CFD simulation of smooth and T-abrupt exits in circulating fluidized bed risers

Particuology 8 (2010) 343–350

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CFD simulation of smooth and T-abrupt exits in circulating fluidized bed risers Xuezhi Wu a,b,∗ , Fan Jiang a , Xiang Xu a , Yunhan Xiao a a b

Key Laboratory of Advanced Energy and Power, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China Graduate University of the Chinese Academy of Sciences, Beijing 100049, China

a r t i c l e

i n f o

Article history: Received 22 July 2009 Received in revised form 9 November 2009 Accepted 24 January 2010 Keywords: T-abrupt exit Smooth exit Gas–solid flow CFB EMMS drag force model

a b s t r a c t Gas–solid flow in circulating fluidized bed (CFB) risers depends not only on operating conditions but also on exit configurations. Few studies investigated the effects of exit configurations on flow structure using computational fluid dynamics (CFD). This paper provides a 2D two-fluid model to simulate a cold bench-scale square cross-section riser with smooth and T-abrupt exits. The drag force between the gas and solid phases plays an important role in CFD. Since the drag force model based on homogeneous twophase flow, such as the Wen-Yu correlation, could not capture the heterogeneous structures in gas–solid flow, the structure-dependent energy-minimization multi-scale (EMMS) drag force model (Wang, Ge, & Li, 2008), applicable for Geldart B particles (sand), was integrated into the two-fluid model. The calculated axial solids hold-up profiles were respectively exponential curve for smooth exit and C-shaped curve for T-abrupt exit, both consistent with experimental data. This study once again proves the key role of drag force in CFD simulation and also shows the validity of CFD simulation (two-fluid model) to describe exit effects on gas–solid flow in CFB risers. © 2010 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

1. Introduction The hydrodynamics of the circulating fluidized bed (CFB) riser is extremely complex, showing that the distribution of axial solids concentration depends not only on operating conditions such as superficial gas velocity, solids flux and particle properties, but also on the exit configuration of the riser (for reviews, see Grace, 1996; Harris, Davidson, & Thorpe, 2003a,b). Generally, two types of exits have been studied, a smooth, ‘single pass’ exit and an abrupt, ‘refluxing’ exit (Harris et al., 2003a,b). The ‘single pass’ exit is smoothly curved and allows for large net solids fluxes while the abrupt exit usually consist of a 90◦ bend, namely the T-abrupt exit, which has been shown in laboratory to cause significant internal refluxing of solids. Senior and Brereton (1992) examined the effects of different exit geometries on solids concentration in the CFB riser, showing that solids concentration was more intense in a riser with abrupt exit than that with an elbow exit. Brereton and Grace (1994) investigated a 152 mm diameter and 9.3 m height CFB riser with three different exit configurations. An abrupt riser exit resulted in considerable increase of solids concentration in the upper region of a riser due to inertial separation

∗ Corresponding author at: Key Laboratory of Advanced Energy and Power, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China. Fax: +86 10 82543102. E-mail address: [email protected] (X. Wu).

of particles near the top. Using the parameter Rf , defined by Senior and Brereton (1992) as the ratio of descending and ascending solid flows, Mickal et al. (2001) explained the effect of the T-abrupt exit in terms of hydrodynamic structure. Gupta and Berruti (2000) drew a conceptual axial solids hold-up profiles, as shown in Fig. 1, illustrating the effects of different operating conditions and riser exit geometries. Fig. 1 showed that with stronger exit restriction, the solids concentration becomes higher in the top zone of the riser. In addition, with stronger exit restriction, the exit effect becomes more noticeable and the solids hold-up profile varied from an exponential curve (the thick line) to a ‘C-shape’ curve (curve C) when solid flux increases. Several studies were devoted to hydrodynamic modeling of risers with exit effects. Kunii and Levenspiel (1995) developed a semi-empirical model for bed hydrodynamics and compared their calculated results with available experimental data. Kim, Kim, & Lee (2002) combined Kunii and Levenspiel (1995) model with Zenz and Weil (1958) empirical axial solids concentration correlation to predict the axial solids hold-up profile in risers with abrupt exits. The calculated results agreed well with the experimental data. Due to difference between experimental apparatus, limitations of measurements, and the inherent complexity of gas–solid flow, experimentally measured exit effects could not accurately describe the flow structure of risers, and neither were the empirical and semi-empirical correlations based on experiments universal enough for wide application to various CFB units. With the recent development of computational fluid dynamics (CFD), many numer-

