Design Simulation of Glass-Fiber-Loaded Flow in ... - ACS Publications

ARTICLE pubs.acs.org/IECR

Design Simulation of Glass-Fiber-Loaded Flow in an Internally Spout-Fluidized Bed for Processing of Thermoplastic Composites. I. Flow Characterization Yuan Zong,† Xiaogang Yang,*,‡ and Gance Dai*,† † ‡

State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China Institute of Arts, Science and Technology, Glynd^ w r University, Wrexham LL11 2AW, United Kingdom ABSTRACT: A novel fiber dispersion process suitable for the manufacture of composites consisting of long glass fibers and thermoplastic is discussed. An internally spout-fluidized bed with a draft tube and disk baffle has been designed to disperse fiber bundles and perform preimpregnation, which can improve the hydrodynamic behavior inside the spout-fluidized bed for more effective dispersion of fiber bundles and impregnation with resin powder when applying such beds in the manufacture of fiberreinforced thermoplastics. Features of the flow field in the spout-fluidized bed are important for fiber dispersion. Therefore, this article discusses the design results in terms of numerical simulations [large-eddy simulations (LESs)], focusing on the likely hydrodynamic impact on fiber dispersion in this particular spout-fluidized bed. Because of a strong interaction between the flow in the spout-fluidized bed and the fibers in the actual process and the limitations on direct measurements of fiber floc breakup in the spout-fluidized bed, the strength of the fiber floc was obtained by strength measurements with a rheometer. In the LES runs, the motion of the fibers was neglected because of their low volume fraction (lower than 0.001%). The turbulence kinetic energy, Reynolds stress, and strain rate were determined by statistical analysis. The LES results clearly indicate that the addition of internals significantly alters the flow patterns in the spout-fluidized bed, in particular changing the characteristics of the round turbulent jet and confined impinging jet. The hydrodynamics analysis showed that the introduction of internals into a spout-fluidized bed improves its capacity and efficiency for dispersing fiber flocs. These results provide important information on the flow fields within spout-fluidized beds for process design and scaleup.

1. INTRODUCTION Glass-fiber-reinforced thermoplastics have been widely used in different industrial applications. Examples include automotive, airplane, and pressure vessels where the use of unreinforced thermoplastics is unable to provide the required mechanical and thermal performance. However, the high viscosity of thermoplastics and the poor dispersion of long fibers impose many problems in the manufacturing process of thermoplastic composites. During the past decade, great efforts have been made to overcome these difficulties. To improve the impregnation with thermoplastic resins, the most attractive techniques that have been developed involve minimizing the distance that the resin must flow to penetrate the reinforcement. This observation led to the development of commingled yarns or powder impregnation. In the majority of dry processes, polymer powder is dispersed in a fluidized bed and deposit onto the fiber surface by additional force.1 For fiber dispersion, additional processing equipment, such as pneumatic spreaders, is usually employed, which increases the cost of production. Recently, State Key Laboratory of Chemical Engineering (China) has pioneered the method of using modified spoutfluidized beds for the dispersion of fiber tows and powder impregnation,2 by which new fiber-reinforced polymer composites with high quality have been obtained. The aim of this work was to explore the dispersion mechanism of the fiber flocs in a modified spout-fluidized bed by means of both floc strength measurements and numerical simulations so that the results can provide essential guidance for the optimization of the fiber floc r 2011 American Chemical Society

dispersion process. The interaction between the resin powder and the fibers will be discussed in a subsequent article. Because the cohesion strength of fiber bundles was not available from existing references, macroscopic floc strength tests for fiber flocs were conducted, and the shear energy (in terms of shear stress) required to break up the fiber flocs was measured using an Advanced Rheometric Expansion System (ARES) rheometer. Turbulent flow behaviors in a spout-fluidized bed with four different allocations of internals were investigated by large-eddy simulation (LES), so that the likely dispersion of fiber flocs in such turbulent shear flows is indicated. Fundamental studies focusing on the conversion of fiber bundles to suspended individual fibers have rarely been reported so far. This deficiency can be attributed to (1) the inherent complexity of fiber flocs, affected by their fragility, coating, and physical properties, and (2) the complex rupture mode of the fiber flocs,3 caused by surface erosion (gradual shearing off of small fragments from the surface) and large-scale splitting (break up into fragments of comparable size). The fragmentation of flocs has been applied in some chemical and biological engineering processes, such as the formation of protein precipitates,4 inorganic nanoparticles,5 and colloid particles,6 but these fragmentation Received: December 15, 2010 Accepted: June 9, 2011 Revised: June 3, 2011 Published: June 09, 2011 9181

dx.doi.org/10.1021/ie102509z | Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research processes were primarily used to deposit flocs in turbulent flows using agitated vessels, centrifuges, and other process devices. The effect of the flow field on the diameter of the flocs has been investigated by several groups.7
9 These studies demonstrated that the size of the flocs depends strongly on their cohesion and the shear stress exerted on them by the flow. Fragmentation was found to occur when the force due to shear stresses is strong enough to overcome the floc cohesion, whereas the flocs hold together when their strength surpasses that of the shear stresses. It is now recognized that the cohesion depends on the physicochemical properties of flocs whereas the hydrodynamics depends on the reactor geometry together with the operating conditions. As the shear stresses are related to the velocity gradient and turbulence fluctuations, investigations also revealed that the unfragmented maximum floc diameter can be correlated to the average turbulence dissipation rate or local shear gradient, specifically, d µ ε
1/4 or d µ Gv
1/2.6,7,10 Although these empirical relations can be̅ used to qualitatively describe the relationships between the floc size and the hydrodynamics, they do not provide physical insight into the complex phenomena of fiber floc deagglomeration or breakup in the turbulent flows generated by mixing devices. In fact, the use of an average turbulence dissipation rate, ε, to characterize the turbulence in the shear flows will lead to the omission of many important details about the local turbulence, which is usually crucial for dispersion of flocs. Ducoste et al.11 proposed correlating the floc size with local shear stress and strain rate. Because the turbulence kinetic energy and dissipation are closely related to the shear velocity gradient, it can be postulated that the floc size can be directly correlated with the local shear velocity gradient. It is evident from the previous studies that fiber floc breakage is likely caused by shear-induced turbulence stresses in turbulent flow and that the final breakage of fiber flocs depends on whether the exerted shear stress force is greater than the floc cohesion force. As turbulent shear stresses arising from turbulent shear flows have a significant impact on the dispersion of fiber flocs, the deliberate application of turbulence modulation in the flow field might be an effective approach to controlling the dispersion of glass fiber flocs. The spout-fluidized bed has been recognized as an effective means for gas
solid mixing and has been extensively employed in solid drying, coating, and blending. Many modifications of spout-fluidized beds have been proposed for the improvement of heat transfer and the enhancement of fluid
solid mixing efficiency,12,13 but the use of a modified spout-fluidized bed for the dispersion of fiber flocs has rarely been reported. To effectively disperse fiber flocs, Dai et al.2 modified a spout-fluidized bed with a draft tube and a disk baffle for use in preparing fiber-reinforced thermoplastic composites. Because of the introduction of internals, the flow patterns in the modified spout-fluidized bed were composed of several “subflows”, which can be classified as combinations of turbulent jets, impinging jets, and wall jets. These typical flows have been extensively studied and are well understood, but the superposition of these flows has not been investigated in its entirety. Thus, a better understanding of the hydrodynamics involved in such modified spout-fluidized beds is crucial in evaluating the practicability of such beds and beneficial in optimizing fiber floc dispersion processes. Even though many experimental studies using various probes to measure two-phase flow inside spout-fluidized beds have been conducted, the detailed turbulence structures and features in spoutfluidized beds are still not fully understood because of restrictions on the experimental conditions. Computational fluid dynamics (CFD) numerical simulations have proven to be useful for obtaining detailed information on the complex flow in spout-fluidized beds.

