Critical comparison of hydrodynamic models for gas-solid fluidized beds—Part I : bubbling gas-solid fluidized beds operated with a jet

In the Eulerian approach to model gas-solid fluidized beds closures are required for the internal momentum transfer in the particulate phase. Firstly, two closure models, one semi-empirical model assuming a constant viscosity of the solid phase (CVM) and a second model based on the kinetic theory of granular flow (KTGF), have been compared in this part in their performance to describe bubble formation at a single orifice and the time-averaged porosity profiles in the bed using experimental data obtained for a pseudo two-dimensional fluidized bed operated with a jet in the center. Numerical simulations have shown that bubble growth at a nozzle with a jet is mainly determined by the drag experienced by the gas percolating through the compaction region around the bubble interface, which is not much influenced by particle-particle interactions, so that the KTGF and CVM give very similar predictions. However, this KTGF model does not account for the long term and multi particle-particle contacts (frictional stresses) and under-predicts the solid phase viscosity at the wall as well as around the bubble and therefore over-predicts the bed expansion. Therefore, in the later part of the paper, the bubble growth at a single orifice and the time-averaged porosity distribution in the bed predicted by the KTGF model with and without frictional stresses are compared with experimental data. The model predictions by the KTGF are improved significantly by the incorporation of frictional stresses, which are however strongly influenced by the empirical parameters in this model. In Part II the comparison of the CVM and KTGF with experimental results is extended to freely bubbling fluidized beds.     

Hydrodynamic modeling of particle rotation for segregation in bubbling gas-fluidized beds

A multi-fluid Eulerian model has been improved by incorporating particle rotation using kinetic theory for rapid granular flow of slightly frictional spheres. A simplified model was implemented without changing the current kinetic theory framework by introducing an effective coefficient of restitution to account for additional energy dissipation due to frictional collisions. Simulations without and with particle rotation were performed to study the bubble dynamics and bed expansion in a monodispersed bubbling gas-fluidized bed and the segregation phenomena in a bidispersed bubbling gas-fluidized bed. Results were compared between simulations without and with particle rotation and with corresponding experimental results. It was found that the multi-fluid model with particle rotation better captures the bubble dynamics and time-averaged bed behavior. The model predictions of segregation percentages agreed with experimental data in the fluidization regime where kinetic theory is valid to describe segregation and mixing.     

Experimental validation of CFD models for fluidized beds: Influence of particle stress models, gas phase compressibility and air inflow models

This work compares numerical simulations of fluid dynamics in fluidized beds using different closure models and air feed system models. The numerical results are compared to experiments by means of power spectral density distributions of fluctuating pressure signals and bubble statistics obtained from capacitance probe measurements. Two different particle rheology models are tested in combination with two different values of the maximum particle volume fraction. The first particle model predicts the particle pressure by an exponential power law and assumes a constant particle viscosity (CPV), and the second model predicts the stresses using the kinetic theory of granular flow (KTGF). Furthermore, two model approaches for the air inflow are evaluated. The first inflow model includes the coupling between the air-feed system and the fluidized bed in the simulation, and the second model assumes a constant mass flow of gas into the fluidized bed. Finally, the influence of the compressibility of the gas phase on the numerical predictions is investigated. The numerical simulations are made using the CFX-4.4 commercial flow solver.The simulations show that the KTGF model gives a more evenly distributed bubble flow profile over the bed cross-section, while the CPV model gives a more parabolic bubble flow profile, with a higher bubble flow in the central part of the bed. This work shows that the KTGF model results are in significantly better agreement with the experiments. It is furthermore shown that the modelling of the air-feed system is crucial to for predicting the overall bed dynamic behaviour.     

A critical comparison of frictional stress models applied to the simulation of bubbling fluidized beds

The behaviour of a gas-solid flow in a bubbling fluidized bed operated near the minimum fluidization condition is strongly influenced by the frictional stresses between the particles, these being highly concentrated and their motion dominated by enduring contact among them and with the walls.The effect of the introduction of frictional stresses in a Eulerian-Eulerian two fluid model based on the kinetic theory of the granular flow is evaluated. The models of Johnson and Jackson [1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67-93], Syamlal et al. [1993. Mfix documentation: volume I, theory guide. Technical Report DOE/METC-9411004, NTIS/DE9400087, National Technical Information Service, Springfield, VA], and Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] are compared with the kinetic theory of the granular flow and with experimental data both in a bubbling fluidized bed with a central jet and in a bubbling fluidized bed with a porous distributor. The predicted evolution of the bubble diameter along the height of the fluidized beds is examined, the shapes of the bubbles predicted by the models are compared and the evolution in time of the bubbles is shown. In the case of the bed with a central jet, the bubble detachment time is also calculated. The results show that the introduction of a frictional stress model improves the prediction of the bubbles diameter in a bubbling fluidized bed with a central jet and positively affects the bubbles diameter distribution in a uniformly fed bubbling fluidized bed. The high sensitivity of the model to the value of the particulate phase fraction at which frictional stresses start to be accounted for is pointed out through a sensitivity analysis performed on the Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] model.     

