The Hydrodynamics and Heat and Mass Transfer of Particles under Conditions of Turbulent Flow of Gas Suspension in a Pipe and in an Axisymmetric Jet

A mathematical model for the calculation of the hydrodynamic and thermal parameters of dispersed impurity in a round pipe and in a jet is given in Eulerian variables. The model is based on a unified set of equations describing the turbulent characteristics of particles in nonisothermal flow and of boundary conditions representing the interaction of the particles with the rough channel surface and the boundary of submerged jet. The effect of the anisotropy of turbulent fluctuations of the particle velocity and of the correlation between the thermal properties of the particle material and carrier gas on the intensity of momentum, heat, and mass transfer in the dispersed phase is investigated. The calculation results are compared with the experimental data.     

Deposition of solid particles in laminar boundary layer on a flat plate

Results are given of experimental and theoretical investigation of deposition of small solid particles on the surface of a flat plate under conditions of vertical laminar boundary layer. The present investigation is aimed at qualitatively and quantitatively estimating the effect made by the parameters of two-phase flow of the “gas—solid particles” type and by the adhesive properties of particles and surface on the deposition of particles on the plate surface. The flow velocity is 1.5 and 3 m/s. In so doing, the value of Reynolds number along the plate does not exceed 10⁵. Synthetic corundum powders with average sizes of 12, 23, and 32 μm are used as the dispersed phase of two-phase flow. The mass concentration of particles in the flow is 0.01 kg/m³. A flat plate of stainless steel is used as the object of investigation. The distributions of gas velocity and concentration of particles within the boundary layer are measured using laser optical diagnostics. The number of particles deposited along the plate surface is measured by the gravimetric method. The adhesive properties of the “particle-surface” pair are studied using the centrifugal method of detachment of particles from the surface. Logarithmic-normal dependences of the number of adhesion of particles on the force of detachment are obtained. The hydrodynamic parameters of two-phase flow in the vicinity of the plate surface are calculated using the model of two-phase laminar boundary layer. The mathematical expression is suggested for the calculation of the magnitude of deposition of solid particles along the surface of a flat plate, which includes the special features of hydrodynamics of flow, the adhesive properties of the particles and surface, and the probabilistic pattern of the process of entrapment of particles by the surface.     

Inertial Settling of Particles from a Gas-Dispersed Flow on a Curvilinear Surface

Consideration is given to problems of settling of particles of a dispersed impurity from a subsonic jet flow on a curvilinear surface. Flow of the carrier medium is modeled based on the equations of vortex flow of a nonviscous incompressible liquid; they are written in the stream function-velocity vortex variables. The interaction of plane and round jets with obstacles of different shapes for the zero and nonzero initial vorticities of the flow is modeled numerically. The coefficient of sedimentation of the impurity is calculated as a function of the particle size and the obstacle shape.__________Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 2, pp. 93–98, March–April, 2005.     

Numerical model of the scattering of a gaseous and dispersed impurity in the atmosphere

A numerical model of the transfer of a gaseous and dispersed impurity in the atmosphere is described. The model is based on the semi-empirical stationary equation of turbulent diffusion in the boundary layer of the atmosphere with account for the gravitational deposition of particles. The altitude profiles of the coefficient of turbulent diffusion and of the wind velocity are approximated according to the Monin-Obukhov theory and the data obtained by Byzova with her coworkers. The atmosphere stratification is determined on the basis of standard meteorological data. The model is compared with experimental data and with well-known techniques used to calculate the propagation of impurity in the atmosphere. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 907-911, September–October, 2008.     

Stokes flow past a swarm of porous approximately spheroidal particles with Kuwabara boundary condition

The solution of the problem of symmetrical creeping flow of an incompressible viscous fluid past a swarm of porous approximately spheroidal particles with Kuwabara boundary condition is investigated. The Brinkman equation for the flow inside the porous region and the Stokes equation for the outside region in their stream function formulations are used. As boundary conditions, continuity of velocity and surface stresses across the porous surface and Kuwabara boundary condition on the cell surface are employed. Explicit expressions are investigated for both inside and outside flow fields to the first order in a small parameter characterizing the deformation. As a particular case, the flow past a swarm of porous oblate spheroidal particles is considered and the drag force experienced by each porous oblate spheroid in a cell is evaluated. The dependence of the drag coefficient on permeability for a porous oblate spheroid in an unbounded medium and for a solid oblate spheroid in a cell on the solid volume fraction is discussed numerically an and graphically for various values of the deformation parameter. The earlier known results are then also deduced from the present analysis.     

