Computational Fluid DynamicsâDiscrete Element Method

Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)

Article

CFD-DEM Investigation of Pressure Signals and Solid Back-mixing in a Full-loop Circulating Fluidized Bed Kun Luo, Shuai Wang, Shiliang Yang, Chenshu Hu, and Jianren Fan Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b04047 • Publication Date (Web): 05 Jan 2017 Downloaded from http://pubs.acs.org on January 5, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Industrial & Engineering Chemistry Research is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

CFD-DEM Investigation of Pressure Signals and Solid Back-mixing in a Full-loop Circulating Fluidized Bed By

Kun Luo, Shuai Wang, Shiliang Yang, Chenshu Hu, Jianren Fan* State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, P. R. China

*

Author for correspondence. Fax: +86-0571-87991863; E-mail: [email protected]

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Computational Fluid Dynamics combined with Discrete Element Method (CFD-DEM) is employed to investigate the pressure signals and solid back-mixing behavior in a three-dimensional full-loop circulating fluidized bed operating in fast fluidization (FF) and dilute phase transport (DPT) regimes. The minimum fluidization velocity is successfully predicted after model validation. The gas-solid full-loop hydrodynamics is accurately captured. Pressure signals under different fluidization regimes shed light on the flow dynamics. The wider solid RTD curve with a longer tail in FF regime indicates that solid flow closes to perfect mixing flow, and more severe solid back-mixing is due to solid internal circulation existing in the riser. The smaller solid RTD curve with a short tail in DPT regime suggests that the solid flow deviates a little from plug flow, and a small-scale solid back-mixing is due to geometry restraint and recirculating gas-solid flow occurring in the lower and upper regions of the riser. Keywords: Circulating fluidized bed; CFD-DEM; full-loop hydrodynamics; pressure signals; solid back-mixing.


Page 2 of 46

Page 3 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. Introduction Because of large capacity, fast reaction rate, excellent heat and mass transfer efficiency1, 2, circulating fluidized bed (CFB) has been widely used in petroleum, chemical, pharmaceutical, metallurgy, energy and environmental engineering fields, such

as coal combustion,

gasification,

catalytic

cracking,

pyrolysis,

and

Fischer-Tropsch synthesis3-7. Based on the widespread engineering applications, in-depth investigations of gas-solid hydrodynamics in CFBs are remarkably helpful for the design, optimization, and operation of the system. Recently, plenty of experimental and numerical investigations have been conducted and lots of information related to the gas-solid hydrodynamics in CFBs have been obtained, such as core-annulus structure8, cluster characteristics9, velocity field10, and effects of internal apparatuses11. Compared with these extensive gas-solid hydrodynamics, the pressure signals and solid back-mixing behavior in the full-loop CFBs have received little attention. Moreover, comprehensive understanding of pressure signals and solid back-mixing behavior plays an important role in determination the conversion and selectivity of chemical reactions12, 13. The pressure signals in CFBs can be used to reflect the particle loading quantity in the system12, 14 and characterize the flow dynamics15, 16. Fluctuations in the pressure signals can be used to identify fluidization regimes16, predict averaged bubble sizes17 and indicate heterogeneity18. Besides, the standard deviation of pressure signals can be used to identify the ideal fluidization velocity19. Thus, the pressure signals will



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 46

shed light on the gas-solid hydrodynamics in the CFB. In addition to the pressure signals, the solid back-mixing behavior in the CFB riser is usually characterized by solid residence time distribution (RTD) 20. In general, the macroscopic flow structure usually exhibits heterogeneous distributions in both axial and radial directions21 of the CFB riser. Take the fast fluidization (FF) regime for example, the axial void fraction profile commonly shows the “S” shape while the radial profile usually exhibits the core-annulus structure in the CFB riser22,

23

,

moreover, plenty of experimental studies have demonstrated that a lot of clusters exist in the bottom dense region and the near wall region24, 25. It can be assumed that these typical structures have a significant influence on the solid RTD in the CFB riser. As we all know, the alternation of operating conditions is of critical importance to the design and operation of CFBs26. The FF regime and the dilute phase transport (DPT) regime are two main fluidization regimes corresponding to the different superficial gas velocities. However, to the author’s knowledge, there have been few studies so far investigating the solid RTD (or solid back-mixing behavior) in the DPT regime. Thus it is necessary to reveal the solid RTD across the wide range of fluidization regimes (i.e., FF and DPT regimes). Although the solid RTD can provide meaningful information, the complex flow behavior in the CFB and the complicated geometry of the CFB make the measurements and modeling of solid RTD extremely hard. Traditionally, the impulse stimulus response technique is usually adopted to obtain the solid RTD in the CFB riser20, 27. On the other hand, a series of empirical models in this area have been developed, one- and two dimensional diffusional model, the stochastic


Page 5 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


model and the core-annulus tracer balance model28. However, the majority of these models are based on simplification or depend heavily on lots of semi-empirical correlations, thus they are physically unrealistic. With the development of numerical algorithms and the increase of computational capacities, computational fluid dynamics (CFD) has become a powerful tool to investigate gas-solid hydrodynamics in the CFB. Two categories of numerical approaches,

namely,

the

Eulerian-Eulerian

(E-E)

approach

and

the

Eulerian-Lagrangian (E-L) approach29 are widely employed. E-E approach regards the gas and solid phases as two interpenetrating continuum media, and Two-fluid Model (TFM) is the typical one of this approach. Hua et al.30 simulated solid RTD in a CFB riser by using TFM with species transport equations considered. E-L approach with each particle tracked individually is another effective method. The Multi-phase Particle-in-cell (MP-PIC) method and the Computational Fluid Dynamics combined with Discrete Element Method (CFD-DEM) are two typical approaches under E-L framework. Specifically, Alobaid et al.31, 32 reviewed the numerical models (i.e., TFM, MP-PIC and CFD-DEM) for dense gas-sold flow in detail and proposed an offset-method for E-L approach with an improvement in the calculation accuracy. As we know, particles are modeled as Lagrangian computational parcels in MP-PIC method, which makes lower computational costs33, 34. Lan et al.35 studied solid RTD in a CFB riser by employing the MP-PIC method. However, this method has disadvantages on the numerical-parcel assumption and the treatment of solid collisions. Thus, the CFD-DEM coupling approach, in which the gas phase is solved



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 46

at computational grid level under Eulerian framework and particles are tracked individually under Lagrangian framework, is the most appropriate method to investigate solid RTD in the CFB. Via the CFD-DEM coupling approach, the trajectory of each particle is monitored at every instant and the solid RDT could be calculated accurately after accounting particles in the whole CFB riser. Most current simulations of CFBs have focused on single key components and even

employing

two-dimensional

simplifications36-38,

which

have

provided

meaningful information and reference value for the further three-dimensional (3-D) full-loop simulations39-41. However, such 3-D simulations show great advantages on better understanding of the entire CFB system. Since the less simplification and assumptions are used, the more detailed information and more accurate understanding of gas-solid hydrodynamics are reached42, 43. Chu et al.44 firstly applied CFD-DEM coupling approach to the investigation of the gas-solid flow dynamics and particle-particle or particle-wall collision features in a full-loop CFB, but only the qualitative descriptions for gas-solid phases were obtained. Moreover, after that, little work focused on the gas-solid flow dynamics in the 3-D full-loop CFB across a wide range of fluidization regimes by using the CFD-DEM coupling approach. Thus, the current work numerically investigates these two key issues in a full-loop CFB apparatus with the CFD-DEM coupling approach. The novelty of this work includes first the fact that the turbulence of gas phase is solved by Large-eddy Simulation (LES), which can improve the simulation accuracy according to our previous work45. Secondly, there has been little work obtaining gas-solid full-loop


Page 7 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


hydrodynamics in a three-dimensional circulating fluidized bed by using CFD-DEM coupling approach. The challenges lie in the complex geometry of the CFB, the computational capacity of the simulation, and the numerical algorithm of the parallelization strategy. Finally, to the author’s knowledge, the pressure signals and solid back-mixing behavior across a wide range of fluidization regimes have been seldom investigated by using this method. Instead of the conventional single-side refeed structure, the dual-side refeed structure (i.e., two sets of recirculation systems are arranged symmetrically) is employed. However, the effect of this structure on the CFB performance (i.e., improvements of flow uniformity) is beyond the scope of the present work. The current work is structured in the following manner. Firstly, the proposed model is validated with the experimental work46 and then used to predict the minimum fluidization velocity. For the proposed model, the gas motion is resolved at the computational grid level under the Eulerian framework, while the solid motion is tracked at the particle scale level under the Lagrangian framework. Subsequently, with the proposed model, the gas-solid full-loop hydrodynamics in the three-dimensional circulating fluidized bed is obtained. After deeply investigating pressure signals, finally, the mechanism of solid back-mixing behavior under different operating conditions is revealed.

