Motion Of Discrete Particles Research Articles

Toward High-Order CFD-DEM: Development and Validation

CFD-DEM is used to simulate solid–fluid systems. DEM models the motion of discrete particles while CFD models the dynamics of the fluid phase. Coupling both necessitates the calculation of the void fraction and the solid–fluid forces resulting in a computationally expensive method. Additionally, evaluating volume-averaged quantities locally restricts particle to cell size ratios limiting the accuracy of the CFD. To mitigate these limitations, we develop a unified finite element CFD-DEM solver which integrates the CFD and DEM solvers into a single software resulting in faster and cheaper coupling between the solvers. It supports dynamically load-balanced parallelization. This allows for more efficient simulations as load balancing ensures the even distribution of workloads among processors; thus, exploiting available resources efficiently. Our solver supports high order schemes; thus, allowing the use of larger elements enhancing the validity and stability of the void fraction schemes while achieving better accuracy. We verify and validate our CFD-DEM solver with a large array of test cases: particle sedimentation, a fluidized bed, the Rayleigh Taylor instability, and a spouted bed.

STRAIN-RATE WEBER NUMBER AS A LOCAL ATOMIZATION CONDITION IN COMPUTATIONAL PROTOCOL FOR SPRAY FLOW SIMULATIONS

Computational simulations of spray flows typically start with bulk liquid flow, bulk-to-droplet conversion algorithm for primary atomization, then tracking of discrete particle motion. The key step is the atomization criterion and subsequent drop size conversion. To facilitate this process, we consider the Weber number, based on strain rate (We<sub><i>st</i></sub>), as the local atomization condition in computational simulations of spray flows. This atomization criterion is tested within the computational protocol developed in this laboratory, which uses the integral theory as the primary atomization algorithm. Based on this definition, We<sub><i>st</i></sub> ~ 10<sup>7</sup> appears to work quite well in specifying the location of primary atomization, across different spray geometries. Therefore, the conservation equations of mass and energy in integral forms can be effectively coupled with the CFD-based momentum solver to simulate spray flows, by using the current atomization criterion.

Analysis of microparticle deposition in the human lung by taguchi method and response surface methodology

The deposition phenomenon of microparticle and SAR-CoV-2 laced bioaerosol in human airways is studied by Taguchi methods and response surface methodology (RSM). The data used herein is obtained from simulations of airflow dynamics and deposition fractions of drug particle aerosols in the downstream airways of asthma patients using computational fluid dynamics (CFD) and discrete particle motion (DPM). Three main parameters, including airflow rate, drug dose, and particle size, affecting aerosol deposition in the lungs of asthma patients are examined. The highest deposition fraction (DF) is obtained at the flow rate of 45 L min−1, the drug dose of 200 μg·puff−1, and the particle diameter of 5 μm. The optimized combination of levels for the three parameters for maximum drug deposition is performed via the Taguchi method. The importance of the influencing factors rank as particle size > drug dose > flow rate. RSM reveals that the combination of 30 L min−1, 5 μm, 200 μg·puff− has the highest deposition fraction. In part, this research also studied the deposition of bioaerosols contaminated with the SAR-CoV-2 virus, and their lowest DF is 1.15%. The low DF of bioaerosols reduces the probability of the SAR-CoV-2 virus transmission.

A hybrid model of collective motion of discrete particles under alignment and continuum chemotaxis

In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to describe the cell migration and self-organization in the zebrafish lateral line primordium, we introduce a simplified model in which the coupling between an alignment and chemotaxis mechanism acts on a system of interacting particles. In particular we rely on a hybrid description in which the agents are discrete entities, while the chemoattractant is considered as a continuous signal. The proposed model is then studied both from an analytical and a numerical point of view. From the analytic point of view we prove, globally in time, existence and uniqueness of the solution. Then, the asymptotic behaviour of a linearised version of the system is investigated. Through a suitable Lyapunov functional we show that for $t\rightarrow +\infty$, the migrating aggregate exponentially converges to a state in which all the particles have a same position with zero velocity. Finally, we present a comparison between the analytical findings and some numerical results, concerning the behaviour of the full nonlinear system.

