A critical comparison of frictional stress models applied to the simulation of bubbling fluidized beds (original) (raw)
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A study of bubbling and slugging fluidised beds using the two-fluid granular temperature model
International Journal of Multiphase Flow, 2001
This paper reports ®nite element numerical simulations of gas±solid¯uidised beds using the two-¯uid granular temperature model. The aim of the study has been to investigate the various phenomena that have been observed in¯uidised beds but have not been subject to numerical investigation. Two¯uidised beds, operating in the slugging and bubbling regimes, were modelled, and the formation, elongation, coalescence and eruption of bubbles described. The eect of an obstruction on the¯uidisation eciency in a¯uidised bed was investigated. Granular temperature distribution inside the¯uidised bed provided an indication of the regions on the obstruction, which could be susceptible to erosion by particle impact. 7 (C.C. Pain). computers, numerical methods and solution techniques are now beginning to provide the tools necessary to model the dynamics of these complex systems.
Chemical Engineering Science, 2003
A multi-uid Eularian CFD model with closure relationships according to the kinetic theory of granular ow has been applied to study the motions of particles in the gas bubbling uidized 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 uidized 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 eect of particle size distribution and energy dissipation due to non-ideal particle-particle interactions into account. ?
Extension of the kinetic theory of granular flow to include dense quasi-static stresses
Powder Technology, 2010
Fluidized bed technology has diverse industrial applications ranging from the gasification of coal in the power industry to chemical reactions for the plastic industry. Due to their complex chaotic non-linear behaviour understanding the hydrodynamic behaviour in fluidized beds is often limited to pressure drop measurements and a mass balance of the system. Computational fluid dynamics has the capability to model multiphase flows and can assist in understanding gas-solid fluidized beds by modeling their hydrodynamics. The multiphase Eulerian-Eulerian gas-solid model, extended and validated here improves on the kinetic theory of granular flow by including a closure term for the quasi-static stress associated with the long term particle contact at high solid concentrations. Similar quasi-static models have been widely applied to slow granular flow such as chute flow, flow down an incline plane and geophysical flow. However combining the kinetic theory of granular flow and the quasi-static stress model for the application of fluidized beds is limited. The objective of the present paper is to compare two quasi-static stress models to the experimental fluidized bed data of Bouillard et al. [4]. A quasi-static granular flow model (QSGF) initially developed by Gray and Stiles [18] is compared to the commonly used Srivastava and Sundaresan . Both models show good agreement with the experimental bubble diameter and averaged porosity profiles. However only the QSGF model shows a distinct asymmetry in the bubble shape which was documented by Bouillard et al. .
Korean Journal of Chemical Engineering, 2013
The hydrodynamics of a vertically vibrating fluidized bed was studied using an Eulerian-Eulerian twofluid model (TFM) incorporating the kinetic theory of granular flow and including the frictional stress effects. Influences of frictional stresses, vibration amplitudes and frequency on behavior of the particles were studied. In the case with vertical vibration, the numerical results showed three regions of solid concentration along the bed height: a low particle concentration region near the bottom of the bed, a high concentration region in the middle of the bed, and a transition region at top of the bed. The accuracy of results was found to be closely related to the inclusion of the frictional stresses. Ability of the two-fluid model for predicting the hydrodynamics of vibrating fluidized beds was discussed and confirmed.
2009
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.
Chemical Engineering Science, 2004
A gas-solid two-uid ow 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 ow, 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 modied frictional shear viscosity model proposed by Syamlal et al. (MFIX documentation. ). The body-tted coordination is used to make the computational grids best t the shape of conical contour of the base in the spouted beds. The eects 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.
