Particle-Scale Investigation of Heat Transfer and Erosion

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Thermodynamics, Transport, and Fluid Mechanics

Particle-scale investigation of heat transfer and erosion characteristics in a three-dimensional circulating fluidized bed Shuai Wang, Kun Luo, Chenshu Hu, and Jianren Fan Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00353 • Publication Date (Web): 25 Apr 2018 Downloaded from http://pubs.acs.org on April 26, 2018

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Industrial & Engineering Chemistry Research

Particle-scale investigation of heat transfer and erosion characteristics in a three-dimensional circulating fluidized bed By

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

*

Author for correspondence. Fax: +86-0571-87953687; E-mail: [email protected]

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Industrial & Engineering Chemistry Research 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 Comprehensive understanding of heat transfer and erosion characteristics is of significance for circulating fluidized bed (CFB) optimization. In this work, a high-fidelity simulation of the full-loop CFB is conducted using the CFD-DEM method. After qualitative and quantitative model validations, the impact of superficial gas velocity on flow dynamics, particle temperature evolution, and cyclone erosion is comprehensively explored. The results show that increasing superficial gas velocity decreases solid holdup and improves flow uniformity. Probability density of particle temperature in different CFB components shows distinctive distributions. The average particle temperature augments as the superficial gas velocity augments in fast fluidization regime, while it shows the opposite tendency in dilute phase transport regime. Meanwhile, the cyclone erosion region gradually concentrates in the inter-section of cylinder and cone parts. The results benefit for in-depth understanding of heat transfer and erosion characteristics in CFB apparatuses. Keywords: heat transfer; erosion; CFD-DEM method; two-phase flow; mathematical modeling.


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1. Introduction In the past few decades, circulating fluidized bed (CFB) technique has been one of the most promising techniques in physical and chemical engineering fields because of its higher thermal efficiency over a wide range of operating conditions1. For a CFB boiler, heat produced from vigorous burning rate is carried out via convective, conductive, and radiative heat transfers. Thus the system maintains at a lower temperature, leading to a lower emission of SO2 and NOx2. Although plenty of experiments have been conducted about voidage field3, pressure signal4, solid residence distribution5, and solid dispersion property6 in CFBs for decades, the gas-solid hydrodynamics and heat transfer are not yet comprehensively understood due to the complex multi-phase and multi-physics processes. Generally, superficial gas velocity dominates solid dispersion, bubble coalescence, collision dynamics, and heat transfer process. For optimizing the thermal process in CFBs, fundamental knowledge of the relationship of flow dynamics and heat transfer with the superficial gas velocity is urgently required. In the past decades, some experimental methods have been adopted to investigate how the superficial gas velocity affects thermal performance7-9. However, the experiments suffer from hard operation and high cost. As an alternative, computational fluid dynamics (CFD) methods have become attractive with the rapid development of computational technologies. Specifically, CFD methods for modeling dense two-phase flow in fluidized beds are commonly categorized as methods based on Eulerian-Eulerian framework and methods based on Eulerian-Lagrangian framework10-14. Among them, the CFD-DEM method shows a



promising performance for simulating dense two-phase flows in lab-scale and pilot-scale units15, 16. Technically, in this method, the gas motion and solid motion are respectively descript under Eulerian framework and Lagrangian framework. Generally, the CFD-DEM simulations can provide particle-scale information (i.e., particle trajectory) and collision details (i.e., force acting on each particle or wall), which are extremely difficult to be obtain by experiments or other CFD methods. Therefore, the CFD-DEM method proves efficient to capture the most of features on microscopic and macroscopic scales of flow dynamics and heat transfer in complex apparatuses involving dense two-phase flows17-20. In the past decades, the CFD-DEM method were extensively employed to scrutinize heat transfer properties in fluidized beds. Specifically, heat transfer in packed and bubbling fluidized beds with simple geometries was firstly investigated by some researchers21-24, and the results demonstrated that the inter-particle and inter-phase heat transfers have a close relation with the superficial gas velocity. In addition to packed and bubbling fluidized beds, heat transfer in spouted beds has some unique characteristics. Wang et al.25 pointed out that the larger superficial gas velocity enhances the convective heat transfer in spout region while weakens it in annulus region. As another influence factor, immersed tube bundles intensify the heat transfer of solid phase via improving the flow and temperature uniformity in bubbling fluidized beds26-30. Besides, bubbles in fluidized beds de- or accelerate the frequency of formation, coalescence, and eruption with changing of superficial gas velocity31. It is found that heat transfer is vigorous in the wake of rising bubbles, whilst enervated


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in the clouds of the bubbles21, 32, 33. From the abovementioned literatures, it can be seen that the heat transfer behaviors have a strong dependence on geometry of units and operating conditions, especially superficial gas velocity. However, the majority of CFD-DEM simulations are limited to two-dimensional or simple geometries. On the other hand, the majority of studies are focused on fixed bed, bubbling fluidized bed and turbulent fluidized bed, which are operated at lower superficial gas velocities. To the author’s know, there are few CFD-DEM simulations modeling heat transfer behaviors in CFBs which are operated at the higher superficial gas velocities. The only simulation work was carried out by Wahyudi et al.34, and they demonstrated that the extended CFD-DEM method was useful to explore hydrodynamics and heat transfer in CFBs. However, their work was mainly focused on CFB riser with a little of information obtained. Usually, a three-dimensional full-loop CFB includes a riser, a cyclone, a loop seal, and a return leg, and these parts are strong coupled35, 36. The difficulties of CFD-DEM simulations for the full-loop CFB lie in: (i) intensely turbulent flow; (ii) complex geometry; (iii) massive particles. For each issue, we put forward the corresponding solution in the present study. The intensive turbulence is dealt with large-eddy simulation (LES), which integrates the advantages of direct numerical simulation (DNS) and Reynolds-averaged Navier-Stokes (RANS) methods37. The complicated geometry is handled with the finite volume method, in which the geometrical domain is divided into structure and unstructured cells. Meanwhile, the inter-particle collisions are coped with grid-based detection search algorithm, whose operation count is reduced



to O(N) compared to other detection algorithms30, 38, 39. As we all know, the erosion is more serious in the cyclone than that in the other two CFB parts because of the more intensive and vigorous gas-solid flow19, 40, 41. However, to the author’s knowledge, there have been scarce investigations towards the cyclone erosion at the particle-scale level for decades40. Based on the abovementioned issues, the present article numerically studies heat transfer and erosion characteristics in a three-dimensional full-loop CFB by extending the cold CFD-DEM method used in our previous work37. Moreover, the turbulence of gas phase is resolved using large-eddy simulation (LES). Thus this advanced CFD-DEM method in the current work is also called LES-DEM method. Firstly, the details of mathematical model are presented. After the model validation and grid sensitivity test, the hydrodynamics in the CFB is analyzed. Then, the probability density distributions of particle temperature in different CFB parts are presented. Eventually, the impacts of superficial gas velocity on particle temperature evolution and cyclone erosion are synthetically investigated.

