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.     

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.     

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.     

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.     

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.     

Mixing and circulation of solids in spouted beds: particle tracking and Monte Carlo emulation of the gross flow pattern

Mixing and circulation of monosized particles in laboratory-scale tapered spouted beds have been characterized experimentally by measuring non-invasively the 3-D trajectory of a single tracer via a radioactive velocimetry technique. Processing the obtained Lagrangian trajectory allowed determination of the mixing dynamics in the longitudinal, radial and circumferential directions, of the return length and return time distributions, and of the mean Eulerian flow fields. A conceptual solids flow structure has been delineated. A four-zone 2-D axisymmetrical Monte Carlo model has been developed for emulating the elementary steps in play in the longitudinal mixing, i.e., the direction of slowest mixing, and in the return (or circulation) time and length of the solids phase. The four-zone solids flow structure is viewed as: (i) a spout region with a constant upward particle velocity, (ii) an annulus region above the conical base with a downward velocity radial profile, (iii) an annulus region within the conical base where the linear velocity, considered to be parallel to the cone wall, is equal to that of the incoming particles, (iv) a fountain in which the particle movement is characterized by the particle residence time, an exiting radius, and an average fountain height. The model proved successful in restoring the measured return time and return length distributions, and the mixing response curves.     

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).     

A study of solid behavior in spouted beds using 3-D particle tracking

A non-invasive γ-ray emission system, employing eight NaI detectors, has been developed to follow the motion of a single radioactive particle in a three-dimensional spouted bed reactor. The count-rates measured simultaneously by the detectors are converted into tracer coordinates (x, y, z) using a pre-established calibration model which accounts for every physical and geometrical aspects involved in the spouting facility. Typically four hundred thousands successive coordinates, obtained over 3.5 hours of particle tracking, are used for determining the average particle velocity field and other hydrodynamic quantities such as the cycle time distribution, the spout shape and the solid exchange distribution at the spout boundary, which could not be evaluated accurately using any available techniques.     

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.     

光滑粒子动力学方法在复杂流动中的研究进展

光滑粒子动力学（smoothed particle hydrodynamics,SPH）是一种纯粹的拉格朗日型无网格数值方法,尤其在处理包含自由表面或多相运动界面的复杂流动问题方面具有独特优势。随着计算精度和稳定性等方面的不断完善,SPH方法已被广泛应用于科学和工程的众多领域。介绍了SPH基础理论的最新成果,重点分析了其在界面流、流固耦合、非牛顿流体等领域的研究进展,并对未来发展进行了展望。     

Effect of process conditions on particle growth for spouted bed coating of urea

The aim of this work was to analyze the influences of operational variables on particle growth for urea coating in a conventional spouted bed (CSB). An aqueous polymeric suspension was the coating liquid sprayed on the spouted particles. The effects of inlet air temperature, coating suspension flow rate and atomizing air pressure on particle growth were analyzed by a central composite rotatable design (CCRD) of experiments. The results showed particle growth in the range of 1.1–2.6%, therefore, some results below the expected for a film coating (2–8%). A second-order polynomial model was obtained for estimating particle growth as a function of the statistically significant variables: air temperature, suspension flow rate and atomizing air pressure, with percentage of explained variation R² = 90.72%. The urea growth kinetics during coating was analyzed for the optimal operating condition and a linear growth coefficient of 1.13 × 10⁻³ min⁻¹ was obtained. The volatilization analyses showed that the polymer film coating provided a decrease of the nitrogen loss in the range of 3–57%. And, SEM analyses demonstrated a total, uniform and homogeneous covering of the urea particles surface.     

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.     

