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DEM simulation of gas–solid flow behaviors in spout-fluid bed


Chemical Engineering Science 61 (2006) 1571 – 1584 www.elsevier.com/locate/ces

DEM simulation of gas–solid ?ow behaviors in spout-?uid bed
Wenqi Zhong? , Yuanquan Xiong, Zhuli

n Yuan, Mingyao Zhang
Education Ministry Key Laboratory on Clean Coal Power Generation and Combustion Technology, Thermoenergy Engineering Research Institute, Southeast University, Nanjing 210096, People’s Republic of China Received 13 December 2004; received in revised form 22 August 2005; accepted 23 September 2005 Available online 8 November 2005

Abstract Three-dimensional gas and particle turbulent motions in a rectangular spout-?uid bed were simulated. The particle motion was modeled by discrete element method and the gas motion was modeled by k ? two-equation turbulent model. Shear induced Saffman lift force, rotation induced Magnus lift force as well as drag force, contract force and gravitational force acting on individual particles were considered when establishing the mathematics models. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas-particle interactions in volume fraction, momentum and kinetic energy. The gas–solid ?ow patterns, forces acting on particles, the particles mean velocities, jet penetration depths, gas turbulent intensities and particle turbulent intensities were discussed. Selected stimulation results were compared to some published experimental and simulation results. 2005 Elsevier Ltd. All rights reserved.
Keywords: Numerical simulation; Discrete element method; Turbulent ?ow; Spout-?uid bed; Spouted bed

1. Introduction Spout-?uid beds have been extensively employed in petrochemical, chemical and metallurgic industry. In addition to injecting the spouting gas through a central nozzle, the ?uidizing gas is introduced through a perforated distributor surrounding the central nozzle, which can result in better gas–solid mixing than either spouted beds or ?uidized beds (Vukovic et al., 1984; Sutanto et al., 1985; Pianarosa et al., 2000; Xiao et al., 2002, 2005; Zhong and Zhang, 2005a–c). In resent years, spout-?uid bed coal gasi?ers have been regarded as alternative gas–solid contactors for a laboratory scale advanced pressurized ?uidized bed combustion-combined cycle (APFBC-CC) system and a pressurized partial gasi?cation-combined cycle (PPG-CC) system in our laboratory (Zhang, 1998; Xiao and Zhang, 2002; Xiao et al., 2002, 2005; Zhong and Zhang, 2005a–c). Knowledge of gas and particle dynamics in spout-?uid bed is important for evaluation of particle circulation rate and gas–solid contacting ef?ciency especially for rapid reaction in the bed.

? Corresponding author. Tel.: +86 25 83795119; fax: +86 25 57714489.

E-mail address: wqzhong@seu.edu.cn (W. Zhong). 0009-2509/$ - see front matter doi:10.1016/j.ces.2005.09.015 2005 Elsevier Ltd. All rights reserved.

However, as is the case for all dense gas–solid system, it is dif?cult to obtain the measurement of gas and solid dynamics in the whole space of the bed without disturbing the ?ow ?eld. Numerical simulations have become popular in the ?eld of dense gas–solid two-phase ?ows in resent years. Numerical simulation is a useful tool to get detailed information about the phenomena without disturbing the ?ows. The particle motion in gas–solid systems has been calculated by using two kinds calculation models, the trajectory model and the continuum media model. The discrete element method (DEM) is one of the trajectory models (Cundall and Strack, 1979; Tsuji et al., 1993). Since it being successfully employed in dense phase ?ows in ?uidized bed by Tsuji et al. (1993), signi?cant advances have been accomplished in simulating the gas–solid ?ow systems by DEM (e.g. Tsuji et al., 1993; Hoffmann et al., 1993; Tsuji et al., 1997, 1998; Tsuji, 2000; Helland et al., 2000; Kawaguchi et al., 2000; Yuan, 2000; Yuu et al., 2001; Xiong, 2003; Xiong et al., 2004; Zhou et al., 2004; Takeuchi et al., 2004; Tatemoto et al., 2004; Langston et al., 2004; Bertrand et al., 2005). Due to the development of computer capacities, DEM has become a very useful and versatile tool to study not only the hydrodynamic behaviors of particulate ?ows but also of the chemical

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reactions, and heat and mass transfer at the individual particle scale (Kaneko et al., 1999; Rong and Horio, 1999; Zhou et al., 2004). DEM offers a more natural way to simulate a gas–solid ?ow with particles of different size or different density with each individual particle tracked in the simulation. However, the DEM simulation of spout-?uid bed has largely lagged behind, there has been no information concerning such a method to spout-?uid beds so far. Moreover, almost all researches using DEM neglected the effect of turbulence on the gas-particle motion (Zhou et al., 2004), although both experimental and theoretical results veri?ed the strong intensity of turbulence in ?uidized bed (e.g. Peirano and Leckner, 1988; Zhou et al., 2000, 2002). Signi?cant advances have been accomplished in modeling the turbulent ?ow so far. There are three main methods to work with the turbulence on the gas-particle motion: (1) Direct numerical simulation (DNS), to simulate the turbulent ?ow directly by solving 3-D Navier–Stokes equations, this approach needs a very small time step and ?ne meshes in order to recognize the turbulence variety in small time and space scale. The method might be restricted by computational memories unless mainframe computers are used (Moin and Mahesh, 1998); (2) large eddy simulations (LES), LES can be considered as a spatially ?ltered solution to the Navier–Stokes equations. It also needs a relatively high computational memory but is easier to realize in personal computers. This method has widely applied in resent years (Kogaki et al., 1997; Jordan and Ragab , 1998; Yang, 2000); (3) Reynolds-averaging equations (RAE), application of RAE to consider the gas turbulence needs to establish a turbulence model (generally called as closure model) in order to make the Reynolds stress equations closed (Launder and Spalding, 1974), or to establish a turbulent viscosity function representing the turbulence stress. The latter was considered as one of the most promising approach to solve the turbulent ?ow (e.g. Simonin and Viollet, 1990; Balzer et al., 1995; Ramadhyani, 1997). In this approach, some turbulence model such as zero equation models, one-equation model and k ? two equations model can be used according to the determination of turbulent viscosity coef?cient (Singhal and Spalding, 1981; Pourahmadi and Humphery, 1983; Simonin and Viollet, 1990; Balzer et al., 1995; Ramadhyani, 1997; Lun, 2000). Zhou et al. (2004) numerically simulated the gas and particle motions in a two-dimensional (2-D) bubbling ?uidized bed. The solid phase is modeled with DEM and the gas phase is modeled as two-dimensional Navier–Stokes equations for twophase ?ow with ?uid turbulence calculated by LES. For spout?uid bed, the strong intensity of turbulence of gas–solid motions was detected in bed especially at the distributor region (Zhong and Zhang, 2005a,c). Thus, numerical as well as experimental approaches aiming at grasping more useful information on the ?ow gas–solid turbulent motions in spout-?uid beds are expected. The objective of the present work is to develop a 3-D turbulent model accounting for the gas–solid turbulent ?ow in a spout-?uid bed. The particle motion is modeled by discrete element method and the gas motion was modeled by k ? twoequation turbulent model.