2. Mathematical model As we all know, the LES-DEM method has a capacity of modeling the interaction of turbulent structure with dense dispersed particles in multi-phase systems42. Based on this, we incorporate the heat transfer and erosion sub-models into the LES-DEM method in the present study, so that it can handle multi-phase and multi-physics processes.

2.1. Model of particle motion


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For a specific particle, the forces induced from fluid drag (Fd,i), pressure gradient (Fp,i), collision contact (Fc,ij+Fd,ij) and gravitation (mig) are usually taken into account in CFB simulations43. Equations for translational and rotational motions read44: k dvi mi = Fd ,i + Fp,i − ∑( Fc,ij + Fd ,ij ) + mi g dt j =1

(1)

k dωi Ii = ∑(Tt,ij + Tr,ij ) dt j =1

(2)

where mi is particle mass; ui, ωi, and Ii are particle translational velocity, angular velocity, and moment of inertia, respectively. Boldface letters used in equations stand for the vectors and tensors. The soft-sphere contact model, aiming to simulate dense two-phase flows, uses the spring-dashpot-slider assumption to describe inter-particle collisions45. Specifically, the contact force (Fc,ij) and damping force (Fd,ij) during inter-particle interactions are respectively divided into the normal components (Fcn,ij, Fdn,ij) and the tangential components (Fct,ij, Fdt,ij). Besides, the torque includes the torque stemming from tangential force Tt,ij and the rolling torque Tr,ij46, 47. Equations for calculation of collision forces and torques are listed in Table 1. Further details can refer to the literature37, 48. Table 1. Equations for force and torque calculations. Term

Equation

Contact and damping forces

Fc,ij = Fcn,ij + Fct,ij , Fd ,ij = Fdn,ij + Fdt ,ij

Normal contact force

4 Fcn,ij = Y ∗R∗1/2δn,ij 3/2 n 3

Normal damping force

5 Fdn ,ij = −2   6

ln ( e )

1/2

ln

2

(e) + π

2

(2Y


∗

R ∗δ n ,ij m ∗

)

1/2

vn ,ij


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Tangential contact force

Fct ,ij = 8G∗ R∗1/2δ n,ij1/2δ t ,ij t

Tangential damping force

5 Fdt ,ij = −2   6

Torque due to tangential force

Tt ,ij = Ri × ( Fct ,ij + Fdt ,ij )

Rolling torque

ωrel ,ij R ω + R jω j 4 Ri , ωrel ,ij = i i Tr ,ij = µr Y ∗R∗1/2δ n,ij 3/2 3 Ri + R j ωrel ,ij

Coulomb’s friction law

Fct ,ij + Fdt ,ij = µ Fcn ,ij + Fdn,ij t

1/2

ln ( e ) ln ( e ) + π 2

2

(8G

∗

R*δ n ,ij m ∗

)

1/ 2

vt ,ij

where m∗ = ( mi m j ) ( mi + m j ) and R∗ = ( Ri R j ) ( Ri + R j ) respectively denote the effective mass and

radius

of

particle

1 Y ∗ = (1 − ν i 2 ) Yi + (1 − ν j 2 ) Y j

(

)

1 G ∗ = ( 2 ( 2 − ν i )(1 + ν i ) ) Yi + 2 ( 2 − ν j )(1 + ν j ) Y j

i.

and

respectively represent the equivalent shear modulus and the

effective Young’s modulus, with particle Young’s modulus Yi and particle Poisson’s ratio νi. In addition, δ, e, µ, and µr are displacement of overlap, restitution coefficient, sliding friction, and rolling friction, respectively.

2.2. Model of gas motion Navier-Stokes equations based on volume-averaged operation are employed to describe the gas motion, formulated as: ∂ ∂ (ρ f ε f ) + ( ρ f ε f ui ) = 0 ∂t ∂ xi

(3)

∂τ ∂ ∂ ∂p + ε f ij + ρ f ε f g + F fp ( ρ f ε f ui ) + ( ρ f ε f ui u j ) = −ε f ∂t ∂x j ∂xi ∂x j

(4)

∂ (ρ f ε f Tf ) ∂t

+

∂ ( ρ f ε f u jT f ) ∂x j

=

∂ ∂x j

 kf µ   ∂T + ε f t  f   ε f Prt   ∂x j   c p , f

   − Q fp  

(5)

n

where ε f = 1 − ∑ V p ,i ∆V is fluid volume fraction; u, ρf, p respectively denote fluid i =1

velocity, fluid density, and fluid pressure; kf, cp,f respectively represent fluid thermal


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conductivity and fluid specific heat capacity. Turbulent Prandtl number (Prt) is assigned as 0.85. Moreover, the fluid turbulence is resolved using large-eddy simulation (LES). This model is chosen due to its obvious advantages in simulating turbulent flow in CFB risers categorized as fast fluidization regime49-52 and in cyclone separators with drastically swirling flow53-55. Smagorinsky model56 based on eddy viscosity concept is chosen as the sub-grid scale (SGS) model. τij is the stress tensor, including viscous and sub-grid stress tensor: τ ij = τ f ,ij + τ t ,ij . τf,ij and τt,ij are respectively calculated as:

 ∂ui

τ f ,ij = µ f 

 ∂x j

+

∂u j  2µ f ∂u δ ij k , τ t ,ij = ρ f  2 µ t S ij + 1 δ ijτ kk   − 3 ∂xi  ∂xk 3  

µt = (Cs∆)2 (2Sij Sij )1/2

(6) (7)

where µf, µt, δij, Cs are viscous coefficient, eddy viscosity coefficient, Kronecker function, and Smagorinsky constant, respectively. The filtered strain rate is written as:

Sij = (1 2) ( ∂ui ∂x j ) + (1 2) ( ∂u j ∂xi ) . Ffg and Qfp in Equation (8, 9) are respectively volumetric source terms of inter-phase force and inter-phase heat transfer, formulated as: F fp =

n

∑F

d ,i

∆V

(8)

∆V

(9)

i =1

Q fp =

n

∑Q

f ,i

i =1

where Qf,i denotes inter-phase heat transfer, which is well descript in the following section. n represents the particle number and ∆V is the volume of computational cell.

