Particulate flow modelling in a spiral separator by using the Eulerian multi-fluid VOF approach

The Euler-Euler model is less effective in capturing the free surface of flow film in the spiral separator,and thus a Eulerian multi-fluid volume of fluid(VOF)model was first proposed to describe the particulate flow in spiral separators.In order to improve the applicability of the model in the high solid concentration system,the Bagnold effect was incorporated into the modelling framework.The capability of the proposed model in terms of predicting the flow film shape in a LD9 spiral separator was evaluated via comparison with measured flow film thicknesses reported in literature.Results showed that sharp air–water and air-pulp interfaces can be obtained using the proposed model,and the shapes of the predicted flow films before and after particle addition were reasonably consistent with the observations reported in literature.Furthermore,the experimental and numerical simulation of the separation of quartz and hematite were performed in a laboratory-scale spiral separator.When the Bagnold lift force model was considered,predictions of the grade of iron and solid concentration by mass for different trough lengths were more consistent with experimental data.In the initial development stage,the quartz particles at the bottom of the flow layer were more possible to be lifted due to the Bagnold force.Thus,a better predicted vertical stratification between quartz and hematite particles was obtained,which provided favorable conditions for subsequent radial segregation.

LDA Study of Particulate Flow in a Channel with Deformed Surface Locations and with Flow Conditioner

Hydroabrasion in particulate flows plays an important role in various industrial and natural processes. To predict the effects of particulate flow and the resulting phenomena such as erosion/abrasion in a pipeline, channel or a fitting, it is essential to characterize the effects in a simple standardized geometry. For this purpose, it is vital to initially understand the particulate flow behavior and motion in such geometries. In the present work, two series of experimental works by application of the LDA measurement technique were successfully conducted. First, the particulate flow behavior at downstream of a flow conditioner inside a channel with square cross-section was investigated. Shorter lengths for fully development of velocity profile by using the self-constructed flow conditioner were observed. Moreover, the flow at downstream of the conditioner was modeled with the CFD tool (ANSYS-CFX V. 14.57) and the simulation results were compared and validated by the LDA experimental data. Better agreement between the simulation results and experimental data was observed in the fully developed region. However, there are some deviations due to the actual pressure loss through the experimental loop and the calculated pressure loss value, which includes some assumptions for the loss coefficients. Furthermore, the particulate flow behavior and vortex generation inside the deformed locations of a channel surface were studied in detail. With the help of the Matlab program, it was possible to calculate and visualize the velocity vectors for each measured point inside the channel accurately.

Solid particle size characterization by a high-frequency collision response in pneumatic particulate flow

A novel triaxial vibration method is developed for the real-time characterization of the solid particle size distribution(PsD)in pneumatic particulate flow,which is critical for chemical industry.In this work,the particle-wall collision and friction behaviours were analysed by the time-domain statistical and timefrequency joint methods to narrow the high-frequency response range by the initial experiment of free fall for a single particle,interparticle,and multiple particles.Subsequently,verification experiments of PSD characterization in pneumatic flow were performed.First,the quantitative triaxial energy response model that considers the particle size,shape,and mass factors were established.Second,a good agreement of the particle number identification was found between the triaxial vibration energy and mean particle size of 150-550μm.Moreover,the performance with the best accuracy was focused on a range of 42-43 kHz in the x-axis and z-axis and 36.8-38.8 kHz in the y-axis.Finally,the individual particle energy was inversely analysed by the triaxial vibration response within the optimized frequency bands,and the PSD was characterized in real-time by a low error rate,that is,5.2% from the XZ-axis direction of sand(42-43 kHz)and 5.6% from the XYZ-axis of glass(30.9-33.9 kHz,46.2-47.2 kHz,38.3-41.3 kHz for each axis response).Therefore,this research complements the existing approaches for PsD characterization in particulate multiphase flow.