Why the particle-in-cell method captures instability enhanced collisions

While the particle-in-cell (PIC) method has been the subject of years of theoretical study, the common misconception that PIC approximates the collisionless Vlasov-Maxwell system of equations, or the Vlasov-Poisson system for the electrostatic case, is widely cited. In this paper, a PIC-relevant generalization of the instability enhanced Lenard-Balescu collision operator is derived. The analysis of this collision operator demonstrates that while coulomb collisions are truncated by the electric field grid resolution, longer range collisions that arise from imperfect shielding in the presence of instabilities persist. These instability enhanced collisions are completely captured by PIC as long as there is sufficient grid resolution to resolve the wavenumber of the unstable modes of the instability. The inclusion of this behavior is akin to particle wave interactions in the Vlasov based quasilinear theory but with one important difference. Quasilinear theory requires an initial spectral energy density which cannot be supplied self-consistently from within the theory because its initial value is determined by non-Vlasov collisional effects. With the proper electric field grid resolution, the initial spectral energy density is included self-consistently, along with the generation of plasma waves originating from discrete particle motion. Predictions of the grid resolution effect are found to be in agreement with PIC simulations at varying grid resolutions.

CFD-DEM simulations of particle separation characteristic in centrifugal compounding force field

The separation of particles in centrifugal compounding force field is complex due to the interaction of centrifugal force, viscous drag force, inter-particle contact force and particle-particle collision force. In this work, the CFD-DEM modeling is applied for the first time in the study of particle separation in an innovative centrifugal separator. Some key features of the flow in centrifugal separator are described by using CFD modeling. The DEM is used to model the motion of discrete particles by applying Newton's laws of motion. The particle–fluid and particle–particle interaction forces are examined to explain the separation of particles by density. This approach provides a convenient way to better understand the flow and separation performance of particles in centrifugal compounding force field. Then, a central composite experimental design is used to investigate the relationship between the independent (rotation speed and fluidization water flow rate) variables and the responses (ρ50 and Ep), possible interactions between the independent variables and their effects on the separation performance of the rotation bowl. The results suggest that the fluidization water flow rate have more impact on ρ50 and Ep than rotation speed. The fluidization water flow rate improves the separation efficiency.

Impact velocity-dependent restitution coefficient using a coupled Eulerian fluid phase-Eulerian solid phase-Lagrangian discrete particles phase model in gas-monodisperse particles internally circulating fluidized bed

A Coupled Eulerian fluid phase-Eulerian solid phase-Lagrangian discrete particles phase model (CEEL) is proposed to study of the hydrodynamics of gas and monodisperse particles in an internally circulating fluidized bed (ICFB). The impact velocity-dependent coefficient of restitution (CoR) used in the kinetic theory of granular flow (KTGF) is determined from the dynamic information of Lagrangian discrete particle phase using discrete element method (DEM). The interphase momentum exchange coefficient between Eulerian fluid phase and Eulerian solid phase gives back to the Lagrangian discrete particle phase. Numerical simulations show that the impact velocity-dependent CoR decreases with the increase of solid volume fraction and impact velocity of discrete particles. The predicted velocities and circulation mass fluxes of Eulerian solid phase and Lagrangian discrete particles phase are close to each other in the ICFB. The granular temperature and rotational granular temperature of Eulerian solid phase and Lagrangian discrete particles phase are predicted. Present CEEL model provides all fields of continuous fluid phase, Eulerian solid phase and the motion of discrete particles in the ICFB.

Large scale density perturbations from a uniform distribution by wave transport

It has long been known that a uniform distribution of matter cannot produce a Poisson distribution of density fluctuations on very large scales 1/k > ct by the motion of discrete particles over timescale t. The constraint is part of what is sometimes referred to as the Zel'dovich bound. We investigate in this paper the transport of energy by the propagation of waves emanating incoherently from a regular and infinite lattice of oscillators, each having the same finite amount of energy reserve initially. The model we employ does not involve the expansion of the Universe; indeed there is no need to do so, because although the scales of interest are all deeply sub-horizon the size of regions over which perturbations are evaluated do far exceed ct, where t is the time elapsed since a uniform array of oscillators started to emit energy by radiation (it is assumed that t greatly exceeds the duration of emission). We find that to lowest order, when only wave fields ∝ 1/r are included, there is exact compensation between the energy loss of the oscillators and the energy emitted into space, which means P(0)=0 for the power spectrum of density fluctuations on the largest scales. This is consistent with the Zel'dovich bound; it proves that the model employed is causal, has finite support, and energy is strictly conserved. To the next order when near fields ∝ r−2 are included, however, P(0) settles at late times to a positive value that depends only on time, as t−2 (the same applies to an excess (non-conserving) energy term). We further observe that the behavior is peculiar to near fields. Even though this effect may give the impression of superluminal energy transport, there is no violation of causality because the two-point function vanishes completely for r>t if the emission of each oscillator is sharply truncated beyond some duration. The result calls to question any need of enlisting cosmic inflation to seed large scale density perturbations in the early Universe.