Nonlinear Wave Simulation on a Surface of Liquid Film Entrained by Turbulent Gas Flow at Weightlessness

The article considers the joint flow of a liquid film entrained by turbulent gas. Since liquid velocity is small in comparison with gas velocity, the problem is reduced to the calculation of pressure and shear stresses produced by the gas flowing over a wavy wall with small amplitude. Further, these data are used at the boundary conditions, when the flow of a liquid film is considered separately. As a result, we obtain a new system of equations for modeling the dynamics of long-wave perturbations on the surface of a viscous liquid film entrained by turbulent gas at microgravity. At small Reynolds numbers typical to the condition of microgravity, it was proved that this system is reduced to one evolution equation for the film thickness. Some numerical solutions of this equation have been received in this work.     

Modeling Erosion Wear Rates in Slurry Flotation Cells

In processes using slurry as the working fluid, wear due to solid particles impinging on elements of the process units is a serious reliability issue. This study considers modeling wear damage in flotation cells, which are widely used in mineral processing. Flotation cells are typically cylindrical vessels where an impeller is used to agitate the fluid, enabling the liberation of the minerals from the slurry. Some solids, particularly those entrained in the impeller stream, can impact on the wall of the cell, leading to material loss and eventually to loss of structural integrity. The problem of predicting the remaining life of the unit due to erosion requires understanding of various sub-processes: flow modeling, particle–fluid interaction, energy interactions at the surface, and the mechanism of erosion itself. In this study, empirically developed equations for the flow field of cylindrical mixing vessel with a Rushton turbine are used in formulating a model relating and the damage accumulation rate to a simple set of measurable variables. To validate a model, a PIV technique was used to measure velocities in the flow field and near the wall on a physical model of the cell with transparent walls and particles that match the refractive index of the fluid. An Eulerian–Langrangian approach has been used to determine the particle trajectories and the effect of a squeeze film is incorporated into the model to modify the velocity distribution of particles prior to impacts. An analytical model based on equations of impulse and momentum for a particle of any shape striking a flat massive surface has been used to describe the energy lost at the walls. Finally, a damage model is developed that takes into account impact velocity, attack angle, properties of the impinging particles and the surface. This model is verified against a second physical model that measures material loss rate at different locations within the cell.     

Investigation of the Behavior of Reflected Particles under Conditions of Heterogeneous Flow past Blunt Bodies

The results are given of an experimental investigation of the velocity of large particles of glass in the vicinity of a blunt body subjected to a heterogeneous flow. The particle inertia varies from Stk _f = 10.5 to Stk _f = 82. The velocity distribution is obtained for particles of different forms, such as incident, reflected from the model, reprecipitating on the surface, and so on. The dependence of the size of the region of existence of reflected particles on the inertia of the dispersed phase is determined.     

An improved stochastic separated flow model for turbulent two-phase flow

 An improved stochastic separated flow model is proposed to obtain reasonable statistical characteristics of a two-phase flow. Effects of the history of a particle and its current trajectory position on the mean-square fluctuating velocity of the dispersed phase are continuously considered in this model. Comparing with the conventional model, results using the improved model are more reasonable and can also be obtained more easily. Furthermore, the improved model requires less computational particles for simulating dispersed-phase turbulence at the beginning of the stochastic trajectory. In this paper, an application in turbulent two-phase flow of planar mixing layer is carried out. Numerical results including velocity, mean-square fluctuating velocity, particle number density and pdf of fluctuation velocity of dispersed phase are shown to compare well with experimental data.     

