Critical comparison of hydrodynamic models for gas-solid fluidized beds—Part I : bubbling gas-solid fluidized beds operated with a jet

In the Eulerian approach to model gas-solid fluidized beds closures are required for the internal momentum transfer in the particulate phase. Firstly, two closure models, one semi-empirical model assuming a constant viscosity of the solid phase (CVM) and a second model based on the kinetic theory of granular flow (KTGF), have been compared in this part in their performance to describe bubble formation at a single orifice and the time-averaged porosity profiles in the bed using experimental data obtained for a pseudo two-dimensional fluidized bed operated with a jet in the center. Numerical simulations have shown that bubble growth at a nozzle with a jet is mainly determined by the drag experienced by the gas percolating through the compaction region around the bubble interface, which is not much influenced by particle-particle interactions, so that the KTGF and CVM give very similar predictions. However, this KTGF model does not account for the long term and multi particle-particle contacts (frictional stresses) and under-predicts the solid phase viscosity at the wall as well as around the bubble and therefore over-predicts the bed expansion. Therefore, in the later part of the paper, the bubble growth at a single orifice and the time-averaged porosity distribution in the bed predicted by the KTGF model with and without frictional stresses are compared with experimental data. The model predictions by the KTGF are improved significantly by the incorporation of frictional stresses, which are however strongly influenced by the empirical parameters in this model. In Part II the comparison of the CVM and KTGF with experimental results is extended to freely bubbling fluidized beds.     

循环硫化床上升管中动态行为的拟流体模拟

The kinetic theory of granular flow (KTGF) is modified to fit the Einstein′s equation for effective viscosity of dilute flow. A pseudo-fluid approach based on this modified KTGF is used to simulate the dynamic formation and dissipation of clusters in a circulating fluidized bed riser. The agglomeration of particles reduces slip velocity within particle clusters, and hence results in two reverse trends: discrete particles are lifted by air while particle clusters fall down along the wall. The dynamic equilibrium of these two types of motion leads to the characteristic sigmoid profile of solid concentration along the longitudinal direction. The predicted solid velocity, lateral and longitudinal profiles of solid volume fraction and annulus thickness are in reasonable agreement with experimental results.     

MASS TRANSFER RELATIONSHIPS IN FLUIDIZED-BED COMBUSTORS

It is proposed that the transfer of oxygen from the bulk phase to the surface of a burning carbon particle immersed in a fluidized bed of incombustible particles can be characterized by the transfer associated with the interparticulate gas flow enhanced by the fluctuations in the gaseous environment around the burning particle. The enhancement is attributed to the movement of bubbles in the vicinity of the carbon particle and is predicted by a semi-empirical function of the bubble frequency. The resulting expression is incorporated in a recently proposed unsteady-state model for mass transfer (La Nauze et al., Chem. Eng. Sci., 39, 1623-1633 (1984)rpar; The new formulation correctly predicts the order and trends for the mass transfer coefficient for petroleum coke burning in a bed of sand fluidized by air over a wide range of conditions. In order to test the validity of the model, experiments have been performed using a helium/oxygen gas mixture instead of air. The model successfully predicts the mass transfer coefficient for this situation.     

Flow of gas and particles in a bubbling fluidized bed with a filtered two-fluid model

Numerical simulations of gas-particles flow in a bubble fluidized bed with two large eddy simulations of gas and solid phases are presented. For gas phase and solid phase, the sub-grid scale model for the viscosity is based on the Smagorinsky form. The sub-grid model for the particle pressure proposed by Igci et al. (2008) is modified by replacing the minimum fluidization velocity. The collisional interaction of particles is considered by the kinetic theory of granular flow. Flow behavior of gas and particles is performed by means of these two sub-grid scale models. The subgrid closure for the particle phase viscosity and pressure led to a qualitative change in the simulation results. Predictions are compared with experimental data measured by Yuu et al. (2000) and Taghipour et al. (2005) in the bubbling fluidized beds. The distributions of concentration and velocity of particles are predicted in the bubbling fluidized bed. The predicted filtered particle phase pressure increases and the filtered particle phase viscosity decreases with the increase of particle concentration. The qualitative importance of the model constant c_s of particles is demonstrated.     

