LES-DEM investigation of gas–solid flow dynamics in an internally circulating fluidized bed

Chemical Engineering Science 101 (2013) 213–227

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LES-DEM investigation of gas–solid flow dynamics in an internally circulating fluidized bed Mingming Fang, Kun Luo, Shiliang Yang, Ke Zhang, Jianren Fan n State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China

H I G H L I G H T S








Flow dynamics of a baffle-type ICFB is investigated using the LES-DEM method. Circulation characteristics and the governing mechanisms are revealed and discussed. Influences of different parameters on the circulation behavior are evaluated. Particularity and similarity with the previous investigations are addressed. Solid residence time and its variation with different parameters are figured out.

art ic l e i nf o

a b s t r a c t

Article history: Received 9 October 2012 Received in revised form 13 June 2013 Accepted 18 June 2013 Available online 26 June 2013

Gas–solid flow dynamics is numerically simulated in an internally circulating fluidized bed (ICFB) featuring a centrally located baffle plate and uneven aeration. Its detailed features are derived using the computational fluid dynamics-discrete element method (CFD-DEM). The gas motion is resolved by means of large eddy simulation (LES) while the dynamics of solid phase is handled by the soft-sphere model. The internal circulation of the solids (spherical particles, with diameter of 1.2 mm and density 1000 kg/m3) is modeled to clarify the flow characteristics of the bed for different design or operating parameters, such as superficial gas velocity, gap height, inclination angle of the gas distributor, baffle plate or side wall of the bed. Both the gas–solid flow and the underlying mechanisms of solids circulation are addressed together with the simulation results. Meanwhile, the operational control behavior of different parameters is quantified by estimating both the solids circulation flux (SCF) and the gas bypassing flux (GBF). The computational results indicate that the performance of the bed can easily be regulated by adjusting the aeration to each chamber of the bed and that within the range tested, increasing gap height enhances solids circulation and suppresses gas bypassing. There is an optimal value for the inclination angle of both side wall and baffle plate. However, increasing the inclination angle of the gas distributor continuously suppresses solids circulation. Furthermore, the residence time of solids in each chamber is figured out and its variations with these design and operating parameters are examined. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Dynamic simulation Multiphase flow Fluidization Mathematical modeling Discrete element method Internally circulating fluidized bed

1. Introduction An internally circulating fluidized bed (ICFB) is a unit featuring appropriate internal structures to divide the bed into different chambers and promote the internal circulation of solids by means of differentiated aeration among these chambers. Well aerated parts engender carry-over reporting to the denser, less aerated chamber(s); the latter supplies material to the former through a suitably located port. Internal circulation provides lateral mixing, which largely remains absent in a bubbling bed. There are two

n

Corresponding author. Tel./fax: +86 571 87951764. E-mail address: [email protected] (J. Fan).

0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.06.038

major kinds of ICFBs: the draft-tube type (LaNauze, 1976) and the baffle type (Kuramoto et al., 1986). Due to its special layout and aeration arrangement, these ICFBs exhibit exclusive flow characteristics and advantages over other conventional fluidized beds. Compared with the circulating fluidized bed (CFB), both construction cost and heat loss are reduced. Shorter and more evenly distributed solids residence time within each chamber (Milne et al., 1999) may provide better mixing and higher conversion efficiency of solids than the bubbling/spouted bed reactors (Lee et al., 1992; Xie, 2003). Meanwhile, intensified attrition of particles makes the use of calcium sorbents more efficient and an improved pollutant control performance is reported compared with other reactors (Chu and Hwang, 2005). Accordingly, ICFBs have been applied to different fields, e.g. biomass gasification

