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     

Simulation of particles and gas flow behavior in a riser using a filtered two-fluid model

Flow behavior of gas and particles is predicted by a filtered two-fluid model by taking into the effect of particle clustering on the interphase momentum-transfer account. The filtered gas–solid two-fluid model is proposed on the basis of the kinetic theory of granular flow. The subgrid closures for the solid pressure and drag coefficient (Andrews et al., 2005) and the solid viscosity (Riber et al., 2009) are used in the filtered two-fluid model. The model predicts the heterogeneous particle flow structure, and the distributions of gas and particle velocities and turbulent intensities. Simulated solids concentration and mass fluxes are in agreement with experimental data. Predicted effective solid phase viscosity and pressure increase with the increase of model constant c_g and c_s. At the low concentration of particles, simulations indicate that the anisotropy is obvious in the riser. Simulations show the subgrid closures for viscosity of gas phase and solid phase led to a qualitative change in the simulation results.     

CFD–DEM simulation of the gas–solid flow in a cyclone separator

In this work, a numerical study of the gas–solid flow in a gas cyclone is carried out by use of the combined discrete element method (DEM) and computational fluid dynamics (CFD) model where the motion of discrete particles phase is obtained by DEM which applies Newton’s equations of motion to every individual particle and the flow of continuum fluid by the traditional CFD which solves the Navier–Stokes equations at a computational cell scale. The model successfully captures the key flow features in a gas cyclone, such as the strands flow pattern of particles, and the decrease of pressure drop and tangential velocity after loading solids. The effect of solid loading ratio is studied and analysed in terms of gas and solid flow structures, and the particle–gas, particle–particle and particle–wall interaction forces. It is found that the gas pressure drop increases first and then decreases when solids are loaded. The reaction force of particles on gas flow is mainly in the tangential direction and directs mainly upward in the axial direction. The reaction force in the tangential direction will decelerate gas phase and the upward axial force will prevent gas phase from flowing downward in the near wall region. The intensive particle–wall collision regions mainly locate in the wall opposite to the cyclone inlet and the cone wall. Moreover, as the solid loading ratio increases, number of turns travelled by solids in a cyclone decreases especially in the apex region of the cyclone while the width of solid strands increases, the pressure drop and tangential velocity decrease, the high axial velocity region moves upwards, and the radial flow of gas phase is significantly dampened.     

CFD simulation of hydrodynamics of gas-liquid-solid fluidised bed reactor

A three dimensional transient model is developed to simulate the local hydrodynamics of a gas-liquid-solid three-phase fluidised bed reactor using the computational fluid dynamics (CFD) method. The CFD simulation predictions are compared with the experimental data of Kiared et al. [1999. Mean and turbulent particle velocity in the fully developed region of a three-phase fluidized bed. Chemical Engineering & Technology 22, 683-689] for solid phase hydrodynamics in terms of mean and turbulent velocities and with the results of Yu and Kim [1988. Bubble characteristics in the racial direction of three-phase fludised beds. A.I.Ch.E. Journal 34, 2069-2072; 2001. Bubble-wake model for radial velocity profiles of liquid and solid phases in three-phase fluidised beds. Industrial and Engineering Chemistry Research 40, 4463-4469] for the gas and liquid phase hydrodynamics in terms of phase velocities and holdup. The flow field predicted by CFD simulation shows a good agreement with the experimental data. From the validated CFD model, the computation of the solid mass balance and various energy flows in fluidised bed reactors are carried out. The influence of different interphase drag models for gas-liquid interaction on gas holdup are studied in this work.     

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     

A model for collisional exchange in gas/liquid/solid fluidized beds

A new model is presented for numerical simulations of collisional transfer of mass, momentum and energy in gas/liquid/solid fluidized beds. The mathematical formulation uses a collision model similar to that of Bhatnagar, Gross, and Krook (BGK), in a particle distribution function transport equation, in order to approximate the rates at which collisions bring about local equilibration of particle velocities and the masses, compositions, and temperatures of liquid films on bed particles. The model is implemented in the framework of the computational-particle fluid dynamics (CPFD) numerical methodology, in which the particle phase is represented with computational parcels and the continuous phase is calculated on Eulerian finite-difference grid. Computational examples using the Barracuda^® code, a commercial CFD code owned by CPFD Software, LLC, show the ability of the model to calculate spray injection and subsequent liquid spreading in gas/solid flows.     