2. Computational models 2.1. Gas phase The continuity and momentum equations in a 3-D geometry come as j ( jt j ( jt
g) +

j ( jxi

g uj ) = 0,

(1)

j ( g ui uj ) jxj jp j =? + ( ij ) jxi jxj ? np (fD + fLM + fLS ) +
g ui ) +

g g,

(2)

where is the void fraction, g is the gas density, and ui and uj are the gas velocity, i, j = 1, 2, 3, which represent x, y and z directions, ij is the turbulence stress, it can be modeled as
ij

=( +

t)

juj jui + jxi jxj

?

2 3

g k ij

(3)

in which is the gas dynamic viscosity, t is the turbulent viscosity modeled as t = C g k 2 / t , k is turbulence energy, ij is the Kronecker number, t is the turbulence dissipation rate, C is a empirically assigned constant. In Eq. (2), np (fD + fLM + fLS ) is the interfacial momentum transfer term per unit volume. In which, np is the number of particles per unit volume and fD is the drag force for single particle. The interphase interactions between the solid and the gas per unit volume due to ?uid drag force (Kafui et al., 2002) is given by the following correlation: np fD = (u ? vp ), (4)

where vp is the mean velocity of the particles in the unit volume. Ergun’s equation (Ergun, 1952) was used for the dense phase and Wen and Yu’s equation (Wen and Yu, 1966) for the dilute phase, and the coef?cient was summarized as follows: ? (1 ? ) ? [150(1 ? ) + 1.75Rep ], ( 0.8), 2 dp = ? 0.75CD (1? ) ?2.7 Rep ( > 0.8). d2
p

(5)

CD =

24 (1 + 0.15Re0.687 ), (Rep 1000), p Rep 0.43 (Rep > 1000).
g

(6)

Rep =

|u ? vp |dp

(7)

in which CD is the drag coef?cient for a single sphere. The terms fLM and flS in Eq. (2) are the Saffman lift force and Magnus lift force for single particle, which will be described in the next section.

W. Zhong et al. / Chemical Engineering Science 61 (2006) 1571 – 1584 Table 1 The values of empirically assigned constant in k ? C 0.09 C1 1.44 C2 1.92 C3 1.2

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two equations model
k
n

i kn spring

1.0

1.33

i spring kt
f

The gas turbulence kinetic energy equation was sited from Crowe (2000), which can be expressed as j j j ( k) + ( kuj ) = jt jxj jxj + Gk + Gk =
t g

dash-pot

j j friction slide dash-pot (b)
t

+
k

t k

jk jxj (8) ju jv + jy jx
2

k + Sd , 2

(a)

2

ju jx

2

+
2

jv jy

2

+

jw jz
2

+ ,

Fig. 1. Model of particle–particle contact forces. (a) Normal force and (b) tangential force.

ju jw + + jz jx
k Sd 2

+

jw jv + jz jy

(9) (10)

The gas ?ow in spout-?uid bed can be assumed to satisfy the following function: p=
g RT

(16)

= |u ? vp | + ( v v ? u v)

in which R = 287.1N m/(kg K), T = (273.15 + 25) K. 2.2. Particle phase The particle motion was calculated three-dimensionally. Individual particle motion was traced by using the DEM as in the previous successful work (e.g. Tsuji et al., 1993; Hoffmann et al., 1993; Tsuji et al., 1997, 1998; Tsuji, 2000; Helland et al., 2000; Kawaguchi et al., 2000; Yuan, 2000; Yuu et al., 2001; Xiong, 2003; Xiong et al., 2004; Zhou et al., 2004; Takeuchi et al., 2004; Tatemoto et al., 2004; Langston et al., 2004; Bertrand et al., 2005). In the present work, the shear induced Saffman lift force and rotation induced Magnus lift force were considered as well as the drag force, contract force and gravitational force. According to Newton’s equation of motion, the motion of a particle is calculated as mp dvp = fC + fD + fLS + fLM + mp g, dt d p Mp = , dt Ip (17) (18)

the term |u ? vp |2 in Eq. (10) is the generation term caused by particle resistance, and the term ( v v ? u v) is the redistribution term representing the exchange of kinetic energy between particle and gas. Where, u is the gas ?uctuating velocity, v is the particle ?uctuating velocity. According to Xiong (2003) and Xiong et al. (2004), the re-distribution term can be re-scaled as ( v v ? u v) = ?2 k 1 ? = 4dp 3CD
p l l l d l

