Fluid hydrodynamic characteristics in supercritical water fluidized bed: A DEM simulation study

Chemical Engineering Science 117 (2014) 283–292

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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces

Fluid hydrodynamic characteristics in supercritical water fluidized bed: A DEM simulation study Youjun Lu n, Jikai Huang, Pengfei Zheng State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi, China

H I G H L I G H T S


DEM simulation of fluid hydrodynamic in SCW fluidized bed was performed.
We found some new hydrodynamic phenomenon in SCW fluidized bed.
The results are very useful for the operation and design of SCW fluidized bed.

art ic l e i nf o

a b s t r a c t

Article history: Received 15 April 2014 Received in revised form 1 June 2014 Accepted 18 June 2014 Available online 23 June 2014

Supercritical water (SCW) fluidized bed is a new and promising reactor for gasification of wet biomass. In this paper, the particle distribution and fluid hydrodynamic characteristics in SCW fluidized bed were studied comprehensively by the discrete element method (DEM). The results from DEM simulation show that there exists a non-bubbling fluidization when superficial velocity is in the range of minimum fluidization velocity and minimum bubbling velocity although the particles are categorized as Geldart B. Particle circulation, including internal circulation and gross circulation are responsible for solids mixing in SCW fluidized bed. Particle circulation in SCW fluidized bed is not only induced by bubble motion, but also influenced by the vortices in bubbles. Other characteristics such as voidage distribution, particle and fluid velocity, granular temperature, and particle Reynolds number in SCW fluidized bed, are also discussed. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Supercritical water fluidized bed Discrete element method Particle distribution Fluid hydrodynamic

1. Introduction With the extensive consuming of fossil fuel, hydrogen is gaining more and more attention worldwide as an alternative fuel. A promising and clean technology to produce hydrogen is thermochemical gasification of biomass in supercritical water (Hao et al., 2003; Matsumura et al., 2005). Supercritical water (SCW) is a special kind of fluid that can gasify wet biomass without the energy-consuming drying process, and the gas products are mainly hydrogen and carbon dioxide. In previous work (Lu et al., 2008), we successfully developed a SCW fluidized bed to gasify wet biomass, avoiding reactor plugging which often takes place in the tubular reactor. However, during the process of experiments some unexpected circumstances occurred such as the inhomogeneous distribution of temperature in SCW fluidized bed, instability of the gaseous product, particles overflowing from the reactor and so on (Lu et al., 2013). All these problems result from a lack of

n

Corresponding author. Tel.: þ 86 29 82664345; fax: þ 86 29 8266 9033. E-mail address: [email protected] (Y. Lu).

http://dx.doi.org/10.1016/j.ces.2014.06.032 0009-2509/& 2014 Elsevier Ltd. All rights reserved.

optimized design and operation in SCW fluidized bed. The optimization of design and operation should be based on the comprehensive understanding of particle distribution, fluid hydrodynamic and heat transfer characteristics in SCW fluidized bed. Therefore an in-depth investigation of the fluid hydrodynamic characteristics in SCW fluidized bed is very necessary. There are a large number of investigations about traditional fluidized bed, but little work has focused on high-pressure and high-temperature fluidized bed and work on SCW fluidized bed is even rarer. Liu et al. (1996) studied liquid–solid fluidized bed, in which solid particles (Geldart groups A, B and D) were fluidized by supercritical CO2 fluid. A criterion was also proposed to determine the fluidization regime. Marzocchella and Salatino (2000) studied the fluidization characteristics of two granular materials belonging to Geldart groups A and B powders in CO2 at 308 K and at 0.1– 8 MPa. Vogt et al. (2005) carried out a comprehensive experiment to investigate the fluidization behavior with supercritical carbon dioxide at pressures up to 30 MPa for various solids (Geldart A and B powders). Results showed that Ergun's equation is also applicable to the flow of a supercritical fluid through a fixed bed and that the Wen and Yu relationship can be used for the determination of