Solid-liquid mass transfer in a gas-liquid-solid fluidized bed

Solid-liquid mass transfer in co-current two- and three-phase fluidized beds of water, air and benzoic acid pellets is studied. An axial dispersion model is used to describe the liquid flow when evaluating the solid-liquid mass transfer. The axial concentration profile of benzoic acid in the liquid is compared to that obtained experimentally and is found to be accurate. Three-phase fluidized bed solid-liquid mass-transfer coefficients are higher than the corresponding two-phase bed coefficients. The mass-transfer coefficient increases with increasing gas rate and is independent of liquid rate over the entire range studied. The mass-transfer coefficient also appears to be dependent on particle size, but only at high gas rates. At low or zero gas rates, k is nearly independent of particle size. A generalized correlation is developed which accurately and conveniently predicts the mass transfer in both two- and three-phase fluidized beds. Comparison to the solid-liquid mass-transfer characteristics of slurry bubble columns is also performed.     

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

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

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.     

Inlet boundary conditions for the simulation of fluid dynamics in gas-solid fluidized beds

The interaction between a fluidized bed and the air-supply system is studied numerically in a cold circulating fluidized bed unit. The bed was operated with Group B solids and with an air-distributor pressure-drop similar to that often applied under industrial conditions. The simulations and experiments are compared through power spectral density distributions of pressure fluctuations in the bed and air plenum. This work focuses on the inlet boundary conditions of the numerical simulations, i.e., the purpose is to include a representation of fluctuations in pressure and flow in the air-supply system. The fluctuations are computed and coupled with the simulations of the flow field in the bed and the air plenum, based on an Eulerian approach. Parametric models are employed for spectral estimates as the time consumption for the three-dimensional simulation limits the length of the pressure time series. The simulations provide satisfactory agreement with experiments, and it is seen that, under certain conditions, there is a strong interaction between the fluidized bed and the air-supply system in the form of pressure waves, as well as pressure and flow pulsations from the air-supply system, which propagate through the entire system. It is demonstrated that for such a system, the assumption of a uniform inlet gas flow over the air distributor, assumed in most previous fluidized-bed studies, is not appropriate. This study demonstrates the importance of further development of numerical models for simulating the hydrodynamics of fluidized beds, in particular for industrially sized units.     

A second-order moment method of dense gas-solid flow for bubbling fluidization

A gas-solid two-fluid model with the second-order moment method is presented to close the set of equations applied to fluidization. With the kinetic theory of granular flow, transport equations for the velocity moments are derived for the particle phase. Closure equations for the third-order moments of velocity and for the fluid-particle velocity correlation are presented. The former is based on a modified model with the contribution of the increase of the binary collision probability, and the latter uses an algebraic model proposed by Koch and Sangani [1999. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. Journal of Fluid Mechanics 400, 229-263]. Boundary conditions for the set of equations describing flow of particles proposed by Strumendo and Canu [2002. Method of moments for the dilute granular flow of inelastic spheres. Physical Review E 66, 041304/1-041304/20] are modified with the consideration of the momentum exchange by collisions between the wall and particles. Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized bed. Predictions are compared with experimental data measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168]. in the bubbling fluidized beds. The simulated second-order moment in the vertical direction is 1.1-2.5 [Muller, C.R., Holland, D.J., Sedeman, A.J., Scott, S.A., Dennis, J.S., Gladden, L.F., 2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and 1.1-4.0 [Yuu, S., Umekage, T., Johno, Y., 2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168] times larger than that in the lateral direction because of higher velocity fluctuations for particles in the bubble fluidized bed. The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. [2004. Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour-Daniel lecture. Powder Technology 148, 123-141.] are computed from the simulated hydrodynamic velocities. The predictions are in agreement with experimental second-order moments measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and fluctuating velocity of particles measured by Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168].     

