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A modified cohesion model for CFD–DEM simulations of fluidization
... We employ the Hertzian spring-dashpot model to quantify the contact forces for particle-particle and particle-wall interaction, see [50] for further details. We use the real Young's modulus in all the cases of this study with no softening correction. ...
... We use a maximum cutoff distance = ( + )∕ to accelerate the simulation, where for > the van der Waals force is not accounted for. The van der Waals force , between particles and is modeled as [50], ...
... The van der Waals force , between particle and wall experienced by particle is modeled as [50], ...
We have performed Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations of air and particles in a commercial ELLIPTA® inhaler. We simulated the fluidization, deagglomeration and transport of carrier and API particles, with two realistic inhalation profiles that are representative of moderate asthma and very severe COPD patients, and three different mouthpiece designs. In each of the ten cases simulated, we determined the fine particle fraction (FPF) in the stream leaving the mouthpiece, the temporal evolution of the spatial distribution of the particles, the mean air (slip) velocity seen by the carrier particles, and the average numbers and normal impact velocities of carrier-carrier and carrier-wall collisions inside the inhaler. In the cases examined, the air-carrier and carrier-carrier interactions affected the FPF, while the carrier-wall interactions were too infrequent to have a substantial effect. The simulations revealed the benefit of loading both blisters even when only a single medication needs to be delivered
... where is the distance between the particle surfaces, and is the Hamaker constant. To avoid singularity, it is assumed that the force saturates at a minimum separation, min = 1 × 10 −9 m (Gu et al., 2016;Yang et al., 2000). Due to its short range nature, the force is cut off at max = ∕4 to accelerate the simulations (Aarons & Sundaresan, 2006;Gu et al., 2016). ...
... To avoid singularity, it is assumed that the force saturates at a minimum separation, min = 1 × 10 −9 m (Gu et al., 2016;Yang et al., 2000). Due to its short range nature, the force is cut off at max = ∕4 to accelerate the simulations (Aarons & Sundaresan, 2006;Gu et al., 2016). The magnitude of the electrostatic force is given by Coulomb's law according to ...
... The spring stiffness used in the soft-sphere collision model described in Appendix A.2.2 is determined based on the collision time col , resulting in artificially 'soft' particles to enable larger time steps. A modified van der Waals model was recently proposed to be compatible with the soft-sphere collision model (Gu et al., 2016). The modification ensures the work done by the van der Waals force remains unchanged when particles overlap, such that its overall effect is insensitive to the choice of and consequently the results remain unchanged as is adjusted. ...
Particle deposition in fully-developed turbulent pipe flow is quantified taking into account uncertainty in electric charge, van der Waals strength, and temperature effects. A framework is presented for obtaining variance-based sensitivity in multiphase flow systems via a multi-fidelity Monte Carlo approach that optimally manages model evaluations for a given computational budget. The approach combines a high-fidelity model based on direct numerical simulation and a lower-order model based on a one-dimensional Eulerian description of the two-phase flow. Significant speedup is obtained compared to classical Monte Carlo estimation. Deposition is found to be most sensitive to electrostatic interactions and exhibits largest uncertainty for mid-sized (i.e., moderate Stokes number) particles.
... The spring stiffness k used in the soft-sphere collision model described in § Appendix A.2.2 is determined based on the collision time τ col , resulting in artificially 'soft' particles to enable larger time steps. A modified van der Waals model was recently proposed to be compatible with the soft-sphere collision model [117]. The modification ensures the work done by the van der Waals force remains unchanged when particles overlap, such that its overall effect is insensitive to the choice of k and consequently the results remain unchanged as ∆t is adjusted. ...
... This is accomplished by modifying the saturation distance and Hamaker constant when two particles are in direct contact. A value of k r = 7000 N/m is used and the simulation spring stiffness k is chosen such that k r /k = 700 as described in Gu et al. [117]. ...
... In this work, particle contact mechanics are based on the DMT theory due to the low values of λ T under consideration and to be consistent with the cohesion model of Gu et al. [117]. where E[x (i) p ] is the electric field interpolated to the position of particle i. ...
Particle deposition in fully-developed turbulent pipe flow is quantified taking into account uncertainty in electric charge, van der Waals strength, and temperature effects. A framework is presented for obtaining variance-based sensitivity in multiphase flow systems via a multi-fidelity Monte Carlo approach that optimally manages model evaluations for a given computational budget. The approach combines a high-fidelity model based on direct numerical simulation and a lower-order model based on a one-dimensional Eulerian description of the two-phase flow. Significant speedup is obtained compared to classical Monte Carlo estimation. Deposition is found to be most sensitive to electrostatic interactions and exhibits largest uncertainty for mid-sized (i.e., moderate Stokes number) particles.
... In Discrete Element Method (Cundall and Strack, 1979;Tsuji et al., 1993), the position, linear velocity, and angular velocity of the particles are evolved by solving Newton's equations of motion, which can be found in Liu et al. (2021). The particle-particle and particle-wall contact force interactions are quantified using a Hertzian spring-dashpot model; for more details, see Gu et al. (2016). Both static friction and rolling friction are accounted for in the model. ...
... We set a maximum cutoff distance s max = (r i + r j )/r i r j , beyond which the van der Waals force is deactivated. The force f v,ik between particles i and k is expressed as (Gu et al., 2016), ...
... The force f v,iw between a particle i and a wall is expressed as (Gu et al., 2016), ...
The transport and aerosolization of particles are studied in several different dry powder inhaler geometries via Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations. These simulations combine Large Eddy Simulation of gas with Discrete Element Model simulation of all the carrier particles and a representative subset of the active pharmaceutical ingredient (API) particles. The purpose of the study is to probe the dominant mechanism leading to the release of the API particles and to demonstrate the value of the CFD-DEM simulations where one tracks the motion of all the carrier and API particles. Simulations are performed at different inhalation rates and initial dose loading conditions for the screen-haler geometry, a simple cylindrical tube inhaler, and five different geometry modifications that took the form of bumpy walls and baffles. These geometry modifications alter the residence time of the powder sample in the inhaler, pressure drop across the inhaler, the severity of gas-carrier interactions, and the number of collisions experienced by the carrier particles, all of which are quantified. The quality of aerosolization is found to correlate with the average air-carrier slip velocity, while collisions played only a secondary role. Some geometry modifications improved aerosolization quality with very little increase in the pressure drop across the device.
... proposed to be compatible with the soft-sphere collision model outlined in § 2.3 [91]. ...
... where k r is the "real" spring stiffness of the particle that would result in negligible overlap during collisions. A value of k r = 7000 N/m is used and the simulation spring stiffness k is chosen such that k r /k = 700 as described in [91]. The offset s 0 and shifted saturation distance s s min can be obtained by solving the following nonlinear equations ...
... The results were also found to be insensitive to the restitution coefficient and inclusion of fluid torque. In the remainder of this work, particle contact mechanics are based on the DMT theory due to the low values of λ T under consideration and to be consistent with a recently proposed cohesion model that enables larger simulation timesteps [91], which has been discussed in § 2.6. ...
In recent years, public awareness of the impact caused by micron-sized particles such as infectious aerosols or dust has increased drastically, ranging from severe public health concerns to various environmental issues. In addition, airborne dust and volcanic ash ingested by aircraft engines compromise the durability, performance, and safety of engine turbine components. The transport and deposition of fine (<≈O(10 μm) particulates in turbulence (e.g., dust or powder) is largely controlled by cohesive forces such as electrostatics and van der Waals. Due to their small size and cohesive nature, tracking individual particles in turbulence is challenging, and is further complicated by significant uncertainties in material properties. Although computational methods with varying levels of complexity have been developed over past decades, accurate predictive models of cohesive particle transport and deposition do not yet exist for large-scale simulations. The main objective of this work is to develop a numerical framework tailored for resolving cohesive particle interactions in turbulence. Efficient algorithms are developed to optimally resolve particle contact forces in a direct numerical simulation (DNS) framework. The framework is then used to study the effect of electrostatics on particle transport in turbulence. It is found that the short-range electric potential plays a key role in particle clustering even in dilute suspensions. A follow-up study of charged aerosols in ionized air identifies a feedback mechanism capable of generating atmospheric turbulence via an electrohydrodynamic body force. Turbulence-induced breakup of an aggregate of solid particles subject to van der Waals is also investigated. A phenomenological model of the breakup process is developed that acts as a granular counterpart to the Taylor analogy breakup (TAB) model commonly used for droplet breakup. Such a model is capable of predicting the onset of aggregate breakup in the absence of a resolved turbulent flow field. Finally, particle deposition in a turbulent pipe flow is studied in the presence of van der Waals and electrostatics. The sensitivity of deposition rate to uncertainties in cohesive forces is efficiently quantified using a multi-fidelity framework. Deposition is found more sensitive to electrostatics than van der Waals across all particle sizes and exhibits largest uncertainty for mid-sized particles.
... T t,iw is the torque acting on particle i from a wall. The contact force for particle-particle and particle-wall interaction is quantified using a Hertzian springdashpot model; see Gu et al. [51] for further details. Softening correction is not included in this study as the real Youngs' modulus is used in all the cases. ...
