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This review is an extension of our 2014 circulating fluidized bed (CFB) plenary lecture. A derivation of multiphase mass, momentum and energy balances is presented, with a review of elementary kinetic theory, to explain the concepts of granular temperature and pressure and the core-annular flow regime commonly observed in CFB. The kinetic theory shows that the particle concentration is given by the reciprocal of a fourth order parabola of dimensional tube radius, in agreement with experiments. Computed flow regimes and heat and mass transfer coefficients in fluidization are also discussed. [ABSTRACT FROM AUTHOR]

The most common technology for postcombustion of CO2 capture is the amine solvent scrubber. The energy consumption for capturing CO2 from flue gases using amine solvent technology is 15-30% of the power plant electricity production. Hence, there is a need to develop more efficient methods of removing CO2. A circulating fluidized bed using sodium or potassium carbonates is potentially such a process, as their high decomposition pressures allow regeneration at low temperatures using waste heat rather than steam from the power plant. But equilibrium data for the sorbents require the use of several cooled stages to achieve high CO2 conversions. Here, a method of computing such a number of stages for a given CO2 conversion was developed using multiphase computational fluid dynamics. It was found that it required six equilibrium stages to remove 96% of CO2 with the initial mole fraction of 0.15 in a sorption riser. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5267-5279, 2017 [ABSTRACT FROM AUTHOR]

A 1 m in diameter and 3.55 m tall fluidized bed riser internally with water tubes, which required six equilibrium stage of riser-sorber for capturing about 95% of CO2 emitted from a coal power plant, were designed to replace the multisingle risers. At the optimum operating condition, the temperature of the cooling tubes in the bottom, the middle and the top of the riser were kept constant values at 50, 40, and 30°C, respectively. The hot water (57°C) from lowest exchanger section can be used to preheat the spent sorbent for the regeneration in a downer. The rest of the heat for the regenertion is obtained from the stack gas (100-130°C). This new concept promises to reduce the energy consumption for CO2 removal from flue gas. The only energy requirement is for pumping fluid and fluidizing particles in the bed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5280-5289, 2017 [ABSTRACT FROM AUTHOR]

Multiphase CFD simulations have shown how to design reactors using Fischer–Tropsch chemistry. The new design uses large catalyst particles to eliminate large bubbles, has no cooling tube bundles and produces up to 50,000 bbl/day of Diesel fuel in a 7 m diameter, 12 m high reactor at a pressure of 3 MPa and a temperature of 530 K. [ABSTRACT FROM AUTHOR]

Abstract: A fluidized bed, with a conical inlet to promote spouted bed type flow, carbonate based sorber design for removal of CO2 from flue gases is presented. CFD simulations for a binary mixture show that a plug flow model is a good first approximation for the bubble-free fluidization achieved using two binary mixtures of 75 and 375μm particles. For a 75μm binary mixture, bubbles appeared initially similar to spouted bed behavior. A binary mixture of 375μm particles fluidized as an oscillating bed without bubble formation. The CFD model was used to compute wall-to-bed heat transfer coefficients needed for an optimal design. Equilibrium limitations require the use of several stages for removal of 90% CO2 [Copyright &y& Elsevier]

Abstract: The transition flow between turbulent and fast fluidization regimes in high solid particle density circulating fluidized bed reactor was successfully investigated in this study. In addition, the effects of computational cell and simulation time were compared. Then, the comprehensive explanation and in-depth system parameters were discussed. The results showed the unique system characteristics. For the transition flow between turbulent and fast fluidization regimes, lower range of energy spectrum than the turbulent and fast fluidization regimes was found. As the increasing of gas inlet velocity, the axial and radial solid particle dispersion coefficients increased and decreased, respectively. For the axial and radial gas dispersion coefficients, both of them were increased with the increasing of gas inlet velocity. At the near wall region, the transition flow had no obvious power spectrum peak except the one below 0.2Hz, while, at the center region, the maximum peak at 5.0Hz was found. All the velocities had no significant correlation with solid volume fraction. The solid particle–solid particle interaction or collision then governs the system characteristic. The transition flow between turbulent and fast fluidization regimes will be an alternative choice for applying with circulating fluidized bed reactor in other new physical and chemical processes. [Copyright &y& Elsevier]