2.3. Model of inter-phase interactions Generally, inter-phase momentum exchange occurs via drag force term, which is written as:



Fd ,i =

V p ,i 1 − ε f ,i

β i ( u f ,i − v p ,i )

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(10)

here, Vp,i and vp,i stand for volume and velocity of particle i, respectively; εf,i and uf,i respectively denote volume fraction and velocity of fluid phase interpolated into where particle i is located in. Using the Gidaspow drag model, the inter-phase momentum exchange coefficient βi reads57:

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

ε f > 0.8 (11)

ε f ≤ 0.8

where dp,i represents particle diameter. CD denotes fluid drag coefficient for an individual particle, expressed as:

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

Re p ,i < 1000

(12)

Re p ,i ≥ 1000

here, particle Reynolds number Rep,i closely relates to gas-solid parameters and inter-phase slip velocity:

Re p ,i =

ε f ρ f u f ,i − v p ,i d p ,i µf

(13)

2.4. Model of heat transfer According to plenty of published literatures about heat transfer in fluidized beds18, 29, 30, 58-60

, three mechanisms are usually considered: conduction, convection and

radiation. However, when the bed temperature is lower than 600 K, the radiation can be ignored due to its negligible contributions18, 30, 58. Motivation of the current work is to study particle temperature evolution in a full-loop CFB, where particle temperature


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is lower than this critical value (i.e., 600K). Therefore, we only consider the convective and conductive heat transfers. In principle, thermal convection is ascribed to the particle-fluid heat transfer (Qi,f), while thermal conduction is attributed to the particle-particle (Qi,j) and particle-wall heat transfer (Qi,wall). Energy balance of a specific particle i is expressed as:

mi c p ,i

dTp,i dt

k

= Qi , f + ∑ Qi , j + Qi ,wall

(14)

j =1

where cp,i denotes particle specific heat capacity. Tp,i stands for particle temperature. The convective heat transfer term can be formulated as:

Qi , f = hi , f π d p2,i (T f ,i − Tp,i )

(15)

where Tf,i is fluid temperature interpolated into where particle i is located in. The heat transfer coefficient hi,f can be formulated as61:

hi, f =

Nup,ik f

(16)

d p,i

1/3 2 + 0.6ε nf Re1/2 p,i Pr ,  1/3 n 0.8 1/3 Nu p,i = 2 + 0.5ε nf Re1/2 p,i Pr + 0.02ε f Re p,i Pr ,  n 1.8 2 + 0.000045ε f Re p,i ,

Re p,i < 200

200 ≤ Re p,i ≤ 1500

(17)

Re p,i >1500

where kf represents fluid thermal conductivity. Nup,i, and Pr denote particle Nusselt number and Prandtl number, respectively. n is a model constant, chosen as 3.5. Conductive heat transfer stems from inter-particle contacts among particles. Particle uniform temperature assumption is usually used in the CFD-DEM method, that is, each individual particle has a uniform temperature, and the temperature gradient inside particle is not taken into account. The conductive heat transfer is calculated as62:



Qi , j = hi , j ( T j − Ti )

hi, j = 4

kp,ikp, j kp,i + kp, j

Ac,ij

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(18) (19)

where hi,j is conductive heat transfer coefficient. kp is particle thermal conductivity. Moreover, Ac,ij denotes particle contact area, which depends on the overlap and displacement during inter-particle collisions.

2.5. Model of erosion Drastically swirling gas-solid flow exists in the cyclone separator, thus erosion occurs when vigorous particles collide with cyclone surfaces41. The erosion rate mainly depends on particle velocity vp, particle mass mp, and contact angle θ. Compared to TFM, particle-scale CFD-DEM method has an intrinsic capacity of obtaining erosion details on the surface of apparatuses. In the present study, the removed quantity of the surface is simulated by Finnie erosion model63. For tan(θ)1/3, it is calculated as:

E=

mpv 2p cos2 (θ ) 24PH

(21)

where PH denotes the Vickers hardness of surface.

2.6. Numerical scheme In this paper, the heat transfer model is integrated with extending our proposed cold LES-DEM method, whose numerical algorithm, parallel strategy, and geometry treatment have been well summarized in our previous article37. Thus a brief


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introduction is given in here. The full-loop circulating fluidized bed has a complex geometric domain, which is divided into the hybrid computational fluid cells (i.e., structured and unstructured cells). According to the particle position and its corresponding fluid cell, the grid-based collision detection is used to find potential partners, which has an operation count of O(N). Since the size of some computational grids approaches the particle diameter, a divided particle volume method (DPVM) is used to calculate the fluid volume fraction (εf). Technically, each individual particle is divided into 48 elements, followed by identifying which grid cell each of them is located in based on its center position. Thus, a smoother fluid void fraction field is obtained, leading to a highly numerical accuracy64. The finite volume method is employed to discretize fluid governing equations. The PISO (Pressure Implicit Splitting Operation) algorithm is adopted to handle velocity-pressure coupling65. The unsteady term is integrated with a Crank-Nicolson scheme. The convection and diffusion terms are discretized with a central differencing scheme. Moreover, the solid motion is updated by the explicit time integration. As the time marches, the velocity, pressure, temperature of fluid phase are obtained using the initial and boundary conditions. Subsequently, inter-phase drag force and inter-phase heat transfer are calculated, transferred to each individual particle via momentum and energy source terms. For the CFD-DEM method, there are usually 10 ~ 100 DEM steps in each CFD step45, 66, 67. During each DEM step, the velocity, position, and heat transfer of particles after collisions are evaluated. Subsequently, the motion and heat transfer of fluid phase are evaluated via inter-phase



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source terms fed back from the DEM interface. Thus, a calculation cycle is completed.

3. Computational details 3.1. Model validation As we all know, the heat transfer model should be validated before application to the full-loop CFB simulations. Actually, the cold LES-DEM method has been well validated and extensively employed to study dense two-phase flows by our group. Specifically, we investigated solid dispersion properties in a bubbling fluidized bed68, solid circulation in an internal circulating fluidized bed43, solid residence time19, improvement of flow uniformity69, and impact of cyclone arrangements in circulating fluidized beds16. The results from simulations and experiments perform good conformance

across

various

fluidization

regimes,

providing

fundamental

understandings for particulate engineering. Although the heat transfer model incorporated in our LES-DEM method was previously used to study solid mixing with temperature difference and immersed tube

heat transfer, it hasn’t been

comprehensively validated60, 70. Patil et al.8, 22 conducted a series of excellent experiments towards gas-solid heat transfer properties. In the present study, their experimental data is adopted to validate the LES-DEM method with heat transfer model integrated. Specifically, the dimensions in three dimensions of the test rig (i.e., a pseudo two-dimensional bubbling fluidized bed) are 8 cm, 1.5 cm, and 25 cm, respectively. The grid number in three directions is 35, 6, and 110, respectively. In the bed, the hot glass particles (i.e.,


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diameter: 1 mm; temperature: 90 ºC) are fluidized by the cold gas flow (i.e., velocity: 1.2 m/s; temperature: 20 ºC). Detailed gas-solid parameters and computational settings can refer to the literature8, 22, 58.

