Modeling of cluster structure-dependent drag with Eulerian approach for circulating fluidized beds

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.     

Fluid dynamic simulation in a chemical looping combustion with two interconnected fluidized beds

Flow behavior of gas and particles is simulated in a 2-D chemical-looping combustion (CLC) process with two interconnected fluidized beds. A Eulerian continuum two-fluid model is applied for both the gas phase and the solid phase. Gas turbulence is modeled by using a k-ε turbulent model. 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. Instantaneous and local velocity, concentration of particles and granular temperature are obtained. Predicted time-averaged particle concentrations and velocities reflect the classical core-annular flow structure in the air reactor. Flow behavior of bubbles is predicted in the fuel reactor and pot-seal. Computed leakage qualitatively agrees with experimental data in the fuel reactor and pot-seal.     

A particle-to-particle heat transfer model for dense gas-solid fluidized bed of binary mixture

A particle-to-particle collisional heat transfer model in the frame of Eulerian-Eulerian approach was proposed in this paper. By incorporating it into the multi-fluid model to close the enthalpy equations, the heat transfer between different particle classes in a gas bubbling fluidized bed of binary mixture was investigated, based on the CFD simulations of particle mixing in literature (Cooper and Coronella, 2005). The results showed that the particle-to-particle heat exchange coefficient between different particle classes increases with increasing the size of large particle class and the superficial gas velocity. The ratios of the particle-to-particle heat transfer to the gas-to-particle heat transfer range from 8.04% to 15.0% for various calculating conditions. In order to better understand the heat transfer behavior in a dense gas-solid fluidized of binary mixture, it is important to take the particle-to-particle heat transfer into account.     

Simplified model for calculation of devolatilization in fluidized beds

A devolatilization model based on simplification of the earlier model has been developed for fluidized bed conditions. It is simple and computationally fast enough to be incorporated as a submodel into a CFD code, but accurate enough to be suitable for different fuels including biomass with varying particle size, moisture, reactivity and shape. In this new model, the partial differential equation describing heat and mass transfer inside the particle is approximately converted to two differential equations. Drying is described to take place on a shrinking core and pyrolysis, which can take place simultaneously with drying, is described to take place at a specific “characteristic pyrolysis temperature”. The dependence of this temperature on parameters for the kinetics of pyrolysis, bed temperature and particle size can be determined. The model can be extended to include the case, where pyrolysis is considered to consist of parallel reactions of different components.     

Volume contraction behaviour of binary solid-liquid fluidized beds

Contrary to the widely held notion that the total bed height of a binary solid fluidized bed will be the sum of heights of the two individual mono-component beds fluidized at the same velocity, significant negative deviations have been observed in our experimental investigation. The negative deviations, signifying a contraction of the total volume of the binary solid fluidized bed, could sometimes be as high as 25% of the actual volume. The volume contraction has been found to depend mainly upon the degree of solids mixing prevailing in the bed irrespective of whether it is fully fluidized or not. The composition of the binary solid fluidized was another important factor that influenced the contraction behaviour of the bed besides the size ratio of the two constituent solid species of the binary present in the bed.     

On the effect of cluster resolution in riser flows on momentum and reaction kinetic interaction

Fine grid simulations of reactive gas-solid flows in a riser were carried out using an Eulerian multi-fluid kinetic theory of granular flow (KTGF) approach. A translationally periodic section of the riser was used to replicate experimental data collected in the fully developed region of a tall riser. The spatial and temporal resolution was varied in designed experiments to find an appropriate compromise between overall numerical accuracy and computational time. Results revealed that, when first order implicit timestepping is used, no timestep independence could be reached with timestep sizes that are practically feasible. Timestep independence could only be achieved by using second order implicit timestepping. Grid independence was studied in terms of cell width and cell aspect ratio. Solution independence could be reached at a cell width in the range of 10 particle diameters, but no complete grid aspect ratio independence could be achieved. Results suggested that grids with an aspect ratio smaller than one might be necessary to attain grid independent solutions. When sufficiently fine grids are used, however, the effect of a change in aspect ratio is sufficiently small to attain accurate solutions with an aspect ratio of two or lower. Certain important conversion measures were identified for scaling between simulation results collected in a 3D cylindrical domain and those predicted by a 2D planar simulation. System behavior predicted using these scaling rules agreed well with experimental results.     