Conversion analysis of a cylindrical biomass particle with a DEM-CFD coupling approach

Biomass as a renewable energy source has attracted more attention nowadays due to ecological and economical benefits. The main objective of this work is studying the biomass conversion with employing a DEM-CFD coupling approach. In this model, the solid particulates are considered as discrete elements coupled via heat, mass and momentum transfer to the surrounding gas as continuous phase. That is, a comprehensive three-dimensional numerical model is developed and applied to investigate the complex phenomena taking place during biomass conversion in a reactor. In this case, the physical and chemical processes as heat-up, drying, pyrolysis, gasification and combustion are taken into account based on the relevant homogeneous and heterogeneous reactions. This platform predicts the motion of discrete particles based on the newton's equations of motion; and the thermodynamic state of each particle is extended according to the related algorithms. The thermodynamic state estimates the temperature and species distributions inside the particle due to external heat sources and chemical reactions. The reaction rates are described with Arrhenius model, and the reactions in the gas phase are modeled using Partially Stirred Reactor (PaSR) model with the standard k−ϵ turbulent model. The conductive and radiative heat transfer between particles as well as convective heat transfer between particles and gas phase are also observed. Due to layered behavior of biomass materials, the shape of particle is considered as cylindrical rather than spherical to predict more realistic results. In order to improve the numerical modeling of biomass conversion, a shrinkage model is also developed and validated with experimental data in literature.

Understand solids loading effects in a dense medium cyclone: Effect of particle size by a CFD-DEM method

Industrial cyclones, such as gas, hydro and dense medium, are widely used in chemical, mineral and process industries to separate particles from fluids or classify particles by size, density or other solid properties. It is well known that the loading of particles can significantly affect fluid flow in such cyclones but the specific effect can be confusing due to a limited fundamental understanding of the working mechanisms involved. In this work, the problem is partially tackled by analysing the influence of particles of different size on the medium flow in a dense medium cyclone (DMC) by using a combined approach of Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) (CFD-DEM). In the CFD-DEM model, CFD is used to model the motion of slurry medium by numerically solving the local-averaged Navier-Stokes equations at a computational cell scale, facilitated by the Volume of Fluid (VOF) and Mixture multiphase models. DEM is then used to model the motion of discrete particles by applying Newton's laws of motion, facilitated by a coarse-grained (CG) method to model small coal particles. It is found that both the particle and medium flows are sensitive to the particle size. The most notable finding is that spatial distributions of solid flow patterns form due to particles of different size have different trajectories in the cyclone. These lead to significant different distribution of volumetric particle-fluid interaction forces which cause different effects on the fluid flow. The findings are useful for developing a better understanding the working mechanisms of solids loading effects in DMCs and also in other similar swirling multiphase flow systems.

Suspension flow past a cylinder: particle interactions with recirculating wakes

AbstractExperimental observations of the flow of a suspension of solid fraction ${\it\phi}\approx 0.084$ over a circular cylindrical post in a shallow microchannel (depth smaller than the cylinder radius) find that the recirculating wake behind the obstacle at moderate Reynolds numbers is depleted or devoid of particles. Particles injected into the wake exit to regain the depleted state. By numerical simulation of the discrete particle motion, the basis for the depletion behind the cylinder is studied; rather than a shallow channel, the numerical simulations consider a periodic domain, mimicking the flow past an infinite cylinder. The Reynolds number is defined, using the average axial velocity ${\bar{U}}$, diameter of the obstacle $D$ and the kinematic viscosity of the suspension ${\it\nu}$, as $Re={\bar{U}}D/{\it\nu}$, and is studied for $Re<30$ in the simulation – conditions for which the pure fluid exhibits an extended steady closed-streamline (recirculating) wake behind the cylinder; unsteadiness is found to be suppressed by the channel walls in the experiments, allowing steady flow at a larger $Re$ than expected for an infinite cylinder (up to at least $Re=300$). The simulations use the lattice-Boltzmann method to determine the motion of the fluid and neutrally buoyant particles. The trajectory of a single particle (small relative to the cylinder) shows migration to a limit cycle inside the wake. With an increase of the number of particles in the wake alone (no particles in the free stream), particles can escape the wake due to velocity fluctuations. Simulation of the flow of suspensions of ${\it\phi}=0.04,0.06$ and 0.08 demonstrates that there is particle exchange between the wake and the free stream; the net flux of particles out of the wake leads to a particle-depleted wake, qualitatively very similar to the experimental observation.

