Computational fluid dynamics (CFD) modeling of spouted bed: Assessment of drag coefficient correlations

In the computational fluid dynamics (CFD) modeling of gas-solids two-phase flows, drag force is the only accelerating force acting on particles and thus plays an important role in coupling two phases. To understand the influence of drag models on the CFD modeling of spouted beds, several widely used drag models available in literature were reviewed and the resulting hydrodynamics by incorporating some of them into the CFD simulations of spouted beds were compared. The results obtained by the different drag models were verified using experimental data of He et al. [He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994a. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72 (4), 229-234; He, Y.L., Qin, S.Z., Lim, C.J., Grace, J.R., 1994b. Particle velocity profiles and solid flow patterns in spouted beds. Canadian Journal of Chemical Engineering 72 (8), 561-568.] The quantitative analyses showed that the different drag models led to significant differences in dense phase simulations. Among the different drag models discussed, the Gidaspow (1994. Multiphase Flow and Fluidization, Academic Press, San Diego.) model gave the best agreement with experimental observation both qualitatively and quantitatively. The present investigation showed that drag models had critical and subtle impacts on the CFD predictions of dense gas-solids two-phase systems such as encountered in spouted beds.     

Scale-up relationships of spouted beds by solid stress analyses

This article describes a new set of scale-up parameters of spouted beds derived from solid stress analyses. Compared with the first set of scale-up parameters of spouted beds proposed by He et al. [He Y. L., Lim C. J., Grace J. R., Scale-up studies of spouted beds, Chemical Engineering Science, 52 (2), 329-339, 1997], this set introduced a new parameter, the coefficient of restitution of particles, that accounts for the effects of particle-particle collisions in the spout region of a spouted bed. To verify the present set of scale-up parameters, a series of experiments were designed and conducted in two spouted beds of 80 mm and 120 mm in diameter, respectively, operated in the different testing cases consisting of different combinations of the involved scale-up parameters. The results showed that the more closely the scale-up parameters of the spouted beds tested were matched, the higher hydrodynamic similarity could be achieved. The comparisons of the hydrodynamic properties such as fountain height, spout diameter and bed voidage measured in the different testing cases revealed that the coefficient of restitution of particles could significantly impact the particle-particle interactions and thus its effects should be taken into account in scaling-up spouted beds.     

Numerical simulation and experimental study of fluid-particle flows in a spouted bed

In this work, the Eulerian-Eulerian multiphase model is used in the computational simulation of fluid dynamics of spouted beds with two different geometries: conical-cylindrical and conical. For the conical-cylindrical spouted bed, the simulated results of radial velocities of particles with a 1.41 mm diameter along bed heights in the range of 0.022 to 0.318 m are compared with experimental values obtained by He et al. [Y.L. He, C.J. Lim, J.R. Grace and, J.X. Zhu, Measurements of Voidage Profiles in Spouted Beds, Canadian Journal of Chemical Engineering, 72 (1994), 229-234], and show a good agreement. The influence of static bed height on the characteristic curve is assessed through simulations using different airflow rates. The respective minimum spouting velocities are compared with experimental values and with values obtained through empirical correlations reported in the literature. The results of the CFD simulations show a deviation of 3.8% when compared with the experimental data, which is less than the aforementioned correlations. The stages of transition from the condition of static bed to spouting bed are presented through the simulation of solids volume fraction distribution and the radial profile of voidage in the spouting region. The characteristic curve and minimum spouting conditions for a simulated conical bed, with glass particles of 6 mm diameter are compared with the experimental results showing deviations of 12.1% for the pressure drop and 5.6% for the minimum spouting velocity.     

