EXPERIMENTAL AND NUMERICAL STUDY OF THE PARTICLE FLUCTUATING MOTION INDUCED BY COLLISIONS BETWEEN PARTICLES IN A VERTICAL GAS-SOLID FLOW

The effect of interparticle collisions on the gravitational motion of large particles in a vertical convergent channel is experimentally and numerically investigated. A probabilistic collision model is implemented in a three-dimensional Monte Carlo type Lagrangian simulation code. The numerical predictions are compared to the experimental results. It is shown that an interparticle collision model is necessary to reproduce the experimentally observed particle fluctuating motion characteristics. The simulation results using the present probabilistic collision model are found to yield satisfactory agreement with experimental observations, even though the collision frequency seems to be slightly overestimated. In particular, reduction of initial anisotropy of the particle fluctuating motion with increasing particulate mass flow rate is well reproduced by the simulation. A rather good agreement is also observed between experimental results and quantitative predictions of statistical properties of the flow such as particle axial and transverse velocity distributions and standard deviations.     

Numerical analysis of particle transport during solidification using models based on stochastic differential equation

Abstract

In the present work, a comprehensive theoretical model is developed to describe the particle transport mechanisms in a solidifying binary melt in the presence of random thermofluidic fluctuations offered by the surrounding fluid medium. The detailed transport phenomena in the particle and bulk phases are coupled together through a stochastic formalism, capturing the physical mechanisms and consequences of complex interparticle interactions and the associated growth and/or dissolution of the crystals. The equation of the motion of the particles is modelled using the theory of stochastic differential equations. Numerical simulation study reveals the statistically randomised nature of the evolution of particle phase, which otherwise cannot be captured from a purely deterministic viewpoint. The mathematical model is also tested by comparing present numerical results with reported experimental observations; a very good agreement can be observed in this regard, thereby establishing the authenticity of the proposed formulation.     

Computational and experimental studies on bed dynamics of a gas–solid fluidized bed using Geldart-A particle: A comparison

The bed dynamics of a two-dimensional gas–solid fluidized bed is studied experimentally and computationally using Geldart-A particles. Commercial software ANSYS FLUENT 13 is used for computational studies. Unsteady behavior of gas–solid fluidized bed is simulated by using the Eulerian–Eulerian model coupled with the kinetic theory of granular flow. The two-equation standard k?? model is used to describe the turbulent quantities. The simulation predictions are compared with experimentally observed data on volume fraction, bed pressure drop and bed expansion ratio. The results of simulations are found to be in close agreement with the experimental observations, implying that computational fluid dynamics (CFD) can be used for the design of an efficient bench-scale catalytic fluidized bed reactor.     

PARTICLE DISPERSION BY COHERENT STRUCTURES IN FREE SHEAR FLOWS

ABSTRACT

The dispersion of particles in turbulent flows is poorly understood. Previous approaches to this problem have been found to be inadequate for nonisotropic turbulent flows. An approach involving a new physical concept is presented. This approach assumes that coherent vortex structures control the particle dispersion process in free shear flows. A simple computational model employing Stuart's vortices is used to simulate particle motion in a two-dimensional free shear layer. The results of this simulation are in reasonable agreement with previous experiments. For the first time, experimental observations indicating particle dispersion rates greater than fluid dispersion rates in free shear flows can be plausibly explained.     

Simulations of precipitation in ferritic steels

Abstract

A new technique based on Monte Carlo random sampling has been proposed to simulate the precipitation kinetics in alloys. The new approach employs time dependent nucleation and diffusion laws, considers both intergranular and intra-granular precipitation, and also combines precipitation kinetics with intergranular segregation. The simulation can be used not only to predict the average size of precipitate phase particles, but also to predict particle size distributions, volume fraction, and interparticle spacing. The new approach overcomes the shortcomings of earlier model calculations where only the average size of the precipitate phase is considered. In addition, the proposed simulation overcomes the difficulty of connecting Monte Carlo steps to real time using the Metropolis algorithm. The approach has been used to simulate M₂₃C₆ precipitation kinetics in a creep resistant steel, P92: the results are in good agreement with published experimental measurements, and the model is believed to be applicable to other types of precipitates in different alloys.     