Evaluating the stability and volumetric flowback rate of proppant packs in hydraulic fractures using the lattice Boltzmann-discrete element coupling method

The stability and mobility of proppant packs in hydraulic fractures during hydrocarbon production are numerically investigated by the lattice Boltzmann-discrete element coupling method(LB-DEM).This study starts with a preliminary proppant settling test,from which a solid volume fraction of 0.575 is calibrated for the proppant pack in the fracture.In the established workflow to investigate proppant flowback,a displacement is applied to the fracture surfaces to compact the generated proppant pack as well as further mimicking proppant embedment under closure stress.When a pressure gradient is applied to drive the fluid-particle flow,a critical aperture-to-diameter ratio of 4 is observed,above which the proppant pack would collapse.The results also show that the volumetric proppant flowback rate increases quadratically with the fracture aperture,while a linear variation between the particle flux and the pressure gradient is exhibited for a fixed fracture aperture.The research outcome contributes towards an improved understanding of proppant flowback in hydraulic fractures,which also supports an optimised proppant size selection for hydraulic fracturing operations.

Particulate Flow Simulation via a Boundary Condition-Enforced Immersed Boundary-Lattice Boltzmann Scheme

A boundary condition-enforced immersed boundary-lattice Boltzmannmethod (IB-LBM) for the simulation of particulate flows is presented in this paper. Ingeneral, the immersed boundary method (IBM) utilizes a discrete set of force densityto represent the effect of boundary. In the conventional IB-LBM, such force density ispre-determined, which cannot guarantee exact satisfaction of non-slip boundary condition. In this study, the force density is transferred to the unknown velocity correctionwhich is determined by enforcing the non-slip boundary condition. For the particulateflows, accurate calculation of hydrodynamic force exerted on the boundary of particlesis of great importance as it controls the motion of particles. The capability of presentmethod for particulate flows is depicted by simulating migration of one particle in asimple shear flow and sedimentation of one particle in a box and two particles in achannel. The expected phenomena and numerical results are achieved. In addition,particle suspension in a 2D symmetric stenotic artery is also simulated.

Algorithm design and the development of a discrete element method for simulating particulate flow and heat transfer

An algorithm using the discrete element method(DEM)for simulating the particulate behaviour of flow and heat transfer is developed and described,the reasonable hypothesis and the ingenious design of which have been presented in detail.The organizational structure of the developed algorithm contains an efficient method for determining particle collisions,the status analysis for each particle and the particulate-kinematics analysis during the time step.The reasonability and correctness of the developed DEM algorithm are validated by laboratory experiments:the discharge process of glass beads from a silo;and heating of metal alloy particles in a calciner.Afterwards,a group of validated mechanics parameter values for coal and sand have been tested and verified in the article,preparing for the simulation of the pyrolysis process in a downer or screw reactor in subsequent research projects.

MATHEMATICAL MODELS AND NUMERICAL SIMULATION FOR DENSE PARTICULATE FLOWS

Sedimentation of particles in inclined and vertical vessels is numerically simulated by the Eulerian two-fluid model. The numerical results show an interesting phenomenon with two circulation vortexes in a vertical vessel but one in the inclined vessel. Sensitivity tests indicate that the boundary layer effect is the key to induce this phenomenon. A numerical method based on 2D unstructured meshes is presented to solve the hard-sphere discrete particle model. Several applications show the numerical method has a good performance to simulate dense particulate flows in irregular domains without regard to element types of the mesh.

Direct numerical simulation of the motion of circular pollutant particles in Newtonian fluid

An improved implementation of distributed multiplier/fictitious domain method is presented for the direct numerical simulation of particulate flow. The key improvement is to replace a finite element triangulation for the velocity and a “twice coarser' triangulation for the pressure with a rectangular discretization for the velocity and pressure. For code validation, the sedimentation of a single particle in a two dimensional channel was simulated. The results showed that the simulation is independent of the mesh size as well as the time step. The comparison between experimental data and this simulation showed that our code can give a more accurate simulation on the motion of particles than previous DLM code. The code was then applied to simulate the sedimentation of 600 particles in a rectangular box. The falling course is presented and discussed. At the same time, this simulation also demonstrates that the method presented in this paper can be used for solving the initial problems involving a lager number of particles exactly with computing durations kept at acceptable levels.

