Fluidization of elongated particles—Effect of multi-particle correlations for drag,lift, and torque in CFD-DEM

Having proper correlations for hydrodynamic forces is essential for successful CFD-DEM simulations of a fluidized bed. For spherical particles in a fluidized bed, efficient correlations for predicting the drag force, including the crowding effect caused by surrounding particles, are already available and well tested. However, for elongated particles, next to the drag force, the lift force, and hydrodynamic torque also gain importance. In this work, we apply recently developed multi-particle correlations for drag, lift and torque in CFD-DEM simulations of a fluidized bed with spherocylindrical particles of aspect ratio 4 and compare them to simulations with widely used single-particle correlations for elongated particles. Simulation results are compared with previous magnetic particle tracking experimental results. We show that multi-particle correlations improve the prediction of particle orientation and vertical velocity. We also show the importance of including hydrodynamic torque.     

Study of the filter cake formed due to the sedimentation of monodispersed and bidispersed particles using discrete element method–computational fluid dynamics simulations

This study aims to investigate the sedimentation and the consolidation of the packed bed/cake formed due to the monodispersed and bidispersed particles under different flow conditions. Mutual interactions between the bidispersed particles and the liquid are considered by using a polydispersed drag model. The attractive force is considered by using the JKR model. Sensitivity of the void fraction of a sedimented packed bed/cake due to particle–particle interaction parameters is studied. Furthermore, the effect of the fluid flow is analyzed by performing the simulations in two stages. In the first stage, packed bed/cake is formed by the sedimentation of the particles in the absence of the fluid forces and in the second stage flow through the packed bed/cake is simulated by using the CFD coupled with the discrete element method. Based on the simulations, correlations between the sedimented and the consolidated void fractions are developed. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1294–1303, 2019     

Voidage characteristics and prediction of bed expansion in liquid-solid inverse fluidized bed

Studies on voidage fluctuations, axial voidage profile and bed expansion are carried out by measuring the local void fraction using particles of wide ranging characteristics in liquid-solid inverse fluidized bed. The quality of fluidization is elucidated by the local voidage fluctuations. The RMS voidage fluctuation depicts a maximum with respect to average bed void fraction and increases with increase in Archimedes number. The fluidization quality has been quantified using average normalized RMS voidage fluctuation in terms of Transition number. The axial void fraction is almost uniform throughout the bed except for particles with size distribution. All the literature and present experimental data on bed expansion are unified in terms of Richardson and Zaki equation using experimental terminal velocities. A new correlation is proposed for predicting the wall effect corrected experimental terminal velocities, as a substitute for standard drag equation. The bed expansion data are also predicted using the drift flux model.     

Drag force and clustering in bubble swarms

In this article, results of detailed numerical simulations are reported meant to provide a closure relation for the drag force acting on bubbles rising in a dense swarm. The formation of clusters of bubbles in a periodic domain and the effect thereof on the rise velocity and effective drag coefficient on the bubbles are studied. Using smaller bubble sizes than presented in our earlier work, we are also able to refine our correlation for the drag coefficient acting on bubbles rising in a swarm, such that it is applicable for a large range of bubble sizes. The simulations are performed with an advanced Front‐Tracking model in which Lagrangian marker points are used to track the gas–liquid interface, while accounting for surface tension and substantial interface deformation. Simulations were performed using periodic domains to simulate rising air bubbles in water from 1.0 mm up to 6.0 mm in diameter. The effect of liquid phase viscosity was also studied to extend the range of validity of the drag correlation. For the 1.0 and 1.5 mm cases, strong horizontal clustering effects are observed. Especially, at high gas fractions, the bubbles tend to form rigid horizontal arrays, which have been shown to strongly increase the drag force acting on the bubbles in the cluster. For viscous liquids, the tendency to form horizontal clusters is lower, and even vertical clustering is observed. The bubble slip velocity was compared with the experimental results of Zenit et al., which agree very well taking into account the differences between simulations and experiments. Based on our simulations, a new drag correlation was proposed, taking into account Eötvös numbers ranging from 0.13 to 4.9, and Morton numbers in the range 3.8 ≤ ? log Mo < 6.6, and gas hold‐ups up to 40% (30% for Eo < 0.3). At lower values for ?log Mo, the Reynolds number drops to the order of unity, and the correlation overpredicts the drag coefficient, which defines the range of applicability of the currently proposed drag correlation. The correlation itself describes a linear increase of the normalized drag coefficient as a function of the gas hold‐up. The strength of linear increase is stronger at lower Eötvös numbers. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1791–1800, 2013     