Characterization and CFD-modeling of the hydrodynamics of a prismatic spouted bed apparatus

Recently the importance of spouted bed technology has significantly increased in the context of drying processes as well as granulation, agglomeration or coating processes. However, the understanding of the complex interactions within and between the single phases is still low and needs further improvement. Several research groups apply both continuum as well as discrete element simulations to understand the hydrodynamics of the spouting process. This work focuses on the simulation of the hydrodynamic behavior of a prismatic spouted bed apparatus by applying the Euler/Euler continuum approach in the commercial computational fluid dynamics (CFD) software package FLUENT 6.2. The simulations are validated by experiments. Calculated and experimental (by PIV-measurements) obtained velocity vector maps, as well as measured and calculated gas phase pressure fluctuations over the entire bed are compared. The aim of this work is to improve the understanding of the hydrodynamics of the spouting process.     

Hydrodynamics of spouted and spout-fluidized beds at high temperature

Hydrodynamic parameters were investigated in a 0.15 m diameter half-column spout-fluidized bed at temperatures up to 880°C for ratios of auxiliary air flow to total air flow from 0 to 0.62 and four narrow size ranges of silica sand. Equations in the literature gave poor agreement with the minimum spouting velocity over the entire temperature range. For large particles U_m generally increased with temperature, while for small particles it decreased. Auxiliary air had more influence at elevated temperatures than at room temperature. Pulsations leading to choking appeared to cause spout termination at elevated temperatures. The McNab and Bridgwater (1977) equation correctly predicted the observed trends for maximum spoutable bed depth at high temperatures.     

A revised mono-dimensional particle bed model for fluidized beds

The formulation of the equations of change proposed by Foscolo and Gibilaro in their original mono-dimensional particle bed model (PBM) for the prediction of the fluid-bed stability of Geldart's group A powders has been revisited along with the relevant closure relationships. The buoyancy has been expressed in accordance with its “classical” definition, which regards it as being equal to the weight of the fluidizing fluid displaced by the particle phase. A new constitutive equation has been developed for the drag force; this proves more accurate than the expression used in the original PMB particularly in the intermediate flow regimes comprised between the viscous and inertial ones. The “elastic” force has been estimated by employing a rigorous approach which needs not resort to equilibrium-based relations. The result, enhanced in accuracy and breadth of validity, considers “elastic” force and drag force proportional. The equations of change themselves have been partly revised. The pressure gradient is no longer shared by the two phases in proportion to their volume fractions, but has been accounted for only in the continuous one. Conversely, the “elastic” force has been included, with opposite signs, in the linear momentum equations pertaining to both phases, so that the principle of action and reaction, to which the force is subjected, is fulfilled. The revised model has been validated by performing a fluid-bed stability analysis on a wide range of Geldart's group A powders at different operating temperatures. Predicted values for the minimum bubbling voidage estimated by means of the revised model have been compared with experimental values and with predictions from both the original Foscolo and Gibilaro model and that previously revised by Jean and Fan. The latter has been found to be always in good agreement with the model proposed here, whereas the former has seemed to somewhat underestimate the bed minimum bubbling voidage thus anticipating the transition between homogeneous and bubbling fluidization. All of the models have proved to yield predictions whose validity is strongly dependent on the particular powder in hand and on the operating conditions considered.     

Comparison of cohesive zone elements and smoothed particle hydrodynamics for failure prediction of single lap adhesive joints

This research investigates the use of a meshless smoothed particle hydrodynamics (SPH) method for the prediction of failure in an adhesively bonded single lap joint. A number of issues concerning the SPH based finite element modelling of single lap joints are discussed. The predicted stresses of the SPH finite element model are compared with the results of a cohesive zone based finite element model. Crack initiation and crack propagation in the adhesive layer are also studied. The results show that the peel stresses predicted by the SPH finite element model are higher and the shear stresses are lower than those predicted by the cohesive zone finite element model. The crack initiation and propagation response of the two models is similar, however, the SPH finite element model predicted a lower failure load than the cohesive zone finite element model. It is concluded that the current implementation of SPH method is a promising method for modelling cohesive failure in bonded joins but requires further development to allow for interfacial crack growth and better stress prediction under tensile loading to compete with existing methods.