2. Mathematical Model 2.1 Governing equations for gas motion In the current work, the gas phase is regarded as a continuous medium whose



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 46

motion is solved under the Eulerian framework. Moreover, the gas motion is governed by the Navier-Stokes equations with taking the presence of solid phase into account. Turbulence is modeled with a Large-eddy Simulation (LES) approach, where the flow variables are decomposed into a resolved component and an unresolved sub-grid component. The mass and momentum equations for gas motion are formulated as

∂(ρ fε f ) ∂t

+

∂ ( ρ f ε f u% f ,i ) ∂t

∂ ( ρ f ε f u% f ,i ) ∂xi +

=0

∂ ( ρ f ε f u% f ,i u% f ,i ) ∂x j

(1)

= −ε f

∂p% f ∂xi

∑ −

n i =1

fd ,i

∆V

+ ρfεf g +

(

∂ ε f (τ% f ,ij + τ% SGS f ,ij ) ∂x j

)

(2)

where ρ f , u% f ,i and p% f stand for the density, the velocity and the pressure of gas phase, respectively. g and t are the gravitational acceleration and the time instant, respectively.

τ% f ,ij is the filtered viscous stress tensor, which is evaluated as  ∂u% f ,i

τ% f ,ij = µ f  

 ∂x j

+

∂u% f , j  2 ∂u% f ,k δ ij  − µf ∂xi  3 ∂xk

(3)

where µ f stands for the fluid viscosity coefficient and δ ij represents the Kronecker function. is the sub-grid stress tensor, which is modeled with Smagorinsky model47. τ% fSGS ,ij It can be written as

1   % % τ% fSGS ,ij = ρ f  2ν f ,t S f ,ij + τ f ,kkδ ij  

3



(4)

∂u% 1 ∂u% where S% f ,ij ( = ( f ,i + f , j )) is the deformation tensor of the filtered field. ν f ,t 2 ∂x j ∂xi stands for the eddy viscosity coefficient, which is evaluated as


Page 9 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ν f ,t = ( Cs ∆ ) ( 2 S% f ,ij S% f ,ij )

1/2

2

(5)

where Cs is the Smagorinsky constant coefficient and can be calculated with the correlation proposed by Lilly48. The wall function49 is adopted to resolve the gas motion in the near wall region.

ε f and fd ,i are the void fraction and the drag force exerting on particle i, and they can be formulated as

εf

∑ =1−

fd ,i =

n i =1

Vi ,t

(6)

∆V

Vi β f ↔s (1 − ε f )

(u

f

− vi )

(7)

where n donates the total number of particles in the current computational cell, and ∆V represents the volume of current cell. Vi ,t and vi are the volume in the current

cell and the velocity vector of particle i, respectively. β f ↔ s is the interphase momentum exchange coefficient, and can be calculated with the correlation proposed by Gidaspow50. It is expressed as

β g ↔s

ρ f ε f (1 − ε f ) | u f − vi | −2.65 3 εf  4 CD d p ,i  = 2 150(1 − ε f ) µ f + 1.75ρ f (1 − ε f ) | u f − vi |  ε f d p2 ,i d p ,i 

ε f ≥ 0.8 (8)

ε f < 0.8

 24 0.687  Re (1 + 0.15 Re p ,i ) Re p ,i < 1000 CD =  p ,i 0.44 Re p ,i ≥ 1000  Re p ,i =

ρ f ε f u f − vi d p ,i µf

where dp,i represents the diameter of particle i.

2.2 Governing equations for solid motion


(9)

(10)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 46

In the current work, the solid motion is solved under the Lagrangian framework, and each particle is tracked individually by using the DEM. For the solid motion in the circulating fluidized bed, the forces exerting on particle i consist of the gravitational force (g), the drag force (fd,i), the pressure gradient force (fp,i) and the collision force (Fc,ij). The solid motion is governed by Newton’s law of motion, and the equations can be formulated as

mi

k dvi = mi g + fd ,i + f p ,i − ∑ j =1 Fc ,ij dt

(11)

d ωi = Ti dt

(12)

f p ,i = −Vi ∇p f

(13)

Ii

where mi , I i , ωi and Ti stand for the mass, the moment of inertia, the rotational velocity and the torque of particle i, respectively. k is the total number of particles and wall colliding with the particle i. In the dense gas-solid two-phase flow, the macroscopic gas-solid hydrodynamics is dominated by not only interphase interactions but also particle-particle or particle-wall collisions. Moreover, the collision prediction is the key to successfully modeling the hydrodynamics of the dense gas-solid two-phase flow. In the current work, the colliding procedure is described by using the soft-sphere contacting model originally proposed by Cundall and Stack51. For a colliding pair of particle i and particle j, the collision force Fc,ij can be divided into components along the normal (Fcn,ij) and the tangential (Fct,ij) directions of this colliding pair, respectively. Particularly, the tangential component is limited by the Coulomb’s friction law when


Page 11 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


sliding between particles occurs. Details of the equations are as follow

Fc ,ij = Fcn ,ij + Fct ,ij

(14)

Fcn ,ij = kn ,ijδ n ,ij n + γ n ,ij vn ,ij

(15)

Fct ,ij = min{( kt ,ijδ t ,ij t + γ t ,ij vt ,ij ), µ p Fcn ,ij }

(16)

where n and t represent the variable components along the normal and tangential directions, respectively. n and t stand for the normal and tangential unit vectors in the colliding pair, respectively. δ n,ij and δ t ,ij are the relative displacements in the normal and tangential directions, respectively. vn,ij and vt,ij are the normal and tangential components of the relative velocity in the colliding pair, respectively. µ p is the friction coefficient of solid phase. The coefficients k and γ representing the stiff coefficient and the damping coefficient respectively can be calculated from the material properties (e.g., Young’s modulus, Poisson ratio, and restitution coefficient) according to the literature52, 53. The calculation procedure is summarized in Table 1. Table 1. The stiffness and damping coefficients in the soft-sphere contacting model normal stiffness coefficient kn,ij and tangential stiffness coefficient kt,ij

4 kn,ij = Y * R*δ n,ij , kt ,ij = 8G* R*δ n,ij 3 normal damping coefficient γn,ij and tangential damping coefficient γt,ij γ n ,ij = 2

5 5 β S n ,ij m * , γ t ,ij = 2 β St ,ij m* 6 6

where the variables marked with * stand for an averaged value, and they are calculated as:

1 Y * = (1 −ν i2 ) Yi + (1 −ν 2j ) Y j , 1 R* = 1 Ri + 1 Rj , 1 m* = 1 mi + 1 m j

β = ln(e)

ln2 (e) + π 2 , 1 G* = 2 ( 2 +νi )(1 −νi ) Yi − 2 ( 2 +ν j )(1 −ν j ) Yj

Sn,ij = 2Y * R*δ n,ij , St ,ij = 8G* R*δn,ij



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2.3 Numerical scheme The governing equations for gas motion are discretized by finite volume method based on collocated grids and transformed to linear algebraic equations. The time integration is evaluated by using Crank-Nicholson scheme54. For the convective term, a second-order Central Differencing Scheme (CDS) is used for momentum. For the diffusion term, the CDS is used. Pressure Implicit with Splitting of Operator (PISO) algorithm55 is applied for treating the velocity and the pressure. The governing equations for solid phase are integrated explicitly to obtain the particle positions, velocities in the new time step. The coupling between the CFD solver and the DEM solver is fulfilled through the void fraction and momentum source terms. At each time step, the computational cell of the particle locating is acquired via its position. Then, the void fraction of the computational cell and the forces acted by the gas phase on the particle are calculated. Based on the evaluated void fraction and the momentum source term, the governing equations for gas motion are solved. In the meanwhile, the forces acting on particles are transferred to the DEM solver. After that the collision detection is applied to the calculation of the collision forces in the colliding particle-particle or particle-wall pairs. Thus the governing equations for solid motion are solved, finally, the position and velocity of each particle are updated for the next calculation time step.

