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.     

Analysis of Mobility Effects in Particle-Gas Flows by Particle-Resolved LBM-DEM Simulations

Particle-resolved direct numerical simulations are performed to simulate the flow through particle assemblies that are either static or freely moving to demonstrate the influence of particle mobility. To obtain a comprehensive understanding for this influence essential parameters such as the Reynolds number, solids volume fraction, particle-fluid density ratio, collision parameters and particle shape are varied. The influence of particle mobility is assessed by evaluating the particle-fluid forces, the particle ensemble structure and particle velocities. It is found that the ability of existing correlations for static particle systems to predict drag and lift forces correctly in dynamic particle-gas flows is limited and that drift forces perpendicular to the drag force play an important role.     

Direct numerical simulation of moderate-Reynolds-number flow past arrays of ellipsoids

Through particle-resolved direct numerical simulations of flow past arrays of ellipsoids, the hydrodynamic force on ellipsoids depends on the particle orientation, aspect ratio, particle Reynolds number, and solid volume fraction is revealed at moderate Reynolds numbers. The results show that the mean drag force on arrays of prolate/oblate ellipsoids decreases/increases as the Hermans orientation factor increases when flows are in the reference direction defined by the average symmetric axis of particles. The individual drag force on a prolate/oblate ellipsoid increases/decreases with the increase of incidence angle, and it is also affected by the orientation of surrounding particles. The individual lift force is also significant when the aspect ratio is away from unity at large particle Reynolds numbers. Based on simulation results, correlations for the hydrodynamic force on ellipsoids at arbitrary particle Reynolds numbers, solid volume fractions, Hermans orientation factors, incidence angles, and aspect ratios are formulated.     

Fluidization of elongated particles—Effect of multi-particle correlations for drag,lift, and torque in CFD-DEM

Having proper correlations for hydrodynamic forces is essential for successful CFD-DEM simulations of a fluidized bed. For spherical particles in a fluidized bed, efficient correlations for predicting the drag force, including the crowding effect caused by surrounding particles, are already available and well tested. However, for elongated particles, next to the drag force, the lift force, and hydrodynamic torque also gain importance. In this work, we apply recently developed multi-particle correlations for drag, lift and torque in CFD-DEM simulations of a fluidized bed with spherocylindrical particles of aspect ratio 4 and compare them to simulations with widely used single-particle correlations for elongated particles. Simulation results are compared with previous magnetic particle tracking experimental results. We show that multi-particle correlations improve the prediction of particle orientation and vertical velocity. We also show the importance of including hydrodynamic torque.     

Lift and drag forces on a sphere attached to a wall in a Blasius boundary layer

Lift and drag forces on a sphere attached to a planar wall, over which a laminar flat plat boundary layer flows, are examined numerically in this study. Particle Reynolds number ranged from 0.1–250, which represents steady, laminar flow about the sphere, and the plate Reynolds number was held constant at 32 400. A finite-volume computational fluid dynamics program was utilised. Simulation results were validated against analytical results for drag and lift in creeping flow and against experimental results available in the literature for lift at higher particle Reynolds number. The model results were curve-fitted and interpolating drag and lift coefficient functions are reported. The lift and drag results are shown to be weakly dependent upon plate Reynolds number. The resulting correlations are expected to be useful in the development of particle impending motion and aerosol entrainment predictions of particles adhering to planar walls.     

Effect of particle orientation on the drag force in random arrays of prolate ellipsoids in low-Reynolds-number flows

Direct numerical simulations are performed to study the effect of particle orientation on flows through fixed random arrays of prolate ellipsoids at low Reynolds numbers. The Hermans orientation factor and Beta distribution are introduced to quantify the mean orientation and orientation deviation of the particles. The simulation results show that the effect of particle orientation is profound especially when the solid volume fraction and the aspect ratio are large. With the increase of Hermans orientation factors, the drag force decreases when the flow follows a reference direction defined by the average direction of all particles' semi-major axes, while increases when the flow is perpendicular to the reference direction. Comparisons show that the traditional drag force correlations for ellipsoidal particles significantly under-predict the drag force. Based on current simulation results, new drag relations are proposed for prolate ellipsoidal particles at arbitrary aspect ratios, Hermans orientation factors and solid volume fractions.     