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.     

A bubbling fluidization model using kinetic theory of rough spheres

Collisional motion of inelastic rough spheres is analyzed on the basis of the kinetic theory for flow of dense, slightly inelastic, slightly rough sphere with the consideration of gas–solid interactions. The fluctuation kinetic energy of particles is introduced to characterize the random motion of particles as a measure of the translational and rotational velocities fluctuations. The kinetic energy transport equation is proposed with the consideration of the redistribution of particle kinetic energy between the rotational and translational modes and kinetic energy dissipation by collisions. The solid pressure and viscosity are obtained in terms of the particle roughness and restitution coefficient. The partition of the random‐motion kinetic energy of inelastic rough particles between rotational and translational modes is shown to be strongly affected by the particle restitution coefficient and roughness. Hydrodynamics of gas–solid bubbling fluidized beds are numerically simulated on the basis of the kinetic theory for flow of rough spheres. Computed profiles of particles are in agreement with the experimental measurements in a bubbling fluidized bed. The effect of roughness on the distribution of energy dissipation, kinetic energy, and viscosity of particles is analyzed. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Hydrodynamics of binary fluidization in a riser: CFD simulation using two granular temperatures

A new computational fluid-dynamic (CFD) model with a separate granular temperature (2/3 random particle kinetic energy per unit of mass) equation for each phase or particle size was developed using constitutive equations derived earlier by Huilin, Gidaspow and Manger. In agreement with the experiment and model of Mathiesen, Solberg and Hjertager the new model computes the observed core-annular flow regime. It predicts the trends of the observed radial and axial particle diameter distributions. For elastic particles the computed particle velocity distributions are parabolic. They are close to the laminar type approximate analytical solution for flow in a pipe, where the mean velocity equals the inlet flux divided by the particle density and volume fraction. The computed turbulent intensity is lower for large particles than for small particles, as measured. This is in agreement with an approximate analytical solution for the granular temperature in the developed flow region of a riser for elastic particles. Computations show that for sufficiently inelastic particles the granular temperature in the center can be lower than near the wall resembling the measured particle fluctuating velocity distribution.     

Study of wall boundary condition in numerical simulations of bubbling fluidized beds

The influence of the solid-phase wall boundary condition was investigated in Eulerian-Eulerian numerical simulations of a bubbling fluidized bed. Parametric studies of the particle-wall restitution coefficient and specularity coefficient were performed to evaluate their impact on the predicted flow hydrodynamics in terms of bed expansion, local voidage, and solid velocity. Both two- and three-dimensional simulations were conducted and compared with available experimental data on solid velocity and bubble properties. It is found that the wall effect plays an important role in CFD models. Such factors as the voidage at the bubble boundary, averaging method, and minimum bubble size also influence the mean bubble diameter.     

Numerical simulations of gas-solid flow in tapered risers

Hydrodynamic behavior of gas-solid flow in tapered risers was simulated using the two-fluid model based on the kinetic theory of granular flow representing the constitutive relations of the solid phase. Present numerical model was verified by comparing with experimentally measured solid mass fluxes, particle concentrations and velocities in column risers. Computed results showed that the core-annular flow structure existing in the column riser may disappear in the tapered risers. The distributions of particle concentration tend to be more uniform in the tapered riser than that in the column riser under the same operating conditions. The uniform particle distribution can be achieved by changing the inclined angle of the tapered riser under specific operating conditions.     

CFD simulation of dilute phase gas-solid riser reactors: Part I—a new solution method and flow model validation

A three-dimensional simulation of a dilute phase riser reactor (solid mass flux: ) is performed using a novel density based solution algorithm. The model equations consisting of continuity, momentum, energy and species balances for both phases, are formulated following the Eulerian-Eulerian approach. The kinetic theory of granular flow is applied. The gas phase turbulence is accounted for via a k-ε model. An extra transport equation describes the correlation between the gas and solid phase fluctuating motion. The solution algorithm allows a simultaneous integration of all the model equations in contrast to the sequential multi-loop solution in the conventional pressure based algorithms, used so far in riser simulations. The simulations show an unsteady behaviour of the flow, but a core-annulus flow pattern emerges on a time-averaged basis. The abrupt nature of the T type outlets causes a significant recirculation of gas and solid from the top of the riser. The flow near the outlets is highly non-symmetric and has a three-dimensional character. A significant decrease of the gas phase turbulence and particle granular temperature across the riser length is attributed to the presence of small particles, which is qualitatively consistent with the experimental data from literature.     

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.     