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the minimum fluidization velocity (umf). Experimental correlations for homogeneous bed expansion, minimum bubbling velocity (umb) were also derived. When it comes to SCW fluidized bed, Potic et al. (2005) introduced the concept of a micro-fluidized bed, which was a cylindrical quartz reactor with an internal diameter of only 1 mm used for process conditions up to 773 K and 244 bar. In our previous work (Lu et al., 2013), the hydrodynamic of a SCW fluidized bed with internal diameter 35 mm and length 600 mm were studied by experiment. The experimental condition was set within the range of 633–693 K and 23–27 MPa and an experimental correlation about the minimum fluidization velocity was obtained. Because of the extreme environment in SCW fluidized bed, experimental investigation is very difficult to carry out and usually expensive. In recent years, thanks to the rapid development of computer technology, numerical simulation is becoming a more and more important and powerful tool to study fluidized bed. There are mainly two methods available in fluidized bed modeling: the two fluid method (TFM) and discrete element method (DEM). Particle phase and fluid phase are treated as interpenetrating continuous medium in TFM, and the hydrodynamic model conservation of mass and momentum was described by conservation equations respectively (Gidaspow and Ettehadieh, 1983). Compared with TFM, DEM allows the dynamic simulation of solid phase motion by tracking individual particle along the system. DEM was first proposed by Cundall and Strack (1979) and first combined with computational fluid dynamic (CFD) to study fluidized bed by Tsuji et al. (1993). Recently, the DEM–CFD method has been employed by many researchers to investigate traditional fluidized bed (Xu and Yu, 1997; Tsuji et al., 1998; Kaneko et al., 1999; Rhodes et al., 2001a,b; Kafui et al., 2002; Limtrakul et al., 2004; Zhu et al., 2008; Darabi et al., 2011; He et al., 2012; Yang et al., 2013). In present work, the DEM method was used to study the particle distribution and fluid hydrodynamics characteristics in SCW fluidized bed. First, the relationship between bed pressure drop and superficial velocity was established by increasing the superficial velocity (step by step). The minimum fluidization point was located at the turning point in the relation curve of bed pressure drop and time. Then the minimum bubbling velocity was also obtained at the expansion curve by figuring out the deviation point from homogeneous fluidization regime. The axial velocity distribution of fluid and particles were made comparison to estimate the influence of fluid phase on particle motion. What's more, many other characteristics in SCW fluidized bed were shown, such as voidage distribution, granular temperature, particle Reynolds number and so on.

2. Model description and the numerical method 2.1. Model description CFD was coupled with DEM to study SCW fluidized bed. In the CFD–DEM model, particles and fluid were considered as discrete phase and continuum phase, respectively. Each particle is tracked by giving an identity code, whose movement was acquired by solving Newton's second law of motion. Each particle has two types of motion, i.e. translational and rotational motion. The motion of each individual particle is governed by the laws of conservation of linear momentum (Newton's second law of motion) and angular momentum. These equations for the ith particle are given by the following equation: mi Ii

d vi ¼ mi g þ F d  V i ∇P þ F c dt

d ωi ¼ Ti dt

ð1Þ ð2Þ

where mi is the mass of the particle, g is the acceleration due to gravity, Vi is the volume of particle, and P is the gas-phase pressure, Fd is the drag force. Fc is the contact force, including particle–particle contact force and particle-wall contact force. Ii, νi, and ωi are the moment of inertia, linear velocity and angular velocity, of the ith particle respectively. Ti is the torque arising from the tangential components of the contact force of the particle. The fluid phase was treated as continuous phase whose motion was defined by equations of continuity and momentum balance based on the local mean variables on fluid cell. What's more, heat transfer and chemical reaction phenomenon are not taken into consideration in this paper. The constitutive equations of fluid phase were expressed as follow: ∂ε þ ∇ðεuf Þ ¼ 0 ∂t ∂ðρf εuf Þ ∂t

þ∇ðρf εuf uf Þ ¼  ε∇P  F f ;p þ ∇ðετ Þ þ ρf εg

ð3Þ ð4Þ

where ρf, ε, uf are the density, volume fraction and velocity of continuous phase, respectively; P is the pressure, Ff,p is the volumetric fluid–particle interaction force, and τ is the viscous stress tensor. Generally, the volumetric drag force between fluid and particle phase in fluid–solid systems is calculated from the product of a fluid–particle interaction coefficient and the slip velocity between two phases. F f ;p ¼ βðuf  vp Þ

ð5Þ

where νp is the mean velocity of the particles in unit volume. Numerous empirical correlations for calculating the fluid–particle interaction coefficient β have been reported in literature, such as Wen and Yu (1966), Gidaspow (1994) and Syamlal and O'Brien (1989), which are frequently adopted in fluidized fluid–particle suspension simulation. The correlation given by Gidaspow (1994) was used in this paper, which is a combination of the work of Ergun (1952) and Wen and Yu (1966). The equation of Ergun (1952) is found applicable in SCW fluidized bed through a fixed bed according to our experiment results (Lu et al., 2013). The equation of Wen and Yu (1966) and Ergun (1952) are widely adopted in investigation of gas–solid fluidized bed, liquid–solid fluidized bed and also fluidized bed under elevated pressure or supercritical CO2 conditions. The correlation is given by the following equation: 8 3εð1  εÞρf > > C d juf  vi jε  2:65 ε Z 0:8 > > < 4dp ð6Þ β ¼ 150ð1  εÞ2 μ 1:75ρ ð1  εÞju  v j > i f f f > > þ ε o 0:8 > 2 : dp dp ε The standard drag coefficient Cd is expressed as follows: 8 < 24 ð1 þ Re0:687 Þ Re o 1000 C d ¼ Re : 0:44 Re Z 1000

