Lagrangian–Eulerian simulation of slugging fluidized bed

This work studies gas–solid slugging fluidized beds with Type-D particles, using two-dimensional simulations based on discrete element model (DEM). DEM performance is quantitatively validated by two commonly accepted correlations for determining slugging behavior. The voidage profiles simulated with bed height corresponding to Baeyens and Geldart (1974) correlation for onset of slugging demonstrate a transitional flow pattern from free bubbling to slugging. The present calculated values for the maximum slugging bed height are in good agreement with the correlation from Matsen et al. (1969). Simulations show that fluidized beds with Type-D particles can operate in the round-nosed slugging regime and also shows that wall slugs and square-nosed slugs tend to be formed with increase in superficial gas velocity and in bed height, respectively.     

Numerical simulation of gas-solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

A laser-fluorescence technique for turbulent two-phase flow measurements

A non-intrusive measurement technique has been developed for accurate determination of gas and particle velocities in a turbulent two-phase flow field. The principle of the technique is based on the discrimination between the scattered light from particles and the fluorescence emission from particles coated with a fluorescent dye. A high-powered, argon-ion based, single-channel, on-axis backscatter laser-Doppler velocimetry system was used. The fluorescent dye was Rhodamine 6G. A study of the gas-solid two-phase flow behaviour in the freeboard of a cold gas-fluidized bed was undertaken. The solid phase contained two particle groups: bed material (sand) and fuel particles (wood). Measurements of the axial velocity and turbulence intensity distributions of the gas phase and both particle groups within the solid phase were made along the column centre and across the freeboard. Excellent discrimination of velocities from the two phases and from the two particle groups within the solid phase was achieved.     

Discrete particle simulations of bubble-to-emulsion phase mass transfer in single-bubble fluidized beds

A classical Euler–Lagrangian model for gas–solid flows was extended with gas component mass conservation equations and used to obtain fundamental insights into bubble-to-emulsion phase mass transfer in bubbling gas–solid fluidized beds. Simulations of injected single rising bubbles under incipient fluidization conditions were carried out, using Geldart-A and -B particles. Phenomena observed in the simulations and those of various theoretical models used to derive phenomenological models were compared to challenge the assumptions underlying the phenomenological models. The bubble-to-emulsion phase mass transfer coefficients calculated for the simulations using Geldart-B particles were in a good agreement with predictions made using the Davidson and Harrison (1963) model. The bubble-to-emulsion phase mass transfer coefficients for Geldart-A particles were, however, much smaller than the predictions obtained from theoretical models (e.g. Chiba and Kobayashi (1970)). The newly developed model allows a detailed analysis of various hydrodynamic aspects and their effects on the mass transfer characteristics in and around rising bubbles in fluidized beds.     

Influences of the fluidizing and spouting pulsation on particle motion in spout-fluid beds

Effects of variable airflow on particle motion in spout-fluid beds are studied. Computational fluid dynamics using Navier–Stokes equations for the gas phase coupled with the discrete element method using Newton’s laws for the solid phase have been employed. Results indicate that increasing the fluidizing velocity diminishes dead zones and increases both the total height of the bed and the traversed distance by particles in the steady spout-fluid bed. In pulsed airflows, two configurations are investigated, namely, the spouted pulsed-fluidized bed with pulsed flow of the fluidizing velocity, and the pulsed-spouted fluidized bed with pulsed flow of the spouting velocity. The positive effect of pulsation on particle motion is shown and the effects of parameters, such as amplitude and frequency, on the dynamics of the bed are investigated in each configuration. An increase of up to 19% in traversed distance is found for the range studied, which suggests flow pulsation as a promising technique for increasing particle mixing in spout-fluid beds.     

稠密气固两相流各向异性颗粒相矩方法

基于气体分子动力学和颗粒动理学方法,考虑颗粒速度脉动各向异性,建立颗粒相二阶矩模型.应用初等输运理论,对三阶关联项进行模化和封闭.考虑颗粒与壁面之间的能量传递和交换,建立颗粒相边界条件模型.采用Koch等计算方法模拟气固脉动速度关联矩.考虑气体-颗粒间相互作用,建立稠密气体-颗粒流动模型.数值模拟提升管内气固两相流动特性,模拟结果表明提升管内颗粒相湍流脉动具有明显的各向异性.预测颗粒速度、浓度和颗粒脉动速度二阶矩与Tartan等实测结果相吻合.模拟结果表明轴向颗粒速度脉动强度约为平均颗粒相脉动强度的1.5倍,轴向颗粒脉动能大约是径向颗粒脉动能3.0倍.     

