Dispersion Coefficient Of Particles Research Articles

Particle motion analysis of a new three-phase fluidized bed flotation column with glass sphere particles

Analysis of the particle movement within the unit vessel is necessary for the design, optimization and scale-up of the new three-phase fluidized bed flotation column (TFC). This work aimed to examine the motion and distribution of assisted fluidized particle-glass spheres in the TFC and to provide a better assessment of particle collision and dispersion behavior by quantifying particle velocities. Tracer particles were analyzed by high-speed camera techniques to determine particle velocity fluctuations in a three-phase fluidized bed consisting of glass spheres, water, and bubbles. A correlation model for determining the particle velocity in a three-phase fluidized bed is proposed after a systematic analysis of the particle velocity. The model covers a wide range of superficial gas velocities (0–0.339 m/s), superficial liquid velocities (0.169–0.425 m/s) and initial static bed heights (0.162–0.262 m). Aiming to evaluate particle collisions in the TFC, this paper derives the particle collision frequencies using a modified collision model and investigates the effect of a wide range of operating parameters on particle collisions. Finally, a new method for estimating dispersion due to particle motion is developed based on the study of particle dispersion coefficients.

MP-PIC study of particle flow characteristics of pneumatic conveying process in a vertical pipe

The transportation of granular materials is commonly achieved through pneumatic conveying. In this study, the multiphase particle-in-cell model was adopted to investigate the dense phase pneumatic conveying in a vertical pipe. The simulation results were consistent with experimental data, with an error of less than 4%. The study examined the effects of varying particle size distribution (PSD), pipe diameters, and superficial gas velocities on the flow field and particle characteristics in this process. The findings revealed that the largest dispersion coefficient of particles was along the conveying direction. PSD has slight effect on dispersion coefficients. However, when the superficial gas velocity is increased from 1 m/s to 2.5 m/s, particle dispersion coefficients increases by approximately 115.22%. Formation and evolution of the plug can be observed during the pneumatic conveying process. PSD has a limited influence on particle slip velocity, but affects the particle Reynolds number.

Numerical evaluation of multi-scale properties in biomass fast pyrolysis in fountain confined conical spouted bed

Biomass fast pyrolysis is one of the promising ways to convert cellulose and lignin into available biochar, bio-oil and product gases. In the current work, the process of biomass fast pyrolysis is numerically studied via the reactive multiphase particle-in-cell (MP-PIC) model in a conical fountain confined spouted fluidized bed to investigate gas-solid motion (e.g., gas and solid fluxes) and particle-scale characteristics (e.g., particle velocity, residence time, temperature, heat transfer coefficient and dispersity). Simulation results have been well validated with experimental data. Biomass and sand behaviors in scenarios with and without fountain confiners have been comprehensively compared. It is recommended to insert a fountain confiner in spouted bed reactor because it can significantly increase the yields of Gas1 and tar of about 115.1% and 118.8%, respectively. The presence of the fountain confiner has resulted in an upward shift of the maximum temperature and HTC for biomass and sand particles, resulting from the enlarged amount of particle accumulation. Due to large temperature difference, biomass and sand particles have highest HTCs at inlet of about 200 W/m2·K and 120 W/m2·K, respectively. The axial dispersion coefficients of biomass and sand particles are two orders larger than the radial one, resulting from distinctive flow pattern in the spouted bed. The axial dispersion coefficients of biomass and sand particles in the fountain confined spouted bed are 1.93 × 10−3 m2/s and 2.40 × 10−4 m2/s, respectively. The relationships between particle parameters in conventional and fountain confined spouted beds are compared. The findings of this study can provide valuable insights into assisting designers in optimizing the design of such reactors.

