Hydrodynamic and Mixing Characteristics of GasâSolid Flow in a

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Hydrodynamic and mixing characteristics of gas-solid flow in a pulsed spouted bed Maysam Saidi, Hassan Basirat Tabrizi, John R. Grace, C. Jim Lim, and Goodarz Ahmadi Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b01645 • Publication Date (Web): 27 Jul 2015 Downloaded from http://pubs.acs.org on August 2, 2015

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Industrial & Engineering Chemistry Research

Hydrodynamic and mixing characteristics of gas-solid flow in a pulsed spouted bed Maysam Saidi1, Hassan Basirat Tabrizi2,*, John R. Grace3, C. Jim Lim4, Goodarz Ahmadi5 1,2

Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

3,4

Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC, Canada 5

Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, USA

Abstract The flow behavior and particle motion in a pulsed gas-solid spouted bed was investigated using the Eulerian-Lagrangian approach. The Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) was used to evaluate the gas flow field and particle trajectories. The model was four-way coupled to account for fluid-particle, particle-fluid and particle-particle interactions. A column of 150 mm × 15 mm cross-section and height 750 mm containing 24,500 particles of diameter 2.5 mm was investigated. Gas entered through a 10 mm × 15 mm slot at the base of the bed. Steady spouting was compared with pulsed spouting at frequencies of 1, 4, and 10 Hz, with superficial velocity amplitude of 0.5 and 1 m/s, and a mean superficial spouting velocity of 2 m/s. In addition to comparing the bed pressure drop versus time and its Fourier decomposition, the hydrodynamics in the spout and annulus regions were examined. A new procedure was introduced to assess spouted bed mixing and homogeneity. Flow pulsation was shown to provide stronger upward air momentum, less horizontal gas percolation, better circulation, higher downward particle flux near the sidewalls, better mixing and greater homogeneity. Keywords: Spouted Bed, Pulsation, Computational Fluid Dynamics, Discrete Element Method, EulerianLagrangian, Mixing Distribution 1

M. Saidi, PhD candidate, [email protected] H. Basirat Tabrizi, Professor, Corresponding author, +98-21-64543455, [email protected] 3 J.R. Grace, Professor, [email protected] 4 C.J. Lim, Professor, [email protected] 5 G. Ahmadi, Professor, [email protected] 2

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Introduction A pulsed spouted bed, in which the airflow rate varies in a periodic manner with time, is a hybrid technique for improving some characteristics of gas-solid spouted beds. Mathur and Gishler1 invented the spouted beds to overcome disadvantages of fluidized beds for coarse particles. Since then, many experimental and numerical studies have been performed on flow characteristics, operational parameters and performance of spouted beds. Despite the similarity between some aspects of spouted beds of coarse particles and fluidized beds of fine particles, there are marked differences, such as random motion in fluidized beds and steady motion in conventional spouted beds. In spouted beds, particles flux is upward in the central spout region, returning downward in a moving-packed-bed annulus zone near the wall, as shown in Fig. 1. Gasification, coating, drying and mixing are among the applications of gas-solid spouted beds. The industrial-scale applications of conventional cylindrical spouted beds have been limited due to difficulties in scale-up and slot-rectangular spouted beds (SRSBs) with rectangular crosssection column with a slot at the base represent an appropriate alternative.2 Devahastin and Mujumdar3 studied the effect of flow pulsation on hydrodynamics and mixing characteristics of a cylindrical spouted bed dryer experimentally and observed spouting, transition, and slugging regimes. They reported that flow pulsation resulted in better performance in terms of the maximum spoutable bed height, solid circulation rate and mixing of food particles. Niamnuy et al.4 conducted an experimental investigation of the hydrodynamic characteristics of a pulsed cylindrical spouted bed. They observed higher maximum spoutable bed height for different pulsation frequencies compared to steady inlet flow because of reduced radial percolation of upward momentum of an intermittent jet. Studies have also been carried out on flow pulsation in fluidized beds. Zhang and Koksal5 investigated the heat transfer and hydrodynamics in a pulsed bubbling fluidized bed using a solenoid valve at frequencies of 1, 3, 5, 7 and 10 Hz. Except for the 1 Hz case, they observed that the pressure drop variation was triangular in response of the square on-off periods of the solenoid-valve. The flow pulsation led to increased convective heat transfer from an immersed cylinder, especially for smaller particles, lower airflow velocities and higher frequencies. Nitz