ð7Þ

The Reynolds number (Re) of particle i is as follows: Re ¼

ρf εjuf  vi jdp μf

ð8Þ

There are two methods to deal with particle contact: hardsphere model proposed by Allen and Tildesley (1989) and softsphere model proposed by Cundall and Strack (1979). It is nowadays common practice to use the soft-sphere approach to simulate the collision dynamics in dense particulate flow (Tsuji et al., 1993). In the soft-sphere approach, the contact force Fc between two spherical particles can be modeled by the simple concept consist of spring, dash-pot and friction slider as shown in Fig. 1. Therefore, the contact force between two particles depends on the parameters of spring constant, damping and friction coefficients which

Y. Lu et al. / Chemical Engineering Science 117 (2014) 283–292

285

Fig. 1. Models of contact forces.(a) Normal force and (b) tangential force.

can be obtained from the physical properties of the particles. But the shortcoming of soft-sphere model is significant that the timeconsuming is enormous. The details of the soft-sphere approach were illustrated in previous work (Tsuji et al., 1993; Xu and Yu, 1997). 2.2. Numerical simulation method The fluidized bed geometry chosen for the current study is 35 mm wide and 210 mm high with a thickness of 0.5 mm. The computational domain is discretized by uniform grids of 1.75 mm  1.75 mm, i.e. the grid number distribution is 20 in width and 120 in height. 10,000 spherical particles with diameter of 0.5 mm and density of 2580 kg/m3 are used in the simulations. The bottom boundary was defined as a prescribed velocity-inlet condition whereas at the top boundary a prescribed pressure was imposed. The initial bed was obtained by the free sedimentation of particles which were distributed randomly in fluidized bed at first, and the initial bed height H0 is 6.63 cm with the bed voidage 0.433. The Semi-implicit Method for Pressure-Linked Equations (SIMPLE) algorithm was adopted to solve the equations of fluid motion and the convergence criterion is 0.001. All used simulation parameters are listed in Table 1. The key to a successful numerical simulation of the hydrodynamic in fluidized bed is establishing a true relationship between the bed pressure drop and the superficial fluid velocity. If the relationship is obtained by following the procedures used in our previous physical experiments (Lu et al., 2013) which involve controlled increase (step by step) in superficial fluid velocity and the system is allowed to reach equilibrium after each increment in velocity, an excessive CPU time may be required in DEM simulation. To avoid this, we adopt a strategy proposed by Rhodes et al. (2001b), in which the constant fluid velocity is maintained for the shortest time possible without compromising the accuracy of the results. However, the effect of pressure fluctuations caused by the velocity increase cannot be eliminated if the duration for the constant velocity is too small, or if the increment in gas velocity is too large. According to the suggestion of Rhodes et al. (2001b), we set the increment of fluid velocity at approximately one-fiftieth of the estimated minimum fluidization velocity, and the duration for the superficial velocity to be maintained constant after each

increment was set at 2.0 s. In order to verify the rationality of this velocity increase strategy, a “simulation experiment” was carried out that the velocity increment is maintained 0.2 cm/s while the duration is 1.0 s. The simulation results show that the deviation of bed pressure drop between two simulation condition is within 5.8% in fixed bed and within 0.6% after fluidization. Therefore, the time duration per step was set at 2.0 s, which can eliminate the effects caused by the velocity increase. Also, we obtained enough data to make the results more convincing from a statistical standpoint. The minimum fluidization velocity (umf) can be determined from the simulated relationship between the bed pressure drop and superficial velocity. We obtained the minimum fluidization velocity with different conditions by adopting the strategy discussed above. Fig. 2 shows a comparison of the simulation results with the empirical correlation in our previous work (Lu et al., 2013). As can be seen from the figure, the simulated results fit quite well with the empirical correlation, which conforms the accuracy of the model.