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doi:10.1016/j.partic.2010.01.007

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X. Wu et al. / Particuology 8 (2010) 343–350

Nomenclature a CD0 dcl dp e f Fd g g0 Gs H H0 Hd k Nst P U u z

inertial term, m/s2 standard drag coefficient for a particle cluster diameter, m particle diameter, m restitution coefficient volume fraction of dense phase drag force in a control volume, N/m3 gravitational acceleration, m/s2 radial distribution function solids flux, kg/m2 s total bed height, m initial bed height, m heterogeneity index turbulent kinetic energy of gas phase, m2 s2 mass-specific energy consumption for suspending and transporting particles, W/kg pressure, Pa superficial velocity, m/s real velocity, m/s bed height, m

Greek letters ˇ drag coefficient in a control volume, kg/m3 s ε turbulent energy dissipation in the gas phase, m2 s voidage εg εs solids concentration εsm solid packing limit εmf minimum fluidization voidage  viscosity, Pa s  density, kg/m3  stress tensor, Pa  granular temperature, m2 /s2 Subscripts g gas phase s solid phase, or slip p particle c dense phase f dilute phase

ical studies have been devoted to gas–solid flow in CFB risers (reviewed by Gidaspow, Jung, & Singh, 2004; Li et al., 2005), though few simulation work has been aimed at exit effects. De Wilde, Marin, & Heynderickx (2003) used the two-fluid model with the kinetic theory of granular flow (KTGF) to simulate a 3D riser with a T-abrupt exit. The simulation results indicated that the opening area at the exit region directly affected the behavior of the gas–solid flow in the riser. However, their calculated results were not compared with experimental data but only described qualitatively for flow characterization of risers with exit effects. Drag force was considered by many researchers as a key parameter for simulating CFB systems (Qi, Li, Xi, & You, 2007; Wang, Ge, & Li, 2008; Wang & Li, 2007; Yang, Wang, Ge, & Li, 2003). O’Brien and Syamlal (1993) found that drag correlations must be corrected to account for cluster formation, and obtained a modified drag correlation under two test conditions (Gs = 98 and 147 kg/m2 s) according to experimental data. Qi, You, Boemer, & Renz (2000) claimed that if the drag correlation derived from Ergun equation (Ergun, 1952) based on homogeneous flow was used, the simulated gas–solid flow in CFB risers would be very dilute. Li et al. (2005) pointed out that the drag coefficients based on average approaches

Fig. 1. Conceptual axial solids hold-up profiles in fast fluidization and pneumatic transport flow regimes, illustrating the effect of an abrupt riser exit configuration (Gupta & Berruti, 2000), with curves A–C representing respectively small, more profound and extreme exit effects.

were inadequate to represent the gas–solid contacting in CFB systems, proposing that the drag coefficient significantly depends on structural changes. Yang et al. (2003) first integrated the energyminimization multi-scale (EMMS) drag force model developed by Li’s team into the two-fluid model. Because the EMMS model was a mechanism model describing the heterogeneous structures (clusters) in CFB risers, the calculated axial solids hold-up profile agreed well with experimental data. Wang et al. (2008) extended the EMMS drag model using a stochastic geometry approach named doubly stochastic Poisson process, claiming the model to be applicable to both Geldart A and B particles. In this study, the effects of exit configurations, smooth and Tabrupt, on the flow structure in a bench-scale rectangular CFB riser were investigated experimentally, followed by numerical simulation based on the combination of a 2D two-fluid model and the EMMS drag force model (Wang et al., 2008). The calculated results were then compared with the experimental results. 2. Experimental apparatus The experimental apparatus used in this study is illustrated in Fig. 2. The system consists of a 0.27 m × 0.27 m square cross-section riser with a height of approximately 10 m, a U valve, a standpipe and a cyclone. The particles used in the experiments were sand, 2630 kg/m3 in density and 330 ␮m for average diameter. When steady state was established, the solids flux (Gs ) was calculated by measuring the solids mass passing through the stand pipe during a given interval; the axial average solids concentration was calculated by vertical pressure measurements. 3. Modeling 3.1. Two-fluid model The two-fluid model (for reviews, see Enwald, Peirano, & Almstedt, 1996) consists of mass and momentum conservation equations, as well as constitutive laws for gas and solid phases. The k–ε model is implemented to describe the turbulence of gas phase. For solid phase, the turbulence equation is derived from the kinetic theory of granular flow (Gidaspow, 1994; Jenkins & Savage, 1983). The governing equations of the two-fluid model are listed in Table 1 (Syamlal, Rogers, & O’Brien, 1993).