2.4 Model validation The proposed model in the current work has been validated with the experimental work conducted by Müller et al.56,

57

in our previous work58. The


Page 12 of 46

Page 13 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


simulated results shown good agreements with the experimental data at two different heights of the bubbling fluidized bed. Moreover, we also applied this model in dense particulate systems, such as internal circulating fluidized bed59 and spout fluidized bed60, and good results were achieved. However, due to the complex geometry of the circulating fluidized bed and the intensely turbulent flow in it, the proposed model is also validated with the experimental work carried out by Ibsen et al.46 in the current work. The test rig is a lab-scale circulating fluidized bed riser with the quasi-3D geometry. The simulation is conducted with the same width, height and two depths (four times (4dp) and eight times (8dp) of the particle diameter). A full three-dimensional simulation is time-consuming with the particle diameter of 0.164 mm, which needs a huge computational capacity. Thus we adopt two depths, aiming to investigate the influence of bed depth on the gas-solid fluid dynamics. The gas-solid parameters adopted in the current validation are summarized in Table 2. The time steps chosen for the gas and solid phases are 2.5 × 10-6 s and 2.5 × 10-7 s, respectively. Total 20 s are performed, and the statistical procedure is carried out over the last 15 s of the total calculation time. Table 2. Gas-solid parameters adopted in the current validation Simulation domain Width (W) × Depth (D) × Height (H), mm

32 × 0.656 (4dp) and 1.312 (8dp) × 1,000

Grid cells, x-y-z

64 × 1 (4dp) and 2 (8dp) × 2,000

Gas properties Density, kg/m3

1.2

Temperature, K

298

Viscosity, kg/m·s

1.8 × 10-5

Velocity, m/s

1.0

Time step, s

2.5 × 10-6



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Solid properties Number Density, kg/m3

162,000 (4dp), 324,000 (8dp) 2,400

Restitution

0.97

coefficient Diameter, mm

0.164

Friction coefficient

0.1

Young’ modulus, Pa

1.0 × 108

Poisson ratio

0.33

Time step, s

2.5 × 10-7

As illustrated in Figure 1, the numerical results with eight times of particle diameter (8dp) agree better than that with four times of particle diameter (4dp), indicating that the three-dimensional simulation of the circulating fluidized bed has advantages over the two-dimensional simulation. The center regions of the bed with the solid upward motion and the near wall regions of the bed with the solid downward motion show the typical core-annulus structure in the circulating fluidized bed riser. In general, the numerical results show agreements with the experimental data in some extent. The deviations are attributed to the small depth adopted in the current validation. Although the validation in the current work mainly focuses on the fast fluidization regime, the CFD-DEM coupling approach is also reasonable for the dilute phase transport study according to the literature61,

62

. Thus, from qualitative to

quantitative, we conclude that the proposed model is appropriate and reasonable to investigate gas-solid flow dynamics in the three-dimensional circulating fluidized beds under different operating conditions.


Page 14 of 46

Page 15 of 46

1.50

(a)

Exp. (Ibsen et al., 2004) Sim. Bed_thickness_4d Sim. Bed_thickness_8d

1.25 1.00 0.75 0.50 0.25 0.00

1.25

Exp. (Ibsen et al., 2004) Sim. Bed_thickness_4d Sim. Bed_thickness_8d

(b)

1.00 0.75 0.50 0.25 0.00 -0.25

-0.25 -0.50 -0.50

Solid axial velocity(m/s)

1.50

Solid axial velocity(m/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-0.25

0.00

0.25

0.50

-0.50 -0.50

-0.25

0.00

0.25

0.50

y/R (-)

y/R (-)

(a)

(b)

Figure 1. Comparison of the time-averaged solid axial velocity at different heights of the bed. (a) H = 0.2 m; (b) H = 0.4 m.

3. Computational Details 3.1 Geometry and mesh According to the experiments and simulations of full-loop CFBs39-43,

63-67

, a

pilot-scale or industry-scale CFB usually consists of a riser, a cyclone, a standpipe and a loop-seal. Generally speaking, ten meters of dimensions of these apparatuses and millions of or even billions of particles in these systems are beyond the computational capacity of the CFD-DEM coupling approach. Thus, it is necessary to scale down these apparatuses in CFD-DEM simulations. Specifically, for simplifying the geometry of the CFB, according to the Grace et al.68, we choose the L-valve type of loop-seal, and this type is also widely employed in the experimental and numerical work14, 20.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a)

(b)

(c)

Figure 2. Geometry and computational grids of the investigated CFB (sample surface is used to obtain time evolutionary solid flux in the two L-valves). (a) Front view of the geometry; (b) sample surface in the geometry; (c) computational grids.

The geometry of the investigated object in the current work is similar to the CFB used in the literature14,

20

, but the dual-side refeed structure (i.e., two sets of

recirculation systems are arranged symmetrically) is adopted due to its improvements of gas-solid flow uniformity (i.e., homogeneous) in the riser, which is discussed in our another work. The geometry shown in Figure 2(a, b) has been scaled down to meet the numerical limitations of CFD-DEM coupling approach. The system consists of a 0.065 m diameter, 1.2 m tall riser and the associated cyclones, standpipes, L-valves. Particles enter the riser from two symmetrically rectangle side ports 0.017 m in edge length and 0.029 m above the gas distributor (from the center line of L-valve). Particles exit the riser through two symmetrically rectangle side ports 0.06 m in height, 0.022 m in width about 1.17 m above the gas distributor. Particles exiting the riser are transported via the top cross over and then captured by the cyclones and transported


Page 16 of 46

Page 17 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


downward through the standpipes 0.02 m in diameter and finally returned to the riser through the L-valves. The computational grids are illustrated in Figure 2(c), and a total number of 150,028 hexahedron elements are generated by the commercial software Gambit 2.4.6. Moreover, the independence studies of grid resolution are carried out in our previous work39.

3.2 Simulation settings A total number of 300,000 particles categorized as Geldart Group D with a diameter of 1.6 mm and a density of 1,500 kg/m3 are tracked in the system. Detailed information of the physical and numerical parameters adopted in the current simulation are summarized in Table 3. Different boundary conditions are applied to the boundaries of the bed. The velocity inlet boundary condition is applied for the bed inlet and aeration inlet, while the no-slip and outlet boundary conditions are applied for the walls and top boundaries, respectively, of the bed. Moreover, for the pressure boundary condition, the fixed value of ambient atmosphere is assigned to the outlet of the cyclone whilst Neumann boundary condition is used for all the other boundaries of the system.

Table 3. Simulation settings in this study Gas properties Gas density (ρf) [kg/m3]

1.225

Gas viscosity (µf) [kg/(m·s)]

1.8 × 10-5

Superficial gas velocity (Uf) [m/s]

5.5, 6.0*, 6.5*, 7.0*, 7.5*, 8.0*

Revert aeration (Ur)[m/s]

0.5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Outlet pressure (Pf)[Pa]

1.01 × 105

Total grid number (Nf) [-]

150,028

Gas motion time step (s)

1.0 × 10-5

Solid properties Total particle number (Np) [-]

300,000

Particle density (ρp) [kg/m3]

1,500

Particle diameter (dp) [mm]

1.6

Young’s modulus (Y) [Pa]

5.0 × 107

Poisson ratio (ν) [-]

0.33

Restitution coefficient (e) [-]

0.90

Friction coefficient (µp) [-]

0.10

Solid motion time step (s)

1.0 × 10-6

Note: data with superscript * represent simulation parameters for comparisons

Due to the restriction of the soft-sphere contacting model employed in the current simulation on the time step for resolving the solid motion, different time steps of 1×10−5 s and 1×10−6 s are respectively used for solving gas and solid motions. Before calculation, 300,000 particles are randomly generated in the riser and standpipes. Under the influence of gravity, particles fall freely and finally pack in the bottom region of the bed. After the kinematic energy in the whole system dissipates to zero, the fluidized gas and revert aeration with values of 5.5 m/s and 0.5 m/s respectively are introduced into the system. The total calculation time for each case is 40 s.

4. Results and Discussion


Page 18 of 46

Page 19 of 46

4.1 Minimum fluidization velocity (Umf) prediction The minimum fluidization velocity (Umf) of the specific particles used in the current work is predicted by the model. Three-dimensional simulations are conducted in a domain of 0.056 m × 0.056 m × 0.5 m with gradually increasing and decreasing the superficial gas velocity, and the pressure drop across the bed is recorded against the superficial gas velocity. It can be seen that the pressure drop increases with increasing the superficial gas velocity. When the superficial gas velocity reaches a certain critical value, the pressure drop reaches its maximum, while upon further increasing the superficial gas velocity, the pressure drop firstly decreases slightly, and finally attains a constant value. The minimum fluidization velocity can be estimated via observation of the regime change point. As illustrated in Figure 3, the minimum fluidization velocity predicted from the simulation is 0.625 m/s, which agrees well with the calculated Umf of 0.63 m/s from the Wen-Yu correlation. 1000 Increasing Uf

Bed pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Regime change

Decreasing Uf

800

600

400

200

Predicted Umf = 0.625 m/s 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Uf (m/s) Figure 3. Pressure drop profiles used for predicting the minimum fluidization velocity (Umf).

4.2 Solid flux The time evolutionary solid flux of recirculation system is an important variable.



In the current work, the solid flux is sampled from two surfaces (as shown in Figure 2) located in the recirculation system (i.e., L-valve). As illustrated in Figure 4, the solid flux reaches a maximum value, subsequently, decreases and oscillates around a steady value. It is demonstrated that the system is in start-up process from 0 to 5.0 s, and reaches a macroscopic steady state after about 5.0 s. When the flow reaches a statistical steady state, simulation results are saved every 0.05 s for post-processing considering the computational cost. For more accurate analysis, the time-averaged results are obtained by averaging the transient data from 10.0 s to 40.0 s. It is noted that the profiles of solid flux in two surfaces are similar and both osculate throughout the duration of the test, which indicates that the dual recirculation system is configured properly and working well, in addition, reflects the heterogeneous nature of gas-solid two phase flow. 160

Sample surface 1 Sample surface 2

Uf = 5.5 m/s

140

Solid flux (kg⋅m-2⋅s-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 46

120

Start-up process

100 80 60 40 20 0

Steady state

-20 0

5

10

15

20

25

30

35

40

Time (s) Figure 4. Time evolutionary solid flux sampled from two surfaces in the recirculation system, Uf = 5.5 m/s.