ARTICLE

Zhong et al.14 employed an Eulerian
Lagrangian CFD modeling approach to study the gas
solid turbulent flow in a spoutfluidized bed. The particle motion was modeled using the discrete element method (DEM), and the carrier gas flow was modeled using the k
ε turbulence model. Wu and Arun15 employed an Eulerian
Eulerian two-fluid model to simulate the gas
particle flow behavior of spouted beds and found that the simulations predicted the overall flow patterns well. Zhao et al.16 investigated the dynamics of particulate materials in twodimensional spouted beds with draft plates by using the DEM to describe particle motion and the low-Reynolds-number k
ε turbulence model to solve for the fluid flow. Because the k
ε turbulence model was employed in these works, the detailed turbulence structures were not obtained in the simulations. As for the dispersion of fiber flocs, details of the turbulence microstructures of shear flows in spout-fluidized beds are needed. It is now generally accepted that large-eddy simulations (LESs) can provide detailed turbulence information, except for dissipated eddies. Thus, the present study used LESs to acquire details on the fluid flow in a spout-fluidized bed with internals. Because fibers with a large aspect ratio tend to aggregate and because the volume concentration of the fibers in the spout-fluidized bed was lower than 0.001%, the effect of fibers on the flow can be neglected. This article considers only the flow in the spoutfluidized bed; that is, it completely ignores the presence of the fiber flocs. It should be noted that the purpose of the present work was to demonstrate the possibility of dispersing fiber flocs in different turbulent flow regions in a spout-fluidized bed and not to directly quantify the concentration distribution of fiber flocs in the bed. Quantification of the concentration distribution of fiber floc dispersion in the spout-fluidized bed will be presented in another article. This article is organized as follows: Section 2 describes experimental details on measuring the strength of fiber flocs. Mathematical modeling and numerical details related to using LESs in an internally spout-fluidized bed are given in section 3. Section 4 presents comprehensive experimental and LES results with a detailed discussion. Finally, some important conclusions drawn from the present work are given in section 5.

2. EXPERIMENTAL OBSERVATIONS 2.1. Model Suspension. Direct observation of fiber dispersion in a spout-fluidized bed is difficult, as fibers are slender, opaque, and moving rapidly in the highly turbulent flow. To understand the inherent properties of the glass yarn, a strength test was conducted with a model suspension. The sample used in the measurement was a chopped fiber bundle suspended in syrup in a rheometer. The fiber bundles were continuous Roving “T911” glass fibers as provided by Taishan Fiberglass Inc. (Taian, China), which were also subjected to dispersion in the spout-fluidized bed. The diameter of each individual filament was 17 μm, and the length was 18 mm. In the experiments, fibers were stained red so that good observations could be made. The syrup used was obtained from Shanghai Haocheng Foods Co. Ltd. and had a viscosity of about 12 Pa 3 s at 20 °C. After being carefully chopped from the strands of continuous Roving fibers, a strongly oriented dense bundle of fibers was obtained; it was then packed and added into the rheometer for test. 2.2. Apparatus and Procedures. A glass fiber yarn consists of thousands of individual glass fibers, and its volume cannot be neglected when compared with the concentric gap in a conventional 9182

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 1. Concentric cylindrical rheometer used in the experiment: (a) photograph, (b) dimensional sketch.

rheometer. Insufficient fiber suspension can take place when the glass fiber yarn is placed in a narrow gap filled with a Newtonian fluid. To circumvent this problem, a concentric cylindrical rheometer was redesigned with a larger gap so that fiber dispersion in the shear flow generated in the gap of the rheometer can be easily observed and the strength of the fiber aggregation can be measured. The concentric cylindrical rheometer was made of plexiglass to allow good observations. The actual geometry of the rheometer is shown in Figure 1. The diameter of the internal bob was 39 mm, and the internal diameter of the cup was 45 mm. The height of the bob was 50 mm, and that of the cup was 65 mm. Gaps of 7 mm below and 8 mm above the bob were maintained. To minimize end effects of the cylinder on the flow, the bob was made with a recessed bottom, which has been shown to be able to effectively eliminate the end effects caused by contact between the fluid and the bottom of the cylinder.17 Measurement of the fiber aggregation strength was performed with the aid of ARES (TA Instruments Co.). The results obtained using the standard concentric cylinder geometry were used as the benchmark to validate and calibrate the measurement of the concentric cylindrical rheometer. After the calibration was done, it was verified that the average shear stress and average shear rate generated by the flow between the outer cup wall and internal rotational bob of the concentric cylindrical rheometer can be estimated at a given angular velocity (Ω) and measured torque (M) (Couette analogy) using the equations17
 M 1 1 Ω¼
ð1Þ 4πμh Rb 2 Rc 2 "

σ bc

# ðk2 + 1Þ ¼ M, γ_ bc ¼ 4πRc 2 h

! k2 + 1 Ω k2
1

ð2Þ

where h is the bob height, k is the ratio of the radius of the cup to that of the bob (Rc/Rb), and the subscript bc denotes the average value. The cohesion strength of the fiber floc was acquired by slowly increasing the rotor torque with the programmable controller of

ARES until the dispersion of fibers was observed. The whole test time was set to be 400 s, which is much longer than the mean residence time of glass fiber in a spout-fluidized bed as indicated by Li18 and is acceptable for the current study. The criteria used for judging the occurrence of fiber dispersion was that the diameter of the fiber bundle was smaller than 1 mm, and the breakage behavior of fiber flocs was monitored by tracing the changes in floc size with variations in the shear rate.

3. NUMERICAL SIMULATIONS 3.1. Governing Equation. In LESs, the flow variables are decomposed into resolved scales, associated with the larger eddies, and the modeled subgrid scales, related to the more universal smaller eddies. The resolved scale j is obtained ̅ through a filtering procedure Z j ðxÞ ¼ jðx 0 Þ Gðx, x0 Þ dx 0 ð3Þ D

where D is the computational domain, G is the filter function, and x and x0 represent the vector positions. The filtered continuity and Navier
Stokes equations for the previous decomposition and filtering procedure can be written as ∂u̅ i ¼0 ∂xi ∂u̅ i ∂ 1 ∂p̅ ∂ ∂u̅ i ∂u̅ j + ðui uj Þ ¼
+ν + F ∂xi ∂xj ∂xj ∂xi ∂t ∂xj ̅ ̅

ð4Þ !


