Estimation of particle dynamics in 2-D fluidized beds using particle tracking velocimetry

The experimental characterization of particle dynamics in fluidized beds is of great importance in fostering an understanding of solid phase motion and its effect on particle properties in granulation processes. Commonly used techniques such as particle image velocimetry rely on the cross-correlation of illumination intensity and averaging procedures. It is not possible to obtain single particle velocities with such techniques. Moreover, the estimated velocities may not accurately represent the local particle velocities in regions with high velocity gradients. Consequently, there is a need for devices and methods that are capable of acquiring individual particle velocities. This paper describes how particle tracking velocimetry can be adapted to dense particulate flows. The approach presented in this paper couples high-speed imaging with an innovative segmentation algorithm for particle detection, and employs the Voronoi method to solve the assignment problem usually encountered in densely seeded flows. Lagrangian particle tracks are obtained as primary information, and these serve as the basis for calculating sophisticated quantities such as the solid-phase flow field, granular temperature, and solid volume fraction. We show that the consistency of individual trajectories is sufficient to recognize collision events.     

Numerical simulation of counter-current flow field in the downcomer of a liquid–solid circulating fluidized bed

A comprehensive study on the hydrodynamics in the downcomer of a liquid–solid circulating fluidized bed (LSCFB) is crucial in the control and optimization of the extraction process using an ion exchange LSCFB. A computational fluid dynamics model is proposed in this study to simulate the counter-current two-phase flow in the downcomer of the LSCFB. The model is based on the Eulerian–Eulerian approach incorporating the kinetic theory of granular flow. The predicted results agree well with our earlier experimental data. Furthermore, it is shown that the bed expansion of the particles in the downcomer is directly affected by the superficial liquid velocity in downcomer and solids circulation rate. The model also predicts the residence time of solid particles in the downcomer using a pulse technique. It is demonstrated that the increase in the superficial liquid velocity decreases the solids dispersion in the downcomer of the LSCFB.     

基于有效参数法的固定床化学链燃烧数值模拟

本文基于有效参数法和变核颗粒模型,对固定床化学链燃烧进行数值模拟．计算并分析不同颗粒参数对二维固定床化学链燃烧结果的影响．在有效参数模型中,颗粒填充床被看作均匀的流体域．本文主要模拟了组分场和温度场,通过改变颗粒直径、孔隙率、内部粒子直径三组参数,取得了不同条件下二维固定床化学链燃烧床层所能达到的最高温度以及反应所用的时间．通过对不同参数模拟结果的分析,得出颗粒内部结构对反应特性的影响规律．     

SPH-based simulation of granular collapse on an inclined bed

The paper presents a numerical model for simulating a granular flow and its deposition on an inclined bed. A granular material is described as an elastic–plastic continuum and its constitutive law, namely Hooke's law, is discretized on the basis of the Smoothed Particle Hydrodynamics (SPH) method. In the equation of motion, however, the artificial viscosity, which is widely used in SPH, is not applied. The diffusive term derived from Hooke's law is introduced with a diffusion coefficient that varies depending on the stress and strain rate based on the Drucker–Prager yield function. The model is verified and validated through two numerical tests. It is shown that the basic elastic–perfectly plastic characteristics are reproduced with a simple shearing test. The effects of the diffusion coefficient and spatial resolution are investigated to show the validity of the model. In the simulation of the gravitational collapse of a granular column on an inclined bed, the performance of the model from the final deposition profile, the time history of the front position of the granular flow, the maximum runout distance, and the velocity profile are investigated for several cases of basal inclinations. The calculated results show good agreement with the experimental results.     

CFD-simulation of a circulating fluidized bed riser

In the current work,a model of the fluid mechanics in the riser of a circulating fluidized bed(CFB)has been implemented using computational fluid dynamics(CFD).The model developed shall be used in future as the basis of 3D-reactor model for the simulation of large scale CFB combustors.The two-fluid model(TFM)approach is used to represent the fluid mechanics involved in the flow.The computational implementation is accomplished by the commercial software FLUENT.Different closure formulations are tested on a simplified geometry.Two different turbulence formulations,namely the swirl modified RNG k–εmodel and the Realizable k–εmodel,are tested in combination with two different approaches to solid phase turbulence,namely the dispersion and per phase approach.One focus of the current work is put on the study of different drag correlations.Besides the drag correlations by Syamlal et al.[Syamlal,M.,Rogers, W.,O’Brien,T.J.(1993).MFIX documentation theory guide.Technical Report DOE/METC-94/1004,U.S. Department of Energy(DOE).Morgantown Energy Technology Center:Morgantown,WV]and Gidaspow [Gidaspow,D.(1994).Multiphase flow and fluidization.New York:Academic Press]the EMMS model has been used to determine the momentum exchange between the two phases.The resulting formulation is then used to simulate a 1-m×0.3-m cold CFB setup and is validated by experimental results[Schlichthrle, P.(2000).Fluid dynamics and mixing of solids and gas in the bottom zone of circulating fluidized beds. Unpublished doctoral dissertation,Technische Universitaet Hamburg-Harburg,Shaker Verlag:Aachen].     

