Average Solid Fraction Research Articles

Cross-stream oscillations in the granular flow through a vertical channel

The gravity flow of a granular material between two vertical walls separated by a width $2W$ is simulated using the discrete element method (DEM). Periodic boundary conditions are applied in the flow (vertical) and the other horizontal directions. The mass flow rate is controlled by specifying the average solids fraction $\bar {\phi }$ , the ratio of the volume of the particles to the volume of the channel. A steady fully developed state can be achieved for a narrow range of $\bar {\phi }$ , $\bar {\phi }_{max} \geq \bar {\phi } \geq \bar {\phi }_{cr}$ , and the material is in free fall for $\bar {\phi } < \bar {\phi }_{min}$ . For an intermediate range of $\bar {\phi }$ ( $\bar {\phi }_{cr} > \bar {\phi } \geq \bar {\phi }_{min}$ ), there are oscillations in the horizontal coordinate of the centre of mass, velocity components and stress. As $\bar {\phi }$ decreases in the range $\bar {\phi }_{cr} > \bar {\phi } \geq \bar {\phi }_{min}$ , the amplitude of the oscillations increases proportional to $\sqrt {\bar {\phi }_{cr} - \bar {\phi }}$ and the frequency appears to tend to a non-zero value as $\bar {\phi } \rightarrow \bar {\phi }_{cr}$ , indicating a supercritical Hopf bifurcation. The relation between the dominant frequency and the higher harmonics of the position, velocity and stress fluctuations are explained using the momentum balance. It is found that dissipation in the inter-particle and particle–wall contacts is critical for the presence of an oscillatory state.

On the effects of the flow macro‐scale over sub‐grid modelling in dense gas–solid fluidized flows

AbstractMultiscale modelling of gas–particle fluidized flows is frequently approached by means of sub‐grid modelling, which provides constitutive closures for filtered formulations applied to large scale simulations. A widely practiced procedure for the derivation of sub‐grid models consists of filtering over predictions from highly resolved simulations under two‐fluid modelling. The present work is intended as a contribution in this field by providing new supporting evidence for the enhancement of sub‐grid closure models. Most of the efforts in the area have been directed to providing sub‐grid models dependent on meso‐scale filtered effects alone, and under low gas Reynolds number suspension conditions. In this work, macro‐scale conditions are added to the analysis thereby accounting for flow topology, particularly for dense gas–solid fluidized flows. Two macro‐scale variables are considered in the simulations, namely the domain average solid volume fraction and the domain average gas Reynolds number. So, in addition to the usual meso‐scale filtered markers, relevant filtered parameters are also related to those macro‐scale conditions. The filtered parameters of interest here are the effective interphase drag coefficient and filtered and residual stresses in both of the phases. Various domain average solid volume fractions and domain average gas Reynolds numbers were enforced, thereby providing for a variety of macro‐scale dense conditions. It was found that both these macro‐scale parameters considerably affect the meso‐scale and the resulting filtered parameters of dense gas–solid flows, even though this occurs in a milder way when compared to results for dilute flow conditions available in the literature.

A scale sensitive filtered sub-grid drag model for fluidized gas-particle flows

A new sub-grid drag model is proposed for fluidized gas-particle flows which stands among those derived from filtering over results of meso-scale highly resolved simulations with microscopic two-fluid modeling. Filtered sub-grid models frequently correlate to meso-scale effects alone, taking no account of any micro-scale or macro-scale effects, a clear drawback in view of the lack of scale separation characteristic of gas-particle fluidized flows. The currently proposed sub-grid drag model accounts for the micro-scale effect through a range of particle Froude numbers, while the macro-scale effect is accounted for in average, by considering ranges of average solid volume fractions and gas flow Reynolds numbers. For the sake of comparing the current model to similar models, we use the expression “accounting” to mean the background of consideration of micro and macro-scale aspects that are accounted for in the models. In this particular sense, the proposed model represents a gain over previous versions.

