Drag Force (drag + force)

Distribution by Scientific Domains


Selected Abstracts


Collective Grain Interactions II.

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 8 2005
Non-linear Collective Drag Force
Abstract It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges , = Zde2a /Ti,Di , 1 and Ti /Te , 1 (,eZd being the grain charge in units of electron charge, a being the grain size, ,Di being the ion Debye radius and Te,i being electron and ion temperatures, respectively). For present dusty plasma experiments , , 10,50, the large charges of grains are screened non-linearly and the ion scattering creates non-linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non-linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non-linear screening at non-linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non-linear drag force caused by scattering inside the non-linear screening radius or even larger. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


Coupled seepage and stress fields in roller compacted concrete dam

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2005
Chai Junrui
Abstract Based on the characteristic of seepage through layered roller compacted concrete dam (RCCD), the interaction between seepage and stress in RCCD is analysed and the mathematical model for coupled seepage and stress fields in RCCD is proposed. The flow through layers in RCCD exerts normal seepage pressure and tangent drag force on the dam body. The equivalent crack openings of layers vary with the stress conditions. The coupled model is established by these relationships. The coupled model is also applied to the Longtan RCCD project by means of the finite element method and the interative solution. It can be concluded from the computation results that the coupling effect makes the stress components larger and the stress concentration near the dam heel more obvious. Copyright © 2004 John Wiley & Sons, Ltd. [source]


The effect of column diameter and bed height on minimum fluidization velocity

AICHE JOURNAL, Issue 9 2010
Akhil Rao
Abstract Experiments show that the minimum fluidization velocity of particles increases as the diameter of the fluidization column is reduced, or if the height of the bed is increased. These trends are shown to be due to the influence of the wall. A new, semicorrelated model is proposed, which incorporates Janssen's wall effects in the calculation of the minimum fluidization velocity. The wall friction opposes not only the bed weight but also the drag force acting on the particles during fluidization. The enhanced wall friction leads to an increase in the minimum fluidization velocity. The model predictions compare favorably to existing correlations and experimental data. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source]


A CFD,PBM coupled model for gas,liquid flows

AICHE JOURNAL, Issue 1 2006
Tiefeng Wang
Abstract A computational fluid dynamics,population balance model (CFD-PBM) coupled model was developed that combines the advantages of CFD to calculate the entire flow field and of the PBM to calculate the local bubble size distribution. Bubble coalescence and breakup were taken into account to determine the evolution of the bubble size. Different bubble breakup and coalescence models were compared. An algorithm was proposed for computing the parameters based on the bubble size distribution, including the drag force, transverse lift force, wall lubrication force, turbulent dispersion force, and bubble-induced turbulence. With the bubble breakup and coalescence models and the interphase force formulations in this work, the CFD-PBM coupled model can give a unified description for both the homogeneous and the heterogeneous regimes. Good agreement was obtained with the experimental results for the gas holdup, liquid velocity, and bubble size distribution. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source]


Effect of filament drawdown on aerodynamic drag and heat transfer in fiber spinning

AICHE JOURNAL, Issue 5 2004
C. Miller
Abstract The momentum and thermal boundary layer equations are solved numerically to assess the effects of filament drawdown on aerodynamic drag and heat transfer in melt fiber spinning. It is found that, relative to the case without drawdown (constant filament velocity and diameter), the aerodynamic drag on the filament increases substantially, but the heat transfer rate is suppressed. Moreover, the air velocity profile eventually becomes fully developed (unlike the zero drawdown case), and the (velocity) boundary layer thickness, rather than continuing to grow with distance beneath the spinneret, eventually becomes proportional to the filament diameter, and thus decreases with increasing axial distance. Quantitative results are presented for the dimensionless drag force per unit length along the filament (the Drag number) and the Nusselt number as functions of the dimensionless axial distance and a new dimensionless parameter, the Drawdown Reynolds number. © 2004 American Institute of Chemical Engineers AIChE J, 50: 898,905, 2004 [source]


Instabilities in two-fluid magnetized media with inter-component drift

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2002
P. V. Tytarenko
Abstract We analyse the stability of a magnetized medium consisting of a neutral fluid and a fluid of charged particles, coupled to each other through a drag force and exposed to differential body forces (for example, as the result of radiation forces on one phase). We consider a uniform equilibrium and simple model input physics, but do not arbitrarily restrict the relative orientations of the magnetic field, slip velocity and wavevector of the disturbance. We find several instabilities and classify these in terms of wave resonances. We briefly apply our results to the structure of SiO maser regions appearing in the winds from late-type stars. [source]