Discrete element simulation of particle flow in arbitrarily complex geometries

Conventional simulations of dense particle flows in complex geometries usually involve the use of glued particles to approximate geometric surface. This study is concerned with the development of a robust and accurate algorithm for detecting the interaction between a spherical particle and an arbitrarily complex geometric surface in the framework of soft-sphere discrete element model (DEM) without introducing any assumptions. Numerical experiments specially designed to validate the algorithm shows that the new algorithm can accurately predict the contact state of a particle with a complex geometric surface. Based on the proposed algorithm, a new solver for simulation of dense particle flows is developed and implemented into an open source computational fluid dynamics (CFD) software package OpenFOAM. The solver is firstly employed to simulate hydrodynamics in a bubble fluidized bed. Numerical results show that a 3D simulation can predict the bubble size better than a 2D simulation. Subsequently, gas–solid hydrodynamics in an immersed tube fluidized bed is simulated. Results show that bubble coalescence and breakup behavior around the immersed tubes are well captured by the numerical model. In addition, seven different particle flow patterns around the immersed tubes are identified based on the numerical results obtained.     

EFFECTS OF PARTICLE CHARACTERISTICS ON THE PERFORMANCE OF A FAST FLUIDIZED BED REACTOR

A heterogeneous model for the fast fluidized bed reactor which carries out a gas-solid non catalytic reaction is presented. The hydrodynamics of the fast fluidized bed is characterized by the model of Kwauk et al. (1985) which assumes the existence of two phases; a dense phase and a dilute pneumatic transport phase. For a given solid flowrate, the length of the reactor occupied by each phase depends on gas velocity, particle diameter and density and average voidage within the reactor. The gas-solid reaction is assumed to follow the shrinking core model. The solids are assumed to be completely backmixed in the dense phase and move in plug How in the dilute pneumatic transport phase. The gas phase is assumed to be in plug flow in both phases

For given gas and solid flowrates, the transition from the dense phase flow to the fast fluidized bed (containing two regions) as functions of particle size and density is determined using the model of Kwauk et al. (1985). The numerical solution of the governing mass balance equations show that for given solid and gas flowrates, (and average voidage) the gas phase conversion shows an unusual behavior with respect to particle diameter and density. Such behavior is resulted from the effects of particle diameter and density on the reactor volume occupied by each phase and the effect of particle diameter on the apparent reaction rate. The numerical results show that a fast fluidized bed gives the best conversion at large particle density and for the particle diameter which results the fast fluidized bed to be operated near the pure dense phase flow.     

Computational fluid dynamics simulations of interphase heat transfer in a bubbling fluidized bed

Numerical simulations based on the Eulerian-Eulerian approach have been performed in the study of interphase heat transfer in a gas solid fluidized bed. The kinetic theory of granular flow (KTGF) has been used to describe the solid phase rheology. An assessment of drag models in the prediction of heat transfer coefficients shows that no major difference is observed in the choice of the drag model used. Fluctuations of the interphase heat transfer coefficient have been found to be closely related to the bubble motion in the bed. Effects of the wall boundary condition, inlet gas velocity, initial bed height and particle size on the predicted heat transfer coefficient have also been investigated. Typical temperature profiles in the bed show that thermal saturation is attained instantaneously close to the gas distributor. Simulated results of the coefficients are in fair agreement with those reported in literature.     

Evaluation of wall boundary condition parameters for gas–solids fluidized bed simulations

Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas–solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas–solids flow. A model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (Li and Benyahia, AIChE J. 2012;58:2058–2068) is implemented in the open‐source CFD code‐MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial‐slip boundary conditions for the solids phase. Through a series of two‐dimensional numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient. Published 2013 American Institute of Chemical Engineers AIChE J, 59: 3624–3632, 2013     

磁场对湿颗粒流化床系统中介尺度结构影响机制研究

湿颗粒系统在自然界及工业过程非常普遍,例如喷雾造粒、反应器中矿物黏结、催化以及制药等,这其中含有大量典型介尺度结构如颗粒聚团、结块以及气泡等结构,这些结构的存在导致颗粒系统的流动及热质传递特性发生明显改变。针对鼓泡流化床湿颗粒系统中颗粒聚团以及气泡等介尺度结构,应用离散单元模型并引入外加磁场,研究磁场作用下湿颗粒系统中介尺度结构的演化机制,探究磁场力、液桥力、接触力对气泡演化过程的影响。研究发现,在不考虑磁场的条件下,颗粒易形成聚团并存在气泡边界不规则等现象,引入外加匀强磁场后,磁场力对鼓泡流化床内气泡结构存在破坏和抑制作用。     