Optimal design of gas distributor in fluidized bed for synthesis of silicone monomer

The structure of the gas distributor is closely related to the production efficiency of organosilicon monomers. To improve the production efficiency of organosilicon monomers, this study uses Eulerian-Eulerian two fluid model and proposes a design formula for the gas distributor to optimize the gas distributor. It is proposed that the pressure drop of the gas distributor, the velocity nonuniformity coefficient, the relative standard deviation of the solid holdup, and the solid particle dispersion coefficient are used to evaluate the performance of the gas distributor. The results show that the performance of the gas distributor is significantly improved when the opening ratio Φ = 0.53% is optimized to Φ = 0.18%, in which the relative standard deviation of the solid holdup is reduced by 22%, and the solid particle dispersion coefficient is reduced by 40%. On this basis, this article studies the influence of different arrangements of vent holes on gas-solid fluidization characteristics. The results show that the circular arrangement of vent holes is helpful to the mixing of gas and solid.

Segregation behavior of particles with Gaussian distributions in the rotating drum with rolling regime

The mixing and segregation of granular materials are essential to provide valuable insights and references for practical industrial production. In this paper, the segregation behaviors of particles with Gaussian distributions and 40% filling level in the rotating drum with rolling regime were numerically studied by the discrete element method. The effects of rotation speed and particle size parameter λ (size ratio of the largest versus smallest particles) on the segregation behavior (mixing index, segregation rate), flow characteristics (particle velocity and trajectory, gyration degree and radius, particle size distributions) and the microscopic properties (collision, contact force, axial diffusion, and kinetic energy) of granular systems were systematically investigated. The results show that the segregation rate and degree of particles with Gaussian distributions gradually increase with the increase of the rotation speed and particle size parameter λ. The radial and axial segregation patterns become more obvious with the increase of λ. And the variation of the flow characteristics of particles with different sizes in the same system is also inconsistent. The microscopic properties of Gaussian-dispersed particles change with the rotation speed and λ. The rapid radial segregation depends on the larger pores existed in the granular system, which leads to a gradual increase of the axial dispersion coefficient of large particles and a gradual decrease of the axial dispersion coefficient of small particles.

A Population Balance Methodology Incorporating Semi-Mechanistic Residence Time Metrics for Twin Screw Granulation

This work is concerned with the incorporation of semi-mechanistic residence time metrics into population balance equations for twin screw granulation processes to predict key properties. From the historical residence time and particle size data sourced, process parameters and equipment configuration information were fed into the system of equations where the input flow rates and model compartmentalization varied upon the parameters. Semi-mechanistic relations for the residence time metrics were employed to predict the particle velocities and dispersion coefficients in the axial flow direction of the twin screw granulation. The developed model was then calibrated for several experimental run points in each data-set. The predictions were evaluated quantitatively through the parity plots. The root mean square error (RMSE) was used as a metric to compare the degree of goodness of fit for different data-sets using the developed semi-mechanistic relations. In summary, this paper presents a more mechanistic but simplified approach of feeding residence time metrics into the population balance equations for twin screw granulation processes.

Super-quadric CFD-DEM simulation of chip-like particles flow in a fluidized bed

Chip-like particles may be practised in fluidized beds in some emerging industries, but its fluidization is not well understood. In this work, the computational fluid dynamics-discrete element method (CFD-DEM) is extended to integrate with a super-quadric model to study the fluidization behaviours of chip-like particles in a three-dimensional bubbling fluidized bed (BFB). After model validation, the typical fluidization behaviours of chip-like particles in the BFB are described in terms of bubble dynamics, pressure signals, particle orientation, particle mixing, and particle dispersion. Particularly, the ordered arrangement of chip-like particles appears at the near-wall region while random arrangement occurs in other regions. The effects of superficial gas velocity and aspect ratio on the mixing and dispersion characteristics of chip-like particles are discussed. The results show that increasing aspect ratio induces a higher mean pressure drop and promotes the initial mixing state. Particle dispersion coefficients range from 10-3 m2/s to 10-2 m2/s, whose vertical component is one order of magnitude larger than the horizontal components. Larger aspect ratios and superficial gas velocities lead to larger particle dispersion coefficients. The fundamental study sheds light on the design and optimization of fluidized beds of chip-like particles including solar panel waste recycling.