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and Taranto6 studied drying of beans using a pulsed rotary fluidized bed with the gas distributed alternatively among different sections of the drying chamber. Comparing the effectiveness of their pulsed fluidized bed with a conventional one, they found that similar performance could be obtained with the pulsed system at reduced air consumption. Akhavan et al.7 used a pulsation-assisted fluidized bed to dry pharmaceutical granules and reported an improved drying rate and homogeneity. Hadi et al.8 investigated particle mixing in a pulsed rectangular fluidized bed experimentally, and found that pulsation increased the mixing rate and homogeneity of fluidized beds. Increased bubble size was also observed, based on pressure signal analysis, as a beneficial result of decreased gas channeling. Ali and Asif9 studied the effect of flow pulsation on fluidization of nano-powders in the pharmaceutical and paint industries. They reported lower minimum fluidization velocity, less agglomeration, and improved homogeneity in a pulsed fluidized bed. Khosravi Bizhaem and Basirat Tabrizi10 studied the hydrodynamic characteristics of a pulsed fluidized bed by measuring the pressure drop, bubble size and rise velocity. They observed decreased bubble size, increased pressure drop, and decreased agglomeration when the pulsation frequency increased from 1 to 10 Hz. Saidi et al.11 investigated the effect of pulsation on segregation of binary particles differing in size in a cylindrical fluidized bed. They investigated three compositions of binary particles (flotsam rich, jetsam rich, and equally mixed) and three configurations of inlet air (continuous, pure pulsed, and combined). They observed significant increased segregation as the pulsations eliminated dead zones and static channel-like structures. Ultrasound and microwave-assisted pulsed spouted bed shave also received some attention in the literature. It has been shown12-15 that this kind of pulsation leads to better performance, especially in food processing industries.

Comment [m1]: Reviewer 2: Q2

In addition to the experimental studies, several numerical simulations have been conducted on flow pulsation effects on fluidized beds based on both the Eulerian-Lagrangian and EulerianEulerian approaches. In the Eulerian-Lagrangian approach, the motion of particles is tracked by calculating the contact force on each particle, while the fluid is treated as a continuous phase, whereas in the Eulerian-Eulerian approach, the fluid and solid phases are treated as interpenetrating continua. The Discrete Element Method (DEM) and Two Fluid Model (TFM) are

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the most appropriate models applying these approaches in fluidized bed and spouted bed studies. Wang and Rhodes16,17 used a Discrete Element Method to study the effect of pulsation on fluidization, employing different frequencies, amplitudes and pulsation types. They reported ordered pressure fluctuations and a regular bubble pattern for both sinusoidal and square pulsations. Better fluidization occurred at base flows between the packed bed and bubbling regimes. Gui and Fan18 studied the influence of pulsation on a bubbling fluidized bed containing an immersed tube using the Discrete Element Method and Large Eddy Simulation (DEM-LES). They observed that the pressure drop, interparticle forces and gas-particle forces fluctuated with the same frequency as the imposed flow pulsation. They also indicated that highfrequency pulsations suppressed the fluctuating motion of the particles. Berrouk and Wu19 calculated the dimensionless distance from the wall (y+) in the fluidized bed simulated by Gui et al.20 and concluded that the computational grid was not sufficiently fine for Large Eddy Simulation. In addition, the calculated integral time scale of turbulence showed that the particle response time was not sufficiently small to respond to turbulent fluctuations. Li et al.21 used the TFM to study flow behavior and bubble characteristics in a 2D pulsed fluidized bed. A low frequency of 0.4 Hz caused intermittent fluidization, while a moderate frequency of 4 Hz led to resonant fluidization, and a high frequency of 40 Hz produced normal fluidization. They observed that pulsations led to higher bed expansion ratio and less bed fluctuation, indicating better quality fluidization. In contrast to numerical studies on pulsed spouted bed and spout-fluid bed, there are numerous steady flow analyses of spouted beds.22-31 The literature indicates that nearly all studies on flow pulsation have focused on fluidized beds; studies of pulsed spouted beds are lacking. The present study focuses on the influence of flow pulsation in gas-solid spouted beds. The hydrodynamic and mixing characteristics of a pulsed spouted bed are investigated using the coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM). The effects of flow rate and pulsation frequency and amplitude on pressure drop, particle flux, and voidage are evaluated. A novel procedure is also introduced to compare the spouted bed performances concerning mixing and homogeneity.

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2.

