scholarly journals DPM Simulations of A-Type FCC Particles’ Fast Fluidization by Use of Structure-Dependent Nonlinear Drag Force

Processes ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1574
Author(s):  
Guorong Wu ◽  
Yanggui Li
Keyword(s):  
Drag Force ◽  
Fine Particles ◽  
Fluid Model ◽  
Particle Diameter ◽  
Flow Structures ◽  
Time Step ◽  
Obvious Effect ◽  
Space Resolution ◽  
Drag Model ◽  
Back Mixing

Nonlinear drag force has been a research frontier in complex gas-solid systems. The literature has reported that the commonly-used drag correlations often overestimate drag force and, thus, cause unrealistic homogeneous flow structures in gas-solid fluidized beds of fine particles. For solving this problem, the structure-dependent drag model, derived from energy-minimization multi-scale approach, is used in discrete simulations of fluid catalytic cracking particles in a small riser. The gas phase is dealt with by computational fluid dynamics. Particles are considered as a discrete phase and described by Newton’s second law of motion. Gas-particle phases are coupled according to Newton’s third law of motion. Simulations show that use of structure-dependent drag model results in drag reduction, the effect of which is not so apparent as that in simulations of the two fluid model. The particle clustering tendency, however, is more distinct and leads to more heterogeneous flow structures in riser flow with a much greater amplitude of outlet solid flux fluctuations. Moreover, the behaviors of particle and gas back-mixing can be captured in the present simulations, which was supported by past simulations and experimental data. The simulation time resolution is discussed. The spring constant can be artificially brought down for safe setting of larger time step when modelling the collision process between fine particles with a higher calculation load. To appropriately mimic the continuous decay of van der Waals force may, however, need a much smaller time step. There is also an obvious effect of space resolution on simulations. When using a grid size smaller than 3 times the particle diameter, the simulated clusters turn extraordinarily large, and the effect of gas-solid back-mixing turns insignificant.

Effect of microstructural anisotropy on the fluid–particle drag force and the stability of the uniformly fluidized state

2012 ◽  
Vol 713 ◽  
pp. 27-49 ◽  
Author(s):  
William Holloway ◽  
Jin Sun ◽  
Sankaran Sundaresan
Keyword(s):  
Friction Coefficient ◽  
Drag Force ◽  
Fluid Model ◽  
Stokes Number ◽  
Spherical Particles ◽  
Force Model ◽  
Drag Model ◽  
Fluidized State ◽  
Two Fluid Model ◽  
Two Fluid

AbstractLattice-Boltzmann simulations of fluid flow through sheared assemblies of monodisperse spherical particles have been performed. The friction coefficient tensor extracted from these simulations is found to become progressively more anisotropic with increasing Péclet number, $Pe= \dot {\gamma } {d}^{2} / D$, where $\dot {\gamma } $ is the shear rate, $d$ is the particle diameter, and $D$ is the particle self-diffusivity. A model is presented for the anisotropic friction coefficient, and the model constants are related to changes in the particle microstructure. Linear stability analysis of the two-fluid model equations including the anisotropic drag force model developed in the present study reveals that the uniformly fluidized state of low Reynolds number suspensions is most unstable to mixed mode disturbances that take the form of vertically travelling waves having both vertical and transverse structures. As the Stokes number increases, the transverse-to-vertical wavenumber ratio decreases towards zero; i.e. the transverse structure becomes progressively less prominent. Fully nonlinear two-fluid model simulations of moderate to high Stokes number suspensions reveal that the anisotropic drag model leads to coarser gas–particle flow structures than the isotropic drag model.

Computations of Particle-Laden Turbulent Jet Flows Based on Eulerian Model

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Pandaba Patro ◽  
Sukanta K. Dash
Keyword(s):  
Gas Flow ◽  
Fine Particles ◽  
Solid Phase ◽  
Fluid Model ◽  
Particle Diameter ◽  
Velocity Profiles ◽  
Solid Particles ◽  
Jet Flows ◽  
Particle Sizes ◽  
Turbulent Characteristics