A revised mono-dimensional particle bed model for fluidized beds

The formulation of the equations of change proposed by Foscolo and Gibilaro in their original mono-dimensional particle bed model (PBM) for the prediction of the fluid-bed stability of Geldart's group A powders has been revisited along with the relevant closure relationships. The buoyancy has been expressed in accordance with its “classical” definition, which regards it as being equal to the weight of the fluidizing fluid displaced by the particle phase. A new constitutive equation has been developed for the drag force; this proves more accurate than the expression used in the original PMB particularly in the intermediate flow regimes comprised between the viscous and inertial ones. The “elastic” force has been estimated by employing a rigorous approach which needs not resort to equilibrium-based relations. The result, enhanced in accuracy and breadth of validity, considers “elastic” force and drag force proportional. The equations of change themselves have been partly revised. The pressure gradient is no longer shared by the two phases in proportion to their volume fractions, but has been accounted for only in the continuous one. Conversely, the “elastic” force has been included, with opposite signs, in the linear momentum equations pertaining to both phases, so that the principle of action and reaction, to which the force is subjected, is fulfilled. The revised model has been validated by performing a fluid-bed stability analysis on a wide range of Geldart's group A powders at different operating temperatures. Predicted values for the minimum bubbling voidage estimated by means of the revised model have been compared with experimental values and with predictions from both the original Foscolo and Gibilaro model and that previously revised by Jean and Fan. The latter has been found to be always in good agreement with the model proposed here, whereas the former has seemed to somewhat underestimate the bed minimum bubbling voidage thus anticipating the transition between homogeneous and bubbling fluidization. All of the models have proved to yield predictions whose validity is strongly dependent on the particular powder in hand and on the operating conditions considered.     

Segregation in polydisperse fluidized beds: Validation of a multi-fluid model

In many industrial-scale fluidized-bed reactors, particle mixing and segregation play an important role in determining reactor performance. Detailed information about the particle size distribution (PSD) throughout the bed at different operating conditions is crucial for design and scale up of practical systems. In this work, a multi-fluid model based on the Euler-Euler approach and the direct quadrature method of moments (DQMOM) is used to describe particle segregation, and the model predictions are validated with available experimental and simulation data. For binary mixtures, multi-fluid simulations are compared with digital image analysis experiments for beds of glass beads. By properly defining the solid-solid drag force, the multi-fluid model can reproduce the segregation rate found experimentally for different flow conditions with binary mixtures. Segregation phenomena in gas-solid fluidized beds with a continuous PSD are also investigated. Here, the multi-fluid simulations are compared with discrete particle simulations (DPS). Using the moments of the PSD from DPS, the weights and abscissas used in DQMOM are initialized in the multi-fluid model. The segregation rate and the local moments of the PSD predicted by the multi-fluid model are compared to the DPS results. The dependence of the results on the number of DQMOM nodes is also investigated.     

Hydrodynamic modelling of binary mixture in a gas bubbling fluidized bed using the kinetic theory of granular flow

A multi-fluid Eularian CFD model with closure relationships according to the kinetic theory of granular flow has been applied to study the motions of particles in the gas bubbling fluidized bed with the binary mixtures. The mutual interactions between the gas and particles and the collisions among particles were taken into account. Simulated results shown that the hydrodynamics of gas bubbling fluidized bed related with the distribution of particle sizes and the amount of energy dissipated in particle-particle interaction. In order to obtain realistic bed dynamics from fundamental hydrodynamic models, it is important to correctly take the effect of particle size distribution and energy dissipation due to non-ideal particle-particle interactions into account.     