颗粒在斜槽中流动的实验研究

用示踪颗粒法对细玻璃球在斜槽中的低速流动进行了实验研究。结果发现 ,颗粒的流动行为与斜槽表面特征密切相关 ,对光滑表面存在明显的壁面滑移 ,而对粗糙壁面 ,在低速流情况下不存在滑移。实验测量了不同条件下的速度分布和流层厚度 ,并分析了斜槽倾角、流率及壁面状况对流动的影响     

Influence of Turbulence on the Deposition of Particles from a Gas‐Dispersed Flow on the Wall

Simulation of the scattering and deposition of dispersedphase particles in the region of interaction of a turbulent flow with an obstacle is considered. The regimes and distinctive features of deposition of particles in the vicinity of a critical point are investigated under different conditions. The sedimentation coefficient of the impurity is calculated as a function of the parameters of unperturbed flow and the particle size. The results of the calculations are compared to the data obtained without allowance for the influence of the fluctuations of the carrierflow velocity on the motion of the impurity.     

Gasdynamic acceleration of microparticles and their interaction with a solid body

Based on the physicomathematical model developed before, verified by comparison results of calculations with experimental data, parameters of a gas-dispersed jet, interacting with a solid body, are numerically investigated. In a wide range of temperature and pressure values in a mixing chamber, material density, the size and mass fraction of particles, the nozzle geometry and the streamlined body form, ratio of specific heat capacities, and the Mach number of carrier gas, calculations are made, which allows one to determine the impact of specified factors on the boundary of a perfectly inelastic collision of particles with the body, accompanied by different physical processes (erosion, cold deposition, ultradeep penetration). Since temperature falls below the Debye value at high expansion of flow, the impact of a significant change of the heat capacity and thermal conductivity of particles are taken into account. Radial distributions of density and velocity of the dispersed mass are plotted, which characterize the “quality” of two-phase flow as a tool for the ground modelling of interaction of a flying vehicle with a dust-laden atmosphere (containing, for example, particles of volcanic outbursts or ice crystals) as well as in technologies of surface treatment.     

Experimental investigation on hydrodynamic behavior in a spouted bed with longitudinal vortex generators

A spouted bed with longitudinal vortex generator (LVG) of sphere was built to enhance radial movement of particles. Particle Image Velocimetry (PIV) was applied to explore effects of longitudinal vortex flow and physical properties of particles on their radial velocity in a 152-mm-diametered spouted bed. The results show that, Compared with the conventional spouted bed, the existence of longitudinal vortex generator gives rise to a large amount of secondary fine vortex flow in the cross section of spouted bed. The enhancement factors of particles movement η with different particle densities are all greater than 1. The smaller the particle density, the more significant the effect of the longitudinal vortex on the radial velocity of the particles. The single-row LVGs can produce a good radial enhancement effect of particle movement when the particle handling capacity is small (H₀ = 165 mm). With the increase of the height of the static bed (H₀), the enhancement of the radial velocity of particles in the spouted bed by multi-row LVGs (three rows) increases gradually, which indicates that the multi-row LVGs have a better overall effect on the enhancement of particle motion in the spouted bed with more particle handling capacity (H₀ = 195 mm, 225 mm).     

On the magneto-hydrodynamic flow past a rotating disk in a fluid-particle suspension with a circular magnetic field

The flow of an incompressible, viscous, electrically conducting fluid with a suspension of inert particles over a rotating disk in the presence of a circular magnetic field is investigated. The governing equations of motion are reduced to a set of nonlinear ordinary differential equations by similarity transformations, and solved numerically by using least squares finite element method. The radial velocity of the panicles attains its maximum on the surface of the disk and the particles slip in the tangential direction. The flow boundary layer is thickened and the axial flow field is reduced as a result of the magnetic field. The particle density is maximum near the surface of the disk.     

Effect of large blowing rates on the compressible boundary layer flow at the stagnation point of a rotating sphere

Summary The effect of a large surface blowing (injection) rate on the steady laminar compressible boundary-layer flow at the forward stagnation point of a rotating sphere has been studied. The resulting coupled nonlinear ordinary differential equations have been solved using two methods, namely, the method of matched asymptotic expansion and the implicit finite difference scheme in combination with the quasilinearization technique. It is found that the boundary layer thickness increases considerably with the blowing rate. The location of the dividing streamline moves away from the surface with increasing blowing rates, but moves towards the surface when the total enthalpy at the wall or the rotation parameter increases. For large blowing rates and small rotation parameter the surface heat transfer and the surface shear stress in the tangential direction tend to zero, but the longitudinal shear stress remains finite but small. Also, for this case, the longitudinal shear stress at the wall is approximately found to be directly proportional to the sum of the total enthaply at the wall and to the square of the rotation parameter and inversely proportional to the blowing rates. The rotation parameter induces overshoot in the longitudinal velocity, and the magnitude of the velocity overshoot increases significantly with rotation and blowing parameters. However, there is no overshoot in the longitudinal velocity in the absence of rotation whatever may be the values of the blowing parameter.     