(a)

(b)

(c)

(d)

Figure 1. Instantaneous solid flow pattern and particle temperature in the pseudo two-dimensional bubbling fluidized bed with a diameter of 1 mm and a mass of 125 g: (a, c) visual images from the experiment8; (b, d) snapshots from the current simulation. Copyright 2015, A.V. Patil.

Figure 1 qualitatively compares the instantaneous solid flow pattern and particle temperature in the current simulation with that in the experiment. Particles are fluidized by the gas flow, and small bubbles are generated at the bottom of bed. Subsequently, they rise up, coalesce, and form a large bubble. The large bubble breaks up at the bed surface and throws particles to the freeboard. It is noted that the simulation result (Figure 1a) shows good agreement with the experimental image (Figure 1b) considering the bubble diameter and bed expansion height. Particles at the bottom of bed are quickly cooled by fluidized gas whilst particles near the top of bed keep high temperature. It is observed that a narrow cold zone exists at the center of bed, diminishing with the increase of axial height (Figure 1d). This particle temperature distribution is accurately captured by the current model, showing



conformance with the experimental observation (Figure 1c).

(a)

(b)

(c)

(d)

Figure 2. Instantaneous solid flow pattern and particle temperature in the pseudo two-dimensional bubbling fluidized bed with a diameter of 1 mm and a mass of 125 g: (a, c) visual images from the experiment8; (b, d) snapshots from the current simulation. Copyright 2015, A.V. Patil.

As illustrated in Figure 2, a large bubble is stretched into two separated bubbles and a cold zone exists at the center of bed. Particles circulate from the corner to the center and mix with cold gas flow, finally, exchange heat. It is noted from Figure 2d that the cold gas flow is heated when penetrating hot particle layers, via convective heat transfer. Thus, the gas flow has a higher temperature in bubbles than in other regions, which has a similar tendency with the experimental observation. Average particle temperature (ºC)

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

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95

Exp: Ubg=1.2m/s Sim: Ubg=1.2m/s Exp: Ubg=1.54m/s Sim: Ubg=1.54m/s Exp: Ubg=1.71m/s Sim: Ubg=1.71m/s

90 85 80 75 70 65 60 55

0

1

2

3

4

5

6

7

8

9

10

Time (s) Figure 3. Comparison of numerical results with experimental data in the pseudo two-dimensional


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fluidied bed with a diameter of 1 mm and a mass of 75 g.

In addition to the qualitative comparisons, curves in Figure 3 compare the time-evolution profiles of average particle temperature. It can be seen that the temperature profile in experiment has a deeper slope than that in simulation at 1.2 m/s. As pointed out by Patil et al.22, the momentary stagnation of particles at lower gas velocities leads to longer contact times, and this mechanism results in the above discrepancies. However, for higher gas velocities (1.54 m/s and 1.71 m/s), the simulation results agree well with experimental data. Therefore, via qualitative and quantitative validations, the proposed model proves reasonable to be used to simulate hydrodynamics and heat transfer in full-loop CFBs.

3.2 Simulation conditions Figure 4 shows the investigated object, a lab-scale CFB with a height of 1200 mm. The lower square cross-section of the riser is 53×53 mm2 while the upper cross-section is 58×58 mm2. The cyclone has a height of 230 mm whilst the height of standpipe is 955 mm. Other dimensions of the whole rig are shown in Figure 4a. The whole calculation domain is meshed into 80600 hexahedron elements. The size of each grid cell is about 4.5 mm, nearly three times of the particle diameter, 1.6 mm. The grids of cyclone are shown in Figure 4b.



(a)

(b)

Figure 4. (a) Geometry and dimensions (unit: mm) of the investigated CFB, and the heating section is marked by red color; (b) computational grids of the cyclone.

In the current work, we tracked a number of 200000 biomass-like particles in the system. Details of pressure and velocity boundary conditions are summarized in our previous work69. In addition, particles initially packed in the riser and dipleg have a temperature of 298 K. The upper section of the riser is assigned as a fixed temperature, 373 K, and assumed as heating section34, 71. The fresh cold gas flow are introduced from the distributor with a fixed temperature of 298 K and various superficial gas velocities (i.e., Uf = 6.0 ~ 8.0 m/s). Detailed simulation conditions are summarized in Table 2. Table 2. Gas-solid parameters. Gas property Density

1.225 kg/m3

Viscosity

1.8 × 10-5 kg/(m·s)


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Temperature

298 K

Specific heat capacity

1007 J/(kg·K)

Thermal conductivity

0.0256 W/(m·K)

Superficial gas velocity

6.0, 6.5, 7.0, 7.5, 8.0 m/s

Aeration gas velocity

1.0 m/s

Atmosphere pressure

1.01 × 105 Pa

Solid property Diameter

1.6 mm

Density

1500 kg/m3

Temperature

298 K

Specific heat capacity

800 J/(kg·K)

Thermal conductivity

1.0 W/(m·K)

Young modulus

5.0 × 107 Pa

Poisson ratio

0.33

Restitution coefficient

0.90

Friction coefficient

0.10

Rolling friction coefficient

0.125

Initially, 200000 particles are packed in the riser and dipleg, respectively. Subsequently, these particles form packed beds after the whole kinetic energy decays to zero. Gas flow and revert aeration are successively introduced into the system. Finally, particles are fluidized and circulate in the full-loop CFB. It was demonstrated in our previous work that the system reached equilibrium state after 5 s19, 72. Gas-solid



time steps are respectively 1×10-5 s and 1×10-6 s based on the calculation criterion16, 67. Each case is run for a physical time of 20 s, and the last 15 s is used for statistics.