Kinetic theory of instability-enhanced collisional effects

The Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy is used to derive a generalization of the Lenard–Balescu plasma kinetic equation that accounts for wave-particle scattering due to instabilities that originate from discrete particle motion. Application to convective instabilities is emphasized for which the growing waves either propagate out of the domain of interest or modify the particle distribution to reduce the instability amplitude before nonlinear amplitudes are reached. Two such applications are discussed: Langmuir’s paradox and determining the Bohm criterion for multiple ion species plasmas. In these applications, collisions are enhanced by ion-acoustic and ion-ion two-stream instabilities, respectively. The relationship between this kinetic theory and quasilinear theory is discussed.

Electrostatic effects on inertial particle transport in bifurcated tubes

Most aerosols found naturally in the ambient environment or those dispersed from artificial devices such as dry powder inhalers, are electrically charged. It is known that a strong electrostatic charge on aerosols can result in transport behavior dramatically different from that of uncharged aerosols, even in the absence of an external electric field. In the present work, we study pneumatic transport of corona-charged particles in bifurcated tubes. This is accomplished by tracking the motion of discrete particles numerically under the influence of drag, gravitational, and electrostatic forces. The model aerosol is fly ash powder, whose size and charge distributions have been determined experimentally. The electrical mobility of the charged particle cloud is modeled through coulombic interactions between discrete point charges. For the case of polydispersed particles electrically charged across a distribution, the deposition efficiency was found to be greater than what is indicated by the mean charge and size. In particular, use of negatively charged fly ash powder of mean size of 2 μm and mean charge of −1.5 C/kg led to significant increase in deposition efficiency (∼29%) compared with uncharged fly ash powder of the same size distribution (∼8%). Analysis of particle residence times suggests significant interaction between electrical and drag forces. These findings could have implications for pneumatic powder conveying or pulmonary drug delivery applications. © 2009 American Institute of Chemical Engineers AIChE J, 2009

CFD-DEM modelling of multiphase flow in dense medium cyclones

Dense medium cyclone (DMC) is a high-tonnage device that is widely used to upgrade run-of-mine coal in coal preparation. It is simple in design but the flow pattern within it is complex due to the size and density distributions of the feed and process medium solids, and the turbulent vortex formed. This paper presents a mathematical model to describe this flow system by means of combining Discrete Element Method (DEM) with Computational Fluid Dynamics (CFD). The DEM is used to model the motion of discrete particles by applying Newton's laws of motion. The CFD is used to model the motion of slurry medium by numerically solving the local-averaged Navier–Stokes equations facilitated with the Volume of Fluid (VOF) and Mixture multiphase flow models. The approach is shown to be able to reproduce typical flow phenomena in DMCs. The effect of medium-to-coal ratio and the so-called “surging” phenomenon are analyzed. An attempt is made to explain the observed phenomena in terms of particle–particle, particle–fluid and particle–wall interaction forces. The approach offers a convenient way to examine the flow and performance of DMC in relation to geometric, material and operational conditions.

Flow field characterization of friction stir processing using a particle-grid method

Flow behavior in friction stir processing of metals is investigated by tracking the motion of discrete particles and grid deformation in a plasticine workpiece. Mechanical and thermal similarities between plasticine and metals are discussed. These similarities along with ease of particle/grid setup and post-processing examination make plasticine an ideal analog material for friction stir processing. Uniformly spaced steel particles are arranged along lines parallel to the tool feed direction at the mid-pin depth in the plasticine. During friction stir processing of the plasticine, the forward motion of the tool is stopped nearly instantaneously in order to freeze the flow of material around the tool. X-ray images of particle streamlines are acquired after processing. The particle spacing before and after processing is used to calculate velocities, strains, and strain-rates along streamlines. Results from the particle streamlines show substantial slip at the material/pin interface. The maximum velocity of the material in contact with the pin is only 6.0–7.0% of the pin speed. Generally, material initially at the far advancing side of the pin is compressed, while the remaining material near the pin is stretched during processing. The highest strain and strain-rate are 4.4 and 1.3 s −1, respectively, which occurs in the material that contacts the pin. The gross flow of material around the tool pin is also observed from contrasting colors of the plasticine, which are arranged as markers in several layers parallel to the feed direction. Markers at the mid-pin depth in the processed zone exhibit significant deformation and irregular flow.

