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.     

Fluid dynamic stability of fluidised suspensions: the particle bed model

The equations of change for a fluidised suspension are closed by application of a simple model for the interaction of a single particle with the fluid; this relationship delivers the total force on elements of the particle phase including a fluid dynamic formulation for the 'particle phase pressure gradient'; numerical solutions of the non-linear equations, for small imposed perturbations of voidage, show clearly the development of shocks (bubbles) for unstable (aggregate) beds and the return to the homogeneous state for stable (particulate) systems; the linearised equations yield the general criterion for bed stability as a simple algebraic expression and quantitative predictions of disturbance propagation velocities in good agreement with published data.     

Gas mixing in the cocurrent downflow circulating fluidised bed

An experimental study on the gas dispersion behaviour of a cocurrent downflow gas-solids suspension in a 140 mm i.d. circulating fluidised bed (CDCFB) using the steady-state tracer method is presented. The influence of gas velocity, solids circulating rate and particle density on radial gas dispersion has been examined. Gas dispersion can well be described by an eddy diffusion mechanism and a proposed two dimensional dispersed plug-flow model can fit the experimental data very well. Correlations of the radial diffusion coefficient were obtained. It is found that the axial diffusion coefficient obtained in the CDCFB is much lower than that in conventional circulating fluidised beds.     

Aggregate behaviour of liquid fluidised beds

New and long published experimental observations of the onset of aggregate (bubbling) behaviour in liquid fluidised beds are shown to be in agreement with the predictions of a recently published model of the fluidisation process. For a given liquid, the transition from particulate to aggregate fluidisation depends on both the density and size of the suspended particles: the lower the particle density the larger is the size necessary for a transition to occur: thus for fluidisation by ambient water, lead particles larger than 200 μm and soda glass particles larger than 2000 μm will exhibit aggregate behaviour; below a critical particle density no such transition is possible.     

Measurements and numerical predictions of gas vortices formed by single bubble eruptions in the freeboard of a fluidised bed

Gas vortices generated in the freeboard of a bubbling fluidised bed have become the centre of increasingly more research due to the advances in experimental technology. The behaviour of gas flow in the freeboard of a bubbling fluidised bed is of interest for applications such as the gasification of coal where reactions of gas mixtures, as well as gas–particle heat and mass transfer take place. Knowledge of the hydrodynamics of the gas within the freeboard can be hard to characterise, especially the detailed behaviour of gases escaping from bubbles that erupt at the bed surface. In the present study, experiments were conducted on a rectangular three-dimensional gas–solid fluidised bed. The experiments used a particle imaging velocimetry (PIV) measurement technique to visualise and measure the gas flow within the freeboard after a single bubble eruption. A computational study was carried out using Eulerian–Eulerian, kinetic theory of granular flow approach with a quasi-static flow model and with LES used to account for gas turbulence. Results from a three dimensional simulation of the experimental fluidised bed were compared with experimental velocity profiles of gas flow in the freeboard of the gas–solid fluidised bed after a bubble eruption. The CFD simulations showed a qualitative agreement with the formation of the gas vortices as the bubble erupted. Consistent with experimental findings the CFD simulations showed the generation of a pair of vortices. However, the simulations were unable to demonstrate downward flow at the centre of the freeboard due to particles in free fall after a bubble eruption event was observed in the experiments. Velocity profiles from the CFD data are in reasonably good agreement with the characteristic trends observed in the experiments, whereas the CFD model was able to predict the gas vortices phenomena and the velocity magnitudes were over-predicted.     

Attrition of porous glass particles in a fluidised bed

Fluidisation is frequently accompanied by unwanted attrition of the bed material. This paper focuses on the mechanical aspects of fines creation by attrition in fluidised beds supported by multi-orifice distributor plates. The attrition rates of low-density porous glass particles were measured; these particles show abrasive wear behaviour rather than breakage. Positron emission particle tracking (PEPT) was used to follow particle motion in three dimensions within the fluidised bed. For a single orifice distributor with background fluidisation, the attrition rate increased exponentially with increasing orifice gas velocity. For a multi-orifice distributor, however, attrition rates were roughly proportional to excess gas velocity, except near to a critical ratio of particle to orifice diameter; as this ratio approached 2, attrition was observed to increase by an order of magnitude. A method is proposed for estimating attrition rates from a combination of small-scale experimental results and theoretical calculations of distributor jet entrainment rates.     

STEADY-STATE EXPANSION CHARACTERISTICS OF MONOSIZE SPHERES FLUIDISED BY LIQUIDS

Velocity-voidage experiments conducted on beds of truly monosized and spherical plastic particles fluidised by solutions of glycerol, enable the change of behaviour at high expansion conditions to be correlated with the unhindered particle Reynolds number.     