3. Results and discussion 3.1. Bed pressure drop versus superficial fluid velocity The relation curve of bed pressure drop and superficial velocity versus time is shown in Fig. 3. As can be seen from the figure, the onset of fluidization is at 20 s with the minimum fluidization velocity (umf) of 3.9 cm/s, which corresponds to the turning point in the curve. What's more, it can be observed that the curve of bed pressure drop versus time can be divided into three stages. Stage I, fixed bed regime with the time between 0 and 20 s and superficial velocity between 1.9 and 3.9 cm/s, in which the superficial velocity is lower than umf. The bed pressure drop increases step by step with the superficial velocity and without fluctuation. Stage II, homogeneous fluidization regime with the time between 20 and 44 s and superficial velocity between 3.9 and 6.3 cm/s, in which the superficial velocity is in the range of the minimum fluidization velocity and minimum bubbling velocity (umb). The pressure drop stops increasing with superficial velocity, but fluctuates around a fixed value and decays rapidly.

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Table 1 Physical and numerical parameters. Term

Value

Particle phase Particle shape Particle density Particle diameter Number of particles Restitution coefficient Spring constant Friction coefficient Particle–particle Particle–wall Damping coefficient Particle–particle Particle–wall

Spherical 2580 kg/m3 5  10  4 m 10,000 0.9 5  104 N/m 0.3 0.2 0.18 0.22

Term

Value

Fluid phase Pressure Temperature Density Viscosity Computational domain Bed thickness Initial bed height Solid phase time step Gas phase time step Minimum fluidization velocity Minimum fluidization voidage Grid size

25 MPa 659 K 283.79 kg/m3 3.67  10  5 Pa s 35 mm  210 mm 5  10  4 m 6.63  10  2 m 1  10  6 s 1  10  5 s 39 mm/s 0.433 1.75 mm  1.75 mm

1200

6 1: P=24MPa,T=659K 2: P=25MPa,T=659K 3: P=25MPa,T=689K 4: P=25MPa,T=709K 5: P=26MPa,T=659K

1000

Pressure drop (Pa)

umf,cor(cm/s)

5

4 3

1

4 2

3

800

600

400

5

200 0.5

2 2

3

4

5

6

umf,sim(cm/s)

15

1600 1400

5

1000 800

0

u (cm/s)

Pressure drop (Pa)

10 1200

Stage I

Stage III

Stage II

-5 400

umf

umb

200 0

20

40

60

80

1.5

2.0

2.5

3.0

3.5

4.0

u/umf Fig. 4. Bed pressure drop versus fluidization number.

Fig. 2. Comparison of minimum fluidization velocity between simulated results (umf ;sim ) and empirical correlation (umf ;cor ).

600

1.0

100

-10 120

time(s) Fig. 3. Bed pressure drop and superficial velocity versus time.

Stage III, bubbling fluidization regime with the time after 44 s and superficial velocity bigger than 6.3 cm/s, i.e. the minimum bubbling velocity. In which the curve fluctuates more violently with the increase of superficial velocity as more and more bubbles nucleate, grow up and creak in SCW fluidized bed. Instantaneous bed pressure drop under each superficial velocity was time-averaged, and the relationship between bed pressure drop and fluidization number (superficial velocity divided by umf) was shown in Fig. 4. It can be figured out that bed pressure drop increases with the increase of superficial velocity before the minimum fluidization point, then the curve becomes flat after

the superficial velocity exceeds umf. In present work, bed pressure drop was obtained by subtracting surface pressure from bottom pressure of the fluidized bed, then subtracted by the head of liquid corresponding to bed height. The bed pressure drop increases slightly with superficial velocity after fluidization because of the increasing viscous resistance by walls. Three snapshots of particles in the three stages discussed above are shown in Fig. 5. Fig. 5a shows the fixed bed with the superficial velocity 0.8umf, which belongs to stage I and almost no particle moves. Fig. 5b shows the homogeneous fluidization regime when the superficial velocity is 1.5umf. It can be observed that although the particles used in this paper are certainly categorized as Geldart group B under ambient conditions, there exists a non-bubbling fluidization in SCW fluidized bed when the superficial velocity is in the range of the minimum fluidization velocity and minimum bubbling velocity. The bubbling fluidization regime is shown in Fig. 5c when the superficial velocity is 2.5umf. Bubbles are quite small and scattered in SCW fluidized bed and the bed expansion is more obvious. The distribution characteristics of bubbles benefits the mixing state of fluid phase and solid phase. The power spectrum of SCW fluidized bed pressure drop is obtained by fast Fourier transform(FFT) as shown in Fig. 6 when the superficial velocity is 2.5umf. It can be seen from the figure that the dominant frequency is 6.25 Hz. Generally speaking, the fluidized bed pressure drop fluctuation is mainly caused by dynamics of the random motion of heterogeneities such as gas pockets (bubbles) and particle clusters in fluidized gas–solid suspensions (He et al., 1997; Xu et al., 1998). The power of low frequency, which represents the influence of bubble, is higher than that of high frequency which stand for particle clusters or particle collision.