∂τij ∂xj

ð5Þ

where F is the fluid density and τij = ui uj
u̅ i u̅ j is the SGS (subgrid-scale) stress, representing the interaction between small and large scales. The key for an LES problem is to find an appropriate model for the SGS stresses represented by τij. Smagorinsky19 postulated that the form of SGS stresses as τij ¼ 2νT Sij 9183

ð6Þ

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 2. Schematic diagrams of four configurations of the spout-fluidized bed used in the simulations: (a) case A, (b) case B, (c) case C, (d) case D, (e) mesh setup for CFD modeling.

where the eddy viscosity νT and the strain rate in the resolved velocity field are estimated by ∂ui ∂uj νT ¼ CΔ 2 jS̅ j, S̅ ij ¼ ̅ + ̅ ∂xj ∂xi

ð7Þ

Δ is a length scale associated with the filter width (or mesh size), and C is a constant (Smagorinsky’s constant). In the current study, Δ ¼ ðΔ x Δ y Δ z Þ1/3, and the filter width x(y,z) was taken to be the same as the mesh size in the x (y, z) direction. The real flow behavior of eddies in spout-fluidized beds is highly complicated, and the value of C might depend on the local flow behavior. For

simplicity, we have taken C = 0.1 for homogeneous and isotropic turbulence, as in Yeh and Lei,20 and found that this value was suitable for this study. 3.2. Geometry of the Spout-Fluidized Bed and Numerical Details. It is expected that introduction of a draft tube and a disk baffle has a significant impact on the hydrodynamics in the bed, which, in turn, affects the dispersion of the fiber flocs. To assess the effects, four different configurations of the spout-fluidized bed were considered in the simulation, as shown in Figure 2. The diameter of the bed was 280 mm, and its height was 1250 mm. A cone bottom with an expansion angle of 60° was employed to avoid detaining pockets of stagnated particles. A concentric 9184

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 3. Comparisons of the predicted (a) axial mean velocity on the centerline and (b) radial profiles of shear Reynolds stress (u′v′/Uc2).

circular draft tube with an internal diameter of 90 mm and a length of 700 mm was fitted to convert the setup from case A to case B, for which the distance between the spout nozzle and the draft tube was kept to 217 mm. When a disk baffle was installed above the draft tube, the setup was converted to either case C or case D. The gap between the draft tube and the disk baffle was kept to 100 mm. The only difference between cases C and D was consideration of the effect of disk baffle rotation. Spouting air directly entered the bed through the spout nozzle, whereas fluidizing air was introduced into the bed through the orifices on the gas distributor. The volumetric flow rate of the spouting gas used in the simulation was 160 m3/h, and that of the fluidizing gas was 40 m3/h, the same as those used in the experiments. All four configurations were simulated so as to understand the effects of the internals on the flow behavior in the bed. For simulation of case D, the disk baffle was assumed to rotate at a speed of 600 rpm. In the simulations no-slip boundary conditions were imposed on the bed walls. The exits of the bed were defined as pressure outlets at the ambient pressure. The spout nozzle and fluidizing gas distributor were defined as velocity inlets with the specified velocities for spouting gas and fluidizing gas, respectively. The disk baffle in case C was treated as a stationary wall, whereas that in case D was specified as a rotational wall with an angular speed of 62.83 rad/s. Pressure
velocity coupling was obtained using the SIMPLE algorithm, the discretization scheme for pressure was second-order, and the scheme for momentum was bounded central differencing. Typical values of under-relaxation factors used in the simulations were 0.3
0.5. The time step for all cases was 0.0001 s. The convergence criteria were that, for all parameters, the residuals were less than 1  10
4. All simulations were conducted using the commercial CFD software Fluent 6.3.26. 3.3. Validation. To ensure that our LESs were able to effectively capture the actual turbulent shear flow features in the spout-fluidized bed, a validation simulation for a confined round turbulent jet was conducted before the LES was applied to the spout-fluidized bed. The reason for the selection of the turbulent confined round jet is that the configuration and flow characteristics of the jet are similar to those in the entrance of the spoutfluidized bed. A quantitative comparison between the LES calculation results and the previously published data for a jet at a Reynolds number of 1200021,22 is shown in Figure 3. The diameter of the jet nozzle was 2 mm, and that of the enclosure

was 100 mm. The nozzle was located 15 mm inside the enclosure to allow for the entrainment of surrounding fluid into the jet near the nozzle tip. It can be seen from Figure 3 that the LES-calculated axial mean velocity at the centerline is in good agreement with the results reported by Fukushima et al.21 and Lubbers et al.22 A comparison of the LES-calculated turbulence shear stress u′v′/Uc2 with the experimental data is presented in Figure 3b, where it can be seen that the u′v′/Uc2 values obtained using the LES are more consistent with the experimental data22
25 than are those obtained by Kandakure et al.26 It should be noted that Kandakure et al.26 employed the k
ω turbulence model in their simulations, which might be inadequate for direct comparison with the LES. It seems that our LESs properly captured the hydrodynamics of the turbulent confined round jet. With confidence and some reservations, we employed the LES for modeling the hydrodynamics in the spout-fluidized bed. 3.4. Effect of Grid Size. The average grid size was about 3 mm in the simulations. However, a refined mesh with Y+ ≈ 5 (grid I) in the vicinity of the walls, consistent with the mesh-size requirement for the LES, was employed. A grid-dependence check was conducted in the present work. Figure 4 shows a comparison of the radial profiles of the mean velocity and turbulence kinetic energy using two different grids. The refined mesh with Y+ ≈ 5 close to the walls was employed in all of our LESs. Grid II is a further refinement with the number of mesh cells doubled compared to the refined mesh but with the mesh uniformly distributed. It can be seen from Figure 4 that the difference between the two grids is small and the maximum discrepancies of the mean velocity and turbulence kinetic energy profiles are smaller than 10%. Taking the computation cost into account, the grid I mesh with the average grid size of 3 mm was employed.

4. RESULTS AND DISCUSSION 4.1. Strength of the Fiber Floc. Because the present investigation is concerned with glass fiber dispersion in the turbulent shear flow of a spout-fluidized bed, it is important to characterize how the fiber floc disintegrates as a result of the shear. Kuroda et al.27 found that fiber dispersion occurs in a stochastic manner and that the flow field can affect the fiber dispersion more than the maximum stress imposed on the fibers. As for the present study, fiber flocs experience different flow types in a spout-fluidized bed, 9185

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 4. Comparison of the radial profiles of (a) mean velocity and (b) turbulence kinetic energy with different grid.

which is much more efficient than a simple shear flow. Therefore, it is sufficient to take the maximum shear stress for effective dispersion of the fiber floc to define the strength of the fiber floc. Direct assessment of the inherent strength of the fiber flocs in gas turbulent shear flow is difficult because of restrictions on the means of measurement available for spout-fluidized beds. In the present study, the strength of the fiber flocs was acquired by observing the disintegration of individual fiber flocs in the cylindrical rheometer and monitoring the corresponding shear stress. The effect of the fiber floc concentration on the overall rheological performance can be considered negligible. The shear stress inside the gap of the cylindrical rheometer acts in the direction on a plane with a normal in the r direction. Each fiber bundle or fiber floc consists of many individual fibers and can be envisaged as the integration of many tiny cylindrical sticks by bonding. These sticks are aligned in parallel and piled up together with a certain cross-sectional area, but are very small. When such a fiber bundle is immersed into the shear flow, the shear will act on the fiber bundle, and the fiber bundle will disintegrate when the shear stress is greater than the strength of the cohesion among the fibers. The maximum shear stress in the concentric cylinder, corresponding to the shear stress causing the disintegration of the fiber bundle, was defined as the strength of the fiber floc. In fact, it would be expected that the fiber flocs in a spout-fluidized bed would experience complicated shear flows, which has been shown to be more effective than simple shear flow for fiber floc disintegration. The method of obtaining the strength of fiber flocs described above offers a means of determining suitable fiber bundles for processing with a spout-fluidized bed because the cohesion strength of fiber bundles varies with their size, composition, and length. Figure 5 shows the shear stress response of the suspension at different shear rates that were calibrated by using eqs 1 and 2. When the shear rate was low (0.06
3.06 s
1), the fiber bundle was only oriented and underwent no apparent disintegration in the flow, as shown in Figure 6. Further increase in the shear rate resulted in dispersion of the fiber flocs. Occasionally, erosion of several individual fibers from the surface of a fiber bundle initialized the dispersion process, causing the bundle to separate into daughter bundles. It was also found that daughter bundles were dispersed first, which might have high potential to contain voids and notches to serve as easy fracture paths.27 Therefore, it is not possible to completely determine a “critical” stress or strain for