The most common technology for postcombustion CO2 capture for existing power plants is the amine solvent scrubber. The energy consumption for capturing CO2 from flue gases using amine solvent technology is 15 to 30% of the power plant electricity production. Hence, there is a need to develop more efficient methods of removing CO2. Here, we show a novel design, obtained using multiphase CFD, and of a fluidized-bed reduced pressure regenerator, coupled with a fluidized-bed sorber, which has the potential to reduce the energy consumption. The undesirable core-annular flow regime in the riser-sorber is eliminated using multiple jet inlets and large particles leading to a shorter height. Up to 88% of the heat liberated in the riser-sorber is recovered in the downer-regenerator. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4519-4537, 2013 [ABSTRACT FROM AUTHOR]

Abstract: Many chemical processes, such as polysilicon production in fluidized beds, can be improved by elimination of bubbles. Theory suggests that this can be done using coarse particles in place of Geldart B particles used to-day. CFD simulations using a mixture of 3.5mm and 5mm glass beads show that in a large bed this coarse mixture fluidizes without bubble formation over a large range of gas velocities. Visual observations and measurements in a two-dimensional bed confirm this discovery. Both CFD computations and experiments in small diameter beds show that this mixture undergoes slugging, as expected for fluidization in small diameter beds. For B particles a bottom bubble-less layer is computed. [Copyright &y& Elsevier]

Second-order moment method of particles is proposed on the basis of the kinetic theory of granular flow. Closure equations for the third-order velocity moments are presented to account for the increase of the probability of collisions of particles on the basis of the elementary kinetic theory and order of magnitude analysis. The boundary conditions for the set of equations describing flow of particles are proposed with the consideration of the momentum exchange by collisions between the wall and the particles. The distributions of velocity, concentration and moments of particles are predicted. Simulated results are compared with experimental data measured by Tartan and Gidaspow and Bhusarapu et al. in risers, and Tsuji et al. in a vertical pipe. The effects of the closure equations for the third-order velocity moments and the fluid-particle velocity correlation tensor on flow behavior of particles are analyzed. © 2012 American Institute of Chemical Engineers AIChE J, 2012 [ABSTRACT FROM AUTHOR]

Abstract: A comprehensive understanding of turbulence and dispersion is essential for the efficient design of a conventional fluidized bed reactor. However, the available information is restricted to that in a two-dimensional (2-D) plane, because of the experimental and simulation limitations. It is, therefore, of importance to evaluate the remaining third dimension of the system and compare these results with the corresponding data obtained from the 2-D analysis for validation. In this study, computational fluid dynamics (CFD) based upon the kinetic theory of granular flow with a modified interphase exchange coefficient was successfully used to compute the system hydrodynamics of fluid catalytic cracking (FCC) particles in a thin bubbling fluidized bed with 2-D and three-dimensional (3-D) computational domains. In addition, the shortcoming of the current CFD model was evaluated. With respect to the bed height, the bed expansion ratio and solid volume fraction revealed similar results from both 2-D and 3-D computational domains. The turbulent granular temperature was higher than that of the laminar ones in the lower section of the bed while the laminar granular temperature dominates the system in the upper section. However, the granular temperatures obtained from the 3-D computational domain were slightly lower than that from the 2-D computational domain. The computation also showed that the dispersion coefficients are in good agreement with the literature measurements and so the 2-D computational domain can be used to simulate the bubbling fluidized bed system. Finally, all the evaluated system hydrodynamic values in the thin radial system direction were lower in the 3-D computational domain than in the thick radial system direction. [Copyright &y& Elsevier]

Abstract: Solids slugging phenomena were studied in a symmetric IIT riser using gamma ray densitometers. No core-annular regime was observed at high solids fluxes. Computations using the kinetic theory based IIT CFD code confirmed the elimination of the undesirable core-annular regime. The computer code was also used to calculate dispersion coefficients. The computed radially averaged total granular temperatures, axial and radial solids dispersion coefficients and axial gas dispersion coefficients agreed well with the literature. The −5/3 Kolmogorov energy spectrum law was followed at high frequencies. The dimensionless form of the spectral distribution showed good agreement with the Hinze correlation for single phase flow turbulence. The IIT CFD code computed high slip and anisotropy in the fluidized bed system. [ABSTRACT FROM AUTHOR]