Model description and numerical method

Computational Fluid Dynamics and the Discrete Element Method were used to solve the continuum flow field and the discrete particle phase equations in a four-way coupled approach. The governing equations for the gas phase based on mass and momentum balances, including the effect of local voidage are ∂ ( ερ g ) + ∇ ⋅ ( ερ g ur g ) = 0 ∂t

(1)

r ∂ ( ερ g ur g ) + ∇ ⋅ ( ερ g ur g ur g ) = −ε∇ p + ερ g gr − ∇ ⋅ τg − S p ∂t

(2)

r where ε , ρg , u g , and p are, respectively, voidage, density, velocity and pressure,

and τg = −εµ g ( ∇ ur g + (∇ ur g ) T ) is the stress tensor of the gas phase for an incompressible fluid. For these dense gas-solid flows the effect of gas velocity fluctuations is negligible.18 Neglecting turbulence is also acceptable for these relatively large particles and the domination of particle collisions. The effect of particles on the gas phase is shown in Equation (2), with a source term due to the momentum exchange: r Sp =

1 V cell

∑

∀ i∈ cell

Vi β r r (u g − v i ) 1− ε

(3)

r where V cell , V i , vi and µ g are gas cell volume, particle volume particle velocity, and viscosity,

respectively. The governing equations for translational and rotational motion of a solid particle are r r r r Vβ r r d2 r mi 2i = mi g + i (u g − vi ) + ∑ (Fcn,ij + Fct,ij ) dt 1− ε j Ii

r r r dωi = ∑ (ri n ij × Fct,ij ) dt j

(4) (5)

r r r r where mi , ri , ωr i , Ii , ri , n ij , Fcn,ij and Fct,ij are, respectively, the particle mass, position, angular

velocity, moment of inertia, radius, collision normal unit vector, normal contact force, and tangential contact force. The momentum exchange coefficient ( β ) is calculated using empirical correlations given by Ergun32 ( ε < 0.8 ) and Wen and Yu33 ( ε ≥ 0.8 ). These are34 5



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µg   (1 − ε ) 2 1− ε  2  150 + 1.75 Rep  ε ε  dp   β =  µ  g3 − 2.65    d 2  4 C D R e p (1 − ε ) ε   p 

 24 (1 + 0.15 Re p 0.687 )  C D =  Re p  0.44 

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ε < 0.8

(6) ε ≥ 0.8

Re p < 1000

(7)

Re p ≥ 1000

where Re p =

r r ρgε u g − vi d p

(8)

µg

Re p is the particle Reynolds number, and CD is the drag coefficient for spherical particles.

Particle collisions are modeled using a combination of mechanical springs, dashpots and sliders with specific stiffness, damping coefficient and friction coefficient. The contact force is calculated as a summation of the elastic and inelastic forces using the spring-damper system, analogous to the Voigt-Kelvin model of viscoelasticity. In a sliding situation, the tangential force r

r

is taken to be equal to the friction force. The normal ( Fcn,ij ) and tangential ( Fct ,ij ) collision contact forces are defined as

r r r Fcn,ij = −k n δ3/2 n n ij − ηn v n,ij

(9)

r  − k t δ t − η t vr t ,ij r  Fct ,ij =  r r  −λ Fcn ,ij tij

where k ,

r

η, λ , δ,

r r Fct ,ij ≤ λ Fcn ,ij r r Fct ,ij > λ Fcn ,ij

(10)

r r r vn,ij , v t,ij and tij are the spring stiffness, damping coefficient, friction

coefficient, displacement, normal relative velocity, tangential relative velocity and tangential direction of collision, respectively. The normal and tangential spring stiffness and the normal (and tangential) damping coefficients are35,36 kn =

4 3

kt = 8

1 − ν i2 1 − ν j −1 + ) ri + rj E i Ej ri rj

ri r j ri + r j

2

(11)

(

δn (

2 − ν i 2 − ν j −1 + ) Gi Gj

(12)

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ηn = α


mi m j mi + m j

1

k n δn4

(13)

Here ri and rj are the radii of the colliding particles and G is shear modulus, related to Young's modulus ( E ) and Poisson's ratio ( ν ) by G = E / 2(1 + ν ) . The coefficient α is an empirical constant related to the restitution coefficient.36 For particle-wall collisions, the wall is treated as a particle of infinite radius and mass. The solution procedure using OpenFOAM, an open source C++ based code, employed an initial condition for both phases and boundary conditions for the gas phases, then calculated gasparticle interactions, particle-particle and particle-wall collisions. After updating particles positions and calculating the voidage, the modified Navier-Stokes equation was solved at each time step to update the flow field using the finite volume method in a collocated grid arrangement. The discretization using Gaussian integration and flux interpolation utilized bounded second order linear upwind differencing for the convection divergence and unbounded second order linear differencing for the diffusion Laplacian. The bounded implicit scheme of Euler was employed for time derivatives. To obtain convergence of both the CFD and DEM, a time step of the order of 10-5 s was chosen to satisfy the Courant number limitation and the contact time criteria.37,38 Typically, each simulation was solved for 10 seconds to reach reliable time-averaged solutions.

3.