CFD study of the reactive gas-solid hydrodynamics in a large-scale catalytic methanol-to-olefin fluidized bed reactor

Lacking the understanding of multiphase flow in the fluidized bed methanol-to-olefin (MTO) process hinders the reactor design, operation, and optimization. Accordingly, a three-dimensional multiphase particle-in-cell model is established to study hydrodynamics and thermochemical characteristics during the MTO process in a fluidized bed reactor. After model validation, the influences of several critical operating parameters on reactor performance are discussed. The results show that particles in the medium part and freeboard of the reactor have heterogeneous velocity, temperature, and heat transfer coefficient (HTC) distributions. Thermal quantities of gas and solid phases are uniformly distributed in the medium part and freeboard of the reactor. The particle-averaged HTC under ranges from 60 to 120 W/(m2·K). Increasing wall temperature enlarges the particle HTC due to the enhanced exothermic reactions. Decreasing the particle diameter gives rise to a larger particle HTC. The vertical particle dispersion coefficient (Dz) is in the range of 0.01 m2/s to 0.03 m2/s. Methanol converts into olefin in a short period. Increasing methanol to catalyst ratio and wall temperature increases olefin including C2H4, C3H6, C4H8, and C5H10, and promotes the gas thermal properties. Particles with multi-sizes show a better MTO conversion performance than those with mono-sizes regarding the particle HTC and gas products.

Multiphase particle-in-cell simulation study of sorption enhanced steam methane reforming process in a bubbling fluidized bed reactor

The hydrodynamics and thermochemical characteristics of the sorption enhanced steam methane reforming process in a fluidized bed reactor are studied with a multiphase particle-in-cell model, featuring steam methane reforming and CaO carbonation reaction kinetics. After model validation, the high-fidelity information of solid phase at the particle-scale level is presented with the discussion of the effects of several critical operating parameters on the gas thermal properties. The results show that bubble evolution leads to bed expansion and the density-segregation mechanism causes the elutriation of dolomite particles. The highest velocity and Reynolds number of particles are observed around the bubble, and the magnitudes of these variables are higher than that in the dense region. The heat transfer coefficients (HTC) of Ni-catalyst and dolomite particles range from 100 W/(m2·K) to 600 W/(m2·K), which increase with the slip velocity and Reynolds number but decrease with solid volume fraction. The time-averaged particle dispersion coefficient in × , y, and z directions for the Ni-catalyst particles are 1.63 × 10-4, 1.82 × 10-4, and 9.92 × 10-4 m2/s, respectively while for the dolomite particles are 2.17 × 10-4, 2.52 × 10-4, and 1.3 × 10-3 m2/s, respectively. The temperature of bubbles near the wall is lower than that in the core region. Superficial gas velocity shows a positive effect on CH4 and H2O, gas temperature, and gas density while a negative effect on CO and H2, gas specific heat capacity. Bed temperature significantly influences the gas properties and gas product yields due to its intrinsic relation with chemical reactions. Ni-catalyst particle diameter performs an insignificant impact on the thermochemical characteristics in the bed.

Nanoparticle dispersion in porous media: Effects of hydrodynamic interactions and dimensionality

AbstractWe investigate the effect of steric and hydrodynamic interactions (HI) on quiescent diffusion and flow‐driven transport of finite‐sized nanoparticles through periodic 2D (two‐dimensional) and 3D (three‐dimensional) nanopost arrays using Stokesian dynamics simulations. We find that steric and HI hinder particle diffusivity under quiescent conditions and enhance longitudinal dispersion under flow. Moreover, the presence of HI leads to a power‐law increase in the longitudinal dispersion coefficient with Pe due to spatial variations in the fluid velocity. Lastly, our simulations reveal that longitudinal particle dispersion coefficients behave similarly in 2D and 3D when HI are included.