X. Wu et al. / Particuology 8 (2010) 343–350

345

tia difference between the dilute phase and the clusters, which is particularly important for Geldart B particles. Eqs. (8) and (9) show the empirical correlation between cluster voidage εc and average voidage εg . Eq. (10) is the energy minimum criterion. Detailed derivations are depicted by Wang et al. (2008). 3.3. Calculation method The EMMS drag force model with 10 independent variables (Usc , Usf , Usi , Upc , Upf , Uc , Uf , ac , af , dcl ) is solved through the set of nonlinear equations in Table 2. The drag force coefficient can be expressed as:

⎧   3 ៝ ⎪ ៝  −2.65 if εg ≥ 0.7, ⎪ ⎨ 4dp CD0 (1 − εg )εg g · ug − us · εg Hd   ˇ= (1 − εg )g u៝g − u៝s  (1 − εg )2 g ⎪ ⎪ + 1.75 if εg < 0.7, ⎩ 150 2 dp

εg dp

(11) where Hd is the heterogeneity index, accounting for the hydrodynamic disparity between homogeneous and heterogeneous fluidization, defined as: Hd =

Fd,EMMS , Fd,Wen-Yu

(12)

where Fd,EMMS = εg [f (1 − εc )(g + ac ) + (1 − f )(1 − εf )(g + af )](s − g ),(13)

  3 CD0 (1 − εg )εg g · u៝g − u៝s  · ε−2.65 . g 4ds

Fd,Wen-Yu = Fig. 2. Schematic diagram of the experimental CFB.

3.2. EMMS drag force model The equations of the extended EMMS model (Wang et al., 2008) are listed in Table 2. In this model, the gas–solid flow in the riser is characterized by two-phase structures consisting of a particle-rich dense phase (clusters) and a fluid-rich dilute phase. The momentum balance and continuity equations for the dense phase, the dilute phase are represented as Eqs. (1)–(5). The added mass force balance (Eq. (7)) cannot be neglected here because of the large iner-

(14)

The Wen-Yu correlation Fd,Wen-Yu (Wen & Yu, 1966) is one of the typical expressions of the drag force in heterogeneous fluidization, which can be viewed as a contrast factor without considering the heterogeneous structure. The CFD simulations were carried out with the code MFIX, which was previously used to model the flow in a bubbling fluidized bed (Gera, Syamlal, & O’Brien, 2004). The governing equations and the kinetic theory of granular flow (KTGF) described in the previous section (Table 2) were implemented by this code. After solving the set of nonlinear Eqs. (1)–(10) for given Gs and Ug , the

Table 1 Governing equations of two-fluid model. Mass conservation equations ∂ (εg g ) + ∂x∂ (εg g ugi ) = 0 ∂t

Gas phase stress gij = 2gt Sgij

i

∂ ∂t

(εs s ) +

∂ ∂xi

(εs s usi ) = 0

Momentum conservation equations ∂ ∂t ∂ ∂t

(εg g ugi ) +

∂ ∂xj

(εs s usi ) +

∂ ∂xj

(εg g ugj ugi ) = −εg (εs s usj usi ) =

∂p −εs ∂xg i

Ssij =

2



∂xj

sij = −Ps +

+

 ∂ugi ∂xj

 ∂k

∂ugj

+



∂xi



1 ∂ugi 3 ∂xi

−



∂gij

+ +

∂xj ∂sij ∂xj

− ˇ(ugi − usi ) + εg g gi + ˇ(ugi − usi ) + εs s gi

εs s εs s

∂k + usj ∂x

 ∂ε

 ∂ε

∂t

j

+ usj ∂x

∂t

j

=

∂ ∂xi

=

∂ ∂xi



∂xi



−



∂u b ∂x i i

1 ∂usi 3 ∂xi

s =

+ εs sij

∂usj

+ εs k

C1ε sij

 ε

ıij + 2s Ssij

Dsij =

1 2



∂xi

+ ˘k − εs s ε

K 2 D2 ε2 +4K4 εs [K2 D2 +2K3 Dsij Dsij ] s

−K1 εs Dsii +

 ∂usi ∂xj

+

1

∂usj

sii

sii

2εs K4



∂xi



Solid phase bulk viscosity

s =

Solid phase shear viscosity

5  d 96 s p



 ∂ε

 εs εt ∂x i

Ps = εs s s [1 + 4 εs go ]