Hydrodynamics and scale-up of liquid-solid circulating fluidized beds: Similitude method vs. CFD

Hydrodynamics and scale-up of liquid-solid circulating fluidized beds (LSCFBs) are investigated using similitude method and computational fluid dynamics (CFD) technique. Similitude method is applied to establish the dynamic similarity among LSCFBs by tuning physical properties of liquids and solids, operating conditions and bed dimensions to match several scaling sets of dimensionless groups. The hydrodynamic behaviors in these constructed LSCFBs are simulated by a validated CFD model [Cheng, Y., Zhu, J., 2005. CFD modeling and simulation of hydrodynamics in liquid-solid circulating fluidized beds. Canadian Journal of Chemical Engineering 83, 177-185] and compared in terms of the axial and radial flow structures characterized by the solids fraction, particle and liquid velocities and solids mass flux. The results demonstrate that only the full set scaling parameters obtained from similitude method, i.e., five dimensionless groups together with fixed bed geometry, particle sphericity, particle size distribution as well as particle collision properties, can ensure the similarity of hydrodynamics in the fully developed region of different LSCFBs. Developing flow structures in LSCFBs are strongly influenced by some parameters such as turbulent kinetic energy at the inlet so that the proposed similitude method may not always be applicable.     

Simulation of the Hydrodynamics and Drying in a Spouted Bed Dryer

Gas-particle flow behavior in a spouted bed of spherical particles was simulated using the Eulerian-Eulerian two-fluid modeling approach, incorporating a kinetic-frictional constitutive model for dense assemblies of the particulate solid. The interaction between gas and particles was modeled using the Gidaspow drag model and the predicted hydrodynamics is compared with published experimental data. To investigate drying characteristics of particulate solids in axisymmetric spouted beds, a heat and mass transfer model was developed and incorporated into the commercial computational fluid dynamics (CFD) code FLUENT 6.2. The kinetics of drying was described using the classical and diffusional models for surface drying and internal moisture drying, respectively. The overall flow patterns within the spouted bed were predicted well by the model; i.e., a stable spout region, a fountain region, and an annular downcomer region were obtained. Calculated particle velocities and concentrations in the axisymmetric spouted bed were in reasonable agreement with the experimental data of He et al. (Can. J. Chem. Eng. 1994a, 72:229; 1994b, 72:561). Such predictions can provide important information on the flow field, temperature, and species distributions inside the spouted bed for process design and scale-up.     

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.     

Simulations of flow behavior of gas and particles in a spouted bed using a second-order moment method-frictional stresses model

Flow behavior of gas and particles is simulated in the spouted beds using an 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 interaction of particle collisions is modeled by means of a second-order moment method, while the frictional 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. The distributions of concentration, velocity, second-order moments and granular temperature of particles are obtained in the spouted bed. Calculated particle velocities, concentrations and spout diameter in a spouted bed are in agreement with experimental data obtained by He et al., 1994a, He et al., 1994b. Simulated results indicate that the second-order moment component in the axial direction is higher that the second-order moment component in the lateral direction in both the spout and the fountain. In the annulus, the values of second-order moments are very small. The simulated mean value of the ratio of the normal second-order moment in the axial direction to the normal second-order moment in the lateral direction is in the range of 2.5–3.2 in the spout and the annulus. The bubblelike normal Reynolds stresses per unit bulk density is predicted from the simulated velocity of particles. The predicted bubblelike Reynolds stresses are very low in spouted bed. The values of the normal second-order moments are on the average three magnitudes in order larger than that of the bubblelike Reynolds stresses per unit bulk density in a spouted bed.     

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.     

Spout Shape Predictions in Spouted Beds

A theoretical study to predict spout‐annulus interface variation with bed level for different column geometries of spouted beds is proposed. A previous mathematical model (Krzywanski et al., 1989), developed for spout shape predictions in two‐dimensional spouted beds, is here proposed to be applied also for cylindrical, conical or cone‐based cylindrical columns. Its predictions depend on the average spout diameter and on the spout expansion angle. While there exists empirical equations available to estimate the first model parameter, the second one requires a rigorous stress analysis of the particles at the entrance of the bed. To avoid this difficulty, this work proposes a simple mathematical strategy to calculate the spout expansion angle. The reliability of this approach was checked by comparison with several experimental results obtained in cone‐based cylindrical (Lim et al., 1974; Wu et al., 1987; He et al., 1998) and rectangular (Zanoelo, 1994) spouted beds.     

