Settling velocity of droplets in turbulent flows

Two parameters of particle or droplet dynamics which are of importance in describing their behaviour in turbulent pipe flows are their settling velocity and eddy diffusivity. It is usually assumed that the settling velocity in turbulent flow is equal to that in still fluid and on the basis of this assumption the eddy diffusivity is usually determined experimentally from the distribution of droplets or particles in horizontal turbulent flow. Since the settling velocity has a strong influence on the resultant value of the eddy diffusivity, the influence of turbulence on settling velocity is investigated in this work. A simple stochastic model of settling in turbulent flow is developed and it is shown that a considerable retardation of still fluid settling velocity is possible for a wide range of conditions.     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

潮湿细煤气流分级机内气固两相流的CFD模拟

以CFD计算软件FLUENT为平台,采用Realizablek-着湍流模型和欧拉-拉格朗日方法的离散相模型对实验室研制的潮湿细煤气流分级机内的空气流场进行数值模拟,得到分级机中流场的气流速度、流场静压、流场湍动能的分布情况,以及不同粒径细粒煤在分级机中的运动轨迹。数值计算结果表明:分级机内多孔层的设置可造成压强和流速阶跃,增强多孔层上方区域的流速,提升气体对细粒煤的携带作用;导流板的设置使入料口到细料出口间出现了较强的流带,有利于细粒煤分离;导流板和倾斜多孔层的设置使分级机内压差最大且湍流较弱,有利于颗粒分散,实现小颗粒与大颗粒的分离,提高分级效率同时也有利于中等粒径团聚体的破碎、分散,但对大粒径团聚体的分裂破坏作用有限。     

Fluid–particle correlated motion and turbulent energy transfer in a two-dimensional particle-laden shear flow

Discrete vortex simulations of a dilute two-dimensional particle-laden shear layer with one-way coupling were performed to study fluid–particle correlated motion and the transfer of turbulent kinetic energy between the phases. The resulting modification of carrier phase turbulence, estimated according to current computational models, was evaluated. Particle Stokes numbers were between 1.0 and 4.5, so that the particles showed considerable temporal concentration fluctuations due to centrifuging by the fluid flow structures, and the mass loading was 12% corresponding to a volume fraction of 6.0×10^?5.Fluid velocities and particle concentration and velocities and their covariances, which appear in a commonly used model equation for carrier phase turbulence modification, were evaluated. Additionally, the probability density functions of fluid velocity fluctuations viewed by the particles are presented and compared with their Eulerian counterparts. It was found that particles view reduced velocity fluctuations due to preferential clustering. The model for carrier-phase turbulence modification predicted turbulence reduction, depending on the particle Stokes number. The mechanism responsible for turbulence reduction was the correlated velocity fluctuations of fluid and particles and this reduction could reach values up to one third of the fluid flow dissipation. Preferential particle concentration together with a relative velocity between the phases could generate turbulent kinetic energy of the gas phase, however this production was nearly an order of magnitude smaller compared to reduction of turbulence due to the correlated motion. The findings were compared with experiments available in the literature and help to clarify the view when turbulence reduction or augmentation occurs.     

NUMERICAL CALCULATIONS OF TUBE BUNDLES EROSION BY TURBULENT PARTICLE-LADEN GAS FLOWS

Erosion of tubes in tube bundles by particles suspended in gas flows is a major problem in the power industry. In this paper, a numerical study has been conducted for the flow of a dilute particle-laden gas moving past two row in-line tubes undergoing erosion. An orthogonal-curvilinear co-ordinate system was used to calculate turbulent flow around the tubes. The prediction of particle trajectories took into account the effect of the turbulence with a stochastic particle dispersion model. The results from this study included the distributions of particle collision frequency and erosion damage of tube surfaces.     

