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

ABSTRACT

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.     

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.     

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.     

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.     

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.     

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.     

Effects of momentum transfer on particle dispersions of dense gas–particle two-phase turbulent flows

A modified momentum transfer coefficient of dense gas–particle two-phase turbulent flows is developed and its effect on particle dispersion characteristics in high particle concentration turbulent downer flows has been numerically simulated incorporating into a second-order moment (USM) two-phase turbulent model and the kinetic theory of granular flow (KTGF) to consider particle–particle collisions. The particle fractions, the time-averaged axial particle velocity, the particle velocities fluctuation, and their correlations between gas and particle phases based on the anisotropic behaviors and the particle collision frequency are obtained and compared using traditional momentum transfer coefficients proposed by Wen (1966), Difelice (1985), Lu (2003) and Beetstra (2007). Predicted results of presented model are in good agreement with experimental measurement by Wang et al. (1992). The particle fluctuation velocity and its fluctuation velocity correlations along axial–axial and radial–radial directions have stronger anisotropic behaviors. Furthermore, the presented model is in a better accordance with Lu’s model in light of particle axial velocity fluctuation, particle temperature, particle kinetic energy and correlations of particle–gas axial–axial velocity fluctuation. Also, they are larger than those of other models. Beetstra’s model is not suitable for this downer simulation due to the relative lower particle volume fraction, particle collision and particle kinetic energy.     

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.     

Stochastische Simulation der Schädigungsentwicklung in einem martensitischen Stahl

A probabilistic simulation model was developed for damage accumulation in the martensitic steel F82H‐mod under fatigue loading. Empirical relations for crack initiation, crack growth and coalescence of cracks are derived from an observation of experimental crack patterns and inserted in a stochastic simulation model based on a random cell structure. The simulation results are compared with the experimentally observed crack patterns.     

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.     

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.     

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.     

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     

Numerical simulation and measurement of liquid hold-up in biporous media containing discrete stagnant zones

We have studied hydrodynamic dispersion in single-phase incompressible liquid flow through a fixed bed made of spherical, permeable (porous) particles. The observed behaviour was contrasted with the corresponding fluid dynamics in a random packing of impermeable (non-porous) spheres with an interparticle void fraction of 0.37. Experimental data were obtained in the laminar flow regime by pulsed field gradient nuclear magnetic resonance and were complemented by numerical simulations employing a hierarchical transport model with a discrete (lattice Boltzmann) interparticle flow field. Finite-size effects in the simulation associated with the spatial discretization of support particles or dimension and boundaries of the bed were minimized and the simulation results are in reasonable agreement with experiment.     

滚动碰撞式调制质量阻尼器力学模型及参数分析

滚动碰撞式调制质量阻尼器(PTRMD)由调谐质量阻尼器及颗粒阻尼器发展而来,其在土木工程减振控制领域中的研究仍处于初步分析与探索阶段,阻尼器自身参数及外部激励条件对其减振性能的影响尚不明确。在考虑颗粒与主体结构碰撞和摩擦效应的基础上,建立PTRMD力学模型,并将颗粒和结构的振动过程划分为非碰撞过程、碰撞过程及黏滞振动过程;建立PTRMD-单自由度结构运动微分方程并分别对其进行求解;基于数值仿真分析方法,分别对碰撞间隙比、颗粒运动频率比、滚动摩擦因数、碰撞恢复系数、颗粒质量与简谐激励强度及频率等参数对PTRMD减振性能的影响进行研究。结果表明:颗粒运动频率比较小时,PTRMD减振效果随碰撞间隙比的增加而基本成线性增加,且受激励幅值的影响较小;当颗粒运动频率比较大时,其减振效果随碰撞间距比的增加先增大后减小,且受激励幅值影响较大。     

Resolution of cross-type optical particle separation

A real-time, continuous optical particle separation method, termed cross-type optical particle separation, is investigated theoretically and experimentally. The trajectory of a particle subject to cross-type optical particle separation is predicted by solving the particle dynamic equation and compared with experimental data. For various flow velocities and particle sizes, the retention distances are measured where the displacement perpendicular to the fluid flow direction is referred to as the retention distance. The measured retention distances are in good agreement with theoretical predictions. The retention distance increases as the particle size increases due to the radiation force, but decreases as the flow velocity increases since the residence time of a particle in the laser beam decreases with increasing flow velocity. To evaluate the performance of the cross-type optical particle separation method, size-based separation resolution is derived theoretically in terms of the refractive index of the particle and instrumental fluctuations. Furthermore, an expression for the maximum resolution is derived.     

Optimum design of agitator geometry for a dry stirred media mill by the discrete element method

Three different agitator geometries for a dry stirred media mill with a horizontal drum were studied experimentally and by DEM (discrete element method) simulation. Two optimized models, model A with stirring arms oriented in the same direction and model B with inclined stirring arms, achieved more rapid grinding with the lower adhesion of particles to the mill than the conventional stirring arms. Model A achieved the finest grinding with sharpest particle distribution.DEM simulation results suggested that rapid mixing, large collision energy, and a large number of collisions result in rapid grinding. DEM simulations of model A confirmed that the particle collision energy in this model was the highest of the models tested and resulted in the largest energy consumption and the largest temperature increase. In model B, DEM simulation results suggested that collision energy increased locally at the wall and resulted in a local temperature increase at the shaft. The high number of collisions in model B also resulted in rapid grinding but with a broad particle distribution. The decrease of the particle adhesion in models A and B was caused by a decrease in the collision energy between particles and the wall in the normal direction.     

Erosion of polymers and polymer composites surfaces by particles

Surface erosion due to solid particle impact is a major concern in engineering applications of handling solid-particulate flow. A semi-empirical model is developed for numerical erosion simulation of polymers and polymer composites. The novelty of the developed model is the correct capturing of the angle of maximum erosion for different erosion modes of polymeric materials and relating it to measurable mechanical properties of the target materials. The model incorporates both the material removal due to elastic–plastic collision of the particles at oblique and normal impact angles. The oblique impact model is derived for ploughing and fracture governed mechanisms of material removal. A simplified correlation is used to consider the relative effect of each mechanism on the total erosion at oblique impact angles. The model indicates the variation in velocity exponent to the mechanism of material removal. The theoretically derived model for single-particle impact is correlated to the available experimental results of multi-particle impacts through the empirical coefficients. The predictions are in good agreement with the extensive literature data for polymers and polymer composites. Further, to propose a single model of erosion for polymer and its composite, the relationship between the empirical coefficients in the developed model and the target material properties is established.     

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.