3.3 Grid sensitivity study The computational grids are complex for a three-dimensional full-loop CFB, thus the grid sensitivity test should be carried out before simulations. The size of fine, mediate and coarse meshes is 4 mm, 4.5 mm, and 5 mm, respectively. Considering the importance of solid behaviors in the CFB, Figure 5 compares the cross-sectional solid velocity and its standard deviation among three sets of computational grids. It is observed that the profile agrees well with one another, demonstrating the reasonability of the selected grid size. In order to comprise computational cost and numerical accuracy, the mediate grid (i.e., 4.5 mm) is used for successive simulations in the current work. Us (m/s)

0.2 0.1 0.0

Us_SD (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

Page 20 of 45

4.0 mm

4.5 mm

5.0 mm

0.3 0.2 0.1 0.0

0.2

0.4

0.6

0.8

1.0

1.2

Bed height (m)

Figure 5. Cross-sectional solid velocity along the bed height for grid sensitivity study.

4. Results and discussions 4.1 Effect of superficial velocity on bed hydrodynamics Solid holdup has a close relationship with heat transfer in fluidized beds34, thus the gas-solid hydrodynamics are comprehensively studied at first. Figure 6 shows


Page 21 of 45 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


particle temperature and void fraction distributions in the full-loop CFB over time at 6.0 m/s. Cold gas flow is introduced to the bed from the bottom distributor and L-valve. The gas-solid flow is complex and heterogamous due to intense gas turbulence, drastic gas-solid momentum exchange, and clusters occurring in the whole riser, especially the lower part73. In addition, it is noted that particle temperature has a lower value in the lower section of bed. Generally, two basic mechanisms exist in the heat transfer processes, that is, conductive and convective heat transfers. The former is via inter-particle contacts while the latter is through inter-phase contacts. Lu et al.58 and Whyudi et al.34 demonstrated that particle-wall conductive heat transfer contributes a little while the convective heat transfer without direct-contact (i.e., fluid-wall, particle-fluid-wall) plays a significant role in the fluidized beds. Particles with higher temperature and velocity lead to a serious erosion of cyclone separator, which will be discussed in the next section.

t=5s

t = 10 s

t = 15 s

t = 20 s

Figure 6. Evolution of particle temperature and void fraction, Uf = 6.0 m/s.



Page 22 of 45

According to our previous work, in the circulating fluidized bed, gas-solid flow is categorized as fast fluidization (FF) regime below 7.0 m/s while it is classified as dilute phase transport (DPT) regime above 7.0 m/s72. The gas-solid hydrodynamics is distinctive at these two fluidization regimes. Figure 7 illustrates particle temperature and void fraction distributions at DPT regime. Particles with higher velocities lead to a homogeneous distribution, and a lot of cold gas flow results in lower particle temperature. At the bottom part of riser (ie., dense region), the void fraction is large due to drastic drag force by gas flow from distributor and L-vale15.

t=5s

t = 10 s

t = 15 s

t = 20 s

Figure 7. Evolution of particle temperature and void fraction, Uf = 8.0 m/s.

Figure 8a shows the time-averaged void fraction in the riser. Void fraction is heterogeneous at FF regime while homogeneous at DPT regime. At lower superficial gas velocities (i.e., FF regime), the void fraction is small near the wall regions due to solid back-mixing. In contrast, at higher superficial gas velocities (i.e., DPT regime) the void fraction is almost uniform in the whole riser. However, it is obviously small


Page 23 of 45

in the bottom region due to massive particles recycling from dipleg. Along the center line of riser, the time-averaged solid holdup at various superficial gas velocities is compared with the experimental measurements after nondimensionalization in Figure 8b. It is observed that the simulation results agree well with experiments74. Some discrepancies in the bottom regions stem from different geometry configurations and operating conditions used in the current simulation. The solid holdup gradually declines along the riser height, reaching maximum value in the recycling port. In addition, increasing superficial gas velocity decreases solid holdup above the recycling port. Profiles of the solid holdup are similar with the previous observations in literature49, 75. 1.0

Dimensionless bed height (-)

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


Exp. Jiradilok et al. Sim. Uf = 6.0m/s Sim. Uf = 6.5m/s Sim. Uf = 7.0m/s Sim. Uf = 7.5m/s Sim. Uf = 8.0m/s

0.8

0.6

0.4

0.2

0.0 0.00

0.05 0.10 0.15 Solid holdup (-)

(a)

0.20

(b)

Figure 8. (a) Time-averaged gas volume fraction, slice X = 0 m; (b) time-averaged solid holdup along the bed height.



In order to acquire more quantitative information, the probability density distribution of solid holdup is illustrated in Figure 9a. In contrary to the bubbling fluidized bed21, 76, the peak of distribution augments as the superficial gas velocity augments. Meanwhile, solid holdup distribution becomes narrower. Figure 9b presents average value ( ε s ) and standard deviation (σ) of solid holdup, which are defined as:

εs = σ=

1 Nc ∑ εs,i Nc i=1

(22)

2 Nc 1 ε ε − ( ) ∑ s i s , Nc i=1

(23)

where Nc is the total number of computational cells; εs,i is the solid holdup of computational cell i. The decreasing standard deviation reveals that particles become more uniformly distributed as the superficial gas velocity augments. Meanwhile, decreasing solid holdup reveals that the gas-solid interaction gradually dominates solid behaviors, leading to an alternation from conductive heat transfer to convective heat transfer.

0.20 0.15 0.10 0.05

Average solid holdup (-)

0.25

0.00 0.00

0.026

0.090

Uf = 6.0m/s Uf = 6.5m/s Uf = 7.0m/s Uf = 7.5m/s Uf = 8.0m/s

0.025 0.075

0.024 0.023

0.060

0.022 0.045

0.021 0.020

0.030

0.05

0.10

0.15

0.20

Solid holdup (-)

0.25

0.30

Standard deviation (-)

0.30

Probability density (%)

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 24 of 45

6.0

6.5

7.0

7.5

8.0

Superficial gas velocity (m/s)

(a)

(b)

Figure 9. (a) Probability density distribution of solid holdup; (b) average solid holdup and its standard deviation.