+

+

,
d

(11) (12)

d

g |u ? vp |

,

l

k = 0.35 ,

(13)

where l is the Lagrangian time scale of gas phase, d is the response time scale of particle phase, g is particle density, is the turbulent Schmidt number, here = 0.7. The turbulence momentum dissipation equation was sited from Bertodano et al. (1994), which can be described as j ( jt =
g

)+

j ( jxj +

g uj k) t k

j jxj + k k

j jxj
g

where fc is the contact force, fD is the drag force, fLS is the Saffman lift force and fLM is the Magnus lift force. vp is the particle velocity, p is the particle rotational velocity, Mp is the particle torque and Ip is the particle motion of inertia. 2.2.1. Contact force fC Cundall and Strack’s (1979) DEM model opened new possibilities for using discrete particle simulation to calculate the dense phase ?ows in ?uidized bed (Tsuji et al., 1993). Contact forces are described in term of a mechanical model involving a spring, dashpot and friction. The contact force fC is divided into normal (fcnij ) and tangential (fctij ) forces, they are modeled in Fig. 1. These forces can be expressed as the following equations (Tanaka et al., 1991): fC = fcnij + fctij , (19)

(C1 Gk ? C2
k Sd .

) + Sd ,

(14) (15)

Sd = C3

The values of empirically assigned constant in k ? two equations model used in the present work are listed in Table 1, they are cited from the previous work (Singhal and Spalding, 1981; Pourahmadi and Humphery, 1983; Simonin and Viollet, 1990; Balzer et al., 1995; Ramadhyani, 1997).

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1.5 nij

fcnij = (?kn fctij = ?kt

?

n vrij

· nij )nij ,

(20) (21)

tij

?

t vtij ,

where kn and n are the spring and damping coef?cients in normal direction, respectively. kt and t are the spring and damping coef?cients in tangential direction, respectively. nij and tij are the normal and tangential displacements between particle i and particle j, respectively. If |fcti j | > f |fcnij |, the sliding between particles should be considered, and the tangential force is given by fctij =
f |fcnij |

In general, few particles are in contact with particle i at the same time. Therefore the total force acting on particle i can be obtained by taking the summation of the above forces with respect to j (Tsuji et al., 1993): fC =
j

(fcnij + fctij ).

(23)

vtij . |vtij |

(22)

i kn spring

n

i spring kt
f

The same relations as the above equations are derived for contact with the wall when the particle j is replaced by wall, as are modeled in Fig. 2. The spring coef?cients kn and kt are calculated from the following equations based on the methods of Hertz’s and Mindlin and Deresezewicz (1953), respectively, and the damping coef?cients n and t are determined from the method of Tanaka et al. (1991). They are listed in Table 2. Where p and w are the Poisson ratio of particle and wall respectively. Ep and Ew are longitude elastic moduli of particle and wall respectively. Gp and Gw are transverse elastic moduli of particle and wall respectively. When Eqs. (28) and (31) are used, the value of restitution coef?cient e depends only on the value of coef?cient (Tanaka et al., 1991), the relation between them was reference to (Tsuji et al., 1993). The restitution coef?cient is constant in present work, it is e = 0.9. 2.2.2. Drag force fD The drag force fD for single particle is calculated as fD =
1 8 g 2 dp CD |ur |ur ,

dash-pot

friction slide wall (a) (b) dash-pot
n

wall

(34)

Fig. 2. Model of particle-wall contact forces. (a) Normal force and (b) tangential force.

where the translational relative velocity, ur is de?ned as ur = (u ? vp ). The drag coef?cient CD is given by Eq. (6).

Table 2 Calculated correlations for the spring coef?cient and the damping coef?cient Particle–particle Correlations Number Particle–particle Correlations
2 4 1? p 1? 2 w + Ep 3 Ew ?1

Number

kn =

E p dp 3(1 ? 2 ) p

(24)

kn =

dp 2

(29)

kt =

2Gp dp 0.5 2? p n
0.25 n

(25)

kt = 8 0.5 n

2? p 2? w + Gp Gw

dp 2

(30)

n= t = n

mk n

(26) (27)

n= t = n

0.25 n

mk n

(31) (32)

Gp =

Ep 2(1 + p )

(28)

Gp =

Ep Ew , Gw = 2(1 + p ) 2(1 + w )

(33)

W. Zhong et al. / Chemical Engineering Science 61 (2006) 1571 – 1584

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2.2.3. Saffman lift force (shear lift force) fLS Saffman lift force is also called shear lift force. Saffman (1965) and Saffman (1968) indicated if the particle is relatively large and the ?uid has a relatively large velocity gradient when it ?ows around the particle, a lift force will be generated due to the velocity difference between the top and bottom of the particle whether the particle rotates or not. The direction of this lift force is vertical to the direction of relative velocity between the particle and ?uid. The gas velocity is signi?cant different between the central dilute region and annular dense region in a spouted bed (Mathur, 1974) and a spout-?uid bed (Pianarosa et al., 2000). Entrainment of particles from the annular dense region into the spout region by spouting gas is obvious, which lead to a continuous and stable spout or jet in the spout-?uid bed. A shear lift force will generate due to the velocity gradient when particles entrained into spout region. The force should not be neglected especially when particles in the boundary of central dilute region and the annular dense region. The Saffman lift force is calculated by fLS = 1.615(u ? vp )( (n = x, y, z)
g g) 0.5 2 dp CLS

where vr is relative velocity between gas and particle, vr = u ? vp . r is the rotation angular relative velocity between gas and particle, r = g ? p and g = 0.5? × u. CLM is Magnus lift coef?cient. CLS in the present work is calculated from the correlation developed by (Lun and Liu, 1997), which is expressed as ?| | ? r dp , (Rep 1), ? CLM = ||vr || ? r ? dp (0.178+0.822Re?0.522 ), (1<Rep <1000), p |vr | (39)
p was assumed to satisfy the correlation (Rubinow and Keller, 1961) as follows: 2 2 mp dp d p p dp = Ct | 10 dt 64 r| r

(40)

ju ju sgn , jn jn (35)

in which the coef?cient Ct is calculated from the correlation proposed by Dennis et al. (1980): ? 5.32 37.2 ? ? 0.5 + Re , (Re < 20), Re Ct = 6.45 (41) 32.1 ? ? + , (Re 20) Re Re0.5 where Re is particle rotation Reynolds number, which is de?ned as Re =
2 p dp | r |

in which CLS is the Saffman lift coef?cient. CLS in the present work is calculated from the correlation developed by Mei (1992), which is expressed as ? ? (1 ? 0.3314 0.5 ) exp(?0.1Rep ) (Rep 40), (36) +0.3314 0.5 , CLS = ? 0.0524 0.5 (Rep )0.5 , (Rep > 40), where, = 0.5dp ju . |(u ? vp )| jn (37)

4

.

