Experimental studies of particle flow dynamics in a two-dimensional spouted bed

In this paper, both time-averaged and fluctuating behaviors of granular solids in a two-dimensional spouted bed (2DSB) were investigated by particle image velocimetry (PIV). A self-developed algorithm for the high-gradient granular flow field was employed to measure particle velocity sequences together with power spectral density, mean particle velocity and granular temperature. The incoherent spout was characterized as an ‘X’ geometry marked with a periodic upwardly moving neck consisting of particle clusters. In the annulus, particles move periodically as a process of acceleration-deceleration-stagnation that has the same domain frequency as the pressure drop of 2DSB. The time-averaged downward velocities have a maximum at a certain position between the spout wall and conical wall. In the spout, the longitudinal profiles of vertical particle velocities along the axis exhibit a fast acceleration followed by a long flat peak, while the normalized lateral profiles at all bed levels tend to collapse into a third polynomial curve with an inflection point. A mushroom-like distribution of the granular temperature exists in 2DSB. The peaks of granular temperature occur not only near the spout-annulus interface, but also at the corner zone between the annulus and the fountain.     

Local porosity in conical spouted beds consisting of solids of varying density

Local bed voidage has been measured in conical spouted beds by means of an optical fibre, for different geometric factors of the contactor (angle and inlet diameter) and under different experimental conditions (height of the stagnant bed, particle diameter and air velocity). The study has been carried out with glass beads and materials of lower density (high- and low-density polyethylene, polypropylene and extruded and expanded polystyrene). From the results, a correlation has been proposed for calculation of the local bed voidage in the spout and annular zones. The effect of the experimental conditions on the bed voidage in the solid ascent (core) and descent (periphery) regions of the fountain has been studied and the fountain has been proven to be of greater importance in the design of conical spouted beds, as solid density and shape factor are lower.     

DEM simulation of the particle dynamics in two-dimensional spouted beds

A Discrete Element Method (DEM) is used together with the continuum model of turbulent fluids to simulate the periodic spouting of granular solids in a two-dimensional spouted bed. The bed is contained in a rectangular column of 152 mm width and 15 mm depth with a tapered base. Glass beads with a diameter of 2 mm are used as bed material. Simulations using the DEM together with a low Reynolds number k-ε turbulence model for the fluid phase yield predictions of the unstable spout regime, characterized as a periodic upward-moving particle jet. The simulation results compare well to experimental data obtained using a particle image velocimetry (PIV) technique, including fluid flow fields, time-averaged particle velocity profiles, and spout shape. Finally, DEM predictions for distribution of drag and net force on the particles, particle concentration fields, gas velocity and turbulence field are discussed.     

Numerical simulation and experimental study of fluid-particle flows in a spouted bed

In this work, the Eulerian-Eulerian multiphase model is used in the computational simulation of fluid dynamics of spouted beds with two different geometries: conical-cylindrical and conical. For the conical-cylindrical spouted bed, the simulated results of radial velocities of particles with a 1.41 mm diameter along bed heights in the range of 0.022 to 0.318 m are compared with experimental values obtained by He et al. [Y.L. He, C.J. Lim, J.R. Grace and, J.X. Zhu, Measurements of Voidage Profiles in Spouted Beds, Canadian Journal of Chemical Engineering, 72 (1994), 229-234], and show a good agreement. The influence of static bed height on the characteristic curve is assessed through simulations using different airflow rates. The respective minimum spouting velocities are compared with experimental values and with values obtained through empirical correlations reported in the literature. The results of the CFD simulations show a deviation of 3.8% when compared with the experimental data, which is less than the aforementioned correlations. The stages of transition from the condition of static bed to spouting bed are presented through the simulation of solids volume fraction distribution and the radial profile of voidage in the spouting region. The characteristic curve and minimum spouting conditions for a simulated conical bed, with glass particles of 6 mm diameter are compared with the experimental results showing deviations of 12.1% for the pressure drop and 5.6% for the minimum spouting velocity.     