Y. Lu et al. / Chemical Engineering Science 117 (2014) 283–292

14

14

14

u=0.8umf

Stage II

Stage I

10

10

10

8

6

Bed height(cm)

12

Bed height(cm)

12

Bed height(cm)

u=2.5umf Stage III

u=1.5umf

12

8

6

8

6

4

4

4

2

2

2

0

0

0 -1

287

0

-1

1

x/R

0

1

-1

0

1

x/R

x/R Fig. 5. Snapshots of particles in various fluidization regimes.

0.20

0.8 This work Richardson-Zaki (1954) Vogt et al. (2005)

0.7 0.15

Voidage

Power

n=2.39

0.10

0.6

Stage I

Stage II

Stage III

n=2.29

n=1.6

0.5 0.05

umb

umf

0.00 0

5

10

15

20

25

30

35

40

45

0.4

50

3

Frequency(Hz)

3.2. Bed expansion The overall voidage of SCW fluidized bed is plotted over superficial velocity as shown in Fig. 7, which is expressed in a double logarithmic coordinate. Three stages: fixed bed, homogeneous fluidization and bubbling fluidization discussed above can be also found in Fig. 7. In fixed bed, the bed voidage remains constant with the increasing of superficial velocity before incipient fluidization point. The minimum fluidization velocity can be figured out 3.9 cm/s, which is in agreement with previous results

5

6

7

8

9 10 11 12 13 14

u (cm/s)

Fig. 6. Power spectrum of bed pressure drop at u ¼ 2:5umf .

This indicates that the fluid hydrodynamics in SCW fluidized bed are mainly dominated by bubble dynamics. Besides, the power in frequency from 20 to 50 Hz indicates that fluid hydrodynamic in SCW fluidized is influenced by particle clusters or collision in a certain extent, while that influence can be usually neglected in traditional gas fluidized bed under low operating velocity.

4

Fig. 7. Bed expansion with superficial velocity.

of bed pressure drop. In homogeneous fluidization regime, it is found that bed voidage increases linearly with superficial velocity in double logarithmic coordinate, and the deviation from homogeneous fluidization indicates the onset of bubbling fluidization. Besides, the minimum bubbling velocity can be figured out 6.3 cm/s, i.e. 1.62umf, with the minimum bubbling fluidization voidage 0.559. Then the trend of bed voidage over superficial velocity is no longer obvious. The minimum fluidization velocity separates from the minimum bubbling velocity of Geldart B particle in SCW fluidized bed, which is different from fluidized bed in ambient conditions. In general, Richardson–Zaki relationship (1954) was used to describe the expansion in homogeneous fluidization regime and the following relationship is given: u ¼ εn ut

ð9Þ

Y. Lu et al. / Chemical Engineering Science 117 (2014) 283–292

Here the exponent n is calculated as follows: 8 dp > > > Ret o 0:2 4:65 þ19:5 > > D  > > > > dp >  0:03 > 0:2 o Ret o 1 > > 4:35 þ 17:5 D Ret <  n¼  dp > > Ret 0:1 1 o Ret o 200 4:35 þ 18 > > D > > > >  0:1 > > 200 o Ret o500 4:45 URet > > > : 2:39 Ret 4 500

8

Vogt et al. (2005) proposed an empirical correlation for homogeneous bed expansion in supercritical CO2 fluidized bed which was given n ¼ 11:8Ret 0:23

The frequency distribution of voidage under different operating conditions (u ¼ 1:5 umf ; 2:5 umf ; 3:5 umf ) are displayed in Fig. 8. As can be seen from the figure, the distributions under different velocities are all single-peak and the peak moves towards higher value with the increasing of superficial velocity. When the superficial velocity is low (u ¼ 1:5 umf ), voidage distributes quite uniformly in the bed, which is in accordance with the feature of homogeneous fluidization of fluidized bed. With the increasing of superficial velocity, more fluid phase penetrates into emulsion phase and more bubbles nucleate and grow up in SCW fluidized bed, and results in the increase of bed voidage. Here the singlepeak feature of voidage distribution in bubbling fluidization indicates the small difference between emulsion phase and bubbles, and therefore a high fluidization quality in SCW fluidized bed is achieved. 3.4. Fluid and particle velocity The lateral distributions of time-averaged axial velocity of particle and fluid in SCW fluidized bed (at h ¼2 cm, 6 cm and 10 cm) are shown in Fig. 9 when superficial velocity is 2:5 umf . As can be seen from Fig. 9a that particle velocity distribution differs a 0.35 u=1.5umf

Frequency ratio

u=2.5umf u=3.5umf

0.25 0.20 0.15 0.10

0 -4 h=2cm h=6cm h=10cm

-8 -12

-0.5

0.0

0.5

1.0

x/R 20

Vertical velocity of SCW(cm/s)

3.3. Frequency distribution of voidage

4

-16 -1.0

ð10Þ

A comparison of the simulated relationship of bed voidage and superficial velocity (ε–u) with the empirical correlations are also shown in Fig. 7. It can be seen that the homogeneous bed expansion under SCW condition cannot be described by the result of Richardson and Zaki (1954) or Vogt et al. (2005) properly and more experimental and simulation work are needed to conform this result.