4.3 General gas-solid hydrodynamics An in-depth understanding of the gas-solid hydrodynamics in circulating


Page 21 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


fluidized beds can shed light on material mixing, chemical reaction and production formation in the system. However, the gas-solid full-loop hydrodynamics is hardly obtained by experiments due to the difficulty in measurements. Taking the advantages of the CFD-DEM coupling approach, the gas-solid hydrodynamics across the full loop is obtained in the current work.

(a)

(b)

(c)

Figure 5. Contour plots of the time-averaged gas velocities, Uf = 5.5 m/s. (a) X-component; (b) Y-component; (c) Z-component.

Figure 5 presents the contour plots of the time-averaged gas velocities under Uf = 5.5 m/s in the CFB. It is noted that the gas flow crosses and evolves in the radial direction, and the axial velocity is one order of magnitude larger than the radial one (coordinate system is shown in Figure 2). In the vicinity of the riser bottom, non-uniform distribution of gas velocities can be obtained due to the dual-side



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 46

recirculation solid phase and the intensely gas-solid momentum exchanges69, 70. As the height increases, the non-uniform distribution characteristics diminishes. Interestingly, in the top region of the riser, the gas radial velocities are strengthened, while the gas axial velocity is weakened. The reasons lie in: (i) gas flow changing directions by geometry restraint; (ii) solid back-mixing from the ceiling of the riser. As donated in Figure 5(c), the fishing tail phenomenon in the cyclone is accurately captured, that is, the gas motion in the center region of the cyclone does not coincide with the axis of the geometry of the cyclone, which is consistent with the numerical and experimental results aimed at the cyclone36, 71.

(a)

(b)

(c)

Figure 6. Contour plots of the time-averaged solid velocities, Uf = 5.5 m/s. (a) X-component; (b) Y-component; (c) Z-component.

As illustrated in Figure 6, the contour plots of the time-averaged solid velocities


Page 23 of 46

looks similar to that of gas phase, due to the intensive interactions between the two phases. Results show: (i) the solid radial motion is more chaotic than the gas radial motion; (ii) the solid radial velocities with positive and negative values coexist in the same height of the riser. It indicates that the radial motion of solid phase mainly from the central region to the near wall region of the riser, forming the solid internal circulations, which is consistent with the model and experiments27, 72. Considering the gas-solid intensive interaction, the gas-solid velocities show fluctuations in the radial direction while smooth in the axial direction. Besides, the solid radial velocities inside the CFB are smaller than their counterparts of the gas flow, while they are about one order of magnitude smaller than the solid axial velocity.

8

0.5

7

Y-line 6

0.4

5

0.3 0.2

4

X-line 3

0.1

2

0.0

0 -1.0

Gas axial velocity X-line Y-line -0.8

-0.6

-0.4

-0.2

Solid axial velocity X-line Y-line

0.0

0.2

0.4

0.6

0.8

0.6 0.5 Y-line

6

0.4

5

0.3 0.2

4

X-line 3

0.1

2

0.0

-0.1

1

-0.2

0 -1.0

1.0

Gas axial velocity X-line Y-line -0.6

-0.4

-0.2

Us_z(m/s)

0.5

7

Y-line 0.4

5

0.3

4

0.2

X-line

0.1

2

0.0

-0.8

-0.6

-0.4

-0.2

0.0

Axial solid velocity X-line Y-line 0.2

0.4

r/R @ H=0.6m (-)

0.6

0.8

1.0

Gas axial velocity (m/s)

8

Solid axial velocity (m/s)

0.6

6

Axial gas velocity X-line Y-line

0.4

0.6

0.8

1.0

Us_z(m/s)

9

0.7

Uf = 5.5 m/s

7

0 -1.0

0.2

(b)

9

1

0.0

r/R @ H=0.4m (-)

(a)

3

-0.1


-0.2 -0.8

r/R @ H=0.2m (-)

8

0.7

Uf = 5.5 m/s

0.7

Uf = 5.5 m/s

0.6 0.5 Y-line

6

0.4 0.3

5

0.2

4

X-line

3

0.1 0.0

2

-0.1

1

-0.2

0 -1.0

Gas axial velocity X-line Y-line

-0.1


-0.2 -0.8

-0.6

-0.4

-0.2

0.0

0.2

r/R @ H=0.8m (-)


0.4

0.6

0.8

1.0


1


7

0.6



8

Us_z(m/s)

9

0.7

Uf = 5.5 m/s


Us_z (m/s)

9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(c)

(d)

Figure 7. Radial profiles of the time-averaged gas-solid axial velocities at different heights of the riser, Uf = 5.5 m/s. (a) 0.2 m; (b) 0.4 m; (c) 0.6 m; (d) 0.8 m.

From qualitative to quantitative, the time-averaged gas-solid axial velocities in the central slices X = 0 and Y = 0 of the riser at different heights are presented in Figure 7. Combined with Figure 5(c) and Figure 6(c), it reflects the typical core-annulus flow structure of fast fluidization regime of the CFB under Uf = 5.5 m/s. The gas-solid velocities both shows an inverted bowl pattern. The velocity difference of gas-solid phases in the radial direction decreases with the increase of riser height. Besides, the solid velocity is large in the center region and small in the near wall region, and it continuously decreases with the riser elevation. Thus, the solid back-mixing phenomenon near the wall is observed at all heights.

4.4 Pressure signals In addition to the macroscopic hydrodynamics of the gas-solid flow, pressure signals consist of the averaged value, the fluctuations and the power spectra, shedding light on the bed hydrodynamics. The strong non-linear correlation of the gas-solid motions in the CFB causes a chaotic system. In such system, the pressure fluctuations are usually transformed by Freitas et al.73 to identify the flow regime and characterize the response of the system to disturbance16, 74-76. The pressure fluctuation in the CFB mainly results from blocking of the outlets, the generation of small bubbles, the coalescence of rising bubbles, the break-up of big bubbles and the intense gas-solid interactions. In the current work, the pressure drop between fluid inlet (also called


Page 24 of 46

Page 25 of 46

riser inlet) and fluid outlet, and between aeration inlet and fluid outlet (as shown in Figure 2) are obtained. Besides, the spectral analyses of the pressure fluctuation are conducted. 105

2000

Fluid inlet Aeration inlet

Uf = 5.5 m/s

1600 1400 1200 1000 800


Uf = 5.5 m/s

104

Power as MSA (Pa2）

Pressure drop (Pa)

1800

103 102 101 100 10-1 10-2 10-3 10-4 10-5

600 10

12

14

16

18

20

0

10

Time (s)

20

(a)

40

50

(b) 104

Fluiid inlet Aeration inlet

Uf = 6.5 m/s

Uf = 6.5 m/s

103


1800

Pressure drop (Pa)

30

Frequency (Hz)

2000

1600 1400 1200 1000 800


102 101 100 10-1 10-2 10-3 10-4

600

10-5

10

12

14

16

18

20

0

10

Time (s)

20

30

40

50

Frequency (Hz)

(c)

(d) 104

2000

Uf = 7.5 m/s


Uf = 7.5 m/s

103


1800

Pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1600 1400 1200 1000 800


2

10

101 100 10-1 10-2 10-3 10-4

600

10-5 10

12

14

16

Time (s)

18

20

0

10

20

30

40

50

Frequency (Hz)

(e)

(f)

Figure 8. Profiles of pressure drop in the system under three operating conditions. (a, b) Uf = 5.5 m/s; (c, d) Uf = 6.5 m/s; (e, f) Uf = 7.5 m/s.

Figure 8 shows the pressure fluctuation and the associated power evolve with the



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

three different superficial gas velocities (i.e., Uf = 5.5, 6.5, 7.5 m/s), and the power is expressed as mean square amplitude (MSA). Generally, Figure 8(a, c, e) shows that both the area-averaged pressure drop of the fluid inlet and the aeration inlet randomly fluctuate with time, and the latter is slightly smaller than former, since the particles are packed in the L-valve (i.e., aeration inlet) and fluidized in the riser (i.e., fluid inlet). Besides, as the Uf increase from 5.5 to 7.5 m/s, both the magnitude and extent of pressure fluctuations decrease, whilst the magnitude of MSA in the power spectra analysis correspondingly decreases. However, focusing on the power spectra analysis, the magnitude of MSA at all operating conditions exhibits decreasing trend with increasing frequency, which is consistent with the numerical and experiment work of the CFB40, 77. The profiles of MSA at Uf = 5.5 and 6.5 m/s show nearly monotonic behavior, while the MSA at Uf = 7.5 m/s exhibits a peak under the frequency of 10 Hz. Via the power spectra analysis, we can roughly determine that the gas-solid flow in the CFB transforms from fast fluidization (FF) regime (Uf < 7.5 m/s) to dilute phase transport (DPT) regime (Uf > 7.5 m/s). However, it is also necessary to use some supplementary means to determine the regime changes in fluidization77. We will give another method in the next section. Furthermore, due to the interaction between the fluid inlet and aeration inlet, the profiles of pressure drop of these two inlets are correlated.