Figure 5. Shear stress response of the suspension.

characterizing initiation of fiber bundle dispersion, and we only considered using the appropriate stresses as criteria for which consistent dispersive events were observed. Obviously, the fraction of undispersed fiber bundles decreased with increasing shear rates. When the shear rate exceeded 4.09 s
1, the average size of the fiber bundles was smaller than 1 mm, as can be visualized from Figure 6, and the fiber bundles were almost dispersed into acceptable fiber flocs for use. This indicates that the likely required shear stress for such fiber bundle to disintegrate and disperse must be higher than 70 Pa. 4.2. Flow Pattern in the Spout-Fluidized Bed. Because the volume concentration of the fibers in the spout-fluidized bed was lower than 0.001% in the current study, it is expected that the effect of the fibers on the entire flow can be neglected; that is, only one-way coupling was considered. Thus, the first part of the study focused on the flow effect, and the simulations were conducted for the cases that considered only the carrier flow. The LESs were carried out to reveal the turbulent shear flow features in the spout-fluidized bed, in particular upon addition of the draft tube and disk baffle. In contrast to the previous study on a spouted bed15 in which the flow was characterized as consisting of three typical regions, a central spout, an annulus, and a fountain region, the current LES results indicate that the turbulent flow in the 9186

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

Figure 6. Fiber bundle sample processed at different shear rates. (Photographs were taken at the end of shearing.)

internally spout-fluidized bed can be dynamically and geometrically characterized with four regions. These are the entry region below the draft tube, the annulus located between the draft tube and the walls, the impinging region between the draft tube and disk baffle, and the exit zone above the baffle. Figure 7a shows the time-average velocity distribution contours in four different spoutfluidized beds, and the instantaneous velocity fields in these flow regions are shown in Figure 7b,c. It can be seen clearly that the addition of the internals had a significant influence on the flow behavior. This influence can be further analyzed in detail, focusing on the four identified regions. Entry Region and Draft Tube. The flow in the entry region of a spout-fluidized bed has typical characteristics of a jet flow, flowing from the spout nozzle. In this region, introduction of the draft tube was found to dominate the flow, which plays an important role in distributing and modulating the fluid flow, resulting in the presence of a relatively regular flow pattern, as can be seen from Figure 7b. Figure 8 displays profiles of the axial mean velocity along the centerline and radial mean velocity distributions at different cross sections for different cases. For case A without the draft tube, the flow can be characterized as a single jet flow in a confined closure.26 In the initial stage of the flow, the developed jet decayed quite quickly, and the axial mean velocity on centerline decreased with the axial distance. The length of the potential core of the jet was apparently short. The decay coefficient of the centerline axial mean velocity was found to be 6.94. When the draft tube was added, the length of the potential core was extended by 57%, and the axial mean velocity decayed faster than in case A, with a decay coefficient of 9.11. This phenomenon was also reported in previous studies on confined impinging jets (e.g., Ashforth-Frost et al.28 and Baydar and Ozmen29), which can be attributed to the confinement on the entrainment and spread of the jet due to the draft tube. The jet flow for case A spread with a size comparable to that of the enclosure, whereas the spread of jet flow for cases with the draft tube was significantly confined, and the flow behaved similarly to flow through a pipe, so that the mean axial velocity remained almost unchanged until the flow left the draft tube, as shown in Figure 8a. Careful observation of Figure 8a revealed that, even though the axial mean velocity when the jet flow was led into the draft

ARTICLE

tube remained unchanged for cases B
D, the axial mean velocity in the draft tube was lower for case B than for cases C and D. This is because, upon introduction of the disk baffle for cases C and D, part of flow from the draft tube was forced to circulate from the impinging region back to the entry part. To highlight this point, Figure 7d shows the velocity distributions in the impinging and annulus regions. It can be clearly seen from the figure that the direction of the gas flow close to the wall was indeed downward. Therefore, the flow rates in the draft tube for cases C and D were slightly higher than that for case B. Annulus and Impinging Region. The impinging region was defined as the region in which the jet flow touched the wall of the spout-fluidized bed. For case A, a jet flow developed initially but formed a pipe flow when the jet flow spread to touch the wall so that the axial mean velocity was almost unchanged. For case B, the turbulent flow exiting from the draft tube formed a second jet flow, which can be seen clearly from the axial mean velocity variation and the sudden change in the radial mean velocity distribution at z/DN = 32.2 (see Figure 8a,c). The axial mean velocity distribution on the centerline exhibited such behavior, that is, remaining unchanged in the draft tube and gradually decreasing after the secondary jet flow was generated. Because of the effect of the entrainment of the secondary jet flow, it was found from the simulation that the turbulence intensity in the annulus region was enhanced and the axial velocity of the flow in this region increased by about 1.34 m/s compared to case A without the draft tube. It was also observed from the simulation that the disk baffle transferred the jet flow into a impinging jet, simultaneously affecting the flow behavior in the annulus and exit regions. Thus, it can be seen from Figure 8a that the axial mean velocity decreased steeply in the impinging region because of the turbulent jet being forced to alter the flow direction from axial to radial. Obviously, the function of the disk baffle is to convert the jet flow to a flow akin stagnation flow. The radial mean velocity increased rapidly from zero at the stagnation point to a maximum at the position r/Db ≈ 0.15 and then decreased to a local minimum at r/Db ≈ 0.2. It increased and attained a second maximum at r/Db ≈ 0.3 and then decreased toward the wall. It is interesting to note that the position of the appearance of the first maximum radial mean velocity corresponds to the outer fringe of the disk baffle. In the formation of the impinging jet, large-scale toroidal vortices were generated both above and beneath the impinging jet. These two toroidal vortices squeezed the impinging jet so as to form an initial accelerated and then decelerated jet flow, which resulted in a local maximum radial mean velocity, corresponding to the position of r/Db ≈ 0.3, as can be seen in Figures 7c and 8c. Popiel and Trass30 indicated that the ring-shaped toroidal vortices formed on the impingement surface would separate from the wall boundary between the stagnation region and wall jet region. Our results seem to be consistent with their findings. As mentioned above, with the impediment of the disk baffle, the secondary jet flow generated by the draft tube was forced to alter the flow direction to form a radial impinging jet. When hitting the wall, this impinging jet generated strong shear both upward and downward, and the downward shear flow entrained the gas into the annulus and exit regions, intensifying the turbulence in these regions. Moreover, it was found that the maximum velocities in the annulus for cases C and D weare enhanced to some extent to reach 13.42 and 12.64 m/s, respectively. Obviously, this will be beneficial to fiber floc suspension. 9187

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 7. (a) Distribution of the mean flow for all cases. Velocity vector distributions for (b) the entry region of cases A and B, (c) the impinging and exit region for all cases, and (d) the impinging region. U0 = 65.0 m/s.