0.30

Vertical velocity of particle(cm/s)

288

16

12

8 h=2cm h=6cm h=10cm

4

0 -1.0

-0.5

0.0

0.5

1.0

x/R Fig. 9. Time-averaged axial velocity of particle phase(a) and fluid phase (b).

lot at various bed height. Particle average velocity is positive in the center while negative near the walls, indicating that there exists circulation of particle phase in SCW fluidized bed with ascending in bed center and descending near the walls. In contrast, as can be seen from Fig. 9b that the averaged fluid velocity at various bed heights is always positive. At the bottom of bed (h ¼2 cm), because particle and fluid motion are mainly influenced by the uniform distribution of the distributer, the variation of particle and fluid velocity along bed width are relatively small, except near the walls. At the middle of bed (h¼6 cm) because of the viscous resistance induced by the walls, fluid accumulates in axial region and results in a quasi-parabolic distribution of fluid axial velocity with higher in axial region and lower near the walls. Because of the influence of drag force, higher fluid velocity also lead to higher particle velocity in the axial region. At the surface of fluidized bed (h¼10 cm), bubble creaking promotes the lateral mixing of particles and fluid, so particle and fluid velocity curve become relatively flat again. We also made comparison of the time-averaged axial velocity between particle and fluid phase in fluidized bed (h¼6 cm), as shown in Fig. 9a and b. The results showed that the velocity distribution of particles correspond fairly closely with fluid, which indicates that particle motion in SCW fluidized bed is mainly dominated by fluid phase, while the influence of particle contact is rather small.

0.05

3.5. Solids mixing

0.00 0.2

0.4

0.6

0.8

Voidage Fig. 8. Frequency distribution of voidage.

1.0

There is a close relationship between bubble motion and solids mixing in bubbling fluidized bed. According to Stein et al. (2000), bubbles are usually the kinetic energy source of particle motion,

Y. Lu et al. / Chemical Engineering Science 117 (2014) 283–292

universal results about particle motion, the distribution of timeaveraged particle velocity vectors based on fluid cell is shown in Fig. 10c. The phenomenon that particles ascending up in axial region and descending down near the walls can be clearly figured out. What's more, different mechanisms of particle circulation discussed above can be also figured out, including internal circulation and gross circulation. The unique feature of particle motion may benefit solids mixing in SCW fluidized bed. 3.6. Granular temperature Granular temperature is an important parameter to measure the inhomogeneity of particle velocity and defined as follows:

θs ¼

1 N k k 2 N k k ∑ θ θ þ ∑ θ θ 3N k ¼ 1 x x 3N k ¼ 1 y y k

k

θkx ¼ uk;x  ux

ð12Þ

θky ¼ uk;y uy

ð13Þ

Here uk;x , uk;y are the lateral and axial velocity of kth particle respectively, ux , uy are the local average lateral and axial velocity respectively and calculated as follow: ux ¼

1 N ∑ u N k ¼ 1 k;x

ð14Þ

uy ¼

1 N ∑ u N k ¼ 1 k;y

ð15Þ

Granular temperature is based on the fluctuating velocity of particles, which is in analogy with the temperature in the kinetic theory of gases. The granular temperature is an indirect parameter indicating the intensity of particle interaction (Li and Kuipers,

12

12

10

10

10

Vortices

6

8

6

8

6

4

4

4

2

2

2

0 -1.0

-0.5

0.0

r/R

0.5

1.0

0 -1.0

-0.5

0.0

x/R

0.5

1.0

0 -1.0

Internal circulation

Bed height(cm)

12

Bed height(cm)

14

Gross circulation

14

8

ð11Þ

Here θx , θy are the random fluctuation velocity in x and y direction, defined as the difference between the instantaneous particle velocity and the local mean particle velocity in x and y direction respectively, and N is the total number of particles in the k k local region. θx and θy are calculated as follow:

