Wet

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Experimental Study and DEM Numerical Simulation of Dry/Wet Particle Flow Behaviors in a Spouted Bed Tianqi Tang, Yurong He,* Anxing Ren, and Tianyu Wang

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School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China ABSTRACT: In this study, wet particle flow behaviors were investigated in a spouted bed using numerical simulations and experiments. Effects of liquid contents and viscosities were investigated. For the experiment, instantaneous particle distribution and particle velocity distributions were explored. Liquid content and viscosity affected flow pattern together. Keeping increasing liquid content and viscosity, the flow pattern displayed flow instabilities, and the gas channel became curved. Numerical simulation results of time-averaged particle velocities agreed well with the experimental data. The regime map of domination forces is shown. Drag force has little effect on particle flow behaviors with liquid viscosity exceeding 10 mPa·s, and contact and liquid bridge forces were almost 50− 50. Furthermore, effects of liquid content and viscosity on particle granular temperature and velocity were explored. The experimental and numerical simulation results might provide theoretical guidance for reactor design and further investigation on particle flow behaviors with cohesive liquid.

1. INTRODUCTION Spouted beds are important industrial reactors with excellent mixing and circulation characteristics for coarse and nonspherical particles.1,2 Due to their unique advantages, spouted beds have been widely used in particle coating,3 drying,4 biomass combustion,5 and renewable energy.6 Moreover, with the development of spouted beds, they have also been applied to the drying of biomass, the pyrolysis of biomass, waste plastics and tires, and the gasification of low-rank coal.7 Thus, spouted beds play an important role in the renewable energy usage and industrial process. Spout-fluid beds find widespread application in the process industry for efficient contacting of large particles with a gas. By analyzing the pressure drop signal, the spout fluidized bed regime is split into a fixed bed regime, internal spout regime, spouting with aeration regime, slugging bed regime, spout-fluidization regime, and jet-in-fluidized-bed regime. Moreover, fluidized-bed with single, double, and multiple gas inlets have attracted more and more attention from researchers, including in relation to pressure fluctuations in the single spout fluidized beds8 and particle velocity distribution in multiple spout fluidized beds.9 However, most research on spouted beds focused on dry particle systems. In fact, cohesive liquid has a notable effect in actual industrial processes since, strictly speaking, most real industrial systems contain cohesive liquid. For example, road dust was collected under wet conditions with a vacuum cleaner,10 which is beneficial for the environment. Investigating particle and droplet mixing flow behaviors could predict dust capture efficiency.11 In addition, liquid in particle systems result in different flow behaviors between dry and wet particle systems,12 and agglomeration might form and result in bonding of the industrial reactor.13 Wet particles also play © XXXX American Chemical Society

important roles in improving energy quality, avoiding overturn,14 and predicting erosion.15 Thus, flow behaviors of the wet particles are important and need further investigation. For investigating gas−solid flow behaviors in spouted beds directly, different experimental measurement methods have been applied to obtain macro-scale characteristics, including pressure drop and particle velocity. Huang et al.16 studied mixing characteristics of the annular spouted bed successfully via experiment with several angled air nozzles and found that the static bed height had a great effect on the final mixing index. Link et al.17 obtained the flow regime by analyzing pressure drop fluctuations through fast video recordings, which is meaningful for the prediction of the appropriate regimes of different spout fluidized beds. Van Buijtenen et al.18 have conducted abundant experiments to investigate particle flow behaviors in spout fluidized beds for the dry particle system, including the collision properties of particles in a single spout fluidized bed, particle flow behaviors in a multiple spout fluidized bed, and the effect of spout elevation on the bed dynamics.19 As mentioned above, macro-parameters and characteristics, including pressure drop, particle velocity, and mixing characteristics, could be explored by experimental measurement. Moreover, with a further investigation, related experimental techniques have been applied for the wet particle system. For example, Zhu et al.20 examined the effects of cohesion on the spout−annulus interface and particle velocity profiles in distinct zones. Ahmadi Motlagh et al.21 conducted Received: May 4, 2019 Revised: July 23, 2019 Accepted: July 25, 2019

A

DOI: 10.1021/acs.iecr.9b02448 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

flow behaviors by experiment and numerical simulation in a spouted bed. A DEM model combining the liquid bridge module and rolling friction was established. Particle flow behaviors with different liquid viscosities and liquid contents were measured and analyzed with PIV (particle image velocimetry) technology. A comparison of time-averaged particle velocity distribution was conducted to validate the accuracy of the numerical method. Then, investigations of the effects of liquid content and liquid viscosity on particle flow behaviors were carried out. For a better explanation, quantitative force analyses were also applied.

liquid injection experiments in a lab-scale fluidized bed and explained the relationship between superficial gas velocity and liquid distribution pattern. The agglomeration of particles in a conical spouted bed was investigated using multiple experimental means and detected by different signals.22 Yang and Hsiau23 investigated transport properties of wet granular materials in a shear cell apparatus and pointed out that the fluctuation velocities and the self-diffusion coefficients were smaller than those in granular systems with higher liquid contents. Ma et al.24 investigated the bubbling behaviors of cohesive Geldart B particles in a 2D fluidized bed and found that the bubble shape is evaluated by the aspect ratio and shape factor. For investigating micro- and mesoscale characteristics of multiphase flow, numerical simulation has become an effective method with the development of CFD (computational fluid dynamics). This method could overcome the defects of experimental measurement. For example, Gonzalez-Quiroga25 showed that the specific carrier gas inlet design could guarantee pressure distributing evenly at entrances of the rotating fluidized bed by CFD. Since 1993, a modified soft sphere model was used, which was improved by Tsuji et al.26 based on the model proposed by Cundall and Strack.27 So far, the DEM (discrete element method) has been widely used to investigate the complex granular flow28 and concrete flow29 and also plays an important role to analyze particle flow behaviors in mixers30 and rotating drums.31,32 For example, Liu et al.33 investigated the effect of Magnus lift force with considering rotational Reynolds number via a discrete particle method. Luo et al.34 explored the effects of gas and solid properties on an internally circulating fluidized bed, which is one of the most important reactors in industrial processes. Some researchers also conducted investigations on spouted beds using the DEM.35,36 Moreover, the wet particle system was also investigated by numerical simulations from researchers. Zhang et al.37 validated the DEM-CFD approach via experiment and empirical correlations and analyzed particle velocity and particle granular temperature distributions. Zhu et al.38 and Xu et al.39 investigated wet particle mixing characteristics and particle circulation fluxes under stable spouting conditions, respectively. Song et al.40 investigated the particle flow pattern of wet particle systems and predicted particle rebound and adhesion behaviors. In addition, Van Buijtenen et al.41 and Ma et al.42 studied the effect of the interparticle interaction on the bed dynamics considering a variable restitution coefficient. Sun et al.43 calculated the aggregation process and flow behavior of cohesive powders in a full-loop circulating fluidized bed with a population balance equation. As mentioned above, it could be found that wet particle flow behaviors are worth studying due to different flow behaviors, and it might influence the design of industrial reactor and process controlling. Particularly, particles might form agglomerates in terms of different structures under different operating conditions, and flow regime might change with the variation of cohesive liquid. Although, wet particle flow behaviors have been studied by experiments and numerical simulations, the effects of liquid content and viscosity on the gas−solid interaction process was not clear. Thus, it is necessary to develop a deeper investigation on the microinteraction between particles under different conditions. This paper mainly investigates the wet particle flow behaviors with a focus on the effect of liquid contents and viscosities on particle