Page 25 of 45

4.2 Solid temperature distribution Figure 10-13 presents quantitative descriptions of heat transfer in the each CFB part and the whole system at two typical superficial gas velocities, focusing on the dynamics evolution of particle temperature at time instant of 5 s, 10 s, 15 s, and 20 s. As illustrated in Figure 10, at 6.0 m/s, the probability density of particle temperature initially shows a double-peak distribution, which evolves and finally forms a single-peak distribution over time. The double-peak distribution is due to temperature difference between particles in the riser and dipleg during start-up processes. After 5.0 s, the system achieves steady state for all superficial gas velocities, thus the distributions appear the single peak at 10 ~ 20 s. From our previous knowledge, it is noted that the system forms steady state at 1.5 s for superficial gas velocity of 8.0 m/s69, thus there are only single-peak distributions for time evolutions. It can be seen that the particle temperature distribution at 8.0 m/s is narrower than that at 6.0 m/s, because particles have uniform temperature at higher superficial gas velocities. 6

6 t = 5.0s t = 10.0s t = 15.0s t = 20.0s

5

5

4 3 2 1 0 298

t = 5.0s t = 10.0s t = 15.0s t = 20.0s

Riser: Uf = 8.0m/s


Riser: Uf = 6.0m/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


4 3 2 1

300

302

304

306

0 298

300

Temperature, °C

302

304

306

Temperature, °C

(a)

(b)

Figure 10. Probability density distribution of particle temperature in the riser: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.



Figure 11 shows the particle temperature distribution in the cyclone at different superficial gas velocities. Generally, in the cyclone, swirling gas-solid flow is heterogeneous and intensive40, 53, and the superficial gas velocity seldom affects solid residence time69, thus the histogram distributions at 6.0 m/s (i.e., FF regime) are similar with that at 8.0 m/s (i.e., DPT regime). It is observed that the translational motion of probability density distributions becomes smaller over time at this two fluidization regimes, owing to the decrease of temperature difference between gas and particles, which remarkably declines the convective heat transfer. At any time instant, particles in the cyclone have higher temperature than that in the riser. 5

5 t = 5.0s t = 10.0s t = 15.0s t = 20.0s

4

3

2

1

0 298

300

302

304

t = 5.0s t = 10.0s t = 15.0s t = 20.0s

Cyclone: Uf = 8.0m/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

Page 26 of 45

306

4

3

2

1

0 298

300

Temperature, °C

302

304

306

Temperature, °C

(a)

(b)

Figure 11. Probability density distribution of particle temperature in the cyclone: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.

Probability density distribution of particle temperature in the dipleg at 5.0 s and 6.0 m/s has a sharp peak as shown in Figure 12a, due to the initial packed bed in the dipleg. Double-peak distribution occurs at 5.0 s under these two fluidization regimes. As shown in Figure 12b, at each time instant, particle temperature has a larger value at 8.0 m/s (i.e., DPT regime) than that at 6.0 m/s (i.e., FF regime). Particles have the


Page 27 of 45

lowest velocity in the dipleg, where the conductive heat transfer plays a dominated role. 5

5

4

3

t = 5.0s t = 10.0s t = 15.0s t = 20.0s

12 10 8 6 4 2 0 298.00

298.25

t = 5.0s t = 10.0s t = 15.0s t = 20.0s

Dipleg: Uf = 8.0m/s




Dipleg: Uf = 6.0m/s

298.50

Temperature, °C

2

4

3

2

1

1

0

0 298

300

302

304

298

306

299

300

Temperature, °C

301

302

303

304

305

306

Temperature, °C

(a)

(b)

Figure 12. Probability density distribution of particle temperature in the dipleg: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.

Particle temperature distribution in the system is illustrated in Figure 13. Obviously, heat transfer in the riser and dipleg contributes a lot for that in the system. At 60. m/s (i.e., FF regime), the histogram distibution has an extended tail, which is not obvious at 8.0 m/s (i.e., DPT regime). 5

5

4

3

2

1

0 298

t = 5.0s t = 10.0s t = 15.0s t = 20.0s

System: Uf = 8.0m/s


t = 5.0s t = 10.0s t = 15.0s t = 20.0s

System: Uf = 6.0m/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


4

3

2

1

300

302

304

306

0 298

300

302

304

306

Temperature, °C

Temperature, °C

(a)

(b)

Figure 13. Probability density distribution of particle temperature in the system: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.



Page 28 of 45

4.3 Impact of superficial gas velocity on temperature evolution Generally, superficial gas velocity affects fluidization behavior and heat transfer property59,

70

. Two parameters are usually used to assess the probability density

distribution of particle temperature, i.e., average particle temperature, and stand deviation22. The latter characterizes the width of distributions. Specifically, the average particle temperature Tp and its standard deviation σ at a specific time instant are formulated as:

Tp =

σ=

Np 1 T ∑ i =1 p ,i Np

2 Np 1 T − T ( ) ∑ p,i p N p i=1

(24)

(25)

here, Np denotes particle number; Tp,i is particle temperature. It is noted from Figure 14 that there is no direct correlation between the superficial gas velocity and heat transfer performance in the riser. It suggests that heat transfer behavior relies heavily on fluidization degrees. Average particle temperature increases linearly over time at lower superficial gas velocities, while it presents wavy profiles at higher ones. It demonstrates that the heat flux is carried out thoroughly at lower superficial gas velocities due to the higher particle-wall contact frequency. As we all know, particles leave the riser, and are separated by cyclone, finally are transported from dipleg to riser, forming a complete circulation. At higher superficial gas velocities, time needed for the circulation decreases, showing a great influence on heat transfer behaviors. Standard deviations at all superficial gas velocities increase sharply due to start-up processes, and then oscillate around constant values.


Page 29 of 45

Increasing superficial gas velocity decreases the standard deviations, due to more

Standard deviation of particle temperature (°C)

uniform particle temperature distribution in the riser.

Average particle temperature (°C)

302.5

Riser

302.0 301.5 301.0 300.5 300.0 299.5

Uf = 6.0 m/s Uf = 6.5 m/s Uf = 7.0 m/s Uf = 7.5 m/s Uf = 8.0 m/s

299.0 298.5 298.0 0

4

8

12

16

0.8 Uf = 6.0 m/s Uf = 6.5 m/s Uf = 7.0 m/s Uf = 7.5 m/s Uf = 8.0 m/s

Riser 0.6

0.4

0.2

0.0

20

0

4

8

12

16

20

Time (s)

Time (s)

(a)

(b)

Figure 14. Particle temperature evolution in the riser: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.

As illustrated in Figure 15a, profiles of average particle temperature increase sharply and then gradually augment in the cyclone. Turning points depend on the time needed for establishing equilibrium state. Different fluidization regimes (i.e., FF and DPT) of the CFB lead to distinctive fluctuations of temperature curves. Combining large solid velocity and small solid residence time properties in the cyclone, the


standard deviations of temperature are relatively larger than that in other components. 302.5


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


Cyclone

302.0 301.5 301.0 300.5 300.0 299.5


299.0 298.5 298.0 0

4

8

12

16

20

10 Uf = 6.0 m/s Uf = 6.5 m/s Uf = 7.0 m/s Uf = 7.5 m/s Uf = 8.0 m/s

Cyclone 8

6

4

2

0 0

4

8

12

16

Time (s)

Time (s)

(a)

(b)

Figure 15. Particle temperature evolution in the cyclone: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.