Abstract: Conventional design of circulating fluidized beds requires the knowledge of dispersion and mass transfer coefficients, expressed in dimensionless forms as Sherwood numbers. However, these are known to vary by five or more orders of magnitude. Furthermore, the Sherwood numbers for fine particles reported in the literature are several orders of magnitude lower than the Sherwood number of two for diffusion to a single particle. We have shown that by replacing the particle diameter in the conventional Sherwood number with cluster or bubble diameter, the modified Sherwood number is again of the order of two. We have also shown that the kinetic theory based computational fluid dynamics codes correctly compute the dispersion and mass transfer coefficients. Hence, the kinetic theory based computational fluid dynamics codes can be used for fluidized bed reactor design without any such inputs. [Copyright &y& Elsevier]

Abstract: Multiphase kinetic theory has been generalized to include rotation of particles with unequal masses and diameters. Inelastic binary collisions of particles with normal and tangential restitution coefficients are considered. New expressions for number of binary collisions, viscosities and conductivities were developed. Collision integrals produced new expressions for energy dissipation involving tangential and normal restitution coefficients. Computed radial profiles of granular temperatures of 530 and 156μm glass beads flowing in a two story riser matched the experimentally measured profiles of granular temperatures using a particle image velocity technique without rotation. The measured and the computed particle concentration profiles were nearly flat in the central portion of the riser without rotation. Computations show that rotation can alter these profiles. Sufficient particle spin can drive the particles to concentrate near the center of the tube. [Copyright &y& Elsevier]

Abstract: The effect of electric field on the hydrodynamics of nanoparticles was studied in a fluidized rectangular bed, with electrodes attached to two parallel walls. It was shown that the electric field of the order of 3 times the gravity markedly decreased the bed expansion and increased the solids volume fraction of nanoparticles fluidized by air. In these experiments, a light diode assembly was utilized to infer the local solids volume fractions within a rectangular bed of 10 nm silica particles. These experimental measurements yielded a two dimensional solids volume fraction distribution within the rectangular bed. The experimental results provided some new insights into the distribution of solids within the bed. The agglomerate diameters were computed using a momentum balance with the drag given by the Ergun equation and the empirical Richardson–Zaki method. Both methods yielded agglomerate diameters of the order of 100 μm and showed dependence on the strength of the electric field. The electric field decreased the granular temperature of the nanoparticles. [Copyright &y& Elsevier]

Abstract: The knowledge of dispersion coefficients is essential for reliable design of gasifiers. However, a literature review had shown that dispersion coefficients in fluidized beds differ by more than five orders of magnitude. This study presents a comparison of the computed axial solids dispersion coefficients for cork particles to the NETL riser cork data. The turbulence properties, the Reynolds stresses, the granular temperature spectra and the radial and axial gas and solids dispersion coefficients are computed. The standard kinetic theory model described in Gidaspow''s 1994 book, Multiphase Flow and Fluidization, Academic Press and the IIT and Fluent codes were used to compute the measured axial solids volume fraction profiles for flow of cork particles in the NETL riser. The Johnson–Jackson boundary conditions were used. Standard drag correlations were used. This study shows that the computed solids volume fractions for the low flux flow are within the experimental error of those measured, using a two-dimensional model. At higher solids fluxes the simulated solids volume fractions are close to the experimental measurements, but deviate significantly at the top of the riser. This disagreement is due to use of simplified geometry in the two-dimensional simulation. There is a good agreement between the experiment and the three-dimensional simulation for a high flux condition. This study concludes that the axial and radial gas and solids dispersion coefficients in risers operating in the turbulent flow regime can be computed using a multiphase computational fluid dynamics model. [Copyright &y& Elsevier]

A literature review shows that dispersion coefficients in fluidized beds differ by more than five orders of magnitude. To understand the phenomena, two types of hydrodynamics models that compute turbulent and bubbling behavior were used to estimate radial and axial gas and solid dispersion coefficients. The autocorrelation technique was used to compute the dispersion coefficients from the respective computed turbulent gas and particle velocities. The computations show that the gas and the solid dispersion coefficients are close to each other in agreement with measurements. The simulations show that the radial dispersion coefficients in the riser are two to three orders of magnitude lower than the axial dispersion coefficients, but less than an order of magnitude lower for the bubbling bed at atmospheric pressure. The dispersion coefficients for the bubbling bed at 25atm are much higher than at atmospheric pressure due to the high bed expansion with smaller bubbles. The computed dispersion coefficients are in reasonable agreement with the experimental measurements reported over the last half century. [Copyright &y& Elsevier]