2. MODEL DESCRIPTION 2.1. Gas Phase. The gas phase, described by the Eulerian method, was calculated as a continuous phase. The mass and momentum conservation equations modeled by the local average Navier−Stokes equations proposed by Anderson and Jackson44 are defined as follows: ∂(εgρg u g, i) ∂ (εgρg ) + =0 ∂t ∂xi

(1)

∂ ∂ (εgρg u g, i) + (εgρg u g, iu g, j) ∂t ∂xj = −εg

∂p ∂ + (εgτg, ij) − Fgp + εgρg gi ∂xi ∂xj

(2)

where εg is the porosity, -; ρg is the gas density, kg·m−3; ug is the gas velocity, m·s−1; g is the gravitational acceleration, m· s−2; p is the pressure, Pa·s; and τg is defined as ij ∂u g, i ∂u g, j 2 ∂u g, k yzzz − + τg, ij = μjjjj δijz j ∂xj ∂xi 3 ∂xk zz k {

(3)

2.2. Solid Phase. The solid phase solved by Newton’s second law directly is treated as a discrete phase. For the softsphere model proposed by Cundall and Strack27 and modified by Tsuji et al.,26 limited deformation between particles is allowed. Motion of particles is solved in translational and rotational types. For translational motion, particles are governed by pressure gradient force, drag force, gravitational force, and contact force between the colliding particles or the particles and walls (see Figure 1). In addition, the liquid bridge force is considered in the wet system.

Figure 1. Schematic description of particle colliding with considering liquid bridge and rolling friction. B


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Industrial & Engineering Chemistry Research mp

Vpβ d 2r = −Vp∇p + (u g − vp) + mp g + Fc + Flb 2 1 − εg dt

Fcp,n = −

(4)

dωp dt

= Tp = rp × Ft = rp × (Fc,t + Flb,t ) + Tr

(5)

where Ip is the moment of inertia, kg·m2; Tp is the torque, N· m; and Ft is generated by the contact force and the liquid bridge force in the tangential direction. In addition, Tr is generated by rolling friction, which was proposed by Brilliantov18 and is given as below: ω Tr = −μr FnR p |ω|

Fv,n = 6πμ lb R vr,n

(7)

Hcr = R(0.5θ + 1) 3 Vlb̂

(13)

Here, V̂ lb is the dimensionless liquid bridge volume and is defined as below:

(8)

where kn is the normal spring stiffness, N·m ; kt is the tangential spring stiffness, N·m−1; δ is the elastic deformation, m; vr is the relative velocity, m·s−1; and μf is the coefficient of sliding friction, -. According to the expression, the elastic deformation and damping effect were described by the position-dependent spring obeying Hooke’s law and the velocity-dependent dashpot, respectively. 2.2.2. Liquid Bridge Force. The liquid bridge force is added to investigate the effect on the collisions between the particles or the particles and walls. The liquid bridge force consists of a capillary force and a viscous force. Moreover, for the wet particle system, the liquid was assumed to distribute on all particle surfaces with uniform liquid volume. Liquid transfer between particles was neglected. 2.2.2.1. Capillary Force. According to a total energy theory,45 the capillary force of a fixed liquid volume was calculated between particles. The expression is shown below: 2πγ R cos θ − 2πγ R sin φ sin(φ + θ ) H /2d + 1

(12)

Furthermore, the critical rupture distance Hcr is an important parameter for the calculation of the liquid bridge force. When the distance between particles or a particle and a wall was larger than Hcr, the liquid bridge ruptured. The relationship between Hcr and the liquid bridge volume was proposed by Lian et al.49 and defined as

−1

Fcp,n = −

(11)

y i8 R Fv,t = 6πμ lb R vr,tjjj ln + 0.9588zzz H { k 15

where μr is the rolling friction coefficient, Fn is the normal contact force, and ω is the rotational velocity. 2.2.1. Contact Force. Contact force, occurring between particles or a particle and a wall, was solved using a linear spring-dashpot (LSD) soft-sphere model. The contact force was divided into two directions: the normal component and tangential component, which are described as follows:27 l −k tδt − ηt vt |Ft | ≤ μf |Fn| o o o o Ft = o vt m o o |Ft | > μf |Fn| o −μf |Fn| o o |vt| n

R H

where the parameter μlb is the liquid viscosity, Pa·s. The viscous force in the tangential direction was solved by Goldman et al.48 and was defined as

(6)

Fn = −k nδn − ηn vn

(10)

The value of H is negative when particles overlap, which does not correspond to a real physical process. Thus, the minimum value of H was set as 10−5 m to ensure that the normal capillary force was positive. The setting of the minimum value was also suitable for calculating the normal viscous force. 2.2.2.2. Viscous Force. Viscous force is as important as capillary force. The effect of viscous force becomes more effective when the liquid viscosity or relative velocity is higher than usual. On the basis of lubrication theory46 and the work of Adams and Edmonson,47 the normal component was given as

Here, mp is the particle mass, kg; r is the position of the particle center, m; t is the time, s; Vp is the particle volume, m3; vp is the particle velocity, m·s−1; Fc is the contact force, N; and Flb is the liquid bridge force, N. For rotational motion, the angular velocity driven by torques was given as follows: Ip

4πγ R cos θ − 2πγ R sin φ sin(φ + θ ) H /d + 1

Vlb̂ =

Vlb R3

(14)

2.3. Interphase Exchange. The momentum exchange between the gas and solid phase has been studied. As a function of the product of the interphase momentum exchange coefficient and the relative velocities of the two phases, the rate of momentum exchange Fgp between the solid and gas phases was composed of the sum of the drag forces acting on the individual particles in a computing cell. Fgp =

1 Vcell

n

∑ k=1

Vpβ 1 − εg

(u g − v kp)

(15)

The drag force had an influence on the flow behaviors of a particle in the DEM simulation, which was indicated by Beetstra et al.50 The Beetstra drag force model, derived from lattice-Boltzmann simulations, was justified for Reynolds numbers up to 1000. It can be written as

(9)