... where A is the Hamaker constant and s is the distance between the particle surfaces. A maximum cutoff distance s max = (r i + r j )/r i r j is used to accelerate the simulation [51]. The van der Waals force is not accounted for s > s max . ...
... s min is a separation distance commensurate with intermolecular spacing where the van der Waals cohesive force is assumed to saturate. Even when the separation distance is smaller than this value, the van der Waals force is capped at the value evaluated at s min , which is 1 nm in this study [51,53]. ...
Drug delivery via dry powder inhaler (DPI) is a complex process affected by multiple factors involving gas and particles. The performance of a carrier-based formulation depends on the release of active pharmaceutical ingredient (API) particles, typically characterized by fine particle fraction (FPF) and dispersion fraction (DF). Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) can capture relevant gas and particle interactions but is computationally expensive, especially when tracking all carrier and API particles. This study assessed the efficacy of two coarse-grained CFD-DEM approaches, the Discrete Parcel Method and the representative particle approach, through highly-resolved CFD-DEM simulations. The representative particle approach simulates all carrier particles and a subset of API particles, whereas the Discrete Parcel Method tracks parcels representing a specified number of carrier or API particles. Both approaches are viable for a small carrier-API size ratio which requires modest degrees of coarse-graining, but the Discrete Parcel Method showed limitations for a large carrier-API size ratio. The representative particle approach can approximate CFD-DEM results with reasonable accuracies when simulations include at least 10 representative API particles per carrier. Using the representative particle approach, we probed powder characteristics that could affect FPF and DF in a model problem and correlated these fractions with the maximum carrier-API cohesive force per unit mass of API particles.
... The results were also found to be insensitive to the restitution coefficient and inclusion of fluid torque. In the remainder of this work, particle contact mechanics are based on the DMT theory owing to the low values of λ T under consideration and to be consistent with a recently proposed cohesion model that enables larger simulation timesteps (Gu, Ozel & Sundaresan 2016), which is discussed in § 2.3.2. ...
... As described previously, the spring stiffness k used in the soft-sphere collision model is determined based on the collision time τ col according to (2.10), resulting in artificially 'soft' particles to enable larger time steps. A modified van der Waals model was recently proposed to be compatible with the soft-sphere collision model outlined in § 2.3.1 (Gu et al. 2016). The modification ensures the work done by the van der Waals force remains unchanged when particles overlap, such that its overall effect is insensitive to the choice of k and consequently the results remain unchanged as Δt is adjusted. ...
... The simulation configuration outlined in § 2 is used, with Re λ = 64 and Ad = 0.3 and 3. It should be noted that although Gu et al. (2016) demonstrated previously that simulations of gas-fluidization of cohesive particles are insensitive to the particle stiffness using the modified cohesion model employed here, the present study represents the first application of this model to large (with respect to the Kolmogorov length scale) and dense (near close packing) particle aggregates. Table 2 summarizes the non-dimensional time-rate-of-breakup and breakup time for different model parameters and conditions, with the values used to generate the results reported in § 3 highlighted in bold. ...
We present a numerical study analysing the breakup of a single cohesive particle aggregate in turbulence. Solid particles with diameters smaller than the Kolmogorov length scale (and placed in homogeneous isotropic turbulence. Parameters are chosen relevant to dust or powder suspended in air such that cohesion due to van der Waals is important. Simulations are performed using an Eulerian-Lagrangian framework that models two-way coupling between the fluid and solid phases and resolves particle-particle interactions. Aggregate breakup is investigated for different adhesion numbers) are initially aggregated into a spherical 'clump' of diameter], Taylor microscale Reynolds numbers and non-dimensional clump sizes. The intermittency of turbulence is found to play a key role on the early stage breakup process, which can be characterized by a turbulent adhesion number that relates the potential energy of the van der Waals force to turbulent shear stresses. A scaling analysis shows that the time rate of breakup for each case collapses when scaled by and an aggregate Reynolds number proportional to. A phenomenological model of the breakup process is proposed that acts as a granular counterpart to the Taylor analogy breakup (TAB) model commonly used for droplet breakup. Such a model is useful for predicting particle breakup in coarse-grained simulation frameworks, such as Reynolds-averaged Navier-Stokes, where relevant spatial and temporal scales are not resolved.
... However, this is not the case for cohesive fine particles. Previous studies have shown that particle cohesion needs to be scaled down to compensate for the effects of a larger deformation caused by a reduced particle stiffness [29][30][31][32] . Different scaling laws have proposed for this purpose, depending on the employed contact model and adhesive force model. ...
... The reduced cohesive force F R is calculated as F O ( k R / k O ) 1/2 with F O being the original adhesion force, k R and k O the reduced and the original spring constants, respectively. Gu et al. [30] considered the van der Waals force model for both linear Hookean and Hertzian contacts, in which the reduced Hamaker constant A R is calculated as A O ( k R / k O ) 1/2 for the linear Hookean contact model and A O ( Y R / Y O ) 2/5 for the Hertzian contact model, where Y represents the particle Young's modulus. For the JKR model, Haervig et al. [33] proposed a scaling law where the surface energy density is scaled as γ R = γ O ( Y R / Y O ) 2/5 , with γ the surface energy density. ...
... It is worth noting that stiffness scaling only affects contact adhesion, the presence of non-contact cohesive interaction would inevitably result in a sharp force jump when two particles just come into contact and consequently leading to large numerical errors. To avoid numerical instabilities caused by this force discontinuity (as schematically shown in Fig. 1 ), Gu et al. [30] proposed a modified cohesion model based on the analysis of head-on collision between two particles. The relationship between van der Waals force and particle surface separation is modified while the work done by non-contact van der Waals interaction is preserved. ...
The application of discrete element modelling (DEM) to cohesive fine powders in industrial processes, such as additive manufacturing, requires accurate and efficient calculations of van der Waals interaction forces. In DEM community, it is a general practice to reduce particle stiffness to accelerate the simulations; however, this study shows that, for cohesive particles, there are many cases where previously proposed scaling methodologies fail to preserve the original particle behaviour. The reason was attributed to an underestimated sliding and rolling resistances and a poorly resolved non-contact cohesive interaction, thus limiting the applicability of these approaches for contact-dominated systems. To address these significant issues, a new stiffness scaling methodology is proposed for the modelling of cohesive fine powders, which includes a scaling law for contact adhesion, a modified sliding and rolling resistances, and a new force-estimation scheme for the calculation of non-contact van der Waals interaction. The new approach was verified with a series of simple cases; stiffness independent results were demonstrated for head-on particle-particle collisions, particle-wall collisions, and particle-agglomerate collisions. The predictions of stop distance of a particle sliding and/or rolling over a flat surface was preserved when the stiffness was scaled down almost four orders of magnitude, which was not possible with previous scaling approaches. The new approach was further validated by packing of cohesive fine particles. This work confirmed that not only was the packing density insensitive to the particle stiffness, but the details of the packing structure (coordination number and packing density distribution) were also maintained when the original particle stiffness was scaled down by three orders of magnitude. Finally, the applicability of the new approach was explored by simulations of homogeneous simple shearing, which was found to be controlled by system cohesiveness and inertial number.
... Similarly, Yao and Capecelatro (2021) followed Gu, Ozel, and Sundaresan (2016) and defined cohesive forces as F vdW ∝ −2 2 that act in a finite gap in between particles and becomes constant for particle overlap. These forces are added to the classic spring-dashpot model for contact, so that they can directly enter (3.10). ...
... These forces are added to the classic spring-dashpot model for contact, so that they can directly enter (3.10). Full details are provided in Gu et al. (2016) and Yao and Capecelatro (2021). Yao and Capecelatro (2021) investigated the deagglomeration of cohesive aggregates by isotropic turbulence and determined 0.19 ≤ T ≤ 0.98. ...
Cohesive particulate flows play an important role in environmental fluid dynamics, as well as in a wide variety of civil and process engineering applications. However, the scaling laws, constitutive equations and continuum field descriptions governing such flows are currently less well understood than for their non-cohesive counterparts. Grain-resolved simulations represent an essential tool for addressing this shortcoming, along with theoretical investigations, laboratory experiments and field studies. Here we provide a tutorial introduction to simulations of fine-grained sediments in viscous fluids, along with an overview of some representative insights that this approach has yielded to date. After a brief review of the key physical concepts governing van der Waals forces as the main cohesive effect for subaqueous sediment suspensions, we discuss their incorporation into particle-resolved simulations based on the immersed boundary method. We subsequently describe simulations of cohesive particles in several model turbulent flows, which demonstrate the emergence of a statistical equilibrium between the growth and break-up of aggregates. As a next step, we review the influence of cohesive forces on the settling behaviour of dense suspensions, before moving on to submerged granular collapses. Throughout the article, we highlight open research questions in the field of cohesive particulate flows whose investigation may benefit from grain-resolved simulations.
... In the DEM, each particle is tracked using Newton's second law, and cohesion is incorporated directly [10]. Although the DEM has been widely used for cohesive flows (e.g., [3,[11][12][13][14][15][16][17][18]), it is computationally expensive when compared to other methods, such as the continuum theory [19]. The DEM is therefore less useful for direct application to commercial units as well as most lab-scale flows [20,21]. ...