Computational Investigation of Horizontal Slug Flow in Pneumatic Conveying

Dense-phase pneumatic transportation of bulk materials in the form of slug flow has become a very important technology in industry. In order to understand the underlying mechanisms of slug flow, this paper presents a numerical study of slug flow in horizontal pneumatic conveying by means of discrete particle simulation. To be computationally efficient, the motion of discrete particles is three-dimensional and the flow of continuum gas is two-dimensional, and periodic boundary conditions are applied to both gas and solid phases horizontally. The proposed numerical model is qualitatively verified by comparing the calculated and measured results in terms of particle flow pattern and gas pressure drop. Then the influence of operational conditions such as gas and solid flowrates on slug behavior is numerically investigated. It is shown that slug velocity linearly increases with gas flowrate but is not sensitive to solid flowrate, and slug length increases with both gas and solid flowrates. The results qualitat...

A CFD–DEM study of the cluster behavior in riser and downer reactors

This paper presents a numerical study of the particle cluster behavior in a riser/downer reactor by means of combined computational fluid dynamics (CFD) and discrete element method (DEM), in which the motion of discrete particles is obtained by solving Newton's equations of motion and the flow of continuum gas by the Navier–Stokes equations. It is shown that the existence of particle clusters, unique to the solid flow behavior in such a reactor, can be predicted from this first principle approach. The results demonstrate that there are two types of clusters in a riser and downer: one is in the near wall region where the velocities of particles are low; the other is in the center region where the velocities of particles are high. While the extent of particle aggregation appears to be similar, the duration time for the first type in a downer is shorter than in a riser. Furthermore, it is demonstrated that the formation of clusters is affected by a range of variables related to operational conditions, particle properties, and bed properties and geometry. The increase of solid volume fraction, sliding and rolling friction between particles or between particles and wall, or damping coefficient can enhance the formation of clusters. The use of multi-sized particles can also promote the formation of clusters. But the increase of gas velocity or use of a wider bed can suppress the formation of clusters. The van der Waals force may enhance the formation of clusters when solid concentration is high but suppress the formation of clusters near the wall region when solid concentration is low.

Simulation study of an electrogasdynamic power converter using CFD

An electrogasdynamic (EGD) power converter, a device that converts mechanical energy into electric energy without moving parts, is described. A mathematical model that describes the complex two-phase fluid flow and electric field interaction was developed using a commercial CFD program. The axi-symmetric Navier-Stokes equations were solved for the carrying gas stream. Compressible flow was considered because of the high velocity (Ma > 1) inside the converter. The aerosol particles were tracked using a Lagrangian approach. Discrete particle motion and the electric field were coupled through the Poisson equation. The results indicated that because of the high velocities, particle motion is governed by the drag forces, the Coulomb forces having a minor effect. It was found that particle diameter and charge to mass ratio were the most important factors in the conversion efficiency. Copyright , Manchester University Press.

Discrete particle motion on sieves—a numerical study using the DEM simulation

This paper presents a mathematical investigation of particulate motion on an inclined screening chute using the Discrete Element Method (DEM). Special attention has been paid to the implementation of an apertured boundary and the algorithm for allowing particles to pass through apertures or to rebound when approaching the screen surface. Computational experiments have been conducted to examine the undersize particle motion across the material layer and through the apertures for bimodal mixtures comprising two different sizes of spherical polyethylene pellets. Discrete particle motion at different regions along the screen has been discussed in relation to the physical mechanisms inherent in the solids separation process and their determinative role on screening efficiency. Simulations have demonstrated the negative effect of near-mesh size particles and the positive role of relatively large particles on screening operations and the crucial effect of particle segregation in material layers. Comparison of screening rate along the screen with experiments has demonstrated adequate agreement. This computational study has shown the advantages of using DEM to understand the complex solids separation process. Further works are envisaged to focus on the development of advanced experimental techniques and the implementation of DEM for sieving processes involving moving screens.

A Numerical Simulation of Separation of Crop Seeds by Screening—Effect of Particle Bed Depth

Effective separation and grading of cereal grains and crop seeds are of importance in the production of quality cereal foods. This paper presents a two-dimensional numerical study of the separation process of crop seeds by screening, using the Discrete Element Method (DEM) modelling technique. Computational experiments have been conducted for the separation of two common crop seeds, soybeans and mustard seeds, using a vibrating screen. The screening rate and the required screen length at different feeding rates are discussed in relation to the discrete particle motion on the screen. This study has demonstrated the crucial effect of particle bed depth on screening efficiency. For a screening system involving granular materials, the critical feeding rate for the most effective screening operation can be determined via conducting the DEM simulation.