Prediction of Particle Deposition Using a Simplified Particle Model in Fully Developed Channel Flow

In this study the Eulerian particle model was modified to predict the particle deposition rate in fully developed channel flow. The modified model is less complicated and has much lower computation time. The performance of the simplified model was examined by comparing the particle deposition rate in a vertical channel with the experimental data for fully developed channel flow available in the literature. The effects of turbophoretic force, thermophoretic force, electrostatic force, gravitational force, Brownian/turbulent diffusion, and the wall roughness on the particle deposition rate were examined. The predictions of the modified particle model were in agreement with the experimental data.     

Modeling of particle deposition in a vertical turbulent pipe flow at a reduced probability of particle sticking to the wall

Particle deposition on the wall in a dilute turbulent vertical pipe flow is modeled. The different mechanisms of particle transport to the wall are considered, i.e., Brownian motion, turbulent diffusion and turbophoresis. The Saffman lift force, the electrostatic force, the virtual mass effect and wall surface roughness are taken into account in the model developed. A boundary condition that accounts for the probability of particle sticking to the wall is suggested. An analytical solution for deposition of small Brownian particles is obtained. A particle relaxation time range, where the model developed is reliably applicable, is evaluated. Computational results obtained at different particle-wall sticking probabilities in the wide particle relaxation time range are presented and discussed.     

CFD modeling and validation of the turbulent fluidized bed of FCC particles

An experimental and computational study is presented on the hydrodynamic characteristics of FCC particles in a turbulent fluidized bed. Based on the Eulerian/Eulerian model, a computational fluid dynamics (CFD) model incorporating a modified gas‐solid drag model has been presented, and the model parameters are examined by using a commercial CFD software package (FLUENT 6.2.16). Relative to other drag models, the modified one gives a reasonable hydrodynamic prediction in comparison with experimental data. The hydrodynamics show more sensitive to the coefficient of restitution than to the flow models and kinetics theories. Experimental and numerical results indicate that there exist two different coexisting regions in the turbulent fluidized bed: a bottom dense, bubbling region and a dilute, dispersed flow region. At low‐gas velocity, solid‐volume fractions show high near the wall region, and low in the center of the bed. Increasing gas velocity aggravates the turbulent disorder in the turbulent fluidized bed, resulting in an irregularity of the radial particle concentration profile. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column

The numerical approaches have been used in many studies to predict the flow pattern inside the bubble column reactors because of the difficulties that are still found in designing and scaling-up the bubble columns. This review makes an effort to show suitable interfacial forces i.e., drag force, lift force, turbulent dispersion models and virtual mass and turbulence models such as standard k–ɛ model, Reynolds Stress Model, Large Eddy Simulation to predict flow pattern inside the bubble column using Eulerian–Eulerian. The effect of various interfacial forces and turbulence models on gas–liquid velocity and gas hold-up in bubble column is critically reviewed.     

Convective diffusion of particles deposition under electrostatics from turbulently-mixed conditions

A theoretical model is presented to describe inertialess particle deposition onto smooth surfaces under the influence of electrostatic force. Both Boltzmann and combined diffusion and field charging mechanisms are investigated. A modified Fick's law equation accounting for Brownian and turbulent diffusion, spatially-independent external force, i.e. gravitational and Coulombic force, is presented based on the simplified three-layer model. The results show that the concentration boundary layer thickness is very thin and the previous three-layer model can be further simplified. The Coulombic force influences the particle deposition significantly and for considerably high charge and electric field, deposition is independent on turbulent intensity. The model predictions agree very well with the literature DNS results.     

Bumpy Particle Adhesion and Removal in Turbulent Flows Including Electrostatic and Capillary Forces

The effect of electrostatic and capillary forces on bumpy particle adhesion and removal in turbulent flows is studied. We use the JKR theory and account for the increase of adhesion by capillary force. The effects of electrostatic forces and nonlinear hydrodynamic drag are included in the analyses. The criteria for incipient rolling and sliding detachments and electrostatic lifting removal are evaluated. A turbulence burst model is used for evaluating the peak air velocity near the substrate. The critical shear velocities for detaching particles of different sizes under different conditions are evaluated. The electric field strength needed for electrostatic removal of particles with different charges is also estimated. The results are compared with those obtained in the absence of the capillary force. Comparisons of the model predictions with the available experimental data are also presented.     