Development of a multi-fluid model for poly-disperse dense gas-solid fluidised beds, Part II: Segregation in binary particle mixtures

Particle mixing and segregation rates in a bi-disperse freely bubbling fluidised bed have been studied with a new multi-fluid model (MFM) based on the kinetic theory of granular flow for multi-component systems (see Part I). The MFM simulation results have been compared with digital image analysis experiments obtained by Goldschmidt et al. [2003. Digital image analysis of bed expansion in dense gas-fluidised beds. Powder Technology 138, 135-159] for bi-disperse mixtures of glass beads. In strong contrast to MFMs previously described in the literature, that strongly overestimate the segregation rates, the new MFM seems to underestimate the segregation rates at longer times. This underprediction of the segregation rate is probably related to the neglect of frictional stresses associated with long-term multiple-particle contacts resulting in an overestimation of the mobility of the emulsion phase, which is corroborated by discrete particle simulations without friction between the particles and the particles and the wall. The level of the granular temperature of the segregating system, as computed with the new MFM, compares reasonably well with the granular temperatures found in the DPM simulation.     

Dynamic characteristics of binary mixtures in a two-jet fluidized bed

Aiming to understand biomass-related pyrolysis and gasification processes, which have received particular interests recently due to increasing concerns over fossil fuels and carbon emissions, this work conducts a detailed experimental study of the fluidization characteristics and jet dynamics of biomass mixtures in a fluidized bed. Both single jet and two jets dynamics are investigated, and a parametric study of the influence of particle properties and operational conditions on the dynamic performance of the bed, especially on the jet penetration depth and jet frequency of the binary mixtures, is conducted. Detailed frame-by-frame image analysis coupled with physical parameters reveals many interesting phenomena, which includes multistage flow pattern development and a stochastic nature of jet dynamics, as well as a strong dependence of the jet penetration depth and jet frequency on the bed materials.     

Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds

This paper discusses the simulation of bubbling gas-solid flows by using the Eulerian two-fluid approach. Predictions of particle motion, bed expansion, bubble size and bubble velocity in bubbling beds containing Geldart B particles are compared with experimental results and correlations found in the literature. In addition, gas mixing in a bed of Geldart A particles is investigated.An in-house code has been developed based on the finite-volume method and the time-splitting approach using a staggered grid arrangement. The velocities in both phases are obtained by solving the 2D Reynolds-averaged Navier/Stokes equations using a partial elimination algorithm (PEA) and a coupled solver. The k-ε turbulence model is used to describe the turbulent quantities in the continuous phase.In general, the model predictions are in good agreement with experimental data found in the literature. Most important observations are: the level of the restitution coefficient was found to be crucial in order to obtain successful results from 2D axisymmetric simulations of a system containing Geldart B particles. Bubble size and bubble rise velocities are not as sensitive to the restitution coefficient. The turbulence model is of outmost importance concerning gas mixing in a fluidized bed of Geldart A particles.From these numerical analyzes an optimized granular flow two-fluid model can be designed for the purpose of simulating reactive systems in fluidized bed reactors.     

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.     

Computational study of pressure-drop hysteresis in fluidized beds

Cohesive forces are implemented in a discrete-particle fluidized bed simulation using both a square-well potential and a Hamaker model for van der Waals forces. This simulation is used as a tool to gain greater understanding of the hysteresis behavior that has been observed experimentally during fluidization-defluidization cycles. For the parameters investigated, the results show that cohesive forces are significant in the pressure overshoot observed during the fluidization process. Furthermore, the mechanisms by which the specific cohesive mechanisms causing the pressure overshoot are different depending on the cohesion model being used. Although both models indicate that particle-particle cohesion dominates the overshoot, the square-well model predicts that cohesive interactions between particles and distributor plate also play a role, while the Hamaker model for van der Waals forces predicts that particle-sidewall friction may be enhanced by the presence of cohesion. The results are in accordance with a one-dimensional force balance on the system, and provide alternative explanations for trends in existing datasets.     

Investigation and scale-up of hot-melt coating of pharmaceuticals in fluidized beds

This study was performed to investigate and scale-up the hot-melt coating process in fluidized beds. A series of well-designed experiments was carried out in a pilot scale unit with 20 kg product capacity to investigate the effects of process variables on the efficiency of the coating of Cefuroxime Axetil with stearic acid. Results showed that the efficiency is at the highest when the fluidization air flow rate is adjusted by considering the changes in the amount of materials present in the unit as well as the changes in the terminal velocities of particles during the process.With the objective to scale-up the hot-melt coating process from pilot to production scale, a dynamic thermodynamic model based on conservation equations of mass and energy was developed. Predictive accuracy of the model was assessed by applying it to the pilot scale unit and comparing its predictions with the online measurements taken on the same unit. Results showed that the predictions of the model agree well with the measurements. Utilizing this model and taking several experiments performed in the pilot scale unit as a basis, scaling up of the hot-melt coating process was carried out. Comparisons of the model predictions with the measurements taken on the production scale unit (200 kg product capacity) revealed that the model is able to reproduce the product attributes and the outlet air temperatures across scales. Therefore, it proves to be a promising tool that can be used in the scale-up of the hot-melt coating processes in fluidized beds.     