Multi-mechanism theory of aerosol capture by fibrous filters, including fiber diameter/orientation dispersity and particle morphology effects. Preliminary tests vs. data for mobility-selected submicron particles

In Paper I (Sep. Purif. Technol. 257 (2021) 117676) we showed that a semi-analytic, multi-mechanism expression for the single-fiber capture fraction, ηcap,SF, (derived using asymptotically valid approximations: Ref<0.4, Pef≫1, R≪1, R⋅Pef1/3 arbitrary and Stkp≤Stkpcrit), facilitates a deterministic-, pseudo-continuum aerosol population-balance (PB-) approach to predicting fibrous filter performance. There we explicitly considered “deep” (Lf/df,g≫1), low solidity idealized fibrous filters (FFs) challenged by polydispersed aerosols—especially single-mode log-normal (LN) ASDs of modest spread captured by a spatially uniform array of fibers of a single diameter in crossflow. However, realistic fibrous filter media often possess a LN distribution of fiber diameters, as well as a near-Gaussian orientation distribution narrowly spread about normal incidence (θ=π/2). Moreover, even if this were not so, there would be meso-scale departures from a uniform average fiber solid fraction. We show here that our tractable aerosol PBE-approach to idealized FF performance (Paper I) can be generalized to incorporate these particular structural features of commercially available fibrous filter media. But, to clarify whether these generalizations are likely to be useful, if not fully sufficient, for practical circumstances, it is also necessary to compare such methods/predictions against selected sets of well-defined experimental results. We initiate this program here, having chosen the recent experiments of Kang et al. (2019) carried out using a commercially available fiberglass filter with Lf/df,g≃300, mean solid fraction of 0.039, and df,g=2.5μm, successively challenged by mobility-selected KCl(s) particles (with diameters between ca. 20 and 600nm) at the carrier gas velocities of 15 and 10 cm/s—capture conditions dominated by the transport mechanism of Brownian diffusion and convection, with “interception” (associated with non-negligible dp/df) becoming important above ca. dp=100nm. We conclude from these data that the effective interception diameter, dp,icpt,eff, of the particles studied is systematically larger than their stated mobility diameters—a situation which will deserve further attention in future studies. Encouraged by these preliminary but instructive comparisons, we expect that, for many current and future design purposes, our present class of semi-analytic/non-stochastic/multi-mechanism methods will provide a welcome complement, if not alternative, to much more computationally-intensive simulation methods for realistic fibrous media that have been described and implemented in the recent aerosol filtration literature. The consequences of including these structural features of fibrous filters in the presence of aerosol size- and shape polydispersity will be the subject of future studies, based on the generalized Population Balance Equation developed/proposed in Section 3.3.

FBR for Polyolefin Production in Gas Phase: Validation of a Two‐Phase Compartmentalized Model by Comparison with CFD

AbstractTwo different modeling approaches are applied in this work to the simulation of fluidized bed reactors containing solid particles of Geldart A‐B type and operated at typical conditions for polyolefins production. On one side, a fully detailed computational fluid‐dynamics (CFD) model is developed, considering a 2D planar geometry and a multi‐fluid description with kinetic theory of granular flows. On the other, a conventional three‐phase, 1D compartmentalized model (SCM) is also developed, implementing the fluid dynamic description based on popular, semi‐empirical relationships available in the literature. Given the huge difference of computational effort associated with the corresponding numerical solutions, our aim is to confirm the reliability of the simplified model by comparison with the results of the detailed CFD model. The results show that the oversimplified compartmentalized approach is capable to predict the solid mixing features established inside the reactor operated in bubbling fluidization regime with good reliability for non‐reactive polyethylene particles. Average solid volume fractions are particularly close to the values predicted by the CFD model when monodisperse particles are considered inside the examined range of gas velocity values. A generally good agreement is also found when solids with broad size distribution are analyzed.

Effect of specimen geometry and orientation on tensile properties of Ti-6Al-4V manufactured by electron beam powder bed fusion

Tensile testing is often proposed as the preferred methodology to qualify builds and materials produced through additive manufacturing. While there is already work demonstrating the difference in measured properties between tensile specimens produced in different build orientations, this does not extend to different specimen geometries. In addition, the body of knowledge in this domain is typically made up of studies that utilize custom combinations of specimen geometries, part finishing, and post-processing, making it challenging to compare results. To study the impact of geometry of tensile specimens on tensile testing results, a selection of standard specimen types provided in ASTM E8/E8M was prepared in Ti-6Al-4V using an electron beam powder bed fusion additive manufacturing machine. These specimens were characterized to observe any porosity defects, dimensional deviations, and surface topography that could impact performance. It was found that changes in specimen geometry, specimen size, build orientation, and the internal porous defects; have significant effects on the tensile properties of the specimens. The horizontally built specimens had higher yield and tensile strengths, but lower elongation compared to vertically built specimens. With an increase in cross-sectional area, an increase in the yield, tensile strength, and elastic modulus was observed. With an increase in surface area to volume ratio, there was a decrease in the yield and tensile strength. The average solid fraction of the specimens had no influence on any measured tensile properties. Furthermore, with an increase in maximum pore size, the elongation of the specimen decreased.