In this work, the cohesion-specific inputs for a recent continuum theory for cohesive particles are estimated for moderately cohesive particles that form larger agglomerates via discrete element method (DEM) simulations of an oscillating shear flow. In prior work, these inputs (critical velocities of agglomeration and breakage and collision cylinder diameters) were determined for lightly cohesive particles via the DEM of simple shear flow—i.e., a system dominated by singlets and doublets. Here, the DEM is again used to extract the continuum theory inputs, as experimental measurements are infeasible (i.e., collisions between particles of a diameter of <100 μm). However, simulations of simple shear flow are no longer feasible since the rate of agglomeration grows uncontrollably at higher cohesion levels. Instead, oscillating shear flow DEM simulations are used here to circumvent this issue, allowing for the continuum theory inputs of larger agglomerate sizes to be determined efficiently. The resulting inputs determined from oscillating shear flow are then used as inputs for continuum predictions of an unbounded, gas–solid riser flow. Although the theory has been previously applied to gas–solid flows of lightly cohesive particles, an extension to the theory is needed since moderately cohesive particles give rise to larger agglomerates (that still readily break). Specifically, the wider distribution of agglomerate sizes necessitates the use of polydisperse kinetic-theory-based closures for the terms in the solids momentum and granular energy balances. The corresponding continuum predictions of entrainment rate and agglomerate size distribution were compared against DEM simulations of the same system with good results. The DEM simulations were again used for validation, as it is currently extremely challenging to detect agglomerate sizes and the number of fractions in an experimental riser flow.
... The granular temperature is evaluated from the normal components of the particle velocity fluctuations tensor as: Table 1. Simulations were carried out within the framework of OpenFOAM [27], LIGGGHTS [28] and CFDEMCoupling [14], which has successfully been used to study the gas-solid flows [2,[29][30][31][32]. Uniform hexahedral meshes were used in each set of simulations and the optimal grid size was chosen based on the previous studies [33] and reported in Table 1. ...
Spout-fluid beds are unique systems that require thorough study prior to their industrial application. In this study, the hydrodynamics of spout-fluid beds were investigated using 3D computational fluid dynamics coupled with discrete element method (CFD-DEM). Three flow regimes, including jet-in-fluidized bed, spouting-with-aeration, and intermediate/spout-fluidization were studied, and the particle mixing was quantified in these regimes using the Lacey mixing index. The results showed that both axial and lateral mixing rates are better in jet-in-fluidized bed and the spouting-with-aeration flow regimes, with the axial mixing being superior to the lateral in all flow regimes. Examining the diffusivity coefficient revealed that mixing in the jet-in-fluidized bed flow regime is better due to the formation and eruption of bubbles in the annulus. Additionally, the granular temperature was analyzed in all flow regimes, and higher particle velocity fluctuations were observed in the spouting-with-aeration and the jet-in-fluidized bed flow regimes due to the higher spout gas velocity and formation of bubbles in the annulus. This study provides valuable insights into the hydrodynamics of spout-fluid beds in different flow regimes, which can aid in the design and optimization of spout-fluid bed reactors for various industrial applications.
... Using a reduced stiffness allows one to use a larger time step to resolve interparticle collisions, which considerably reduces the computation cost (Tsuji et al., 1993). It has been proved that the stiffness can be reduced by several orders of magnitude without altering the simulation results (Moreno-Atanasio et al., 2007;Gu et al., 2016;Chen et al., 2019a). The time step Dt used to solve the equation of motions in Eq. (1) is sufficiently small to prevent excessive overlaps between contact particles and to ensure realistic force transmission. ...
We perform discrete element simulations to investigate the influence of the flow velocity, the particle size, and the particle-particle sliding friction on flow patterns and packing structures of dense granular flow around an immersed cylindrical tube. Results indicate that varying the flow velocity and particle radius does not obviously affect the scaled velocity field. However, increasing the velocity enhances the vertical motion of particles near the void space and increasing the particle size reduces the particle flowability in the horizontal direction. Both effects result in the enlargement of the void space below the tube. Moreover, larger particle friction leads to a looser packing structure and a larger void region. The width and the depth of the void region increase with the friction in an exponential form. The simulation results in this work help to understand the origin of the complex flow structures in moving bed particle heat exchangers.
... An artificially small Young's modulus (10 MPa) was used for the glass beads to avoid a prohibitively small DEM time step [39,40]. This is common practice to speed up DEM simulations, and was previously found not to have a significant impact on the bubble dynamics for non-cohesive particles [41][42][43][44]. The angle of repose, , was measured experimentally by piling the glass beads on a horizontal surface, and the friction coefficient between particles, , was set to 0.35 according to the approximation obtained from the Mohr-Coulomb criterion. ...
An adequate use of gas pulsation can create an ordered, dynamically structured bubble flow in a bed of Geldart B particles. A structured bed is more homogeneous, responds to external control and is scalable. While earlier studies have focused on describing the self-organization of the gas bubbles, the solid mixing and gas-solid contact patterns have remained unclear. In this work, the solids circulation and mixing behavior in structured and unstructured beds at various pulsation frequencies are compared with a traditional fluidized bed operation. The degree of lateral mixing is hereby quantified through an effective lateral dispersion coefficient extracted from CFD-DEM (discrete element modelling) simulations in a thin fluidized bed system. Mixing shows major quantitative and qualitative differences amongst the investigated cases. The coordinated motion of the gas bubbles wraps the solid flow into a series of compartments with minimal interaction, whereby effective lateral dispersion coefficients are an order of magnitude lower than in an unstructured operation. More importantly, unlike a traditional bed, dispersion in a structured bed is driven by advection and is no longer a diffusive process. Compartmentalization decouples the time scales of micro- and macromixing. Every pulse, the compartments rearrange dynamically, causing a level of local axial mixing that is scale-independent. While further work is necessary to fully understand the compartmentalization at a larger scale, the circulation described here indicates that a dynamically structured bed can provide a tight control of mixing at low gas velocities and a narrower distribution of stresses in the solid phase compared to traditional devices.
... Although it is a general practice to use reduced particle stiffness to accelerate DEM simulations; however, our recent study [37] showed that, for cohesive particles, there are many cases where the previously proposed scaling laws fail to preserve original particle behaviour, especially for contact-dominated systems, leading to under-predicted sliding and rolling resistances and a poorly resolved non-contact van der Waals interaction [37]. Different from the existing scaling approaches [36,45], the new scaling methodology consists of three key components: an established scaling law for contact adhesion (i.e. Eq. (7)), a modified normal contact force for the calculation of sliding and rolling resistances (i.e. ...
Particle properties play a key role in determining the flowability of cohesive fine powders and consequently the quality of parts fabricated by additive manufacturing. However, how the characteristics of a spread powder layer are linked to particle properties remains not well understood, largely due to the limitations of available numerical models and characterisation approaches. This study thus established an efficient discrete element modelling framework to address these issues, combining GPU computing with a novel methodology for particle stiffness scaling. The validity of the DEM model was verified on both packing and spreading of cohesive fine powders. The effect of particle cohesion on the characteristics of a spread powder layer was systematically analysed for non-cohesive and weakly to strongly cohesive powders. The structure of spread powder layer was qualitatively illustrated and quantitatively evaluated by not only commonly used metrics, such as coordination number, packing density and surface profiles but also particle clustering and pore characteristics. While reducing particle cohesion leads to an enhanced powder flowability, different regimes were identified in the relationship between layer characteristics and particle cohesion. The results showed that powder spreadability has a complicated dependence on the strength of particle cohesion, where the underlying mechanisms can be understood in part via a dimensionless inertial length. These findings not only provide valuable metrics to quantitatively evaluate the quality of a spread powder layer, but also enable a better understanding of the physics underlying the spreading of cohesive fine powders.
... Besides, the efficiency is preferred when the macroscope description of the fluid field and the solids is more important than the local/individual behavior. Lots applications of the existing CFDEM approaches with the IBM in simulating fluidized bed problems can be found, including fluid catalytic cracking, solid fuel combustion and coating [37,38]. However, the fluid field with a high resolution and the accurate description of the interaction phenomenon are required in several applications. ...
In order to study the movement of rigid bodies with arbitrary shapes in the fluid, a resolved CFDEM coupling algorithm is proposed. The proposed method combines the computational fluid dynamics for the fluid and the discrete element method for the rigid bodies. The behavior of the fluid phase is simulated based on the Navier-Stokes equations in the Eulerian framework, whereas the motion of the rigid bodies is governed by the Newton's second law in the Lagrangian description. The major difficulty, namely, the representation of the moving boundaries of the solids, is solved by the immersed boundary method. The interaction forces between the fluid and the solids in different frameworks are derived according to the velocity boundary conditions on the immersed boundary points. Aiming at achieving the strong interaction effects between the fluid and the solids, several iterations are carried out to solve the coupling system.
... where A is the Hamaker constant, r is the particle radius, and s is the distance between the particle surfaces. In present simulations, a minimum separation distance m in s is introduced to avoid unrealistic singularity incurred at particle contact, and maximum (corresponded to the inter-molecular spacing), taking the inspiration from [38]. ...