(42)

3. Computational conditions The geometry of the vessel and array of numerical grids is showed in Fig. 3. The spout-?uid bed has a cross section of 300 mm × 15 mm and height of 1212 mm. The spout nozzle is 20 mm × 15 mm. A V type gas distributor, having a 60 ? inclination angle was at the bottom of the bed. This simulated vessel has a similar geometry as our previous experiments (Zhong and Zhang, 2005a–c), but only half of the size due to restriction of the simulated particles by our computer. The physical and numerical parameters are summarized in Table 3. In experiments, the minimum spouting velocity, ums , is determined by visual observation when the spouting fountain just vanished with decreasing gas velocity (Mathur, 1974; Vukovic et al., 1984; Sutanto et al., 1985). The minimum spouting velocity at spouting gas nozzle based on our experiment on the spout?uid bed vessel (300 mm × 30 mm × 2000 mm) for the same operating conditions as the simulations were found to be 24 m/s (dp = 1.5–2.5 mm, mean diameter is about 2.0 mm) and 33 m/s (dp = 2.0–3.0 mm, mean diameter is about 2.5 mm). The minimum spouting velocity based on simulation was determined by decreasing super?cial gas velocity gradually (Takeuchi et al., 2004) or by increasing spouting gas velocity step by step (Kawaguchi et al., 2000). For the present work, simulations were performed with decreased spouting gas velocity step by step from 27 to 20 m/s and from 36 to 30 m/s for two kinds of particles, respectively. The simulations at 22 and 30 m/s can

2.2.4. Magnus lift force fLM When the gas ?ow is not uniform at various locations, the particle will rotate due to the velocity gradient. At a low Reynolds number, the rotation of particle will bring the ?uid moving around the particle, which leads to the increasing of ?uid velocity in the same side as the ?ow direction and the decreasing of ?uid velocity in the opposite side. A lift force will generate due to the velocity difference between the different sides of the particle. The lift force is called as Magnus lift force. The direction of Magnus lift force is vertical to the direction of relative velocity between particle and ?uid. A rotation induced Magnus lift force will generate due to the velocity gradient when particles entrained into the spout region with rotation, which should not be neglected especially when particles in the boundary of central dilute region and the annular dense region. The Magnus lift force is calculated by the following correlation (Lun and Liu, 1997; Lun, 2000): fLM = 1 8
2 g vr 2 dp CLM

× vr , | r | · |vr |
r

(38)

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W. Zhong et al. / Chemical Engineering Science 61 (2006) 1571 – 1584

uf ufx

ufz

uf

uf

z x us
150mm

us

Fig. 3. Geometry of vessel and array of numerical grids.

Table 3 Physical and numerical parameters Properties Bed cross section, A Vessel height, Hb Cell size ( x × y × z) Spouting gas velocity, us Fluidizing ?ow rate, Qf Gas density, g Gas viscosity, Initial bed height, H0 Maximum number of particle, n Particle density, p Particle diameter, dp spring coef?cient, k Restitution coef?cient, e Friction coef?cient Particle–particle, p Particle-wall, w Poisson’s ratio Particle, p Wall, w Modulus of longitudinal elasticity Particle, Ep Wall, Ew Time step of calculation, t Value 300 mm × 15 mm 1212 mm 10 mm × 5 mm × 17.32 mm 0.39–3.65 ums 0.78Qmf 1.166 kg/m3 18.2 × 10?6 Pa/s 500 mm 62 000 1020 kg/m3 1.5–2.5 mm, 2.0–3.0 mm, Gaussian distribution 800 N/m 0.9 0.3 0.25 0.33 0.33 3.0 × 109 N/m2 3.0 × 109 N/m2 1.0 × 10?6 s