CFD simulation of gas,solid bubbling fluidized bed: A new method for adjusting drag law

THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 1 2009
Farshid Vejahati
Abstract In computational fluid dynamics modelling of gas,solid two phase flow, drag force is one of the dominant mechanisms for interphase momentum transfer. Despite the profusion of drag models, none of the available drag functions gives accurate results in their own original form. In this work the drag correlations of Syamlal and O'Brien (Syamlal and O'Brien, Int. J. Multiphase Flow. 1988; 14(4):473,481), Gidaspow (Gidaspow, Appl. Mech. Rev. 1986; 39:1,23), Wen and Yu (Wen and Yu, Chem. Eng. Prog. Symp. Ser. 1966; 62(2):100,111), Arastoopour et al. (Arastoopour et al., Powder Technol. 1990; 62(2): 163,170), Gibilaro et al. (Gibilaro et al., Chem. Eng. Sci. 1985; 40:1817,1823), Di Felice (Di Felice, Int. J. Multiphase Flow. 1994; 20(1):153,159), Zhang-Reese (Zhang and Reese, Chem. Eng. Sci. 2003; 58(8):1641,1644) and Hill et al. (Hill et al., J. Fluid Mech. 2001; 448:243,278) are reviewed using a multi-fluid model of FLUENT V6.3.26 (FLUENT, 2007. Fluent 6.3 User's Guide, 23.5 Eulerian Model, Fluent, Inc.) software with the resulting hydrodynamics parameters being compared with experimental data. The main contribution of this work is to propose an easy to implement and efficient method for adjustment of Di Felice drag law which is more efficient compared to the one proposed by Syamlal-O'Brien. The new method adopted in this work showed a quantitative improvement compared to the adjusted drag model of Syamlal-O'Brien. Prediction of bed expansion and pressure drop showed excellent agreement with results of experiments conducted in a Plexiglas fluidized bed. A mesh size sensitivity analysis with varied interval spacing showed that mesh interval spacing with 18 times the particle diameter and using higher order discretization methods produces acceptable results. Dans la modélisation par la dynamique des fluides par ordinateur de l'écoulement diphasique gaz-solide, la force de traînée est l'un des mécanismes dominants dans le transfert de quantité de mouvement interphase. Malgré la profusion des modèles de traînée, aucune des fonctions de traînée disponibles ne donnent de résultats précis dans leur forme originale. Dans cet article, les corrélations de traînée de Syamlal and O'Brien (Syamlal and O'Brien, Int. J. Multiphase Flow. 1988; 14(4):473,481), Gidaspow (Gidaspow, Appl. Mech. Rev. 1986; 39:1,23), Wen and Yu (Wen and Yu, Chem. Eng. Prog. Symp. Ser. 1966; 62(2):100,111), Arastoopour et al. (Arastoopour et al., Powder Technol. 1990; 62(2):163,170), Gibilaro et al. (Gibilaro et al., Chem. Eng. Sci. 1985; 40:1817,1823), Di Felice (Di Felice, Int. J. Multiphase Flow. 1994; 20(1):153,159), Zhang-Reese (Zhang and Reese, Chem. Eng. Sci. 2003; 58(8):1641,1644) et Hill et al. (Hill et al., J. Fluid Mech. 2001; 448:243,278) sont examinées à l'aide du modèle multi-fluides du logiciel FLUENT V6.3.26 (FLUENT, 2007. Fluent 6.3 User's Guide, 23.5 Eulerian Model, Fluent, Inc.), les paramètres hydrodynamiques résultants étant comparés aux données expérimentales. La principale contribution de ce travail est de proposer une méthode efficace et facile à mettre en ,uvre pour l'ajustement de la loi de traînée de Di Felice qui est plus efficace comparativement à celle proposée par Syamlal-O'Brien. La nouvelle méthode adoptée dans ce travail montre une amélioration quantitative par rapport au modèle de traînée ajusté de Syamlal-O'Brien. La prédiction de l'expansion de lit et de la perte de charge montre un excellent accord avec les résultats des expériences menées dans un lit fluidisé en plexiglass. Une analyse de sensibilité de la taille des mailles avec des mailles de taille variable variés montre qu'une taille de maille égale à 18 fois le diamètre des particules et l'utilisation de méthodes de discrétisation d'ordre supérieur donnent des résultats acceptables. [source]