Detailed computer simulation of ion implantation processes into crystals

Abstract

A modified version of the binary collision computer code Marlowe that can deal with low energy implant simulations is presented. In this version the trajectories of the particles are calculated by numerically solving their equations of motion instead of simply using the asymptotes, which is the usual approach. The model has been applied to the simulation of 0·5 keV boron implants into amorphous and crystalline silicon. The agreement with the experimental secondary ion mass spectrometry profiles is better than that obtained using the asymptotic approximation.

MST/3302     

Numerical simulation of smoke clearing with nanoparticle aggregates

Smoke reduction processes in an indoor room‐scale chamber are generated by injecting nanoparticle aggregates. A numerical model, with a flow solver implemented with a particle collision model, is used to simulate the smoke‐reduction effect. The collision model, developed particularly for simulating collisions among particles with significantly different sizes, enables real‐time simulations of three‐dimensional, two‐phase flow when flow/particle interactions need to be considered. The accuracy of the collision model is estimated by comparing with the exact solution from the Smoluchowski equation. The simulated smoke reduction results are compared with measured data with good agreement. Optimized particle size distributions are studied using the simulation. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical and theoretical study of particle saltation on an obliquely oscillating plate

Particle saltation on an obliquely oscillating plate is simulated using a mass-point model that considers gravity, fluid resistance, restitution, and friction. The calculated results are in good agreement with results obtained experimentally for particles with different diameters and restitutions. A large particle with high restitution bounces forward and backward repeatedly, whereas a particle with low restitution only bounces forward and consequently has a high transport velocity. The mechanism for the difference in the motion of the particles can be explained by taking into account the phase angle of the oscillating plate and the impulse during particle collision.     

THE CALCULATION OF PARTICLE DEPOSITION FROM A TURBULENT FLOW IN A PARALLEL VERTICAL PLATE

The formation of ash deposits may cause slagging and fouling problems in furnaces. The difficulties of predicting particle depositions are caused by the complexity of two-phase flow, which includes the particle size effects in a turbulent flow and the interparticle force between particles. Although some models were proposed to predict the particle deposition, few attempts were made for larger particles in the region of the dimensionless relaxation time (τ⁺) greater than 20. Thus, a reliable deposition model experimental results are needed for model verification, In this study, the modified turbulent intensity and apparent turbulent viscosity of the fluid were used to describe particles in suspension flow. And, an isothermal flow model was developed for calculating particle deposition rate in a parallel vertical plate, and for comparison with the experimental data. The predicted particle deposition rates under selected conditions are found to be in good qualitative agreement with available experimental results.     

Capturing non-Brownian particle transport in periodic flows

In this paper we computationally examine the motion of a dilute suspension of slightly non-neutrally buoyant solid spheres as they migrate across the curved fluid streamlines of a viscous cellular flow. This is done by incorporating particle-fluid interactions into a continuum-based Lagrangian advection model derived from the Basset–Boussinesq–Oseen (BBO) equation, where the flow field is mimicked by using a perturbed streamfunction. Although the purely regular cellular flow is able to capture maximum velocity and particle diameter effects that are observed experimentally, it has several shortcomings. Most significantly, it is unable to capture the secondary island structures that exist in many rotating flow systems, nor the impact that these structures are observed to have on particle migration. Our results in this work demonstrate significant interplay between the underlying fluid structure and the non-trivial equilibrium locations of the non-Brownian particles, in agreement with previous experimental work. We also evaluate the effect of the Saffman lift force on the lateral migration of the solid spheres.     

Simulation and verification of particle flow with an elastic collision by the immersed edge-based smoothed finite element method

The immersed edge-based smoothed finite element method (IES-FEM) is proposed for the study of elastic collision particulate flow. Particle collision becomes more realistic by using the penalty function and the hyperelastic constitutive model. The effects of grid resolution and Reynolds numbers on particle terminal velocity and drag coefficient are discussed to verify the calculation accuracy and stability. Single-particle collisions with the bottom and side walls are analyzed and experimentally verified. Results show that the calculation error of IES-FEM is less than 0.6% when the fluid grid size is 0.5 times the particle mesh size and the time step is 10^–4 s. Particle drag coefficient and flow characteristics agree well with the published models and experiment results. To demonstrate the capabilities of IES-FEM in complex elastic particle systems, the collision and rebound of multiple particles are determined, including the drafting–kissing–tumbling of two circular particles; the chase, collision, and deformation of rectangular particles; and the repeated formation and separation of particle clusters. This work extends the application of IES-FEM in particle-resolved direct numerical simulation methods, which will provide an optional tool for future elastic blood cell flow and collision.     