Local structure of a binary finely dispersed fluidized bed

Results are given of calculations of the quantities characterizing the random pseudoturbulent motions of the phases in a homogeneous fluidized bed consisting of particles of two sorts, differing in size. The dependence of the coefficients of pseudoturbulent diffusion of the particles, the mean-square velocities of the pulsations, etc., on the partial concentrations of the particles, the ratio of their sizes, and other parameters is evaluated. For granular beds, fluidized by a gas or a drop-type liquid, intense chaotic fluctuations of both phases are characteristic; these determine to a considerable degree the observed macroscopic properties of the bed and affect its effectiveness as a working body in various types of heat exchangers and chemical reactors. Such random (pseudoturbulent) motions are particularly considerable for beds of small particles under homogeneous fluidization conditions, where mixing due to the rise of cavities in the bed, filled only with the fluidizing medium, is practically absent. A similar situation is encountered in reactor and regenerating units for catalytic cracking [1, 2], in beds with a drop-type liquid phase, in rarefied two-phase systems under the conditions of strong fluidization or of the transport of bulk materials in a dilute phase, etc. The characteristics of pseudoturbulence in locally homogeneous flows of monodisperse two-phase systems have been investigated, for example, in [3–5]. However, real fluidized beds are generally polydis-perse; the presence of particles of different sizes in the bed has a very considerable effect, on the intensity of the pulsations, the effective diffusion coefficients of the phases of the bed, the effective viscosities, etc. [1, 6]. In addition, the chaotic mixing in polydisperse beds determines some of the technological characteristics, specifically, the rate of entrainment of small particles by the flow of the fluidizing medium and the settling of large particles, the degree of separation of the fractions of the disperse phase, which is very important in determination of the limits of the existence of the fluidized state, and in the modeling of numerous processes of the separation of particles with respect to size or density [1, 6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 118–126. March–April, 1976.     

The Effect of Droplets Evaporation on Turbulence Modification and Heat Transfer Enhancement in a Two-Phase Mist Flow Downstream of a Pipe Sudden Expansion

Turbulent droplet-laden flow downstream of a sudden pipe expansion is numerically studied using an Eulerian two-fluid model. The model is used to investigate the effect of droplet evaporation on the particle dispersion and on the gas phase turbulence modification. Turbulence suppression in the case of evaporating droplets is hardly observed near the wall, and the level of turbulence tends to the corresponding value for the single-phase flow regime. In the flow core, where evaporation is insignificant, a decrease in the level of gas turbulence (to 20 % as compared to a single-phase flow) can be observed. The maximal effect of droplet evaporation is obtained in the wall region of the tube. A considerable increase in the maximal value of heat exchange on adding the evaporating droplets to the separated flow is shown (more than 1.5-fold as compared to the single-phase flow at a small value of droplet mass concentration of M _L1≤ 0.05). The addition of the solid non-evaporating particles causes a slight increase in the maximum value of heat transfer in the case of small particles and a decrease in heat transfer in the case of large particles.     

Experimental investigation of bubbling in particle beds with high solid holdup

A series of experiments on bubbling behavior in particle beds was performed to clarify three-phase flow dynamics in debris beds formed after core-disruptive accident (CDA) in sodium-cooled fast breeder reactors (FBRs). Although in the past, several experiments have been performed in packed beds to investigate flow patterns, most of these were under comparatively higher gas flow rate, which may be not expected during an early sodium boiling period in debris beds. The current experiments were conducted under two dimensional (2D) and three dimensional (3D) conditions separately, in which water was used as liquid phase, and bubbles were generated by injecting nitrogen gas from the bottom of the viewing tank. Various particle-bed parameters were varied, including particle-bed height (from 30 mm to 200 mm), particle diameter (from 0.4 mm to 6 mm) and particle type (beads made of acrylic, glass, alumina and zirconia). Under these experimental conditions, three kinds of bubbling behavior were observed for the first time using digital image analysis methods that were further verified by quantitative detailed analysis of bubbling properties including surface bubbling frequency and surface bubble size under both 2D and 3D conditions. This investigation, which hopefully provides fundamental data for a better understanding and an improved estimation of CDAs in FBRs, is expected to benefit future analysis and verification of computer models developed in advanced fast reactor safety analysis codes.     