Exit Region. As discussed in the previous subsection, the impinging jet flow formed because of the presence of the disk baffle, and the strong upward shear flow in the exit region, resulting from the flow of the impinging jet impinging on the wall, experienced a redistribution process. Figure 8d illustrates the profiles of the radial mean velocity for all cases in the middle of the exit region

(z/DN = 38.9). It can be seen that the flow for case A in this region had typical characteristics similar to those of fully developed turbulent flow in a circular pipe (i.e., the radial component of the velocity was almost negligibly small). In contrast, for case B, the secondary jet flow from the draft tube developed quite well at this position, and the radial mean velocity profile exhibited the 9188

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 8. Mean distributions of (a) axial velocity along the centerline, (b) radial velocities at z/DN = 17.2 and 23.9, (c) radial velocity at z/DN = 32.2, (d) radial mean velocity at z/DN = 38.9. U0 = 65.0 m/s.

Figure 9. Profiles of mean velocity components in the impinging region: (a) radial component, (b) circumferential component. U0 = 65.0 m/s.

feature of self-preservation that was indicated in previous studies on confined jet flow. For cases C and D, the upward shear flow (wall jet) along the bed wall was still developing in this region, and the flow expanded greatly toward the center of the bed, having a center-pointed (negative) radial component of the velocity, as shown in Figure 8d. The upward shear flow also induced

significant entrainment and caused a large recirculation vortex behind the disk baffle, as can be observed by the existence of two apparent recirculation loops symmetrical to the centerline. Effect of Rotation of Disk Baffle on the Flow. It is expected that rotation of the disk baffle would have an impact on the flow patterns in a spout-fluidized bed, in particular the flow in the 9189

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 10. Profiles of turbulence kinetic energy at different positions: (a) along the centerline and at z/DN = (b) 32.2, (c) 38.9, (d) 5.0, and (e) 7.7.

neighboring zones of the disk baffle. Unfortunately, such an effect cannot be seen clearly from the distribution of mean velocities. To reveal the effects of the disk-baffle rotation on the flow, the distributions of the dimensionless radial component Ur and circumferential component Uθ at different radii of the baffle, normalized with U0, are shown in Figure 9. In this figure, the horizontal axis displays the dimensionless distance z/H, where z is the distance measured from the surface of the disk baffle and H is the gap between the disk baffle and the outlet of the draft tube. Many previous studies have indicated that disk rotation would skew the flow of the impinge boundary layer on the disk because of the centrifugal force acting on the fluid, resulting in an intensified interaction between the free shear layer of the impinging jet and the rotational radial wall jet.31
34 However, as can be seen from Figure 9, the differences between cases C and D for the radial and circumferential components are not so obvious. Minagawa and Obi35 proposed the use of the dimensionless parameter δ to account for the effect of the centrifugal force. As for case D, it was found that δ ≈ 0.2, indicating that the secondary jet flow prevails over the induced flow due to rotation. The effect of disk rotation on the boundary layer on the surface of the disk is negligibly small in case D. It is interesting to note that, when observing the fiber dispersion in case D, rotation of the disk baffle was found to be able to slightly improve the fiber dispersion.18 This can be attributed to the complex dispersion modes of the fiber bundles, and it is discussed later in this article.

4.3. Turbulence Characterization. As mentioned previously, dispersion of a floc depends on both turbulent stresses and floc cohesion. In the present study, the carrier fluid was air, and its viscosity was small so that it was impossible to disperse fiber bundles by utilizing viscous shear force. The only feasible way to break up fiber bundles was to take advantage of the features of turbulent shear flow, namely, the significant enhancement of the Reynolds stress due to the effect of the turbulence eddy viscosity. As the cohesion strength of the fiber bundles was obtained by using a rheometer, it was essential to explore whether the turbulent stress generated in the turbulent flow in the modified spout-fluidized beds was strong enough to subdue the cohesion strength of the fiber bundles so that the fiber flocs could disperse during the flow. To address this issue, we now consider the turbulence kinetic energy and Reynolds stress in different cases. Figures 10a
c illustrates the variations of the turbulence kinetic energy along the centerline and the radial distributions of the turbulence kinetic energy at two different cross sections (z/DN = 32.2 and 38.9) of the bed. Figure 10d shows the profile of the turbulence kinetic energy in the r direction at z/DN = 5.0 (in the entry region) and z/DN = 7.7 (in the draft tube). Because addition of the internals altered the flow patterns in the bed, it can be seen from the figure that the effects of the internals, particularly the draft tube, were significant. Without the draft tube, the jet flowed from the spouting nozzle, developing strong shear flow downstream of the fringe of the nozzle. The shear rate reached a maximum at z/DN ≈ 5. This dynamic behavior can be 9190

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 11. Profiles of normal Reynolds stress variation along the centerline for (a) Fuz′2 and (b) Fur′2. Profiles of the axial normal Reynolds stress Fuz′2 (c) at the entry region for z/DN = 5.0 and (d) in the draft tube for z/DN = 7.7.

visualized from Figure 7b as the ring-shaped vortices generated around the periphery of the nozzle are shedding and spreading, eventually merging to form large-scale eddies. The maximum turbulence kinetic energy was achieved at the position r/Dt = 0.2. Addition of the draft tube confined the spread of shear flow but enhanced the shear rate as a result of the shear flow to be reinforced in the draft tube. Such turbulence modulation resulted in a notable redistribution of the turbulence kinetic energy, as can be seen from Figure 10. However, introduction of the disk baffle restrained the turbulence kinetic energy in the area between the exit of the draft tube and the disk baffle, partly associated with a reduction in the shear rate (i.e., ∂Vz/∂r). For cases C and D, development of the first jet flow from the spouting nozzle was further confined by the circulation formed in the annulus region. Consequently, the turbulence kinetic energy in the entry region slightly decreased as compared to that in case A (see Figure 10a). It can also be seen from Figure 10 that the overall intensity of the turbulence kinetic energy became small for cases C and D behind the disk baffle, but the turbulence kinetic energy for case B increased slightly and then decreased. A likely explanation is that the turbulent flow tends to be more uniform downstream of the disk baffle, where the shear flow of the wall jet experiences redevelopment and fewer large eddies are present, as indicated in Figure 7c. It is interesting to note that the radial distributions of turbulence kinetic energy at z/DN = 32.2 for cases C and D

present bimodal peaks, as shown in Figure 10b. This behavior is obviously associated with the shear flow features in the impinging region, where the secondary jet flow from draft tube is converted to a radial iminging jet. The positions of these peaks correspond to the locations with the larger local shear rates. Figure 10c shows that, except for case A, all other cases presented bimodal peak distributions of the radial turbulence kinetic energy at z/DN = 38.9. Among the cases with draft tubes, case B exhibited twice as many peak values of turbulence kinetic energy as cases C and D, as a result of strong shear layers building up because of a straightforward secondary jet flow from the draft tube. Because of redistribution of the flow field behind the disk baffle, the peaks in the turbulence kinetic energy profiles for cases C and D moved toward the wall, and their values were significantly reduced in comparison to those of case B. This indicates that the shear rates generated by the wall jet (caused by the impinging jet on the bed wall) were smaller in cases C and D, as is evident from Figure 7c. Because turbulence generation is strongly associated with shear, this implies that the overall shear rate was strongest in case B, but this might be harmful for long fiber suspension and transport because the fibers will strongly interact with large eddies. Parts a and b of Figure 11 show the variations of the axial normal stress ρuz′2 and radial normal stress Fur′2, respectively, along the centerline, and parts c and d of Figure 11 show the distributions of Fuz′2 and Fur′2, respectively, in the r direction at 9191

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 12. Profiles of normal Reynolds stress for Fuz′2 at z/DN = (a) 32.2 and (b) 38.9 and for Fur′2 at z/DN = (c) 32.2 and (d) 38.9.