Simulation conditions

The spouted bed column has a 0.15 m × 0.015 m rectangular cross-section with a height of 0.75 m. Gas enters from a slot of width 0.01 m. The dimensions of the generated mesh for the simulation of the slot-rectangular spouted bed are shown in Fig. 2. There are 40 and 60 cells along the width and height of the column, respectively. The mesh is finer in regions of higher velocity gradient, especially in the central and lower regions. The column is filled with 24,500 spherical particles of diameter 2.5 mm and density 2526 kg/m3. These particles are initially positioned without contact with one another. At the start of the simulation, they are released to fall under gravity. The boundary conditions for the fluid phase were no-slip at walls, timevarying velocity at the spouting inlet and zero gauge static pressure at the outlet. Partial slip 7



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and rebound are provided for the particle boundary condition. Key properties of the particles and gas phase are reported in Table 1. The wave form of the flow pulsation of the entering air is depicted in Fig. 3. It is represented as a function of mean superficial velocity ( U m ), pulsation amplitude ( U a ), pulsation frequency (f), and time (t) by U s = U m + ( − 1) [

4.

2 f . t]

(14)

Ua

Simulation verification

The experimental and numerical investigation of Link et al.22 for a spout-fluid bed was selected for comparison with the proposed model where the geometry, dimensions and particle properties were similar to the present simulation, but it differs in the gas entry boundary condition in being a steady spout-fluid bed (without pulsations). For this comparison, our gas entry boundary condition consists of two steady (non-varying) background velocities of 1.5 m/s for fluidization of the annular region surrounding the central orifice and 30 m/s (superficial velocity of 2 m/s) for the central spouting inlet, as shown in Fig. 1. Figure 4 compares our r predicted vertical time-averaged particle flux given by ΦP = (1 − ε)ρp vp over a horizontal cross-

section 0.13 m above the inlet with Link et al.22 experimental and simulation. The particles are seen to rise in the central region and return downward near the sidewalls. There is good agreement between the present model predictions and Link et al.22 experimental data and simulation results. 5.

Results and Discussion

5.1.

Pressure drop

The total pressure drop from the slot to the freeboard versus time for steady and pulsed spouting with pulsation amplitudes of 0.5 and 1 m/s are shown, respectively, in Figs. 5 and 6. The amplitude of Fourier decomposition of pressure drop is computed using the Discrete Fourier Transform and the results are plotted in the same figures. In the spouting regime, the steady spouting shows some fluctuations in magnitude of bed pressure drop versus time, as 8


Comment [m2]: Reviewer1: Q4

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seen in Fig. 5a. The most important contributions to the pressure drop are due to the weight of the particles, inertia of the accelerated particles and friction. Although constant pressure drop versus time is expected for ideal steady spouting, in the real situation there are time variations due to the changes in the number of participating particles. The dominant frequency of around 7.3 Hz for steady inlet flow is known as the natural frequency of the system. The dominant frequency occurred at 7 Hz for pulsation at 1 Hz in Fig. 5b,diminishes for pulsations at 4 and 10 Hz, in Figs. 5c and 5d, all for inlet pulsation amplitude of 0.5 m/s. The reason for the similarity of dominant frequency of 1 Hz pulsation and steady flow is that the time between pulsations was not short enough to change the dominant frequency. Increasing the spouting inlet amplitude to 1 m/s, removed the dominance of the frequency close to the natural frequency for the 1 Hz flow pulsation, as seen in Fig. 6b. For both amplitudes studied, the dominant frequency of pressure drop is equal to the flow pulsation frequency in the 4 Hz case. In the case of 10 Hz pulsations, although a peak is seen in the power spectrum at 10 Hz, a stronger peak is seen at 5 Hz. In this case, it appears that the particles cannot fully follow the flow because of its high change rate.

5.2.

Air velocity

Since the airflow plays the major role in driving the particles in spouted beds, the timeaveraged air velocity vector fields within the 0.3 m height of the column are depicted in Figs. 7 and 8. The strong upward velocity above the spouting inlet, the percolation of air from the central spout to annulus region, and higher upward velocity near the sidewalls in the lower regions of annulus are similar for different cases. Figs. 7b and 7d show the effect of pulsation magnitude that leads to less horizontal percolation in the lower regions of the bed and stronger upward momentum in comparison to steady spouting shown in Fig. 7a. While the upward momentum directly depends on the flow pulsation amplitude, comparing Fig. 7d for 10 Hz pulsation with Fig. 7c for 1 Hz pulsation, an inverse relation can be noticed between flow pulsation frequency and the strength of upward air momentum. The positive effect of flow pulsation on increasing the upward momentum and decreasing the horizontal air percolation is

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in agreement with the earlier experimental findings of Niamnuy et al.4, which showed higher maximum spoutable bed height.