Analytical models for the mean flow inside dense canopies on gentle hilly terrain

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008
D. Poggi
Abstract Simplifications and scaling arguments employed in analytical models that link topographic variations to mean velocity perturbations within dense canopies are explored using laboratory experiments. Laser Doppler anemometry (LDA) measurements are conducted in a neutrally-stratified boundary-layer flow within a large recirculating flume over a train of gentle hills covered by a dense canopy. The hill and canopy configuration are such that the mean hill slope is small and the hill is narrow in relation to the canopy (H/L , 1 and Lc/L , 1, where H is the hill height, L the half-length, and Lc the canopy adjustment length-scale). The LDA data suggest that the often-criticized linearizations of the advective terms, turbulent-shear-stress gradients and drag force appear reasonable except in the deep layers of the canopy. As predicted by a previous analytical model, the LDA data reveal a recirculation region within the lower canopy on the lee slope. Adjusting the outer-layer pressure perturbations by a virtual ground that accounts for the mean streamline distortions induced by this recirculation zone improves this model's performance. For the velocity perturbations in the deeper layers of the canopy, a new analytical model, which retains a balance between mean horizontal advection, mean pressure gradient and mean drag force but neglects the turbulent-shear-stress gradient, is developed. The proposed model reproduces the LDA measurements better than the earlier analytical model, which neglected advection but retained the turbulent-shear-stress gradient in the lower layers of the canopy and near the hill top. This finding is consistent with the fact that the earlier model was derived for tall hills in which advection inside the canopy remains small. In essence, the newly-proposed model for the narrow hill studied here assumes that in the deeper layers of the canopy the spatial features of the mean flow perturbations around their background state can be approximated by the inviscid mean-momentum equation. We briefly discuss how to integrate all these findings with recent advances in canopy lidar remote-sensing measurements of general topography and canopy height. Copyright © 2008 Royal Meteorological Society [source]


A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 620 2006
M. A. C. Teixeira
Abstract An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, ,, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on , and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one. Copyright © 2006 Royal Meteorological Society [source]


The effect of rotation on the pressure drag force produced by flow around long mountain ridges

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 608 2005
Helen Wells
Abstract The impact of rotation on the orographic drag experienced by air flowing around a wide mountain is investigated. The work builds on numerical modelling studies performed by Ólafsson and Bougeault, who investigated the effect of rotation and surface friction on the drag experienced by flow around a single elongated mountain perpendicular to the direction of the flow. The region of parameter space they explored is extended by performing a series of idealized model experiments with a larger range of ridge lengths. The drag force in these simulations is compared with the predictions of a heuristic flow-blocking model devised by Shutts. The results show that Shutts's model overestimates the effect of rotation upon the drag force. However we find that Shutts's model predicts both the drag force exerted on the upstream side of the ridge and the upstream features reasonably well. Finally the implications of the results for NWP parametrizations of subgrid-scale orographic drag are discussed. Copyright © 2005 Royal Meteorological Society [source]


Two-dimensional Numerical Modeling Research on Continent Subduction Dynamics

ACTA GEOLOGICA SINICA (ENGLISH EDITION), Issue 1 2004
WANG Zhimin
Abstract Continent subduction is one of the hot research problems in geoscience. New models presented here have been set up and two-dimensional numerical modeling research on the possibility of continental subduction has been made with the finite element software, ANSYS, based on documentary evidence and reasonable assumptions that the subduction of oceanic crust has occurred, the subduction of continental crust can take place and the process can be simplified to a discontinuous plane strain theory model. The modeling results show that it is completely possible for continental crust to be subducted to a depth of 120 km under certain circumstances and conditions. At the same time, the simulations of continental subduction under a single dynamical factor have also been made, including the pull force of the subducted oceanic lithosphere, the drag force connected with mantle convection and the push force of the mid-ocean ridge. These experiments show that the drag force connected with mantle convection is critical for continent subduction. [source]


Efficiency Optimization and Prediction in High-Gradient Magnetic Centrifugation

CHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 8 2010
J. Lindner
Abstract In order to separate small magnetizable particles down to the micro- and nanometer scale, high-gradient magnetic separation is a well-established process. The superposition of magnetic filtration with centrifugation, called magnetic field-enhanced centrifugation, permits continuous separation. The separation efficiency of magnetic filters and the prediction of the efficiency is described. The separation efficiency of one single stage could be enhanced from 51 to 78,% by increasing the wire number and improving the wire cross section. The separation efficiency on different particle sizes at different filter stage numbers and comparison to the prediction of separation efficiency based on magnetic forces and the fluid drag force is demonstrated. [source]