z/DN = 5.0 (in the entry region) and z/DN = 7.7 (in the draft tube). Figure 12 displays the axial and normal Reynolds stress distributions at cross sections z/DN = 32.2 and z/DN = 38.9 for all four cases, whereas the contours of the shear stress Fur′ur′ for all cases are shown in Figure 13. It can be seen from Figure 11 that the normal Reynolds stress component Fuz′ 2 is much greater than the other Reynolds stress components for all cases, with the maximum falling in the entry region. The maximum values were achieved at the same position as the maximum turbulence kinetic energy and in all cases were greater than 140 Pa, which is much higher than the critical cohesion strength of fiber bundles. This implies that most fiber bundles will be disintegrated by the turbulent shear flow in this region. We now consider the radial normal Reynolds stress distributions Fuz′2 and Fur′2 in the impinging region and exit region (corresponding to z/DN = 32.2 and 38.9, respectively). For cases C and D, the Reynolds stresses had distributions similar to the turbulence kinetic energy distributions, but there were tiny difference among the profiles. This might have resulted from the effects of rotation of the disk baffle. At position z/DN = 38.9, the profiles of the normal Reynolds stresses Fuz′2 and Fur′2 for the two cases were highly similar, with the normal Reynolds stresses being increased toward the bed wall, apparently resulting from the entrainment effect of the upflowing wall jet. By contrast, the radial normal Reynolds stress in case A was relatively small. Examination of Figure 13 reveals that the resolved shear Reynolds stress distribution was roughly antisymmetric about the centerline

because of the changes of the mean shear rate from positive to negative, which is consistent with the results reported by Webster et al.36 and Beaubert and Viazzo.37 The sign of the shear stress agrees with the net transport of high momentum away from the centerline. It should be noted here that, as can be seen from Figure 13, the overall magnitudes of the shear stress in cases C and D were lower than that in case B, which might be beneficial for the formation of a relatively uniform fiber floc suspension in the upper part of the spout-fluidized bed. 4.4. Implications of the Effects of Turbulent Shear Flow on Fiber Dispersion. From the above analysis, it is evident that introduction of a draft tube and disk baffle has prominent effects on the flow behaviors in spout-fluidized beds. The presence of the draft tube, which serves as a confinement part, generates a secondary jet flow and a circulation flow in the annulus. These features promote mixing in liquid
bubble and particulate flow systems. Many previous studies have employed ejectors with a draft tube to investigate the effects of the draft tube size on the dispersion of bubble/drops in the ejectors,26,38,39 and these studies have clearly indicated that the enhanced turbulence intensity induced by the addition of a smaller draft tube leads to a smaller size of the dispersed bubbles/drops, a lower entrainment rate, and a low dispersed-phase holdup in the draft tube. In the present study, the ratio of the diameter of the draft tube to that of the spout-fluidized bed was about 0.32, and this small value will be beneficial to an increase in turbulence. In fact, as can be seen from Figure 11, the axial Reynolds stress values in the draft tube fell 9192

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 13. Resolved shear components of Reynolds stress Fuz′ur′ for cases (a) A, (b) B, (c) C, and (d) D.

into the range of 100
180 Pa, which is far greater than the cohesion strength of the fiber flocs, 70 Pa. This indicates that disintegration of the fiber bundles occurs mainly in the draft tube. Shah et al.40 also indicated that improvement of the normal Reynolds stress distribution can efficiently control the dispersion of fiber flocs. It thus can be conjectured that the axial normal Reynolds stress is primarily responsible for the fiber dispersion in the draft tube. Moreover, addition of the draft tube generates a circulating flow between the draft tube and the annulus. Fiber flocs are entrained and transported through the draft tube and further entrained in the impinging region. These well-dispersed fiber flocs will be further transported through the upper part of the spout-fluidized bed, whereas poorly dispersed flocs, which usually have larger volumes or are heavier than well-dispersed fiber flocs, will sediment and fall into the annulus. The formed turbulent downward flow in the annulus will re-entrain these fiber flocs in the entry region. Such repeated entrainment will eventually result in effective fiber dispersion. It can be concluded that subjecting fiber flocs to the action of stronger hydrodynamic stresses for longer times in a spout-fluidized bed would be conducive to the attainment of a higher dispersion efficiency of fiber flocs.27 We now turn our attention to the likely impact of the disk baffle on the dispersion of fiber flocs. As discussed in the preceding sections, it is clear that addition of a disk baffle is able to reinforce the turbulence in the annulus because of the formation of a downward-flowing wall jet and to redistribute the shear flow in the exit region. Although this addition does not enhance the Reynolds stresses in the impinging and exit regions for cases C and D compared with case B, a redistribution of the Reynolds

stresses to form a “flatter” distribution will help maintain good fiber floc dispersion in the upper part of the spout-fluidized bed. To better understand this mechanism, it might be useful to have a brief discussion by analogy dispersion of fiber flocs with dispersion of particles in turbulent gas flows. Viollet and Simonin41 proposed the use of a model for the description of particle drift and dispersion in turbulent flow in which the drift velocity ud was found to be given by " # 1 1 ∇ðRF FF Þ + ∇ðRG FG Þ ð8Þ ud ¼
DtGF RF FF RG FG where R and F denote the volume fraction and density, respectively, of each phase, and DtGF stands for the turbulent gas
particle interaction dispersion coefficient and is modeled as 1 0 0 DtGF ¼ τtGF uG uF 3

ð9Þ

where τtGF is the eddy
particle interaction time, which can be interpreted as the eddy
fiber interaction time in this case. For the flow in the exit region, (1/RGFG)3(RGFG) is negligibly small, and eq 8 can be simplified as   1 ∂ðRF FF Þ ∂ðRF FF Þ ∂ðRF FF Þ t ez + eθ + er ud ¼
DGF RF FF ∂z r∂θ ∂r ð10Þ For turbulent fiber suspension above the draft tube where the turbulent shear is still developed, a careful analysis reveals that the radial gradient component prevails over the axial gradient component. 9193

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research

ARTICLE

Figure 14. Instantaneous contours of shear strain rate at t = 10 s for cases (a) A, (b) B, (c) C, and (d) D. (Only shear strain rates ranging from 0 to 500 s
1 are displayed, with values of 500 s
1 or higher represented by red.)

As an approximation, the ∂(RGFG)/∂z term can be dropped, which leads to the following expression for the radial drifting velocity component udr udr 
DtGF

1 ∂ðRF FF Þ RF FF ∂r

ð11Þ

Equation 11 clearly shows that the radial drift velocity of the fiber floc depends on the local fiber floc volume fraction distribution. Many previous studies have demonstrated that fibers prefer to migrate from regions with high shear rate to regions with lower shear rates, which is similar to the dynamic behavior of particle transport in turbulent shear flows.42
44 Figure 14 shows the instantaneous contours of the magnitudes of the second invariant of the rate-ofdeformation tensor in the spout-fluidized bed for all cases. It can be seen from the figure that, for cases C and D, the shear rate in the vicinity of the wall is higher than that in the central area. Obviously, based on the above discussion, it can be speculated that the radial volume fraction distribution of fiber flocs for cases C and D will exhibit such behavior, namely, a higher volume fraction around the centerline and a lower concentration nearing the bed wall. Thus, it can be seen from eq 11 that the radial drift velocity will be overall positive and its direction will point toward the wall, which will be beneficial to the dispersion of fibers. The same argument can also be applied to the annulus region. In contrast, for case B, a much higher shear rate occurs downstream of the draft tube. Although a positive radial drift velocity will be achieved, the large eddies due to very strong shear generated by the flow of the secondary jet exiting the draft tube will violently interact with fiber flocs, prevailing over the effect of the drift and causing unfavorable dispersion or even reaggregation of fiber flocs. Consequently, most of fiber flocs will