THEORY OF NONFLUIDIZED GAS SOLIDS FLOW AND ITS APPLICATION

A theory of nonfluidized gas-solids flow, which combines the theory of multiphase flow with the mechanics of particulate media, was proposed on the basis of understanding that the particles contact each other, solids and gas are in movement, and the drag force on the particles caused by interstitial gas flow is similar to gravity force having the property of mass force. Then this theory was verified by experiments on vertical and inclined moving beds, and was applied to calculation and design of equipment and devices with moving beds, such as pneumatic moving bed transport,dipleg, V-value, L-valve, orifice flow, and arching prevention. It can be used to guide the design and operation of moving beds and fixed beds.     

Insights in hydrodynamics of bubbling fluidized beds at elevated pressure by DEM–CFD approach

A numerical simulation was conducted to study the effect of pressure on bubble dynamics in a gas–solid fluidized bed. The gas flow was modeled using the continuum theory and the solid phase, by the discrete element method (DEM). To validate the simulation results, calculated local pressure fluctuations were compared with corresponding experimental data of 1-mm polyethylene particles. It was shown that the model successfully predicts the hydrodynamic features of the fluidized bed as observed in the experiments. Influence of pressure on bubble rise characteristics such as bubble rise path, bubble stability, average bubbles diameter and bubble velocity through the bed was investigated. The simulation results are in conformity with current hydrodynamic theories and concepts for fluidized beds at high pressures. The results show further that elevated pressure reduces bubble growth, velocity and stability and enhances bubble gyration through the bed, leading to change in bed flow structure.     

Modeling of Axisymmetric Two-phase Dilute Flows

This paper deals with the numerical treatment of Eulerian approach for dilute two-phase compressible flows (gas-particles mixtures) in axisymmetric configurations. For dilute flows, two classes of models depending on the dispersed phase volumetric fraction can be found. The volume occupied by the particles may be considered, that yields a model in which the gas phase and the dispersed phase equations are coupled through the void fraction and the source terms (Delhaye model). The void fraction effects can be neglected, that means the gas phase is a carrier phase for the particles (Ishii model). The mathematical nature of the two models is demonstrated from analysis of characteristic directions. For the Delhaye's model, a centered scheme is used to solve the system of partial differential equations, while an upwind TVD scheme is used for the Ishii's one. Then, it is shown that the problem of symmetry boundary conditions does not depend on the physical approach, as long as the flow remains dilute. However, a classical treatment for symmetry boundary conditions at the geometrical axis leads to large errors. A particular treatment for this boundary is presented: a new class of particles, described by a supplementary system of equations, is required.     

Flow regime diagrams for gas-solid fluidization and upward transport

Flow regime maps are presented for gas-solids fluidized beds and gas-solids upward transport lines. For conventional gas solids fluidization, the flow regimes include the fixed bed, bubbling fluidization, slugging fluidization and turbulent fluidization. For gas solids vertical transport operation, solids flux must be incorporated in the flow regime diagrams. The flow regimes then include dilute-phase transport, fast fluidization or turbulent flow, slug/bubbly flow, bubble-free dense-phase flow and packed bed flow. In practical circulating fluidized beds and transport risers, operation below the fast fluidization regime is commonly impossible due to equipment limitations. Practical flow regime maps are proposed with the flow regimes, including homogeneous dilute-phase flow, core-annular dilute-phase flow (where there are appreciable lateral gradients but small axial gradients) and fast fluidization (where there are both lateral and axial gradients). The boundary between fast fluidization and dilute-phase pneumatic transport is set by the type A choking velocity, at which the uniform suspension collapses and particles start to accumulate in the bottom region of the transport line, while the mechanism of transition from fast fluidization to dense-phase flow depends on the column and particle diameters.     

Magnetic field assisted fluidization： A modified Richardson-Zaki equation

Magnetic particles can be uniformly fluidized by coupling the gas flow with an externally imposed magnetic field. Interparticle forces generated by the magnetic field cause aggregation of the particles in chain-like structures preferentially oriented along the magnetic field lines. In the present paper, we study the implications of the formation of these special types of aggregates on the empirical Richardson-Zaki （RZ） equation, originally proposed to describe the expansion of fluidized beds of non-aggregated particles. We have addressed two important issues, namely the flow regime, which is a function of the size of the aggregates, and the effect of shape and orientation of the chain-like aggregates with respect to gas flow on fluid drag. We propose a modified RZ equation （MRZE） in which the velocity scale, given by the terminal settling velocity of the individual aggregates, and the RZ exponent are predetermined as a function of the chain length. The chain length depends on the ratio of the magnetic energy to gravitational energy, and is estimated from the magnetic field intensity, and particle magnetization, size and density. Predictions of the MRZE are successfully compared with published results in the literature on the expansion of magnetic particles in the presence of externally applied magnetic fields.     