Modelling of particle resuspension by a turbulent airflow and the role of particle size,surface roughness and electric charge

A resuspension model based on the Lennard–Jones intermolecular potential is applied to a monolayer deposit of spherical particles. The model considers the interactions between a particle and a surface under the influence of an external turbulent airflow. The particle–surface interaction was modelled with and without particle deformation due to elastic flattening. The resuspension rate was calculated by a kinetic force-balance approach whereby particle detachment occurs when the instantaneous joint contribution of the lift and drag forces exceeds the total adhesive force of the particle–surface system. Enhanced aerodynamic particle removal driven by the moment of the lift and drag forces was determined. Model predictions suggest that inclusion of the moment of the aerodynamic forces provides a suitable model for particle detachment (initiated by rolling). The importance of elastic deformation was found to depend on adhesive forces, characteristics of the substrate surface (surface roughness) and particle size. The model was applied to a number of laboratory experiments. For one set of experiments, we identified two resuspension regimes depending on whether small non-deformable or large deformable (equivalently, strongly or weakly bound) particles resuspended at high or low friction velocities. A modified model incorporating the effect of particle charge is also presented. Results indicate that particle resuspension is possible even when electrostatic forces are present, but the resuspension rate decreases considerably, depending on particle size, particle charge and surface roughness.     

Bumpy Particle Adhesion and Removal in Turbulent Flows Including Electrostatic and Capillary Forces

The effect of electrostatic and capillary forces on bumpy particle adhesion and removal in turbulent flows is studied. We use the JKR theory and account for the increase of adhesion by capillary force. The effects of electrostatic forces and nonlinear hydrodynamic drag are included in the analyses. The criteria for incipient rolling and sliding detachments and electrostatic lifting removal are evaluated. A turbulence burst model is used for evaluating the peak air velocity near the substrate. The critical shear velocities for detaching particles of different sizes under different conditions are evaluated. The electric field strength needed for electrostatic removal of particles with different charges is also estimated. The results are compared with those obtained in the absence of the capillary force. Comparisons of the model predictions with the available experimental data are also presented.     

PARTICLE DEPOSITION IN A NEARLY DEVELOPED TURBULENT DUCT FLOW WITH ELECTROPHORESIS

This study is concerned with deposition of neutral and charged particles in nearly developed turbulent duct flows. The cases that the duct is vertical or horizontal and when the particles carry Boltzmann, static electrification, as well as saturation charge distributions are analyzed. The mean turbulent flow field is evaluated with the aid of the FLUENT code, using the Reynolds stress transport model. Deposition rate of particles in the size range of 0.01–100 μm are studied and the effects of electric field intensity on particle deposition velocity are evaluated. The simulation results are compared with the available experimental data, the earlier numerical results and those obtained from empirical equations for fully developed duct flows. It is shown that the electrostatic effect significantly increases the particle deposition rate.     

Effect of particle deposition on the reduction of water flux in reverse osmosis

The phenomenon of particle deposition from a liquid stream flowing inside a membrane duct was studied. The rate of particle deposition is determined by trajectory calculation. Deposition occurs if a particle trajectory intersects the membrane surface.The forces considered include the gravitational force, the drag force and the surface forces. The major contribution to particle deposition is due to radial flow. At low water flux, both Brownian and surface forces are important. Furthermore, with a repulsive double layer force, a barrier may be present near the membrane surface, which would limit particle deposition significantly. Comparison with experimental data on water flux reduction indicates that the analysis given in this work provides a useful framework which can be applied for the assessment of water flux reduction due to particle deposition.     

Wind Tunnel Modeling of Small Particle Deposition

An inexpensive microsphere dispersion, deposition, and sampling system is described. This system was used to examine the transport and deposition of small particles (? 1 μm diameter) across the aerodynamic boundary layer which developed over a prototype deposition surface (smooth, flat, acrylic plate). Unit density, polystyrene latex microspheres (0.8 and 1.1 μm diameter) were deposited onto both oil-coated and dry, upper and lower surfaces. Observed deposition velocities were significantly larger than those reported in the literature, possibly because low relative humidities increased electrostatic charge on the experimental plate. The experimental results were greater than those predicted by a turbulent flow particle deposition model.     

基于气泡群相间作用力模型的加压鼓泡塔流体力学模拟

目前,多数文献报道了冷态加压湍动鼓泡塔内流动特征,并且通过实验数据回归相关经验关联式。然而,此类关联式适用范围有限,难以直接外推到工业鼓泡塔反应器条件。因此,在FLUENT平台上建立了基于气泡群相间作用力的、动态二维加压鼓泡塔计算流体力学模型。通过数值模拟考察了操作压力为0.5~2.0 MPa,表观气速为0.20~0.31 m·s^-1,内径0.3 m鼓泡塔内流场特性参数分布,并且与冷态实验数据进行比较。结果表明,采用修正后的气泡群曳力模型、径向力平衡模型以及壁面润滑力模型描述气泡群相间作用力,能够较为准确地反映平均气含率和气含率径向分布随操作压力和表观气速变化的规律。     

Experimental study and computational fluid dynamics modeling of deposition of hydrate particles in a pipeline with turbulent water flow

The present paper describes a study of Freon R11 hydrate deposition in a turbulent flow of water. Eulerian–Eulerian CFD model was built in order to study the process numerically, the model was validated with experimental data from the multiphase flow loop. Different mechanisms for particulate stress were studied in the work in terms of their performance results, compared to experimental data. The model considered an expression for variable hydrate particle size which was validated in a series of population balance numerical experiments.     