Simulation of flow and drying characteristics of high-moisture particles in an impinging stream dryer via CFD-DEM

Impinging stream dryer (ISD) is an alternative for drying high-moisture particulate materials. Due to the complex multiphase transport phenomena that take place within an ISD, use of a reliable computational model instead of a tedious experimental route to aid the design of the dryer is desirable. In the present study, computational fluid dynamics were used in combination with the discrete element method (CFD-DEM) to predict, for the first time, the multiphase transport phenomena within a coaxial ISD; results from a model that does not consider particle-particle interactions (CFD) were also obtained and compared with those from the CFD-DEM model. In all cases, high-moisture particles having negligible internal transport resistance were assumed. Both models were used to simulate the gas-particle motion behavior, particle mean moisture content, particle mean residence time, and particle residence time distribution. The simulated results from both models were compared with the experimental data whenever possible. The results showed that the CFD-DEM model could be utilized to predict the particle motion behavior and led to more physically realistic results than the CFD model. The CFD-DEM model also gave predictions that were in better agreement with the experimental mean particle residence time and moisture content data.     

Development and verification of coarse-grain CFD-DEM for nonspherical particles in a gas–solid fluidized bed

Computational fluid dynamics coupled with discrete element method (CFD-DEM) has been widely used to understand the complicated fundamentals inside gas–solid fluidized beds. To realize large-scale simulations, CFD-DEM integrated with coarse-grain model (CG CFD-DEM) provides a feasible solution, and has led to a recent upsurge of interest. However, when dealing with large-scale simulations involving irregular-shaped particles such as biomass particles featuring elongated shapes, current CG models cannot function as normal because they are all developed for spherical particles. To address this issue, a CG CFD-DEM for nonspherical particles is proposed in this study, and the morphology of particles is characterized by the super-ellipsoid model. The effectiveness and accuracy of CG CFD-DEM for nonspherical particles are comprehensively evaluated by comparing the hydrodynamic behaviors with the results predicted by traditional CFD-DEM in a gas–solid fluidized bed. It is demonstrated that the proposed model can accurately model gas–solid flow containing nonspherical particles, merely the particle dynamics are somewhat lost due to the scaleup of particle size. Finally, the calculation efficiency of CG CFD-DEM is assessed, and the results show that CG CFD-DEM can largely reduce computational costs mainly by improving the calculation efficiency of DEM. In general, the proposed CG CFD-DEM for nonspherical particles strikes a good balance between efficiency and accuracy, and has shown its prospect as a high-efficiency alternative to traditional CFD-DEM for engineering applications involving nonspherical particles.     

Three‐Dimensional Numerical Simulation of Dense Pneumatic Conveying of Pulverized Coal in a Vertical Pipe at High Pressure

A two‐fluid model based on the kinetic theory of granular flow was used to study three‐dimensional steady state flow behavior of dense phase pneumatic conveying of pulverized coal in a vertical pipe, where the average solid concentration ranges from 11 % to 30 %, and the transport pressure ranges from 2.6 Mpa to 3.3 Mpa. Since the solid concentration is rather high, a k–?–k_p–?_p model which considers the turbulence interaction between the gas and particle phase, was incorporated into the two‐fluid model. The simulation results including profiles of gas and particle phase axial velocity, profiles of solid concentration, profiles of the turbulence intensity of the particle phase, as well as the value of the pressure gradient were reported. Then, the influences of solid concentration and transport pressure on the flow behaviors were discussed. The experiment was also carried out to validate the accuracy of the simulation results which showed that the predictions of pressure gradient were in good agreement with the experimental data. Simulation results indicate that the location of maximal solid concentration deviates from the pipe center and the deviation becomes more obvious with the solid concentration increasing, which is analogous to the phenomenon in the liquid/solid flow. Besides, pressure gradient declines as the transport pressure decreases, which is validated by experiment described in the paper. Moreover, the analysis indicates that it is necessary to consider the turbulence of particles for the simulation of dense phase pneumatic conveying at high pressure.     

