Annular wall layer thickness in circulating fluidized bed risers

The thickness of downward-flowing annular wall layers in circulating fluidized bed risers has been determined in the literature based on measured radial profiles of both local particle velocity and solids flux. The thickness of the wall layer is shown to be larger based on solids flux profiles than when based on particle velocity profiles, because fluctuations in local instantaneous particle velocity are correlated with fluctuations in local solids concentration. A new correlation is developed to predict the time-average thickness of the downflowing particle streamer layer based on solids flux measurements as a function of the cross-sectional average voidage. It successfully accounts for the variation of the wall layer thickness with axial location and solids circulation rate.     

Discrete element method modeling of non-spherical granular flow in rectangular hopper

Discrete element method (DEM) was developed to simulate the corn-shaped particles flow in the hopper. The corn-shaped particle was described by four overlapping spheres. Contact force and gravity force were considered when establishing the model. In addition, the velocity distribution and voidage variance of corn-shaped and spherical particles were investigated. The results show that the vertical velocity difference between centre and side wall and the horizontal velocity of corn-shaped particles are relatively larger than that of spherical particles. The mean voidage for corn-shaped particles is smaller than for spherical particles in any hopper. And the mean voidage values decrease with the increase of the ratio of width and length (D/L) and the ratio of height and width (H/D) for both corn-shaped and spherical particles. The local voidage profiles in hoppers with different D/L were also studied. It demonstrates that the wall effect on the voidage of spherical particles is more remarkable than that of the corn-shaped particles. The voidage fluctuations of corn-shaped and spherical particles decrease obviously with increasing D/L when the particles are far away from the wall. And when the particles are discharging, the wall effect on the spherical particles is more remarkable than the condition of packing naturally.     

Voidage distribution around bubbles in a fluidized bed: Influence on throughflow

In this work, a new method for measuring void fraction distribution around endogenous bubbles in a 2D fluidized bed is presented. The technique is based on illuminating a transparent-wall 2-dimensional bed with diffuse light from the rear and recording the distribution of light that penetrates the bed. The recording is made with a high speed video-camera, which gives frames with grey level corresponding to the light penetration and from which the voidage distribution around the bubbles can be determined. In this way, voidage distribution in the region very close to the bubble contour (r/R_b ? 1.2) is obtained, which was not possible in previous studies due to limitations in spatial resolution. A correlation is proposed for the voidage at the contour of the bubble, with the voidage depending on the radial position and the polar angle ε(r, θ).In addition, the effect of the voidage distribution on the throughflow crossing the bubbles was studied and an increase of 20% was determined for the average bubble geometry of the more than 100 bubbles analysed.     

A priori modelling of an adiabatic spouted bed catalytic reactor

An a priori reactor model for an adiabatic spouted bed reactor has been developed. This model uses first-principles mass and energy balances to predict the concentration and temperature profiles in the spout, annulus and fountain regions of the reactor. The particle circulation and voidage profiles in the spout are calculated using previously developed analytical techniques. Particle circulation patterns in the annulus are determined by a minimum path-length analysis. The spout and fountain are shown to contribute significantly to the overall conversion in the bed. Predicted and experimental conversions at flowrates up to 1.2U_ms show that extension of the fountain reaction zone and increased particle circulation with increasing inlet flow makes up for the higher average voidage in the spout and fountain. Experimental data confirm the calculated results for a stably spouting bed with CO oxidation over a Co₃O₄/αAl₂O₃ catalyst. The effects of flowrate and inlet reactant concentration are confirmed.     

Experimental Study on Bubble Rising and Descending Velocity Distribution in a Slurry Bubble Column Reactor

To determine bubble rising and descending velocity simultaneously, a BVW‐2 four‐channel conductivity probe bubble parameters apparatus and its analysis are used in gas‐liquid and gas‐liquid‐solid bubble columns. The column is 100 mm in internal diameter and 1500 mm in height. The solid particles used are glass beads with an average diameter of 17.82 μm, representing typical particle size for catalytic slurry reactors. The effects of superficial gas velocity (1.0 cm/s ≤ U_g ≤ 6.4 cm/s), solid holdup (0 % ≤ ?_s ≤ 30 %), and radial location (r/R = 0, 0.4, and 0.7) on bubble velocity distributions are determined. It is found that increasing U_g can increase the velocity of bubbles but do not exert much influence on bubble velocity distribution. Solid holdup mainly affects the distribution of bubble velocity while the radial direction affects bubble velocity distribution only slightly. The ratio of descending bubbles to rising bubbles increases from the bubble column center to the wall. It can be proved experimentally that large bubbles do not always rise faster than small bubbles at higher U_g (for example 6.4 cm/s).     