Particle-fluid heat transfer and dispersion in fluidised beds

The dynamic response of a gas fluidised bed has been measured for a range of particle sizes of lead glass ballotini and a range of particle Reynolds numbers. A dispersion model has been formulated that includes the effects of gas and particle mixing, fluid-to-particle heat transfer and intraparticle thermal conductivity, and the dynamic thermal response in theory has been found by solving the partial differential equations in the Laplace transform domain. The coefficient of thermal dispersion, the particle-to-fluid heat transfer coefficient and the intraparticle thermal conductivity have been found for the experimental response by non-linear regression. The coefficient of axial dispersion was found to be large and the particle to fluid heat transfer coefficients agreed with an established correlation for fixed and fluidised beds. The intraparticle thermal conductivity agreed with literature values for lead glass, the estimates showed no trend with flowrate, and the standard deviation of the estimate was three times smaller than the deviation found from similar experiments in fixed beds.     

Multi-dimensional model of a spouted bed

A multi-dimensional model is developed to describe the fluid and particle dynamic behaviour of spouted beds. The position of the spout-annulus interface is determined by a variational analysis. Two-fluid equations are used to represent gas and solids motions in the spout while the vector Ergun equation and soil mechanics equations are employed to describe, respectively, gas and solids behaviour in the annulus. Using numerical finite difference methods, the set of governing equations is solved subject to carefully chosen boundary conditions. The model predictions of key hydrodynamic characteristics are in reasonable agreement with available measured data selected from the literature to represent a wide range of experimental conditions.     

Convective heat transfer for power law fluids in packed and fluidised beds of spheres

The forced convection heat transfer characteristics for an incompressible and steady flow of power law liquids in fixed and extended beds of spherical particles has been studied numerically. The sphere-sphere hydrodynamic interactions have been accounted for by using a simple cell model. Within the framework of such a cell model, the momentum and energy equations have been solved using a finite difference method to obtain the velocity and temperature fields. Extensive numerical estimates of the local and average Nusselt numbers as functions of the physical, rheological and kinematic variables have been presented and discussed for the two commonly employed thermal boundary conditions. In broad terms, the Nusselt number for power law fluids (both shear-thinning and shear-thickening conditions) normalized with respect to the corresponding value for a Newtonian fluid shows weak additional dependence on the power law flow behaviour index. The shear-thinning behaviour is seen to promote heat transfer and as expected the shear-thickening behaviour impedes heat transfer in fixed and fluidised beds. All in all, the present results encompass wide ranges of conditions as follows: Reynolds number: 1-500; Peclet number: 1-500; bed voidage: 0.4-0.8 and the flow behaviour index: 0.5-1.8 thereby covering extremely shear-thinning and shear-thickening types of fluid behaviours. The paper is concluded by presenting detailed comparisons with the limited analytical and/or experimental results available for liquid-solid mass transfer in such systems.     

Hydrodynamic modelling of dense gas-fluidised beds: comparison and validation of 3D discrete particle and continuum models

A critical comparison of a hard-sphere discrete particle model, a two-fluid model with kinetic theory closure equations and experiments performed in a pseudo-two-dimensional gas-fluidised bed is made. Bubble patterns, time-averaged particle distributions and bed expansion dynamics measured with a nonintrusive digital image analysis technique are compared to simulation results obtained at three different fluidisation velocities. For both CFD models, the simulated flow fields and granular temperature profiles are compared. The effects of grid refinement, particle-wall interaction, long-term particle contacts, particle rotation and gas-particle drag are studied. The mechanical energy balance for the suspended particles is introduced, and the energy household for both CFD models is compared. The most critical comparison between experiments and model results is given by analysis of the bed expansion dynamics. Though both models predict the right fluidisation regime and trends in bubble sizes and bed expansion, the predicted bed expansion dynamics differ significantly from the experimental results. Alternative gas-particle drag models result in significantly different bed dynamics, but the gap between model and experimental results cannot be closed. In comparison with the experimental results, the discrete particle model gives superior resemblance. The main difference between both CFD models is caused by the neglect of particle rotation in the kinetic theory closure equations embedded in the two-fluid model. Energy balance analysis demonstrates that over 80% of the total energy is dissipated by sliding friction. Introduction of an effective restitution coefficient that incorporates the additional dissipation due to frictional interactions significantly improves the agreement between both models.     