Analogous description of the hydrodynamics of gas-solid fluidized beds and bubble columns

In this paper we stress analogies in the hydrodynamic behaviour of gassolid fluidized beds and bubble columns. Using published experimental data, it is demonstrated that the analogous hydrodynamic-behaviour is not only qualitative but also quantitative in nature. Specifically, we show the following.(1) The gas holdup in the homogeneous regimes of bubble columns and fluidized beds can be modelled in a unified way using V_slip = υ_∞(1 − ϵ_d)ⁿ⁻¹, where V_slip refers to the slip velocity between the dispersed (bubbles or particles) and continuous phases and ϵ_d the dispersed phase holdup. The Richardson-Zaki exponent n decreases with increasing gas density.(2) The transition from homogeneous to heterogeneous flow regimes in gasliquid bubble columns and gassolid fluid beds is delayed by increasing system pressure. Extrapolation of the influence of increased gas density allows us to consider liquidliquid dispersions and liquidsolid fluid beds as limiting cases.(3) In the heterogeneous flow regime of operation the classic two-phase theory of fluidized beds can be applied with profit to also describe the hydrodynamics of gasliquid bubble columns provided that the “dilute” phase is identified with the fast-rising large bubbles and the “dense” phase is identified with the liquid phase containing entrained “small” bubbles. Tentative analogies can also be drawn for the interphase mass transfer processes.(4) The “dense” phase backmixing can be modelled in a unified manner.(5) The two-phase theory can be extended to describe slurry reactors.It is argued that, because of cross-fertilization of concepts and information, appreciation of analogies can be invaluable tool in scaling up.     

Influence of void fraction calculation on fidelity of CFD‐DEM simulation of gas‐solid bubbling fluidized beds

The correct calculation of cell void fraction is pivotal in accurate simulation of two‐phase flows using a computational fluid dynamics‐discrete element method (CFD‐DEM) approach. Two classical approaches for void fraction calculations (i.e., particle centroid method or PCM and analytical approach) were examined, and the accuracy of these methodologies in predicting the particle‐fluid flow characteristics of bubbling fluidized beds was investigated. It was found that there is a critical cell size (3.82 particle diameters) beyond which the PCM can achieve the same numerical stability and prediction accuracy as those of the analytical approach. There is also a critical cell size (1/19.3 domain size) below which meso‐scale flow structures are resolved. Moreover, a lower limit of cell size (1.63 particle diameters) was identified to satisfy the assumptions of CFD‐DEM governing equations. A reference map for selecting the ideal computational cell size and the suitable approach for void fraction calculation was subsequently developed. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2000–2018, 2014     

Assessment of gel formation in colloidal dispersions during mixing in turbulent jets

Onset of gel formation upon mixing between colloidal dispersions and coagulant solutions in turbulent jets was studied using a combination of computational fluid dynamics (CFD) and population balance equation (PBE). To describe the interaction between turbulence fluctuations and particle aggregation, a micromixing model based on presumed probability density function was implemented inside the CFD code. Furthermore, effect of the solid phase on the fluid flow was modeled through an effective viscosity of the mixture evaluated from PBE. The results are presented in the parameter space of the primary particle diameter and the solid volume fraction where strong interplay between mixing and aggregation mechanisms controls the gelation phenomena and consequently also the fluid dynamics. Simulation results are in good agreement with observations from gelation experiments of concentrated nanoparticle suspensions injected into coagulant solutions. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4567–4581, 2013     

CFD–DEM investigation into the scaling up of spout‐fluid beds via two interconnected chambers

The hydrodynamics and chamber interaction in a three‐dimensional spout‐fluid bed with two interconnected chambers are investigated via computational fluid dynamics coupled with discrete element method (CFD–DEM), because multiple interconnected chambers are key to scaling up spout‐fluid beds. The overall solid motion, spouting evolution, and spout‐annulus interface is studied, followed by time‐averaged hydrodynamics, particle‐scale information, spout‐annulus interaction, and inter‐chamber interaction. The results show that inter‐chamber interactions lead to unique characteristics distinct from that for a single‐chamber system, including (1) asymmetry of the hydrodynamics within each chamber, (2) alternative spouting behavior in the two chambers, (3) smaller pressure drop in terms of magnitude and fluctuations, (4) two peaks in the solid residence time (SRT) frequency histogram of the annulus, (5) average SRT in the spout is twice that in a single‐chamber, and (6) larger solid dispersion in all three directions. The results provide meaningful understanding for the scale‐up of spout‐fluid beds. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1898–1916, 2016     