SPH method for two-fluid modeling of particle–fluid fluidization

In this paper a smoothed particle hydrodynamics (SPH) method is proposed for solving the two-fluid model of dense particle–fluid fluidizations. The particle–fluid two-phase flow fields are represented with two types of SPH particles, where the interactions between particles of the same type constitute the inner-phase stress while those between particles of different types result in the drag force. Two typical fluidization systems, namely the liquid–solid sedimentation and single-orifice gas–solid bubbling fluidization, are simulated with this approach, showing good agreement with experimental data.     

Minimum spouting velocity for the pyrolysis of scrap tyres with sand in conical spouted beds

The effect of temperature (in the 298-973 K range) on minimum spouting velocity has been studied in conical spouted beds made up of mixtures of tyre and sand particles, for different sizes of tyre particles and for different tyre/sand ratios. The good fit to the experimental results confirms the validity of the correlations already proposed by Olazar et al. [M. Olazar, M.J. San José, A.T. Aguayo, J.M. Arandes, J. Bilbao, Stable operation conditions for gas-solid contact regimes in conical spouted beds, Ind. Eng. Chem. Res. 31 (1992) 1784-1791] for room temperature, which is due to the fact that they take into account the density and viscosity of the gas. For fine particles, the effect of density prevails on the effect of viscosity and the equations proposed by Bai et al. [D. Bai, Y. Masuda, N. Nakagawa, K. Kato, Hydrodynamic behavior of a binary solids fluidized bed, J. Chem. Eng. Jpn. 29 (1996) 211-216] are suitable for the calculation of the average particle size and density, in order for them to be used in the calculation of minimum spouting velocity. For coarse particles, the effect of gas viscosity is insignificant compared to the effect of density and the equation of Goossens et al. [W.R.A. Goossens, G.L. Dumont, G.L. Spaepen, Fluidization of binary mixtures in the laminar flow region, Chem. Eng. Prog. Symp. Ser. 67 (1971) 38-45] is suitable for the calculation of the average particle size required for ascertaining minimum spouting velocity.     

IMAGING OF PARTICLE MOTION IN FLUID-SOLID SYSTEMS USING A GAMMA CAMERA

A new approach is presented for the characterization of particle motion in fluid-solid systems based on dynamic imaging with a gamma scintillation camera. A two-dimensional spouted bed of 200-500 micron diameter anion exchange resin beads was used as a test system. One or several beads were radiolabeled with the 140 keV gamma emitting radionuclide 99m-Tc pertechnetate, and particle velocity, panicle path, the spatial distribution of particle residence times, and local bed density were determined from the measured temporal and spatial distributions of particle activity. While care must be exercised in the interpretation of data when the scale for changes in the spatial distribution of activity approaches the limits of camera resolution, the method is quantitative, non-invasive, and well suited to the study of systems having symmetry in one spatial dimension.     

IMAGING OF PARTICLE MOTION IN FLUID-SOLID SYSTEMS USING A GAMMA CAMERA

A new approach is presented for the characterization of particle motion in fluid-solid systems based on dynamic imaging with a gamma scintillation camera. A two-dimensional spouted bed of 200-500 micron diameter anion exchange resin beads was used as a test system. One or several beads were radiolabeled with the 140 keV gamma emitting radionuclide 99m-Tc pertechnetate, and particle velocity, panicle path, the spatial distribution of particle residence times, and local bed density were determined from the measured temporal and spatial distributions of particle activity. While care must be exercised in the interpretation of data when the scale for changes in the spatial distribution of activity approaches the limits of camera resolution, the method is quantitative, non-invasive, and well suited to the study of systems having symmetry in one spatial dimension.     

Numerical Simulation of a Spouted Bed Using Computational Fluid Dynamics (CFD)