5.3.

Particle flux

Predicted time-averaged vertical particle flux contours and particle flux actual vectors are shown in Figs. 8 and 9. It is seen that the particles move upward in the spouting region and return downward near the sidewalls. The boundaries between zones of upward and downward particle flux are shown by zero-value-lines. Maximum upward and downward particle fluxes occur, respectively, at the center and near the sidewalls. Taller and broader regions of upward particle flux and higher values of downward particle flux are obtained when steady spouting in Fig. 8a changes to pulsed flows in Figs. 8b and 8c. Increasing the amplitude of the flow pulsations causes an increase in the magnitude of time-averaged downward particle flux near the sidewalls from about -200 kg/m2s in steady flow to -300 kg/m2s and -500 kg/m2s in the pulsed flows, respectively, with amplitudes of 0.5 m/s and 1 m/s. The changes due to pulsation are also reflected by an increase in the angle of the region with upward particle flux, leading to a decrease in the extent of the dead zone and an increase in the number of participating particles. This effect could be observed from the descent of the -100 kg/m2s lines, especially for the higher amplitude (Fig. 8) and higher frequency (Fig. 9).

5.4.

Mixing and homogeneity

Mixing and homogeneity are important considerations for spouted beds. Increased movement of particles in all regions leads to better mixing and homogeneity, enhancing the performance in most applications such as coating and drying. Although different criteria and mixing indices are available for compositions of dissimilar particles based on the presence of each type of particles in the domain, in columns containing only one type of particles there is no criterion. Ideal mixing and homogeneity are attained when all particles visit all domains over a limited interval of time. A new procedure for assessing mixing and homogeneity is defined by dividing the domain into the same discrete cells as the CFD grids. For each particle, the host cell is determined after each time step. The number of host cells visited by each particle is then

10


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calculated. The result is a curve where the x-axis and y-axis provide the number of host cells and the number of guest particle, respectively and show the distribution of the number of the particles that have passed through certain number of cells in a given time interval. The peak at a host cell value of 1 corresponds to particles which are stationary over the time interval, undergoing no mixing. On the other hand, for ideal mixing and homogeneity and no dead zone, all of the particles will have visited all cells, ultimately providing a peak with the host cell number equal to the total number of cells. Figure 10 shows the distribution predicted by the DEM simulation for different intervals of time. To omit the initial transition effects, the first second is excluded. The sharp peak for host cells near 1 corresponds to the dead zones in the column. The peak of the distribution curve shifts to the right with time interval increasing from 1 s to 9 s. Comparison of the pulsed flow in Fig. 10b with steady spouting in Fig. 10a shows that the distribution shifts to the right faster when the flow is pulsed, implying increased mixing. Figure 11 shows the effect of flow pulsation frequency and amplitude on the mixing in the interval from 1 to 10 s. For all studied cases, pulsation moves the distribution curves to the right. The shift is slight for lower pulsation amplitude, but becomes more noticeable for higher pulsation amplitudes and frequencies, indicating improved mixing. It should be pointed out that pulsing the flow leads to higher magnitude of instantaneous spouting velocity which raises the particles to higher heights (especially for 1 Hz pulsations); therefore, although more particles visit more cells, this may not necessarily be helpful for mixing and homogeneity. However, comparing the results for pulsation frequency of 4 and 10 Hz with 1 Hz in Fig. 11b, shows marked rightward movements of the distribution.

Conclusions


Numerical modeling of a pulsed slot-rectangular spouted bed was performed, and the effects of pulsation on the flow features and particle motion behavior were evaluated. Due to the lack of quantitative experimental studies on pulsed spouted beds, the CFD-DEM simulations were compared with particle flux profiles for a steady spout-fluid bed reported by Link et al.22. Ordered pressure drop fluctuation in response to flow pulsation was seen for spouted beds in 11



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this study, as in previous studies on fluidized beds.5,16,18 The simulated time-averaged airflow velocity vectors showed that the effect of pulsation was to increase the upward momentum and decrease the horizontal air percolation, especially at high pulsation amplitudes and low pulsation frequencies. This led to higher maximum spoutable bed height as reported earlier.3,4 Particle flux contours and the proposed procedure for assessing mixing showed enhancement of particle motion and benefits of flow pulsation. Better circulation of particles in the bed, higher downward time-averaged particle flux near the walls and higher mixing was predicted for pulsation of higher amplitudes and frequencies. Based on detailed information from CFDDEM, this study suggests that flow pulsation can enhance spouted bed performance in terms of particle circulation, mixing, and bed homogeneity.