Hydrodynamic predictions of dense gas–particle flows using a second-order-moment frictional stress model

Based on the Eulerian–Eulerian two-fluid continuum approach, an improved unified second-order-moment two-phase turbulence model combining with the kinetic theory of particle collision frictional stress model is developed to simulate the dense gas–particle flows in downer, where the effective coefficient of restitution is incorporated into the particle–particle collision. The interaction term between gas and particle turbulence is fully taken into account by the transport equation of two-phase stress correlation. Hydrodynamics of high density particle flow, measured by Wang et al. [27] are predicted and the simulated results are in good agreement with experimental data. On the conditions of considering the realistic energy dissipation due to frictional stress, particle concentration and particle axial averaged velocity are closely the measured and they are better than without frictional stress model. Furthermore, the particle Reynolds stress is redistributed and the particle temperature is reduced. Effect of frictional stress leads to increase obviously the collision frequency at the outlet and inlet regions and the magnitude of frequency of particle collisions is 10².     

THE PSEUDOHOMOGENEOUS FLOW APPROXIMATION FOR DISPERSED TWO-PHASE SYSTEMS

ABSTRACT

The unsuitabllity of a continuum model for turbulent flow of solid-liquid mixtures has been demonstrated by a number of experimental studies which employed industrial slurries and a wide range of pipe diameters. However effective particle sizes and slurry viscosities are difficult to define for such mixtures. Using spherical glass particles of median diameter 125 μm and 240 μm, vertical flow experiments have been conducted in a test pipeline 26.17 mm in diameter. These experiments confirm earlier sand flow measurements by showing that wall friction decreases as particle size increases, in the absence of Bagnold stress or Coulombic friction effects.

Using a turbulent flow simulation, and assuming a linear increase of solids concentration in a thin layer near the pipe wall, dimensionless excess wall frictional resistances have been calculated. These predictions are likely to be valid for fine particles which do not display Bagnold stress or Coulombic friction effects.

The turbulent flow simulations confirm the effects observed in the experiments. They show that the pseudohomogeneous flow assumption is not useful for pressure drop prediction with slurries of fine particles.     

Unilateral interactions in granular packings: a model for the anisotropy modulus

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.     

CFD-DEM combined the fictitious domain method with monte carlo method for studying particle sediment in fluid

The interaction between a particle and the viscous fluid and then the particle-wall collision in the flow field plays an important role in the study of particulate flow. In this paper, we examine the velocity characteristics of a spheroidal particle sediment in the fluid and its rebound dynamics by applying the Computational Fluid Dynamics-Discrete Element Method (CFD-DEM). The Fictitious Domain method and Monte Carlo method are combined to improve the accuracy of the hydrodynamic force acting on the particle. A soft-sphere scheme of DEM is used to model the collision of particles, and the hydrodynamic force on the particle is fully solved directly from the CFD-DEM. The numerical results are verified by comparing the previous numerical and experimental results. The results are in good agreement with the corresponding published data. The simulation results show that the critical factor that affects the particle rebound is Stokes number (St). No rebound occurs when Stokes number is equal to 3.74. Initially, the results show that the ellipsoid particle shows large “wiggles” down the square tube at 45° angle with respect to the horizontal axis. These large “wiggles” gradually reduce after a time, and the ellipsoid finally settles into a stable horizontal state in the center of the square tube due to the effect of fluid viscosity dissipation.     

Comparison of three separated flow models

 An improved stochastic separated flow (ISSF) model developed by the present authors is compared with two other widely used trajectory models, the deterministic separated flow (DSF) model and the stochastic separated flow (SSF) model, in numerical simulations of gas–particle flows behind a backward-facing step. The DSF and ISSF models are found to need only 250 computational particles to obtain a statistically stationary solution of mean and fluctuating velocities of the particles, while the SSF model requires as many as 10,000 computational particles. Apart from comparing the sensitivity of required computational particles for different models, prediction capability of different models on mean velocities, fluctuating velocities and re-circulation region are also compared in this paper. Predicted results of streamwise mean velocity of particle phase agree well with experimental data for all the three models. For the mean fluctuating velocity of the particle phase, predictions using the ISSF model agree well with experiment data, while the DSF and the SSF models have a significant difference. Only the SSF and the ISSF models are capable of predicting re-circulation regions of the particle phase. As a comparison, the ISSF model has a distinct advantage over the other two models both in terms of accuracy and efficiency. Received 20 October 2001 / Accepted 5 February 2002     