Catalytic Ozone Decomposition in a Gas‐Solids Circulating Fluidized‐Bed Riser

Computational fluid dynamics (CFD) modeling of the catalytic ozone decomposition reaction in a circulating fluidized‐bed (CFB) riser, using iron‐impregnated fluid catalytic cracking particles as catalyst, is carried out. The catalytic reaction is defined as a one‐step reaction, and the reaction equation is modified by with respect to the particle surface area, A_p, and an empirical coefficient. The Eularian‐Eularian method with the kinetic theory of granular flow is used to solve the gas‐solids two‐phase flow in the CFB riser. The simulation results are compared with experimental data, and the reaction rate is modified by using an empirical coefficient, to provide better simulation results than the original reaction rate. Moreover, the particle size has great effects on the reaction rate. The generality of the CFD model is further validated under different operating conditions of the riser.     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

Numerical determination of fluid-to-particle mass and heat transfer coefficients in packed bed reactors

A method based on particle-resolved CFD is built and validated, to calculate the fluid-to-particle mass and heat transfer coefficients in packed beds of spheres with different tube-to-particle diameter ratios (N) and of various particle shapes with N = 5.23. This method is characterized by considering axial dispersion. The mass and heat transfer coefficients increase by 5%–57% and 9%–63% after considering axial dispersion, indicating axial dispersion should be included in the method. The mass and heat transfer coefficients are reduced as N decreases. The catalyst particles without inner holes show higher mass and heat transfer coefficients than the ones with inner holes, because of unfavorable fluid flow in inner holes. The bed of trilobes has the highest mass and heat transfer coefficients, being 85% and 95% higher than the one of spheres. This work provides a versatile method and some useful guidance for the design of packed bed reactors.     

CFD modeling of solid-liquid fluidized beds of mono and binary particle mixtures

CFD simulation of bed expansion of mono size solid-liquid fluidized beds has been performed in creeping, transition and turbulent flow regimes, where Reynolds number (Re_∞=d_pV_S∞ρ_L/μ_L) has been varied from 0.138 to 1718. It has been observed that the predicted values of bed voidage using the drag law of Joshi [1983. Solid-liquid fluidized beds: some design aspects. Chemical Engineering Research and Design 61, 143-161] and Pandit and Joshi [1998. Pressure drop in packed, expanded and fluidized beds, packed columns and static mixers—a unified approach. Reviews in Chemical Engineering 14, 321-371] (which has been derived from the first principals), exhibited an excellent agreement with the Richardson and Zaki equation. CFD simulations have also been performed for the prediction of segregation and/or intermixing of binary particle systems having the ratio of terminal settling velocity over a range from 3.2 to 1.06. The Reynolds number has also been varied over the range of 0.33 to 2080. It has been observed that the present CFD model explains all the qualitative and quantitative observations reported in the published literature (complete segregation, partial segregation, complete intermixing, etc) and these predictions are in good agreement with the experimental results. The present CFD model also predicts successfully the layer inversion phenomena which occur in the binary particle mixtures of different size as well as density. Further, the critical velocity at which the complete mixing of the two particle species occurs has also been predicted.     

Computational study of the flow characteristics and separation efficiency in a mini-hydrocyclone

The development of a simple and feasible fluid–solid separation device is critical to further advancement in the use of micro-technology. The mini-hydrocyclone, which possesses a concise geometry and simple operational process, has been proposed as a promising solution to bridge this gap since the cut-size decreases with decreasing hydrocyclone diameter. In this work, we investigated the fluid flow and particle separation ability of a 5 mm diameter mini-hydrocyclone through computational fluid dynamics (CFD) modelling. Direct numerical simulation (DNS) results with CFD have shown that the flow transition and subsequent unsteady state behaviour occurred in the mini-hydrocyclone at a low Reynolds number (Re_in = 300) because of the onset of centrifugal instability. The centrifugal instability offered an insight into the flow transition and the development of turbulent flow in hydrocyclones which have not been studied. The centrifugal instability in the mini-hydrocyclone begins as Görtler vortices developing in the boundary layer and they subsequently affect the flow field. Particle motion tracing showed that improved separation with finer cut size, d₅₀, and steeper separation sharpness were obtained as the inlet velocity was increased. The improvement can be explained by the flow characteristics when the flow transits to turbulent flow.