Enhanced strength-ductility synergy in a rheo-diecasting semi-solid aluminum alloy

Common strengthening strategies for casting aluminum alloys sacrifice ductility. Herein, the strength-ductility synergy of a rheo-diecasting semi-solid Al–Si–Mg–Cu–Fe–Sr alloy was tailored by optimizing the pouring temperature and subsequent heat treatment. The results demonstrated that with decreasing pouring temperature from 700 °C to 670 °C, the average grain diameter of primary α-Al grains and porosity decreased, while the average shape factor and solid phase fraction increased, resulting in improved mechanical properties of the alloy. After T6 heat treatment, changes in the morphologies of eutectic Si phases and Al3Fe phases were observed, and Mg2Si precipitates were formed, which further enhanced the mechanical properties of the alloy.

A CPFD simulation on the particle flow characteristics in a packed moving bed solar receiver with an added insert

An alternative particle receiver using downward particle flow in a quartz tube with a conical hopper at the bottom has been evaluated to eliminate particle loss associated with directly irradiated solid particle solar receivers (SPSR). A computational particle fluid dynamic (CPFD) simulation is performed to investigate the particle flow characteristics in the packed moving bed quartz tube SPSR with embedded insert. Whether an insert is added in the tube or not, a consistent regular pattern is achieved for the time-varied average solid fractions at different packed heights in the tube. However, inconsistent distribution of axial particle velocity on the cross-sectional area is obtained, and the particle layer thickness affects the uniformity of the axial particle velocities. The thinner particle layer leads to a uniform distribution of axial particle velocities, and the average axial particle velocity is higher than that with a thick particle layer, which can enhance the operating safety and heat transfer of the solar receiver according to the previous investigations. In this study, the particle layer thickness of 5 mm is recommended according to the CPFD simulation. In addition, the radial movement in the semi-annular flow channel is negligible if sufficient particles are provided by the top particle dispenser. The conclusions in this cold state numerical study can provide the basis for the establishment of a further accurate thermal model for the solar receiver.

Fluid-particle suspension by gas release from a granular bed

We have studied experimentally particle suspension when injecting a gas at the bottom of an immersed granular layer confined in a Hele-Shaw cell. This work focuses on the dynamics of particles slightly denser than the surrounding fluid. The gas, injected at constant flow-rate, rises through the granular bed then forms bubbles which entrain particles in the above liquid layer. The particles settle down on the edges of the cell, avalanche on the crater formed at the granular bed free surface, and are further entrained by the continuous bubbling at the center. We report the existence of a stationary state, resulting from the competition between particle entrainment and sedimentation. The average solid fraction in the suspension is derived from a simple measurement of the granular bed apparent area. A phenomenological model based on the balance between particle lift by bubbles at the center of the cell and their settling on its sides demonstrates that most of the particles entrained by bubbles come from a global recirculation of the suspension.

Droplet motion on contrasting striated surfaces

Liquid droplets move readily under the influence of surface tension gradients on their substrates. Substrates decorated with parallel microgrooves, or striations, presenting the advantage of homogeneous chemical properties yet varying the topological characteristics on either side of a straight-line boundary, are considered in this study. The basic type of geometry consists of hydrophobic micro-striations/rails perpendicular to the boundary, with the systematic variation of the width to spacing ratio, thus changing the solid–liquid contact fraction and inducing a well-defined wettability contrast across the boundary. Droplets in the Cassie–Baxter state, straddling the boundary, move along the wettability contrast in order to reduce the overall surface free energy. The results show the importance of the average solid fraction and contrasting fraction in a wide range of given geometries across the boundary on droplet motion. A unified criterion for contrasting striated surfaces, which describes the displacement and the velocity of the droplets, is suggested, providing guidelines for droplet manipulation on micro-striated/railed surfaces.

