of rectangular particles are closely related to the working conditions. The long axis of rectangular particles is consistent with the flow direction in shrinking fluid domains and is perpendicular to the flow direction in expanding fluid domains. The angle distribution law of rectangular particles in moving wedge fluid domains is determined. These findings provide a theoretical foundation for particle sedimentation and suspension flow, which is helpful for the further separation and orientation control of mixed particles.     

Interception of two spherical drops in linear Stokes flow

A boundary-integral method is developed for computing the interception of two spherical drops with arbitrary radii and viscosities in infinite linear Stokes flow. At any instant, the flow is computed in a frame of reference with origin at the center of one drop, using a cylindrical polar coordinate system whose axis of revolution passes through the center of the second drop. Taking advantage of the axial symmetry of the interfaces in the drop coordinates, the problem is formulated as a system of integral equations for the zeroth, first, and second Fourier coefficients of the normal component of the jump in the interfacial traction and for the meridional and azimuthal components of the interfacial velocity with respect to the meridional angle. The integral equations are solved with high accuracy using a boundary-element method featuring adaptive boundary-element distribution and automatic time-step adjustment according to the interfacial gap. Simulations of two drops intercepting in uniaxial straining flow provide accurate data on the drop collision velocity and particle stress tensor for gaps as small as 10⁻⁴ times the drop radius. Simulations of two drops intercepting in simple shear flow confirm that slightly offset drops collide during the interception. Accurate data are presented for Batchelor’s relative mobility functions in linear Stokes flow used to describe the relative droplet motion.     

Motion of a spherical particle inside a liquid film

The motion of a spherical particle inside a liquid film coated on a plane wall is considered under conditions of Stokes flow in the limit of vanishing capillary number where the interfacial deformation is infinitesimal. The problem is formulated in terms of a system of one-dimensional integral equations for the velocity and traction Fourier coefficients along the trace of the interface, wall, and particle contour in a meridional plane, and the solution is found using a boundary-element method. Comprehensive results for the force and torque resistance coefficients are presented in the case of particle rotation and translation in quiescent fluids. The velocity of translation and angular velocity or rotation of a freely suspended particle in simple shear flow are computed and discussed over a broad range of conditions.     

大悬浮轻颗粒固液两相流中的有序结构

应用三维颗粒图像跟踪技术,对竖直管内向上大悬浮轻颗粒固液两相流中分散相即颗粒相瞬时分布进行非接触测量,由此对顺流方向颗粒串组成的有序相分布结构进行观察研究.实验发现,当液体流动速度大于某一确定值时会有明显的颗粒串出现,此时颗粒由于受液体速度梯度诱导的强升力作用而紧贴管壁运动;随着液体流动速度的降低,颗粒串逐渐消失而颗粒沿管径向的分布会向着管中心方向发展;当液流速度进一步降低,颗粒开始在水平方向团聚.分析表明液体流动的剪切作用是颗粒串生成和稳定的机制.实验还显示,随着颗粒相平均份额的增加,流动中串间颗粒的相互作用加强,颗粒分布结构也随之受到影响.     

A NUMERICAL MODEL FOR STEADY NONPOINT SOURCE DISPERSION OF WIND-BLOWN FINE PARTICLES FROM STORAGE PILES AND EXPERIMENTAL STUDY

This study is concerned with modeling of the loss of fine dust from storage piles and their dispersion in the atmosphere. The results of downwind particulate dispersion are tested by means of a two-dimensional wind tunnel model using tracer particles. The study shows that a wind barrier located two to three pile heights upstream will effectively reduce the wind blowing of fine particles from storage piles and the downwind particle density. The tracers used in the experiment are smoke, magnesia, latex, and glass particles. The particle sizes studied range from 15 μm to 75 μm. Experimental results indicate that the effects of particle settling due to gravity force will be negligible when the particle settling velocity is less than 0.03 m/s. If particle size is less than 15 μm, particles will most likely remain in a suspension state over a long distance. Finite difference techniques are used for steady state numerical simulation of particulate dispersion. The effects of the particle sizes, wind velocity, and the ground conditions on the downwind particle density distribution are presented.     