Relative importance of the lift force on heavy particles due to turbulence driven secondary flows

Saffman lift forces on dense particles due to gradients in both streamwise and cross-stream velocities in a downward, fully developed turbulent square duct flow at Re_τ = 360 are studied using large eddy simulations. Volume fraction of the dispersed phase is low enough (≤ 10^− 5) that the one-way coupling approach is reasonable, i.e., two-way coupling and particle-particle collisions are not considered. Eulerian and Lagrangian approaches are used to treat the continuous and dispersed phases, respectively. Subgrid stresses are modeled with the dynamic subgrid kinetic energy model of Kim and Menon [W.W. Kim and S. Menon. Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows, AIAA 97-0210, 1997.]. The particle equation of motion includes drag, lift forces due to both the streamwise and cross-stream velocity gradients, gravity, and is integrated using the fourth-order accurate Runge-Kutta scheme. Dependence of particle drag and lift forces on duct cross-sectional location and particle response time is demonstrated using the mean value contours and probability density functions (PDFs) of particle forces. It is shown that the streamwise component of the mean drag force experienced by particles of all response times is a deceleration force, i.e. on average, fluid streamwise velocity lags the particle streamwise velocity. Secondly, the two wall-normal (or lateral) components of the mean drag force are oriented such that the particles experience a net mean force toward the duct corners. PDFs of particle drag force components show that smaller response time particles experience a wider range of drag force about the mean value, as compared to the more inertial particles. Contours of mean wall-normal lift forces due to streamwise velocity gradients show that this force predominantly acts toward the duct walls and that the maximum lift force occurs close to the walls. PDFs of lift force due to streamwise velocity gradients show that the range of fluctuations increases with particle response time, but the dependence on particle response time is weaker compared to drag force. Lift forces due to cross-stream velocity gradients are at least an order of magnitude smaller than lift forces due to streamwise velocity gradients and are found to decrease in their range of fluctuations with particle response time. It is demonstrated that lift forces due to secondary flow velocity gradients are not as important as those due to streamwise velocity gradients in a square duct flow.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

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.     

Effects of air temperature and humidity on particle deposition

Particle deposition in a fully developed turbulent duct flow was studied. The random walk model of Lagrangian approach was used to predict the trajectories of 3000 particles with a density of 900 kg/m³. The effects of thermophoretic force and air humidity were also considered. The results were compared with the previous studies with a particle size range of 0.01–50 μm and air flow velocity of 5 m/s. The profile of dimensionless deposition velocity with relaxation time presents a V-shaped curve and the results are in good agreement with the previous studies.The effects of air temperature and humidity on particle deposition with a particle size of 1 μm were also investigated. The results show that thermophoretic force accelerates particle deposition onto the duct walls with increasing temperature difference between air flow and the duct wall surface. Meanwhile, it was found that particle deposition velocity increases with air humidity.     

Prediction of turbulent gas‐solid flow in a duct with a 90° bend using an Eulerian‐Lagrangian approach

A dilute, particle‐laden turbulent flow in a square cross‐sectioned duct with a 90° bend is modeled using a three‐dimensional Eulerian‐Lagrangian approach. Predictions are based on a second‐moment turbulence closure, with particles simulated using a Lagrangian particle tracking technique, coupled to a particle‐wall interaction algorithm and a random Fourier series method used to model particle dispersion. The performance of the model is tested for a gas‐solid flow in a horizontal‐to‐vertical duct, with predictions showing good agreement with experimental data. In particular, the consistent use of anisotropic and fully three‐dimensional approaches throughout yields predictions that result in fluctuating particle velocities in acceptable agreement with data. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Pneumatic transport of granular materials with electrostatic effects

The methodology of coupling large eddy simulation (LES) with the discrete element method was applied for computational studies of pneumatic transport of granular materials through vertical and horizontal pipes in the presence of electrostatic effects. The LES numerical results obtained agreed well with the law of the wall for various y⁺‐ranges. The simulations showed that a thin layer of particles formed and remained adhered to the pipe walls during the pneumatic conveying process due to the effects of strong electrostatic forces of attraction toward the pipe walls. Particle concentrations were generally higher near the pipe walls than at the pipe center resulting in the ring flow pattern observed in previous experimental studies. The close correspondence between particle velocity vectors and fluid drag force vectors was indicative of the importance of fluid drag forces in influencing particle behaviors. In contrast, the much weaker particle–particle electrostatic repulsion forces had negligible effects on particle behaviors within the system under all operating conditions considered. The electrostatic field strength developed during pneumatic conveying increased with decreasing flow rate due to increased amount of particle‐wall collisions. Based on dynamic analyses of forces acting on individual particles, it may be concluded that electrostatic effects played a dominant role in influencing particle behaviors during pneumatic conveying at low flow rates, whereas drag forces became more important at high flow rates. © 2011 American Institute of Chemical Engineers AIChE J, 2012