−1

where γ is the surface tension, N·m ; R is the particles radius, m; φ is the half-filling angle, rad; θ is the contact angle, rad; H is the distance between the two particles, m; and d is the immersion height, m, which is defined as d = R − R cos(φ). Similar to the interaction between particles, the capillary force between a particle and a wall is expressed as follows:

βBeetstra = K1μ

(1 − εg)2

K1 = 180 + 18 C

d p2εg εg4 1 − εg

+ K 2μ

(1 − εg)Re d p2

(16)

(1 + 1.5 1 − εg ) (17) DOI: 10.1021/acs.iecr.9b02448 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research K 2 = 0.31

εg−1 + 3εg(1 − εg) + 8.4Re−0.343 1 + 103(1 − εg)Re 2εg − 2.5

(18)

The Re for the solid phase was defined as Re =

ρg εgd p|u g − vp| μ

(19)

2.4. Granular Temperature. The granular temperature, based on the random fluctuation of particle velocity, is one of the most important parameters for measuring the kinetic behavior in particulate systems. Tartan and Gidaspow51 and Jung et al.52 proposed two granular temperatures owing to different oscillations of the particles. The first was a granular temperature caused by oscillations of the particles. The second was a bubble granular temperature due to motion of the bubbles and gave rise to Reynolds type stresses. The granular temperature is determined by the second moment of particle velocity fluctuation, which was expressed as 1 ⟨CiCj⟩(r , t ) = n

Np

∑ [vp,k i(r , t ) − ci(r , t )]

Figure 2. Structure of a spouted bed.

k=1

[vp,k j(r ,

t ) − cj(r , t )]

(20)

Table 1. Parameters Used in the Simulation

where Np is the number of particles in a cell and i is the direction. The cell-average mean velocity c was defined as ci(r , t ) =

1 n

variable Particle particle diameter, dp particle number, Np particle density, ρp bed size in x, y, and z directions cell numbers in x, y, and z directions coefficient of restitution, e coefficient of sliding friction, μf,p−p coefficient of sliding friction, μf,p−w′ coefficient of rolling friction, μr normal spring stiffness, kn tangential spring stiffness, kt gas spouted gas velocity, Usp density, ρg viscosity, μ outlet pressure, P liquid relative liquid volume, V*lb liquid viscosity, μlb contact angle, θ surface tension, γ

Np

∑ vp,k i(r , t ) k=1

(21)

Bubble granular temperature is expressed as follows ⟨Ci*C*j ⟩(r , t ) =

1 Mf

Mf

∑ [cik(r , t ) − ci (r)][cik(r , t ) − ci (r)] k=1

(22)

where the time-average mean velocity in a cell is expressed as ci (r) =

1 Mf

Mf

∑ cik(r, t ) m=1

(23)

2.5. Boundary Condition. In this study, we extended our previous work53 to investigate wet particle flow behaviors with different liquid contents and viscosities in spouted beds. As shown in Figure 2, the size of the spouted bed is 150 × 20 × 800 mm, which is similar to the one designed in the experiment. At the bottom of the spouted bed, the spouted gas entered through the 10 mm wide spouting region in the center. The gas velocity for the spouting is shown in Table 1. For the gas phase, a pressure outlet boundary condition was applied to the top outlet of the bed, and a no-slip boundary condition was adopted at the walls. A modified multiphase flow with interphase exchanges (MFIX) DEM code, developed at National Energy Technology Laboratory (NETL), was used for the simulations in this study. In the numerical simulation, the hydrodynamic equations of the gas phase were solved with a finite volume method and a discretization on a staggered grid. All of the simulations of the dry and wet granular systems were carried out for 15 s, and the time-averaged results were obtained from the last 10 s. In the simulations, uniform glass spherical particles with a diameter of 3.00 mm and a density of 2545 kg/ m3 were used. The physical properties and particle collision

value 3.00 11000 2545 150 × 20 × 800 15 × 3 × 80 0.97 0.10 0.30 0.125 1000 286

unit mm kg/m3 mm

N/m N/m

41.2 1.2 1.8 × 10−5 1.3 × 105

m/s kg/m3 Pa·s Pa

0.10%, 0.50% 10, 20, 50, 100 30 0.019

mPa·s deg N/m

parameters are summarized in Table 1. We neglected physical properties in the wet particle system.52−54

3. EXPERIMENTAL DEVICE In Figure 3, the experimental device was given. In this experiment, the compressed air was applied for the spouted gas, which could overcome the resistance of mass flow meter and provide enough spouted gas pressure. During the experiment, lights are fed by a continuous voltage to enable the high speed footage capture. According to the experimental case setting, particles are weighted, and density and volume are calculated. As liquid content is required, the liquid content was calculated and measured and mixed with particles in advance. For cohesive D


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flow dynamics were investigated. The spout gas velocity for all cases was 41.2 m/s. Particle number was 11 000. For the wet particle system, the liquid volume contents of 0.10% and 0.50% were applied for the experiment. Moreover, liquid viscosities were 10 mPa·s, 20 mPa·s, 50 mPa·s, and 100 mPa·s, respectively. Corresponding numerical simulations were applied.

4. RESULTS AND DISCUSSION 4.1. Model Validation. 4.1.1. Dry Particle System. In this work, a comparison of simulation and experimental results was conducted. In Figure 4 a and b, instantaneous particle distributions from the experiment and numerical simulation are shown and compared, respectively. Before the experiment and numerical simulation, particles were distributed in the spouted bed with a 90 mm initial bed height. It showed that particles were carried to the freeboard with the effect of spouting gas and moved downward near the walls. Particles formed the fountain region at the upper bed. A numerical simulation under the same case was conducted to validate that the numerical model was reasonable. For the simulation, the rolling friction module was included, which is a major source of energy loss in the particle system and could not be ignored. It could be found that particle flow behaviors from numerical simulation agreed well with those of experimental results. In addition, time-averaged velocity vector distributions were similar, which demonstrated that the numerical simulation method was reasonable enough. Figure 5 shows a comparison of time-averaged particle velocity distributions in axial directions in a dry particle system at bed heights of 50 mm and 70 mm. For the simulation, the rolling friction module was included. It could be found that particle velocities decreased with the consideration of rolling friction. As shown in Figure 5, numerical results showed good agreement with the experimental data by adding a rolling friction module. Thus, it could be found that the consideration of rolling friction will get more accurate results close to the actual process. Moreover, in the spout region, particle velocities reached a peak with the effect of spouted gas. Near the walls, particle velocities were close to 0 m/s due to less of a free path of particles and higher particle volume fraction. 4.1.2. Wet Particle System. For the wet particle system, a comparison of experimental data and simulation results is shown in Figure 6. In this work, different liquid viscosities of cohesive liquid were mixed with particles. For a better description of particle velocity distributions under different liquid contents and viscosities, the numerical simulation results and experimental data with liquid viscosities of 20 mPa·s and

Figure 3. Structure of experiment device.