Upstream swimming and Taylor dispersion of active Brownian particles

Locomotion of self-propelled particles such as motile bacteria or phoretic swimmers often takes place in the presence of applied flows and confining boundaries. Interactions of these active swimmers with the flow environment are important for the understanding of many biological processes, including infection by motile bacteria and the formation of biofilms. Recent experimental and theoretical works have shown that active particles in a Poiseuille flow exhibit interesting dynamics including accumulation at the wall and upstream swimming. Compared to the well-studied Taylor dispersion of passive Brownian particles, a theoretical understanding of the transport of active Brownian particles (ABPs) in a pressure-driven flow is relatively less developed. In this paper, employing a small wave-number expansion of the Smoluchowski equation describing the particle distribution, we explicitly derive an effective advection-diffusion equation for the cross-sectional average of the particle number density in Fourier space. We characterize the average drift (specifically upstream swimming) and effective longitudinal dispersion coefficient of active particles in relation to the flow speed, the intrinsic swimming speed of the active particles, their Brownian diffusion, and the degree of confinement. In contrast to passive Brownian particles, both the average drift and the longitudinal dispersivity of ABPs exhibit a nonmonotonic variation as a function of the flow speed. In particular, the dispersion of ABPs includes the classical shear-enhanced (Taylor) dispersion and an active contribution called the swim diffusivity. In the absence of translational diffusion, the classical Taylor dispersion is absent and we observe a giant longitudinal dispersion in the strong flow limit. Our continuum theory is corroborated by a direct Brownian dynamics simulation of the Langevin equations governing the motion of each ABP.

Determination of Dynamic Dispersion Coefficient for Solid Particles Flowing in a Fracture With Consideration of Gravity Effect

Abstract A robust and pragmatic method has been developed and validated to analytically determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture, in which gravity settling has been considered due to its significant impact on particle flowing behavior. More specifically, a two-dimensional (2D) advection–diffusion equation together with the initial and boundary conditions has been formulated to describe the flow behavior of finite-sized particles on the basis of coupling the Poiseuille flow with vertical settling. Meanwhile, three types of instantaneous source conditions (i.e., point source, uniform line source, and volumetric line source) have been considered. Explicit expressions, which can directly and time-efficiently calculate dynamic dispersion coefficient, have been derived through the moment analysis and the Green’s function method. By performing the simulation based on the random walk particle tracking (RWPT) algorithm, the newly developed model has been verified to determine particle dispersion coefficients agreeing well with those obtained from the RWPT simulations. It is found that the point source is the most sensitive to gravity effect among different source conditions, while the volumetric line source is affected more than the uniform line source. For particle size larger than its critical value, an increased particle size leads to a decreased asymptotical dispersion coefficient for all the source conditions due to the significant gravity effect, while gravity positively affects the dispersion coefficient at early times for the point source condition. In addition, average flow velocity positively affects the dispersion coefficient for all the source conditions, while the associated gravity effect is influenced only at early times for the point source condition.

Pore-network modeling of particle dispersion in porous media

Coupling with the random walk particle tracking method and pore-network modeling simulation, this work systematically analyzed dispersion of particles with different particle sizes in pore-network models with variable heterogeneity. The newly developed pore-network model has been verified against results from the published papers. Effect of particle size on dispersion coefficient varies and depends upon the heterogeneity of porous media. Dispersion coefficient of particles is found to be greatly affected by particle size in a homogeneous model; however, for a heterogeneous model, throat velocity difference caused by heterogeneity plays an important role on particle dispersion. Comparing particle dispersion coefficient with and without size-exclusion effect in a homogeneous model, for large particles (i.e., 5×10−7 m), size-exclusion effect needs to be considered, especially at late times. In other words, without size-exclusion, particle dispersion coefficient is overestimated, while the size-exclusion effect becomes more important as flow rate increases. In the heterogeneous models, however, size-exclusion effect of particles (i.e., 5×10−7 m) can be neglected. Effects of the widely used uniform distribution and volumetric distribution profiles on particle dispersion have been compared in different pore-network models. The dispersion difference between volumetric and uniform distributions increases with particle size and heterogeneity of the pore-network model. For a homogeneous model, dispersion coefficient with uniform distribution leads to a larger value than that with volumetric distribution; however, as heterogeneity increases, dispersion coefficient with volumetric distribution shows a larger value.