s,dilute =

∂k

k ∂xi

Solid phase pressure

s =



εs  t

Granular energy equation

 ∂usj

4 2 ε  d g (1 5 s s p 0

ıij

Turbulence equations for gas phase

∂pg ∂xi

Solid phase stress

 ∂usi 1

1 2

Sgij =



+ e)



s 

s 

+

2s,dilute (1+e)g0



1+

4 (1 5

+ e)εs g0

2

4 2 ε  d g (1 3 s s p 0

+ e)

s 

Radial distribution function



g0 =

1−



εs εsm

1/3 −1

∂usj ∂xi

2



− s C1ε ε + ˘ε

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X. Wu et al. / Particuology 8 (2010) 343–350 Table 2 Equations of EMMS model.

Mass conservation for gas

3 1 − εc 1 3 2 f Usc f + Cdi f Usi2 − (1 − εc )(p − f )(g + ac ) = 0(1) Cdc 4 4 ds dcl 1 − εf 3 2 Cdf f Usf − (1 − εf )(p − f )(g + af ) = 0 (2) 4 dp 1 − εf f 1 1 − ε c 2 2 f Usf Cdf + f Usi2 − Cdc g Usc =0 (3) Cdi dp 1−f dcl ds (4) Ug − Uf (1 − f ) − Us f = 0

Mass conservation for particle

Us − Usf (1 − f ) − Usc f = 0

(5)

Definition of mean voidage

εg = εf (1 − f ) + εs f

(6)

Force balance for clusters Force balance for dilute phase Pressure drop balance between clusters and dilute phase

Added mass force balance Cluster voidge

ac − af =

(7)

1 1+2f 2 1−f

(εf − εc )f [p (1 − εf ) + g εf ] εc = εg + nε , n = 2



ε =

Energy minimum criterion

s2 (p − g )g

(8)

ε2s (1 − εs )4

1 + 4εs + 4ε2s − 4ε3s + ε4s 1 Nst = [mf Ff Uf + mc Fc Uc + mi Fi Uf (1 − f )] → min p (1 − εg )

(9) (10)

heterogeneity index (Hd ) for each voidage (εg ) was obtained and integrated with the MFIX code. Fig. 3 describes the solving procedure of CFD simulation in combination with the EMMS drag model in detail. Fig. 4 shows calculated Hd from EMMS drag force model at Gs = 61 kg/m2 s, Ug = 6.85 m/s and Gs = 110 kg/m2 s, Ug = 6.85 m/s. 4. Simulation conditions An experimental study was carried out to measure solids circulation rates and solids concentration profiles in a square crosssection riser with smooth or T-abrupt exit of a bench-scale cold circulating fluidized bed (CFB), followed by corresponding CFD sim-

Fig. 4. Heterogeneity index Hd calculated from EMMS drag model.

ulations. Fig. 5(a) and (b) shows the bed geometries and two exit configurations. The simulation parameters for both exit configurations are summarized in Table 3. For Case 1 (smooth exit), Cases 2 and 3 (T-abrupt exit), the air velocity and solids mass flux were respectively specified at the air inlet and the solid inlet. Atmospheric pressure was specified at the outlet. Tangential and normal velocities of both Table 3 Simulation parameters.

Fig. 3. Procedure of CFD simulation in combination with EMMS drag model.