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(Zhang et al., 2012), coal gasification and combustion (Kim et al., 1997; Lee et al., 1998), solid waste disposal (Mukadi et al., 1999; Mukadi et al., 2000), desulfurization (Chu and Hwang, 2002, 2005), and even a membrane reactor (Xie et al., 2009). The gas–solid flow patterns of the ICFBs are essential for realizing the merits mentioned above. Knowledge of solids internal circulation is vitally important to the design, control and optimization of ICFBs. In addition, the solids circulation flux (SCF, solids flux through the gap below the baffle, denotes unit capacity for granular material processing), the gas bypassing flux (GBF, gas exchange flux through the gap below the baffle, indicates the gas leakage between the chambers) and the solids residence time (SRT, the time solids spend in different parts of the unit, is a key parameter of many processes, e.g. gasification and pyrolysis) are three important parameters of the bed that have to be determined to quantify the influence of different design and operating parameters on ICFB performance. As a result, there is growing interest in the investigation of ICFBs. Song et al. (1997) studied the influence of different gas distributors on bed performance, and the conical distributor displayed the best capability to control solids circulation. Ahn et al. (1999) observed a rise in SCF with increasing orifice diameter in the draft tube. The effect of temperature on solids circulation was studied by Namkung et al. (2000), finding that both the average voidage in the annulus and the SCF increase as temperature rises. Kim et al. (2002) found that solids with larger diameter reduce the SCF. Similar results were also obtained by Shih et al. (2003), and the effect of draft-tube height and its inner diameter on the circulation of solids was also studied. Fang et al. (2003) studied solids circulation in adjacent twin fluidized beds and proposed a model to calculate the flow rate of solids through the orifices of the central separating wall. Chu and Hwang (2005) investigated solids attrition and desulfurization, pointing out that attrition is stimulated by larger velocity differences between the two chambers and that the use of larger particles lowers the desulfurization efficiency of the system. Jeon et al. (2008) measured the SCF in a square ICFB and proposed a correlation of the gas bypassing fraction with the velocities to the two chambers. The flow dynamics of the gas–solid in an industrial ICFB is very difficult to depict in detail, even for cold-state operation. In addition to the experimental approaches, numerical modeling has become a powerful tool to tackle these complexities. Meanwhile, the influence of each design or operating parameter on performance can conveniently be evaluated. Numerical modeling has the potential to handle complex multiphase flows, such as those encountered in ICFBs, making use of parallel computation, professional software and computational algorithms. It is also indispensable in process design, control and optimization of complex multiphase systems (Schwarz, 1994). Mukadi et al. (1999, 2000) successfully modeled the thermal treatment of industrial solid waste in an ICFB. Marschall and Mleczko (1999) proposed a model to analyze the effect of various design and operating parameters on bed performance, and confirmed that the height of the annulus between reactor and draft-tube is crucial to circulation control. Besides, Kim et al. (2000) presented a model based on bed hydrodynamics, reaction kinetics and an empirical correlation of pyrolysis yields to predict the fuel gasification characteristics of a specific ICFB. Bin et al. (2002) conducted a two-dimensional DEM simulation of an ICFB, and the intensification of solids horizontal dispersion was addressed. Recently, Feng et al. (2012) carried out a two-dimensional simulation of a baffletype ICFB using an Eulerian–Eulerian model (EEM) and studied the influence of several operating parameters on the bed performance. However, such studies mainly focus on draft-tube-type ICFBs while comparatively less attention has been paid to baffle-type units. Moreover, up-to-date reports on issues such as flow dynamics, operational control and solids residence time distributions in the ICFBs are still limited (Bin et al., 2002).

To provide a deeper insight into the gas–solid flow characteristics and the underlying mechanism of solids circulation, the present work proposes a numerical study of a lab-scale baffle-type ICFB using the computational fluid dynamics-discrete element method (CFD-DEM). The lower part of the simulated unit is split into a reaction chamber (RC) and a heat exchange chamber (HEC) by a centrally located baffle (Fig. 1). Internal circulation of spherical solids with uniform diameter of 1.2 mm and density 1000 kg/m3 is established to illustrate flow dynamics of biomass particles. Furthermore, simulations are carried out to verify the process control and estimate the intensification of the circulation for different design and operating parameters (e.g. the bed aeration setups, gap heights, inclination angle of gas distributor, baffle plate and side wall of the HEC) to provide additional information for the proof-of-concept design of these units.