Measurements and computation of low mass transfer coefficients for FCC particles with ozone decomposition reaction

The mass transfer coefficients and Sherwood numbers for catalyzed fluid cracking catalyst particles were measured and computed in a two‐dimensional (2‐D) bubbling fluidized bed, with ozone decomposition reaction. The measured and computed Sherwood numbers, using 3‐ and 2‐D kinetic theory based computational fluid dynamics simulations, were of the order of 10^?6–10^?2. The low Sherwood numbers were in reasonable agreement with the literature data for small particles, at low Reynolds numbers. The computational fluid dynamics simulations showed that it is possible to compute conversions in fluidized bed reactors without using the conventional model with empirical mass transfer coefficients. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

基于格子Boltzmann方法的单颗粒绕流数值模拟

采用格子Boltzmann方法（LBM）研究了单颗粒绕流流动过程。通过使用LBM中的LBGK（lattice Bhatnagar-Gross-Krook）模型和二阶精度的曲线边界条件处理方法,实现了对单颗粒绕流问题的定常及非定常流动过程中涡结构的模拟。采用动量交换法分别计算了Reynolds数在0.1～200范围内27个不同Reynolds数时的曳力系数,并将计算结果拟合得到基于LBM数值模拟的曳力曲线。计算结果表明,LBM在气固两相流的模拟计算中具有精确、可靠的优点,使用LBM模拟计算曳力曲线的方法经济、易行,并且可以克服由传统实验方法获得曳力曲线的局限性。     

Hydrodynamic forces on monodisperse assemblies of axisymmetric elongated particles: Orientation and voidage effects

We investigate the average drag, lift, and torque on static assemblies of capsule-like particles of aspect ratio 4. The performed simulations are from Stokes flow to high Reynolds numbers (0.1 ≤ Re ≤ 1,000) at different solids volume fraction (0.1 ≤ ɛ_s ≤ 0.5). Individual particle forces as a function of the incident angle ϕ with respect to the average flow are scattered. However, the average particle force as a function of ϕ is found to be independent of mutual particle orientations for all but the highest volume fractions. On average, a sine-squared scaling of drag and sine-cosine scaling of lift holds for static multiparticle systems of elongated particles. For a packed bed, our findings can be utilized to compute the pressure drop with knowledge of the particle-orientation distribution, and the average particle drag at ϕ = 0° and 90°. We propose closures for average forces to be used in Euler–Lagrange simulations of particles of aspect ratio 4.     

Comparative analysis of subgrid drag modifications for dense gas‐particle flows in bubbling fluidized beds

Many subgrid drag modifications have been put forth to account for the effect of small unresolved scales on the resolved mesoscales in dense gas‐particle flows. These subgrid drag modifications significantly differ in terms of their dependencies on the void fraction and the particle slip velocity. We, therefore, compare the hydrodynamics of a three‐dimensional bubbling fluidized bed computed on a coarse grid using the drag correlations of the groups of (i) EMMS, (ii) Kuipers, (iii) Sundaresan, (iv) Simonin, and the homogenous drag law of (v) Wen and Yu with fine grid simulations for two different superficial gas velocities. Furthermore, we present an (vi) alternative approach, which distinguishes between resolved and unresolved particle clusters revealing a grid and slip velocity dependent heterogeneity index. Numerical results are analyzed with respect to the time‐averaged solids volume fraction and its standard deviation, gas and solid flow patterns, bubble size, number density, and rise velocities. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4077–4099, 2013     