Comparison of numerical simulations and experiments in conical gas-solid spouted bed

Flowbehavior of gas and particles in conical spouted beds is experimentally studied and simulated using the twofluid gas-solid model with the kinetic theory of granular flow. The bed pressure drop and fountain height are measured in a conical spouted bed of 100mmI.D. at different gas velocities. The simulation results are compared with measurements of bed pressure drop and fountain height. The comparison shows that the drag coefficient model used in cylindrical beds under-predicted bed pressure drop and fountain height in conical spouted beds due to the partial weight of particles supported by the inclined side walls. It is found that the numerical results using the drag coefficient model proposed based on the conical spouted bed in this study are in good agreement with experimental data. The present study provides a useful basis for further works on the CFD simulation of conical spouted bed.     

Computer simulations of gas-solid flow in spouted beds using kinetic-frictional stress model of granular flow

A gas-solid two-fluid flow model is presented. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated in the simulations of spouted beds. This model treats the kinetic and frictional stresses of particles additively. 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 et al. (J. Fluid Mech. 210 (1990) 501) and the modified frictional shear viscosity model proposed by Syamlal et al. (MFIX documentation. US Department of Energy, Federal Energy Technology Center, Morgantown, 1993). The body-fitted coordination is used to make the computational grids best fit the shape of conical contour of the base in the spouted beds. The effects of inclined angle of conical base on the distributions of particle velocities and concentrations in the spout, annulus and fountain zones were numerical studied. Calculated particle velocities and concentrations in spouted beds were in agreement with experimental data obtained by He et al. (Can. J. Chem. Eng. 72 (1994a) 229; (1994b) 561) and San Jose et al. (Chem. Eng. Sci. 53 (1998) 3561).     

Minimum spouting velocity of dense particles in shallow spouted beds

Quantitative method is used to experimentally measure the minimum spouting velocity in shallow conical spouted bed. And a new minimum spouting correlation for shallow conical spouted beds is developed. It is based on spherical ZrO₂ particles whose density is as high as 5890 kg/m³ while the other U_ms correlations published so far are mainly based on relatively deep conical beds composed of lower density particles with density around or lower than 3000 kg/m³. The new U_ms correlation can predict U_ms of heavy particles well within the range of the experimental matrix. © 2011 Canadian Society for Chemical Engineering     

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.     

Experimental and CFD Study of Heat Transfer in Spouted Beds: Analysis of Nusselt Number Correlations

Theoretical Foundations of Chemical Engineering - The application of CFD to evaluate heat transfer in spouted beds remains scarce. Furthermore, the few reported studies about this have used a...     

HYDRODYNAMICS AND STABILITYOF SLOT-RECTANGULAR SPOUTED BEDS. PART I: THIN BED

Spouted beds of rectangular cross-section with gas entry through bottom slots have been proposed as a means of overcoming scale-up difficulties of conventional spouted beds. A study was undertaken of bed hydrodynamics in a thin slot-rectangular column of width 150 mm and slot width 2 to 20 mm for four types of particles. Flow regimes and bed hydrodynamics are qualitatively similar to those in cylindrical spouted beds, but there are significant quantitative differences caused by the different geometry. Slot width exerts a strong influence on such features as flow regimes, maximum spoutable bed height, minimum spouting velocity, pressure drop and fountain height.     

HYDRODYNAMICS AND STABILITYOF SLOT-RECTANGULAR SPOUTED BEDS. PART I: THIN BED

Spouted beds of rectangular cross-section with gas entry through bottom slots have been proposed as a means of overcoming scale-up difficulties of conventional spouted beds. A study was undertaken of bed hydrodynamics in a thin slot-rectangular column of width 150 mm and slot width 2 to 20 mm for four types of particles. Flow regimes and bed hydrodynamics are qualitatively similar to those in cylindrical spouted beds, but there are significant quantitative differences caused by the different geometry. Slot width exerts a strong influence on such features as flow regimes, maximum spoutable bed height, minimum spouting velocity, pressure drop and fountain height.     

Coupling of smoothed particle hydrodynamics and finite volume method for two-dimensional spouted beds

A coupled method with smoothed particle hydrodynamics (SPH) and finite volume method (FVM) is proposed in this work for the simulation of the particle dynamics in two-dimensional spouted beds. Based on the pseudo-fluid model, SPH is used for discrete phase to trace the movement of each individual particle and FVM for continue phase to compute the turbulent fluid. Two phases are coupled through effects of drag force, gas pressure and volume fraction of each phase. A two-dimensional tapered-based spouted bed is chosen as a case study to demonstrate the performance of the SPH–FVM coupled algorithm. The simulation results show a good agreement with the experimental data and other simulation results by the two-fluid model and discrete element method in the literature. The spouted shape, time-averaged particle velocities and particle vertical velocities in the spout are analyzed and the distribution of gas flow field and turbulent kinetic energy are then discussed. It indicates that the present method is more suitable to study the fluidization within the spouted beds.     