Page 26 of 46

Page 27 of 46

1800

Averaged pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



1600

1400

1200

1000

800

600 5.5

6.0

6.5

7.0

7.5

8.0

Uf (m/s) Figure 9. Profiles of the time-averaged pressure drop at different superficial gas velocity (Uf).

The effects of the superficial gas velocity on the time-averaged value of the pressure drop signals of the fluid inlet and aeration inlet are quantified in Figure 9. The error bar stands for the stand deviation of pressure drop. Both profiles show similar trends, that is, the relationship between the superficial gas velocity and the averaged pressure drop is non-monotonic (i.e., increase at first and then decrease). At smaller Uf, the increase of averaged pressure drop mainly results from the intensive turbulence and gas-solid internal circulation. With the increase of Uf in further, the averaged value and the stand deviation of pressure drop decline for both the fluid inlet and aeration inlet. The reduced stand deviation of the pressure drop indicates that the solid back-mixing or gas-solid internal circulation diminishes, and the flow is more regular.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a)

(b)

Page 28 of 46

(c)

Figure 10. Time-averaged properties in the CFB, Uf = 5.5 m/s. (a) Full-loop distribution of pressure; (b) contour plots of pressure and void fraction; (c) cross-section averaged solid holdup along the height of the riser.

Figure 10 presents some important time-averaged properties related to pressure signals under Uf = 5.5 m/s. The pressure signals in the CFB is close related to the particle loading quantity and the momentum exchange between gas phase and solid phase12,

14

. As illustrated in Figure 10(a, b), it is noted that the pressure is

comparatively large in the bottom regions of the riser and the L-valve, due to high solid load and intense solid mixing in these regions. Along the axial direction of riser, pressure decreases because of the energy exchange from gas phase to solid phase for overcoming gravity. The profile of the full-loop pressure (as shown in Figure 10(a)) agrees with the empirical and numerical knowledge40, 42, 43, 65, 66. Moreover, for each recirculation system, pressure has a sudden alternation in the middle of the standpipe, which can be explained from the contour plot of void fraction. As illustrated in Figure 10 (b), the packed bed with a slowly downward motion forms in the each standpipe, and the interface between gas phase and packed bed cause the sudden alternation of


Page 29 of 46

pressure. Figure 10(c) shows the cross-section averaged solid holdup in the CFB riser. The profile of solid holdup exhibits an exponential distribution along the height and performs the “dilute in the top region and dense at the bottom region” feature. The deviation of the profile in the bottom region is mainly due to the recirculation effect. 0.035

0.01 Exp. (Wang et al., 2013) Current simulation dp*/dH*

0.028

0.00

0.021 -0.01 0.014

dp*/dH* (-)

Uf = 5.5 m/s

p* (-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-0.02

0.007

0.000

-0.03 0.0

0.2

0.4

0.6

0.8

1.0

H* (-) Figure 11. Profiles of dimensionless pressure (compared with the experimental data78) and dimensionless pressure gradient along the height of riser, Uf = 5.5 m/s, p* = p/Pf, H* = H/H0.

Figure 11 presents the profiles of dimensionless pressure and dimensionless pressure gradient in the riser. For comparison, the pressure and the height are simplified into dimensionless forms. It is noted that the profile in the current simulation shows an agreement with the experimental data78, and the pressure decreases with the bed elevation. Particularly, the deviation lies in the different operating conditions and different particle properties used in the experiment and the current simulation. The predicted “Z” shape shows pressure gradient is large both at the bottom and the top in riser, which is attributed to the effects of inlet and outlet arrangements.

4.5 Solid back-mixing ACS Paragon Plus Environment


In addition to the pressure signals, the solid back-mixing is another research focus, and it has significant influences on the performance of CFBs. Quantitatively, the solid back-mixing behavior can be reflected by the solid residence time distribution (RTD). As we all know, the trajectory of each individual particle is accurately described by CFD-DEM coupling approach, thus the residence time of a specific particle can be obtained by tracking its motion in the CFB riser. 0.35

0.35

Uf = 5.5 m/s

Uf = 6.5 m/s

0.30

0.25

0.25

0.20

0.20

E(t)

E(t)

0.30

0.15

0.15 0.10

0.10

0.05

0.05 0.00

0.00 0

5

10

15

20

25

30

35

40

0

5

10

15

20

25

30

35

40

Residence time (s)

Residence time (s)

(a)

(b)

0.35

Uf = 7.5 m/s

0.30 0.25

E(t)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 46

0.20 0.15 0.10 0.05 0.00

0

5

10

15

20

25

30

35

40

Residence time (s)

(c) Figure 12. Influence of superficial gas velocity (Uf) on solid residence time distribution (RTD). (a) Uf = 5.5 m/s; (b) Uf = 6.5 m/s; (c) Uf = 7.5 m/s.

Figure 12 presents the influence of superficial gas velocity (Uf) on solid RTD. In general, the RTD curves in all cases exhibit a feature of early peak with an extended


Page 31 of 46

tail and can be fitted with the lognormal distribution. Besides, it is noted that the Uf has a significant influence on the maximum peak height, spread and general shape of the solid RTD. At the Uf of 5.5 m/s, the RTD curve is broad and skewed heavily to the right with a long tail. In contrary, at the Uf of 7.5 m/s, the RTD curve is narrow and relative un-skewed and with a short tail. These conclusions are consistent with the experimental work conducted by Harris et al.20. As illustrated in Figure 12, the solid RTD is a probability density function, we can characterize it by using statistical moments. In order to completely characterize the distribution, all moments (i.e., the mean residence time, tm, stand deviation, σ, skewness, s3 and coefficient of variation, Cv) are taken into account. The detailed descriptions of these moments can be referred to the literature20.

4 3 2 1 0

Standard deviation, σ (s) Skewness, (s3) Coefficient of variation, Cv

8

0.70 0.65

2.4

6

0.60 0.55

2.0

4

1.6

0.50 0.45 0.40

2 1.2 0

0.35

Coefficient of variation, Cv

5

2.8

Mean residence time, tm (s)

Skewness, (s3)

6

10

Mean residence time, tm (s)

7

Standard deviation, σ (s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.30 5.5

6.0

6.5

7.0

7.5

8.0

Uf (m/s)

Figure 13. Influence of superficial gas velocity (Uf) on all moments of solid residence time distribution (RTD).

Figure 13 presents the influence of superficial gas velocity (Uf) on all moments of solid RTD. As the superficial gas velocity increases, it is observed that the mean solid residence time (tm) and the standard deviation (σ) decrease, besides, the coefficient of deviation (Cv) decreases and then increases, the skewness is relatively unaffected



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

firstly and then increases. The profiles show agreements with the experimental work carried out by Harris et al.20. As we can see, the coefficient of variance and the skewness change their trends when the Uf is greater than 7.5 m/s. As mentioned earlier, the fluidization regime changes from the fast fluidization (FF) regime to the dilute phase transport (DPT) regime, leading to the solid flow changing from perfect mixed flow to plug flow. Figure 14 presents the instantaneous distribution of solid flow under different superficial gas velocities. When the value of Uf is between 5.5 m/s and 7.0 m/s, as mixed flow, particles have upward motion in the central region of the riser, and downward motion near the wall region, which causes solid back-mixing and makes solid residence time large. When the value of Uf is between 7.5 m/s and 8.0 m/s, as plug flow, nearly all particles have upward motion, which makes solid residence time small. Interestingly, the geometry restraint will lead to some extent solid back-mixing in the top region of the riser. Besides, the solid back-mixing occurs in the lower part of the riser.


Page 32 of 46

Page 33 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 14. Influence of superficial gas velocity (Uf) on instantaneous solid flow, colored by solid axial velocity, slice between Y = -0.05 m and Y = 0.05 m.

Figure 15 illustrates the cross-sectional views of solid motion in the riser under different superficial gas velocities. The size of each particle is enlarged 10 times and the amount of particles is reduced for the better visual effect. Combined with the Figure 14, for the value of Uf smaller than 7.5 m/s, the downward particles focus on the near wall region and form internal circulations, consequently resulting in back-mixing behavior. Besides, along the height of the riser, the back-mixing degree decreases in some extent. For the value of Uf larger than 7.5 m/s, just the particles in the top regions and inlet regions flow downward because of geometry restraint and recirculating gas-solid flow.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 15. Influence of superficial gas velocity (Uf) on instantaneous solid flow in different cross-sections, colored by solid axial velocity, depth of each slice is 0.01 m.