Particle‐resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds

Particle‐resolved direct numerical simulations (PR‐DNS) of a simplified experimental shallow fluidized bed and a laboratory bubbling fluidized bed are performed by using immersed boundary method coupled with a soft‐sphere model. Detailed information on gas flow and individual particles’ motion are obtained and analyzed to study the gas–solid dynamics. For the shallow bed, the successful predictions of particle coherent oscillation and bed expansion and contraction indicate all scales of motion in the flow are well captured by the PD‐DNS. For the bubbling bed, the PR‐DNS predicted time averaged particle velocities show a better agreement with experimental measurements than those of the computational fluid dynamics coupled with discrete element models (CFD‐DEM), which further validates the predictive capability of the developed PR‐DNS. Analysis of the PR‐DNS drag force shows that the prevailing CFD‐DEM drag correlations underestimate the particle drag force in fluidized beds. The particle mobility effect on drag correlation needs further investigation. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1917–1932, 2016     

The influence of binary drag laws on simulations of species segregation in gas-fluidized beds

Monodisperse drag laws have been traditionally employed in polydisperse systems using ad hoc assumptions due to the lack of adequate drag laws for polydisperse systems. A key component of both continuum and discrete models used to study segregation in gas fluidized beds is the drag law. In this work, both the ad hoc approach and a new drag treatment developed specifically for polydisperse mixtures using lattice-Boltzmann simulations [M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, J. Fluid Mech. 528 (2005) 233–254] are incorporated into a Multi-Phase Particle-in-Cell (MP-PIC) framework to evaluate their impact on simulations of gas-fluidized, binary mixtures. In particular, several systems composed of Geldart group B particles that differ in size and/or density are considered, with special attention paid to axial species segregation at low fluidization velocities. For a system with size difference only, the Van der Hoef et al. [M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, J. Fluid Mech. 528 (2005) 233–254] drag treatment presents a higher degree of mixing than the ad hoc treatment. For a system with size and density differences, where the small particle is the denser and less massive one, the ad hoc treatment predicts a higher degree of mixing than the Van der Hoef et al. [M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, J. Fluid Mech. 528 (2005) 233–254] treatment. For systems with density differences only or both size and density differences where the large particle is the denser one, both drag treatments generate essentially the same segregation profiles. The relative segregation tendencies predicted by each drag treatment is explained through a qualitative analysis of drag force coefficients of each species in the mixture. The simulation results indicate that the drag law treatment plays a crucial role in the qualitative and quantitative nature of segregation predictions at low gas velocities.     

Direct numerical simulation of moderate-Reynolds-number flow past arrays of ellipsoids

Through particle-resolved direct numerical simulations of flow past arrays of ellipsoids, the hydrodynamic force on ellipsoids depends on the particle orientation, aspect ratio, particle Reynolds number, and solid volume fraction is revealed at moderate Reynolds numbers. The results show that the mean drag force on arrays of prolate/oblate ellipsoids decreases/increases as the Hermans orientation factor increases when flows are in the reference direction defined by the average symmetric axis of particles. The individual drag force on a prolate/oblate ellipsoid increases/decreases with the increase of incidence angle, and it is also affected by the orientation of surrounding particles. The individual lift force is also significant when the aspect ratio is away from unity at large particle Reynolds numbers. Based on simulation results, correlations for the hydrodynamic force on ellipsoids at arbitrary particle Reynolds numbers, solid volume fractions, Hermans orientation factors, incidence angles, and aspect ratios are formulated.     

Computation of the mass transfer coefficient of FCC particles in a thin bubbling fluidized bed using two- and three-dimensional CFD simulations

In this study, the standard kinetic theory based model with a modified drag correlation was successfully used to compute the mass transfer coefficients and the Sherwood numbers of FCC particles in a thin bubbling fluidized bed column using the additive diffusional and chemical reaction resistances concept. Also, the effects of the computational domain (two- or three-dimensional) and the reaction rate constant (low and high) are discussed.The computations show that the Sherwood numbers are in agreement with the measurement ranges for small particles in the fluidized bed system. The mass transfer coefficients and the Sherwood numbers are high near the inlet section, and decrease to a constant value with increasing height in the column. The two-dimensional computational domain simulations provide enough information to explain the phenomena inside a symmetrical system, but three-dimensional computational domain simulations are still needed for asymmetrical systems. Finally, the mass transfer coefficients and the Sherwood numbers increased with the larger reaction rate constant.     