Measurement of Two Kinds of Granular Temperatures, Stresses, and Dispersion in Bubbling Beds
Industrial & Engineering Chemistry Research, 2005
A CCD camera technique was developed to measure instantaneous particle velocities in a thin bubbling bed for fluidization of 530 µm glass beads. The hydrodynamic velocities were computed by averaging the instantaneous velocities over the velocity space using the concepts of kinetic theory. Laminar-type kinetic stresses and granular temperatures were computed from the measurement of instantaneous velocities. Bubblelike granular temperatures were computed from the hydrodynamic velocities. The measured Reynolds normal stresses per unit bulk density in the vertical direction were 8 times larger than the measured Reynolds normal stresses per unit bulk density in the lateral direction because of higher velocity fluctuations for particles in the bubble-flow region. The sum of the measured shear stresses was equal to the pressure drop minus the weight of the bed of solids within experimental error. The restitution coefficients for 530 µm glass beads, estimated from the ratio of shear to normal stresses, are in the range of 0.99. The mixing in the bubbling and turbulent fluidized beds is due to laminarlike particle oscillations measured by the conventional granular temperature and due to bubblelike granular temperatures produced by the motion of bubbles. The bubblelike granular temperature is much larger than the particle granular temperature. In the center of the riser, the particle granular temperature was about 3 times larger than the Reynolds-like granular temperature. These observations are consistent with the literature of particle dispersion in bubbling beds, such as the early Ruckenstein analysis of homogeneous and bubbling beds.
Chemical Engineering Science, 2008
Computational fluid dynamic (CFD) models must be thoroughly validated before they can be used with confidence for designing fluidized bed reactors. In this study, validation data were collected from a fluidized bed of (Geldart's group B) alumina particles operated at different gas velocities involving two fluidization hydrodynamic regimes (bubbling and slugging). The bed expansion, height of bed fluctuations and frequency of fluctuations were measured from videos of the fluidized bed. The Eulerian-Eulerian two fluid model MFIX was used to simulate the experiments. Two different models for the particle stresses-Schaeffer [Syamlal, M., Rogers, W., O'Brien, T.J., 1993. MFIX documentation: theory guide. Technical Report DOE/METC-94/1004 (DE9400087), Morgantown Energy Technology Centre, Morgantown, West Virginia (can be downloaded from Multiphase Flow with Interphase eXchanges (MFIX) website http://www.mfix.org ); Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66, 61-74.] and Princeton [Srivastava, A., Sundaresan, S., 2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129(1-3), 72-85.] models-and different values of the restitution coefficient and internal angle of friction were evaluated. 3-D simulations are required for getting quantitative and qualitative agreement with experimental data. The results from the Princeton model are in better agreement with data than that from the Schaeffer model. Both free slip and Johnson-Jackson boundary conditions give nearly identical results. An increase in coefficient of restitution (e) from 0.8 to 1 leads to larger bed expansions and lower heights of fluctuations in the bubbling regime, whereas it leads to unchanged bed expansion and to a massive reduction in the height of fluctuations in the slugging regime. The angle of internal friction () in the range 10-40 • does not affect the bed expansion, but its reduction significantly reduces the height of fluctuations. (N. Reuge), pannalas@ornl.gov (S. Pannala), Madhava.Syamlal@NETL.DOE.GOV (M. Syamlal), Brigitte.Caussat@ensiacet.fr (B. Caussat).
The generality of the standard 2D TFM approach in predicting bubbling fluidized bed hydrodynamics
Powder Technology, 2013
Hydrodynamic simulations of a pseudo-2D bubbling fluidized bed were carried out and compared to experiments conducted over a wide range of flow conditions. The primary purpose of this study was to assess the generality of the standard 2D Two Fluid Model (TFM) closed by the Kinetic Theory of Granular Flows (KTGF) which is regularly used in the literature to simulate bubbling fluidized beds. Comparisons of the bed expansion ratio over wide ranges of fluidization velocity, bed loading and particle size showed systematic differences between simulations and experiments, indicating that the generality of this modelling approach is questionable. More detailed flow velocity measurements collected via Particle Image Velocimetry (PIV) showed that the model greatly over-predicts flow velocities in the bed. Subsequent 3D simulations showed this over-prediction to be the result of 2D simulations neglecting the wall friction at the front and back walls of the pseudo-2D bed. 2 List of symbols 2.1 Main Symbol definitions α Volume fraction φ Kinetic energy transfer rate (kg/m.s 3) γ Dissipation rate (kg/m.s 3) s Θ Granular temperature (m 2 /s 2) ρ Density (kg/m 2) ς Specularity coefficient τ Stress tensor (kg/m.s 2