Acknowledgement This research was enabled in part by supports from Ministry of Science, Research and Technology of Iran (MSRT), Natural Sciences and Engineering Research Council of Canada (NSERC), Compute Canada Calcul Canada and WestGrid.

Nomenclature


C D = drag coefficient, -

d = diameter, m

e = restitution coefficient, E = Young's modulus, kg m-1 s-2 f = pulsation frequency, Hz F = force, kg m s-2 g = gravity, m s-2 G i = shear modulus, kg m-1 s-2

H = column height, m k = stiffness coefficient, kg m-0.5 s-2

L = column thickness, m m = mass, kg 12


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r n ij = unit vector in normal direction of particles i and j collision

Np = number of particles p = pressure, kg m-1 s-2 r = particle radius, m Re = Reynolds number r Sp = source term, kg m-2 s-2 t = time, s r tij = unit vector in tangential direction of particles i and j collision

u = local gas velocity, m s-1 U = superficial velocity, m s-1

v = particle velocity, m s-1 Vcell = volume of CFD cell, m3 Vi = volume of particle i, m3

W = column width, m Wslot = slot width, m

Greek letters α = empirical constant related to restitution coefficient β = momentum exchange coefficient, kg m-3 s δ = displacement, m

ε = voidage, -

ηt = damping coefficient, kg s-1 λ = friction coefficient, µ = viscosity, kg m-1 s-1 ν = Poisson's ratio, ρ = density, kg m-3 τ = stress tensor, kg m-1 s-2

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Φ p = particle flux, kg m-2 s-1

Subscripts a= amplitude cn= direction normal to direction of collision ct= direction tangential to direction of collision g= gas i= particle index ij= collided particle indices j= particle index f= fluidizing m= mean n= normal p= particle s= spouting t= tangential

References 1. 2.

3. 4. 5. 6.

Mathur, K. B.; Gishler, P. A technique for contacting gases with coarse solid particles. AIChE J. 1955, 1, 157-164. Grace, J. R.; Lim, C. J. Scaleup, slot-rectangular, and multiple spouting; In Spouted and spout-fluid beds: fundamentals and applications; Epstein, N. and Grace, J. R., Ed.; Cambridge University Press: Cambridge, UK, 2011; 283-296. Devahastin, S.; Mujumdar, A. S. Some hydrodynamic and mixing characteristics of a pulsed spouted bed dryer. Powder Technol. 2001, 117, 189-197. Niamnuy, C.; Kanthamool, W.; Devahastin, S. Hydrodynamic characteristics of a pulsed spouted bed of food particulates. J. Food Eng. 2011, 103, 299-307. Zhang, D.; Koksal, M. Heat transfer in a pulsed bubbling fluidized bed. Powder Technol. 2006, 168, 21-31. Nitz, M.; Taranto, O. P. Drying of beans in a pulsed fluid bed dryer: Drying kinetics, fluiddynamic study and comparisons with conventional fluidization. J. Food Eng. 2007, 80, 249256.

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7.

8. 9. 10. 11.

12. 13.

14.

15.

16. 17. 18. 19.

20. 21. 22. 23. 24.