Besides the instantaneous solid motion, from qualitative to quantitative, Figure 16 presents the time-averaged properties of gas-solid phases in the riser. As illustrated in Figure 16(a), the gas axial velocity of all cases show an invert bowl pattern, and it indicates that the magnitude of solid axial velocity decrease from the central region to the near wall region due to the no-slip boundary condition. As presented in Figure 16(b), the solid axial velocity shows similar features with the gas axial velocity when the Uf is smaller than 7.0 m/s, and it demonstrates that the solid flow is mixed flow. Interestingly, with the further increase of Uf, the feature of solid axial velocity exhibits the shape of a saddle, which is the typical structure of plug flow. Thus, we conclude that, the solid residence time is large in the fast fluidization (FF) regime with a mixed flow and small in the dilute phase transport (DPT) regime with a plug flow. Figure 16(c) shows the solid holdup under different superficial gas velocity. It clearly shows the typical core-annulus structure in the FF regime and gentle shape in the DPT


Page 34 of 46

Page 35 of 46

regime. 8.0

1.0


7.0 7

6.5

6



7.5

6.0 Uf = 5.5m/s 5.5

Uf = 6.0m/s Uf = 6.5m/s

5.0 0.5 0.0 -1.0

5

4

3

2

Uf = 7.0m/s

1

Uf = 7.5m/s

0 0.88

Uf = 8.0m/s -0.8

-0.6

-0.4

-0.2

0.92

0.96

0.8

0.6

0.4

0.2

0.0

1.00

0.2

0.4

0.6

Uf = 7.0m/s

Uf = 6.0m/s

Uf = 7.5m/s

Uf = 6.5m/s

r/R (-)

0.0

Uf = 5.5m/s

0.8

1.0

-0.2 -1.0

-0.8

-0.6

-0.4

r/R (-)

-0.2

Uf = 8.0m/s 0.0

0.2

0.4

0.6

0.8

1.0

r/R (-)

(a)

(b)

0.14 0.12

Solid holdup (-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.10

Uf = 5.5m/s

Uf = 7.0m/s

Uf = 6.0m/s

Uf = 7.5m/s

Uf = 6.5m/s

Uf = 8.0m/s

0.08 0.06 0.04 0.02 0.00 -1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

r/R (-)

(c) Figure 16. Influence of superficial gas velocity (Uf) on time-averaged gas-solid axial velocity and solid holdup, radial profiles at H = 0.6 m. (a) Time-averaged gas axial velocity; (b) time-averaged solid axial velocity; (c) time-averaged solid holdup.

5. Conclusion In this work, the pressure signals and solid back-mixing behavior are investigated in a 3-D full-loop dual-side refeed CFB by using the CFD-DEM coupling approach. The proposed model is validated, besides, the intrinsic mechanisms of gas-solid full-loop hydrodynamics are revealed. Moreover, the pressure signals and solid back-mixing behavior under different superficial gas velocities are deeply studied.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Based on the numerical results, conclusions are drawn: 1) Good agreements of numerical results with the experimental data demonstrate the reasonability of the CFD-DEM coupling approach. The minimum fluidization velocity (Umf) is successfully predicted by the model. The CFB system reaches a macroscopic steady state after 5.0 s under the superficial gas velocity of 5.5 m/s. 2) The full-loop hydrodynamics of gas-solid flow is accurately captured. Not only do particles in the riser move upward with the fluidizing gas, but also they turn back and forth in the radial direction. Considering the gas-solid intensive interaction, the gas-solid velocities show fluctuations in the radial direction while smooth in the axial direction. 3) The gas-solid flow in the CFB transforms from fast fluidization (FF) regime (Uf < 7.5 m/s) to dilute phase transport (DPT) regime (Uf >7.5 m/s) judged by power spectra analysis. Across the full loop, the pressure distribution has a close relationship with the solid holdup distribution. Large absolute values of pressure gradient result from the inlet and outlet effects. 4) The solid RTD curves in all cases exhibit a feature of early peak with an extended tail and can be fitted with the lognormal distribution. The wider solid RTD curve with a longer tail in the FF regime indicates that solid flow closes to perfect mixing flow, and more severe solid back-mixing is due to solid internal circulation existing in the riser. The smaller solid RTD curve with a short tail in the DPT regime suggests that the solid flow deviates a little from plug flow, and a small-scale solid back-mixing is due to geometry restrain and recirculating gas-solid flow occurring in


Page 36 of 46

Page 37 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the lower and upper regions.

Acknowledgements Financial supports from the National Natural Science Foundation of China (Nos. 51390491 and 51390493), the National key Research & Development Plan (2016YFB0600102) and the National Program for Support of Top-notch Young Professionals are sincerely acknowledged. This work is also partially supported by the Fundamental Research Funds for the Central Universities of China.

Notation CD

=

Drag force coefficient, dimensionless

Cs

=

Smagorinsky constant coefficient

Cv

=

Coefficient of variation, dimensionless

dp,i

=

Diameter of particle i, m

dp*/dH*

=

Dimensionless pressure gradient, dimensionless

Fc,ij

=

Contact force between particle i and particle j, N

fd,i

=

Drag force exerted on particle i, N

fp,i

=

Pressure gradient force exerted on particle i, N

g

=

Gravitational acceleration, m/s2

G*

=

Equivalent shear modulus of solid phase, Pa

Ii

=

Moment of inertia of particle i, kg·m2

k

=

Total number of particles in contact with the current one, dimensionless

kn,ij

=

Normal stiffness coefficient of solid phase, N/m



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

kt,ij

=

Tangential stiffness coefficient of solid phase, N/m

mi

=

Mass of particle i, kg

m*

=

Effective particle mass, kg

Nf

=

Total grid number, dimensionless

Np

=

Total particle number, dimensionless

n

=

Normal unit vector between colliding particles, dimensionless

n

=

Number of particle locating in the current cell and the model parameter, dimensionless

pf

=

Pressure, Pa

Pf

=

Outlet pressure, Pa

P_ave

=

Time-averaged pressure, Pa

R

=

Particle radius, m

R*

=

Effective particle radius, dimensionless

Rep,i

=

Reynolds number of particle i, dimensionless

Sf,ij

=

Local rate of strain of resolved flow, 1/s

Sn, St

=

Normal and tangential stiffness, N/m

t

=

Time instant, s

t

=

Tangential unit vector between colliding particles, dimensionless

tm

Ti

=

Mean residence time, s Toque exerted on particle i, N·m


Page 38 of 46

Page 39 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Uf

=

Superficial gas velocity, m/s

Umf

=

Minimum fluidization velocity, m/s

Ur

=

Revert aeration, m/s

Ug_x

=

X-component of time-averaged gas velocity, m/s

Ug_y

=

Y-component of time-averaged gas velocity, m/s

Ug_z

=

Z-component of time-averaged gas velocity, m/s

Us_x

=

X-component of time-averaged solid velocity, m/s

Us_y

=

Y-component of time-averaged solid velocity, m/s

Us_z

=

Z-component of time-averaged solid velocity, m/s

uf

=

Fluid velocity in the computational cell, m/s

u% f ,i , u% f , j

=

Filtered large-scale velocity, m/s

vi

=

Velocity of particle i, m/s

vn,ij

=

Normal component of relative velocity between colliding pair, m/s

vt,ij

=

Tangential component of relative velocity between colliding pair, m/s

Vi,t

=

Volume of the particle i in the current cell, m3

∆V

=

Volume of the current cell, m3

x, y, z

=

Coordinate axis, dimensionless

Y, Y*

=

Actual and effective Young’s modulus, MPa

Greek symbols

β g ↔s

=

Inter-phase momentum transfer coefficient, kg/(m3·s)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

δij

=

Kronecker delta, dimensionless

δn,ij

=

Normal displacements between particle i and particle j, m

δt,ij

=

Tangential displacements between particle i and particle j, m

εf

=

Void fraction, dimensionless

σ

=

Stand deviation of residence time, s

µf

=

Fluid dynamic viscosity, kg/(m·s)

µp

=

Friction coefficient, dimensionless

ρf

=

Fluid density, kg/m3

ρp

=

Particle density, kg/m3

vf,t

=

Eddy viscosity coefficient, kg/(m·s)

ωi

=

Angular velocity of particle i, rad/s

γn,ij

=

Damping coefficient in normal direction, kg/s

γt,ij

=

Damping coefficient in tangential direction, kg/s

τf,ij

=

Viscous stress tensor, Pa

τf,ijSGS

=

Sub-grid stress tensor, Pa

ν

=

Poisson ratio, dimensionless

e

=

Restitution coefficient, dimensionless

Subscripts c

=

contact force

f

=

fluid phase (i.e., gas phase)