velocity ?eld is based on the SMAC method (Amsden and Harlow, 1970). The SMAC method has been successfully applied to simulation of multiphase turbulence ?ow and validated for studying the ?ow structures (Yamamoto, 1999). The procedure was to obtain a velocity prediction ?rst, and then correct the velocity and pressure ?eld by a corrector. On the inlet side, a solid plane wall normal to z-axis was assumed except for the opening of the nozzle. The no-slip condition was applied at this wall. For the out?ow boundary Sommerfeld’s non-re?ective condition and Neuman’s condition jp/jz = 0 were applied. This method was also described in detail in previous publications (Takeuchi et al., 2004). A two-way coupling numerical iterative scheme (Lun, 2000; Xiong, 2003; Xiong et al., 2004) was used to incorporate the effects of gas-particle interactions in volume fraction, momentum and kinetic energy. The calculation of particle motions started up with a packed bed. Particles were loaded into the bed row by row and layer by layer to form an initial packed bed with height of 500 mm and voidage about 0.42, the distance between the centers of two neighboring particle is 2 rmax , rmax is the maximum particle diameter. The time step was determined from the viewpoint of the stability and computation time expense of calculation. The method proposed by Tsuji et al. (1993) was used to determinate the time step. Besides, by comparing of the calculations with several time steps, i.e., i × 10?7 s, i × 10?6 s and i × 10?5 s, where i = 1, 2, it was found that the time step 1 × 10?6 could make calculations stable under most operating conditions, and also no much computation time is needed. 4. Results and discussion 4.1. Flow patterns in spout-?uid bed A total of 3 s simulation was conducted to observe the gas and particle ?ow patterns. A series of instantaneous snapshots were generated every 0.001 s. A full development of a jet in the spout-?uidized bed at us = 0.76ums and Qf = 0.78Qmf with time are presented in Fig. 4. The ?ow pattern was known as “jet in ?uidized bed” or “internal jet” according to Vukovic et al. (1984) and Sutanto et al. (1985). In this case, particles in the central spout region accelerated by the gas traveling at relatively high speed to the top of the bed surface, while particles in the annular region form a packed bed and ?ow steadily downwards, feeding into the spouting (or jet) along its entire length especially in the V-shape distributor region. These results agree with the previous experimental investigation on spout-?uid beds (e.g. Vukovic et al., 1984; Sutanto et al., 1985; Pianarosa et al., 2000; Zhong and Zhang, 2005a–c) and jetting ?uidized bed (e.g. Kimura et al., 1995; Yang, 1998). Continuous circulation of particles can result in a continuous and stable spout or jet in spout-?uid bed. Images of a jet developing in the spout-?uidized bed at the same operating conditions except bed size are showed in Fig. 5. These photos were obtained in our previous investigation (Zhong and Zhang, 2005a–c) on a spout-?uidized bed with its cross section of 300 mm × 30 mm and height of 2000 mm, the time interval between successive frames is 0.0125 s.The simulation results were similar to the

just form stable spouting, thus, the velocities were determined as approximate minimum spouting velocities. The gas phase was solved by non-staggered SIMPLE method (Miler and Schmidt, 1988). Time-advancement of pressure and

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W. Zhong et al. / Chemical Engineering Science 61 (2006) 1571 – 1584

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Fig. 5. Photos of development of a jet in the spout-?uid bed (us = 0.76ums ,Qf = 0.78Qmf ).

Fig. 4. Development of a jet in the spout-?uid bed (dp = 2.0–3.0 mm, us = 0.76ums , Qf = 0.78Qmf ). (a) t = 0 s, (b) t = 0.002 s, (c) t = 0.005 s, (d) t = 0.008 s, (e) t = 0.011 s, (f) t = 0.014 s, (g) t = 0.017 s, (h) t = 0.20 s, (i) t = 0.023 s, (j) t = 0.26 s, (k) t = 0.29 s,.

experiment results except the bubbles on the top of the jet. Much larger bubbles were observed in the experiments than the simulation, as is presented in Figs. 4 and 5. Fig. 6 illustrates the instantaneous snapshots of ?ow patterns in the spout-?uidized bed at various spouting gas velocity for uf = 0.78umf . For us < ums , the spouting gas is not

able to penetrate the bed, only form a internal jet as shown in Fig. 4, Fig. 6(a) and (b). When the spouting gas velocity is beyond the minimum spouting velocity (us > ums ), a spout forms. However, when the spouting gas velocity is even greater (us > 2.5ums ), the bed is in the transport ?ow pattern. These results agree with the previous experimental investigation on spout-?uid beds (Vukovic et al., 1984; Sutanto et al., 1985). Previous DEM simulation of ?ow patterns in a cylinder spouted bed (Kawaguchi et al., 2000) presented in Fig. 7. The minimum spouting velocity based on their simulation is 1.46 m/s (super?cial velocity), which was obtained by increasing spouting gas velocity step by step. The present simulated ?ow patterns are similar to them, the difference from which is more obvious entrainments of particles from the annular dense region into the spout region, especially in the distributor region, as shown in Fig. 6(a)–(d). This can lead to a continuous and stable spout or jet in the spout-?uid bed. The higher the spouting gas velocity, the more particles are entrained into the spout region. These results agree qualitatively with visual observation of physical experiments in spout-?uid beds. The following section focuses on discussing the ?ow behaviors of gas and particle corresponding to the ?ow pattern of “internal jet” or in the ?ow regime of “jet in the ?uidized bed”, since the spout-?uid bed coal gasi?er should be operated in the ?ow pattern of “internal jet” or in the ?ow regime of “jet in the ?uidized bed” (Zhong and Zhang, 2005b,c). Operation in this ?ow regime can prolong the resident time of steam and air in the bed, making it un-easy for much steam and air to pass through the bed and wasted, and enhancing the gas diffusion and particles mixing between the spout region and the annular

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W. Zhong et al. / Chemical Engineering Science 61 (2006) 1571 – 1584

Fig. 7. Flow patterns in a spouted bed at various spouting gas velocity simulated by Kawaguchi et al. (2000).

1.4 1.2 ?P/ H0 (X104 Pa/m) 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.5 1.0 us /ums 1.5

simulation experiment

2.0

2.5

Fig. 8. Comparisons of simulated pressure drop with experimental result at different spouting gas velocities for dp = 2.0–3.0 mm and Qf /Qmf = 0.78.

4.2. Flow behaviors of gas and particles Fig. 8 shows the comparisons of simulated pressure drop with experimental result (Zhong and Zhang, 2005a–c) at different spouting gas velocities. It can be seem that the trend of present simulated results are in well agreement with the experimental results. Though, the simulated vessel is half of the experiment vessel, the result implies the hydrodynamic similitude of pressure drop with geometrical similitude at the same dimensionless operating conditions (He et al., 1997; Costa and Taranto, 2003). Fig. 9 presents the radial concentration of particles at the bed elevation H /D = 1.0 with different spouting gas velocities for dp = 1.5–2.5 mm and Qf /Qmf = 0.78. The concentration of particles increases along radial direction. Besides, the concentration of particles in the annular decreases with increasing spouting gas velocity due to the spouting gas transfer into

Fig. 6. Flow patterns in the spout-?uid bed at various spouting gas velocity (dp = 1.5–2.5 mm; Qf = 0.78Qmf ). (a) us = 0.39 ums , (b) us = 0.76 ums , (c) us = 1.22 ums , (d) us = 1.75 ums , (e) us = 2.25 ums , (f) us = 2.45 ums , (g) us = 2.65 ums , (h) us = 2.85 ums , (i) us = 3.05 ums , (j) us = 3.25 ums , (k) us = 3.45 ums , (l) us = 3.65 ums .

dense region, obtaining more uniform axial temperature pro?les in order to improve the gasi?cation ef?ciency.