Particle conveying under microgravity in a vibrating vessel

This paper presents a numerical study on the conveying of particles in a vibrating vessel under microgravity. Such a vessel is composed of parallel plates with sawtooth wavy surfaces, which are specifically designed to convey particles using simple vibration. The numerical model was validated by good agreement between the simulated and experimental results. Then the effects of key variables, including the vessel geometry, vibration amplitude and frequency and gravity level, were systematically investigated by a series of controlled simulations. The results confirm the optimised design from the previous experiments, and numerically demonstrate that using such a system a steady conveying operation can be achieved under microgravity. The convey rate is positively affected by the vibration amplitude and frequency in a complicated way, which cannot be simply described by the commonly used vibration intensity or velocity amplitude. The gravity level also has a significant effect on the convey rate when it is over 0.001g. The convey rate can be estimated by the product of the average solid fraction and velocity. And the effects of the variables can be better understood through the analyses on these two parameters. Finally, a predictive model is proposed to estimate the convey rate under different operational conditions. The findings are useful for the design of particle conveying techniques for outer space applications.

Universal stability curve for pattern formation in pulsed gas-solid fluidized beds of sandlike particles

A granular layer can form regular patterns, such as squares, stripes, and hexagons, when it is fluidized with a pulsating gas flow. These structures are reminiscent of the well-known patterns found in granular layers excited through vibration, but, contrarily to them, they have been hardly explored since they were first discovered. In this work, we investigate experimentally the conditions leading to pattern formation in pulsed fluidized beds and the dimensionless numbers governing the phenomenon. We show that the onset to the instability is universal for Geldart B (sandlike) particles and governed by the hydrodynamical parameters = ua/(utφ¯) and f/fn, where ua and f are the amplitude and frequency of the gas velocity, respectively, ut is the terminal velocity of the particles, φ¯ is the average solids fraction, and fn is the natural frequency of the bed. These findings suggest that patterns emerge as a result of a parametric resonance between the kinematic waves originating from the oscillating gas flow and the bulk dynamics. Particle friction plays virtually no role in the onset to pattern formation, but it is fundamental for pattern selection and stabilization.

Effect of Y Addition on the Semi-Solid Microstructure Evolution and the Coarsening Kinetics of SIMA AZ80 Magnesium Alloy

Semi-solid feedstock of AZ80 magnesium alloy modified by trace rare-earth Y element (0, 0.2, 0.4, 0.8 wt. %) was fabricated by strain-induced melting activation (SIMA) in the form of extrusion and partial remelting. The effect of Y addition on the microstructure evolution of the extruded and isothermally heat treated alloy was observed by using an optical microscope (OM), scanning electron microscope (SEM), X-ray diffraction (XRD) and quantitative analysis. The results show that the Y addition can refine the microstructure and make the β-Mg17Al12 phases agglomerate. During the subsequent isothermal treatment at 570 °C, the average solid grain size, shape factor and liquid fractions increased with the prolonged soaking time. The smaller spheroidal solid grains and larger shape factor were obtained in the semi-solid microstructure due to Y addition. The coalescence and Ostwald ripening mechanism operated the coarsening process of solid grains simultaneously. The coarsening rate constants of AZ80M1 (0.2 wt. % Y addition) of 164.22 μm3 s−1 was approximately four times less than the un-modified AZ80 alloy of 689.44 μm3 s−1. In contrast, the desirable semi-solid structure featured, with fine and well globular solid grains, an appropriate liquid fraction, and shape factor was achieved in AZ80M1 alloy treated at 570 °C for 20–30 min.