The effect of external acoustic fields on hydrodynamic behavior of cohesive micron-size particles in a pseudo-2D fluidized bed is studied using CFD-DEM simulations. The forces acting on a particle consist of the contact force and cohesive force between particles, the drag force by the surrounding fluid and the sound force by an acoustic field. A wide range of sound pressure levels and sound frequencies are investigated in terms of their effects on the pressure drop, bed expansion, distribution of particle velocity and concentration, as well as the sizes of bubbles and agglomerates. Comparing to the system without acoustic force, the application of acoustic field is found to induce the breakup of the formed agglomerates, and ultimately lead to a stable bubbling fluidization regime. A useful range of frequencies between 80 Hz to 100 Hz is found with a pressure level of 120 dB resulting in most remarkable improvement of the process performance.
... Zhang et al. studied the effect of the restitution coefficient on mixing quality . Gu et al. studied the effect of the solid particle spring constant on hydrodynamics of a fluidized bed (Gu et al., 2016). The effect of the elastic modulus on hydrodynamic behavior was simulated in a gas-solid fluidized bed by CFD-DEM simulation (Navarro and de Souza Braun, 2013). ...
In this study, the effects of contact force modeling parameters, which included the particle–particle friction coefficient (A), spring constant (B), ratio of the tangential spring constant to normal spring constant (C), normal restitution coefficient (D), and tangential restitution coefficient (E) presenting in the linear spring-dashpot contact model on the hydrodynamics profile of spouted bed reactor, were investigated via computational fluid dynamics coupled with discrete element method (CFD-DEM) using Multiphase Flow with Interphase eXchange (MFIX). First, the base case simulation was validated with the experimental data. Next, the 2k factorial experimental design and an analysis of variance (ANOVA) were conducted to identify the significant main and interaction contact force modeling parameters. Four response variables were observed: the translation kinetic energy of particles, the rotational kinetic energy of particles, the bed expansion, and the standard deviation of pressure drop. Based on these results, the particle–particle friction coefficient, spring constant, and normal restitution coefficient were the major contact force modeling parameters that affected the system hydrodynamics in the spouted bed system. In addition, the effects of main and interaction contact force modeling parameters were summarized, which enhanced our knowledge of the modeling parameters on system hydrodynamics. Contact force modeling parameters must be carefully selected when simulating the spouted bed reactor or related gas-solid multiphase flow process, such as fluidized bed reactor.
... These studies highlighted that Geldart B particles can exhibit some of the characteristics of Geldart A in the presence of cohesive interparticle force. Other studies demonstrated that the spring stiffness constant used in the DEM model can have a significant influence and to account this effect, an adhesion model was developed (Gu et al., 2016;Kobayashi et al., 2013). ...
This paper presents a numerical analysis of the combined effect
of cohesive van der Waals force and particle shape on bubble dynamics in
gas fluidization. The van der Waals force is incorporated into the CFDDEM
model and the magnitude varies from 0 ~ 20 times Hamaker constant (Ha
= 2.1 × 10-21 J), representing non-cohesive to highly cohesive particles.
Particles with aspect ratios at 0.5 (oblate), 1 (spherical) and 2
(prolate) are employed to represent disc-like, spherical and rod-like
particles, respectively. The results show that under the influence of
cohesive force, features such as bubble splitting and coalescence are
affected significantly by aspect ratios of ellipsoidal particles. With
the increase of Hamaker constant, bubble size and rising velocity
decrease, and the bubble shape becomes irregular and vertically oblong.
Moreover, the increase of van der Waals force leads to the transformation
to non-bubbling fluidization for ellipsoids, but channelling occurs for
spheres.
... The validity of the criterion was verified by comparing the experimental data with the particle simulation of reducing the particle stiffness. Yile Gu et al. [18] used an improved cohesion model for fluidized CFD-DEM simulations. For viscous particles, the predicted flow pattern depends on the value of the particle spring stiffness used in the simulation. ...
The discrete element method (DEM) is commonly used to study various powders in motion during transportation, screening, mixing, etc.; this requires several microscopic parameters to characterize the complex mechanical behavior of the particles. Herein, a new discrete element parameter calibration method is proposed to calibrate the ultrafine agglomerated powder (recycled polyurethane powder). Optimal Latin hypercube sampling and virtual simulation experiments were conducted using the commercial DEM software; the microscopic variables included the static friction coefficient between the particles, collision recovery coefficient, Johnson–Kendall–Roberts surface energy, static friction coefficient between the particles and wall, and collision recovery coefficient. A predictive model based on genetic-algorithm-optimized feedforward neural network (back propagation) was developed to calibrate the microscopic DEM simulation parameters. The cycle search algorithm and mean-shift cluster analysis were used to confirm the input parameters’ range by comparing the mean value of the dynamic angle of repose measured via the batch accumulation test. These parameters were verified by the baffle lifting method and the rotating drum method. This calibration method, once successfully developed, will be suitable for use in a variety of fine viscous powder dynamic flow conditions.
... The CFD-DEM modeling approach has been widely employed to investigate the effect of IPF on the hydrodynamics of gas-solid fluidized beds. Some of these studies were devoted to highlighting the influence of the liquid bridge cohesive force on the minimum fluidization velocity, bed pressure drop and expansion, relative normal collision velocity (Boyce et al., 2017;Darabi et al., 2011;Sakai et al., 2012;Wu et al., 2018), and quality of solids mixing (Fan et al., 2018;Lim et al., 2013) as well as the agglomeration tendency of particles in the bed (Girardi et al., 2016;Gu et al., 2016;Mikami et al., 1998;Song et al., 2017). Other investigations focused on the effect of van der Waals force on the hysteresis in the bed pressure drop profile around U mf (Galvin and Benyahia, 2014), fine particles' behavior in the homogenous and bubbling fluidization regimes (Ye et al., 2004), and the mechanism of agglomerate breakage (Kuwagi and Horio, 2002). ...
The influence of cohesive interparticle force (IPF) on gas dynamics in a bubbling gas–solid fluidized bed was numerically investigated while the bed hydrodynamics was described with the help of computational fluid dynamics and discrete element method (CFD-DEM). The model was validated by experimental results in terms of total bed pressure drop profile, probability density distribution of instantaneous local bed voidage signals, and Eulerian solid velocity field. The results showed that the model can satisfactorily predict the hydrodynamics of a bubbling gas–solid fluidized bed that is impacted by the presence of cohesive IPF. The validated CFD-DEM model was adopted to delineate the effects of IPF on the distribution of fluidizing gas between the bubble and emulsion phases and bubble characteristics, such as bubble stability and rise path, which could hardly be explored experimentally. Simulation results revealed that the presence of IPF in the bubbling bed alters the distribution of the fluidizing gas between the bubble and emulsion phases in favor of an increase in the propensity of gas to pass through the bed in the emulsion phase. The results also indicated that the bubble stability increases and the straight rise path of bubbles changes to a tortuous path when enhancing IPF.
A 3D JKR-based discrete element method (DEM) is employed to investigate the oblique collisions of micron-sized particles. The energy dissipation pathways are analyzed and the effect of particle size, and impact angles on the critical sticking velocity is discussed. An explicit formula is put forward as a sticking/rebound criterion for collisions of micron-sized particles covering different impact angles, particle sizes, and size ratios. We then propose a fast DEM based on scaling laws to reduce particle Young’s modulus, surface energy and to modify rolling and sliding resistances simultaneously. A novel inversion method is then presented to help users quickly determine the damping coefficient, particle stiffness, and surface energy to reproduce a prescribed experimental result. After validating this inversion method, we apply the fast adhesive DEM to packing problems of microparticles. Measures of the packing fraction, averaged coordination number, and distributions of local packing fraction and contact number of each particle are in good agreement with results simulated using the original value of particle properties. The new method should be helpful to accelerate DEM simulations for systems associated with aggregates or agglomerates.
In the past few decades, multi-scale numerical methods have been developed to model dense gas-solid flow in fluidized beds with different resolutions, accuracies, and efficiencies. However, changes in fluidized beds’ simulations are still not elucidated: (i) the proper selection of the sub-models, parameters, and numerical resolution; (ii) the multivariate coupling of operating conditions, bed configurations, polydispersity, and additional forces. Accordingly, a state-of-the-art review is performed to assess the applicability of multi-scale numerical methods in predicting dense gas-solid flow in fluidized beds at specific fluidization regimes (e.g., bubbling fluidization region, fast fluidization regime), with a focus on the inter-particle collision models, inter-phase interaction models, collision parameters, and polydispersity effect. A mutual restriction exists between resolution and efficiency. Higher-resolution methods need more computational resources and thus are suitable for smaller-scale simulations to provide a database for closure development. Lower-resolution methods require fewer computational resources and thus underpin large-scale simulations to explore macro-scale phenomena. Model validations need to be further conducted under multiple flow conditions and comprehensive metrics (e.g., velocity profiles at different heights, bubbles, or cluster characteristics) for further improvement of the applicability of each numerical method.