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0.5 Percentage of collided particles

0.5 particle-wall particle-particle

Concentration of particles

0.4

0.4

Averaged value=28.8%

0.3 us /ums =0.39 us /ums =0.76 us /ums =1.22 us /ums =1.75

0.3

0.2

0.2 Averaged value=4.95% 0.1

0.1

0.0 0.0

0.0 0.1 0.2 0.3 0.4 0.5 r/R 0.6 0.7 0.8 0.9 1.0 0.000 0.005 0.010 0.015 Time (s)
Fig. 10. Variations of percentage of collided particles with time (dp = 2.0–3.0 mm, us = 0.76ums , Qf = 0.78Qmf ).

0.020

0.025

0.030

Fig. 9. Radial concentration of particles with different spouting gas velocities (H /D = 1.0, dp = 1.5–2.5 mm, Qf /Qmf = 0.78).

annular, the voidage in the annular dense region increases. For us /ums = 0.39, the radial concentration of particles increase slightly. It is noted that the concentration of particles in the center of the bed at us /ums = 0.39 is greater than other three curves. Since the sampling location (H /D = 1.0) is above the internal jet, which can be seemed in Fig. 6(a), the particle concentration has little grads. For the other three simulation conditions, i.e., us /ums = 0.76, us /ums = 1.22 and us /ums = 1.75, the concentrations of particles in the spout region increase slightly with spouting gas velocity, which implies that the entrainment of particles from the annular dense region into the spout region increases with spouting gas velocity. Experimental results (Kimura et al., 1995; Yang, 1998; Pianarosa et al., 2000; Zhong and Zhang, 2005b) indicated that entrainments of particles along the spout or jet height especially in the distributor region increase by increasing spouting gas velocity. The higher the spouting gas velocity, the more particles are entrained into the spout region. The ?ow patterns based on simulations (Fig. 6a–d) show the same trend. Variations of percentage of collided particles with time at us = 0.76ums and Qf = 0.78Qmf are presented in Fig. 10. In order to obtain the percentage of collided particles, an arithmometer was used in the program. For DEM simulation, every particle has a unique ID number and is tracked during calculation. In every time step, the program must judge whether a certain particle collides with other particle(s) and whether a certain particle collides with wall. The collision information can be recorded by the arithmometer. The percentage of collided particles represents the particles in collision. It is noted that a strong peak of particle–particle colliding exits at the beginning, which implies an impulsive start-up process when particle begin to move. The initial particle–particle collision percentage is over 50% corresponds to the start-up stage with packed bed, and then decreases ?uctuating with time due to the stable jet development in bed. The existence of a peak for particle–particle colliding in the start-up process was also reported by Zhou et al. (2004). While, the percentage of particle-wall colliding is

Mean percentage of collided particles (%)

40 35 30 25 20 15 10 5 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 us /ums dp =2.0-3.0mm dp =1.5-2.5mm

Fig. 11. Mean percentage of collided particles with various spouting gas velocity (Qf = 0.78Qmf ).

almost zero at the beginning. The mean particle–particle and particle-wall collisions percentage are 28.8% and 4.95%, respectively. Fig. 11 shows the mean percentage of particles colliding with various spouting gas velocity and particle diameter. The ratio of particle–particle colliding decreases with spouting gas velocity, which agrees with previous investigation (Zhou et al., 2004), while the value increases with particle diameter. It is noted that the mean percentage of particle-wall colliding shows almost no variation with spouting gas velocity and particle diameter in the present work. However, these values are much higher than that in a bubble ?uidized bed by Zhou et al. (2004), which implies more intensive particle interactions in spout-?uid bed. This might result in the intensive motions of gas and particles by adding the spouting gas and ?uidizing gas into the bed synchronously, and the motions are restricted in thin situational vessel.

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Percentage of force adding to particles (%)

100 90 80 70 60 50 40 30 20 10 0 0.0 0.1 0.2 0.3 0.4 0.5 r/R 0.6 0.7 0.8 0.9 1.0 Drag force fD Contact force fC Gravitational force fG Magnus lift force fLM Saffman lift force fLS

1.4 1.2 ?P/H0 (X104 Pa /m) 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.5 1.0 us /ums Experiment

Calculation with fLM with fLM with fLM, fLS without fLM, fLS

1.5

2.0

2.5

Fig. 12. Percentage of forces adding to particles (H /D=1.6, dp =2.0–3.0 mm, us /ums = 0.76 and Qf /Qmf = 0.78).

Fig. 13. Effect of Saffman lift force and Magnus lift force on the simulated pressure drop at different spouting gas velocities for dp = 2.0–3.0 mm and Qf /Qmf = 0.78.