Comparison and evaluation of interphase momentum exchange models for simulation of the solids volume fraction in tapered fluidised beds

An Eulerian computational fluid dynamics (CFD) model with granular flow extension was used to simulate a gas–solid fluidised bed in a tapered reactor. Various drag coefficient models were evaluated, which are used to calculate the drag force, describing the momentum transfer between the gas and solid phases. Comparison and evaluation between time-averaged solids volume fractions obtained from experiments and from simulations with several drag coefficient models were made. The predicted results obtained by the different drag models were verified using experimental data of Depypere et al. (2009). Initial results using a 2-phase Eulerian model showed poor agreement with experimental results. However, extending the Eulerian model to include 3 solid phases—with different mean particle diameter per phase in order to account for the particle size distribution of the fluidised solid material—yielded good agreement with experimental results. Furthermore, quantitative analyses showed that the modified Gidaspow drag model gave the best agreement between CFD simulations and experimental data.     

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     

Parameter estimation for a solids mixing|segregation model for gas fluidised beds

Gibilaro and Rowe in their model of a gas fluidised bed containing two particulate species introduced four arbitrary parameters linked to the known mechanisms giving rise to particle movement in such beds. In this work, these parameters are made deterministic by linking them to the physics of the bubbling bed and the particle properties. Segregation patterns are predicted from these parameters iteratively by allowing for the accompany variation with bed height of minimum fluidisation velocity and local bed behaviour. Good agreement between predicted and experimental patterns is found. So too is the dependence of mixing index on gas velocity. Agreement breaks down for high jetsam concentration systems. The model is not directly applicable when a defluidised region forms at the bottom of the bed.     

Mixing and segregation in a bidisperse gas–solid fluidised bed: a numerical and experimental study

In many industrial applications of dense gas–solid fluidised beds, mixing and segregation phenomena play a very important role. The extent of mixing and segregation is strongly influenced by the bubble characteristics. Therefore, the extent of mixing and segregation, induced by a single bubble injected in a monodisperse and bidisperse fluidised bed at incipient fluidisation conditions and in freely bubbling fluidised beds has been studied both with well-defined experiments and with a 3D Euler–Lagrangian model. Particle image velocimetry (PIV) was successfully applied to obtain the ensemble averaged particle velocity profile in the vicinity of the bubble in dense gas–solid fluidised systems.

The bubble size of a single injected bubble in a fluidised bed at minimum fluidisation conditions calculated with a 3D discrete particle model (DPM) depended strongly on the selected gas-particle drag model. The widely used Ergun equation combined with the Wen and Yu [Powder Technol. 98 (1998) 38; Chem. Eng. Sci. 47 (1992) 1913] relations overpredicted the bubble size due to an overprediction of the drag force. The DPM with the drag model proposed by Koch and Hill [Annu. Rev. Fluid Mech. 33 (2001) 619], based on Lattice–Boltzmann simulations, gave much better agreement with the experimental findings.

The segregation rates in a bidisperse freely bubbling fluidised bed predicted by the DPM agreed very well with the experimentally measured segregation rates by Goldschmidt [M.J.V. Goldschmidt, Hydrodynamic modelling of fluidised bed spray granulation, PhD thesis, Twente University, 2001].     

CFD study of solids concentration in a fluidised-bed coater with variation of atomisation air pressure

The solids volume fraction inside a tapered fluidised bed coater was simulated with the use of an Eulerian computational fluid dynamics (CFD) model with atomisation nozzle sub-model. The drag force, describing momentum transfer between the gas and solid phases was calculated using the drag model proposed by [1]. In order to account for the particle size distribution of the fluidised solid materials, a 4-phase Eulerian model was used. The model-predicted results for different atomisation air pressures were verified using published experimental data [2]. It was shown that the model proved to be highly sensitive to changes in the fluidisation air flow rate with regard to the model-predicted solids volume distribution.     

Influence of solid-phase wall boundary condition on CFD simulation of spouted beds

The influence of solid-phase wall boundary condition in terms of specularity coefficient and particle–wall restitution coefficient on the flow behavior of spouted beds was investigated using two-fluid model approach in the computational fluid dynamics software FLUENT 6.3. Parametric studies of specularity coefficient and particle–wall restitution coefficient were performed to evaluate their effects on the flow hydrodynamics in terms of fountain height, spout diameter, pressure drop, local voidage and particles velocity. The numerical predictions were compared with available experimental data in the literatures to obtain the suitable values of specularity coefficient and particle–wall restitution coefficient for spouted beds. The simulated results show that the solid-phase wall boundary condition plays an important role in CFD modeling of spouted beds. The specularity coefficient has a pronounced effect on the spouting behavior and a small specularity coefficient (0.05) can give good predictions, while the particle–wall restitution coefficient is not critical for the holistic flow characteristics.