Portraying the Countercurrent Flow on Packings by Three-Dimensional Computational Fluid Dynamics Simulations

CHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 10 2008
Y. Y. Xu
Abstract The design of packed columns requires the detailed description of the hydrodynamics on the surface of the packings. To analyze the local flow behavior of the liquid phase, a three-dimensional Computational Fluid Dynamics (CFD) model was developed that applies to the two-phase countercurrent flow on an inclined and flat plate. This model, based on the volume-of-fluid (VOF) method, considers the gravity, the surface tension and the drag force between the two phases. The development of such a model allows investigation of the influences of the liquid and gas flow rates on the flow behavior such as the film flow and the rivulet flow. A validation of the model was performed using data from the literature and from experiments conducted in this work. Simulation and experimental results demonstrate that the specific wetted area on the plate decreases with decreasing liquid load. Moreover, CFD simulations reveal that the presence of the countercurrent gas phase tends to increase the fluctuation and the thickness of the film flow, which is in accordance with experimental data. It also affects the flow behavior of the rivulet flow and changes the velocity profiles for both film and rivulet flow behavior. On the other hand, the simulation results indicate that CFD is a potent tool for analyzing and investigating the flow phenomena in chemical engineering. [source]


Distorted Froude-scaled flume analysis of large woody debris

EARTH SURFACE PROCESSES AND LANDFORMS, Issue 12 2001
Nicholas P. Wallerstein
Abstract This paper presents the results of a movable-boundary, distorted, Froude-scaled hydraulic model based on Abiaca Creek, a sand-bedded channel in northern Mississippi. The model was used to examine the geomorphic and hydraulic impact of simplified large woody debris (LWD) elements. The theory of physical scale models is discussed and the method used to construct the LWD test channel is developed. The channel model had bed and banks moulded from 0·8 mm sand, and flow conditions were just below the threshold of motion so that any sediment transport and channel adjustment were the result of the debris element. Dimensions and positions of LWD elements were determined using a debris jam classification model. Elements were attached to a dynamometer to measure element drag forces, and channel adjustment was determined through detailed topographic surveys. The fluid drag force on the elements decreased asymptotically over time as the channel boundary eroded around the elements due to locally increased boundary shear stress. Total time for geomorphic adjustment computed for the prototype channel at the Q2 discharge (discharge occurring once every two years on average) was as short as 45 hours. The size, depth and position of scour holes, bank erosion and bars created by flow acceleration past the elements were found to be related to element length and position within the channel cross-section. Morphologies created by each debris element in the model channel were comparable with similar jams observed in the prototype channel. Published in 2001 John Wiley & Sons, Ltd. [source]


Numerical study of lid-driven flow in orthogonal and skewed porous cavity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2008
D. Jaya Krishna
Abstract Effects of Reynolds number, Darcy number, porosity, aspect ratio and skewness are studied in detail for lid-driven cavity flows filled with fluid-saturated porous medium. A generalized non-Darcy approach has been considered to account for linear and non-linear drag forces. The governing equations are solved by using finite volume method. A quadrilateral cell in a semi-staggered arrangement has been employed and is transformed into a standard square element using local body-fitting co-ordinates by co-ordinate transformation. Details of the flow physics reveal that by the reduction of Darcy number, the primary vortex becomes weaker and tends to move towards the lid. As a measure of volume flow rate maximum stream function value is considered. It is found that, with the reduction in Darcy number and with the increase in Reynolds number and skewness the maximum stream function value reduces. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Unstructured finite volume discretization of two-dimensional depth-averaged shallow water equations with porosity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010
L. Cea
Abstract This paper deals with the numerical discretization of two-dimensional depth-averaged models with porosity. The equations solved by these models are similar to the classic shallow water equations, but include additional terms to account for the effect of small-scale impervious obstructions which are not resolved by the numerical mesh because their size is smaller or similar to the average mesh size. These small-scale obstructions diminish the available storage volume on a given region, reduce the effective cross section for the water to flow, and increase the head losses due to additional drag forces and turbulence. In shallow water models with porosity these effects are modelled introducing an effective porosity parameter in the mass and momentum conservation equations, and including an additional drag source term in the momentum equations. This paper presents and compares two different numerical discretizations for the two-dimensional shallow water equations with porosity, both of them are high-order schemes. The numerical schemes proposed are well-balanced, in the sense that they preserve naturally the exact hydrostatic solution without the need of high-order corrections in the source terms. At the same time they are able to deal accurately with regions of zero porosity, where the water cannot flow. Several numerical test cases are used in order to verify the properties of the discretization schemes proposed. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Passive control of the flow around a square cylinder using porous media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004
Charles-Henri Bruneau
Abstract The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two-dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier,Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control. The numerical results reveal the ability of porous media to both regularize the flow and to reduce the drag forces up to 30%. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Fluid-particle drag in low-Reynolds-number polydisperse gas,solid suspensions