This article reviews recent developments in computational modeling of dry powder inhalers (DPIs). DPIs deliver drug formulations (sometimes blended with larger carrier particles) to a patient’s lungs via inhalation. Inhaler design is complicated by the need for maximum aerosolization efficiency, which is favored by high levels of turbulence near the mouthpiece, with low extrathoracic depositional loss, which requires low turbulence levels near the mouth-throat region. In this article, we review the physical processes contributing to aerosolization and subsequent dispersion and deposition. We assess the performance characteristics of DPIs using existing simulation techniques and offer a perspective on how such simulations can be improved to capture the physical processes occurring over a wide range of length- and timescales more efficiently.
A CFD-DEM model for aerated vibratory convection was developed to explore the coupled gas-solid interactions governing bulk powder bed dynamics. Each simulation was prepared by carefully characterizing the rough, porous conveyor baseplate and four candidate particle sizes representative of typical powder beds. Trends in the vibratory convection of particles between 20 and 250 μm in diameter could be explained by considering each powder's minimum fluidization velocity and the magnitude of van der Waals cohesive forces. Simulations of fine powders under high cohesive forces exhibited competing effects from drag and cohesion; drag promotes powder-frit liftoff while cohesion suppresses contact separation. Experimental convection velocities were observed to be in good agreement with the simulated mean powder velocity for throw numbers between 0.25 and 0.50.
Gas cyclones are common device in various industries to separate solid particles and/or droplets from gas streams. Nonetheless, the mathematical modelling of gas cyclone has been very challenging since huge number of multi-sized particles are involved in the system. In this work, a numerical study of the gas-solid flow in a gas cyclone with wide range of particle size distribution (from 1 to 200 µm) is carried out by developing a coarse-grained combined Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD) model. It shows that the coarse-grained CFD-DEM model is able to capture the typical flow features in a gas cyclone including the solid strands and dust ceiling phenomena. It also shows that modelling of van der Waals force is critical for the prediction of separation efficiency in gas cyclone especially for fine particles. Furthermore, it is tried to explain how the dust ceiling is formed.
The fluidization behavior of cohesive particles was investigated using an Euler-Euler approach. To do so, a two-fluid model (TFM) platform was developed to account for the cohesivity of particles. Specifically, the kinetic theory of granular flow (KTGF) was modified based on the solid rheology developed by Gu et al. J. Fluid Mech. 2019. The results of our simulations demonstrated that the modified TFM approach can successfully predict the formation of particle agglomerates and clusters in the fluidized bed, induced by the negative (tensile-dominant) pressure. The formation of such granules and clusters highly depended on the particle Bond number and the tensile pressure prefactor. To evaluate fluidization regimes, a set of simulations was conducted for a wide range of particle cohesivity (e.g., Bond number and tensile pressure prefactor) at two different fluidization numbers of 2 and 5. Our simulation results reveal the formation of four different regimes of fluidization for cohesive particles: (i) bubbling, (ii) bubbling-clustering, (iii) bubble-less fluidization, and (iv) stagnant bed. Comprehensive analysis of the shear-to-yield ratio reveals that the observed regime map is attributed to the competition between the shear stress and yield stress acting on the particles. The obtained regime map can be extended to incorporate the effect of dimensionless velocity and dimensionless diameter as a comprehensive fluidization chart for cohesive particles. Such fluidization charts can facilitate the design of fluidized beds by predicting the conditions under which the formation of particle agglomeration and clustering is likely in fluidized beds.
The effects of processing intensity, time, and particle surface energy on mixing of binary cohesive powder blends in high‐intensity vibration system were investigated via discrete element method simulations. The mixedness was quantified by the coefficient of variation, Cv; lower being better. The mixing rate, which is the speed at which homogeneity was achieved, was inversely proportional to the mixing Bond number, defined as the ratio of particle cohesion to the shear force resulting from the mixing intensity. Results show that both increasing processing intensity and reducing surface energy led to a faster mixing rate. However, the mixedness improved initially as mixing action (the product of mixing rate and mixing time) increased, but later deteriorated upon its further increase. Thus, both mixing rate and mixing intensity need to be tuned for optimum mixing performance depending on the cohesion level of particles; too high or too low mixing action should be avoided.
Gas-solid fluidized beds have drawn the attention of engineers and researchers as an effective technology for a large variety of applications, and numerical simulations can play an increasingly relevant role in their development and optimization. Although real-time simulations will require substantial progress in the accuracy, capability, and efficiency of numerical models, future developments could herald a new era of so-called virtual reality for process engineering, featuring interactive simulations instead of stepwise experimental scale-up studies and cost-intensive empirical trial-and-error methods. This review paper provides a significant body of knowledge on the developments of CFD mathematical models and how they can be applied in various fluidized-bed systems. The review is divided into three main parts. The first part (Mathematical modeling) describes the state-of-the-art numerical models of gas-solid flows (two-fluid model, soft-sphere model, hard-sphere model, and hybrid model) and their fundamental assumptions (gas-solid, particle-particle, and particle-wall interactions). Special attention is devoted to the forces and the moments of the forces acting on particles, the parcel modeling, the homogeneous and structure-dependent drag models, the non-spherical particle models, the heat and mass transfer, and the turbulence. The second part of this review (State-of-the-art studies) is dedicated to the body of literature, focusing on how these numerical models are applied to fluidized-bed systems used in chemical and energy process engineering. Relevant works on simulation in the literature up to 2021 are analyzed, complemented by an overview of popularly used commercial and in-house simulation codes. Particular attention is paid to those studies that include measurement validation, to achieve a fundamentally competitive comparison between the different numerical models. The pros and cons of applying CFD models to fluidized-bed systems are studied and assessed based on the existing body of literature. The third part of this review (Conclusion and prospects) highlights current research trends, identifying research gaps and opportunities for future ways, in which CFD can be applied to fluidized beds for energetic and chemical processes.
For many of the one billion sufferers of respiratory diseases worldwide, managing their disease with inhalers improves their ability to breathe. Poor disease management and rising pollution can trigger exacerbations that require urgent relief. Higher drug deposition in the throat instead of the lungs limits the impact on patient symptoms. To optimise delivery to the lung, patient-specific computational studies of aerosol inhalation can be used. However in many studies, inhalation modelling does not represent situations when the breathing is impaired, such as in recovery from an exacerbation, where the patient’s inhalation is much faster and shorter. Here we compare differences in deposition of inhaler particles (10 and 4 micron) in the airways of three patients. We aimed to evaluate deposition differences between healthy and impaired breathing with image-based healthy and diseased patient models. We found that the ratio of drug in the lower to upper lobes was 35% larger with a healthy inhalation. For smaller particles the upper airway deposition was similar in all patients, but local deposition hotspots differed in size, location and intensity. Our results identify that image-based airways must be used in respiratory modelling. Various inhalation profiles should be tested for optimal prediction of inhaler deposition.
Particle agglomeration in turbulent flows is an extremely complex process, and comprehensive study is beneficial to the development of turbulent agglomeration technology. The effects of vortex generator structure on particle agglomeration were investigated based on a combined computational fluid dynamics (CFD) and discrete element method (DEM) approach, including the geometric size, spanwise pitch, longitudinal pitch, row number, arrangement and form of the vortex generator. A dimensionless parameter K (the ratio of vorticity to strain rate, abbreviated as K) was defined to evaluate the agglomeration ability of the vortex generator, and the traditional agglomeration kernel function was modified by adding a correction coefficient α (agglomeration efficiency). By comparing the traditional agglomeration model and the modified agglomeration model with the experimental results, it showed that the modified agglomeration kernel model can simulate a result closer to the real agglomeration process.
Much confusion exists on whether force‐based or energy‐based descriptions of cohesive‐particle interactions are more appropriate. We hypothesize a force‐based description is appropriate when enduring‐contacts dominate and an energy‐based description when contacts are brief in nature. Specifically, momentum is transferred through force‐chains when enduring‐contacts dominate and particles need to overcome a cohesive force to induce relative motion, whereas particles experiencing brief contacts transfer momentum through collisions and must overcome cohesion‐enhanced energy losses to avoid agglomeration. This hypothesis is tested via an attempt to collapse the dimensionless, dependent variable characterizing a given system against two dimensionless numbers: a generalized Bond number, BoG–ratio of maximum cohesive force to the force driving flow, and a new Agglomerate number, Ag–ratio of critical cohesive energy to the granular energy. A gamut of experimental and simulation systems (fluidized bed, hopper, etc.), and cohesion sources (van der Waals, humidity, etc.), are considered. For enduring‐contact systems, collapse occurs with BoG but not Ag, and vice versa for brief‐contact systems, thereby providing support for the hypothesis. An apparent discrepancy with past work is resolved, and new insight into Geldart's classification1 is gleaned. This article is protected by copyright. All rights reserved.
Continuous vibrating spatial particle ALD reactors were developed to achieve high powder throughput while minimizing reactor footprint. Unlike fluidized bed reactors, continuous vibrating spatial particle ALD reactors operate below fluidization, using linear vibration to convey particles through alternating regions of precursor gas. Fine powder convection in these vibrating bed reactors is still not well understood, so cohesive discrete-element-method (DEM) simulations were performed to investigate the solids flow behavior. Using a Fast Fourier Transform (FFT) algorithm, we constructed a sum-of-sines model for the reactor kinematics based on accelerometer data. Accelerometer results and DEM simulations revealed the role of high-frequency excitations and need for backsliding and sticking avoidance in horizontal conveyors at low-g accelerations. From these observations, we propose a novel sawtooth excitation to enable convection of cohesive fine powders at low flow velocities. The model results were compared to data from an in-house continuous vibrating spatial particle ALD reactor.