In this article, computational fluid dynamics (CFD) technology is used to model a spouted bed(SB). The multifluid Eulerian-Eulerian approach based on kinetic theory of granular flows and Gidaspow's drag model for the interaction between gas and particles are applied in the modeling. The effects of the SB properties—that is, cone angle, particle size, cylinder diameter, and static bed height of particles—on its dynamics performance are investigated. The simulated results—that is, flow pattern of particles, fountain height, voidage, and particle velocity of the spout zone—are presented. It is shown that periodic fluctuation of spouting appears in an SB with conical angle of 30° and inlet velocity at 16.6 m/s. When the SB cylinder diameter becomes 0.52 m, periodic fluctuation appears, too. The stable spouting of the SB with a 90° cone angle could be obtained at an inlet air velocity of 24.3 m/s. The fountain height of particles decreased with an increase in particle size and the static bed height of particles. It is kept at about 0.19 m when different SB cylinder diameters in the range of 0.36 to 0.48 m are used. In the spouting region, the voidage decreased with static particle height in bed, but the particle velocity increased. For a certain particle size, the voidage decreased with an increase in particle height, but the velocity of the particles increased. It was also found that the cylinder diameter did not affect the volume fraction of particles except for the cylinder diameter 0.52 m and the change in particle velocity was minimal in the spout zone. With the different static bed height of particles used, the voidage and particle velocity did not change much at the same level of spout zone.     

DEM simulation on particle mixing in dry and wet particles spouted bed

In this paper, the mixing characteristics of the dry and wet particles in a rectangular spouted bed are simulated using a three-dimensional discrete element method (DEM). In particular, the influence of turbulence and liquid bridge force is investigated using the standard k-ε two-equation model and the Mikami model. The Ashton mixing index is adopted to evaluate the dynamic mixing process of the particle system. The geometry of the simulated bed is the same as that of the experimental bed by Liu et al. [G. Q. Liu, S. Q. Li, X. L. Zhao, Q. Yao. Chem. Eng. Sci. 63 (2008) 1131-1141]. The effect of the spouting gas velocity on the mixing process is discussed for the mixing of dry particles (without the liquid bridge force), while the effect of the moisture content is discussed for the mixing of wet particles (with the liquid bridge force).     

Bridging diverse physical scales with the discrete-particle paradigm in modeling colloidal dynamics with mesoscopic features

Microstructural dynamics and boundary singularities generate complex multiresolution patterns, which are difficult to model with the continuum approaches using partial differential equations. To provide an effective solver across the diverse scales with different physics the continuum dynamics must be augmented with atomistic models, such as non-equilibrium molecular dynamics (NEMD). The spatio-temporal disparities between continuum and atomistic approaches make this coupling a computationally demanding task. We present a multiresolution homogeneous particle paradigm, as a cross-scale model, which allows producing the microscopic and macroscopic modes in the mesoscopic scale. We describe a discrete-particle model in which the following spatio-temporal scales are obtained by subsequent coarse-graining of hierarchical systems consisting of atoms, molecules, fluid particles and moving grid nodes. We then show some examples of 2-D and 3-D modeling of the Rayleigh-Taylor fluid instability, phase separation, colloidal arrays and colloidal dynamics in the mesoscale by using fluid particles as the exemplary discretized model. The modeled multiresolution patterns are similar to those observed in laboratory experiments. We show that they can mimic scales ranging from single micelle, colloidal crystals, colloidal aggregates up to the macroscopic phenomena involving the clustering of red blood cells in the vascular system. We can summarize the computationally homogeneous discrete-particle model in the following hierarchical scheme: non-equilibrium molecular dynamics (NEMD), fluid particle model (FPM), thermodynamically consistent DPD and smoothed particle hydrodynamics (SPH).     

Discrete element method simulation of three-dimensional conical-base spouted beds

A discrete element method (DEM) simulation of three-dimensional conical-base spouted beds is presented. The overall height and diameter of the vessel are 0.5 and 0.15 m, respectively, and the nozzle diameter is 0.02 m. The inclined angle of the conical section varies from 0 to 60 degrees. The gas flow is described by the continuity and Navier-Stokes equations and solved by a finite difference method of second order accuracy in space and time. For gas-particle interaction, the Ergun equation (for void fraction smaller than 0.8) and the Wen-Yu model (for void fraction of 0.8 and above) are employed. A new method for treatment of the boundary condition for 3-D gas flow along the cone surface is proposed. This boundary condition satisfies both the continuity and momentum-balance requirements for the gas phase. Usefulness of the present simulation for studying gas flow pattern and particle motion in conical-base spouted beds is demonstrated. The effects of the inclined angle and draft tube on gas and particle flow in spouted beds are discussed.     