A new model for ejected particle velocity from erupting bubbles in 2-D fluidized beds

A new model is proposed for obtaining the velocity profile of the particle ejected from the bubble dome in a freely bubbling 2-D fluidized bed. Its basis is the supposition that the initial velocity of the ejected particles, with a direction perpendicular to the dome contour, depends on bubble velocity and bubble growth velocity. This model differs from those previously appearing in the literature in that it is valid not only for vertical-ascent circular bubbles.Experiments were carried out in a freely bubbling 2-D fluidized bed using a high-speed video camera to measure the velocity profile. Upon comparing these results with the proposed model, it was established that, excepting some isolated cases, the model properly predicts the magnitude and direction of the maximum particle ejection velocity and the velocity profile.Using the work of Shen et al. (2004. Digital image analysis of hydrodynamics two-dimensional bubbling fluidized beds. Chemical Engineering Science 59, 2607-2617), we obtain two general equations for the bubble velocity and the bubble growth velocity in a 2-D fluidized bed. These expressions, together with the proposed model, can be used to calculate the initial velocity of the ejected particles.     

New closure models for CFD modeling of high-density circulating fluidized beds

Experimental results from a high-density circulating fluidized bed (CFB) riser have been used to develop new closure models for the drag coefficient and the gas-solid mixture viscosity. The models predict a rapid increase in both viscosity and drag associated with the high solids concentrations near the riser wall. These new models have been incorporated into the commercial Computational Fluid Dynamics software FLUENT and the predictions of FLUENT have been compared with experimental data from the literature. With the inclusion of the new closure models, FLUENT was able to predict the radial distribution of solids concentration and solids mass flux found experimentally in three different cold-flow CFB risers operated at solids mass fluxes between 148 kg/m²·s and 455 kg/m²·s and superficial gas velocities between 4.7 and 10 m/s. These conditions lead to average solid concentrations in excess of 10 vol%, which corresponds to high-density CFB operation.     

Granular pressure and particle velocity fluctuations prediction in liquid fluidized beds

A numerical modelling approach for the dynamic simulation of solid-liquid fluidized beds is evaluated. This approach is based on an Eulerian two-fluid formulation of the transport equations for mass, momentum and fluctuating kinetic energy. The solid-phase fluctuating motion model is derived in the frame of granular medium kinetic theory accounting for the viscous drag influence of the interstitial liquid phase. Solid-liquid fluidized bed two-dimensional simulations were performed for flow configurations taken from the experimental work of Zenit et al. [1997. Collisional particle pressure measurements in solid-liquid flows. Journal of Fluid Mechanics 353, 261-283], for three types of solid particles of contrasted inertia in water at high particle Reynolds number (nylon, glass and steel beads). Experimental and numerical granular pressures exhibit a satisfactory agreement with both low and high inertia particles, the best level of prediction being observed with the most inertial particles. Sensitivity of the predictions to the phenomenological laws used in the model is also presented and it appears that, due to non-linear correlations, the average granular pressure in the bed is a less sensitive variable than the fluctuating kinetic energy (or granular temperature). The transport mechanisms of the mean granular temperature in the bed are therefore analyzed as a function of the solid fraction and the particle inertia. At low and moderate Stokes number (nylon and glass beads) and in all range of solid-phase fraction, the dominant production mechanism of fluctuating kinetic energy is due to the mean velocity gradient, whereas the main dissipation term is that induced by the viscous drag. At higher Stokes number (steel beads) and concentration, the production of the granular temperature is controlled by the compressibility effects via the granular pressure. In this case, the dissipation is mainly provided by inter-particle collisions.