An improved model for two-phase flow through beds of coarse particles

A one-dimensional model for two-phase flow in packed particle beds is presented. Compared with earlier models, the improved model takes into account the effect of interfacial drag forces between liquid and gas, which are of considerable influence in beds of coarse particles. The model is based on the momentum equations for separated flow, which are closed by empirical relations for the wall shear stress and the interfacial drag. The model is applied to the situation of a one-component two-phase flow in an internally heated bed of uniform spherical particles. An increased dryout heat flux is predicted if liquid enters the bed through the bottom.     

Numerical investigation of flow and heat transfer in a gas-droplet separated turbulent stream using the Reynolds stress transfer model

The results of the numerical modeling of flow structure, turbulence, and heat transfer in a gas-droplet stream after sudden tube expansion on the basis of the Eulerian approach are presented. The gas phase turbulence was modeled using the Reynolds stress transfer model modified to allow for the presence of particles. The results are compared with those obtained using the two-equation k-ε model. The latter results overestimate the heat transfer in the separation flow as compared with the Reynolds stress transfer model. The heat transfer is shown to considerably increase, when evaporating droplets are incorporated in the separation flow (by a factor of more than 1.5 compared with the case of a single-phase flow at a small mass concentration of the droplets M _L1 ≤ 0.05). The addition of the disperse phase in the turbulent gas flow leads a slight increase in the recirculation zone length. Good agreement with the experimental data indicates the adequacy of the numerical model developed.     

The local structure of gas fluidized beds —II. The spatial distribution of bubbles

The spatial distribution of bubbles in gas fluidized beds has been investigated with the measuring system described in Part I of this paper in beds of 0.10, 0.20, 0.45 and 1.0 m dia. The results indicate that in gas fluidized beds a characteristic flow profile of the bubble phase exists such that near the distributor a zone of increased bubble development exists in an annulus near the wall. This zone moves towards the vessel centre-line with increasing height above the distributor. The merging of the annular zone in the vessel centre-line marks the beginning of the transition of the fluidized bed to the state of slugging. The spatial flow profile of the bubble phase is shown to be responsible for the existence of characteristic solids circulation patterns in gas fluidized beds.     

Gas and particle motion in jets in fluidized beds

Entrainment of solid particles by gas jets discharged downwards through slotted nozzles into bubble-free beds of fluidized particles is considered. The gas flow in the jet is calculated for irrotational flow, using a correlation established previously for slot opening as a function of operating variables. The momentum boundary layer thickness and shear stress at the horizontal interface between jet and particles are then calculated by integral boundary layer analysis. The calculated shear stress distributions are consistent with measurements of the momentum of bed particles caused to saltate by the jet, and explain the dependence of particle movement on the various operating variables. The results provide a direct confirmation of a hypothesis due to Owen on the mechanism of saltation.     

Experimental investigation of turbulence modulation in particle-laden coaxial jets by Phase Doppler Anemometry

The effect of solid particles on the flow characteristics of axisymmetric turbulent coaxial jets for two flow conditions was studied. Simultaneous measurements of size and velocity distributions of continuous and dispersed phases in a two-phase flow are presented using a Phase Doppler Anemometry (PDA) technique. Spherical glass particles with a particle diameter range from 102 to 212 μm were used in this two-phase flow, the experimental results indicate a significant influence of the solid particles and the Re on the flow characteristics. The data show that the gas phase has lower mean velocity in the near-injector region and a higher mean velocity at the developed region. Near the injector at low Reynolds number (Re = 2839) the presence of the particles dampens the gas-phase turbulence, while at higher Reynolds number (Re = 11 893) the gas-phase turbulence and the velocity fluctuation of particle-laden jets are increased. The particle velocity at higher Reynolds number (Re = 11 893) and is lower at lower Reynolds number (Re = 2839). The slip velocity between particles and gas phase existed over the flow domain was examined. More importantly, the present experiment results suggest that, consideration of the gas characteristic length scales is insufficient to predict gas-phase turbulence modulation in gas-particle flows.