Numerical simulations using an Eulerian two-fluid model were performed for spatially developing, two-dimensional, axisymmetric jets issued from a 30-mm-diameter circular nozzle. The nozzle was simulated separately for various flow conditions to get fully developed velocity profiles at its exit. The effect of interparticle collisions in the nozzle gives rise to solids pressure and viscosity, which are modeled using kinetic theory of granular flows (KTGF). The particle sizes are in the range of 30 μm to 2 mm, and the particle loading is varied from 1 to 5. The fully developed velocity profiles are expressed by power law, U=Uc(1-(r/R))N. The exponent, N, is found to be 0.14 for gas phase, irrespective of particle sizes and particulate loadings. However, the solid-phase velocity varies significantly with the particle diameter. For particle sizes up to 200 μm, the exponent is 0.12. The center line velocity (Uc) of the solid phase decreases and, hence, the slip velocity increases as the particle size increases. For 1 mm and 2 mm size particles, the exponent is found to be 0.08 and 0.05, respectively. The developed velocity profiles of both the phases are used as the inlet velocities for the jet simulation. The modulations on the flow structures and turbulent characteristics of gas flow due to the solid particles with different particle sizes and loadings are investigated. The jet spreading and the decay of the centerline mean velocity are computed for all particle sizes and loadings considered under the present study. Additions of solid particles to the gas flow significantly modulate the gas turbulence in the nozzle as well as the jet flows. Fine particles suppress the turbulence, whereas coarse particles enhance it.

The Investigation of Back-Mixing Particles near Dust Outlet in Cyclone Separator with Tangential Inlet

2011 ◽  
Vol 239-242 ◽  
pp. 2142-2148
Author(s):  
Hui Min Tan ◽  
Jian Jun Wang ◽  
You Hai Jin
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Particle Diameter ◽  
Particle Mass ◽  
Cyclone Separator ◽  
Axial Distribution ◽  
Computational Fluid Dynamics Analysis ◽  
Back Mixing ◽  
Tangential Inlet

Based on experimental and computational fluid dynamics analysis, the phenomenon of particle back-mixing near the dust outlet in cyclone separator with tangential inlet was studied. The results show that particle back-mixing appears near the dust outlet geometry. Particle back-mixing can be divided into dust hopper back-mixing and discharge cone back-mixing for different generation mechanism. The upward flow coming from dust hopper, which occupies 17.7% of the inlet gas, can induce dust hopper back-mixing. The particle mass flow rate that caused by dust hopper back-mixing occupies 46.6% of total inlet particle mass flow rate. Precessing vortex core, bias flow and high turbulent intensity near the dust outlet can induce discharge cone back-mixing. For both dust hopper back-mixing and discharge cone back-mixing, particle back-mixing is serious near the dust outlet geometry, which occupies 56.8% of total inlet particle mass flow rate. Particle which is smaller than 18μm can mix backward. The axial distribution of particle concentration decreases sharply in a range of 1.5 D (cyclone diameter) height above the dust discharge port. At last, only 2.6% of back-mixing particles with diameter no bigger than 13μm escape from vortex finder. This effect on separator efficiency increases with the particle diameter decreases.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals On the Accelerated Settling of Fine Particles in a Bidisperse Slurry

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Leonid L. Minkov ◽  
Yuliya O. Stepanova ◽  
Johann Dueck ◽  
Elizaveta V. Pikushchak
Keyword(s):  
Fine Particles ◽  
Stokes Equations ◽  
Fine Fraction ◽  
Particle Diameter ◽  
Sedimentation Velocity ◽  
Navier Stokes ◽  
Circulation Zone ◽  
Navier Stokes Equations ◽  
Volume Average ◽  
Bidisperse Suspension

An estimation of increasing the volume average sedimentation velocity of fine particles in bidisperse suspension due to their capturing in the circulation zone formed in the laminar flow of incompressible viscous fluid around the spherical coarse particle is proposed. The estimation is important for an explanation of the nonmonotonic shape of the separation curve observed for hydrocyclones. The volume average sedimentation velocity is evaluated on the basis of a cellular model. The characteristic dimensions of the circulation zone are obtained on the basis of a numerical solution of Navier-Stokes equations. Furthermore, these calculations are used for modelling the fast sedimentation of fine particles during their cosedimentation in bidisperse suspension. It was found that the acceleration of sedimentation of fine particles is determined by the concentration of coarse particles in bidisperse suspension, and the sedimentation velocity of fine fraction is proportional to the square of the coarse and fine particle diameter ratio. The limitations of the proposed model are ascertained.