Particle Detachment from Rough Surfaces in Turbulent Flows: An Analytical Expression for Resuspension Fraction

The critical shear velocity for resuspension of micrometer size particles from rough surfaces was studied. The random variation of surface roughness was accounted for. The recently developed Monte Carlo simulations accounted for the statistical variations of physical parameters that control the particle resuspension process. A sensitivity analysis showed that the surface roughness and its random variation was the key factor affecting the particle resuspension from rough surfaces. The theory of probabilistic transformation was used and an analytical expression for evaluating the resuspension fraction of particles of different sizes from rough surfaces versus the shear velocity was developed. The resuspension fractions as predicted by the analytical model were evaluated for several particles sizes for a range of turbulent flow shear velocities. The resulting resuspension fractions were compared with those obtained from the Monte Carlo simulations as well as the available experimental data. It was found that the predictions of the new analytical equation were in good agreement with the Monte Carlo simulation results and the experimental data, especially for smaller size particles. This new analytical expression could be used as a simple empirical equation for estimating flow-induced resuspension of particles from rough surfaces.     

Simulation of coupling filtration and flow in a dual scale fibrous media

In this article, numerical simulation of suspension (particles filled-resin) flow through a fibrous media taking into account dual scale porosity in LCM (Liquid Composite Molding) processes is presented. During the flow, a strong interaction between the particle motion and the fluid flow takes place at the porous media wall (the fiber bundle surface). In this study, the Stokes–Darcy coupling is used to describe the resin flow at mesoscopic scale to treat the particles in suspension. A “fluid” model to describe the suspension flow, a “filtration” model to describe the particle capture and a “solid” model dedicated to the modeling of mass particles dynamics was used. The “solid” model is also operated to identify the particles retention.For validation, the numerical results of proposed model were compared with the experimental results from the literature and found in good agreement. Then, other numerical results studying the suspension’s rheological behavior are presented.     

Distinct Element Model of Energy Dissipation in Vibrated Binary Particulate Mixtures

Distinct element model (DEM) simulations of energy dissipation in vibrated particle beds are compared with experimental results. DMX, a 3-D DEM of polydisperse spheres in an open-top vibrating cylinder, was used. Simulations were conducted for vibrating mono and binary particle systems. Energy dissipation rate per vibration cycle at different frequencies and maximum accelerations was examined. Experimental data from previous publications were compared with the simulations. Reasonable qualitative agreement was achieved on scaled-up (by number of particles) simulation results. These show that DEM can capture the harmonic phenomena, showing resonance in dissipation at several frequencies at low accelerations (<1 g). At high acceleration levels (>1 g) no harmonics are observed. At low frequency levels where the vibration amplitudes are higher, the DEM reproduces experimental energy dissipation levels better than a continuum viscoelastic model. For a larger diameter vessel (fewer layers and decreased wall effects) the resonant dissipation frequency increases. Quantitative agreement between DMX predictions and the experiments is reasonable given the scatter in the experimental results; at high frequency there is at least an order of magnitude difference in the rate of dissipation, which was also observed in viscoelastic model predictions. Results show that even with using only 100 particles the agreement between DMX predictions and the experiments is qualitatively reasonable. This will enable the examination of many more situations and combinations as it can be carried out relatively “fast.”     

Numerical simulation of gas-particle flows behind a backward-facing step using an improved stochastic separated flow model

An improved stochastic separated flow (ISSF) model developed by the present authors is tested in gas-particle flows behind a backward-facing step, in this paper. The gas phase of air and the particle phase of 150 μm glass and 70 μm copper spheres are numerically simulated using the k–ɛ model and the ISSF model, respectively. The predicted mean streamwise velocities as well as streamwise and transverse fluctuating velocities of both phases agree well with experimental data reported by Fessler. The reattachment length of 7.6H matches well with the experimental value of 7.4H. Distributions of particle number density are also given and found to be in good agreement with the experiment. The sensitivity of the predicted results to the number of calculation particles is studied and the improved model is shown to require much less calculation particles and less computing time for obtaining reasonable results as compared with the traditional stochastic separated flow model. It is concluded that the ISSF model can be used successfully in the prediction of backward-facing step gas-particle flows, which is characterised by having recirculating regions and anisotropic fluctuating velocities. Received 20 June 2000