liquid, silicone oil (Aladdin) was chosen as a cohesive liquid which is stable in physical and chemical properties with the assumption of being nonvolatile for the simulation. Thus, we assume the physical properties remain unchanged. In addition, we used different viscosity silicon oil for the experiment. The experimental period was 30 s for each case, and the volume of cohesive liquid could remain unchanged during the experiment. Then, the wet particles with different specific liquid contents and viscosities were distributed in the spouted bed. The spouted bed would be cleaned carefully to avoid the effect of different cohesive liquids. In addition, a camera was applied to capture the flow behaviors in the spouted bed with 1000 fps and 480 × 640 pixels. After the experiment, the captured pictures were analyzed with the PIV system. For the experiment postprocessing, cross-correlation analyses were applied. The data repeating utilization factor was 50% for avoiding data missing and getting more accurate results. Moreover, results were obtained from the fully developed segment lasting 15 s. The experimental case setting is shown in Table 2. In this experiment, effects of liquid content and liquid viscosity on Table 2. Experimental Cases

case 1−1 case 2−1 case 3−1 case 4−1

liquid content (−)

liquid viscosity (mPa·s)

0.10%

10

0.10%

20

0.10%

50

0.10%

100

case 1−2 case 2−2 case 3−2 case 4−2

liquid content (−)

liquid viscosity (mPa·s)

0.50%

10

0.50%

20

0.50%

50

0.50%

100

Figure 4. Particle distribution from simulation and experiment in dry particle system (left, experimental results; right, numerical simulation). E


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Figure 5. Distribution of time-averaged axial particle velocity by experiment and numerical simulation.

Figure 6. Distribution of time-averaged particle velocity by experiment and numerical simulation.

100 mPa·s were given. Furthermore, the liquid contents of 0.10% and 0.50% are shown in Figure 6a and b, respectively. It could be determined that numerical simulation showed good agreement with experimental data from this work except some differences in the spout region. It could be found that particle velocities decreased largely with an increase of liquid viscosity under different liquid contents. For the numerical simulation, rolling friction and liquid bridge force were considered. The results indicated that the numerical simulation models were reasonable to get more accurate results compared with those without the consideration of rolling friction, which has been demonstrated in section 4.1.1. As the comparison was conducted above, numerical results showed good agreement with experimental ones for both dry and wet particle systems. The results validated that the numerical simulation model used in this work was reasonable enough. 4.2. Effect of Liquid Viscosity and Liquid Content. 4.2.1. Instantaneous Particle Distribution. In Figures 7 and 8, effects of liquid content and viscosity on instantaneous particle distribution are shown. In Figure 7, compared with the dry particle system, cohesive liquid viscosity had a strong effect on particle flow behaviors. With an increase of liquid viscosity, the gas channel became curved gradually. This phenomenon indicated that the effect of liquid bridge force became more evident. Moreover, particles were more difficult to fluidize, and the spout region reduced. The liquid contents were 0.10% and 0.50% for Figure 7 and Figure 8, respectively. Under this occasion of 0.10% liquid content, the particle system was mixed with a certain small

Figure 7. Experimental snapshots of the spouted bed with wet particles (Vlb* = 0.10%).

amount of liquid. Thus, particle systems might be between a dry particle system and a liquid system. For Figure 8, the liquid content was 5 times larger than that of the cases in Figure 7. In the cases of 0.50% liquid content, particle systems might be closer to liquid systems with higher liquid content. Thus, this phenomenon might demonstrate that particle systems varied from a typical spout regime to a defluidized regime, and then converted to typical spout regime with an increase of liquid content. Instead, particle systems kept deviating from the typical flow regime with an increase of liquid content. In addition, corresponding simulation results have been comF


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Figure 8. Experimental snapshots of the spouted bed with wet particles (V*lb = 0.50%).

pared. For the simulation results, a curving spouted gas channel could be observed, and particle agglomeration moved from left to right periodically in the fountain region. This phenomenon was called flow instabilities.55−57 In Figure 9, instantaneous particle distributions were given at different times in the case of a liquid viscosity of 100 mPa·s

Figure 10. Regime map of contact/drag/bridge forces with different liquid contents by numerical simulation.

contents. In Figure 10a, the regime map of liquid content 0.10% is shown with different liquid viscosities. Drag force dominated region I and accounted for more than 50%. In addition, region II and region III represented the main domination regions of contact force and liquid bridge force. In the case of a liquid viscosity of 1.03 mPa·s, the domination effect of drag force was higher than that of liquid bridge force and contact force. With an increase of liquid viscosity, domination effect of liquid bridge force and contact force increased, and drag force accounted for less than 50%. When the liquid viscosity was more than 10 mPa·s, drag force had little effect on particle flow behaviors, and contact force and liquid bridge force were almost 50−50. Moreover, with the liquid bridge force more than 10 mPa·s, the distributions of contact/drag/bridge forces almost overlapped. This phenomenon could be explained by the particle flow behaviors possibly being less affected by cohesive liquid viscosity. In Figure 10b, the regime map of liquid content 0.50% is shown with different liquid viscosities. Compared with the case of liquid content 0.10%, the domination effect of drag force decreased, and the domination of contact and liquid bridge forces increased with a higher proportion.

Figure 9. Experimental snapshots of the spouted bed with wet particles (Vlb* = 0.10%, 100 mPa·s).

and liquid content of 0.10%. At the upper bed, particle agglomerations were carried to the left and right walls periodically by spouted gas. Particle agglomeration was broken up by colliding with walls and moved downward in terms of single particles, as shown in Figure 9f. It could be observed that cohesive liquid viscosity had a strong effect on particle flow behaviors. According to the contour map of particle velocity, particles formed dead zones with a small velocity marked by white triangles. The flow pattern was close to slot-rectangular spouted beds. Moreover, the gas channel became curving instead of a vertical gas channel and oscillated from left to right periodically as marked by purple arrow in the figures. 4.2.2. Force Analysis. For a better explanation, quantitative force analyses were explored. In Figure 10, regime maps of dominating force, including contact force, drag force, and liquid bridge force, have been given under different liquid G


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Figure 11. Distributions of forces imposing on particles by numerical simulation (V*lb = 0.10%).

Figure 12. Liquid bridge and contact forces as a function of particle volume fraction by numerical simulation (V*lb = 0.10%).