Mean Saffman lift force (fLS ) and Magnus lift force (fLM ) were considered as well as drag force (fD ), contract force (fC ) and gravitational force (fG ). Fig. 12 illustrates the percentage of force sadding to particles at H /D = 1.6 mm, every value is a mean absolute value of the particles in a calculated cell. The drag force is the largest in the jet region while the contact force is the largest in the annular region especially near the wall. These indicate that the drag force dominates the particle motion in the jet region while the contact force dominates the particle motion in the dense annular region especially near the wall. Zhou et al. (2004) indicated that the particle mean velocity distribution is not correlated to the gas velocity distribution inside the bed, which indicates that the particle motion in the dense zone is dominated by the particle–particle interactions. The percentage of gravitational force decrease at both central and near-wall regions due the increasing of drag force or contract force, however the absolute value of gravitational force is invariable. The mean percentage of Saffman lift force and Magnus lift force are almost zero in the jet region and annular dense region, while they reach to 6% of the total forces adding to the particles in the boundary of jet region and annular dense region (about r/R = 0.12), which due to the signi?cant difference of gas velocity in the spout jet region and the annular region. Saffman lift force and Magnus lift force contribute to the entrainments of particles from the annular dense region into the spout region, which can lead to a continuous and stable jet in the spout-?uid bed. Fig. 13 shows the effect of Saffman lift force and Magnus lift force on the simulated pressure drop at different spouting gas velocities. The simulated results without Saffman lift force and Magnus lift force are lower than the experimental results. The larger spouting gas velocity, the larger difference can be seen. While, the simulations with these two forces are in well agreement with the experiments. In another study, Xiong (2003) found that Saffman lift force and Magnus lift force take remarkable effect on the simulated results when simulating the particle ?ow behaviors in a high-velocity gas–solid injector. Thus, shear induced Saffman lift force and

rotation induced Magnus lift force is noticeable when simulating the jet, recirculation and boundary ?ows. The radial distributions of the particle velocity magnitude and particle velocity component in y-direction at various vessel heights are plotted in Fig. 14. The particle velocity magnitude decreases with vessel height, they are symmetrical along bed width. The particle velocity component in y-direction is positive in the center and it is negative in the annular region. That is, the particle ?ows at the higher levels move down in the annular region. The predicted trends of descent velocity are in good agreement with the measurements at a fully cylindrical Plexiglas column with its diameter of 152 mm (Pianarosa et al., 2000). However, the particle velocity predictions at present work is about 1.5–2.0 times greater than those measurements. Previous simulations of a spouted bed by Kawaguchi et al. (2000) showed the particle velocity were 2–5 times greater than those measured by He et al. (1994). They explained that this discrepancy was due to the continuity problem of solids ?ow to balance the linear expansion of spout diameter with height and the contraction of cross-sectional area of the annular region. The present discrepancy also to be seemed caused by this. Because, the present simulation work on a thin vessel, the front and back walls restrict the expansion of gas in the y-direction, thus the gas jet expands in the x-direction. The jet diameter based on simulation is 25% larger than those measured in fully cylindrical vessel by Pianarosa et al. (2000), however, it is almost the same as measured in a rectangle rectangular spout-?uid bed (see Figs. 5 and 6b). It is pity that detailed comparisons of the present simulation to any measurement is not available due to the lack of experimental data obtained in a vessel of a same size and same operating conditions. However, the present work might seem successful according the glancing comparisons to previous valuable simulations and experiments. The jet is playing an important role in mass transfer, heat transfer, momentum transfer during the chemical process of spout-?uid bed coal gasi?cation. The jet penetration depth can be considered as one of the key parameters to describe the

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8 Particle velocity magnitude (m/s) 7 6 5 4 3 2 1 0 0.0 (a) Particle velocity component in z direction (m/s) 4 3 2 1 0 -1 -2 0.0 H/D=0.8 H/D=1.0 H/D=1.3 H/D=1.6 0.1 0.2 0.3 0.4 0.5 0.6 r/R 0.7 0.8 0.9 1.0 (a) H/D=0.6 H/D=0.8 H/D=1.0 H/D=1.3 H/D=1.6

0.6 0.5 Gas turbulent intensity 0.4 0.3 0.2 0.1 0.0 0.0 0.1 H/D=0.5 H/D=1.0 H/D=1.5

0.2 0.3

0.4

0.5 0.6 r/R

0.7 0.8

0.9 1.0

0.20 H/D=0.5 H/D=1.0 H/D=1.5

Particle turbulent intensity

0.15

0.10

0.05

0.00 0.0 0.1 0.1 0.2 0.3 0.4 0.5 r/R 0.6 0.7 0.8 0.9 1.0 (b)

0.2 0.3

0.4

0.5 0.6 r/R

0.7 0.8

0.9 1.0

(b)

Fig. 14. Simulation results of the radial distribution of particle velocity at various vessel heights (dp = 2.0–3.0 mm, us = 0.76ums , Qf = 0.78Qmf ).

Fig. 16. Comparison of the gas and particle turbulent intensity radial distributions in various vessel heights (dp = 2.0–3.0 mm, us = 0.76ums , Qf = 0.78Qmf ).

500 Predicted by the simulation Jet penetration depth (mm) 400

300

200 Predicted by the correlation (zhong and Zhang, 2005b)

results exhibit that the jet penetration depth is a function of spouting jet velocity. The jet penetration depth increases with increasing spouting jet velocity, which agrees with our previous experiments. The simulation results ?t the calculations by the correlation based on a large amount of experiment data with little variance (Zhong and Zhang, 2005b). The gas and particle turbulent intensity radial pro?les are presented in Fig. 16. The turbulent in a spout-?uid bed is obviously non-isotropic. Unlike those investigations on isotropic turbulence (Lun, 2000; Zhou et al., 2004), the present gas and particle turbulent intensities are de?ned as
1 3(

100

u2 + u 2 + u 2 ) u ? x y z

0 0.0

0.1 0.2

0.3

0.4 0.5 0.6 us /ums

0.7

0.8

0.9 1.0

Fig. 15. Comparison of jet penetration depth at various vessel heights by simulation with correlation (dp = 2.0–3.0 mm, Qf = 0.78Qmf ).

jet action in spout-?uid beds. Comparison of jet penetration depths at various spouting gas velocities by simulation with that of by correlation is showed in Fig. 15. The simulation

2 2 2 and 1 ( vx + vy + vz ) v , respectively. In which, u is the ? ? 3 mean gas velocity and v is the mean particle velocity. The gas ? turbulent intensity is always much larger than particle turbulent intensity. For both phase, the turbulent intensity are higher in the jet region and interface of the jet region and annular dense region than near the wall. The gas/solid turbulence in these regions would enhance the gas–solid mixing. It is noted that, unlike the gas turbulent intensity, the particle turbulent intensity in the annular dense region has ?uctuations. This indicates that

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the particle–particle interactions dominate the particle motion in the dense zone. 5. Conclusions

helping to understand the complex ?ow ?elds including jet, recirculation and boundary layer ?ows.