Particle diameter, dp (␮m) Particle density, s (kg/m3 ) Riser height, H (m) Riser cross-sectional area, A (m2 ) Superficial gas velocity, Ug (m/s) Solids flux, Gs (kg/m2 s) Coefficient of restitution, e (–) Packed solid volume fraction, εsm (–) Calculation time (s)

Case 1 Smooth exit

Case 2 T-abrupt exit

Case 3 T-abrupt exit

330 2630 10.44 0.27 × 0.27

330 2630 10.515 0.27 × 0.27

330 2630 10.515 0.27 × 0.27

6.85

6.85

6.85

110 0.9

110 0.9

61 0.9

0.63

0.63

0.63

25

25

25

X. Wu et al. / Particuology 8 (2010) 343–350

347

Fig. 5. (a) The riser configuration and (b) the smooth, T-abrupt exits and the inlets geometries.

phases were set to zero (no slip condition) at the wall. Initially, the bed was vacant and air velocity was set as the superficial gas velocity (Table 3). 5. Results and discussion The simulation for any of the above three cases lasted 25 s or longer until the outlet solids flux oscillated around some steady value, as shown in Fig. 6. The average outlet solids flux Gs from 5 to 25 s (dash line in Fig. 6) approximates the measured value in experiments, illustrating the calculated results have reached steady state. Thus the time-averaged values (e.g. solids volume fraction) in 5–25 s would be compared with the corresponding experimental values in the following sections. It can also be observed that the solids flux in Cases 2 and 3 (T-abrupt exit) oscillates much more intensively than that in Case 1 (smooth exit), reflecting enhanced flow instability caused by the strong exit restriction. In addition, for the above three cases, the outlet solids fluxes calculated by WenYu correlation show stronger instability than those calculated by EMMS drag model, because the Wen-Yu correlation magnifies the drag force between the gas and solid phases. 5.1. Axial solids concentration profile Fig. 7 shows the time-averaged axial profiles of solids volume fraction, computed by both Wen-Yu and EMMS drag force models, and their comparison with experimental data, showing that the two-fluid model combined with EMMS drag force model better captures the axial solids hold-up characteristics of the three cases. Both the experimental and calculated average solids concentration of the whole risers in Case 2 (T-abrupt exit) is twice as high as that in Case 1 (smooth exit), owing to the strong restriction of the T-abrupt exit configuration. In Case 1, the experimental and calculated axial solids hold-up profiles are essentially exponential, i.e., the solids concentration decreases with bed height. In Case 2, the experimental and calculated axial solids hold-up profiles present ‘C-shape’ curves, i.e., the solids concentration in the top zone is a little higher than that in the middle of the riser. In Case 3, both

the experimental and calculated axial solids hold-up profiles are exponential, for the smaller solids flux somewhat suppresses the T-abrupt exit effects. The CFD calculated values using EMMS drag show good agreement with experimental data in all the above three cases, forming a contrast against simulation using Wen-Yu drag correlation which did not so well reflect the axial hold-up characteristics for the three cases: much lower than experimental values in the bottom zone of the risers, which can be attributed to cluster formation. The heterogeneity index Hd is about 0.15 when the solids concentration is about 0.1 (see Fig. 4), that is, the Wen-Yu drag correlation overestimates the drag coefficient by 5–6 times in the bottom zone of the risers. In Case 1 (smooth exit), Wen-Yu drag correlation leads to a very dilute bed, which resembles the case reported by Qi et al. (2000). In Case 2 (T-abrupt exit), the calculated solids concentration in the middle and top zones is close to experimental data, which qualitatively reflects the strong T-abrupt exit effects. 5.2. Radial solids concentration profile Compared to axial solids hold-up profile, investigations on radial solids concentration were much maturer. Many correlations on radial solids concentration were proposed based on experimental data, though few of them considered CFB exit effects. Xu, Sun, & Gao (2004) proposed the following radial voidage profile correlation for fast fluidization in CFB risers: 11

a( r ) εs (r) = 1 − ε¯ g R

2.5

+ ( Rr )

+b

,

(15)

in which a=

ln εw , ln ε¯ g − 1 − b

(16)

b=

ln ε0 , ln ε¯ g

(17)

in which ε¯ g is the averaged radial voidage, r is the radial location and R is the hydraulic radius of the square cross-section

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X. Wu et al. / Particuology 8 (2010) 343–350

Fig. 8. Calculated radial profiles of time-average solids volume fraction at different heights and their comparison with values predicted using the correlation of Xu et al. (2004). (Case 1: smooth exit, Gs = 110 kg/m2 s, Ug = 6.85 m/s; Case 2: T-abrupt exit, Gs = 110 kg/m2 s, Ug = 6.85 m/s).

riser, and εw and ε0 can be calculated according to the following equations:



εw = and Fig. 6. Calculated solids flux at outlet. (Case 1: smooth exit, Gs = 110 kg/m2 s, Ug = 6.85 m/s; Case 2: T-abrupt exit, Gs = 110 kg/m2 s, Ug = 6.85 m/s; Case 3: T-abrupt exit, Gs = 61 kg/m2 s, Ug = 6.85 m/s).