The speeds of motion of compression waves through a fluidized bed of 10 nm silica particles were determined by measuring the times of arrival of compression zones using a light probe. A correlation for the modulus of elasticity was determined as a function of void fraction. Using a kinetic theory type equation of state for particles, this experimentally determined modulus gives a value for the granular temperature for 10 nm particles of approximately one (meter per second) squared. This value is close to that obtained by assuming the motion of the 10 nm particles to be due to collision with air molecules with no energy dissipation. The values of the granular temperature were also determined in a two-dimensional (2-D) fluidized bed by measuring the volume fraction distributions of 10 nm silica particles. Granular temperatures were deduced from a one-dimensional particle momentum balance using an ideal equation of state for particles, which is similar to the barometric formula for gases. These granular temperatures agreed with the measurements obtained from wave propagation experiments. [ABSTRACT FROM AUTHOR]

Abstract: A new concept for production of electricity from biomass or coal using molten carbonate fuel cells is proposed. It involves feeding fine coal particles or biomass, for sustainable energy future, with steam into the anode compartment of the fuel cell in which the waste heat from the fuel cell is used to produce synthesis gas which reacts electrochemically. This concept is illustrated using carbon nanoparticles as the fuel. A computational fluid dynamics (CFD) model for the gasifier-fuel cell has been developed. Concentration, temperature and current density profiles have been computed. The computations show that practical current densities can be achieved. However, for the new concept to work well the carbon monoxide produced by the gasification should be allowed to react electrochemically. The computed temperature distributions for adiabatic operation show an initial drop in temperature due to gasification, followed by a rise which will have to be balanced by staggering the cells or by other means using the CFD design method. [Copyright &y& Elsevier]

Abstract: The turbulent fluidization regime is characterized by the co-existence of a dense, bottom region and a dilute, top bed. A kinetic theory based CFD code with a drag corrected for clusters captured the basic features of this flow regime: the dilute and dense regions, high dispersion coefficients and a strong anisotropy. The computed energy spectrum captures the observed gravity wave and the Kolmogorov law at high frequencies. The computed turbulent kinetic energy is close to the measurements for FCC particles. The CFD simulations compared reasonably well with the measured core-annular flow experiments at very high solid fluxes. The computed granular temperatures, solids pressures, FCC viscosities and frequencies of oscillations were close to measurements reported in the literature. The computations suggest that unlike for the flow of group B particles, the oscillations for the FCC particles in the center of the riser are primarily due to the oscillations of clusters and not due to oscillations of individual particles. Hence mixing is not on the level of individual particles. [Copyright &y& Elsevier]

Bubbles were simulated in a two-dimensional fluidized bed with a constant inlet velocity using two computer codes, the IIT code and the MFIX code. The computational results were compared to the Jung et al. (2005) experiments in a thin bubbling bed of 530 µm glass beads. The use of higher order numerics produces better bubble resolution due to smaller numerical diffusion. The computed bubble sizes and their distributions agreed with the experiments. The simulations show that there is no bubble formation for sufficiently elastic particles. CFD computations and previous experiments show that in the bubbling fluidized beds there exist two random oscillations. The first kind is due to random oscillations of particles and is measured by the conventional granular temperature. The second one is due to motion of bubbles and gives rise to Reynolds type stresses. It is shown that the particle granular temperature is much smaller than the bubble-like granular temperature computed from the average of the normal Reynolds stresses, measured by Cody using a shot noise technique. [ABSTRACT FROM AUTHOR]

Abstract: Flow properties of 10 nm silica particles were determined in a two-story circulating fluidized bed riser. The pressure drop has a minimum at a velocity of 0.3 m/s. Particle concentrations were measured with a gamma ray densitometer. The solid fluxes were measured with a suction probe. From these measurements the nanoparticle viscosity was estimated. The measured viscosity is close to an estimate obtained from kinetic theory, assuming Brownian motion of nanoparticles. The viscosity and the previously measured solid stress modulus were used in a multiphase CFD code to study the behavior of explosive dissemination of mixtures of nanoparticles and micron size particles. The dissemination process was divided into two steps: early-time hydrodynamics and dissemination into an atmosphere. In the early-time hydrodynamic step the particles were accelerated by means of a high pressure and high temperature gas from a plastic explosive. When the device containing the particles broke, the early-time hydrodynamic velocities, concentrations, pressure and temperatures were used as the initial conditions for the dissemination step. This study shows how to use CFD to design a dissemination device that will prevent the overheating of a mixture of particles to be disseminated. The computed phenomena were similar to the experimental observations. The nanoparticles formed a cloud with a vortex ring structure for dissemination of small micron size particles and nanoparticles. For the dissemination of 100 μm aluminum and 10 nm silica particles, there was no vortex ring structure. As expected, the larger particles settled on the ground. The computed ground concentrations can be used to compare the model with observations, such as the covering of ground by dust after volcanic eruptions. [Copyright &y& Elsevier]