Biofilm streamer motion under different flow conditions is important for a wide range of industries. The existing work has largely focused on experimental characterisations of these streamers, which is often time‐consuming and expensive. To better understand the physics of biofilm streamer oscillation and their interactions in fluid flow, a computational fluid dynamics–discrete element method model has been developed. The model was used to study the flow‐induced oscillations and cohesive failure of single and multiple biofilm streamers. We have studied the effect of streamer length on the oscillation at varied flow rates. The predicted single biofilm streamer oscillations in various flow rates agreed well with experimental measurements. We have also investigated the effect of the spatial arrangement of streamers on interactions between two oscillating streamers in parallel and tandem arrangements. Furthermore, cohesive failure of streamers was studied in an accelerating fluid flow, which is important for slowing down biofilm‐induced clogging.
We carry out direct numerical simulation combined with adhesive discrete element calculations to investigate collision-induced breakage of agglomerates in homogeneous isotropic turbulence. The adopted method tracks the dynamics of individual particles while they are travelling alone through the fluid and while they are colliding with other particles. Based on extensive simulation runs, an adhesion parameter Ad n is constructed to quantify the possibility of occurrence of sticking, rebound and breakage events. The collision-induced breakage rate is then formulated based on the Smoluchowski equation and a breakage fraction. The breakage fraction, defined as the fraction of collisions that result in breakage, is then analytically estimated by a convolution of the probability distribution of collision velocity and a universal transfer function. It is shown that the breakage rate decreases exponentially as the adhesion parameter Ad n increases for doublets and scales as linear functions of the agglomerate size, with the slope controlled by Ad n. These results allow one to estimate the breakage rate for early stage agglomerates of arbitrary size. Moreover, the role of the flow structure on the collision-induced breakage is also examined. Violent collisions and breakages are more likely caused by particles ejected rapidly from strong vortices and happen in straining sheets. Our results extend the findings of shear-induced fragmentation, forming a more complete picture of breakage of agglomerates in turbulent flows.
Attractive inter-particle forces, such as Van Der Waals forces (vdw), are known to strongly influence the fluidization behavior of particles classified as Geldart C-type, and recent literature suggests that vdw forces may also become important for Geldart A and B type particles at elevated temperatures. Discrete Element Models (DEM) using a soft-sphere collision model have been developed to investigate the effects of particle-particle and particle-gas interactions on the fluidization behavior in great detail. However, it is shown that inconsistent results may be obtained with soft-sphere based DEM, depending on the numerical implementation of the vdw forces, particularly related to the calculation of the vdw forces for overlapping particles during particle collisions, as is usually done in the literature. In this work we present a new numerical approach that allows the calculation of the vdw force for particles that are in contact in a physically sound way, corresponding with theoretical arguments given by Rietema et al. (1993). We also provide a generic protocol to determine the relevant parameters based on our new approach, which will allow future work to simulate gas-solid fluidized beds with attractive inter-particle forces in a soft-sphere DEM framework.
The essence of fibrous filtration is gas-solid flow interaction, and the CFD-DEM (Computational Fluid Dynamic coupled Discrete Element Method) coupling method is an effective method to study such problems. However, the rolling friction coefficient is difficult to obtain accurately. To that end, the effect of changing the rolling friction between particles themselves and between particles and fibres has been studied by numerical simulation, and the coordination number and porosity has been calculated after the material deposition. Comparing the results of the simulations with experimental ones, it is found that the rolling friction coefficient between particles affects significantly the deposition morphology of particles on single fibre. On the other hand, the rolling friction coefficient between particles and fibres has a little effect on it.
Discrete particle simulation can explicitly consider interparticle forces and obtain microscopic properties of the fluidized cohesive particles, but it is computationally expensive. It is thus pivotal to link the microscopic discrete properties to the macroscopic continuum description of the system for large scale applications. This work studies the fluidization of cohesive particles through the coupled computational fluid dynamics and discrete element method (CFD‐DEM). First, discrete CFD‐DEM results show the increased particle cohesion leads to the severe particle agglomeration which affects the fluidization quality significantly. Then, continuum properties are attained by a weighted time‐volume averaging method, showing that tensile pressure becomes significant as particle cohesion increases. By incorporating Rumpf correlation into the solid pressure equation, the tensile pressure could be predicted consistently with the averaged CFD‐DEM results for different particle cohesion. Finally, those overall steady averaged properties of the bed are obtained for understanding the general macroscopic properties of the system. This article is protected by copyright. All rights reserved.
Backwashing is an essential tool for sustainable filtration and is applied to remove particulate matter from membranes. Extensive experimental research has been carried out to improve the performance and efficiency of the backwash process. However, the essential microscopic events controlling backwashing on a membrane pore-scale level are far from being understood. Unraveling these pore-scale resuspension events of colloidal matter during backwash is challenging to comprehend and requires advanced non-invasive observation methodologies.
First, this study applies microfluidic experiments that enable a pore-scale visualization of the resuspension events during backwash. The microfluidic experiments comprise two steps: a filtration and a backwash step. 4.2 μm polystyrene particles were filtered through a pore structure. After the pore structure is clogged, backwash is performed with varying flow rates. The experiments reveal that backwash is decisively controlled by particle clusters instead of single-particle effects. This clarifies that single-particle models are not representative of describing processes occurring during backwash.
Second, multiphase simulations were conducted describing the interplay between hydrodynamic and colloidal interactions during particle resuspension. Two dominant events of backwash were identified from the simulations and the experiments: partial resuspension of particle clusters and orientation of attached particle clusters in the region of lower drag. The orientation of attached clusters into the region of lower drag reduces backwash efficiency since these clusters are shielded from the hydrodynamic flow. Numerical simulations are applied to identify how the size of clogging formation and the colloidal interaction control the backwash. The results reveal that the particle membrane interaction dominantly controls the backwash efficiency, whereas particle interactions show a lesser impact.
The typical granular kinetic model, the cohesive granular kinetic model based on the contact bonding energy (Kim-Arastoopour-Huilin model) and the cohesive granular kinetic model based on the excess compressibility (Ye et al.'s model) were comprehensively compared in terms of kinetic parameters, bed expansion, and bubble behavior. The calculation methods of the contact bonding energy loss and the excess compressibility were presented, and the inter-relationship between the two cohesive parameters was revealed. The three kinetic models predict consistent kinetic parameters in dilute gas-solid flow region, while Ye et al.'s model always predicts a lower value when the solid fraction is above 0.15. The Kim-Arastoopour-Huilin model and Ye et al.'s model predicts opposite variations of solid pressure with increasing cohesion. Increasing cohesion interaction reduces the granular shear viscosity and bulk viscosity. Kim-Arastoopour-Huilin model and Ye et al.'s model outperform the typical kinetic model in terms of the bubble diameter and rising velocity.
We present a multi-purpose CFD-DEM framework to simulate coupled fluid-granular systems. The motion of the particles is resolved by means of the Discrete Element Method (DEM), and the Computational Fluid Dynamics (CFD) method is used to calculate the interstitial fluid flow. We first give a short overview over the DEM and CFD-DEM codes and implementations, followed by elaborating on the numerical schemes and implementation of the CFD-DEM coupling approach, which comprises two fundamentally different approaches, the unresolved CFD-DEM and the resolved CFD-DEM using an Immersed Boundary (IB) method. Both the DEM and the CFD-DEM approach are successfully tested against analytics as well as experimental data.
Fluidized gas-particle systems are inherently unstable and they manifest structures on a wide range of length and time scales. In this article we present for the first time in the literature a coarse-grained drag force model for Euler-Lagrange (EL) based simulations of fluidized gas-particle suspensions. Two types of coarse graining enter into consideration: coarse fluid grids as well as particle coarsening in the form of parcel-based simulations where only a subset of particles is simulated. We use data from well-resolved EL simulations to assemble a model for the filtered drag force that examines fluid and particle coarsening separately. We demonstrate that inclusion of correction to gas-particle drag to account for fluid coarsening leads to superior predictions in a test problem. We then present an ad hoc modification to account for particle coarsening, which improves accuracy of simulations involving both fluid and particle coarsening. We also identify an approximate characteristic length scale that can be used to collapse the results for different gas-particle systems.
Two-dimensional DEM–CFD simulations have been performed in order to examine the effect of surface energy on the transitional behaviour from fixed bed to bubbling bed for Geldart Type A particles. The results of the simulations presented in the paper show that any effect of surface energy on the magnitude of Umf is not due to increasing bed resistance as a result of increasing the interparticle bond strength. It is demonstrated that Umf corresponds to a deterministic (isostatic) state that is in effect the initiation of the transition from solid-like to fluid-like behaviour. It is also shown that the so-called ‘homogeneous expansion' regime is not in fact homogeneous. This is because the system, when U>Umf, consists of agglomerates. Consequently, the idea that bed expansion is due to the ‘elasticity’ of the bed is not tenable. In order to break up the agglomerates and create a fully fluidised bed that will allow bubbling to occur, higher superficial gas velocities are required for higher values of surface energy. Once the bed is fully fluidised and bubbling occurs the effect of surface energy becomes insignificant.