Analysis of particle dispersion coefficient in solid-liquid fluidised beds

Solid liquid fluidised beds (SLFB) are frequently encountered in the mineral processing applications including ore leaching/washing and particle size classification based on difference in settling velocity. Due to complex phase interactions, SLFB shows interesting characteristics such as phase segregation and mixing depending on variation in particle diameter, density difference and slip velocity. To characterise the multifaceted hydrodynamics of SLFB, often a diffusion-like parameter called dispersion coefficient is utilised. In literature, various empirical correlations of this parameter have been proposed however they are mostly system specific and lack a theoretical foundation. In this work, we report a model for dispersion coefficient along the line of definition for diffusion coefficient incorporating the mean free path of collision and interstitial fluid velocity as the characteristic velocity of collision. The model is tuned based on the available experimental data for mono as well as multi-particle system covering wide range of particle diameter (0.39 to 23 mm), liquid superficial velocity (0.0009 to 0.6 m s−1) and Reynolds number (4 to 2820). To evaluate the capability of the proposed dispersion coefficient, mixing and segregation behaviour in binary SLFB system is simulated using a one dimensional convective-diffusive numerical model to predict the volume fraction distribution of each solid phase. Validation of the numerical model against available experimental data shows reasonably good agreement.

CFD simulation of particle residence time distribution in industrial scale horizontal fluidized bed

This work investigates the applicability of two conceptually different methods for simulation of particle residence time distributions (RTDs): the species method and the multi-solid method. Both are Eulerian methods; their key difference is found in the specification of the macroscopic particle dispersion coefficient and its relation to microscale particle diffusivity. The intricate interrelation between particle diffusivity and dispersion coefficient was investigated. It is shown and discussed that, if a-priori knowledge on macroscopic dispersion is available, e.g. from correlations, the species method, which by definition requires data on microscale particle diffusivity, can be used directly with the macroscopic data in both, transient and steady-state simulation. If no such data is available, the multi-solid method has to be used which computes the dispersion coefficient directly, at greater computational expense. Additional advantages of the species model over well-known dispersion model are presented and discussed for the example of an industrial multi-chamber horizontal fluidized bed.

Simulated pulsed flow of gas and particles in a horizontal oppose-pulsed gas jets of bubbling fluidized bed

Flow behavior of gas and particles with a horizontal oppose-pulsed gas jets are simulated by means of a three dimensional Computational Fluid Dynamics (CFD) model with the kinetic theory of granular flow in a gas-particles bubbling fluidized bed. The effects of amplitudes and frequencies on the hydrodynamics of gas and particles are analyzed. The simulation results are presented in terms of phase velocity vector plot, volume fraction of phases, granular temperature, power spectrum and Reynolds stresses in the bed. Results show that the impingement caused by the oppose-pulsed gas jets oscillates with the variation of pulsed gas velocity. The impingement zone with the high solid volume fraction reciprocates from the left side to the right side through the bed center with the variation of pulsed jet gas velocities. The lateral velocity and gas turbulent kinetic energy, granular temperature and Reynolds stresses of gas and particles are larger near the pulsed gas jets than that at the center of the bed. The large dispersion coefficients of particles using the horizontal oppose-pulsed gas jets enhance the mixing of particles in gas-solid fluidized bed.