The Effects of Vibrations on Particle Motion in a Viscous Fluid Cell

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Samer Hassan ◽  
Masahiro Kawaji
Keyword(s):  
Viscous Fluid ◽  
Drag Force ◽  
Particle Motion ◽  
Fluid Model ◽  
Resonance Phenomenon ◽  
Fluid Viscosity ◽  
Mass Force ◽  
Amplitude Data ◽  
Viscous Fluid Model ◽  
Fluid Cell

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities (58.0cP and 945cP), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan et al. (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of 58.5cP and 945cP. While there is a resonance frequency corresponding to the particle peak amplitude for oil (58.0cP), this phenomenon disappeared for glycerol (945cP). This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

A CFD Study of Existing Drag Models for Geldart A Particles in Bubbling Fluidized Beds

2014 ◽  
Author(s):  
Bahareh Estejab ◽  
Francine Battaglia
Keyword(s):  
Experimental Data ◽  
Fluidized Beds ◽  
Fine Particles ◽  
The Other ◽  
Particle Interactions ◽  
Model Group ◽  
Drag Model ◽  
Numerical Studies ◽  
Solid Phases ◽  
Drag Models

In this study, seven drag models are examined to determine how they affect fluidization behavior of Geldart A particles of biomass and coal. Notwithstanding the notable number of numerical studies to find the best drag model for larger particles, there is a dearth of information related to drag models for finer Geldart A particles. Additionally, to our knowledge, these drag models have not been tested with a binary mixture of Geldart A particles. Computational fluid dynamics was used to model the gas and solid phases in an Eulerian-Eulerain approach to simulate the particle-particle interactions of coal-biomass mixtures and compare the predictions with experimental data. In spite of the previous findings that bode badly for using predominately Geldart B drag models for fine particles, the results of our study reveal that if static regions of mass in the fluidized beds are considered, these drag models work well with Geldart A particles. It was found that the seven drag models could be divided into two categories based on their performance. One category included the Gidaspow family of drag models (Gidaspow, Gidaspow-Blend, and Wen-Yu) and the Syamlal-O’Brien drag model; these models closely predicted the experiments for single solids phase fluidization. For binary mixtures, however, the other drag model group (BVK, HYS, Koch and Hill) yielded better predictions.

scholarly journals Analysis of Induced Vibrations in Fully-Developed Turbulent Pipe Flow Using a Coupled LES and FEA Approach

2010 ◽  
Author(s):  
Thomas Shurtz ◽  
Daniel Maynes ◽  
Jonathan Blotter
Keyword(s):  
Structural Model ◽  
Fluid Model ◽  
Surface Displacement ◽  
Turbulent Pipe Flow ◽  
Experimental Investigations ◽  
Time Step ◽  
Pipe Surface ◽  
Wall Displacement ◽  
Fully Developed Turbulent Flow ◽  
Pipe Vibration

This paper presents an approach using numerical simulations that have been used to characterize pipe vibration resulting from fully developed turbulent flow in a straight pipe. The vibration levels as indicated by; pipe surface displacement, velocity, and acceleration are characterized in terms of the influences of geometric and material properties of the pipe, and the effects of varying flow velocity, fluid density and viscosity have considered Reynold’s numbers ranging from 9.1×104 – 1.14×106. A large eddy simulation fluid model was coupled with a finite element structural model to simulate the fluid structure interaction using both one-way and two-way coupled techniques. The one-way technique passes the spatially and temporally varying wall pressure from a completed flow solution with fixed wall boundaries to the structural model. The structural model is then solved for wall displacements. The two-way technique involves the additional passing of wall displacement back to the fluid model which is then resolved given the new boundary location. The structural and fluid models are thus continually updated until convergence is reached at each time step. The results indicate a strong nearly quadratic dependence of pipe wall displacement on fluid average velocity. This relationship has also been verified in experimental investigations of pipe vibration. The results also indicate the pipe vibration has a power law type dependence on several variables. Dependencies on investigated variables are non-dimensionalized and assembled to develop a functional relationship that characterizes turbulence induced pipe vibration.