Incoming and rebounding particle velocities were measured to within several particle diameters of the impaction surface using laser Doppler velocimetry. Impacts occurred normal to the surface and ranged from 1 m/s, near the threshold for particle bounce, to 100 m/s, well into the plastic damage regime. Monodisperse ammonium fluorescein spheres, 2.6–6.9 μm in diameter, impacted target surfaces including polished molybdenum and silicon, cleaved mica, and a fluorocarbon polymer. The incident kinetic energy recovered on rebound depended on particle size and target composition at low velocity (< 20 m/s), where the adhesion surface energy is important. No dependence on target composition was found at higher velocities where up to half of the impact energy was lost to plastic deformation. Plastic deformation was a significant component of energy loss even at impact velocities near critical velocity. Critical velocities for the onset of bounce decreased with a stronger power-law dependence on particle diameter than expected from classical adhesion theory or the elastic flattening model proposed by Dahneke. This is consistent with kinetic energy loss contributions from both plastic deformation and surface forces. Auxiliary experiments conducted with and without continuous discharge of the impact surface indicated the absence of a significant electrostatic contribution to particle adhesion.
Numerical simulation, in which the motion of individual particles was calculated, was performed of a two-dimensional gas-fluidized bed. Contact forces between particles are modeled by Cundall's Distinct Element Method (P.A. Cundall and O.D.L. Strack, Geotechnique, 29 (1979) 47), which expresses the forces with the use of a spring, dash-pot and friction slider. The gas was assumed to be inviscid and its flow was solved simultaneously with the motion of particles, taking into account the interaction between particles and gas. The simulation gives realistic pictures of particle motion. Formation of bubbles and slugs and the process of particle mixing were observed to occur in the same way as in experiments. The calculated pressure fluctuations compared well with measurements.
This reference describes the role of various intermolecular and interparticle forces in determining the properties of simple systems such as gases, liquids and solids, with a special focus on more complex colloidal, polymeric and biological systems. The book provides a thorough foundation in theories and concepts of intermolecular forces, allowing researchers and students to recognize which forces are important in any particular system, as well as how to control these forces. This third edition is expanded into three sections and contains five new chapters over the previous edition.
A discrete particle model for flows of Group A particles in Geldart's classification is studied. In general, Group A particles are fine and light, so that the adhesion force has a strong effect on their fluidization behavior. Inter-particle adhesion force of Group A particle was measured first. Secondly, the DEM–CFD coupling simulation with the measured adhesion force was performed, and the simulated results were compared with the experimental data about a small-scale fluidized bed for verification of the simulation. It was found from the results that there were considerable differences between their flow patterns. In order to reveal the cause of the differences, the effect of the adhesion force in the contact force model was studied on the motion of a single particle colliding with a wall.
The effects of cohesive forces of van der Waals type in the fluidization/defluidization of aeratable type A powders in the Geldart classification are numerically investigated. The effects of friction and particle-size distribution (PSD) on some design-significant parameters, such as minimum fluidization and bubbling velocities, are also investigated. For these types of particles, cohesive forces are observed as necessary to fully exhibit the role friction plays in commonly observed phenomena, such as pressure overshoot and hysteresis around minimum fluidization. This study also shows that a full-experimental PSD consisting of a dozen particle sizes may be sufficiently represented by a few particle diameters. Reducing the number of particle types may benefit the continuum approach, which is based on the kinetic theory of granular flow, by reducing computational expense, while still maintaining the accuracy of the predictions. Published 2013 American Institute of Chemical Engineers AIChE J, 2013
In this paper we study the effect of rolling friction on the dynamics in a single spout fluidized bed using Discrete Element Method (DEM) coupled to Computational Fluid Dynamics (CFD). In a first step we neglect rolling friction and show that the results delivered by the open source CFD–DEM framework applied in this study agree with previous simulations documented in literature. In a second step we include a rolling friction sub-model in order to investigate the effect of particle non-sphericity. The influence of particle–particle as well as particle–wall rolling friction on the flow in single spout fluidized bed is studied separately. Adequate rolling friction model parameters are obtained using first principle DEM simulations and data from literature. Finally, we demonstrate the importance of correct modelling of rolling friction for coupled CFD–DEM simulations of spout fluidized beds. We show that simulation results can be improved significantly when applying a rolling friction model, and that experimental data from literature obtained with Positron Emission Particle Tracking (PEPT) technique can be satisfactorily reproduced.
We have studied plane shear flow of nearly homogeneous assemblies of uniformly sized, spherical particles in periodic domains. Our focus has been on the effect of interparticle attractive forces on the flow behavior manifested by dense assemblies. As a model problem, the cohesion resulting from van der Waals force acting between particles is considered. Simulations were performed for different strengths of cohesion, shear rates, particle stiffnesses, particle volume fractions and coefficients of friction. From each simulation, the average normal and shear stresses and the average coordination number have been extracted. Not surprisingly, the regimes of flow reported by Campbell [C.S. Campbell, Granular Shear Flows at the Elastic Limit, J. Fluid Mech. 465 (2002) 261-291] for the case of cohesionless particles – namely, inertial, elastic–inertial and elastic–quasistatic regimes – persist when cohesion is included. The elastic–quasistatic regime was found to correspond with the coordination number decreasing with increasing shear rate, while in the inertial regime the coordination number increased with shear rate. A striking result observed in the simulations is that the influence of cohesion on stress becomes more pronounced with decreasing particle volume fraction. Furthermore, the window in the shear rate–particle volume fraction space over which the elastic–quasistatic regime is obtained was found to expand as the strength of cohesion was increased. When the particle volume fraction is so high that even a cohesionless system would be in the elastic–quasistatic regime, the addition of cohesion had minimal effect on the stresses. At lower particle volume fractions where a cohesionless assembly would have been in the inertial regime, we present a new scaling which permits collapse of all the data at various strengths of cohesion and shear rates into a single master curve for each particle volume fraction and coefficient of friction. The regimes of flow in this master curve are discussed and the scaling for the normal stress in elastic–quasistatic flow is identified.
By taking into account interparticle cohesion forces, one can derive limiting conditions which result in a classification of powders which is equivalent to the definition given by Geldart [1].Separation of powder type A from powder type C follows from the condition that free particle motion is suppressed by the dominance of cohesion forces in the case of powder type C.Separation of powder group B from powder group A is defined by the unimportance of cohesion forces on fluidization behavior in the case of powders of type B.Separation of powder group D from powder group B is defined by the fact that for minimum fluidization of powders of type D the dynamic pressure of the fluidizing agent exceeds a distinct value depending on particle size and density difference.
The micromechanics of different particle-fluid flow regimes, such as fixed, expanded and fluidized beds, in gas fluidization is investigated for group A and B powders. To establish the connection between macroscopic and microscopic descriptions of complex particle-fluid flows, focus is given to the following two aspects: the formation of a stable expanded bed in relation to the interparticle cohesive, sliding and rolling frictional forces, and the correlation between coordination number (CN) and porosity (epsilon). The method employed is the combined approach of three-dimensional (3D) discrete element method (DEM) and two-dimensional (2D) computational fluid dynamics. The results show that compared to 2D DEM, 3D DEM is more reliable in investigating the micromechanics of granular media, although both can capture key features of different flow regimes. The roles of various forces between particles and between particles and fluid are examined, and the origin of different flow regimes is discussed. It is shown that the cohesive force is critical to the formation of a static expanded bed, while the sliding and rolling frictional forces also play a role here. The criterion for bed expansion is analyzed at bulk and particle scales, and the deficiency at a bulk scale is identified. CN, as a key measure of local structure, is analyzed. It is found that the CN-epsilon relationship for group A powders has a transitional point between the expanded and fluidized bed flow regimes at a bulk scale, unlike group B powders. A new phase diagram is established in terms of CN-epsilon relationship that has two branches representing expanded and fluidized (bed) states, which corresponds to the one in terms of interparticle forces. (C) 2012 Elsevier Ltd. All rights reserved.
Digital high-speed photographic images of microsphere impact with a flat surface were made over a range of incident microsphere velocities. The incident and rebound velocities determined from successive images were used to validate a recently published model for low-speed impact. This model is shown to predict the experimental values of the normal coefficient of restitution and the surface-capture velocity to within 95% confidence.
The approach of combining computational fluid dynamics (CFD) for continuum fluid and the discrete element method (DEM) for discrete particles has been increasingly used to study the fundamentals of coupled particle–fluid flows. Different CFD–DEM models have been used. However, the origin and the applicability of these models are not clearly understood. In this paper, the origin of different model formulations is discussed first. It shows that, in connection with the continuum approach, three sets of formulations exist in the CFD–DEM approach: an original format set I, and subsequent derivations of set II and set III, respectively, corresponding to the so-called model A and model B in the literature. A comparison and the applicability of the three models are assessed theoretically and then verified from the study of three representative particle–fluid flow systems: fluidization, pneumatic conveying and hydrocyclones. It is demonstrated that sets I and II are essentially the same, with small differences resulting from different mathematical or numerical treatments of a few terms in the original equation. Set III is however a simplified version of set I. The testing cases show that all the three models are applicable to gas fluidization and, to a large extent, pneumatic conveying. However, the application of set III is conditional, as demonstrated in the case of hydrocyclones. Strictly speaking, set III is only valid when fluid flow is steady and uniform. Set II and, in particular, set I, which is somehow forgotten in the literature, are recommended for the future CFD–DEM modelling of complex particle–fluid flow.