CFD modeling and validation of the turbulent fluidized bed of FCC particles

An experimental and computational study is presented on the hydrodynamic characteristics of FCC particles in a turbulent fluidized bed. Based on the Eulerian/Eulerian model, a computational fluid dynamics (CFD) model incorporating a modified gas‐solid drag model has been presented, and the model parameters are examined by using a commercial CFD software package (FLUENT 6.2.16). Relative to other drag models, the modified one gives a reasonable hydrodynamic prediction in comparison with experimental data. The hydrodynamics show more sensitive to the coefficient of restitution than to the flow models and kinetics theories. Experimental and numerical results indicate that there exist two different coexisting regions in the turbulent fluidized bed: a bottom dense, bubbling region and a dilute, dispersed flow region. At low‐gas velocity, solid‐volume fractions show high near the wall region, and low in the center of the bed. Increasing gas velocity aggravates the turbulent disorder in the turbulent fluidized bed, resulting in an irregularity of the radial particle concentration profile. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Numerical Simulations of Flow Behaviour of Agglomerates of Nano-Size Particles in Bubbling and Spouted Beds with an Agglomerate-Based Approach

Numerical simulations are performed on the behaviour of agglomerates of nanoparticles in bubbling gas fluidized beds and spouted beds—systems that are widely used in handling and processing particulate solids in various industrial sectors including biomaterials, foods and pharmaceuticals. An Eulerian two-fluid approach is used and the cohesive force between particles is considered. An empirical expression for the solids pressure of agglomerates is used (Jung and Gidaspow, 2002). The interaction between gas and agglomerates is considered with an agglomerate-based approach. Simulated results show that the fluidized bed has a very high expansion ratio with no distinct bubbles in the bubbling fluidized bed. In the spouted bed, however, the concentration of agglomerates is nearly homogeneous in both the dilute and transitional zones. The velocity of agglomerates is found to be higher than that in the annulus region, whereas the concentration distribution shows an opposite trend with a nearly closing packing of agglomerates in the annulus region. A high spouting gas velocity is shown to be required to fluidize agglomerates in the spouted bed. Comparisons of the modelling results are also made with limited experimental results.     

Hydrodynamics of a Novel Biomass Autothermal Fast Pyrolysis Reactor: Flow Pattern and Pressure Drop

A novel biomass, autothermal, fast pyrolysis reactor with a draft tube and an internal dipleg dividing the reactor into two interconnected beds is proposed. This internally interconnected fluidized beds (IIFB) reactor is designed to produce high‐quality bio‐oil using catalysts. Meanwhile, the pyrolysis by‐products, i.e., char, coke and non‐condensable gases, are expected to burn in the combustion bed to provide the heat for the pyrolysis. On the other hand, the catalysts can be regenerated simultaneously. In this study, experiments on the hydrodynamics of a cold model IIFB reactor are reported. Geldart group B and D sand particles were used as the bed materials. The effects of spouting and fluidizing gas velocities, particle size, static bed height and the total pressure loss coefficient of the pyrolysis bed exit, on the flow patterns and pressure drops of the two interconnected beds are studied. Six distinct flow patterns, i.e., fixed bed (F), periodic spouted/bubbling bed (PS/B), spouted bed with aeration (SA), spout‐fluidized bed (SF), spout‐fluidized bed with slugging (SFS) and spouted bed with backward jet (SBJ) are identified. The investigations on the pressure drops of the two beds show that both of them are seen to increase at first (mainly in the F flow pattern), then to decrease (mainly in the PS/B and SA flow patterns) and finally to increase again (mainly in the SA and SF flow patterns), with the increase of the spouting gas velocity. It is observed that a larger particle size and lower static bed height lead to lower pressure drops of the two beds.