Impact of solid and gas flow patterns on solid mixing in bubbling fluidized beds

Bubbling fluidization has been widely applied in industrial processes as an effective means for providing excellent mixing, good heat and mass transfer. Examples include granulation, coating, mixing, power generation from coal, renewable energy production, gasification and pyrolysis. In this study, we attempted to analyse the impact of solid flow patterns, bed design and operational conditions on solid mixing in a bubbling fluidized bed. The solid mixing behaviour was estimated based on the dispersion coefficient of particles, the active index (AI), and the distribution of particle residence time within the entire bed. In our previous studies, four flow patterns have been founded and classified as patterns A, B, C and D. Results presented from this study indicate that the mixing behaviour in a fluidized bed varies significantly with solid flow patterns which is a result of a combination of operational conditions, properties of bed materials and bed designs. Flow pattern D provides the best mixing in the four flow patterns identified by using the PEPT technique. Pattern A provides the worst solid mixing. Pattern B is a typical solid flow pattern reported in literature, but its mixing behaviour is only better than the Pattern A.

Dispersion characteristics of dissimilar materials in a fluidized bed with unevenly distributed fluidizing air

Large-scale internally circulating flows of gas and particles might form under unevenly distributed fluidized air in a fluidized bed. Compared with bed materials, the present study investigated dissimilar particles with different sizes and density moving and mixing through the developed image technique in an internally circulating fluidized bed (ICFB). The concentrations of the tracer particles were obtained by the image analysis method. The inhomogeneity degree and lateral dispersion coefficients of the tracer particles were also calculated, with the results indicating that the degree of inhomogeneity decreases with the increasing dispersed time. The lateral dispersion coefficients of tracer particles with a lower density (for a similar diameter) are larger than those with a higher density. It is clear that the different air distribution methods play an important role in the lateral dispersion of the tracer particles.

Determination of dynamic dispersion coefficients for passive and reactive particles flowing in a circular tube

Using the moment analysis method and the Green’s function, mathematical formulations valid across the full-time scale have been derived to determine dynamic dispersion coefficients for passive and reactive particles flowing in a circular tube with fully-developed laminar flow under different source conditions. The newly proposed formulations were verified through agreements with both analytical solutions and random walk particle tracking (RWPT) simulations. The relationship between particle size and dispersion coefficient for passive particles varies with time and they are positively correlated if Peclet number is larger than its critical value; otherwise, they are negatively correlated. Furthermore, the critical Peclet number decreases as time increases. Compared to an instantaneous point source, the critical Peclet number for a volumetric planar source is much smaller. At a small size ratio, size-exclusion effects on passive particle dispersion can be neglected across the full-time scale for both instantaneous point and volumetric planar sources; whereas, at a large size ratio, its significance needs to be considered, depending upon time and source condition. Using Dre_diff=0.02 (Dre_diff=(D−Dnon_ad)/D, where D and Dnon_ad are dispersion coefficients with and without axial diffusion, respectively) as the critical value, axial-diffusion effects on dispersion are negligible for passive solutes at long times if Peclet number is not smaller than 50; however, due to size exclusion this is not applicable for passive particles. At early times, reaction rate, center-of-mass velocity, and dispersion coefficient are not sensitive to Damköhler number for reactive particles. At long times, reaction rate and enter-of-mass velocity increases in magnitude as the Damköhler number increases, while the dispersion coefficient decreases with increasing Damköhler number. Consequently, reaction at the tube walls greatly affects concentration distributions.

Determination of dynamic dispersion coefficient for particles flowing in a parallel-plate fracture

A robust and pragmatic technique has been developed to determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture. By using local moment analyses, theoretical equations have been formulated to describe flow behaviour of solid particles flowing in a parallel-plate fracture on the basis of the Poiseuille flow under different source conditions. By using the random walk particle tracking (RWPT) algorithm, newly developed models have been verified to determine solute and particle dispersion coefficients agreeing with those obtained from RWPT simulations. At early times, particle dispersion coefficient is not only controlled by the source condition, but also negatively correlated with the center-of-mass velocity. Compared to a point source, at early times, dispersion coefficients of particles originating from a line source are larger; however, after a critical time, all dispersion coefficients approach the values obtained through the extended Taylor theory. Subsequently, the newly developed models have been extended to match experimental measurements, while particle dispersion coefficients are notably less than those calculated by the extended Taylor theory.