Figure 12. According to section 2.2.2, liquid bridge force was a function of liquid viscosity and liquid content. It could be determined that the liquid bridge force increased with an increase of liquid viscosity. As shown in Figure 12a, two peaks appeared at around particle volume fractions of 0.33−0.45 and 0.55−0.66, which corresponded to the fountain region and the region near the walls. For the fountain region, particles might form particle agglomerates under the effect of liquid bridge force. In this region, particle agglomerates were carried to the upper bed and broke gradually under the effect of spouting gas. Between the spout region and both side walls, particle flow behaviors become weakened gradually due to less of a free motion path. This phenomenon resulted in less relative motion and velocity between particles. Moreover, in this region, liquid bridge force dominated particle flow behaviors with a higher proportion combing the regime map, which also resulted in less particle motion and forming more stable particle agglomerates near the walls. As shown in Figure 12b, the effect of liquid viscosity on contact force was given. Contact force was half of the liquid bridge force due to high liquid viscosity in wet particle systems. Two peaks appeared at around a particle volume fraction of 0.22−0.33 and 0.55−0.66, which corresponded to the annulus region and fountain region, respectively. Contact force increased with an increase of liquid viscosity; it was because distance between particles decreased with higher liquid viscosity. The effect and value of contact force increased. According to section 2.2.1, contact force was related with particle physical parameters, relative velocity, and elastic deformation. However, liquid viscosity has a limited effect on distribution of contact force. It could be due to the

In Figure 11, the effect of liquid viscosity on liquid bridge force imposing on particles is shown under a liquid content of 0.10% from simulation results. Distributions of forces imposed on particles were symmetrical. Thus, distributions of forces at the right bed were given for a better and clearer description. Figure 11 shows the distributions of the time-averaged liquid bridge force at different bed heights. At a bed height of 40 mm, the value of liquid bridge force was close to 0 N around x = 105 mm. With an increase of bed height, the point corresponding to 0 N of liquid bridge force was toward 118 mm at a bed height of 80 mm. These positions corresponded to the spout region outline, which demonstrated that the outline of the spout region was inclined in the wet particle systems. Between the spout region and both side walls, particles formed an annulus region and might move downward in terms of agglomerates. Particle motion was limited by the cohesive liquid, and relative velocities were close to 0 m/s, which led to governing forces imposed on particles decreasing gradually. Thus, near the walls, the liquid bridge force was less than that in the annulus region where particles were at lower velocities. Moreover, it could be found that liquid bridge force was opposite in the spout region at the bed height of 40 mm. However, liquid bridge force was close to 0 N at the bed height of 80 mm. This phenomenon might reflect that particles were carried to upper bed in terms of agglomerate under the effect of spouting gas. With an increase of bed height, particle agglomerates were broken into smaller agglomerates or single particle. For a further description, the liquid bridge force and contact force as a function of particle volume fraction were given in H


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Figure 13. Distributions of cloud maps of drag force imposed on particles by numerical simulation (V*lb = 0.10%).

Figure 14. Distributions of torque imposed on particles by numerical simulation (Vlb* = 0.10%).

strong effect of high viscosity cohesive liquid on particle motion, and particle colliding characteristics become weakened in the wet particle systems. In Figure 13, the effect of liquid viscosity on time-averaged drag force was shown. Particles were treated independently while calculating drag force, according to section 2.3. Drag force dominated particle motions in the spout region with lower particle volume fraction. Near the walls, particle velocities decreased with the effect of cohesive liquid and less of a free path. Thus, drag force decreased gradually from the spout region to the dense region. With an increase of liquid viscosity, the drag force decreased in the spout region. It might be explained that particles formed more stable particle agglomerates in the dead zone, and a gas channel formed. Moreover, the momentum exchange between particle and gas phases decreased gradually. In Figure 14, torque exerted on particles is given, and it is generated by tangential liquid bridge force, contact force, and rolling friction. With an increase of liquid content and viscosity, contact force and liquid bridge force dominated particle flow behaviors, as shown in the regime map of contact/drag/bridge forces. The effect of drag force was weakened. This phenomenon corresponded to force analysis as stated. Thus, for the torque distribution, torque increased with an increase of liquid content and viscosity. Moreover, near the walls, particle rotational behaviors reduced compared with that of the spout region, and torque was close to 0 N·m. Particle rotational movement was affected strongly under higher liquid content and viscosity. 4.2.3. Particle Velocity Distribution. In Figure 15, distributions of instantaneous particle kinetic energy for three regions are given in the dry particle system. The particle kinetic energy is shown in eq 24

Figure 15. Instantaneous particle kinetic energy in dry particle system from simulation (point A, fountain region; point B, spout region; point C, annulus region).

E k,t =

1 × mp × (vx × vx + vy × vy + vz × vz) 2

(24)

Three samples represented the fountain region, spout region, and annulus region. As shown in Figure 15, the spouted bed consists of three different regions. Particles moved I


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Figure 16. Vertical particle velocity fluctuation at different samples from numerical simulation (V*lb = 0.10%; point A, fountain region; point B, spout region; point C, annulus region).

Figure 17. Vertical particle velocity fluctuation at different samples from numerical simulation (V*lb = 0.50%; point A, fountain region; point B, spout region; point C, annulus region).

Figure 18. Effect of liquid viscosities and contents on time-averaged particle kinetic energy from simulation.

upward through the gas channel with higher vertical particle velocity. Near the gas inlet, spouted gas dominated particle flow behaviors. Thus, we set the sample point at point B, as shown and marked in Figure 15a. Particle velocity distribution was almost symmetrical by the spout region. Thus, point A was set in the middle of the fountain region at the right bed. Point C was set at the edge of the annulus region. Thus, samples were set at point A (x = 90 mm, h = 105 mm), point B (x = 75 mm, h = 75 mm), and point C (x = 110 mm, h = 75 mm). It was clear that the particle kinetic energy in the spout and fountain regions was higher than that of the annulus region. It was because particles were carried to the upper bed with high velocity spouted gas. From the spout to fountain regions, the effect of spouted gas reduced gradually with less gas velocity. Thus, instantaneous particle kinetic energy decreased slightly compared with that of the spout region. For the annulus

region, the drag force decreased largely from the spout region, as shown in Figure 13. In Figures 16 and 17, instantaneous vertical velocity fluctuations of three samples marked in Figures 17 and 18 were given with different liquid contents and viscosities by numerical simulation. For the fountain region shown in Figure 16a, particle velocities were negative, and the value increased gradually. It might be explained that particles easily formed agglomerates, and particle velocity moved downward with a higher velocity under the effect of gravity. For the spout region, shown in Figure 16b, it could be found that particle velocity decreased with an increase of liquid viscosity. This is because resistance increased with higher liquid viscosity, and the gas channel was curved. Thus, particles flow upward with a smaller velocity, and particle velocity fluctuation was weaker. Moreover, for the annulus region shown in Figure 16c, particle J


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Figure 19. Effect of liquid viscosities and contents on time-averaged vertical particle velocity (simulation results).

Figure 20. Effect of liquid viscosities and contents on time-averaged horizontal particle velocity (simulation results).