Computational investigation of the mechanisms of particle separation and “fish‐hook” phenomenon in hydrocyclones

The motion of solid particles and the “fish‐hook” phenomenon in an industrial classifying hydrocyclone of body diameter 355 mm is studied by a computational fluid dynamics model. In the model, the turbulent flow of gas and liquid is modeled using the Reynolds Stress Model, and the interface between the liquid and air core is modeled using the volume of fluid multiphase model. The outcomes are then applied in the simulation of particle flow described by the stochastic Lagrangian model. The results are analyzed in terms of velocity and force field in the cyclone. It is shown that the pressure gradient force plays an important role in particle separation, and it balances the centrifugal force on particles in the radial direction in hydrocyclones. As particle size decreases, the effect of drag force whose direction varies increases sharply. As a result, particles have an apparent fluctuating velocity. Some particles pass the locus of zero vertical velocity (LZVV) and join the upward flow and have a certain moving orbit. The moving orbit of particles in the upward flow becomes wider as their size decreases. When the size is below a critical value, the moving orbit is even beyond the LZVV. Some fine particles would recircuit between the downward and upward flows, resulting in a relatively high separation efficiency and the “fish‐hook” effect. Numerical experiments were also extended to study the effects of cyclone size and liquid viscosity. The results suggest that the mechanisms identified are valid, although they are quantitatively different. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

NUMERICAL CALCULATIONS OF TUBE BUNDLES EROSION BY TURBULENT PARTICLE-LADEN GAS FLOWS

Erosion of tubes in tube bundles by particles suspended in gas flows is a major problem in the power industry. In this paper, a numerical study has been conducted for the flow of a dilute particle-laden gas moving past two row in-line tubes undergoing erosion. An orthogonal-curvilinear co-ordinate system was used to calculate turbulent flow around the tubes. The prediction of particle trajectories took into account the effect of the turbulence with a stochastic particle dispersion model. The results from this study included the distributions of particle collision frequency and erosion damage of tube surfaces.     

THE COLLISION RATE OF PARTICLES IN TURBULENT FLOW

A review of previous derivations of particle collision rates in turbulent fluid flow shows that these are applicable only to limited cases. A more general derivation is given, taking into account the effects of the inertia of the particles and the difference in densities of the fluid and the particles. A universal solution for the relative velocity of two particles due to turbulent accelerations in a gaseous or liquid system is presented. In gaseous systems the acceleration mechanism becomes predominant at particle sizes far below the Kolmogorov microscale of turbulence. In liquid systems, the particle inertial and added mass effects become important above the Kolmogorov microscale. Here the particle collision rate cannot be estimated from the fluid turbulent velocity fluctuations only.     

Mechanisms of aerosol deposition in a nasal model

Total and regional aerosol deposition were investigated in a model of a normal human nasal airway. Contributions of fluid turbulence and particle inertia were evaluated using monodisperse aerosols. At fixed turbulent flow conditions, deposition percentage increased with particle size greater than 1 μm, suggesting that turbulent inertial deposition is a primary mechanism.

With same size aerosol, deposition increased with increasing fluid turbulence but its contribution was less with larger size aerosol. Turbulent diffusion was the dominant transport mechanism for particles less than 1 μm, where deposition decreased with particle size. Two major deposition sites were visualized with radio-aerosol in the anterior region of the nasal airway. One is close to the ostium internum where turbulent eddies are well developed, and the other is the anterior region of the middle turbinate where direction of airflow changes from upward to horizontal.     

A comprehensive approach in modeling Lagrangian particle deposition in turbulent boundary layers

Modeling of particle deposition on adjacent walls is a key issue in various applications like separation or transport processes. The present paper focuses on the modeling of turbophoretic deposition of particles in the micron size range. The first step is to evaluate the important range where turbophoresis plays an important role in comparison to other mechanisms e.g. gravity or electrostatic separation. The disadvantages of commonly used models will be analyzed and overcome by implementing a more sophisticated approach considering damping of turbulent fluctuations in the wall-boundary layer. In contrast to previous work, commonly used turbulence models are applied to solve the mean flow field of the examples under consideration. The results will show a good prediction of particle deposition in comparison to experimental values [B.Y.H. Liu, J.K. Agarwal, Experimental observation of aerosol deposition in turbulent flow, Aerosol. Sci. 5 (1974) 145-155.] by using the advanced model.     