On the internal solids circulation rates in freely-bubbling gas-solid fluidized beds

The solids mass flux distribution and internal solids circulation rates in freely-bubbling gas-solid fluidized beds has been studied in detail in a pseudo-2D column. A non-invasive Particle Image Velocimetry (PIV) combined with Digital Image Analysis (DIA) technique has been further extended to investigate and quantify the gas and solids phase properties simultaneously for different particle types and sizes (all Geldart B type) at different fluidization velocities. It is found that the solids fluxes increase strongly, practically linearly, as a function of the vertical position and depend on the excess gas velocity but not on the particle size, while the most often used phenomenological two-phase fluidized bed models assume the vertical solids fluxes to be constant. To further investigate this important discrepancy, the underlying assumptions of the phenomenological models have been validated, especially concerning the average solids fraction inside the bubbles, the laterally and time-averaged axial bubble fraction profile (or visual bubble flow rate) and the wake parameter (the amount of solids carried along a bubble relative to the bubble volume). To this end, the PIV/DIA technique was further extended and a new method for the determination of the wake parameter is proposed. From the experimental results, it was concluded that i) the average solids fraction inside the bubbles is about 2.5–3% for glass beads and alumina particles and is practically independent of the excess gas velocity and particle size; ii) the measured laterally and time-averaged bubble fractions are considerably lower compared to often used correlations from literature, which would lead to a significant over-prediction of the visual bubble flow rate and iii) the wake parameter depends strongly on the bubble size and with the developed correlation the axial solids mass fluxes as a function of the vertical position can be well described. Finally, the influence of these findings was evaluated by performing a sensitivity analysis with an existing phenomenological model for fluidized beds with the new values and closures considering the case of the heterogeneously catalyzed steam methane reforming. With the developed findings and correlations the predictions with the two-phase phenomenological models can be further improved, especially concerning the hydrodynamics of the solids phase.

DEM simulation of dendritic grain random packing: application to metal alloy solidification

The random packing of equiaxed dendritic grains in metal-alloy solidification is numerically simulated and validated via an experimental model. This phenomenon is characterized by a driving force which is induced by the solid-liquid density difference. Thereby, the solid dendritic grains, nucleated in the melt, sediment and pack with a relatively low inertia-to-dissipation ratio, which is the so-called Stokes number. The characteristics of the particle packed porous structure such as solid packing fraction affect the final solidified product. A multi-sphere clumping Discrete Element Method (DEM) approach is employed to predict the solid packing fraction as function of the grain geometry under the solidification conditions. Five different monodisperse noncohesive frictionless particle collections are numerically packed by means of a vertical acceleration: a) three dendritic morphologies; b) spheres and c) one ellipsoidal geometry. In order to validate our numerical results with solidification conditions, the sedimentation and packing of two monodisperse collections (spherical and dendritic) is experimentally carried out in a viscous quiescent medium. The hydrodynamic similarity is respected between the actual phenomenon and the experimental model, that is a low Stokes number, o (10−3 ). In this way, the experimental average solid packing fraction is employed to validate the numerical model. Eventually, the average packing fraction is found to highly depend on the equiaxed dendritic grain sphericity, with looser packings for lower sphericity.

Effects of sedimenting particles on the turbulence structure in a horizontal channel flow

This work presents the results of experiments conducted in a horizontal channel to characterize low Reynolds number turbulent flows in the presence of small solid particles. The particle diameter relative to the integral length scale, dp/Λx, is approximately 0.02. Particles and fluid turbulence characteristics are measured for three average solid volume fractions of approximately ϕv = 2.0 × 10−4, 4.0 × 10−4, and 8.0 × 10−4 under conditions where the particle number density is evolving due to deposition. The results indicate that the mean slip between particles and the fluid is important only close to the wall. Away from the wall, the particles and unladen fluid mean velocities are similar. Differences between particles and the unladen fluid statistics are more pronounced in the wall-normal velocity fluctuations than the streamwise velocity fluctuations and Reynolds shear stress due to the stronger effect of the gravitational force in the wall-normal direction. The fluid turbulent intensities show no dependency on loading, but the peak Reynolds shear stress is significantly reduced. A quadrant decomposition of the Reynolds shear stress revealed a corresponding reduction in the ejections and sweeps for the laden flow in comparison with the unladen flow. Swirling strength and vorticity root-mean-square fluctuations decayed due to the damping effect of particles. The influence of particles on the turbulence structure was examined using two-point correlations of the velocity fluctuations and swirling strength, where it was demonstrated that the wall structures are attached eddies which are more extensive (much larger) in the particle-laden flow compared to the unladen flow.