Discrete element simulation of a flat-bottomed spouted bed in the 3-D cylindrical coordinate system

A spouted bed is simulated in three dimensions by a discrete element method (DEM) in a cylindrical coordinate system. The numerical scheme is based on a second order finite difference method in space and a second order Adams-Bashforth method for time advancement. Gas-particle interaction is assumed to obey the Ergun equation (for void fraction less than 0.8) and its corrected model by Wen and Yu (for void fraction greater than 0.8). The spouted bed vessel is a flat-bottomed cylinder in height and in diameter. The gas inlet diameter is . Three hundred thousand monosized spheres of diameter are used in the simulation. The typical characteristics of spouted beds, such as spout, annulus and fountain, are reproduced. Particle velocity profiles show good agreement with experimental results and self-similarity of the radial distribution of axial particle velocities is reported. Gas flow patterns are also studied and the effect a vortex ring fixed at the bottom of the vessel is investigated. The simulation is validated through comparisons with results reported in the literature.     

Bubble evolution through submerged orifice using smoothed particle hydrodynamics: Basic formulation and model validation

Smoothed particle hydrodynamics is used to simulate the bubble evolution in liquid pool through a submerged orifice. Discontinuities in the physical properties along the interface are taken care using appropriate smoothening functions. Surface tension at the interfacial plane is also added in the momentum equation to track the evolution of the bubbles. To prevent abrupt intrusion of one fluid into the other no penetration force is applied for two closely situated particles of different properties. Solid walls are modelled with two layer of virtual particle along the boundary. Further, the use of corrective form of kernel approximation eradicates the inherent particle deficiency at the interface and solid boundary. The model is capable to simulate the growth of the bubble, neck formation and its detachment from the orifice along with the dynamic velocity field in both the phases. Comparison between the numerical bubble contour and published results shows excellent predictability of the model. The volume of the bubble at the detachment and the bubble frequency are compared satisfactorily with available experimental observations.     

Conceptual comparative study between efficient collision-handling algorithms used for Molecular Dynamics (MD) and Discrete Particle Model (DPM)

It is deemed substantial that understanding the conceptual differences between the hard-sphere Discrete Particle Model (DPM) and the event-driven Molecular Dynamics (MD) regarding the collision-event handling will help the design of new algorithms to increase the efficiency of collision-handling operations for DPM. The latter has gone largely unrecognized by most of the DPM-based numerical works on fluidization systems. We elaborated these differences and conceptually compared the only two O(1) time complexity algorithms developed for MD and DPM. It was shown that the hash-table strategy that takes into account the main features of fluidization systems increased considerably the efficiency of collision-handling algorithm for DPM.     

Discrete element study of particle circulation in a 3-D spouted bed

A spouted bed is simulated by a discrete element method in a full 3-D cylindrical coordinate system. The vessel is a flat-bottomed cylinder 0.5 m in height and 0.15 m in diameter. In the simulation 300,000 mono-sized spherical glass beads are used. The numerical scheme is based on a second order finite difference method in space and a second order Adams-Bashforth method for time advancement. Gas-particle interaction is modelled to obey the Ergun equation for void fraction less than 0.8, and the Wen-Yu model, for void fraction greater than 0.8. In the present study, particle motion and circulation are investigated. Predicted streamlines of time-averaged particle flow are almost vertical in the upper part of the bed, gradually bending to the spout core in the lower region. Particle velocities along the streamlines are uniform in the upper part of the annulus, becoming non-linear with respect to the distance from the dead zone in the lower part of the annulus. The predicted total passages of particles across the spout-annulus boundary are in good agreement with measurements reported in the literature. Particles are found to feed from annulus to spout along the entire length of the spout. The net mass flux (from annulus to spout) is found to be constant in the upper part of the bed, increasing gradually with the depth in the lower part.     

循环喷动流化床颗粒抛射高度的计算

通过对循环喷动流化床顶部封闭空间气体射流及气固运动的理论分析 ,得出了循环喷动流化床中颗粒出循环管后抛射高度的计算方法 ,所得计算结果与实测结果误差小于 8% ,为循环喷动流化床的设计提供理论依据