湍动流化床过渡段固含率分布特征的实验及数值模拟

在湍动流化床中,过渡段对于包括甲醇制烯烃在内的气固催化快反应有着重要的作用。采用PV6D反射型光纤探针对内径95 mm的湍动流化床内过渡段的固含率分布和脉动参数进行了测量,分别考察了表观气速和静床高的影响,并采用修正的基于颗粒动力学的三段曳力双流体模型进行模拟。实验表明,湍动流化床过渡段中固含率的轴向分布呈现S型和指数型两种类型,固含率轴向与径向分布都在过渡段内出现最大梯度,表明过渡段中固体浓度分布比稀相段和密相段更不均匀。表观气速和静床高的变化将导致S型和指数型分布的相互转变,并且对过渡段底部与壁面附近的固体高浓度区影响最为显著。局部固含率脉动概率密度分布表明,在静床高较小时,随着气速的增大,床层下部气含率最大值位置将从中心区移动至环隙区,呈现气含率的双峰型分布。本文提出的修正三段曳力模型考虑了颗粒团聚的影响,对过渡段中分布板影响区之外的固含率分布均能较好地模拟。     

Stability of an inclined,pneumatically‐transported system of particles

A linear stability analysis is performed on the base‐state solution describing a pneumatically‐transported system inclined at an angle θ. One of two modes was found to be dominant, depending on the tilting angle: a low‐shear mode whose voidage eigenmode remains nearly symmetric from 0° < θ ≤ θ_c, and a “boundary layer” mode for θ > θ_c, marked by significant asymmetry throughout the domain and a high level of shear inside the thin regions adjacent to the walls. The critical angle θ_c increases with the amount of momentum and energy lost to particle–wall friction and collisions, respectively. The time‐evolution of the latter mode, superimposed onto the base‐state solution, reveals an alternating train of dense and dilute regions near the top of the domain, which agrees qualitatively with the development and propagation of bubbles in inclined systems observed in experiment. An analytic solution corresponding to a vertical system with a uniform base state was also derived to identify the instability mechanisms responsible for a class of non‐oscillatory transverse waves which exist in both vertical and tilted particle systems. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2248–2258, 2016     

Evaluation of radial voidage profiles in packed beds of low‐aspect ratios

The relationship between the radial voidage profile, ?(r), and the radial distribution of centres of mono‐sized spherical particles, f(r), is revised. A close expression is given for the section S(r₁, r_c), the area of the segment of a cylindrical surface of radius r intersected by a particle centred at r_C. From this expression, ?(r) can be evaluated straightforwardly from the knowledge of f(r). The range 1≥ a ≥ 2 of aspect ratios (a = d_T/d_p is then analysed specifically. For this range, the distribution of spherical particles has been characterized theoretically (Govindarao et al., 1992) and a simple expression allows the evaluation of ?(r). The use of this expression for actual catalyst particles, imperfect spheres showing a distribution of sizes, in finally analyzed.     

气固逆流下行流化床中颗粒速度的径向与轴向分布

在内径90 mm、高7 m的逆流下行床冷态实验装置中,研究了气固逆流下行床中循环锅炉灰(dp=300 mm)颗粒速度的径向分布及其沿轴向发展. 结果表明,局部颗粒速度沿径向分布是不均匀的,在完全发展区,颗粒速度中心和边壁低、在r/R=0.85附近颗粒速度最大. 由大量实验数据回归出预测充分发展段局部颗粒速度的关联式,该公式计算值与实验值的平均相对偏差小于±11%. 不同径向位置的局部颗粒速度沿轴向的变化趋势不同,边壁区域(r/R>0.622)颗粒速度沿轴向单调递增,而中心区域(0相似文献   