be entrained by these large eddies and they confined by the secondary jet, resulting in a poor fiber floc suspension in the upper part of the spout-fluidized bed. It should be noted here that adding internals to spout-fluidized beds is, in fact, partitioning the flow into several subflow regions with the hydrodynamic characteristics of either flow contraction or expansion. Blaser45 and Kuroda et al.27 investigated fiber floc deformation in shear and strain flows, and their results suggested that the critical mechanical stress required to break up fiber floc depends on the types of flows applied and how the fiber flocs are elongated in the flow. A strained flow is more effective in breaking up droplets and agglomerating fiber flocs than a simple shear flow. In this sense, formation of complex turbulent shear flow patterns in a spout-fluidized bed by addition of the internals can effectively intensify the vortex stretching through the formation of different turbulent eddies so that fiber flocs can be deformed and stretched, further promoting fiber floc dispersion. This is crucial particularly for the case of long fiber flocs.

5. CONCLUSIONS In this work, the hydrodynamic characteristics of a spoutfluidized bed with addition of different internals for the purpose of effective dispersion of fiber flocs were studied. Because fiber floc breakup in shear flows depends to a great extent on both the floc strength and the features of the applied flow field, fiber floc strength measurements were conducted in a rheometer, and large-eddy simulations of the spout-fluidized bed with internals were carried out to obtain distributions of the turbulence kinetic energy, Reynolds stress, and shear strain rate. The conclusions drawn from the present study are summarized as follows: 9194

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research (1) It was found from the experimental observations that the cohesion strength of the fiber flocs was taken as 70 Pa. (2) The LES results showed that the addition of internals (draft tube and disk baffle) to a spout-fluidized bed can significantly alter the flow field in the spout-fluidized bed. The overall flow inside the bed can be treated as a combination of several subflows, identified by four regions characterized by apparently different flow dynamics. These four regions, in order, are the entry region, annulus region, impinging region, and exit region. (3) The spouting jet entrains fluidizing gas and the gas in the annulus region into the draft tube, generating a shear flow with high velocities that effectively enhances the turbulence intensities. It was found from the simulation that the maximum Reynolds stress can reach a magnitude that is higher than the strength of the fiber flocs and the turbulence kinetic energy can reach a value of about 120 m2/s2. When fiber flocs are transported in the flow, it is expected that such a high turbulence kinetic energy will cause fiber floc deaggregation. (4) Because of the location of the disk baffle above the draft tube, the jet flow from the draft tube is forced to change its status, forming an impinging jet in the region around the baffle. The LES results revealed that this positioning can improve the turbulence characteristics in the annulus and redistribute the flow in the exit region of the bed. The maximum of the velocity in the annulus was found to increase from 1.34 to 12.64 m/s. The wall jet formed downstream of the disk baffle increased the turbulence intensity in the vicinity of the wall in compared to that of the spout-fluidized bed without the baffle. (5) It is beneficial to the dispersion of fiber flocs if the turbulence characteristics of the different regions in a spout-fluidized bed with internals are effectively utilized. The entry region and the entry section of the draft tube serve to generate sufficient turbulence to disperse fiber flocs. Most fiber flocs are able to disperse in these two regions based on the shear rate and turbulence kinetic energy obtained from the LESs. The initially dispersed fiber flocs in the draft tube will further interact with turbulent flow around the impinging region, experiencing severe deformation. The exit region functions to maintain the fiber floc dispersion and to prevent reagglomeration of the flocs.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (G.D.), [email protected] (X.Y.). Tel./fax: +86-21-64252353 (G.D.). Tel.: +44-1978-293090 (X.Y.). Fax: +44-1978-293168 (X.Y.).

’ ACKNOWLEDGMENT Y.Z. acknowledges the support of State Key Laboratory of Chemical Reactors, East China University of Science and Technology, for a Doctoral program scholarship in conducting the study. X.Y. especially thanks Glynd^ w r University for a Research Fellowship and the support of Yulan Magnolia Scientific Talent Fund of Shanghai City, China. The authors also thank the reviewers for their expert guidance on revising the original version of this article.

ARTICLE

’ NOTATION C = Smagorinsky’s constant d = floc size, mm D = computation domain Db = diameter of the spout-fluidized bed, m Dd = diameter of the disk baffle, m DN = diameter of the spouting nozzle, m Dt = diameter of the draft tube, m G = grid filter function Gv = local velocity gradient, s
1 h = bob height, mm H = distance between the disk baffle and the outlet of the draft tube, m k = turbulence kinetic energy, m2 s
3 M = torque, m 3 s R = radius of the spout-fluidized bed, m Rb = bob diameter, mm r = radius of the baffle, m Rc = cup diameter, mm Sij = resolved scale strain tensor ui = filtered velocity component i, m s
1 u0 , v0 = fluctuation velocity, m s
1 U = mean velocity, m s
1 U0, UN = flow velocity at the exit of the spouting nozzle, m s
1 Uc = axial mean velocity along the centerline, m s
1 Uj = velocity of the flow at the entrance of the draft tube, m s
1 Ur, Uθ = radial and circumferential components, respectively, of the mean velocity x = axial distance from the nozzle, m x0 = distance of the virtual origin from the nozzle, m Greek Letters

R = volume fraction γ_ bc = average shear rate, s
1 = local mesh size, m ε = turbulence dissipation rate, m2 s
3 k = ratio of cup and bob radii, k = Rc/Rb νT = eddy viscosity, Pa s F = density, kg m
3 σbc = average shear stress, Pa τij = subgrid scale stress, Pa ω = rotational speed, rad/s Ω = angular velocity, rad s
1 Subscripts

F = fiber phase G = gas phase

’ REFERENCES (1) Padaki, S.; Drzal, L. T. A simulation study on the effects of particle size on the consolidation of polymer powder impregnated tapes. Composites: Part A 1999, 30, 325–337. (2) Dai, G.; Huang, J.; Sun, B.; Zhou, X. D. Agitated-spouted fluidited bed and use in preparing fiber reinforced composite. Chinese Patent 01112947.6 [P], 2001. (3) Kuroda, M. M. H.; Scott, C. E. Blade Geometry Effects on Initial Dispersion of Chopped Glass Fibres. Polym. Compos. 2002, 23, 828–838. (4) Zumaeta, N.; Byrne, E. P.; Fitzpatrick, J. J. Predicting precipitate breakage during turbulent flow through different flow geometries. Colloids Surf. A 2007, 292, 251–263. (5) Wengeler, R.; Nirschl, H. Turbulent hydrodynamic stress induced dispersion and fragmentation of nanoscale agglomerates. J. Colloid Interface Sci. 2007, 306, 262–273. 9195