ε0 =



for ε¯ g < 0.75 , 1.0 − εmf εmf + (¯εg − 0.75), for ε¯ g ≥ 0.75 0.25

(18)

0.895 − εmf (¯εg − εmf ), for ε¯ g < 0.75 . 0.75 − εmf 1 − 0.42(1.0 − ε¯ g ), for ε¯ g ≥ 0.75

(19)

εmf ,

εmf +

Fig. 8 provides CFD calculated radial profiles of time-average solids volume fraction at different riser heights as compared to values predicted using the correlation of Xu et al. (2004). In Case 1

Fig. 7. Comparison between experimental and calculated results of time-averaged axial solids hold-up. (Case 1: smooth exit, Gs = 110 kg/m2 s, Ug = 6.85 m/s; Case 2: T-abrupt exit, Gs = 110 kg/m2 s, Ug = 6.85 m/s; Case 3: T-abrupt exit, Gs = 61 kg/m2 s, Ug = 6.85 m/s).

X. Wu et al. / Particuology 8 (2010) 343–350

349

Fig. 9. Snapshots of voidage distribution in inner flow field of the riser: Case 1, smooth exit (Gs = 110 kg/m2 s, Ug = 6.85 m/s); Case 2, T-abrupt exit (Gs = 110 kg/m2 s, Ug = 6.85 m/s).

(smooth exit), the CFD results show better agreement in trend with data predicted using correlation based on experiments for smooth exit and also better radial symmetry, while in Case 2 (T-abrupt exit), the CFD results present marked radial asymmetryattributed to the strong exit restriction (see Section 5.3). The coexistence of coreannulus flow regions as well as its progressive evolution along the axial direction in both cases can also be seen in Fig. 8. The radial solids concentration profiles flatten with increase of riser height, indicating that the solids distribution becomes more uniform along the axial direction, especially for Case 1. 5.3. Flow structures with exit effects Fig. 9 illustrates the simulated snapshots of voidage distribution in the inner flow fields of risers, indicating that the solids concentration of the whole bed for Case 1 (smooth exit) is relatively dilute, though somewhat denser at the bottom and at the top near the smooth exit where particles assemble close to the packing limit of 0.63, as already shown in Fig. 7 for z = 10 m. For Case 2, both the bottom and the top zones are dense, and the solids concentration varies intensively with time. Fig. 9 also shows the heterogeneous structure of the gas–solid flow, with clusters forming and dissolving dynamically. Some clusters move upward to the top of the riser and mix backward, while others exit at the top, particularly for Case 2. Cluster movements lead to flow instability of the riser and variation of outlet solids mass flux (Fig. 6). Obviously the stronger restriction of T-abrupt exit enhances particle aggregation, back mixing and flow instability. Fig. 10 re-enacts the dynamic characteristics of gas–solid flow by using solids stream lines plotted for both cases at t = 10 s. At the top of the risers, the smooth exit leads the particles to ‘single pass’ through the outlet, while the T-abrupt exit induces curved solids stream lines indicating downward flow. In Case 2 (T-abrupt exit), the down flow is maximal near the wall opposite the outlet, similar to the 3D simulation of De Wilde et al. (2003). The 30◦ -inclined solids inlet effect for both cases are also represented in Fig. 10. Close to the solid inlet, gravity and inertia forces of downward particles are balanced by drag force from the fluidizing air, leading to solids aggregation with solids concentration near the solid inlets much higher than those for any other locations except the top zone of the riser.

Fig. 10. CFD simulated solids stream lines: Case 1, smooth exit (Gs = 110 kg/m2 s, Ug = 6.85 m/s); Case 2, T-abrupt exit (Gs = 110 kg/m2 s, Ug = 6.85 m/s).