Detailed experimental velocity, particle concentration, and stresses for flow of particles in a vertical pipe, riser are needed for verification of various CFD models for multiphase flow. This is the principle-unsolved task of the Fluid Dynamics Multiphase Flow Consortium, organized by Dow Chemical Company. This study provides such information for flow of 530 µm glass beads in the fully developed flow region of a 7 m symmetric riser with a splash plate. Instantaneous particle-velocity distributions were obtained using a particle velocity imaging technique, and a probe inserted into the riser, while the particle concentrations were measured with a gamma-ray densitometer. Time-averaged particle-velocity distributions can be well represented by a parabolic- velocity distribution, with the mean velocity obtained from flux divided trations were measured with a gamma-ray densitometer. Time-averaged paby the measured bulk density. The flow is very anisotropic. The radial granular temperature ptofiles agreew ith an analytical expression similra to the thermal-temperature distribution in Poiseuille flow with viscous heat generation. A numerical solution for the standard isotropic model developed shows that the approximations made in the analytical solutions are reasonable. In the core, the normal Reynolds stresses are much smaller than the velocity averaged particle stresses, whereas near the wall the time averaged normal Reynolds stresses are large. [ABSTRACT FROM AUTHOR]

Abstract: The design of circulating fluidized bed systems requires the knowledge of mass transfer coefficients or Sherwood numbers. A literature review shows that these parameters in fluidized beds differ up to seven orders of magnitude. To understand the phenomena, a kinetic theory based computation was used to simulate the PSRI challenge problem I data for flow of FCC particles in a riser, with an addition of an ozone decomposition reaction. The mass transfer coefficients and the Sherwood numbers were computed using the concept of additive resistances. The Sherwood number is of the order of 4×10−3 and the mass transfer coefficient is of the order of 2×10−3 m/s, in agreement with the measured data for fluidization of small particles and the estimated values from the particle cluster diameter in part one of this paper. The Sherwood number is high near the inlet section, then decreases to a constant value with the height of the riser. The Sherwood number also varies slightly with the reaction rate constant. The conventionally computed Sherwood number measures the radial distribution of concentration caused by the fluidized bed hydrodynamics, not the diffusional resistance between the bulk and the particle surface concentration. Hence, the extremely low literature Sherwood numbers for fluidization of fine particles do not necessarily imply very poor mass transfer. [Copyright &y& Elsevier]

Abstract: The PSRI benchmark challenge problem one is modeled using kinetic theory based CFD with the energy minimization multi-scale (EMMS) drag law. These computations give a better comparison than the previous models to measured solids mass flux, solids density and pressure drop. The computer model was also used to calculate axial and radial normal Reynolds stresses, energy spectra, power spectra, granular temperatures, the FCC viscosity and axial and radial dispersion coefficients. The computed cluster sizes agreed with the published empirical correlations. Then, the mass transfer coefficients and the Sherwood numbers are estimated based on particle cluster sizes. The conventional Sherwood number is scaled with the particle cluster diameter. The Sherwood number is the order of and the mass transfer coefficient is the order of . This Sherwood number is two orders of magnitude smaller than the diffusion controlled limit of two based on particle diameter, in agreement with the experimental data for fluidization of fine particles. [Copyright &y& Elsevier]

The fluidization behavior of binary mixture differing in size in the gas bubbling fluidized bed is experimentally and theoretically studied. The segregation phenomena are analyzed, and the relevancy of the pressure drop profile of binary mixture to the definition of its minimum fluidization velocity is discussed. The distributions of mass fraction of particles along the bed height are measured, and the profiles of the mean particle diameters of binary mixture are determined. A multi-fluid gas–solid flow model is presented where equations are derived from the kinetic theory of granular flows. Separate transport equations are constructed for each of the particle class, allowing for the interaction between size classes, as well as the momentum and energy are exchanged between the respective classes and the carrier gas. The segregations of the mean diameter are predicted. The numerical results are analyzed and compared with experimental data. [Copyright &y& Elsevier]