Wall-to-bed heat transfer in liquid—solid and gas—liquid—solid fluidized beds part I: Liquid—solid fluidized beds

Experimental work was conducted to investigate the effect of particle size and particle density upon the wall-to-bed heat transfer characteristics in liquid—solid fluidized beds with a 95.6 mm column diameter over a wide range of operating conditions. The radial temperature profile was found to be parabolic, indicating the presence of a considerable bed resistance. The effective radial thermal conductivity and the apparent wall film coefficient were obtained on the basis of a series thermal resistance model. The modified Peclet number of the radial thermal conductivity decreases upon the onset of fluidization, has a minimum at a bed porosity of 0.6 to 0.7 and increases with further increase of bed porosity. The modified Peclet number decreases considerably with decreasing particle size or increasing particle density. The apparent wall heat transfer coefficient can be represented well by a Colburn j-factor correlation over a wide range of data as follows: j′_H = 0.137 Re′^?0.271 A close analogy is found to exist between the modified j-factor for wall heat transfer coefficient and that for wall mass transfer coefficient, in liquid—solid fluidized beds.     

Influence of solids concentration and static mixers on fluid dynamics in three-phase fluidized bed bioreactors

The influence of solids concentration and static mixers on the hydrodynamics of the gas phase was studied for a three-phase fluidized bed bioreactor (air, nutrient solution, biocatalyst Ca alginate beads). Axial gas hold-up profiles, radial gas velocity profiles, mean bubble diameter and gas/liquid interfacial area per unit volume were measured in a bubble column (D_R = 0.142 m, H_R = 1.748 m). The influence of solids concentration on the gas hold-up is insignificant; static mixers enhance the gas hold-up in the reactor volume element in which they are installed. Axial gas velocity decreases with increasing solids concentration. At high solids concentrations, static mixers exert little influence on the gas phase but, at low concentrations, they do. A model is suggested to describe the influence of solids concentration (characterized by turbulent viscosity v_t) and static mixers (characterized by profile parameter n) on the gas velocity profile.     

Small-angle neutron scattering of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers

Small-angle neutron scattering was used to characterize the structure of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers dissolved in methanol-d4 (CD₃OD). A radial density profile based on a power law functional form provided a good fit to the scattering data. While a model with homogeneous density profiles in the core and shell, respectively, and with a size distribution (a polydisperse core-shell model) also fits the data comparably well, the extra parameters required for this fit are difficult to justify on the basis of the data. In addition, unconstrained fits using the core-shell model failed to converge to values of the overall molecular size and molecular weight which agreed with values determined from independent light scattering measurements which leads to the conclusion that the power law model is a more appropriate function for describing the radial density function of these molecules. The density profile from either model showed that the polystyrene core of the molecules is not collapsed. Values of the second virial coefficient, A₂, have been calculated from Zimm plots and it was found that A₂ decreased as a function of generation to close to zero for the highest generation (i.e. highest molecular weight) polymers. Finally, it was found that the radius of gyration of the polymers increases with the molecular weight according to the scaling relationship, R_g∼M_w^v with v=0.24±0.04.     

Experimental analysis of temperature and crystallinity profiles of wood sawdust/polypropylene composites during cooling

The temperature profiles of wood sawdust/polypropylene (PP) composite melts during cooling were experimentally investigated with a cooling jacket apparatus connected to the end of an injection‐molding machine. Real‐time melting temperature was measured with an unsheathed thermocouple array coupled with a high‐speed data‐acquisition unit. The crystallinity level of the solidified composites was evaluated with an X‐ray diffractometer. Before the crystallization temperature (T_c) was reached, the cooling rate of the melt layer near the wall was greater than that near the center. After T_c was reached, the opposite behavior was observed. Wood sawdust content did not affect the general temperature and crystallinity profiles across the duct diameter but led to more nonuniform temperature profiles across the duct diameter. The sawdust particles could act as a nucleating agent during the nucleation stage to increase T_c of the PP and as an interfering agent during the crystal growth stage to decrease the overall crystallinity level of the PP. The temperature and crystallinity profiles were not affected by the coolant flow rate. The normalized induction time changed with reduced radius (r/R, where r is the distance between the central duct to any point along the cross‐section of the duct and R is the duct radius) positions and coolant flow rate, especially for neat PP and PP composites with a low sawdust content (10 wt %). © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 1896–1905, 2006     