Akhavan, A.; Van Ommen, J. R.; Nijenhuis, J.; Wang, X. S.; Coppens, M. O.; Rhodes, M. J. Improved drying in a pulsation-assisted fluidized bed. Ind. Eng. Chem. Res. 2009, 49, 302309. Hadi, B.; Van Ommen, J. R.; Coppens, M. O. Enhanced particle mixing in pulsed fluidized beds and the effect of internals. Ind. Eng. Chem. Res. 2012, 51, 1713-1720. Ali, S. S.; Asif, M. Fluidization of nano-powders: effect of flow pulsation; Powder Technol. 2012, 225, 86-92. Khosravi Bizhaem, H.; Basirat Tabrizi, H. Experimental study on hydrodynamic characteristics of gas–solid pulsed fluidized bed. Powder Technol. 2013, 237, 14-23. Saidi, M.; Basirat Tabrizi, H.; Chaichi, S.; Dehghani, M. Pulsating flow effect on the segregation of binary particles in a gas-solid fluidized bed. Powder Technol. 2014, 264, 570576. Mothibe, K. J.; Wang, Y. C.; Mujumdar, A. S.; Zhang; M. Microwave-assisted pulse-spouted vacuum drying of apple cube. Drying Technol. 2014, 32, 1762-1768. Lu, Y; Zhang, M.; Sun, J.; Cheng, X.; Adhikari, B. Drying of Burdock root cubes using a microwave-assisted pulsed spouted bed dryer and quality evaluation of the dried cube. Drying Technol. 2014, 32, 1785-1790. Mothibe, K. J.; Zhang, M.; Mujumdar, A. S.; Wang, Y. C.; Cheng, X. Effects of ultrasound and microwave pretreatments of apple before spouted bed drying on rate of dehydration and physical properties. Drying Technol. 2014, 32, 1848-1856. Wang, Y. C.; Zhang, M.; Adhikari, B.; Mujumdar, A. S.; Zhou, B. The application of ultrasound pretreatment and pulse-spouted bed microwave freeze drying to produce desalted duck egg white powders. Drying Technol. 2013, 31, 1826-1836. Wang, X. S.; Rhodes, M. J. Pulsed fluidization-a DEM study of a fascinating phenomenon. Powder Technol. 2005, 159, 142-149. Wang, X. S.; Rhodes, M. J. Using pulsed flow to overcome defluidization. Chem. Eng. Sci. 2005, 60, 5177-5181. Gui, N.; Fan, J. R. Numerical simulation of pulsed fluidized bed with immersed tubes using DEM–LES coupling method. Chem. Eng. Sci. 2009, 64, 2590-2598. Berrouk, A. S.; Wu, C. L. Large eddy simulation of dense two-phase flows: comment on DEM-LES study of 3-D bubbling fluidized bed with immersed tubes. Chem. Eng. Sci. 2010, 65, 1902-1903. Gui, N.; Fan, J. R.; Luo, K. DEM-LES study of 3-D bubbling fluidized bed with immersed tubes. Chem. Eng. Sci. 2008, 63, 3654-3663. Li, Z.; Su, W.; Wu, Z.; Wang R.; Mujumdar, A. S. Investigation of Flow Behaviors and Bubble Characteristics of a Pulse Fluidized Bed via CFD Modeling. Drying Technol. 2009, 28, 78-93. 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, 3425-3442. 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. Zhao, X. L.; Li, S. Q.; Liu, G. Q.; Yao, Q.; Marshall, J. S. DEM simulation of the particle dynamics in two-dimensional spouted beds. Powder Technol. 2008, 184, 205-213.

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25. Almohammed, N.; Alobaid, F.; Breuer, M.; Epple, B. A comparative study on the influence of the gas flow rate on the hydrodynamics of a gas-solid spouted fluidized bed using EulerEuler and Euler-Lagrange/DEM models. Powder Technol. 2014, 264, 343-364. 26. Yang, S.; Luo, K.; Zhang, K.; Qiu, K.; Fan, J. Numerical study of a lab-scale double slotrectangular spouted bed with the parallel CFD-DEM coupling approach, Powder Technol. 2015, 272, 85-99. 27. Salikov, V.; Antonyuk, S.; Heinrich, S.; Sutkar, V. S.; Deen, N. G.; Kuipers, J. A. M. Characterization and CFD-DEM modelling of a prismatic spouted bed. Powder Technol. 2015, 270, 622-636. 28. Rahimi, M. R.; Azizi, N.; Hosseini, S. H.; Ahmadi, G. CFD simulation of cylindrical spouted beds by the kinetic theory of granular flow. Powder Technol. 2013, 246, 303-316. 29. Hosseini, S. H.; Ahmadi, G.; Olazar, M. CFD study of particle velocity profiles inside a draft tube in a cylindrical spouted bed with conical base, J. Taiwan Inst. Chem. Eng. 2014, 45, 2140-2149. 30. Hosseini, S. H.; Fattahi, M.; Ahmadi, G. Hydrodynamics studies of a pseudo 2D rectangular spouted bed by CFD. Powder Technol. 2015, 279, 301-309. 31. Saidi, M.; Basirat Tabrizi, H.; Grace, J. R.; Lim, C. J. Hydrodynamic investigation of gas-solid flow in rectangular spout-fluid bed using CFD-DEM modeling. Powder Technol. 2015, DOI: 10.1016/j.powtec.2015.07.005. Published Online: July 09, 2015. 32. Ergun, S. Fluid flow through packed column. Chem. Eng. Prog. 1952, 48, 89-94. 33. Wen, C. Y.; Yu, Y. H. Mechanics of fluidization. Chem. Eng. Prog. 1966, 62, 100-111. 34. Gidaspow, D. Multiphase flow and fluidization. Academic Press: San Diego, USA, 1994. 35. Tsuji, Y.; Kawaguchi, T.; Tanaka, T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technol. 1993, 77, 79-87. 36. Tsuji, Y.; Tanaka, T.; Ishida, T. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 1992, 71, 239-250. 37. Van der Hoef, M. A.; Ye, M.; Annaland, M. V. S.; Andrews IV, A. T. Sundaresan, S.; Kuipers, J. A. M. Multi-scale modeling of gas-fluidized beds. Adv. Chem. Eng. 2006, 31, 65-149. 38. Deen, N. G.; Van Sint Annaland, M.; Van der Hoef, M. A.; Kuipers, J. A. M. Review of discrete particle modeling of fluidized beds. 2007, Chem. Eng. Sci. 2007, 62, 28-44.