Hydrodynamics of granular gases of viscoelastic particles

Our study examines the long-time behaviour of a force-free granular gas of viscoelastic particles, for which the coefficient of restitution depends on the impact velocity, as it follows from the solution of the impact problem for viscoelastic spheres. Starting from the Boltzmann equation, we derived the hydrodynamic equations and obtained microscopic expressions for the transport coefficients in terms of the elastic and dissipative parameters of the particle material. We performed the stability analysis of the linearized set of equations and found that any inhomogeneities and vortices vanish after a long time and the system approaches the flow-free stage of homogeneous density. This behaviour is in contrast to that of a gas consisting of particles which interact via a (non-realistic) constant coefficient of restitution, for which inhomogeneities (clusters) and vortex patterns have been proven to arise and to continuously develop.     

Particle Transport and Deposition in a Duct Flow with a Rectangular Obstruction

The airflow field and particle trajectory and deposition in a duct with a rectangular obstruction were studied. The governing conservation equations of mass and momentum were discretized using a finite volume method, and the corresponding velocity vector and pressure fields were evaluated. The particle trajectories were evaluated by solving the Lagrangian equation of motion that included the drag, Saffman's lift, and gravity forces. Effects of different forces as well as the blockage and the obstruction aspect ratios on particle trajectory and deposition were analyzed for a Reynolds number of 200. The simulation results showed that with the increase of Stokes number, particle deposition efficiency on the front side of the obstruction increased and also the presence of the gravitational force in the span-wise direction caused the particles to be deposited on the channel lower wall. The presence of gravity in the stream-wise direction increased the deposition efficiency and in the counter-stream-wise direction decreased the deposition efficiency. Changing the obstruction aspect ratio had no noticeable effect on the deposition but increasing the blockage ratio increased the deposition efficiency. The presence of a lift force had different effects for different blockage ratios and Stokes numbers. But the lift force generally increased the deposition rate, especially at large Stokes numbers and large blockage ratios.     

Analyzing irreversibilities in Stokes flows containing suspended particles using the traction boundary integral equation method

Irreversibilities in suspension flows at low Reynolds numbers have been observed experimentally. These irreversibilities can lead to particle migration, normal stress differences, and complex microstructure including particle chains and agglomerations. The morphology of the microstructure formation and the relationship of the microstructure to the continuum properties of the suspension are current topics of research interest. Detailed information concerning the microstructure is hard to obtain experimentally, and hence, accurate numerical simulation capabilities are becoming relied on more heavily to fill the gap between the mesoscale and continuum properties. In this research, a traction boundary integral equation (TBIE) method is used to analyze irreversibilities in Stokes flow containing suspended particles. The TBIE is particularly well-suited for this type of analysis since the associated discretized sets of linear equations are better conditioned than the more prevalent velocity boundary integral equation (VBIE) method especially as particles tend to aggregate.     

Optical Probe for the In-Line Determination of Particle Shape, Size, and Velocity

A laboratory optical probe was developed to simultaneously determine the following particle characteristics: circularity, particle projection area, equivalent diameter of a circle, length of the particle outline or perimeter, maximum chord length, aspect ratio, and particle velocity. Using the projection area and the perimeter, the particle shape factor circularity can be determined. The aspect ratio was approximated by the ratio of the equivalent diameter to the maximum chord length. The basic measuring principle is multi-point scanning of the particle shadow image by a line of optical fibers. In addition, the particle velocity can be measured by a differential spatial filter of optical fibers. These fibers are step index fibers with a core diameter of 64 µm and cladding of 70 µm. The shadow image of a single particle was generated by a parallel laser beam. The uncertainty of the measured circularity and aspect ratio was investigated by using metal wires with diameters of 0.12 to 0.5 mm as test particles with known circularity and aspect ratio. The standard deviations were 1.9% for the circularity and 15.5% for the approximated aspect ratio. In addition, the optical probe system was investigated by measurements of solid particles with different shapes. As an example, the results of sand, marjoram seed, and metallic oxide particles are shown. Using 1000 sand particles, the correlation between equivalent diameter and particle velocity could be demonstrated. The presented configuration of the optical probe is applicable in the size range of 0.1 to 0.9 mm and up to a particle velocity of 5 m/s.     