Electron microscopy of hexagonal boron nitride powder

The morphology and crystalline state of h-BN powder after one-stage or two-stage baking process were investigated extensively. The particles are scale-shaped and the flat surfaces have a (001) habit plane of hexagonal close-packed structure. The side shape of particles after one-stage baking is round, while that after two-stage baking is dodecan, a twelve-faced prism, with the side habit of (100), (110) or their variants. Lattice image observation shows that the side surface of a one-stage baked particle is wavy and thin, while that of a two-stage baked particle is straight and thick. Many particles after one-stage baking are composed of overlapped grains contacting with each other at (001) flat surfaces forming a twist boundary. These grains have relative rotation angles ranging from 5 ° to 26 ° around the common [001] axis and have a coincidence lattice relation with respect to (001) flat planes. X-ray photoelectron spectroscopy analysis shows that both C and O segregate onto the surface of one-stage baked particles, while only C segregates onto the surface of two-stage baked particles. Formation of coincidence lattice grain boundary and impurity segregation both restrict the growth of diameter and thickness in scale-shaped particles. It is concluded that two-stage baked particles, having side surface habits, are stable against various environments.     

Pseudolaminar Boundary Layer on a Blunt Body Subjected to a Heterogeneous Flow

The distributions of the velocities of air and solid particles in a pseudolaminar boundary layer developing on the surface of a cylinder with a hemispherical end face are experimentally investigated. The experiments reveal a significant rise of fluctuations of the particle velocity in the wall region of the boundary layer. Data are obtained on the decrease in the particle concentration in the vicinity of the model wall compared to its value in the external flow.     

Mass transfer in heterogeneous chemical reactors under variable hydrodynamic conditions

The equation of convective diffusion is solved for a channel with a longitudinal variation of velocity and a laminar flow. A formula is derived for the thickness of the diffusion boundary layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 4, pp. 667–672, April, 1974.     

The atom velocity distribution function in the process of liquid evaporation

Analytical expressions determining the velocity distribution function of evaporating particles were obtained for evaporation into vacuum. The formulas are compared with numerical simulation results; the coincidence can be treated as sufficiently good. The particle distribution function over the longitudinal, i.e., directed from evaporation surface, velocity turns out to be significantly non-Maxwellian. The distribution function over the transverse projections of the velocity is Maxwellian but with a distribution modulus different from the evaporating liquid temperature T. The mean energy of a particle escaping from the surface is 2kT.     

Simulation of Gas-Solid Flow in Vertical Pipe by Hard-Sphere Model

ABSTRACT

This article presents a two-dimensional study of the gas-solid flow in a vertical pneumatic conveying pipe by means of a hard-sphere model where the motion of individual particles can be traced. Simulations were performed for a pipe of height 0.9 m and width 0.06 m, with air as gas phase and particles of density 900 kg/m³ and diameter 0.003 m as solid phase. Periodic boundary conditions were applied to the solid phase in the axial direction. Different cases were simulated to examine the effects of the number of particles used, superficial gas velocity, and restitution coefficient. The results show that the main features of plug flow can be reasonably captured by the proposed simulation technique. That is, increasing the number of particles in a simulation will increase the length of plugs but does not change the velocity of plugs; the solid fraction of a plug is relatively low if the number of particles is small. In particular, it is shown that increasing superficial gas velocity will increase the velocity of plugs and the frequency of plugs, and the pressure drop through a rising plug increases linearly with the plug length, suggesting that the total pressure of a conveying system with a given length can be quantified from the information of plug length and plug frequency. Increasing the restitution coefficient can promote the momentum transfer between particles and hence the raining down of particles from the back of a plug in vertical pneumatic conveying. The simulation offers a useful technique to understand the fundamentals governing the gas-solid flow under pneumatic conveying conditions.