Figure 21. Effect of liquid viscosities and contents on granular temperature (simulation results).

velocities were negative, and close to 0 m/s gradually with an increase of liquid viscosity. This could be explained by the particle movement being limited by a higher liquid bridge force, and the resistance between particles increased, resulting in smaller particle velocities. In conclusion, particle velocity distributions were different in the different regions. In the dilute region, cohesive liquid might accelerate particle velocities with stable agglomeration structure. Conversely, cohesive liquid limited particle movement in the dense region with higher particle volume concentration. Moreover, similar particle velocity distribution was found in the case of a liquid content of 0.50%, shown in Figure 17. Compared with the case of a liquid content of 0.10%, particle velocity decreased slightly.

As shown in Figure 18, the time-averaged particle kinetic energies at the spout, annulus, and fountain regions were given in the wet particle system with the liquid contents of 0.10% and 0.50%. Similarly, particle kinetic energy decreased from spout and fountain regions to annulus regions. With an increase of liquid viscosity, particle kinetic energy decreased. It demonstrated that particles were dominated by cohesive liquid more effectively with an increase of liquid viscosity. In Figure 19, effects of liquid content and viscosity on axial particle velocity distribution along the spout axis are shown. With an increase of bed height, axial particle velocity increased in the spout region and decreased in the fountain region. Axial particle velocity reached a peak at the boundary between spout and fountain regions. With an increase of liquid content, the K


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spout region increased, which corresponds to the results shown in Figure 19. For a liquid content of 0.50%, a similar phenomenon could be obtained, as shown in Figure 23.

height, corresponding to the boundary between spout and fountain regions, increased slightly. It might be explained that the gas channel was more evident with the stronger effect of cohesive liquid. With higher liquid viscosities and contents, axial particle velocities decreased gradually, which demonstrated that cohesive liquid diminished particle fluidization characteristics. Thus, the presence of cohesive liquid could not be neglected in industrial processing and reactor design. In Figure 20, effects of liquid content and viscosity on timeaveraged horizontal particle velocity distribution are shown at a bed height of 50 mm. Similarly, with the increase of liquid content and liquid viscosity, horizontal particle velocities decreased slightly, which demonstrated that cohesive liquid has a non-negligible effect on particle flow behaviors. 4.2.4. Granular Temperature. In Figure 21, effects of liquid content and viscosity on granular temperature are shown by numerical simulation. Due to symmetric distribution of the granular temperature, a granular temperature of the half bed was given for a clearer explanation. With an increase of bed height, granular temperature increased. It was because the spouted gas overcame less resistance from the bed with an increase in bed height due to a particle mass decrease. Moreover, drag force increased as shown and analyzed in Figure 13. Thus, particle movement was more violent under the higher drag force. With an increase of liquid content and viscosity, granular temperature decreased due to stronger liquid bridge force. Particles easily formed agglomerates under the effect of cohesive liquid, which resulted in a less movement free path of particles. Thus, the particle velocity fluctuation decreased in the wet particle system. In Figure 22, distributions of the particle granular temperature cloud map with different liquid viscosities and contents

Figure 23. Effect of liquid viscosities on granular temperature (simulation results, Vlb* = 0.50%).

In Figure 24, effects of liquid content and viscosity on bubble granular temperature are shown by numerical simulation. In Figure 24a, bubble granular temperature distribution as a function of particle volume fraction was given under the case of a liquid content of 0.10%. Bubble granular temperature increased from the dry particle system to the wet particle system. A similar phenomenon appeared under the case of a liquid content of 0.50%. With a small amount of liquid, the particle system was closer to a dry particle system and converted to one closer to liquid systems with higher liquid contents and viscosities. Thus, the bubble granular temperature increased. Compared to cases with different liquid contents, bubble granular temperature reached peaks with less of a particle volume fraction, which demonstrated that the particle movement was limited with an increase of liquid content. 4.2.5. Pressure Drop. Figure 25 showed the dominant frequency of the pressure drop under different liquid contents and viscosities from numerical simulation. For the dry particle system, dominant frequencies were 6.8539 Hz. The dominant frequency decreased gradually with an increase of liquid viscosity and content. This demonstrated that particles were more difficult to fluidize with a higher viscosity liquid, which led to gas and particle flow behaviors becoming weakened.

5. CONCLUSIONS In this study, experimental measurement and numerical simulation were applied to investigate the hydrodynamic characteristics of dry and wet particles in a spouted bed. For the experiment, a PIV system was used to measure particle velocity with different liquid contents and viscosities of a cohesive liquid. For the numerical simulation, a modified DEM combining rolling friction and liquid bridge force was applied. A quantitative analysis of force was conducted for dry and wet particle systems. Moreover, a comparison of particle velocities, kinetic energy, and granular temperature was explored. Model validation has been applied to demonstrate the accuracy and rationality of the simulation method. The simulation results of time-averaged particle velocity distributions showed good agreement with the experimental data for dry and wet particle systems in this study, which demonstrated that the numerical model was reasonable for dry and wet particle systems. Flow instabilities were found in the wet particle system. It was determined that liquid content and liquid viscosity affected flow pattern together. Flow pattern was close to that of a dry particle system with increasing liquid content and viscosity

Figure 22. Effect of liquid viscosities on granular temperature (simulation results, Vlb* = 0.10%).

are given in the spouted bed by numerical simulation. It could be found that particle granular temperature decreased with an increase of liquid viscosity at bed heights of 40 mm and 90 mm marked by the red lines. This phenomenon corresponds to that of Figure 21. However, the height of the high core of granular temperature increased with an increase of liquid viscosity. Moreover, the value of maximum particle granular temperature increased slightly. This phenomenon reflects that particle velocity fluctuation is more violent in the spout region instead of reducing in all fields, as shown in Figure 21. Thus, it was not reasonable to judge that particle granular temperature decreased with an increase of liquid viscosity. In fact, in wet particle systems, particles were carried to the upper bed with the spouted gas in terms of a single particle through the gas channel and more easily carried to the higher bed height. Thus, the height and value of the maximum particle granular temperature increased with an increase of liquid viscosity with a liquid content of 0.10%. In addition, the length of the L


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Figure 24. Effect of liquid viscosities and contents on bubble granular temperature (simulation results).

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Grant No. 91534112, NO. 51706055).