Optical Probe for the In-Line Determination of Particle Shape,Size, and Velocity

A laboratory optical probe was developed to simultaneously determine the following particle characteristics: circularity, particle projection area, equivalent diameter of a circle, length of the particle outline or perimeter, maximum chord length, aspect ratio, and particle velocity. Using the projection area and the perimeter, the particle shape factor circularity can be determined. The aspect ratio was approximated by the ratio of the equivalent diameter to the maximum chord length. The basic measuring principle is multi-point scanning of the particle shadow image by a line of optical fibers. In addition, the particle velocity can be measured by a differential spatial filter of optical fibers. These fibers are step index fibers with a core diameter of 64 µm and cladding of 70 µm. The shadow image of a single particle was generated by a parallel laser beam. The uncertainty of the measured circularity and aspect ratio was investigated by using metal wires with diameters of 0.12 to 0.5 mm as test particles with known circularity and aspect ratio. The standard deviations were 1.9% for the circularity and 15.5% for the approximated aspect ratio. In addition, the optical probe system was investigated by measurements of solid particles with different shapes. As an example, the results of sand, marjoram seed, and metallic oxide particles are shown. Using 1000 sand particles, the correlation between equivalent diameter and particle velocity could be demonstrated. The presented configuration of the optical probe is applicable in the size range of 0.1 to 0.9 mm and up to a particle velocity of 5 m/s.     

Computation of Stokes Flow due to the Motion or Presence of a Particle in a Tube

The computation of Stokes flow due to the motion or presence of a rigid particle in a fluid-filled tube with arbitrary geometry is discussed with emphasis on the induced upstream to downstream pressure change. It is proposed that expressing the pressure change as an integral over the particle surface involving (a) the a priori unknown traction, and (b) the velocity of the pure-fluid pressure-driven flow, simplifies the numerical implementation and ameliorates the effect of domain truncation. Numerical computations are performed based on the integral formulation in conjunction with a boundary-element method for a particle translating and rotating inside a cylindrical tube with a circular cross-section. The numerical results are consistent with previous asymptotic solutions for small particles, and complement available numerical solutions for particular types of motion     

The Prediction of the Emissivity and Thermal Conductivity of Powder Beds

The particle size distribution and packing (loose bulk and tapped density) of a mixture of ground biomass from Douglas fir wood particles was characterized by different practical methods: sieving, digital imaging and scanning electron microscopy. The ground mixture was analyzed using a set of 14 wire mesh sieves. The calculated mean diameter of mixture was 251 µm. The mixture was divided into four size fractions of mean size ranging from 74 to 781 µm. Particle length measured by imaging technique were 3–4 times larger than the mean diameter determined by sieve analysis. Similarly, particle width was 1.0–2.5 times larger than mean particle diameter. The sphericity of particles in each of the four fractions increased with decreasing size of the sieve indicating that smaller particles also have a smaller aspect ratio. Empirical power law equations were developed to correlate the packing and flow ability of ground particles (HR) to the mean diameter, with R² values of 0.88 and 0.91, respectively. The HR values indicated good flow ability for the large particles and poor flow ability for the smallest particles and the entire mixture. HR and porosity ratio reached an asymptote for particles larger than 400 µm.     