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List of Tables Table 1 Properties of particle and gas phases

List of Figures Fig. 1

Particle circulation pattern in a spouted bed.

Fig. 2

Geometry and generated mesh for slot-rectangular spouted bed.

Fig. 3

Schematic of square-wave flow pulsation at spouting inlet.

Fig. 4

Horizontal time-averaged lateral profile of particle flux at z=0.13 m in a spout-fluid bed for us=30 m/s and uf=1.5 m/s.

Fig. 5

Time series of total pressure drop and amplitude of Fourier decomposition in steady and pulsed flow with Ua= 0.5 m/s.

Fig. 6

Time series of total pressure drop and amplitude of Fourier decomposition in steady and pulsed flow with Ua= 1 m/s.

Fig. 7

Time-averaged air velocity vectors for a) steady, b) Ua= 0.5 m/s, f = 4 Hz; c) Ua= 1 m/s, f = 10 Hz; d) Ua= 1 m/s, f = 4 Hz.

Fig. 8

Time-averaged contours of vertical particle flux in steady and pulsed flow with f = 4 Hz.

Fig. 9

Time-averaged contours of vertical particle flux: a) Ua= 0.5 m/s, f = 1 Hz; b) Ua= 0.5 m/s, f = 10 Hz; c) Ua= 1 m/s, f = 1 Hz; d) Ua= 1 m/s, f = 10 Hz.

Fig. 10

Number distribution of particles passing through computational cells for different time intervals from 1 s to 9 s for a) steady spouting and b) pulsed spouting with Ua= 1 m/s, f = 10 Hz.

Fig. 11

Number distribution of particles passing through computational cells for steady and pulsed spouting: a) Ua=0.5 m/s, b) Ua=1 m/s.

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Table 1. Properties of particle and gas phases Particle phase 3

Density (ρp) Diameter (dp) Number of particles (Np) Young's modulus (E) Poisson's ratio (ν) Restitution coefficient (e) Friction coefficient (λ)

2526 kg/m 2.5 mm 24,500 10e8 N/m2 0.35 0.97 0.1

Gas phase Density (ρg) Viscosity (µg) Superficial spouting velocity (Us)

1.2 kg/m3 1.88e-5 kg/m-s Mean: Um= 2 m/s Amplitude: Ua = 0, 0.5, 1 m/s Frequency: f= 1, 4, 10 Hz Variation: Square wave

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Fig. 1 Particle circulation pattern in a spouted bed.

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Fig. 2 Geometry and generated mesh for slot-rectangular spouted bed.

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Fig. 3 Schematic of square-wave flow pulsation at spouting inlet.

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Fig. 4 Horizontal time-averaged lateral profile of particle flux at z=0.13 m in a spout-fluid bed for us=30 m/s and uf=1.5 m/s.

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(a)

(b)

(c)

(d)

Fig. 5 Time series of total pressure drop and amplitude of Fourier decomposition in steady and pulsed flow with Ua= 0.5 m/s.

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(a)

(b)

(c)

(d)

Fig. 6 Time series of total pressure drop and amplitude of Fourier decomposition in steady and pulsed flow with Ua= 1 m/s.

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(a)

(b)

(c)

(d)

Fig. 7 Time-averaged air velocity vectors for a) steady, b) Ua= 0.5 m/s, f = 4 Hz; c) Ua= 1 m/s, f = 10 Hz; d) Ua= 1 m/s, f = 4 Hz.

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(a)

(b)

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(c)

Fig. 8 Time-averaged contours of vertical particle flux in steady and pulsed flow with f = 4 Hz.

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(a)

(b)

(c)

(d)

Fig. 9 Time-averaged contours of vertical particle flux: a) Ua= 0.5 m/s, f = 1 Hz; b) Ua= 0.5 m/s, f = 10 Hz; c) Ua= 1 m/s, f = 1 Hz; d) Ua= 1 m/s, f = 10 Hz.

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(a)

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(b)

Fig. 10 Number distribution of particles passing through computational cells for different time intervals from 1 s to 9 s for a) steady spouting and b) pulsed spouting with Ua= 1 m/s, f = 10 Hz.

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(a)

(b)

Fig. 11 Number distribution of particles passing through computational cells for steady and pulsed spouting: a) Ua=0.5 m/s, b) Ua=1 m/s.

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