Feature-Scale Simulations of Particulate Slurry Flows in Chemical Mechanical Polishing by Smoothed Particle Hydrodynamics

In this paper,the mechanisms of material removal in chemical mechanical polishing(CMP)processes are investigated in detail by the smoothed particle hydrodynamics(SPH)method.The feature-scale behaviours of slurry flow,rough pad,wafer defects,moving solid boundaries,slurry-abrasive interactions,and abrasive collisions are modelled and simulated.Compared with previous work on CMP simulations,our simulations incorporate more realistic physical aspects of the CMP process,especially the effect of abrasive concentration in the slurry flows.The preliminary results on slurry flow in CMP provide microscopic insights on the experimental data of the relation between the removal rate and abrasive concentration and demonstrate that SPH is a suitable method for the research of CMP processes.

DIRECT NUMERICAL SIMULATIONS OF THE DYNAMICS OF PARTICLES WITH ARBITRARY SHAPES IN SHEAR FLOWS

A fluid-structure interaction method based on the arbitrary Lagrangian-Eulerian method and a dynamic mesh method was developed to simulate the dynamics of a rigid particle in shear flows.In the method,the governing equations for the fluid flow and particle motion were sequentially solved in a two-way coupling fashion.The mesh system was deformed or re-meshed by the dynamic mesh method.The method was employed to simulate the dynamics of a single particle suspended in a flow channel and the dynamics of the particle were studied.The simulation results show that the angular velocity is not only a function of the inclination angle,is but also influenced by the aspect ratio yielding a hysteresis,while the angular velocity obtained from the Keller-Scalak model is a function only of the inclination angle and does not show a hysteresis.The present simulations clearly demonstrate that the Fluid-Structure Interaction（FSI） module is very stable,accurate and robust.

A Review on Contact and Collision Methods for Multi-Body Hydrodynamic Problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere,to fluidization in the combustion process,to aerosol deposition in spray medication,along with many others.Due to their strongly nonlinear and multiscale nature,the above complex phenomena still raise a very steep challenge to themost computationalmethods.In this review,we provide comprehensive coverage of multibody hydrodynamic(MBH)problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models.Among these hybridmodels,the Immersed Boundary-Lattice Boltzmann Method(IB-LBM)provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations.This paper elaborates on the mathematical framework,applicability,and limitations of various’simple to complex’representations of closecontact interparticle interactions and collision methods,including short-range interparticle and particle-wall steric interactions,spring and lubrication forces,normal and oblique collisions,and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.

On the Anisotropic Gaussian Velocity Closure for Inertial-Particle Laden Flows

The accurate simulation of disperse two-phase flows,where a discrete particulate condensed phase is transported by a carrier gas,is crucial for many applications;Eulerian approaches are well suited for high performance computations of such flows.However when the particles from the disperse phase have a significant inertia compared to the time scales of the flow,particle trajectory crossing(PTC)occurs i.e.the particle velocity distribution at a given location can become multi-valued.To properly account for such a phenomenon many Eulerian moment methods have been recently proposed in the literature.The resulting models hardly comply with a full set of desired criteria involving:1-ability to reproduce the physics of PTC,at least for a given range of particle inertia,2-well-posedness of the resulting set of PDEs on the chosen moments as well as guaranteed realizability,3-capability of the model to be associated with a high order realizable numerical scheme for the accurate resolution of particle segregation in turbulent flows.The purpose of the present contribution is to introduce a multi-variate Anisotropic Gaussian closure for such particulate flows,in the spirit of the closure that has been suggested for out-of-equilibrium gas dynamics and which satisfies the three criteria.The novelty of the contribution is three-fold.First we derive the related moment system of conservation laws with source terms,and justify the use of such a model in the context of high Knudsen numbers,where collision operators play no role.We exhibit the main features and advantages in terms of mathematical structure and realizability.Then a second order accurate and realizable MUSCL/HLL scheme is proposed and validated.Finally the behavior of the method for the description of PTC is thoroughly investigated and its ability to account accurately for inertial particulate flow dynamics in typical configurations is assessed.

Particle flow simulations with homogenised lattice Boltzmann methods

An alternative approach to simulating arbitrarily shaped particles submersed in viscous fluid in two dimensions is proposed, obtained by adapting the velocity parameter of the equilibrium distribution function of a standard lattice Boltzmann method （LBM）. Comparisons of exemplifying simulations to results in the literature validate the approach as well as the convergence analysis. Pressure fluctuations occurring in Ladd＇s approach are greatly reduced. In comparison with the immersed boundary method, this approach does not require cost intensive interpolations. The parallel efficiency of LBM is retained. An intrinsic momentum transfer is observed during particle-particle collisions. To demonstrate the capa- bilities of the approach, sedimentation of particles of several shapes is simulated despite omitting an explicit particle collision model.