Zweiphasenströmung in Kreiselpumpen für den hydraulischen Feststofftransport

A mathematical model of the trajectories of fluid and particles is developed based on the two dimensional equations of motion in plane flow for the impeller and the casing. The set of differential equations for plane flow is solved numerically using a 4th order Runge–Kutta method using the velocity profile of the fluid and the velocity components of the particles at the inlet of the impeller as initial conditions. The strong effect of the particle density ?_S and of the particle diameter d_S on the particle trajectory is analysed. Based on the solution of the equations of motion of both phases in the impeller and in the casing the velocity ratio of particles and fluid is calculated.     

Numerical simulation of aerosol collection in filters with staggered parallel rectangular fibres

 In this paper, filters with rectangular fibres arranged in a staggered and parallel array and placed transverse to the flow are studied numerically. A two- dimensional flow field is obtained by solving Navier–Stokes equations with the control volume method. Periodic boundary conditions are introduced in the calculation. In order to achieve higher accuracy, a second-order upwind scheme is adopted and a fine mesh is arranged near the fibre and the symmetrical plane of the flow field where large gradients in velocity are expected. Particle trajectories are calculated by solving the corresponding Lagrangian equation of motion to obtain the collection efficiency of a single rectangular fibre, in which positions of the approaching particles on the inlet plane of the flow field are randomly distributed according to the Monte-Carlo principle. The simulation considers all the important mechanisms of particle capture including interception, inertial impaction and Brownian motion. Effects of fibre aspect ratio, filter packing density, particulate size and Reynolds number on the collection efficiency are numerically determined. The volumetric packing density ranges from 0.4 to 4% and the particle diameter is from 0.01 μm to 2 μm. Reynolds number based on the height of computational domain varies from 20 to 100 and the aspect ratio is from 0.1 to 10. Simulations with and without Brownian motion are carried out for different Reynolds numbers, packing densities and aspect ratios and the results show that Brownian effects are significant for particles smaller than 1 μm. Received 25 May 2001     

Particle Detachment from Rough Surfaces in Turbulent Flows: An Analytical Expression for Resuspension Fraction

The critical shear velocity for resuspension of micrometer size particles from rough surfaces was studied. The random variation of surface roughness was accounted for. The recently developed Monte Carlo simulations accounted for the statistical variations of physical parameters that control the particle resuspension process. A sensitivity analysis showed that the surface roughness and its random variation was the key factor affecting the particle resuspension from rough surfaces. The theory of probabilistic transformation was used and an analytical expression for evaluating the resuspension fraction of particles of different sizes from rough surfaces versus the shear velocity was developed. The resuspension fractions as predicted by the analytical model were evaluated for several particles sizes for a range of turbulent flow shear velocities. The resulting resuspension fractions were compared with those obtained from the Monte Carlo simulations as well as the available experimental data. It was found that the predictions of the new analytical equation were in good agreement with the Monte Carlo simulation results and the experimental data, especially for smaller size particles. This new analytical expression could be used as a simple empirical equation for estimating flow-induced resuspension of particles from rough surfaces.     

Yttria-stabilized zirconia in-flight particle characteristics under vacuum plasma spray conditions

This paper deals with the diagnostic yttria-stabilized zirconia (YSZ) in-flight particles in Vacuum Plasma Spray (VPS) process using an optical measurement device. Particle velocity, temperature and diameter were correlated to spray distance under a fixed chamber pressure of about 14 kPa. Experiments were carried out with a two-color pyrometer. Results show that correlations can be satisfactory described with linear relationships. Particle velocity and temperature decrease when increasing spray distance whereas particle diameter exhibits a linear increase with the spray distance.     

Statistical description of a turbulent gas suspension flow of large particles colliding with channel walls

Based on the particle distribution density function method over space, velocity, and angular rotational velocity, a closed system of equations for the first and second moments of the fluctuations of the characteristics of the particles and boundary conditions representing the process of the loss of momentum and onset of rotation of the particles caused by collisions with walls are found.