Effect of the surface roughness and construction material on wall slip in the flow of concentrated suspensions

Recent studies on polyethylene, elastomers, and thermoplastics have revealed that the construction material and surface roughness are two important factors affecting wall slip. In this study, to determine the true rheological behavior of model concentrated suspensions, a multiple‐gap separation method was used in a parallel disk rheometer. The model suspensions studied were poly (methyl methacrylate) particles with an average particle size of 121.2 μm in hydroxyl‐terminated polybutadiene. The aim of this study was to investigate the effect of disk R_a in the range of 0.49–1.51 μm and disk construction material on the wall slip and the true viscosity of the model concentrated suspensions. The wall slip velocity and the viscosity were found to be independent of R_a for particle size‐to‐disk R_a ratios of 80–247. Also, the true viscosity was found not to be affected by the rheometer surface construction material. Glass surfaces resulted in the highest slip velocity, whereas aluminum surfaces resulted in the lowest slip velocity. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3341–3347, 2007     

Gasdynamic model of dilute two-phase combustion fields

A gasdynamic model of two-phase combustion fields is proposed. The model is based on an extension of our dilute heterogeneous-continuum formulation, where now the particle phase is modeled thermodynamically as a particle gas (with a pressure p ₂, temperature T ₂, and internal energy u ₂, given by the kinetic theory for hard spheres with γ ₂ = 5/3), thereby, resulting in particle gas conservation laws for mass, momentum, and total energy. The particles also possess a thermal storage capacity, expressed in terms of an internal energy of the solid e _s = c _s T _s with its own temperature T _s , and the corresponding energy conservation law. The consequence of this formulation is that both phases are hyperbolic, but decoupled; so each phase has it own complete set of eigenvalues and eigenvectors. The conservation laws for each phase can be integrated with a high-order Godunov scheme. Phases are coupled only through drag, heat, and mass transfer. The model is used to simulate aluminum particle combustion in a shock-dispersed-fuel explosion. Taking advantage of the point symmetry inherent in this problem, the flow field is azimuthally averaged in θ and φ directions to extract the mean and root-mean-square radial profiles of the thermodynamic fields, velocity fields, and reaction zone profiles. We find that the particle gas pressure influences the flow only during the initial phase of particle acceleration: as the compaction wave moves through the powder, followed by the rarefaction wave from the free surface. Thereafter, the particle pressure decays rapidly and particle accelerations are dominated by drag. Nevertheless, this seems to affect the dispersion process because the combustion cloud shape is somewhat different from previous results.     

Scale‐dependent nonequilibrium features in a bubbling fluidized bed

We investigate experimentally the nonequilibrium features in a pseudo 2‐D bubbling fluidized bed. Velocities of individual particles are measured by using a particle tracking velocimetry (PTV) method, and void fractions are obtained with the Voronoi tessellation. A bimodal shape of probability density function (PDF) for particle vertical velocity is found in not only time‐averaged but also time‐varying statistics, which is caused by the transition between the dense and dilute phases and breaks the local‐equilibrium assumption in continuum modeling of fluidized beds. The results of time‐varying radial distribution function and voidage distribution also confirm this finding. Moreover, the analysis of voidage, particle velocity, granular temperature and turbulent kinetic energy of particles shows that there is no scale‐independent plateau over the interface, and it seems hard to find a scale‐independent plateau to separate the micro‐ and meso‐scales of fluidized beds, which require sub‐grid meso‐scale modeling for continuum or coarse‐graining methods of gas‐fluidized systems. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2364–2378, 2018     

Voidage profiles in packed beds of spheres

Voidage profiles in randomly packed beds of uniformly sized spheres are analysed by dividing the bed into a number of concentric layers of equal thickness, and by expressing the void fraction in a layer in terms of the contributions to the solid volume by spheres with centres lying in appropriate neighbouring layers. The number of spheres in a layer is expressed as a fraction of the total number in the bed. Sets of number fractions in layers up to a distance of about 4–5 particle diameters from the wall are estimated for different aspect ratios using several sets of reported void fraction data obtained by a variety of experimental methods. The number of fractions in the layer next to the one at 0.5 particle diameter from the wall and at 1.5 particle diameters completely characterize the voidage variations up to a distance of about 2 particle diameters from the wall. In this region the confining effect of the wall gives rise to these two non-random layers of the spheres. The two number fractions are correlated exponentially with the aspect ratio. Beyond this region, the structure of the packing becomes more and more random. A procedure is suggested for predicting the void fractions at distances between 2 and 4 particle diameters.     