Numerical simulation and validation of dilute turbulent gas-particle flow with inelastic collisions and turbulence modulation

This work describes a theoretical and numerical study of turbulent gas-particle flows in the Eulerian framework. The equations describing the flow are derived employing Favre averaging. The closures required for the equations describing the particulate phase are derived from the kinetic theory of granular flow. The kinetic theory proposed originally is extended to incorporate the effects of the continuous fluid on the particulate phase behavior. Models describing the coupling between the continuous phase kinetic energy and particulate phase granular temperature are derived, discussed, and their effect on the flow predictions is shown.The derived models are validated with benchmark experimental results of a fully developed turbulent gas-solid flow in a vertical pipe. The effect of the models describing the influence of turbulence on the particle motion as well as the turbulence modulation due to the presence of particles is analyzed and discussed.     

Forces on the surface of small ellipsoidal particles immersed in a linear flow field

Knowledge of the forces which a fluid motion exerts on the surface of suspended material is important for many processes in which the particles are broken apart by the hydrodynamic forces. In this paper, we examine the stresses on a small ellipsoidal particle which is immersed in either a constant, simple shear, two-dimensional straining or axisymmetric straining flow. Calculations have been performed using Oberbeck's and Jeffery's models and have been appropriately visualized. Furthermore, the motion and orientation of the ellipsoid have been examined and the extreme values of stresses have been analyzed. A simple criterion for the break-up of particles is proposed. The analysis shows that the straining flows are particular important for the load on particles. In contrast, simple shear flows are less crucial as the presence of vorticity leads to a rotation of the particles.     

EFFECT OF VARIABLE ACOUSTIC FIELD AND FREQUENCY ON GAS-SOLID SUSPENSION OF FINE POWDER: A REVIEW

Suspensions of fine particles in either Newtonian or non-Newtonian fluids are often encountered in the physical, engineering, and biological sciences. For example, the manufacture of particle-laden products such as reinforced composites, paints, paper, slurries, and cements involves the processing of particle suspensions. Fine particles become difficult to suspend due to interparticle attraction forces like ver der Waals, capillary, and cohesive forces, which are responsible for converting fine particles into aggregates. These aggregates prevent the particles from being suspended uniformly, hence external forces are essential to break these aggregates. External forces include magnetic fields, electrical fields, acoustic fields, and mechanical vibration, which are useful to break aggregates and suspend particle uniformly. This process is termed homogeneous fluidization. This article presents a comprehensive review of sound-assisted fluidized beds for group C, A, and B and binary materials. Furthermore, this review covers the effect of acoustic field intensity and frequency on minimum fluidization velocity and on bubbling.     

CFB中环核结构的模拟

In this paper, the stochastic particle-trajectory model is proposed for simulating the dynamic behavior of circulating fluidized bed (CFB). In our model, the motion of solid phase is obtained by calculating the individual particle trajectory while gas flow is obtained by solving the Navier-Stokes Equation including two-phase interaction. For the calculation of solid phase, the motion of each particle is decomposed into a collision process and a suspension process. In suspension process, the less important and/or unclear forces are described as a random force considering gravity, drag force and pressure gradient. As a result, the proposed model gives some numerical simulations of CFB. It indicates that the stochastic particle-trajectory model can be used to simulate qualitatively the annulus-core structure of CFB and the influences of stochastic factors cannot be ignored. In a CFB, the coupling of stochastic factors between two phases makes the radial voidage decreased. Moreover, the upward motion of particles is mitigated by both stochastic factors and turbulence between two phases.     