14

Internal circulations

Bed height(cm)

and energy transfer between bubbles and emulsion usually leads to particle circulation in bubbling fluidized bed, including internal circulation on bubble-scale and gross circulation on reactor-scale. In order to make the relationship between bubble motion and particle mixing more clearly and distinctly, the distribution of instantaneous particle velocity vectors at one point of time when the superficial velocity is 2:5 umf are shown in Fig. 10a. Because all the 10,000 vectors are too crowd for analysis, 4000 of them are selected randomly, thus the bubble and particle characteristics can be clearly expressed and also reasonable from a statistical standpoint at the same time. According to traditional views, particle motion is mainly affected by bubble behaviors such as bubble vertical, lateral motion and bubble coalescence, breakage. In SCW fluidized bed, particles in axial region are going up more or less continuous with higher velocity as can be figured out in Fig. 10a, which we believe is caused by the rising bubbles and the wakes below them. According to the previous discussions, fluid velocity near the walls is lower than the axial region, so the particles are descending in wall region due to weak drag force. In addition, from the material balance point of view, rising particles in axial region need to be compensated by descending particles near the walls. Consequently reactor-scale circulation of particle: gross circulation is formed. The passage of a bubble also induces a drift effect in the dense phase which results in a loop displacement of the particles at the scale of the bubble diameter (Norouzi et al., 2011), termed internal circulation. However, there is another important factor in SCW bubbling fluidized bed: vortex, concerning internal circulation. The distribution of instantaneous fluid velocity vectors at the same point in time is shown in Fig. 10b, bubble and emulsion phase is identified by light gray and dark gray color respectively, and fluid vectors are in white. As can be seen from the figure, there are vortices in some bubbles. Vortices in bubbles will play an important role in particle circulation on bubble-scale, i.e. the internal circulation. The internal circulations in SCW fluidized bed are marked by elliptic curves in the Fig. 10a. Thus the solids mixing mechanisms in SCW bubbling fluidized bed may be different from fluidized bed under ambient conditions. These two mechanisms: internal circulation and gross circulation are responsible for solids mixing in fluidized bed (Moslemian, 1987). In order to obtain more

289

-0.5

0.0

0.5

1.0

r/R

Fig.10. Distribution of particle velocity vector. (a) snapshot of particle vector, (b) snapshot of fluid vector, and (c) time-averaged particle vector based on cells.

Y. Lu et al. / Chemical Engineering Science 117 (2014) 283–292

2002). A higher granular temperature usually indicates higher collision frequency between particles in local region. The lateral distributions of granular temperature in the middle of fluidized bed (h ¼6 cm) under various superficial velocities (u ¼ 2:0 umf ; 2:5 umf ; 3:0 umf ) are displayed in Fig. 11. As can be seen from the figure, the overall granular temperature increases with the increasing of superficial velocity, which means that particle interaction becomes more intense in SCW fluidized bed. Most especially at high superficial velocity, granular temperature distribution is low and relatively flat in axial region while there are two obvious peaks on both sides. As discussed before, fluid accumulates in axial region, which will make the corresponding void fraction of fluid higher than near the walls. As a result, larger space is provided for particles in axial region, which results in lower intensity of particle–particle interaction. Conversely, particle phase near the walls is denser and the drag force influence is relatively weaker than in axial region, which promotes interaction between particles. What's more, the location of the peaks are approximately the interface of rising particle flow in the center and falling particle flow near the walls, so that particle velocity changes severely which also enhances particle–particle interaction.

0.16

u=1.5umf u=2.0umf u=2.5umf

0.12

Frequency

290

u=3.0umf 0.08

0.04

0.00 0

150

300

450

600

750

Rep Fig. 12. Frequency distribution of particle Reynolds number.

700

u=1.5umf 600

u=2.0umf u=2.5umf

3.7. Particle Reynolds number Heat transfer coefficient between particle and fluid phase is an important parameter concerning whether the fluidized bed could run efficiently. Besides, as discussed before, particle motion in fluidized bed is significantly influenced by the interaction with fluid phase. Particle Reynolds number (Rep ) is an important nondimensional number used in particle–fluid suspension fluidization and can be seen as a measure of interaction between particle and fluid phase. Particle Reynolds number determines not only the force condition of particle but also heat transfer coefficient between fluid and particles. Fig. 12 shows the frequency distribution of particle Reynolds number with various superficial velocity in SCW fluidized bed. It can be observed that distributions under different superficial velocities are all single-peak. There is a quite uniform distribution of particle Reynolds number in homogeneous fluidization (u ¼ 1:5 umf ), which means that most particles are in similar flow environment. With the increasing of superficial velocity, the peak of distribution curve shifts to higher value and the curve becomes more and more flat. Conclusion can be made that: on one hand, the overall heat transfer between fluid and particle phase in SCW fluidized bed is enhanced with the increasing of superficial velocity; on the other hand, bigger difference in particle motion and heat transfer is induced.