Abstract: Cluster structures affect macroscopic hydrodynamic behavior in gas–solid risers. The moment and energy balances for the dense phase and dilute phase are presented by the multi-scale resolution approach to investigate the dependence of drag coefficient on structure parameters. The modified model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD). Unlike previous works on CSD drag coefficient model, the modified CSD drag model takes wall friction into account. The closure for the drag coefficient depends not only on flow behavior of gas and particles but also on the wall friction. The structure-dependent drag coefficients calculated from the approach of the minimization of energy dissipation by drag force are then incorporated into the two-fluid model to simulate the behavior of gas–solid flow in a riser. The distributions of concentration and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature. The effect of the wall friction on flow behavior of particles is analyzed. [Copyright &y& Elsevier]

Abstract: In this study, the effects of various modeling parameters were explored and summarized in the circulating fluidized bed downer. They are specularity coefficient, restitution coefficient between solid particle and wall, restitution coefficient between solid particles, interphase exchange or drag coefficient model, inlet granular temperature and inlet configuration. The downer of circulating fluidized bed was then successfully simulated using computational fluid dynamics model with the Eulerian approach, the kinetic theory of granular flow and the best fitted modeling parameters. The computations gave a close comparison of the solid volume fraction, solid mass flux and system gauge pressure with three different experimental conditions. Finally, the obtained computational fluid dynamics model was applied to calculate the system hydrodynamic characteristics and the system turbulent properties, which are the solid volume fraction, the axial solid velocity, the radial solid velocity, the power spectrum, the normal Reynolds stresses, the turbulent kinetic energy, the granular temperature and the energy spectrum. These calculated results can be used as an explanation for the in-depth system flow structure in the downer system. [Copyright &y& Elsevier]

Abstract: Flow behavior of gas and solids is simulated in combination the gas–solid two-fluid model with a cluster structure-dependent (CSD) drag coefficient model. The dispersed phase is modeled by a Eulerian approach based upon the kinetic theory of granular flow (KTGF) including models for describing the dispersed phase interactions with the continuous phase. The drag forces of gas–solid phases are predicted from the local structure parameters of the dense and dilute phases based on the minimization of the energy consumed by heterogeneous drag. The cluster structure-dependent (CSD) drag coefficients are incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. Simulation results indicate that the dynamic formation and dissolution of clusters can be captured with the cluster structure-dependent drag coefficient model. Simulated solid velocity and concentration of particles profiles are in reasonable agreement with experimental results. [Copyright &y& Elsevier]

Abstract: Flow behavior of gas and agglomerates is numerically investigated in fluidized beds using a transient two-fluid model. It is assumed that the particles move as agglomerates rather than single particles in the gas–cohesive particles fluidized beds. The present model is coupled a modified kinetic theory model proposed by with an agglomerate-based approach (ABA). The interaction between gas and agglomerates is considered. The agglomerates properties are estimated from the ABA. Predictions are compared with experimental data measured by in a bubbling fluidized bed and in a circulating fluidized bed. The distributions of velocity, concentration and diameter of agglomerates, and pressure drop are numerically obtained. The influences of the contact bonding energy on the distributions of velocity and concentration of agglomerates are analyzed. [Copyright &y& Elsevier]

Abstract: The fluidization behavior of rice husk–sand mixture in the gas bubbling fluidized bed is experimentally and theoretically studied. The relevancy of the pressure drop profile of rice husk–sand mixture to the definition of its minimum fluidization velocity is discussed, and the minimum fluidization velocity of rice husk–sand binary mixture is determined. The distributions of mass fraction of rice husk particles along the bed height are measured, and the profiles of the mean particle diameter of mixture are determined. A multi-fluid gas–solid flow model is presented where equations are derived from the kinetic theory of granular flow. Separate transport equations are constructed for each of the particle classes, allowing for the interaction between particle classes, as well as the momentum and energy are exchanged between the respective classes and the carrier gas. The distributions of the mass fraction of rice husk particles and the mean particle diameter of binary mixture are predicted. The numerical results are analyzed, and compared with experimental data. [Copyright &y& Elsevier]

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). [Copyright &y& Elsevier]