Heat transfer within dynamically structured bubbling fluidized beds subject to vibration: A two-fluid modeling study

Bubbling fluidized beds are often used to achieve a uniform particle temperature distribution in industrial processes involving gas and particles. However, the chaotic bubble dynamics pose significant challenges in scale-up. Recent work (Guo et al., 2021, PNAS 118, e2108647118) has shown that using vibration can structure the bubbling pattern to a highly predictable manner with the characteristic bubble properties independent of system width, opening opportunities to address key issues associated with conventional bubbling fluidized beds. Herein, using two-fluid modeling simulations, we studied heat transfer characteristics within the dynamically structured bubbling fluidized bed and compared to unstructured bubbling fluidized beds and packed beds. Simulations show that the structured bubbling fluidized bed can achieve the most uniform particle temperature distribution because it can achieve the best particle mixing while maintaining a global heat transfer coefficient similar to that of a freely bubbling fluidized bed.     

气固搅拌流化床内压力脉动特性的数值模拟

在传统气固流化床中引入搅拌桨,可减轻聚合物颗粒的黏附并强化流态化过程。采用计算流体力学(CFD)方法对搅拌流化床内的压力脉动特性进行数值模拟,考察流态化过程中的气泡行为。模拟过程采用多重参考坐标系方法解决搅拌桨区域的运动问题,由欧拉双流体模型和颗粒动力学方法模拟气固两相流。床层压力脉动的统计分析和功率谱分析表明,随着搅拌桨转速的增加,流化床内的压力脉动标准偏差和功率谱幅值变小,床层内的平均气泡尺寸减小,床层可由鼓泡流态化向散式流态化转变。     

Validation of the similar particle assembly (SPA) model for the fluidization of Geldart's group A and D particles

The similar particle assembly (SPA) model proposed for large‐scale discrete element method simulation was validated. The SPA model describes the scaling law for the motion of particles in an assembly, which is derived from the equation of motion of a particle. In the SPA model, particles with similar physical or chemical properties are represented by a single particle, which is called the representative particle. The local assembly of particles in the original bed is supposed to be maintained in the bed with the representative particles. The SPA model was validated by numerical simulations of a 2D fluidized bed of noncohesive and cohesive particles. Using the SPA model, the flow behavior of the representative particles of a certain magnification can be made similar to that of the original particles with significantly less computational load. A good approximation of bubble size distribution between the SPA bed and the original bed was obtained. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A critical comparison of frictional stress models applied to the simulation of bubbling fluidized beds

The behaviour of a gas-solid flow in a bubbling fluidized bed operated near the minimum fluidization condition is strongly influenced by the frictional stresses between the particles, these being highly concentrated and their motion dominated by enduring contact among them and with the walls.The effect of the introduction of frictional stresses in a Eulerian-Eulerian two fluid model based on the kinetic theory of the granular flow is evaluated. The models of Johnson and Jackson [1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67-93], Syamlal et al. [1993. Mfix documentation: volume I, theory guide. Technical Report DOE/METC-9411004, NTIS/DE9400087, National Technical Information Service, Springfield, VA], and Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] are compared with the kinetic theory of the granular flow and with experimental data both in a bubbling fluidized bed with a central jet and in a bubbling fluidized bed with a porous distributor. The predicted evolution of the bubble diameter along the height of the fluidized beds is examined, the shapes of the bubbles predicted by the models are compared and the evolution in time of the bubbles is shown. In the case of the bed with a central jet, the bubble detachment time is also calculated. The results show that the introduction of a frictional stress model improves the prediction of the bubbles diameter in a bubbling fluidized bed with a central jet and positively affects the bubbles diameter distribution in a uniformly fed bubbling fluidized bed. The high sensitivity of the model to the value of the particulate phase fraction at which frictional stresses start to be accounted for is pointed out through a sensitivity analysis performed on the Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] model.