LIQUID-SOLID MASS TRANSFER IN A THREE PHASE DRAFT TUBE FLUIDIZED BED REACTOR

Liquid-solid mass transfer coefficients in a three phase draft tube fluidized bed reactor have been measured using spherical ion exchange particles. The particle diameters ranged from 655 to 1119μm and solids volume fractions of approximately 5 and 10% were employed in water at 28°C. The experimental data can be successfully correlated using a Reynolds number derived using Kolmogoroffs theory of isotropic turbulence, although it is doubtful whether isotropic turbulence actually prevails in the fluidized bed over the range of conditions employed. Comparison with correlations determined for bubble columns and gas-liquid fluidized beds is performed. A model which considers the draft tube reactor as comprising two distinct fluid mechanical regions is developed to explain the apparently lower values of mass transfer coefficients obtained in a draft tube as opposed to conventional fluidized bed reactor.     

Experimental validation of CFD simulations of a lab‐scale fluidized‐bed reactor with and without side‐gas injection

Fluidized‐bed reactors are widely used in the biofuel industry for combustion, pyrolysis, and gasification processes. In this work, a lab‐scale fluidized‐bed reactor without and with side‐gas injection and filled with 500–600 μm glass beads is simulated using the computational fluid dynamics (CFD) code Fluent 6.3, and the results are compared to experimental data obtained using pressure measurements and 3D X‐ray computed tomography. An initial grid‐dependence CFD study is carried out using 2D simulations, and it is shown that a 4‐mm grid resolution is sufficient to capture the time‐ and spatial‐averaged local gas holdup in the lab‐scale reactor. Full 3D simulations are then compared with the experimental data on 2D vertical slices through the fluidized bed. Both the experiments and CFD simulations without side‐gas injection show that in the cross section of the fluidized bed there are two large off‐center symmetric regions in which the gas holdup is larger than in the center of the fluidized bed. The 3D simulations using the Syamlal‐O'Brien and Gidaspow drag models predict well the local gas holdup variation throughout the entire fluidized bed when compared to the experimental data. In comparison, simulations with the Wen‐Yu drag model generally over predict the local gas holdup. The agreement between experiments and simulations with side‐gas injection is generally good, where the side‐gas injection simulates the immediate volatilization of biomass. However, the effect of the side‐gas injection extends further into the fluidized bed in the experiments as compared to the simulations. Overall the simulations under predict the gas dispersion rate above the side‐gas injector. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Numerical simulation of horizontal jet penetration in a three-dimensional fluidized bed

The introduction of reactant gas as a jet into a fluidized bed chemical reactor is often encountered in various industrial applications. Understanding the hydrodynamics of the gas and solid flow resulting from the gas jet can have considerable significance in improving the reactor design and process optimization. In this work, a three-dimensional numerical simulation of a single horizontal gas jet into a cylindrical gas-solid fluidized bed of laboratory scale is conducted. A scaled drag model is proposed and implemented into the simulation of a fluidized bed of FCC particles. The gas and particles flow in the fluidized bed is investigated by analyzing the transient simulation results. The jet penetration lengths of different jet velocities have been obtained and compared with published experimental data as well as with predictions of empirical correlations. The predictions by several empirical correlations are discussed. A good agreement between the numerical simulation and experimental results has been achieved.     

Hydrodynamics of fluidization in a semicircular bed with a jet

A hydrodynamic model of fluidization was developed that computes void fractions, pressure and solid and gas velocities in cylindrical fluidized beds. Cmputed time-averaged gas velocity distributions of a jet compared well with Westinghouse experimental data without the use of any fitted parameters. The main empirical input was a drag correlation from the literature.     