Coupled fluid‐particle modeling of a slot die coating system

This work seeks to develop a fundamental understanding of particle motion in the slot die coating process through studying the interaction of forces between particles, with the die walls and the fluid phase. Coupled computational fluid dynamics and the discrete element method is employed for evaluating the motion of individual suspended particles near moving surfaces in a complex three‐dimensional flow field, motivated by the flow of particle laden fluid in a slot die coating system, including the presence of free surfaces. Overall, the particles follow the flow streamlines and their final position in the coating depends on the initial entry region of the particles. Particles experiencing adhesion with each other agglomerate in the low velocity regions of the coating gap, and have long residence times near the edge of the die at the end of the feed slot in the coating gap. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1933–1939, 2016     

化学与湍流团聚耦合促进燃煤细颗粒物团聚与脱除

将化学团聚与湍流团聚技术耦合,实验研究了燃煤细颗粒物在化学与湍流团聚耦合作用下的团聚与脱除效果,以及颗粒物浓度、烟气温度、团聚液喷入量与烟气流速等因素对细颗粒物团聚与脱除效果的影响规律。结果表明,典型工况下化学-湍流耦合团聚能够进一步促进细颗粒物团聚长大以及静电除尘器对细颗粒物的脱除,其作用效果优于单独的化学与湍流团聚。随细颗粒物浓度的升高,团聚与脱除效率均逐渐下降,分别由49.2%与96.7%下降至35.3%与88.2%。随烟气温度与团聚液喷入量的增加,细颗粒物团聚与脱除效率均先升高后降低,并在180℃与12 L/h处达到最高值,团聚与脱除效率分别为44.7%与94.8%。随烟气流速的增加,细颗粒物团聚与脱除效率均逐渐升高,分别由30.5%与86.3%升高至50.2%与97.5%。     

Fluid and particle motion in turbulent dispersion—I: Measurement of turbulence of liquid by continual pursuit of tracer particle motion

A method is proposed for measurement of turbulence quantities of fluid flow. The motion of a swarm of small tracer particles supplied to turbulent flow is continually followed by high-speed cine-photography, from which velocity correlations and energy spectra are evaluated. It is applicable to the heterogeneous fluid flow as well as to the homogeneous fluid flow, and the Eulerian and Lagrangian correlations are determinate simultaneously. Validity of the method is confirmed by the comparison of some turbulence quantities in the present study with those obtained otherwise.     

SIMULATION OF PARTICLE TRANSPORT AND DEPOSITION IN A COMBUSTOR

A computational model for Lagrangian particle tracking for studying dispersion and deposition of particles in a combustor with swirling flow and chemical reaction is developed. The model accounts for the effect of thermophoretic force, as well as the drag and lift forces acting on particles, in addition to the Brownian motion and gravitational sedimentation effects. The mean turbulent gas flow, temperature fields and chemical species concentration in the combustor are evaluated using the stress transport turbulent model of the FLUENT code. The instantaneous fluctuation velocity field is generated by a Gaussian filtered white noise model.

The simulated axial, radial and tangential mean gas velocities are compared with the existing experimental data. Ensembles of particle trajectories are generated and statistically analyzed. The effects of size and initial distribution on particle dispersion and deposition are studied. The particle concentration at different sections are also evaluated and discussed. The results shows that the turbulence dispersion effect is quite important, while the thermophoresis effect is small.     

Particle dispersion in a turbulent natural convection channel flow

Direct numerical simulations of particle dispersion in the turbulent natural convection flow between two vertical walls kept at constant but different temperatures are reported. It is assumed that the particles do not affect the flow (i.e. the dilute phase approximation is adopted). Particles with different levels of inertia, or Stokes numbers (0.843≤St≤17.45), are tracked according to the drag force imposed by the fluid. The gravity force is included for two cases, St=0.843 and St=17.45. The different levels of turbulence near the wall and near the center of the channel produce, as in isothermal turbulent channel or pipe flow, a larger concentration of particles near the wall. This effect becomes more important, and the deposition velocity of particles on the wall increases, as the particle inertia is increased. The simulations at St=8.38 and St=17.45 predict similar concentration profiles and deposition velocities according to the large inertia of these particles. The deposition velocities, obtained when the gravity force is ignored in the particle equations, follow the trend observed and measured for isothermal turbulent channel flows in the diffusion impaction regime. For the conditions considered, the gravity vector imposes a strong descending motion on the particles and this produces the increase of the particle concentration near the wall and a reduction of the deposition velocities in comparison with the results without the gravity force.