20


As observed in Figure 16a, the increase rate of average particle temperature gradually deceases. Temperature difference between each particle and surrounding ones declines from the initial state to equilibrium state in the dipleg. Based on conductive heat transfer equations, the smaller the temperature difference is, the less the heat flux transfers. Due to the lower solid velocity in the dipleg16, 77, profiles of average particle temperature and standard deviation are smooth. As shown in Figure


16b, increasing superficial gas velocity suppresses standard deviations. 302.5


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

Page 30 of 45

Dipleg

302.0 301.5 301.0 300.5 300.0 299.5


299.0 298.5 298.0 0

4

8

12

16

20


Dipleg 0.6

0.4

0.2

0.0 0

4

Time (s)

8

12

16

20

Time (s)

(a)

(b)

Figure 16. Particle temperature evolution in the dipleg: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.

Generally, particle temperature evolutions in the system combine the effect of that in the each single part. As illustrated in Figure 17a, the slope of average particle temperature curves gradually decreases. It is known that the walls are set as adiabatic boundary conditions, thus the heat flux from the heating section of riser is thoroughly transferred to particles and gas flow in the system. However, some hot gas flow leaves the circulating fluidized bed from cyclone separator, carrying the corresponding heat flux originally belonging to the system. It makes the average particle temperature curves non-linear. In view of convective heat transfer equations, more heat flux


Page 31 of 45

transfers via wall-fluid-particle paths as the superficial gas velocity enlarges. The standard deviation in the system as shown in Figure 17b depends on it in the riser and


dipleg. 302.5


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


System

302.0 301.5 301.0 300.5 300.0 299.5


299.0 298.5 298.0 0

4

8

12

16

20


System 0.6

0.4

0.2

0.0 0

4

Time (s)

8

12

16

20

Time (s)

(a)

(b)

Figure 17. Particle temperature evolution in the system: (a) Uf = 6.0 m/s; (b) Uf = 8.0 m/s.

Figure 18 shows that ∆T1 >∆T2 >∆T3, indicating that the heating rate of particles decreases over time, owing to the decrease of gas-solid temperature difference. Moreover, as the superficial gas velocity aggrandizes, the average temperature enlarges in the FF regime (i.e., Uf = 6.0 ~ 7.0 m/s) while it decreases in the DPT regime (i.e., Uf = 7.0 ~ 8.0 m/s). In the FF regime, the larger the superficial gas velocity is, the more intensive gas-solid flow becomes. It enforces the convective heat transfer via wall-fluid-particle path and conductive heat transfer through inter-particle contacts. In the DPT regime, the increment of superficial gas velocity improves flow uniformity. It strengthens the fluid-wall convective heat transfer, thus more heat flux is carried out of the system.


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

Average particle temperature (K)


302.0

t = 20.0 s

301.5 301.0 300.5

∆T3

t = 15.0 s

∆T2

t = 10.0 s

∆T1

t = 5.0 s

300.0 299.5 299.0 298.5 6.0

6.5

7.0

7.5

8.0

Superficial gas velocity (m/s)

Figure 18. Impact of superficial gas velocity on average particle temperature at various time instants.

4.4 Impact of superficial gas velocity on cyclone erosion Figure 19 illustrates the erosion quantity on cyclone surface under different superficial gas velocities. As we all know, erosion quantity and erosion position are usually used to evaluate erosion degree41. It is observed that the erosion mainly occurs at the cylinder and cone parts. The erosion quantity increases as the superficial gas velocity increases, due to more intensive particle-wall collisions. Under all of superficial gas velocities, erosion position concentrates in a strand region, from the upper left zone to lower right zone. These strands have a higher particle concentration, which exacerbate the particle-wall collisions. At the cylinder part, severe erosion locates in the top region. In addition, as the superficial gas velocity augments, erosion position gradually translates from the right zone to left zone, closer to the entrance, where is the first contact region between particle and wall. This tendency agrees well with the observation41. At the cone part, erosion position gradually concentrates in a local region (i.e., the inter-section of cone part and cylinder part) as the superficial gas velocity aggrandizes. At lower superficial gas velocity, the erosion degree is more


Page 32 of 45

Page 33 of 45 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


serious at the cone part than that at the cylinder part. At higher superficial gas velocity, it presents the opposite tendency.

Uf = 6.0 m/s

Uf = 6.5 m/s

Uf = 7.0 m/s

Uf = 7.5 m/s

Uf = 8.0 m/s

Figure 19. Impact of superficial gas velocity on cyclone erosion (E: accumulated erosion quantity, unit: 10-9m3).

Based on Finnie erosion model as formulated in Equation (20, 21), the erosion quantity relies on particle-wall impact angle, impact velocity, and material properties of particle and wall63. In other words, the erosion degree has a great dependence on local gas-solid flow dynamics. Thus, the time-averaged solid flux is used to characterize the erosion behavior. Figure 20 shows the contour and vector plots of time-averaged solid flux φ(x), which combines the solid volume fraction εp(x,t), solid velocity vp(x,t), and solid density ρp: φ p (x ) =

1 Nt

∑

Nt 0

(ε

p

( x, t ) ρ p v p ( x, t ))

where, Nt is the total number of time intervals.


(26)


(a)

(b)

(c)

Figure 20. (a) Solid flux (SF, kg/(m2·s)), (b) solid volume fraction (εp, -); (c) solid velocity (Us, m/s) in the cyclone seperator, Uf = 6.0 m/s.

It is observed that the solid flux presents a strand shape (Figure 20a), corresponding to the erosion tendency. In view of the slices of solid flux, smaller solid flux in the upper region is due to higher solid velocity (Figure 20c) but lower solid volume fraction (Figure 20b). However, although solid velocity is small in the lower region, the large solid volume fraction leads to a large solid flux value. 1.0

1.25

Sim. from current work Exp. from Hoekstra et al.(2000) Exp. from Derksen et al.(2008)

Dimensionless axial velocity (-)

Dimensionless tangential velocity (-)

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 34 of 45

0.5

0.0

-0.5

Sim. from current work Sim. from Wan et al.(2008) Sim. from Zhou et al.(2018)

0.75 0.50 0.25 0.00

-0.25

-1.0 -0.6

1.00

-0.4

-0.2

0.0

0.2

0.4

0.6

-0.50 -0.6

-0.4

-0.2

0.0

X/R (-)

X/R (-)

(a)

(b)


0.2

0.4

0.6

Page 35 of 45 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 21. Radial profiles of gas velocities at H2 = 1.12 m in the cyclone, compared with experiment and simulation data in the literature, Uf = 6.0 m/s: (a) tangential component; (b) axial component.