Effective particle diameters for simulating fluidization of non‐spherical particles: CFD‐DEM models vs. MRI measurements

Computational fluid dynamics—discrete element method (CFD‐DEM) simulations were conducted and compared with magnetic resonance imaging (MRI) measurements (Boyce, Rice, and Ozel et al., Phys Rev Fluids. 2016;1(7):074201) of gas and particle motion in a three‐dimensional cylindrical bubbling fluidized bed. Experimental particles had a kidney‐bean‐like shape, while particles were simulated as being spherical; to account for non‐sphericity, “effective” diameters were introduced to calculate drag and void fraction, such that the void fraction at minimum fluidization (ε_mf) and the minimum fluidization velocity (U_mf) in the simulations matched experimental values. With the use of effective diameters, similar bubbling patterns were seen in experiments and simulations, and the simulation predictions matched measurements of average gas and particle velocity in bubbling and emulsion regions low in the bed. Simulations which did not employ effective diameters were found to produce vastly different bubbling patterns when different drag laws were used. Both MRI results and CFD‐DEM simulations agreed with classic analytical theory for gas flow and bubble motion in bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2555–2568, 2017     

Numerical investigation for the suitable choice of bubble diameter correlation for EMMS/bubbling drag model

Mesoscale bubbles exist inherently in bubbling fluidized beds and hence should be considered in the constitutive modeling of the drag force. The energy minimization multiscale bubbling(EMMS/bubbling) drag model takes the effects of mesoscale structures(i.e., bubbles) into the modeling of drag coefficient and thus improves the coarse-grid simulation of bubbling and turbulent fluidized beds. However, its dependence on the bubble diameter correlation has not been thoroughly investigated. The hydrod...     

Granular pressure and particle velocity fluctuations prediction in liquid fluidized beds

A numerical modelling approach for the dynamic simulation of solid-liquid fluidized beds is evaluated. This approach is based on an Eulerian two-fluid formulation of the transport equations for mass, momentum and fluctuating kinetic energy. The solid-phase fluctuating motion model is derived in the frame of granular medium kinetic theory accounting for the viscous drag influence of the interstitial liquid phase. Solid-liquid fluidized bed two-dimensional simulations were performed for flow configurations taken from the experimental work of Zenit et al. [1997. Collisional particle pressure measurements in solid-liquid flows. Journal of Fluid Mechanics 353, 261-283], for three types of solid particles of contrasted inertia in water at high particle Reynolds number (nylon, glass and steel beads). Experimental and numerical granular pressures exhibit a satisfactory agreement with both low and high inertia particles, the best level of prediction being observed with the most inertial particles. Sensitivity of the predictions to the phenomenological laws used in the model is also presented and it appears that, due to non-linear correlations, the average granular pressure in the bed is a less sensitive variable than the fluctuating kinetic energy (or granular temperature). The transport mechanisms of the mean granular temperature in the bed are therefore analyzed as a function of the solid fraction and the particle inertia. At low and moderate Stokes number (nylon and glass beads) and in all range of solid-phase fraction, the dominant production mechanism of fluctuating kinetic energy is due to the mean velocity gradient, whereas the main dissipation term is that induced by the viscous drag. At higher Stokes number (steel beads) and concentration, the production of the granular temperature is controlled by the compressibility effects via the granular pressure. In this case, the dissipation is mainly provided by inter-particle collisions.     

Effect of pseudoplastic behaviour of liquid in co-current three-phase fluidized beds on bed expansion

Gas hold-up and bed expansion measurements were carried out for a bed of glass beads fluidized in Newtonian liquids and non-Newtonian liquids with gas. The value of gas hold-up increased and decreased with increasing particle size and liquid velocity, respectively. The effect of rheological properties on gas hold-up was insignificant and therefore the gas hold-up data for both Newtonian and non-Newtonian fluids were reasonably fitted by the available correlation which had no liquid viscosity term. The bed voidage increased with increasing superficial liquid velocities and superficial gas velocities. The increase of the viscous non-Newtonian flow behaviours resulted in an increase of the bed voidage. The correlation for the bed voidage in three-phase fluidized beds was developed for gas-Newtonian or non-Newtonian liquid–solid three-phase systems by combining the generalized wake model and the correlation for liquid–solid two-phase systems proposed previously by the authors. The predictions for bed voidage were in reasonable agreement with the present experimental data for three-phase systems with Newtonian and non-Newtonian liquids in a wide range of Reynolds numbers.