Fluid‐particle drag in inertial polydisperse gas–solid suspensions

In this article, we extend the low Reynolds number fluid‐particle drag relation proposed by Yin and Sundaresan for polydisperse systems to include the effect of moderate fluid inertia. The proposed model captures the fluid‐particle drag results obtained from lattice‐Boltzmann simulations of bidisperse and ternary suspensions at particle mixture Reynolds numbers ranging from 0 ≤ Re_mix ≤ 40, over a particle volume fraction range of 0.2 ≤ ? ≤ 0.4, volume fraction ratios of 1 ≤ ?_i/?_j ≤ 3, and particle diameter ratios of 1 ≤ d_i/d_j ≤ 2.5. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

DEM simulation of gas-solid flow behaviors in spout-fluid bed

Three-dimensional gas and particle turbulent motions in a rectangular spout-fluid bed were simulated. The particle motion was modeled by discrete element method and the gas motion was modeled by k-ε two-equation turbulent model. Shear induced Saffman lift force, rotation induced Magnus lift force as well as drag force, contract force and gravitational force acting on individual particles were considered when establishing the mathematics models. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas-particle interactions in volume fraction, momentum and kinetic energy. The gas-solid flow patterns, forces acting on particles, the particles mean velocities, jet penetration depths, gas turbulent intensities and particle turbulent intensities were discussed. Selected stimulation results were compared to some published experimental and simulation results.     

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     

Numerical simulation of three‐dimensional gas‐solid particle flow in a horizontal pipe

A three‐dimensional model of particulate flows using the Reynolds Averaged Navier‐Stokes method is presented. The governing equations of the gas–solids flow are supplemented with appropriate closure equations to take into account all the relevant forces exerted on the solid particles, such as particle‐turbulence interactions, turbulence modulation, particle–particle interactions, particle–wall interactions, as well as gravitational, viscous drag, and lift forces. A finite volume numerical technique was implemented for the numerical solution of the problem. The method has been validated by comparing its results with the limited number of available experimental data for the velocity and turbulence intensity of the gas–particle flow. The results show that the presence of particles in the flow has a significant effect on all the flow variables. Most notably, the distribution of all the parameters becomes asymmetric, because of the gravitational effect on the particles and particle sedimentation. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016     

Numerical Simulation of Interfacial Closures for 3D Bubble Column Flows

Numerical investigation of flow hydrodynamics in a square cross‐sectioned bubble column was conducted in a transient Euler‐Euler environment by applying the simulation tool Ansys CFX 14.0. The influence of the drag coefficient (C_D) was investigated and the results were also compared with drag force models. Furthermore, three different lift force models and a defined lift coefficient were studied. All results were compared with the available experimental data. All simulations were carried out for a single‐hole sparger with given aspect ratio (H/D) and superficial gas velocity.     

Aerosol Particle Removal and Re-entrainment in Turbulent Channel Flows – A Direct Numerical Simulation Approach

Aerosol particle removal and re-entrainment in turbulent channel flows are studied. The instantaneous fluid velocity field is generated by the direct numerical simulation (DNS) of the Navier – Stokes equation via a pseudospectral method. Particle removal mechanisms in turbulent channel flows are examined and the effects of hydrodynamic forces, torques and the near-wall coherent vorticity are discussed. The particle resuspension rates are evaluated, and the results are compared with the model of Reeks. The particle equation of motion used includes the hydrodynamic, the Brownian, the shearinduced lift and the gravitational forces. An ensemble of 8192 particles is used for particle resuspension and the subsequent trajectory analyses. It is found that large-size particles move away roughly perpendicular to the wall due to the action of the lift force. Small particles, however, follow the upward flows formed by the near-wall eddies in the low-speed streak regions. Thus, turbulent near-wall vortical structures play an important role in small particle resuspension, while the lift is an important factor for reentrainment of large particles. The simulation results suggests that small particles (with τ _p ⁺ ≤ 0.023) primarily move away from the wall in the low-speed streaks, while larger particles (with τ _p ⁺ ≥ 780) are mostly removed in the high-speed streaks.     

The Factors Affecting the Particle Distributions Inside the Silane PCVD Reactor for Semiconductor Processing

The distributions of particles inside the silane plasma chemical vapor deposition (PCVD) reactor were theoretically investigated by analyzing the transport phenomena of particles for various plasma conditions. We included the effects of fluid convection, particle diffusion, and external forces (ion drag, electro static, and gravitational forces) onto the particles to analyze the movements of particles inside the plasma reactor. Initially, we assumed that the particles are uniformly distributed inside the plasma reactor and showed how these particles move and how they are distributed for various plasma conditions. The dominant force for the particle movement is the electrostatic force in the sheath region and the ion drag force in the bulk plasma region. Both the electrostatic and ion drag forces are towards the sheath boundaries and most of the particles are concentrated in the regions near the sheath boundaries by the balance of both forces, but the particle concentrations in the sheath region and in the bulk plasma region are almost 0. The particle concentrations at the down stream sheath boundary become higher than at the upstream sheath boundary by the effect of fluid convection. As the electric field strength increases, the particles are pushed more strongly towards the bulk plasma region and the peaks of particle concentrations are shifted more away from the electrodes. As the particle diameter increases from 0.1 mu m to 10 mu m, the relative importance of fluid convection on the particle movement becomes more significant than those of particle diffusion, ion drag force, and electrostatic force and the particle concentrations at the down stream sheath boundary increase, while those at the upstream sheath boundary decrease. It is found that the movements of negative ions as well as the positive ions are also important for determining the ion drag force onto the particles in silane PCVD.     

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.     