The distinct element method is a numerical model capable of describing the mechanical behavior of assemblies of discs and spheres. The method is based on the use of an explicit numerical scheme in which the interaction of the particles monitored contact by contact and the motion of the particles modelled particle by particle. The main features of the distinct element method are described. The method is validated by comparing force vector plots obtained from the computer program BALL with the corresponding plots obtained from a photoelastic analysis.
The behaviour of solids fluidized by gases falls into four clearly recognizable groups, characterized by density difference (ϱs–ϱf) and mean particle size. The most easily recognizable features of the groups are: powders in group A exhibit dense phase expansion after minimum fluidization and prior to the commenment of bubbling; those in group B bubble at the minimum fluidization velocity; those in group C are difficult to fluidize at all and those in group D can form stable spouted beds. A numerical criterion which distinguishes between groups A and B has been devised and agrees well with published data. Generalizations concerning powders within a group can be made with reasonable confidence but conclusions drawn from observations made on a powder in one group should not in general be used to predict the behaviour of a powder in another group.
We report on 3D computer simulations based on the soft-sphere discrete particle model (DPM) of Geldart A particles in a 3D gas-fluidized bed. The effects of particle and gas properties on the fluidization behavior of Geldart A particles are studied, with focus on the predictions of U mf and U mb , which are compared with the classical empirical correlations due to Abrahamsen and Geldart [1980. Powder Technology 26, 35–46]. It is found that the predicted minimum fluidization velocities are consistent with the correlation given by Abrahamsen and Geldart for all cases that we studied. The overshoot of the pressure drop near the minimum fluidization point is shown to be influenced by both particle–wall friction and the interparticle van der Waals forces. A qualitative agreement between the correlation and the simulation data for U mb has been found for different particle–wall friction coefficients, interparticle van der Waals forces, particle densities, particle sizes, and gas densities. For fine particles with a diameter d p < 40 m, a deviation has been found between the U mb from simulation and the correlation. This may be due to the fact that the interparticle van der Waals forces are not incorporated in the simulations, where it is expected that they play an important role in this size range. The simulation results obtained for different gas viscosities, however, display a different trend when compared with the correlation. We found that with an increasing gas shear viscosity the U mb experiences a minimum point near 2.0 × 10 −5 Pa s, while in the correlation the minimum bubbling velocity decreases monotonously for increasing g .
This paper reports on a numerical study of fluidization behavior of Geldart A particles by use of a 2D soft-sphere discrete particle model (DPM). Some typical features, including the homogeneous expansion, gross particle circulation in the absence of bubbles, and fast bubbles, can be clearly displayed if the interparticle van der Waals forces are relatively weak. An anisotropy of the velocity fluctuation of particles is found in both the homogeneous fluidization regime and the bubbling regime. The homogeneous fluidization is shown to represent a transition phase resulting from the competition of three kinds of basic interactions: the fluid–particle interaction, the particle–particle collisions (and particle–wall collisions) and the interparticle van der Waals forces. In the bubbling regime, however, the effect of the interparticle van der Waals forces vanishes and the fluid–particle interaction becomes the dominant factor determining the fluidization behavior of Geldart A particles. This is also evidenced by the comparisons of the particulate pressure with other theoretical and experimental results.
The distinct element method (DEM) has proven to be reliable and effective in characterizing the behavior of particles in granular flow simulations. However, in the past, the influence of different force–displacement models on the accuracy of the simulated collision process has not been well investigated. In this work, three contact force models are applied to the elementary case of an elastic collision of a sphere with a flat wall. The results are compared, on a macroscopic scale, with the data provided by the experiments of Kharaz et al. (Powder Technol. 120 (2001) 281) and, on a microscopic scale, with the approximated analytical solution derived by Maw et al. (Wear 38 (1976) 101. The force–displacement models considered are: a linear model, based on a Hooke-type relation; a non-linear model, based on the Hertz theory (J. Reine Angew. Math. 92 (1882) 156) for the normal direction and the no-slip solution of the theory developed by Mindlin and Deresiewicz (Trans. ASME. Ser. E, J. Appl. Mech. 20 (1953) 327) for the tangential direction; a non-linear model with hysteresis, based on the complete theory of Hertz and Mindlin and Deresiewicz for elastic frictional collisions. All the models are presented in fully displacement-driven formulation in order to allow a direct inclusion in DEM-based codes.
Two microsphere-surface impact models have been developed for implementation with computational fluid dynamic software. The models consider either normal or oblique incidence of a microsphere with the surface. The first model includes the effects of microsphere-surface roughness, and Hertzian and adhesion damping during surface contact. The second model considers the impact of elastic–plastic sphere and a surface, with and without interface adhesion. Analytical solutions for the coefficients of restitution are presented in terms of the impact velocity and material properties. These algebraic models were validated by comparison with the experimental results of several investigators. A user-defined function representing the model was developed to interface with the commercial software package FLUENT®. The combined modelling package's predictions were compared with high-speed digital images of microparticle contact with the surface located on the floor of a wind tunnel.
Because of the balance of forces in fluidised beds, particle interactions can have a strong effect on their microscopic and macroscopic behaviour, leading to agglomeration and defluidisation. Three types of particle interactions are reviewed: van der Waals forces, liquid bridge forces and sintering. Sintering is qualitatively different in its effects because it is a time-dependent process. The observed effects of these three types of interactions on fluidisation behaviour are described and explained in terms of simple models.
Frequently we experience the existance of adhesive forces between small particles. It seems natural to ascribe this adhesion for a large part to London-v.d. Waals forces. To obtain general information concerning their order of magnitude the London-v. d. Waals interaction between two spherical particles is computed as a function of the diameters and the distance separating them. A table is calculated which enables numerical application of the formulae derived. Besides approximations are added, which may be used when the distance between the particles is small. In a separate section it is investigated how the results must be modified, when both particles are immersed in a liquid. Here we are led to the important conclusion that even in that case London-v. d. Waals forces generally cause an attraction.
The effect of contact stiffness on the fluidization behaviour of cohesive powders is analysed using a combined continuum and discrete model for the fluid phase and particulate phase, respectively. Four systems made of particles with two values of contact stiffness (50 and 50 000 N/m) and two values of surface energy (0.37 and have been studied. The analysis has been carried out in terms of the coordination number, average contact forces and deformations and granular temperature. The simulation results show that for the low value of surface energy ( the contact stiffness does not influence appreciably the fluidization behaviour. In contrast, the behaviour of the systems with the large value of surface energy is strongly influenced by the contact stiffness: no fluidization occurs for the system with small contact stiffness and full fluidization is observed for the system with large contact stiffness. These results suggest that the influence of the contact stiffness on the behaviour of powders depends on the cohesivity of the powders: the more cohesive the powder is, the larger are the differences in the behaviour of systems with different contact stiffnesses.
This reference describes the role of various intermolecular and interparticle forces in determining the properties of simple systems such as gases, liquids and solids, with a special focus on more complex colloidal, polymeric and biological systems. The book provides a thorough foundation in theories and concepts of intermolecular forces, allowing researchers and students to recognize which forces are important in any particular system, as well as how to control these forces. This third edition is expanded into three sections and contains five new chapters over the previous edition. • starts from the basics and builds up to more complex systems • covers all aspects of intermolecular and interparticle forces both at the fundamental and applied levels • multidisciplinary approach: bringing together and unifying phenomena from different fields • This new edition has an expanded Part III and new chapters on non-equilibrium (dynamic) interactions, and tribology (friction forces).
This paper presents a simulation study of the packing of uniform fine-spherical particles where the van der Waals force is dominant. It is shown that porosity increases with the decreases of particle size from about 100 to 1 &mgr;m and the simulated relationship can match the literature data well. The packing structure of fine particles is qualitatively depicted by illustrative pictures and quantified in terms of radial distribution function, angular distribution, and coordination number. The results indicate that in line with the increase in porosity, the first component of the split second peak and then the other peaks beyond the second one in the radial distribution function gradually vanish; the first peak becomes narrower, with a sharp decrease to the first minimum. As particle size decreases, the peaks at 120 degrees and then 60 degrees in the angular distribution will gradually vanish; the coordination number distribution shifts to the left and becomes narrower. The mean coordination number can decrease to a value as low as two for 1 &mgr;m particles, giving a very loose and chainlike structure. The interparticle forces acting on individual particles in a stable packing are analyzed and shown to be related to the packing properties.
We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.
OpenFOAM 2.2.2 User Manual
- Opencfd
OpenCFD, OpenFOAM 2.2.2 User Manual, 2013.
- C Kloss
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- S Pirker
C. Kloss, C. Goniva, A. Hager, S. Amberger, S. Pirker, Models, algorithms and validation for opensource DEM and CFD-DEM, Prog. Comput. Fluid Dyn. Int. J. 12 (2)
(2012) 140-152.