Notation The gas and particle turbulent motions in a rectangular spout?uid bed were simulated three-dimensionally. The particle motion was modeled by DEM and the gas motion was modeled by k ? two-equation turbulent model. Saffman lift force (Shear lift force), Magnus lift force as well as drag force, contract force and gravitational force acting on individual particles were considered when establishing the mathematics models. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas-particle interactions in volume fraction, momentum and kinetic energy. Selected stimulated results were compared to some published experimental and simulation results. The following conclusions can be drawn based on the simulations: (1) The greater the spouting gas velocity, the more obvious entrainments of particles from the annular dense region into the spout region, especially in the distributor region. (2) The percentage of particle–particle colliding decreases with spouting gas velocity, while the value increases with particle diameter. The percentage of particle-wall colliding shows almost no variation with spouting gas velocity increasing and particle diameter. The drag force dominates the particle motion in the jet region, while the contact force dominates the particle motion in the dense annular region especially near the wall. The mean percentage of Saffman lift force and Magnus lift force are almost zero in the jet region and dense annular region, while they reach 6% of the total forces adding to the particles in the boundary of jet region and annular dense region. (3) The concentration of particles increases along radial direction and decreases with increasing spouting gas. The radial distribution of the particle velocity magnitude decreases with vessel height, which is positive and symmetrical along bed width. The particle velocity component in z-direction is positive in the center and it is negative in the annular dense region. (4) The jet penetration depth increases with increasing of spouting jet velocity, the simulation results ?t the calculations based on the correlation proposed by our previous experiments. (5) Analyzed by non-isotropic turbulence theory, the results show that the gas turbulent intensity is always much greater (2–3times) than the particle turbulent intensity. For both phase, the turbulent intensity are higher in the jet region and interface of the jet region and annular dense region than near the wall. However, there is still a great need for experimental veri?cation of these simulation results. Besides, a set of measurements of the kinematic ?ow properties such as particle concentration, particle velocities, turbulence intensities, can be very useful in A CD CLM CLS D dp e Ep Ew fC fD fG fLS fLM fcnij fctij g Gp Gw H Hb Ho Ip kn kt mp Mp np


n n p Qf Qmf r R Rep Re u us ums uf uf x uf z u ?

bed cross section area, mm2 drag coef?cient, dimensionless Magnus lift coef?cient, dimensionless Saffman lift coef?cient, dimensionless column width, mm particle diameter, m restitution coef?cient,dimensionless Modulus of longitudinal elasticity for particle, N/m2 Modulus of longitudinal elasticity for wall, N/m2 contact force, N drag force, N gravitational force, N Saffman lift force, N Magnus lift force, N normal contact force, N tangential contact force, N gravitational acceleration vector, m/s?2 transverse elastic moduli of particle, N/m2 transverse elastic moduli of wall, N/m2 local position in axis direction, mm vessel height, mm initial bed height, mm particle motion of inertia spring coef?cient in normal direction, N/m spring coef?cient in tangential direction, N/m particle mass, kg particle torque, Nm number of particles per unit volume, dimensionless normal unit vector, dimensionless maximum number of particle, dimensionless pressure, Pa ?uidizing gas ?ow rate, Nm3 /h minimum ?uidizing gas ?ow rate, Nm3 /h local position in radial direction, mm half bed width, mm particle Reynolds number, dimensionless particle rotation Reynolds number, dimensionless gas velocity, m/s spouting gas velocity, m/s minimum spouting gas velocity, m/s ?uidizing gas velocity, m/s x-direction ?uidizing gas component velocity, m/s z-direction ?uidizing gas component velocity, m/s mean gas velocity, m/s

W. Zhong et al. / Chemical Engineering Science 61 (2006) 1571 – 1584

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ur vp v ? vntij vtij Greek letters
p w ij nij tij

translational relative velocity, m/s particle velocity, m/s mean particle velocity, m/s normal relative velocity, m/s tangential relative velocity, m/s

t x, y, z u v p
n t f t p w g p l d ij t p

particle Poisson’s ratio, dimensionless wall Poisson’s ratio, dimensionless Kronecker number, dimensionless normal displacements between particle i and particle j , m tangential displacements between particle i and particle j ,m time step of calculation, s cell size, mm gas ?uctuating velocity, m/s particle ?uctuating velocity, m/s pressure drop, Pa void fraction, dimensionless damping coef?cients in normal direction, kg/s damping coef?cients in tangential direction, kg/s gas dynamic viscosity, Pa s slide frictional coef?cient,dimensionless gas turbulent viscosity, Pa s particle–particle friction coef?cient, dimensionless particle-wall friction coef?cient, dimensionless gas density, kg/Nm3 particle density, kg/m3 Lagrangian time scale of gas phase, dimensionless response time scale of particle phase, dimensionless gas turbulence stress, Pa turbulent Schmidt number, dimensionless turbulence dissipation rate, m2 /s3 particle rotational velocity, s?1

Acknowledgements Financial supports from the National Key Program of Basic Research in China (G199902210535 and 2004CB217702), and the Foundation of Graduate Creative Program of JiangSu (XM04-28) are sincerely acknowledged. The authors also express sincere gratitude to the respected professors, Prof. Y. Tsuji and Prof. J. R. Grace, for kindly presenting us some of their valuable papers in year 2003, and Prof. M. Horio, E. Anthony and B. Leckner for constructive advices during their visiting periods in our laboratory, which contributed to our research. References
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