AICHE JOURNAL, Issue 6 2009
Xiaolong Yin
Abstract Lattice-Boltzmann simulations of low-Reynolds-number fluid flow in bidisperse fixed beds and suspensions with particle,particle relative motions have been performed. The particles are spherical and are intimately mixed. The total volume fraction of the suspension was varied between 0.1 and 0.4, the volume fraction ratio ,1/,2 from 1:1 to 1:6, and the particle size ratio d1/d2 from 1:1.5 to 1:4. A drag law with improved accuracy has been established for bidisperse fixed beds. For suspensions with particle,particle relative motions, the hydrodynamic particle,particle drag representing the momentum transfer between particle species through hydrodynamic interaction is found to be an important contribution to the net fluid-particle drag. It has a logarithmic dependence on the lubrication cutoff distance and can be fit as the harmonic mean of the drag forces in bidisperse fixed beds. The proposed drag laws for bidisperse fixed beds and suspensions are generalized to polydisperse suspensions with three or more particle species. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]


Electrostatic effects on inertial particle transport in bifurcated tubes

AICHE JOURNAL, Issue 6 2009
Fong Yew Leong
Abstract Most aerosols found naturally in the ambient environment or those dispersed from artificial devices such as dry powder inhalers, are electrically charged. It is known that a strong electrostatic charge on aerosols can result in transport behavior dramatically different from that of uncharged aerosols, even in the absence of an external electric field. In the present work, we study pneumatic transport of corona-charged particles in bifurcated tubes. This is accomplished by tracking the motion of discrete particles numerically under the influence of drag, gravitational, and electrostatic forces. The model aerosol is fly ash powder, whose size and charge distributions have been determined experimentally. The electrical mobility of the charged particle cloud is modeled through coulombic interactions between discrete point charges. For the case of polydispersed particles electrically charged across a distribution, the deposition efficiency was found to be greater than what is indicated by the mean charge and size. In particular, use of negatively charged fly ash powder of mean size of 2 ,m and mean charge of ,1.5 C/kg led to significant increase in deposition efficiency (,29%) compared with uncharged fly ash powder of the same size distribution (,8%). Analysis of particle residence times suggests significant interaction between electrical and drag forces. These findings could have implications for pneumatic powder conveying or pulmonary drug delivery applications. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]


Demarcation of a new circulating turbulent fluidization regime

AICHE JOURNAL, Issue 3 2009
Xiaobo Qi
Abstract Transient flow behaviors in a novel circulating-turbulent fluidized bed (C-TFB) were investigated by a multifunctional optical fiber probe, that is capable of simultaneously measuring instantaneous local solids-volume concentration, velocity and flux in gas-solid two-phase suspensions. Microflow behavior distinctions between the gas-solid suspensions in a turbulent fluidized bed (TFB), conventional circulating fluidized bed (CFB), the bottom region of high-density circulating fluidized bed (HDCFB), and the newly designed C-TFB were also intensively studied. The experimental results show that particle-particle interactions (collisions) dominate the motion of particles in the C-TFB and TFB, totally different from the interaction mechanism between the gas and solid phases in the conventional CFB and the HDCFB, where the movements of particles are mainly controlled by the gas-particle interactions (drag forces). In addition, turbulence intensity and frequency in the C-TFB are significantly greater than those in the TFB at the same superficial gas velocity. As a result, the circulating-turbulent fluidization is identified as a new flow regime, independent of turbulent fluidization, fast fluidization and dense suspension upflow. The gas-solid flow in the C-TFB has its inherent hydrodynamic characteristics, different from those in TFB, CFB and HDCFB reactors. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]