Flow structure of the solids in gas-solid fluidized beds

Existence of clusters in dense fluidized beds was investigated by analyzing the time-position data of a tracer obtained in several radioactive particle tracking experiments. It was found that in the case of sand particles, more gas passes through the bed as bubbles with increasing the superficial gas velocity and in the case of FCC powder, flow of the gas through the bed as bubbles does not increase in the turbulent fluidization regime. Cluster diameters were estimated from their velocities and found that descending clusters are generally larger than ascending ones and the size of both increases with increasing the superficial gas velocity. Bubble velocities evaluated in this work are in good agreement with the correlations in the bubbling regime of the fluidization available in the literature.     

Numerical simulation of single and multiple gas jets in bubbling fluidized beds

The behavior of single and multiple horizontal gas jet injections into a rectangular bubbling fluidized bed are studied with three-dimensional numerical simulations. The jet penetrations as well as the interactions between the jet and the surrounding gas, solids, bubbles, and other jets are investigated. As far as the average jet penetration length is concerned, limited influence of each jet on the others is observed in multiple jet injections until the jets start to overlap. The effect of the secondary gas injection on the flow hydrodynamics in the bed is examined for multiple jet injections with different jetting velocities and arrangements. It is found that the secondary gas injection mainly affects the hydrodynamics of the upper section above the injection level, while its effect is nearly negligible below the injection. Above the injection level, more particles are brought upward and the circulation of solids is promoted. Furthermore, the tendency of slugging inside the bed is observed at high secondary injection flow rates.     

DEM-LES study of 3-D bubbling fluidized bed with immersed tubes

Based on Euler-Lagrange frame, a true three-dimensional numerical simulation of bubbling fluidized bed embedded with two immersed tubes is presented. The solid phase is composed of 178,200 particles of diameter and simulated by discrete element method (DEM, a soft-sphere approach). The gas phase is computed through solving the volume-averaged four-way coupling Navier-Stokes equations in which the Smagorinsky SGS tensor model is used in large eddy simulation (LES). Particle-tube collision is particularly treated as a transformation of DEM. The volume segmentation of a particle sphere for void fraction calculation is solved via a numerical sub-division approach. The numerical results are compared with the experimental results for validation. The results obtained with and without the LES model are also compared. The numerical results show a strong correlation between gas-particle interaction, particle-particle interaction, pressure drop, particle back mixing motion and bubble motion, and all of them follow a similar pattern of synchronous periodic variation though the periodicity may vary depending on different flow conditions. The effects of SGS tensor on evolution of fluidized bed are found in various aspects. Finally, the distribution of particle-tube impact frequency is given.     

Numerical simulations of flow behavior of gas and particles in spouted beds using frictional-kinetic stresses model

Flow behavior of gas and particles is simulated in the spouted beds using a Eulerian-Eulerian two-fluid model on the basis of kinetic theory of granular flow. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. An inverse tangent function is used to provide a smooth transitioning from the plastic and viscous regimes. The distributions of concentration, velocity and granular temperature of particles are obtained in the spouted bed. Calculated particle velocities and concentrations in spouted beds are in agreement with the experimental data obtained by He et al. (1994a, b). Simulated results indicate that flow behavior of particles is affected by the concentration of the transition point in spouted beds.     

Distributor effects near the bottom region of turbulent fluidized beds

The distributor plate effects on the hydrodynamic characteristics of turbulent fluidized beds are investigated by obtaining measurements of pressure and radial voidage profiles in a column diameter of 0.29 m with Group A particles using bubble bubble-cap or perforated plate distributors. Distributor pressure drop measurements between the two distributors are compared with the theoretical estimations while the influence of the mass inventory is studied. Comparison is established for the transition velocity from bubbling to turbulent regime, U_c, deduced from the pressure fluctuations in the bed using gauge pressure measurements. The effect of the distributor on the flow structure near the bottom region of the bed is studied using differential and gauge pressure transducers located at different axial positions along the bed. The radial voidage profile in the bed is also measured using optical fiber probes, which provide local measurements of the voidage at different heights above the distributor. The distributor plate has a significant effect on the bed hydrodynamics. Owing to the jetting caused by the perforated plate distributor, earlier onset of the transition to the turbulent fluidization flow regime was observed. Moreover, increased carry over for the perforated plate compared with the bubble caps has been confirmed. The results have highlighted the influence of the distributor plate on the fluidized bed hydrodynamics which has consequences in terms of comparing experimental and simulation results between different distributor plates.     

Oxygen transfer prediction in aeration tanks using CFD

In order to optimize aeration in the activated sludge processes, an experimentally validated numerical tool, based on computational fluid dynamics and able to predict flow and oxygen transfer characteristics in aeration tanks equipped with fine bubble diffusers and axial slow speed mixers, is proposed. For four different aeration tanks (1;1493;8191 and ), this tool allows to precisely reproduce experimental results in terms of axial liquid velocities, local gas hold-ups. Predicted oxygen transfer coefficients are within ±5% of experimental results for different operating conditions (varying pumping flow rates of the mixers and air flow rates). The actual bubble size must be known with precision in order to have a reliable estimation of the oxygen transfer coefficients.