Page 40 of 46

Page 41 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


i

=

particle i

j

=

particle j

n

=

normal component of variable

t

=

tangential component of variable

=

Central Difference Scheme

Abbreviations CDS CFB

Circulating fluidized bed

CFD

=

Computational Fluid Dynamics

DEM

=

Discrete Element Method

DPT

=

Dilute phase transport

E-E

=

Eulerian-Eulerian

E-L

=

Eulerian-Lagrangian

FF

=

Fast fluidzation

LES

=

Large-eddy Simulation

MP-PIC

=

Multi-phase Particle-in-cell

MSA

=

Mean square amplitude

PISO

=

Pressure Implicit with Splitting of Operator

RTD

=

Residence time distribution

TFM

=

Two-fluid Model

3-D

=

Three-dimensional

References: (1) Basu, P. Combustion of coal in circulating fluidized-bed boilers: a review. Chem. Eng. Sci. 1999,



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

22, 5547-5557. (2) Wang, Q.; Luo, Z.; Fang, M.; Ni, M.; Cen, K. Development of a new external heat exchanger for a circulating fluidized bed boiler. Chemical Engineering & Processing: Process Intensification 2003, 42, 327-335. (3) Corella, J.; Toledo, J. M.; Molina, G. A Review on Dual Fluidized-Bed Biomass Gasifiers. Ind. Eng. Chem. Res. 2007, 46, 6831-6839. (4) Li, C.; Yang, C.; Shan, H. Maximizing Propylene Yield by Two-Stage Riser Catalytic Cracking of Heavy Oil. Ind. Eng. Chem. Res. 2007, 46, 4914-4920. (5) Moutsoglou, A.; Sunkara, P. P. Fischer–Tropsch Synthesis in a Fixed Bed Reactor. Energ. Fuel. 2011, 25, 2242-2257. (6) Scala, F.; Chirone, R. Combustion of Single Coal Char Particles under Fluidized Bed Oxyfiring Conditions. Ind. Eng. Chem. Res. 2010, 49, 11029-11036. (7) Shu, Z.; Fan, C.; Li, S.; Wang, J. Multifluid Modeling of Coal Pyrolysis in a Downer Reactor. Ind. Eng. Chem. Res. 2016, 55, 2634-2645. (8) Chew, J. W.; Hays, R.; Findlay, J. G.; Knowlton, T. M.; Karri, S. B. R.; Cocco, R. A.; Hrenya, C. M. Reverse core-annular flow of Geldart Group B particles in risers. Powder Technol. 2012, 221, 1-12. (9) McMillan, J.; Shaffer, F.; Gopalan, B.; Chew, J. W.; Hrenya, C.; Hays, R.; Karri, S. B. R.; Cocco, R. Particle cluster dynamics during fluidization. Chem. Eng. Sci. 2013, 100, 39-51. (10) Pantzali, M. N.; Lozano Bayón, N.; Heynderickx, G. J.; Marin, G. B. Three-component solids velocity measurements in the middle section of a riser. Chem. Eng. Sci. 2013, 101, 412-423. (11) Samruamphianskun, T.; Piumsomboon, P.; Chalermsinsuwan, B. Effect of ring baffle configurations in a circulating fluidized bed riser using CFD simulation and experimental design analysis. Chem. Eng. J. 2012, 210, 237-251. (12) Li, T.; Dietiker, J.; Shahnam, M. MFIX simulation of NETL/PSRI challenge problem of circulating fluidized bed. Chem. Eng. Sci. 2012, 84, 746-760. (13) Van de Velden, M.; Baeyens, J.; Smolders, K. Solids mixing in the riser of a circulating fluidized bed. Chem. Eng. Sci. 2007, 62, 2139-2153. (14) Li, T.; Dietiker, J.; Shadle, L. Comparison of full-loop and riser-only simulations for a pilot-scale circulating fluidized bed riser. Chem. Eng. Sci. 2014, 120, 10-21. (15) Sasic, S.; Leckner, B.; Johnsson, F. Characterization of fluid dynamics of fluidized beds by analysis of pressure fluctuations. Prog. Energ. Combust. 2007, 33, 453-496. (16) Johnsson, F.; Zijerveld, R. C.; Schouten, J. C.; van der Bleek, C. M.; Leckner, B. Characterization of fluidization regimes by time-series analysis of pressure fluctuations. Int. J. Multiphas. Flow 2000, 26, 663-715. (17) van der Schaaf, J.; Schouten, J. C.; Johnsson, F.; van der Bleek, C. M. Non-intrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series. Int. J. Multiphas. Flow 2002, 28, 865-880. (18) Gheorghiu, S.; Coppens, M. O. Heterogeneity explains features of "anomalous" thermodynamics and statistics. P. Natl Acad. Sci. Usa 2004, 101, 15852-15856. (19) Chen, Y.; Tian, Z.; Miao, Z. Analysis of the pressure fluctuations in binary solids circulating fluidized bed. Energ. Convers. Manage. 2006, 47, 611-623. (20) Harris, A. T.; Davidson, J. F.; Thorpe, R. B. Particle residence time distributions in circulating fluidised beds. Chem. Eng. Sci. 2003, 58, 2181-2202. (21) Lim, K. S.; Zhu, J. X.; Grace, J. R. Hydrodynamics of gas-solid fluidization. Int. J. Multiphas.


Page 42 of 46

Page 43 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Flow 1995, 21, 141-193. (22) Benyahia, S.; Syamlal, M.; O'Brien, T. J. Study of the ability of multiphase continuum models to predict core-annulus flow. Aiche J. 2007, 53, 2549-2568. (23) Kato, K.; Shibasaki, H.; Tamura, K.; Arita, S.; Wang, C.; Takarada, T. Particle holdup in a fast fluidized bed. J. Chem. Eng. Jpn 1989, 22, 130-136. (24) Breault, R. W.; Guenther, C. P.; Shadle, L. J. Velocity fluctuation interpretation in the near wall region of a dense riser. Powder Technol. 2008, 182, 137-145. (25) Varas, A. E. C.; Peters, E. A. J. F.; Kuipers, J. A. M. CFD-DEM simulations and experimental validation of clustering phenomena and riser hydrodynamics. Chem. Eng. Sci. 2016. (26) Peng, B.; Xu, J.; Zhu, J.; Zhang, C. Numerical and experimental studies on the flow multiplicity phenomenon for gas–solids two-phase flows in CFB risers. Powder Technol. 2011, 214, 177-187. (27) Smolders, K.; Baeyens, J. Overall solids movement and solids residence time distribution in a CFB-riser. Chem. Eng. Sci. 2000, 55, 4101-4116. (28) Gao, Y.; Muzzio, F. J.; Ierapetritou, M. G. A review of the Residence Time Distribution (RTD) applications in solid unit operations. Powder Technol. 2012, 228, 416-423. (29) van der Hoef, M. A.; van Sint Annaland, M.; Deen, N. G.; Kuipers, J. A. M. Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy. Annu. Rev. Fluid Mech. 2008, 40, 47-70. (30) Hua, L.; Wang, J.; Li, J. CFD simulation of solids residence time distribution in a CFB riser. Chem. Eng. Sci. 2014, 117, 264-282. (31) Alobaid, F. An offset-method for Euler–Lagrange approach. Chem. Eng. Sci. 2015, 138, 173-193. (32) Alobaid, F.; Ströhle, J.; Epple, B. Extended CFD/DEM model for the simulation of circulating fluidized bed. Adv. Powder Technol. 2013, 24, 403-415. (33) Andrews, M. J.; O'Rourke, P. J. The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. Int. J. Multiphas. Flow 1996, 22, 379-402. (34) Snider, D. M.; Clark, S. M.; O'Rourke, P. J. Eulerian–Lagrangian method for three-dimensional thermal reacting flow with application to coal gasifiers. Chem. Eng. Sci. 2011, 66, 1285-1295. (35) Lan, X.; Shi, X.; Zhang, Y.; Wang, Y.; Xu, C.; Gao, J. Solids Back-mixing Behavior and Effect of the Mesoscale Structure in CFB Risers. Ind. Eng. Chem. Res. 2013, 52, 11888-11896. (36) Chu, K. W.; Wang, B.; Xu, D. L.; Chen, Y. X.; Yu, A. B. CFD–DEM simulation of the gas– solid flow in a cyclone separator. Chem. Eng. Sci. 2011, 66, 834-847. (37) Li, T.; Pannala, S.; Shahnam, M. CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations. Powder Technol. 2014, 265, 13-22. (38) Nikolopoulos, A.; Nikolopoulos, N.; Varveris, N.; Karellas, S.; Grammelis, P.; Kakaras, E. Investigation of proper modeling of very dense granular flows in the recirculation system of CFBs. Particuology 2012, 10, 699-709. (39) Luo, K.; Wu, F.; Yang, S.; Fang, M.; Fan, J. High-fidelity simulation of the 3-D full-loop gas-solid flow characteristics in the circulating fluidized bed. Chem. Eng. Sci. 2015, 123, 22-38. (40) Nikolopoulos, A.; Nikolopoulos, N.; Charitos, A.; Grammelis, P.; Kakaras, E.; Bidwe, A. R.; Varela, G. High-resolution 3-D full-loop simulation of a CFB carbonator cold model. Chem. Eng. Sci. 2013, 90, 137-150. (41) Wang, Q.; Yang, H.; Wang, P.; Lu, J.; Liu, Q.; Zhang, H.; Wei, L.; Zhang, M. Application of CPFD method in the simulation of a circulating fluidized bed with a loop seal Part II—Investigation of