Multiscale mechanical research in a dense granular system between sheared parallel plates

The effects of upper plate friction coefficient on macroscopic granular flows, mesoscopic force distributions, macroscopic stress-strain responses and evolutions of super-strong force chains are analyzed by using a discrete element analytical model using PFC2D software with an average solid fraction of 0.80. Numerical results show that the average velocity decreases with height and is smaller for the case with larger upper plate friction coefficient. Near the upper plate region, macroscopic flow with smaller upper plate friction coefficient induces relatively greater fluctuation velocity. Normal contact forces, tangential contact forces and contact forces exhibit a power law behavior. Moreover, granular flows are mainly influenced by normal contact forces. Plastic deformations of the granular system comprise multiple strengthening-softening plastic deformation phases. In strengthening the plastic deformation phase, normal contact forces increase with increased dimensionless horizontal stress. Meanwhile, contact forces in the softening phase decrease with decreased dimensionless horizontal stress. Average horizontal stress and super-strong force chains increase with increased upper plate friction coefficient to prevent granular flow. Multiscale mechanical analyses directly reflect the macroscopic and mesoscopic properties of granules and elucidate the mechanical mechanisms of dense granular flows.

Numerical Study about the Influence of Small Casting Speed Variations on the Metallurgical Length in Continuous Casting of Steel Slabs

Numerical simulations are prepared to investigate the influence of small casting speed variations between 715 and 735 mm min−1 on the metallurgical length in continuous casting of 285 mm thick steel slabs. The effect of considering/ignoring the melt flow in the numerical continuous casting model for predicting the metallurgical length is also investigated. The simulations are based on an Eulerian two‐phase solidification model including melt (liquid phase) and columnar dendrites (solid phase). Solidification of a binary Fe–C‐alloy is calculated. Two 25 m long straight strand geometries of industrial scale are modeled. Both of these geometries have waved surfaces to consider periodical strand surface bulging. In order to consider a defined mechanical softreduction (MSR) configuration as well, the cross‐section of one of these geometries decreases at a rate of 1 mm m−1 within a defined length. For a given casting configuration and for defined cooling conditions, the influence of small casting speed variations on the metallurgical length, on the average solid fraction and on the enthalpy flux are determined. The simulation results can be used to optimize the settings for operating continuous casting plants, e.g., to adapt the MSR position.

Velocity fluctuation and self diffusion character in a dense granular sheared flow studied by discrete element method

The distribution of average velocities, fluctuation of velocities, regional definition, and granular self-diffusion characters in dense granular flows between sheared parallel plates are discussed. In order to study the above problems, we use computer-established discrete element model with an average solid fraction of 0.80. Theoretical results show that the average velocities decrease with increasing height, and are larger for the case of lower plate with greater velocity; the average velocities in y direction are close to 0 because there is no bulk motion in y direction. Flows of the lower plate with a greater velocity induce relatively greater fluctuation of velocities in the x and y directions, the fluctuation of velocities increases with the height and is larger in the area close to the upper plate. The flows consist of a “solid-like” area in the lower test region, but a “fluid-like” region in the upper, and an “oscillating” region in the middle of the channel. By tracking the movements of granules continually, variations of the mean-square self-diffusion relative displacements with square time are plotted, and the mean self-diffusion relative coefficients are determined. As the fluctuation and self-diffusion analysis directly reflect the macroscopic properties of granules and provide bases and references for researching the flow mechanisms of “dense granular sheared flows”.

Bubbling fluidized bed characterization using Electrical Capacitance Volume Tomography (ECVT)

Abstract Understanding the fundamentals of gas–solid fluidized beds and, in general, multiphase flows has been a significant task since the conception of gas–solid fluidization and fluid particle systems. Various measurement techniques have been applied in an attempt to better understand the fundamentals of the complex gas–solid flow structures that form in fluidized beds. This information may potentially provide a better design, scale-up, and operation of these systems as well as lead to accurate performance predictions of multiphase flow systems. Electrical Capacitance Volume Tomography (ECVT) has now reached a point of development where these multiphase flow structures can be imaged accurately and reliably in three dimensions at good resolutions and sampling rates to provide significant insight into the internal gas–solid flow structures. A 10 cm ECVT sensor was used in order to investigate the bubble behavior of a 10 cm diameter bubbling fluidized bed (BFB) of 185 micron glass beads at various fluidization velocities. Three dimensional images of gas–solid flow structures as well as time average vertical and radial solid fraction profiles are presented in this paper, and average bubble diameter and bubble frequency are discussed and compared to various correlations available in the published literature.