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196

Industrial & Engineering Chemistry Research (6) Yeung, A.; Gibbs, A.; Pelton, R. Effect of Shear on the Strength of Polymer-Induced Flocs. J. Colloid Interface Sci. 1997, 196, 113–115. (7) Bouyer, D.; Coufort, C.; Line, A.; DoQuang, Z. Experimental analysis of floc size distributions in a 1-L jar under different hydrodynamics and physicochemical conditions. J. Colloid Interface Sci. 2005, 292, 413–428. (8) Shamlou, P. A.; Gierczycki, A. T.; Titchener-Hooker, N. J. Breakage of flocs in liquid suspensions agitated by vibrating and rotating mixers. Chem. Eng. J. 1996, 62, 23–34. (9) Tambo, N.; Hozumi, H. Physical characteristics of flocs—II. Strength of floc. Water Res. 1979, 13, 421–427. (10) Coufourt, D.; Bouyer, D.; Line, A. Flocculation related to local hydrodynamics in a Taylor
Couette reactor and in a jar. Chem. Eng. Sci. 2005, 60, 2179–2192. (11) Ducoste, J. J.; Clark, M. M.; Weetman, R. J. Turbulence in Flocculators: Effects of Tank Size and Impeller Type. AIChE J. 1997, 43, 328–338. (12) Hosseini, S. H.; Zivdar, M.; Rahimi, R. CFD simulation of gas
solid flow in a spout bed with a non-porous draft tube. Chem. Eng. Process. 2009, 48, 1539–1548. (13) Zhou, H. S.; Flamant, G.; Gauthier, D. DEM-LES of coal combustion in a bubbling fluidized bed. Part I: Gas
particle turbulent flow structure. Chem. Eng. Sci. 2004, 59, 4193–4203. (14) Zhong, W.; Xiong, Y.; Yuan, Z.; Zhang, M. DEM simulation of gas
solid flow behaviors in spout-fluid bed. Chem. Eng. Sci. 2006, 61, 1571–1584. (15) Wu, Z.; Arun, S. M. CFD modeling of the gas
particle flow behavior in spouted beds. Powder Technol. 2008, 183, 260–272. (16) Zhao, X. L.; Li, S. Q.; Liu, G. Q.; Yao, S. Q. Flow patterns of solids in a two-dimensional spouted bed with draft plates: PIV measurement and DEM simulations. Powder Technol. 2008, 183, 79–87. (17) Steffe, J. F. Rheological Methods in Food Process Engineering, 2nd ed.; Freeman Press: East Lansing, MI, 1996. (18) Li, P. Z. Study characteristics of multiphase in dilute phase spouted-fluidized bed. Thesis, Chemical Engineering Department, East China University of Science and Technology, Shanghai, China, 2006; p 123. (19) Smagorinsky, J. General Circulation Experiments with the Primitive Equations. I. The Basic Experiment. Mon. Weather Rev. 1963 91, 99–164. (20) Yeh, F.; Lei, U. On the motion of small particles in a homogeneous isotropic turbulent flow. Phys. Fluids A 1991, 3, 2571–2586. (21) Fukushima, A.; Aanen, L.; Westerweel, J. Simultaneous velocity and concentration measurements of an axisymmetric turbulent jet using a combined PIV/LIF. Proceedings of the 5th JSME
KSME Fluids Engineering Conference; 2002; pp 17
21. (Nagoya, Japan). (22) Lubbers, C. L.; Brethouwer, G.; Boersma, B. J. Simulation of the mixing of a passive scalar in a round turbulent jet. Fluid Dyn. Res. 2001, 28, 189–208. (23) Berman, N. S.; Tan, H. Two-component laser doppler velocimeter studies of submerged jets of dilute polymer solutions. AIChE J. 1985, 31, 208–215. (24) Hussein, H. J.; George, W. K.; Capp, S. P. Comparison between hot-wire and burst-mode LDA velocity measurements in a fully-developed turbulent jet. AIAA Paper 88-0424. 26th AIAA Aerospace Science Meeting; American Institute of Aeronautics and Astronautics (AIAA): Reno, NV, 1988; pp 11
14. (25) Malmstr€om, T. G.; Kirkpatrick, A. T.; Christensen, B.; Knappmiller, K. D. Centerline velocity decay measurements in low-velocity axisymmetric jets. J. Fluid Mech. 1977, 346, 363–377. (26) Kandakure, M. T.; Patkar, V. C.; Patwardhan, A. W. Characteristics of turbulent confined jets. Chem. Eng. Process: Process Intens. 2008, 47, 1234–1245. (27) Kuroda, M. M. H.; Scott, C. E. Initial Dispersion Mechanisms of Chopped Glass Fibres in Polystyrene. Polym. Compos. 2002, 23, 395– 405. (28) Ashforth-Frost, S.; Jambunathan, K.; Whitney, C. F. Velocity and turbulence characteristics of a semiconfined orthogonally impinging slot jet. Exp. Therm. Fluid Sci. 1997, 14, 60–67.

ARTICLE

(29) Baydar, E.; Ozmen, Y. An experimental investigation on flow structures of confined and unconfined impinging air jets. Heat Mass Transfer 2006, 42, 338–346. (30) Popiel, C. O.; Trass, O. Visualization of a free and impinging round jet. Exp. Therm. Fluid Sci. 1991, 4, 253–264. (31) Astarita, T.; Cardone, G. Convective heat transfer on a rotating disk with a centred impinging round jet. Int. J. Heat Mass Transfer 2008, 51, 1562–1572. (32) Brodersen, S.; Metzger, D. E.; Fernando, H. J. S. Flows generated by the impingement of a jet on a rotating surface: Part I— Basic flow patterns. J. Fluid Eng. 1996, 118, 61–67. (33) Kang, H. S.; Yoo, J. Y. Turbulence characteristics of the threedimensional boundary layer on a rotating disk with jet impingement. Exp. Fluids 2002, 33, 270–280. (34) Motoyuki, I.; Masashi, O. An experimental study of the radial wall jet on a rotating disk. Exp. Therm. Fluid Sci. 1998, 17, 49–56. (35) Minagawa, Y.; Obi, S. Development of turbulent impinging jet on a rotating disk. Int. J. Heat Fluid Flow 2004, 25, 759–766. (36) Webster, D. R.; Roberts, P. J. W.; Ra’ad, L. Simultaneous DPTV/PLIF measurements of a turbulent jet. Experments in Fluids. 2001, 30, 62–72. (37) Beaubert, F.; Viazzo, S. Large eddy simulations of plane turbulent impinging jets at moderate Reynolds numbers. Int. J. Heat Fluid Flow 2003, 24, 512–519. (38) Balamurugan, S.; Gaikar, V. G.; Patwardhan, A. W. Hydrodynamic Characteristics of Gas
Liquid Ejectors. Chem. Eng. Res. Des. 2006, 84, 1166–1179. (39) Kandakure, M. T.; Gaikar, V. G.; Patwardhan, A. W. Hydrodynamic aspects of ejectors. Chem. Eng. Sci. 2005, 60, 6391–6402. (40) Shah, P. N.; Atsavapranee, P.; Wei, T.; Mchugh, J. The role of turbulent elongational stresses on deflocculation in paper sheet formation. Tappi J. 2000, 83, 1–8. (41) Viollet, P. L.; Simonin, O. Modelling dispersed two-phase flows: Closure, validation and software development. Appl. Mech. Rev. 1994, 47, s80. (42) Hookham, P. A. Concentration and velocity measurement in suspensions flowing through a rectangular channel. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1986. (43) Koh, C. J.; Hookham, P.; Leal, L. G. An experimental investigation of concentrated suspension flows in a rectangular channel. J. Fluid Mech. 1994, 266, 1–32. (44) Sanders, H. T.; Meyer, H. Consistency distribution in turbulent flow of fibre suspensions. Tappi J. 1971, 54, 722–730. (45) Blaser, S. Flocs in Shear and Strain Flows. J. Colloid Interface Sci. 2000, 225, 273–284.

9196

dx.doi.org/10.1021/ie102509z |Ind. Eng. Chem. Res. 2011, 50, 9181–9196