A numerical investigation into the solids phase chromatography using a combined continuous and discrete approach

Solids phase chromatography for particle classification is based on different retention times of particles with different properties when they are elutriated through a confined geometry. This work aims at a fundamental understanding of such a technology by using the combined continuous and discrete method. A packed bed is employed as the model confined geometry. The numerical method is compared first with experimental observations, followed by a parametric analysis of the effects on the flow hydrodynamics and solids behaviour of various parameters including the number of injected particles, the superficial gas velocity, the contact stiffness and the diameter ratio of the packed column to the packed particles. The results show that the modelling captures some important features of the flow of an injected pulse of fine particles in a packed bed. An increase in the number of injected particles or the superficial gas velocity reduces the retention time, whereas the contact stiffness does not show much effect over the range of 5 × 10^2 to 5× 10^4 N/m. It is also found that the effect on the retention time of the diameter ratio of the packed column to the packed particles seems complex showing a non-monotonous dependence.     

Hydrodynamic behavior of an internally circulating fluidized bed with tubular gas distributors

To better understand the hydrodynamic behavior of an internally circulating fluidized bed, solids holdup in the down-comer （Eso）, solids circulation rate （Gs） and gas bypassing fraction （from down-comer to riser y~R, and from riser to down-comer yRD） were experimentally studied. The effects of gas velocities in the riser and in the down-comer （UR and UD）, orifice diameter in the draft tube （dor）, and draft tube height （HR） were investigated. Experimental results showed that increase of gas velocities led to increase in Gs and yDR, and slight decrease in yeD. Larger orifice diameter on the draft tube led to higher 8sD, Gs and yDR, but had insignificant influence on YRD. with increasing draft tube height, both Gs and YDR first increased and then decreased, while yRD first decreased and then increased. Proposed correlations for predicting the hydrodynamic parameters agreed reasonably well with experimental values.     

SPH modelling of depth‐limited turbulent open channel flows over rough boundaries

A numerical model based on the smoothed particle hydrodynamics method is developed to simulate depth‐limited turbulent open channel flows over hydraulically rough beds. The 2D Lagrangian form of the Navier–Stokes equations is solved, in which a drag‐based formulation is used based on an effective roughness zone near the bed to account for the roughness effect of bed spheres and an improved sub‐particle‐scale model is applied to account for the effect of turbulence. The sub‐particle‐scale model is constructed based on the mixing‐length assumption rather than the standard Smagorinsky approach to compute the eddy‐viscosity. A robust in/out‐flow boundary technique is also proposed to achieve stable uniform flow conditions at the inlet and outlet boundaries where the flow characteristics are unknown. The model is applied to simulate uniform open channel flows over a rough bed composed of regular spheres and validated by experimental velocity data. To investigate the influence of the bed roughness on different flow conditions, data from 12 experimental tests with different bed slopes and uniform water depths are simulated, and a good agreement has been observed between the model and experimental results of the streamwise velocity and turbulent shear stress. This shows that both the roughness effect and flow turbulence should be addressed in order to simulate the correct mechanisms of turbulent flow over a rough bed boundary and that the presented smoothed particle hydrodynamics model accomplishes this successfully. © 2016 The Authors International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd     

Mixing and segregation of solid particles in a conical spouted bed: Effect of particle size and density

In this work, the mixing and segregation of binary mixtures of particles with different sizes and densities in a pseudo-2D spouted bed were studied experimentally. A binary mixture of solid particles including sand, gypsum, and polyurethane was used. To determine the particles mass fraction, and their mixing and segregation in the bed, an image-processing technique was developed and used. Important hydrodynamic parameters, such as the axial and radial segregation profiles of the solid particles, were measured. The effects of air velocity, particle size, and particle mass fraction were also evaluated. The flow regime in the spouted bed and the time required for reaching the equilibrium state of the solid particles were discussed. The results showed that the segregation of solid particles and the time to equilibrium both decreased when the air velocity increased to much larger than the minimum spouting velocity. The axial segregation increased with the diameter ratio of the particles. Upon completion of the test, coarse particles were concentrated mainly in the spout region, while fine particles were aggregated in the annulus region. Examination of the flow pattern in the spouted bed showed that the particles near the wall had longer flow paths, while those near the spout region had shorter flow paths.     

Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.