Figs. 9 and 10 also re-emphasize the intense radial asymmetry of the gas–solid flow in Case 2 (T-abrupt exit). There is a large vortex near the wall opposite the outlet, which causes refluxing in the whole bed. At the bottom zone near the solids inlet for both cases, there exist smaller vortices with intense oscillation. Both inlet and outlet effects are therefore considered to be the reasons for radial asymmetry. 5.4. Factors influencing exit effects Kunii and Levenspiel (1995) mathematical model for bed hydrodynamics provided a reasonable estimation of solids hold-up profile with exit effects. However, their model relied on an empirical parameter, the influence length of the riser exit, which is an important parameter reflecting the exit effect. There have been conflicting results in the literature concerning the influence of riser exits. Some researchers suggested the influence of the exit extends over a considerable length of the riser (e.g. Lim, Zhu, & Grace, 1995; Martin et al., 1992), some suggested the effect occurs only in the immediate vicinity of the exit (e.g. Bai, Jin, Yu, & Zhu, 1992), while others suggested there was little influence from the exit (e.g. Lackermeier & Werther, 2002). Harris et al. (2003a,b) pointed out that the length of influence of gas–solid flow structure in a riser due to different riser exit geometries depends on many factors, such as exit shape, size of bed, riser height, diameter of particles, superficial gas velocity, solids flux and fluid properties. Gupta and Reddy (2005) claimed that the influence length increased with increasing solids flux. The riser with a T-abrupt exit was also simulated by Yang et al. (2003) and Wang and Li (2007). However, the solids flux used was so small (Gs = 14.3 kg/m2 s) that the influence length of the riser exit could be neglected. In this study, both experimental (Fig. 7) and CFD simulation results (Figs. 7, 9 and 10) showed that the influence length of the riser exits extends almost through the whole length of the risers. While empirical correlation of the influence length could hardly take into account the so many influencing factors, CFD sim-

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ulation provides an important tool to estimate the exit effects of the riser. 6. Conclusions A 2D CFD simulation using the two-fluid model combined with the EMMS drag force model is employed in studying bench-scale CFB risers with smooth and T-abrupt exits. (1) The calculated axial solids hold-up profiles well agree experimental data, that is, an exponential curve for smooth exit and a ‘C-shape’ curve for T-abrupt exit, thus validating the rationality of the model. (2) When the solids flux is as large as 110 kg/m2 s, the T-abrupt exit restriction greatly exacerbates flow instability and radial solids hold-up asymmetry, densifying the top zone of the riser in accordance to both experiment and simulation. The T-abrupt exit effects are not significant when the solids flux is small (61 kg/m2 s or less) for our experimental apparatus. (3) This work once again shows the ability of EMMS drag force model to capture the heterogeneous structures (clusters) of CFB risers. The structure-dependent drag force is one of the key points of CFD simulation. Acknowledgement This work was financially supported by National High-tech Research and Development Program of China under Grant No. 2006AA05A103. References Bai, D. R., Jin, Y., Yu, Z. Q., & Zhu, J. X. (1992). The axial distribution of the crosssectionally averaged voidage in fast fluidized beds. Powder Technology, 71, 51–58. Brereton, C. M. H., & Grace, J. R. (1994). End effects in circulating fluidized bed hydrodynamics. In A. A. Avidan (Ed.), Circulating fluidized bed technology IV (pp. 137–144). PA, USA: Hidden Valley. De Wilde, J., Marin, G. B., & Heynderickx, G. J. (2003). The effects of abrupt T-outlets in a riser: 3D simulation using the kinetic theory of granular flow. Chemical Engineering Science, 58(3–6), 877–885. Enwald, H., Peirano, E., & Almstedt, A.-E. (1996). Eulerian two-phase flow theory applied to fluidization. International Journal of Multiphase Flow, 22(Suppl. 1), 21–66. Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48(1), 89–94. Gera, D., Syamlal, M., & O’Brien, T. (2004). Hydrodynamics of particle segregation in fluidized beds. International Journal of Multiphase Flow, 30, 419–428. Gidaspow, D. (1994). Multiphase flow and fluidization: Continuum and kinetic theory descriptions. New York: Academic Press. Gidaspow, D., Jung, J., & Singh, R. K. (2004). Hydrodynamics of fluidization using kinetic theory: An emerging paradigm 2002 Flour-Daniel lecture. Powder Technology, 148, 123–141.

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