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

solids circulation. Powder Technol. 2014, 253, 822-828. (42) Zhang, N.; Lu, B.; Wang, W.; Li, J. Virtual experimentation through 3D full-loop simulation of a circulating fluidized bed. Particuology 2008, 6, 529-539. (43) Zhang, N.; Lu, B.; Wang, W.; Li, J. 3D CFD simulation of hydrodynamics of a 150MWe circulating fluidized bed boiler. Chem. Eng. J. 2010, 162, 821-828. (44) Chu, K. W.; Yu, A. B. Numerical simulation of complex particle–fluid flows. Powder Technol. 2008, 179, 104-114. (45) Wang, S.; Luo, K.; Yang, S.; Hu, C.; Fan, J. Parallel LES-DEM simulation of dense flows in fluidized beds. Appl. Therm. Eng. 2016. (46) Ibsen, C. H.; Helland, E.; Hjertager, B. H.; Solberg, T.; Tadrist, L.; Occelli, R. Comparison of multifluid and discrete particle modelling in numerical predictions of gas particle flow in circulating fluidised beds. Powder Technol. 2004, 149, 29-41. (47) Smagorinsky, J. General circulation experiments with the primitive equations: I. the basic experiment. Mon. Weather Rev. 1963, 91, 99-164. (48) Lilly, D. K. A proposed modification of the Germano subgrid-scale closure method. Physics of Fluids A: Fluid Dynamics 1992, 4, 633. (49) Breuer, M.; Rodi, W., Large eddy simulation of complex turbulent flows of practical interest. In Flow Simulation with High-Performance Computers II, Vieweg+ Teubner Verlag: 1996; pp 258-274. (50) Gidaspow, D. Multiphase flow and fluidization: continuum and kinetic theory descriptions. Academic press. 1994. (51) Cundall, P. A.; Strack, O. D. L. A discrete numerical model for granular assemblies. Geotechnique 1979, 29, 47-65. (52) Di Renzo, A.; Di Maio, F. P. Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem. Eng. Sci. 2004, 59, 525-541. (53) Pöschel, T.; Salueña, C.; Schwager, T. Scaling properties of granular materials. Phys. Rev. E 2001, 64, 173-184. (54) Versteeg, H. K.; Malalasekera, W. An Introduction to Computational Fluid Dynamics：The Finite Volume Method (2nd Edition). Prentice Hall. 2007, 16. (55) Issa, R. I. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 1986, 62, 40-65. (56) Müller, C. R.; Holland, D. J.; Sederman, A. J.; Scott, S. A.; Dennis, J. S.; Gladden, L. F. Granular temperature: Comparison of Magnetic Resonance measurements with Discrete Element Model simulations. Powder Technol. 2008, 184, 241-253. (57) Müller, C. R.; Scott, S. A.; Holland, D. J.; Clarke, B. C.; Sederman, A. J.; Dennis, J. S.; Gladden, L. F. Validation of a discrete element model using magnetic resonance measurements. Particuology 2009, 7, 297-306. (58) Fang, M.; Luo, K.; Yang, S.; Zhang, K.; Fan, J. LES-DEM investigation of gas-solid flow dynamics in an internally circulating fluidized bed. Chem. Eng. Sci. 2013, 101, 213-227. (59) 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, 583-595. (60) Yang, S.; Luo, K.; Fan, J.; Cen, K. F. Particle-scale investigation of the solid dispersion and residence properties in a 3-D spout-fluid bed. Aiche J. 2014, 60, 2788-2804. (61) Zhou, Z. Y.; Kuang, S. B.; Chu, K. W.; Yu, A. B. Discrete particle simulation of particle–fluid flow: model formulations and their applicability. J. Fluid Mech. 2010, 661, 482-510.


Page 44 of 46

Page 45 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(62) Zhu, H. P.; Zhou, Z. Y.; Yang, R. Y.; Yu, A. B. Discrete particle simulation of particulate systems: A review of major applications and findings. Chem. Eng. Sci. 2008, 63, 5728-5770. (63) Guan, Y.; Chang, J.; Zhang, K.; Wang, B.; Sun, Q.; Wen, D. Three-dimensional full loop simulation of solids circulation in an interconnected fluidized bed. Powder Technol. 2016, 289, 118-125. (64) Kalita, P.; Saha, U. K.; Mahanta, P. Effect of biomass blending on hydrodynamics and heat transfer behavior in a pressurized circulating fluidized bed unit. Int. J. Heat Mass Tran. 2013, 60, 531-541. (65) Lu, B.; Zhang, N.; W, W. 3-D Full-Loop Simulation of an Industrial-Scale Circulating Fluidized-Bed Boiler. Aiche J. 2013, 59, 1108-1117. (66) Thapa, R. K.; Frohner, A.; Tondl, G.; Pfeifer, C.; Halvorsen, B. M. Circulating fluidized bed combustion reactor: Computational Particle Fluid Dynamic model validation and gas feed position optimization. Comput. Chem. Eng. 2016, 92, 180-188. (67) Wang, S.; Lu, H.; Zhao, F.; Liu, G. CFD studies of dual circulating fluidized bed reactors for chemical looping combustion processes. Chem. Eng. J. 2014, 236, 121-130. (68) Grace, J. R.; Avidan, A. A.; Knowlton, T. M. Circulating Fluidized beds. Blackie Academic and Professional. 1997. (69) Meer, E. H. V. D.; Thorpe, R. B.; Davidson, J. F. Flow patterns in the square cross-section riser of a circulating fluidised bed and the e!ect of riser exit design. Chem. Eng. Sci. 2000, 55, 4079-4099. (70) Zhou, J.; Grace, J. R.; Lim, C. J.; Brereton, C. M. H. Particle velocity profiles in a circulating fluidized bed riser of square cross-section. Chem. Eng. Sci. 1995, 50, 237-244. (71) Derksen, J. J.; van den Akker, H. E. A.; Sundaresan, S. Two-way coupled large-eddy simulations of the gas-solid flow in cyclone separators. Aiche J. 2008, 54, 872-885. (72) Rhodes, M. J.; Sollaart, M.; Wang, X. S. Flow structure in a fast fluid bed. Powder Technol. 1998, 99, 194-200. (73) Freitas, L. A. P.; Ozkanm, M. D.; Lim, C. J.; Grace, J. R.; Bai, D. Identification of Flow Regimes in Slot-Rectangular Spouted Beds using Pressure Fluctuations. Can. J. Chem. Eng. 2004, 82, 60-73. (74) He, H.; Lu, X.; Shuang, W.; Wang, Q.; Kang, Y.; Yan, L.; Ji, X.; Luo, G.; Liu, H. Statistical and frequency analysis of the pressure fluctuation in a fluidized bed of non-spherical particles. Particuology 2014, 16, 178-186. (75) Jaiboon, O.; Chalermsinsuwan, B.; Mekasut, L.; Piumsomboon, P. Effect of flow pattern on power spectral density of pressure fluctuation in various fluidization regimes. Powder Technol. 2013, 233, 215-226. (76) Tahmasebpour, M.; Zarghami, R.; Sotudeh-Gharebagh, R.; Mostoufi, N. Characterization of various structures in gas-solid fluidized beds by recurrence quantification analysis. Particuology 2013, 11, 647-656. (77) Anantharaman, A.; Karri, S. B. R.; Findlay, J. G.; Hrenya, C. M.; Cocco, R. A.; Chew, J. W. Interpreting Differential Pressure Signals for Particle Properties and Operating Conditions in a Pilot-Scale Circulating Fluidized Bed Riser. Ind. Eng. Chem. Res. 2016, 55, 8659-8670. (78) Wang, Z.; Sun, S.; Zhao, N.; Wu, S.; Tan, Y. In Numerical Simulation of the Gas-Solid Flow in a Square Circulating Fluidized Bed with Secondary Air Injection, Cleaner Combustion and Sustainable World, 2013; Springer Berlin Heidelberg: 2013; pp 539-552.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 46

For Table of Contents Only Figure * shows the structure of the contents. Taking the advantage of Computational Fluid

Dynamics combined with

Discrete

Element

Method

(CFD-DEM), the gas-solid full-loop hydrodynamics in a three-dimensional circulating fluidized bed (CFB) is accurately captured. The gas-solid phase crosses and evolves in the CFB with the intensive and heterogeneous motion. The pressure signals are obtained from the simulation, shedding light on the flow dynamics in the system. The mechanism of solid back-mixing behavior under different fluidization regimes in the CFB riser lies in the solid residence time distribution (RTD). Detailed information is given in the contents.

Figure *. The structure of the contents.


Computational Fluid DynamicsâDiscrete Element Method

Recommend Documents

Computational Fluid DynamicsâDiscrete Element Method