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NOMENCLATURE DEM = discrete element method dp = particle diameter [m] Fc = contact force [N] Fgp = drag force [N] Flb = liquid bridge force [N] g = gravitational acceleration [m s−2] H = distance between particles [m] Ip = moment of inertia [kg m2] kn = spring stiffness [N m] kt = tangential spring stiffness [N m] LSD = linear spring dashpot mp = particle mass [kg] N = numbers [-] PIV = particle image velocimetry R = particle radius [m] Re = Reynolds number [-] rp = the position of particle center [m] t = time [s] Tp = torque generated by contact force [N m] Tr = torque generated by rolling friction [N m] ug = gas velocity [m s−1] Vlb = liquid bridge volume [m3] Vp = particle volume [m3] vp = particle translational velocity [m s−1]

Figure 25. Effects of liquid content and viscosity on pressure drop dominate frequency (simulation results).

simultaneously within limits. Keeping increasing liquid content and viscosity, the flow pattern appeared to show flow instabilities, and the gas channel became curved. To explain the effect of the liquid bridge force, a quantitative force analysis and a regime of domination forces were explored. When the liquid viscosity was more than 10 mPa·s, drag force had little effect on particle flow behaviors, and contact force and liquid bridge force were almost 50−50. Between the spout region and both side walls, particles formed in the annulus region and moved downward under the strong effect of the cohesive liquid. In addition, particle motion was limited by the cohesive liquid, and relative velocities were close to 0 m/s, which led to governing forces imposed on particles decreasing gradually. In the spout region, liquid bridge force was decreasing and close to 0 N with an increase of bed height, which reflected that particles were carried to the upper bed in terms of agglomerate under the effect of spouting gas. With an increase of bed height, particle agglomerates were broken into smaller agglomerates or single particles.

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SUBSCRIPT c = contact cell = cell numbers cp = capillary g = gas phase f = friction lb = liquid bridge n = normal direction p = solid phase r = rolling t = tangential direction

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 451 86413233. ORCID

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Yurong He: 0000-0003-3009-0468

GREEK LETTERS β = interphase momentum exchange coefficient [-]

Notes

The authors declare no competing financial interest. M


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Industrial & Engineering Chemistry Research γ = surface tension [N m−1] δ = elastic deformation [m] ε = volume fraction [-] θ = contact angle [rad], granular temperature [m2/s2] μ = friction coefficient [-]; liquid viscosity [mPa·s] ρ = density [kg m−3] τ = stress tensor [-] φ = half-filling angle [rad] ω = rotational velocity [rad s−1]

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(20) Zhu, R. R.; Li, S. Q.; Yao, Q. Effect of cohesion on granularfluid flows in spouted beds: PIV measurement and DEM simulations. AIP Conf. Proc. 2013, 1542, 979. (21) Ahmadi Motlagh, A. H.; Grace, J. R.; Briens, C.; Berruti, F.; Farkhondehkavaki, M.; Hamidi, M. Experimental analysis of volatile liquid injection into a fluidized bed. Particuology 2017, 34, 39. (22) Savari, C.; Kulah, G.; Sotudeh-Gharebagh, R.; Mostoufi, N.; Koksal, M. Early detection of agglomeration in conical spouted beds using recurrence plots. Ind. Eng. Chem. Res. 2016, 55, 7179. (23) Yang, W. L.; Hsiau, S. S. Wet granular materials in sheared flows. Chem. Eng. Sci. 2005, 60, 4265. (24) Ma, J.; Liu, D.; Chen, X. Bubble behaviors of large cohesive particles in a 2D fluidized bed. Ind. Eng. Chem. Res. 2016, 55, 624. (25) Gonzalez-Quiroga, A.; Reyniers, P. A.; Kulkarni, S. R.; Torregrosa, M. M.; Perreault, P.; Heynderickx, G. J.; Van Geem, K. M.; Marin, G. B. Design and cold flow testing of a gas-solid vortex reactor demonstration unit for biomass fast pyrolysis. Chem. Eng. J. 2017, 329, 198. (26) Tsuji, Y.; Kawaguchi, T.; Tanaka, T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technol. 1993, 77, 79. (27) Cundall, P. A.; Strack, O. D. L. A discrete numerical model for granular assemblies. Geotechnique 1979, 29, 47. (28) Guo, Y.; Curtis, J. S. Discrete element method simulations for complex granular flows. Annu. Rev. Fluid Mech. 2015, 47, 21. (29) Mechtcherine, V.; Gram, A.; Krenzer, K.; Schwabe, J. H.; Shyshko, S.; Roussel, N. Simulation of fresh concrete flow using Discrete Element Method (DEM): theory and applications. Mater. Struct. 2014, 47, 615. (30) Halidan, M.; Chandratilleke, G. R.; Chan, S. L. I.; Yu, A. B.; Bridgwater, J. Prediction of the mixing behaviour of binary mixtures of particles in a bladed mixer. Chem. Eng. Sci. 2014, 120, 37. (31) Yang, S.; Sun, Y.; Zhang, L.; Chew, J. W. Segregation dynamics of a binary-size mixture in a three-dimensional rotating drum. Chem. Eng. Sci. 2017, 172, 652. (32) Sun, X.; Sakai, M.; Sakai, M. T.; Yamada, Y. A Lagrangian− Lagrangian coupled method for three-dimensional solid−liquid flows involving free surfaces in a rotating cylindrical tank. Chem. Eng. J. 2014, 246, 122. (33) Liu, R. J.; Xiao, R.; Ye, M.; Liu, Z. Analysis of particle rotation in fluidized bed by use of discrete particle model. Adv. Powder Technol. 2018, 29, 1655. (34) Luo, K.; Fang, M.; Yang, S.; Zhang, K.; Fan, J. LES−DEM investigation of an internally circulating fluidized bed: Effects of gas and solid properties. Chem. Eng. J. 2013, 228, 583. (35) Takabatake, K.; Mori, Y.; Khinast, J. G.; Sakai, M. Numerical investigation of a coarse-grain discrete element method in solid mixing in a spouted bed. Chem. Eng. J. 2018, 346, 416−426. (36) Yang, S.; Luo, K.; Fang, M.; Zhang, K.; Fan, J. Parallel CFDDEM modeling of the hydrodynamics in a lab-scale double slotrectangular spouted bed with a partition plate. Chem. Eng. J. 2014, 236, 158. (37) Zhang, H.; Li, S. DEM simulation of wet granular-fluid flows in spouted beds: Numerical studies and experimental verifications. Powder Technol. 2017, 318, 337. (38) Zhu, R. R.; Zhu, W. B.; Xing, L. C.; Sun, Q. Q. DEM simulation on particle mixing in dry and wet particles spout bed. Powder Technol. 2011, 210, 73. (39) Xu, H.; Zhong, W.; Yuan, Z.; Yu, A. B. CFD-DEM study on cohesive particles in a spouted bed. Powder Technol. 2017, 314, 377. (40) Song, C.; Liu, D.; Ma, J.; Chen, X. CFD-DEM simulation of flow pattern and particle velocity in a fluidized bed with wet particles. Powder Technol. 2017, 314, 346−354. (41) Van Buijtenen, M. S.; Deen, N. G.; Heinrich, S.; Antonyuk, S.; Kuipers, J. A. M. A discrete element study of wet particle−particle interaction during granulation in a spout fluidized bed. Can. J. Chem. Eng. 2009, 87, 308. (42) Ma, J.; Liu, D.; Chen, X. Experimental study of oblique impact between dry spheres and liquid layers. Phys. Rev. E 2013, 88, 033018.