Facile method to synthesize magnetic iron oxides/TiO2 hybrid nanoparticles and their photodegradation application of methylene blue

The primary objective of this study is to investigate the effect of slip mechanisms in nanofluids through scaling analysis. The role of nanoparticle slip mechanisms in both water- and ethylene glycol-based nanofluids is analyzed by considering shape, size, concentration, and temperature of the nanoparticles. From the scaling analysis, it is found that all of the slip mechanisms are dominant in particles of cylindrical shape as compared to that of spherical and sheet particles. The magnitudes of slip mechanisms are found to be higher for particles of size between 10 and 80 nm. The Brownian force is found to dominate in smaller particles below 10 nm and also at smaller volume fraction. However, the drag force is found to dominate in smaller particles below 10 nm and at higher volume fraction. The effect of thermophoresis and Magnus forces is found to increase with the particle size and concentration. In terms of time scales, the Brownian and gravity forces act considerably over a longer duration than the other forces. For copper-water-based nanofluid, the effective contribution of slip mechanisms leads to a heat transfer augmentation which is approximately 36% over that of the base fluid. The drag and gravity forces tend to reduce the Nusselt number of the nanofluid while the other forces tend to enhance it.     

Behavior of Compact Nonspherical Particles in the TSI Aerodynamic Particle Sizer Model APS33B: Ultra-Stokesian Drag Forces

The aerodynamic behavior of aggregates consisting of uniform polystyrene latex (PSL) spheres and unaggregated cuboidal Natrojarosite particles in a TSI aerodynamic particle sizer (Model APS33B) has been studied. In initial tests, monodisperse PSL micro-spheres ranging from 0.3 to 7 μm in geometric diameter were generated from aqueous suspensions using a Lovelace nebulizer. APS33B responses for these uniform-sized particles showed multiple peaks. The major (primary) peak, which resulted from the smallest particle, corresponded to the unaggregated single spheres (singlets); the second, third, and fourth peaks were identified as doublets, triangular triplets, and tetrahedral quadruplets, respectively. Both doublets and triplets moved with their long axes in perpendicular (maximum drag) orientation to the flow direction in the APS33B. In contrast, the tetrahedral particles were isometric and had the same dynamic shape factor (drag resistance) for all three primary orientations. The particle Reynolds numbers (Re _p) for these particles were calculated and ranged from 0.2 to 30 in the sensing volume of the APS33B detector (i.e., ultra-Stokesian conditions). Ultra-Stokesian drag forces for all three types of aggregates were, therefore, estimated and expressed as a function of an empirical factor (1 + aRe ^b _p) to the Stokesian drag force. The ultra-Stokesian drag of a Natrojarosite particle was measured in the range 20 Re _p < 50 and could be described with a similar expression. This approach facilitates the study of the dynamic behavior of nonspherical particles and yields new information about the characteristics of drag forces in the ultra-Stokesian regime     

Separation of Cells and Cell-Sized Particles by Continuous SPLITT Fractionation Using Hydrodynamic Lift Forces

Abstract

The use of hydrodynamic lift forces for the separation of particles according to size by continuous SPLITT fractionation is explored. The mechanism for particle separation in the transport mode of SPLITT fractionation is first explained. This is followed by a discussion of the hydrodynamic lift forces that act upon particles entrained in fluid flow between the parallel bounding walls of the SPLITT cell. The effect of the bounding walls on particle motion both parallel and perpendicular to the direction of flow is explained. Computer simulations of particle trajectories are presented that predict extremely high size selectivity for the method. A parallel experimental study was carried out using both polystyrene latex particles and red blood cells. The experimental selectivity was found to be smaller than that predicted theoretically. This discrepancy is attributable to nonidealities in the construction of the SPLITT cell. Nonetheless, the results are promising. Suspensions of polystyrene particle standards (from 2 to 50 μm in diameter) demonstrate that fast and relatively clean size separations are possible provided particles differ sufficiently in size and flow conditions are properly optimized. It is also shown that the system has the potential to quickly and gently separate blood cells from plasma.     

Density segregation of dry and wet granular mixtures in gas fluidized beds

The Discrete Element Method combined with Computational Fluid Dynamics was coupled to a capillary liquid bridge force model for computational studies of mixing and segregation behaviors in gas fluidized beds containing dry or wet mixtures of granular materials with different densities. The tendency for density segregation decreased with increasing fluidizing velocity, coefficient of restitution, and amount of liquid present. Due to the presence of strong capillary forces between wet particles, there was a high tendency for particles to form agglomerates during the fluidization process, resulting in lower segregation efficiency in comparison with fluidization of dry particles. Particle‐particle collision forces were on average stronger than both fluid drag forces and capillary forces. The magnitudes of drag forces and particle‐particle collision forces increased with increasing fluidizing velocity and this led to higher mixing or segregation efficiencies observed in dry particles as well as in wet particles at higher fluidizing velocities. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4069–4086, 2015