Influence of the mass flow rate of secondary air on the gas/particle flow characteristics in the near-burner region of a double swirl flow burner

The influence of the mass flow rate of secondary air on the gas/particle flow characteristics of a double swirl flow burner, in the near-burner region, was measured by a three-component particle-dynamics anemometer, in conjunction with a gas/particle two-phase test facility. Velocities, particle volume flux profiles, and normalized particle number concentrations were obtained. The relationship between the gas/particle flows and the combustion characteristics of the burners was discussed. For different mass flow rates of secondary air, annular recirculation zones formed only in the region of r/d=0.3–0.6 at x/d=0.1–0.3. With an increasing mass flow rate of secondary air, the peaks of the root mean square (RMS) axial fluctuating velocities, radial mean velocities, RMS radial fluctuating velocities, and tangential velocities all increased, while the recirculation increased slightly. There was a low particle volume flux in the central zone of the burner. At x/d=0.1–0.7, the profiles of particle volume flux had two peaks in the secondary air flow zone near the wall. With an increasing mass flow rate of secondary air, the peak of particle volume flux in the secondary air flow zone decreased, but the peak of particle volume flux near the wall increased. In section x/d=0.1–0.5, the particle diameter in the central zone of the burner was always less than the particle diameter at other locations.     

CFD modeling of radial spreading of flow in trickle-bed reactors due to mechanical and capillary dispersion

CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to mechanical and capillary dispersion. Simulations are performed with various particle sizes and the significance of the dispersion mechanisms at the industrially relevant particle size range is analyzed. The effect of the bed porosity distribution and particle size to the simulation results is also discussed. The choice of the radial porosity profile is found to have a significant impact to the simulation results, especially when the column to particle diameter ratio, D/d_p, is small, in which case the wall flow is important. The dependence of the standard deviation of porosity on the sample size is determined experimentally. Introducing just random variation of porosity to the model is found to describe inadequately the dispersive flow behavior. The presented hydrodynamic model with proper capillary and mechanical dispersion terms succeeds in capturing the features of the two independent physical phenomena. Separate models are presented for each dispersion mechanisms and it is shown that they both can have a significant contribution to the overall dispersion of liquid flowing through a packed bed. The hydrodynamic model is validated against the experimental dispersion profiles from Herskowitz and Smith [1978. Liquid distribution in trickle-bed reactors. A.I.Ch.E Journal 24, 739-454], Boyer et al. [2005. Study of liquid spreading from a point source in trickle-bed via gamma-ray tomography and CFD simulation. Chemical Engineering Science 60, 6279-6288] and Ravindra et al. [1997. Liquid flow texture in trickle-bed reactors: an experimental study. Industrial & Engineering Chemistry Research, 36, 5133-5145]. The extent of liquid dispersion predicted by the presented hydrodynamic model is in excellent agreement with the experiments.     

Direct Measurements of Instantaneous Solid Flux in a CFB Riser using a Novel Multifunctional Optical Fiber Probe

With a novel optical fiber probe that can measure instantaneous local particle velocity and solid concentration simultaneously, extensive experiments were conducted to study transient flow structures in a 15.1‐m long circulating fluidized bed (CFB) riser of 100 mm in diameter. This study analyzed the radial and axial distributions of solid concentration, particle velocity, and their variations with nine operating conditions and at six axial levels. Instantaneous local solid concentration and particle velocity were found to be well correlated at most of the radial positions. The detailed time evolution, axial and radial distribution of instantaneous solid flux, and the variation of solid flux with operating conditions were also investigated. The radial solid flux profile showed a flat shape with a maximum at near wall area under most operating conditions. The instantaneous solid flux was found to have a strong fluctuation at a radial position of r/R = 0.8 ~ 0.9.