FULLY RESOLVED NUMERICAL SIMULATION OF TURBULENT PIPE FLOWS LADEN WITH LARGE NEUTRALLY-BUOYANT PARTICLES

In this article,we employ a fully-resolved numerical simulation method（the fictitious domain method）to investigate the effects of large neutrally-buoyant particles on the turbulent flow in a pipe at low Reynolds number and non-dilute regimes.The tube Reynolds number is fixed to be 4 900,the particle-pipe diameter ratio is 0.1,and the particle volume fraction ranges from 0.33%to 10%.Our results indicate that the presence of large particles decreases the maximum root-of-mean-square（rms）of the streamwise velocity fluctuation near the wall by weakening the intensity of large-scale streamwise vortices,although in the region very close to the wall the particles increase the rms of streamwise velocity fluctuation.On the other hand,the particles induce small-scale vortices in the near-wall region,resulting in the enhancement of the rms of radial and circumferential velocity fluctuations there.

Floating Solid Particles Interacting with Tilted Square Obstacles in Fluid Affecting Drag Forces

We have analyzed the kinetics of solid circular particles interacting with fluid,outer boundary and internal square shaped obstacles tilted at a 45°angle.The effects on the motion of particle due to collision with obstacles and wall are inspected.An Eulerian approach is used to study the behavior of particle in the fixed computational mesh.The interactions between fluid,particles and obstacles have been carried out in the whole domain by using fictitious boundary method(FBM).In this work,the particulate flow simulations are computed by using finite element solver FEATFLOW.Numerical results are presented by assigning different alignments to the obstacles and varying their positions in the domain.Particle-wall,particle-particle and particleobstacle collisions are treated by applying a modified collision model proposed by Glowinski et al.The rapid change in drag forces acting on obstacles due to nearby passing particles and its effect on the fluid motion has been investigated.

Direct-forcing immersed boundary lattice Boltzmann simulation of particle/fluid interactions for spherical and non-spherical particles

The lattice Boltzmann method （LBM） is a useful technique for simulating multiphase flows and modeling complex physics. Specifically, we use LBM combined with a direct-forcing （DF） immersed boundary （IB） method to simulate fluid-particle interactions in two-phase particulate flows. Two grids are used in the simulation： a fixed uniform Eulerian grid for the fluid phase and a Lagrangian grid that is attached to and moves with the immersed particles. Forces are calculated at each Lagrangian point. To exchange numerical information between the two grids, discrete delta functions are used. The resulting DF IB-LBM approach is then successfully applied to a variety of reference flows, namely the sedimentation of one and two circular particles in a vertical channel, the sedimentation of one or two spheres in an enclosure, and a neutrally buoyant prolate spheroid in a Couette flow. This last application proves that the developed approach can be used also for non-spherical particles. The three forcing schemes and the different factors affecting the simulation （added mass effect, corrected radius） are also discussed.

Comparison of the standard Euler-Euler and hybrid Euler-Lagrange approaches for modeling particle transport in a pilot-scale circulating fluidized bed

Particle transport phenomena in small-scale circulating fiuidized beds （CFB） can be simulated using the Euler-Euler, discrete element method, and Euler-Lagrange approaches. In this work, a hybrid Euler-Lagrange model known as the dense discrete phase model （DDPM）, which has common roots with the multiphase particle-in-cell model, was applied in simulating particle transport within a mid-sized experimental CFB facility. Implementation of the DDPM into the commercial ANSYS Fluent CFD package is relatively young in comparison with the granular Eulerian model. For that reason, validation of the DDPM approach against experimental data is still required and is addressed in this paper. Additional difficulties encountered in modeling fluidization processes are connected with long calculation times. To reduce times, the complete boiler models are simplified to include just the combustion chamber. Such simplifications introduce errors in the predicted solid distribution in the boiler. To investigate the conse- quences of model reduction, simulations were made using the simplified and complete pilot geometries and compared with experimental data. All simulations were performed using the ANSYSFLUENT 14.0 package. A set of user defined functions were used in the hybrid DDPM and Euler-Euler approaches to recirculate solid particles.