Development of Elastic Drag Coefficient Model and Explicit Terminal Settling Velocity Equation for Particles in Viscoelastic Fluids

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 2962-2983 ◽  
Author(s):  
Zhengming Xu ◽  
Xianzhi Song ◽  
Zhaopeng Zhu
Keyword(s):  
Drag Force ◽  
Shear Viscosity ◽  
Settling Velocity ◽  
Particle Diameter ◽  
Viscoelastic Fluids ◽  
Proppant Transport ◽  
Fluid Elasticity ◽  
Fracturing Fluids ◽  
Proposed Model ◽  
Velocity Equation

Summary Viscoelastic fluids are frequently used as drilling or fracturing fluids to enhance cuttings or proppant transport efficiency. The solid transport performance of these fluids largely depends on the settling behaviors of suspended particles. Different from viscoinelastic fluids, the elastic and viscous characteristics of viscoelastic fluids both affect particle settling behaviors. In this study, to separately quantify the contribution degrees of the shear viscosity and fluid elasticity on the terminal settling velocity, we decompose the total drag force into a viscous drag force and an elastic drag force. Based on the experimental data from the available literature, it is concluded that the elastic drag force is a function of the fluid elasticity, particle diameter, particle terminal settling velocity, and density difference between the fluid and particle. The formula for the elastic drag force is determined on the basis of the force analysis, and a relationship between the elastic drag coefficient and particle Reynolds number (Re) is developed. An explicit equation that directly predicts the terminal settling velocity in viscoelastic fluids is determined by correlating the dimensionless particle diameter and Re. To validate the proposed model, a total of 108 settling experiments in viscoelastic fluids are conducted. The absolute percentage error (APE) between the predicted and measured terminal settling velocities is 15.26%, which indicates that the proposed explicit terminal settling velocity equation can provide satisfactory prediction accuracy of the terminal settling velocity for particles in viscoelastic fluids. Furthermore, an illustrative example is provided to show that the proposed model can be used to calculate the required fluid elasticity to obtain the desired terminal settling velocity when the fluid shear viscosity is fixed. The proposed models are valid with a consistency index range of approximately 0.16 to 1.2 Pa⋅sn, flow behavior index range of approximately 0.282 to 0.579, an Re range of approximately 0.005 to 30, and a fluid relaxation time range of approximately 0.183 to 110 seconds. This study can help operators choose proper drilling/fracturing fluids to enhance the cuttings/proppant transport and maximize drilling/fracturing performance.

scholarly journals Silicone Resin Coating of Micro-Sized Ferrite Particles Using Supercritical Carbon Dioxide

Polymers ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2012
Author(s):  
Idzumi Okajima ◽  
Tatsuya Kanie ◽  
Takeshi Sako
Keyword(s):  
Film Thickness ◽  
Organic Solvents ◽  
Supercritical Co2 ◽  
Fine Particles ◽  
Particle Diameter ◽  
Coating Material ◽  
Silicone Resin ◽  
Coating Film ◽  
Coating Materials ◽  
Coating Method

An environmentally friendly and efficient polymer coating method for micro-sized particles was developed using supercritical CO2. Because this method used supercritical CO2 as the solvent to dissolve the coating material, we avoided environmental pollution from organic solvents, saved the energy required to evaporate/remove organic solvents, realized a uniform coating film on the fine particles, and prevented agglomeration of the coating particles. The solubilities of the five silicone resins used as coating materials were measured using the flow method, and the data were well correlated by Chrastil’s equation with an average deviation of 5.7%. Resins comprising numerous methyl-group side chains exhibited high solubilities and were suitable coating materials. A new semi-flow-type coating method using supercritical CO2 was also developed, which deposited a film with a uniform thickness of 0.2–1.3 μm on whole fine particles. Notably, in this method, the film thickness was easily controlled. A simple and rapid technique was developed for measuring the coating thickness using X-ray fluorescence analysis. The model for calculating the coating film thickness was based on the material balance of the coating material. This model satisfactorily predicted the thickness with an average error of 0.085 μm by measuring the solubility of the coating material in supercritical CO2, integrated flow volume of supercritical CO2, particle diameter, density and charged weight of the fine particle, and coating material density.

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