For assessing whether the LES-DEM method can accurately describe intensely swirling flow in the cyclone, radial profiles of gas velocities are compared with experiment and simulation in the literature. Gas velocity values are normalized by the superficial gas velocity, Uf. It can be observed from Figure 21 that the current results agree well with the experimental measurements53,

78

and simulation results79,

80

.

Some discrepancies close to the wall regions (Figure 21b) are attributed to the different geometry and operating conditions between the current work and other studies. However, in view of the turbulent and dramatic swirling flow in the cyclone, predictions from LES-DEM method are reasonable and acceptable.

5. Conclusions In the present paper, we successfully integrate heat transfer and erosion sub-models into the LES-DEM method with fully model validations, which is then applied to investigate heat transfer and erosion characteristics in a full-loop CFB at the particle-scale level. Via simulation results, conclusions can be drawn: (1) Increasing superficial gas velocity decreases solid holdup and improves flow uniformity. Probability density distributions of particle temperature in different components show distinctive features. Heat transfer in the riser and dipleg contributes a lot for that in the system. (2) Particle temperature increases gradually in the riser and dipleg, while it



initially increases sharply and then augments gradually in the cyclone. Time evolution of average particle temperature is non-linear due to heat loss from cyclone separator. (3) Particle heating rate declines over time. The larger the superficial gas velocity is, the higher the average particle temperature becomes in the FF regime, and it shows opposite tendency in the DPT regime. (4) Erosion region of the cyclone concentrates in the inter-section of cylinder and cone parts with the increase of superficial gas velocity. Cyclone erosion has a close relationship with the solid flux distribution. As a supplement to the work from Wahyudi et al.34, the current work focuses on particle temperature evolution and cyclone erosion at different superficial gas velocities. The impact of other operating conditions (e.g., pressure, solid circulating rate, and material category) and sub-models (e.g., drag force model, contact model, and turbulence model) on heat transfer and erosion characteristics in the full-loop CFB underscores the need for more simulation studies in further work. The insights emanating from present work are convinced worthwhile not only for further academic understanding but also for the design and optimization of such apparatuses in industrial fields.

Acknowledgements The authors sincerely acknowledge the National Key R&D Program of China (No. 2016YFB0600102) for supporting this work.

Nomenclature


Page 36 of 45

Page 37 of 45 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


Ac,ij

Particle-particle contact area, m2

CD

Drag force coefficient

cp,f

Fluid specific heat capacity, J/(kg·K)

cp,i

Particle specific heat capacity, J/(kg·K)

Cs

Smagorinsky constant

dp,i

Particle diameter, m

dvi/dt

Translational acceleration, m/s2

dωi/dt

Rotational acceleration, rad/s2

E

Erosion quantity, m3

Fc,ij

Contact force, N

Fcn,ij

Normal contact force, N

Fct,ij

Tangential contact force, N

Fd,i

Drag force, N

Fd,ij

Damping force, N

Fdn,ij

Normal damping force, N

Fdt,ij

Tangential damping force, N

Ffp

Source item of momentum, kg/(m·s2)

Fp,i

Pressure force, N

g

Gravitational acceleration, m/s2

G*

Equivalent shear modulus, Pa

hi,f

Particle-fluid heat transfer coefficient, W/(m2·K)

hi,j

Particle-particle heat transfer coefficient, W/(m2·K)



kf

Fluid thermal conductivity, W/(m·K)

kp,i, kp,j

Particle thermal conductivity, W/(m·K)

m*

Effective particle mass, kg

mi, mj

Particle mass, kg

n

Normal unit vector

Nup,i

Particle Nusselt number

p

Fluid pressure, Pa

PH

Vickers hardness of material, Pa

Pr

Prandtl number

Prt

Turbulent Prandtl number

Qfp

Volumetric heat flux rate, J/(s·m3)

Qi,f

Particle-fluid convective heat flux, W

Qi,j

Particle-particle conductive heat flux, W

Qi,wall

Particle-wall conductive heat flux, W

R*

Effective radius, m

Ri, Rj

Particle radius, m

Rep,i

Particle Reynolds number

Sij

Filtered strain rate, N/m

Tf

Fluid temperature, K

Tp

Particle temperature, K

Tt,ij

Torque due to tangential force, N·m

Tt,ij

Rolling torque, N·m


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t

Time instant, s

t

Tengential unit vector

Ubg

Backgroud superfical gas velcotiy, m/s

uf

Fluid velocity, m/s

Us

Solid velocity, m/s

Us_SD

Standard deviation of solid velocity, m/s

vi

Particle velocity, m/s

Vp,i

Particle volume, m3

∆V

Cell volume, m3

Y*

Effective Young’s modulus, MPa

Yi, Yj

Particle Young’s modulus, MPa

Greek symbols e

Restitution coefficient

εf

Fluid void fraction

εp

Solid volume fraction

βi

inter-phase momentum exchange coefficient, kg/(m3·s)

δ

Displacement of particle overlap, m

δij

Kronecker delta function

µ

Sliding friction coefficient

µf

Fluid viscous efficient, kg/(m·s)

µr

Rolling friction coefficient



µt

Eddy viscous coefficient, kg/(m·s)

ρf

fluid density, kg/m3

θ

Contact angle, º

τij

Stress tensor, Pa

τf,,ij, τt,,ij

Viscous stress tensor and sub-grid stress tensor, Pa

∆

Sub-grid characteristic length scale, m

Subscripts f

Fluid phase

i

Particle i

j

Particle j

n

Variable in normal direction

p

Particle phase

t

Variable in tangential component

Acronyms CFB

Circulating fluidized bed

CFD

Computational fluid dynamics

DEM

Discrete element method

DNS

Direct numerical simulation

DPT

Dilute phase transport

FF

Fast fluidization

LES

Large eddy simulation


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PISO

pressure implicit with splitting of operator

RANS

Reynolds-averaged Navier-Stokes

TFM

Two-fluid model

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For Table of Contents Only Erosion

5 t = 5.0s t = 10.0s t = 15.0s t = 20.0s



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


Heat transfer

4

3

2

1

0 298

300

302

Temperature, °C


304

306

Particle-Scale Investigation of Heat Transfer and Erosion

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