Granular temperature(m2/s2)

2.0x10-3

u=2.0umf u=2.5umf

1.6x10-3

u=3.0umf

Rep

500

u=3.0umf

400

300

200

100 -1.0

-0.5

0.0

0.5

1.0

x/R Fig. 13. Lateral distribution of particle Reynolds number at various superficial velocities (h ¼ 6 cm).

Particle thermal behavior may change a lot at various location, which may has an important influence on SCW fluidized bed. Lateral distributions of particle Reynolds number in the middle of SCW fluidized bed (h¼ 6 cm) with various superficial velocities are shown in Fig. 13. The distribution is relatively flat in homogeneous fluidization (u ¼ 1:5 umf ), indicating similar heat transfer or force condition of particles in various lateral location. With the increasing of superficial velocity, overall particle Reynolds number increases, and at the same time varies more dramatically along bed width. It is obvious that there are two peaks beside the bed axial line, which indicates local enhanced intensity of interaction between fluid and particle phase. The peaks may be due to the vortices besides the axial line as discussed in Section 3.5. Such features may be crucial to solids motion and heat transfer in SCW fluidized bed.

-3

1.2x10

4. Conclusions -4

8.0x10

4.0x10-4

-1.0

-0.5

0.0

0.5

1.0

x/R Fig. 11. Lateral distribution of granular temperature at various superficial velocities.

SCW bed is a new and promising reactor for biomass gasification, which overcomes many shortcomings in traditional tubular reactor and has many new advantages. The aim of this paper is to conduct a comprehensive study on SCW fluidized bed to provided information of optimization in design and operation. To achieve this goal, DEM was coupled with CFD to study the particle distribution and fluid hydrodynamics characteristics in SCW fluidized bed. The simulation results of minimum fluidization

Y. Lu et al. / Chemical Engineering Science 117 (2014) 283–292

velocity fit our empirical correlation quite well. Main conclusions are obtained as follow: (1) Although the particles are categorized as Geldart B group, there exists a homogeneous fluidization after incipient fluidization. The relationship of Richardson–Zaki and Vogt et al. were found unable to describe the bed expansion properly. Bubbling fluidization in SCW fluidized bed was formed after superficial velocity exceeds the minimum bubbling fluidization velocity. (2) Particle velocity distribution corresponds fairly closely with fluid phase, indicating that particle motion are mainly dominated by fluid phase. (3) Particle circulation in SCW fluidized bed is not only induced by bubble translational motion, but also influenced by the vortices in bubbles. (4) Fluid phase accumulates in axial region, which results in higher velocity of fluid and particles, diluter emulsion phase and reduced particle–particle interaction intensity in this region. (5) The increasing of superficial velocity not only enhances the particle–fluid interaction, but also results in bigger difference of force and heat transfer condition at various locations.

Nomenclature Cd dp Fc Fd F f ;p g H0 h Ii mi n N P Re Rep Ret t Ti u uf umb umf umf ;cor umf ;sim ut uk;x uk;y ux uy Vi

drag coefficient bubble equivalent diameter (m) impact force (N) particle-fluid drag force (N) volumetric fluid–particle interaction force (N) gravity acceleration (m s  2) initial bed height (m) distance of the bubble centroid from the distributor (m) moment of inertia (kg m  2) particle mass (kg) the exponent of Richardson–Zaki relationship the total number of particles in the local region fluid pressure (Pa) Reynolds number particle Reynolds number terminal Reynolds number time (s) torque (N m  1) superficial velocity (m s  1) fluid velocity (m s  1) minimum bubbling velocity (m s  1) minimum fluidization velocity (m s  1) minimum fluidization velocity calculated by empirical correlation (m s  1) minimum fluidization velocity from DEM simulation (m s  1) terminal velocity (m s  1) the lateral velocity of kth particle (m s  1) the axial velocity of kth particle (m s  1) the local average lateral velocity (m s  1) the local average axial velocity (m s  1) particle volume (m3)

Greek letters

β ε θs θkx

fluid-particle inter-coefficient (kg m  3 s  1) voidage (dimensionless) Granular temperature (m2 s  2) the random fluctuation velocity in x direction (m s  1)

θky μf ρf ρs τ

vi

ωi

291

the random fluctuation velocity in y direction(m s  1) fluid dynamic viscosity (kg m  1 s  1) fluid density (kg m  3) particle density (kg m  3) fluid viscous stress tensor (Pa) linear velocity of ith particle (m s  1) angular velocity of ith particle (s  1)

Acknowledgments This work is currently supported by the National Natural Science Foundation of China through Contract no. 51322606 and the National Excellent 100 Doctoral Dissertation through Contract no. 201151.

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