REFERENCES

(1) Mollick, P. K.; Sathiyamoorthy, D. Assessment of stability of spouted bed using pressure fluctuation analysis. Ind. Eng. Chem. Res. 2012, 51, 12117. (2) Yang, S.; Sun, Y.; Zhang, L.; Zhao, Y.; Chew, J. W. Numerical investigation on the effect of draft plates on spouting stability and gas−solid characteristics in a spout-fluid bed. Chem. Eng. Sci. 2016, 148, 108. (3) Kfuri, C. R.; Freitas, L. A. P. A comparative study of spouted and spout-fluid beds for tablet coating. Drying Technol. 2005, 23, 2369. (4) Zielinska, M.; Markowski, M. Drying behavior of carrots dried in a spout-fluidized bed dryer. Drying Technol. 2007, 25, 261. (5) Cheng, H.; Hu, Y. Municipal solid waste (MSW) as a renewable source of energy: Current and future practices in China. Bioresour. Technol. 2010, 101, 3816. (6) Jung, C. H.; Matsuto, T.; Tanaka, N.; Okada, T. Metal distribution in incineration residues of municipal solid waste (MSW) in Japan. Waste Manage. 2004, 24, 381. (7) Erkiaga, A.; Lopez, G.; Amutio, M.; Bilbao, J.; Olazar, M. Influence of operating conditions on the steam gasification of biomass in a conical spouted bed reactor. Chem. Eng. J. 2014, 237, 259. (8) Zhong, W.; Chen, X.; Zhang, M. Hydrodynamic characteristics of spout-fluid bed: Pressure drop and minimum spouting/spoutfluidizing velocity. Chem. Eng. J. 2006, 118, 37. (9) Van Buijtenen, M. S.; Van Dijk, W. J.; Deen, N. G.; Kuipers, J. A. M.; Leadbeater, T.; Parker, D. J. Numerical and experimental study on multiple-spout fluidized beds. Chem. Eng. Sci. 2011, 66, 2368. (10) Murakami, M.; Nakajima, F.; Furumai, H. Size-and densitydistributions and sources of polycyclic aromatic hydrocarbons in urban road dust. Chemosphere 2005, 61, 783. (11) Ali, H.; Plaza, F.; Mann, A. Numerical prediction of dust capture efficiency of a centrifugal wet scrubber. AIChE J. 2018, 64, 1001. (12) Xu, H.; Zhong, W.; Yu, A.; Yuan, Z. Spouting characteristics of wet particles in a conical-cylindrical spouted bed. Ind. Eng. Chem. Res. 2015, 54, 9894. (13) Lin, C. L.; Wey, M. Y. The effect of mineral compositions of waste and operating conditions on particle agglomeration/defluidization during incineration. Fuel 2004, 83, 2335. (14) Munro, M. C.; Mohajerani, A. Determination of the transportable moisture limit of iron ore fines for the prevention of liquefaction in bulk carriers. Marine Structures 2015, 40, 193. (15) Møller, V. B.; Dam-Johansen, K.; Frankær, S. M.; Kiil, S. Simultaneous acid exposure and erosive particle wear of thermoset coatings. J. Coatings Technol. Res. 2018, 15, 457. (16) Huang, H.; Hu, G. Mixing characteristics of a novel annular spouted bed with several angled air nozzles. Ind. Eng. Chem. Res. 2007, 46, 8248. (17) Link, J. M.; Cuypers, L. A.; Deen, N. G.; Kuipers, J. A. M. Flow regimes in a spout−fluid bed: A combined experimental and simulation study. Chem. Eng. Sci. 2005, 60, 3425. (18) Brilliantov, N. V.; Pöschel, T. Rolling friction of a viscous sphere on a hard planedynamics. Europhys. Lett. 1998, 42, 511. (19) Sutkar, V. S.; Deen, N. G.; Kuipers, J. A. M. Spout fluidized beds: Recent advances in experimental and numerical studies. Chem. Eng. Sci. 2013, 86, 124. N


Article

Industrial & Engineering Chemistry Research (43) Sun, L.; Luo, K.; Fan, J. Population balance equation of cohesive particle flow in a circulating fluidized bed. Chem. Eng. Technol. 2017, 40, 1544. (44) Anderson, T. B.; Jackson, R. Fluid mechanical description of fluidized beds. Equation of Motion. Ind. Eng. Chem. Fundam. 1967, 6, 527. (45) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, 1992. (46) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960. (47) Adams, M. J.; Edmondson, B. Forces between particles in continuous and discrete liquid media. Tribology in Particulate Technology; Briscoe, B. J., Adams, M. J., Eds.; 1987 (48) Goldman, A. J.; Cox, R. G.; Brenner, H. Slow viscous motion of a sphere parallel to a plane wall - I motion through a quiescent fluid. Chem. Eng. Sci. 1967, 22, 637. (49) Lian, G.; Thornton, C.; Adams, M. J. A theoretical study of the liquid bridge forces between two rigid spherical bodies. J. Colloid Interface Sci. 1993, 161, 138. (50) Beetstra, R.; Van der Hoef, M. A.; Kuipers, J. A. M. Drag force of intermediate Reynolds number flow past mono-and bidisperse arrays of spheres. AIChE J. 2007, 53, 489. (51) Tartan, M.; Gidaspow, D. Measurement of granular temperature and stresses in risers. AIChE J. 2004, 50, 1760. (52) Jung, J.; Gidaspow, D.; Gamwo, I. K. Measurement of two kinds of granular temperatures, stresses, and dispersion in bubbling beds. Ind. Eng. Chem. Res. 2005, 44, 1329. (53) Tang, T.; He, Y.; Tai, T.; Wen, D. DEM numerical investigation of wet particle flow behaviors in multiple-spout fluidized beds. Chem. Eng. Sci. 2017, 172, 79. (54) Govender, I.; Cleary, P. W.; Mainza, A. N. Comparisons of PEPT derived charge features in wet milling environments with a friction-adjusted DEM model. Chem. Eng. Sci. 2013, 97, 162. (55) Zhong, W.; Zhang, M.; Jin, B.; Chen, X. Flow pattern and transition of rectangular spout-fluid bed. Chem. Eng. Process. 2006, 45, 734. (56) Dogan, O. M.; Freitas, L. A. P.; Lim, C. J.; Grace, J. R.; Luo, B. Hydrodynamics and stability of slot-rectangular spouted beds. Part I: Thin bed. Chem. Eng. Commun. 2000, 181, 225. (57) Freitas, L. A. P.; Dogan, O. M.; Lim, C. J.; Grace, J. R.; Luo, B. Hydrodynamics and stability of slot-rectangular spouted beds part II: increasing bed thickness. Chem. Eng. Commun. 2000, 181, 243.

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