2. Numerical methodology 2.1. Model description The modeling approaches of gas–solid multiphase flow can be classified into different categories depending on the application and information required (van der Hoef et al., 2008). Generally, there are two schools in modeling the dense gas–solid flow, namely the Euler–Lagrange method and the Eulerian–Eulerian method. As a representative of the Euler–Lagrange method, the CFD-DEM approaches (Tsuji et al., 1993) can provide detailed information of solids and overcome the intrinsic drawbacks of Eulerian–Eulerian methods, but they are computationally more demanding. As a suitable tool for fundamental research, they have been widely applied to investigate the complex gas–solid flows commonly encountered in the fluidization field (Deen et al., 2007; Luo et al., 2013, in press; Yang et al., 2013). In this study, this approach is also adopted to explore baffle-type ICFBs. Considering a more physical description of the phases involved in the Eulerian–Lagrangian framework, the governing equations used in this study are summarized in Tables 1 and 2 for the gas phase and the solid phase, respectively. The gas flow is described using the locally averaged Navier–Stokes equations, taking into account the presence of solid particles. Moreover, the unclosed term in the momentum equation is modeled with the Smagorinsky model (Smagorinsky, 1963) as shown in Table 1. The solids dynamics is represented by Newton's laws of motion as in Table 2. The particle–particle and particle–wall interactions are controlled by the soft-sphere model taking simultaneous multi-body contact into account (Cundall and Strack, 1979). Due to the relatively large interphase density difference and particle Stokes number (defined as Stk ¼ τp =τf and representing the ratio of the characteristic time of a particle to that of the flow), only the pressure gradient force, drag force, gravity force and solid contact force are considered for the solids. The drag force, denoting the interphase momentum exchange, is modeled using the Koch–Hill model (Koch and Hill, 2001). The equations in Tables 1 and 2 are solved sequentially using a phase-coupled PISO algorithm (Kuipers et al., 1993). At the beginning of each time step, the DEM solver processes the solid dynamics using the CFD data of the previous time step. At the end of the DEM step, the solids information (e.g. positions, velocities, forces) is stored. Using this information, the CFD solver updates the voidage and interphase momentum exchange based on the time discretization scheme, and solves the governing equations of the fluid phase using the PISO algorithm (Issa, 1986). As such calculations proceed alternately, solution advances and the flow dynamics evolves gradually. Actually, as the small time step of DEM results in only tiny variations of voidage and interphase momentum exchange, one CFD step can cover several

M. Fang et al. / Chemical Engineering Science 101 (2013) 213–227

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Fig. 1. Geometry of the ICFB base-case and its three variants: (a) base case, (with a reaction chamber and a heat exchange chamber separated by a thin baffle and all dimensions in millimeters); (b) cross-section view of a variant with inclined gas distributor; (c) cross-section view of a variant with inclined baffle and (d) cross-section view of a variant with inclined HEC side wall.

Table 1 The governing equations for the gas-phase. The gas-phase mass conservation equation: ∂ðε~ f ρf Þ ∂t

þ ∂x∂ i ð~ε f ρf u~ i Þ ¼ 0

The gas-phase momentum conservation equation: ∂ðε~ f ρf u~ i Þ ∂t

þ ∂x∂ j ð~ε f ρf u~ i u~ j Þ ¼ −~ε f

∂p~ ∂xi

þ

∂2 ðε~ f u~ i Þ ∂xi ∂xj −F p

þ ε~ f ρf g þ

∂ðε~ f T~ ij;f Þ ∂xj

The linear Gaussian interpolation scheme is applied for the convection term, the gradient term and the divergence term. The fully implicit Crank–Nicholson scheme (Crank and Nicolson, 1947) is used with a time step of 0.1 ms for CFD calculation. The position and velocity of each solid are obtained using a second-order leapfrog integration scheme with a time step of 10−5 s (Mishra, 2003).

in which, the sub-grid stress tensor is given by T ¼ 2μ S~ ij þ 1 T δij

2.2. Simulation conditions

with the turbulent viscosity of the above equation expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffi μt ¼ ρf ðC s ΔÞ2 2S~ ij S~ ij

The geometry of the four alternative ICFB designs is presented in Fig. 1, namely the base case and its variants. The lower part of the square bed (Fig. 1a) is equally divided by a baffle, with the left section representing the “reaction chamber” (RC) and the right one the “heat exchange chamber” (HEC). The central baffle, represented as an infinitely thin wall, has a height of 90 mm. Right below the baffle is a rectangular gap with a height of 12 mm; thus solids can circulate from the HEC to the RC through this gap. Cubic cells with a side length of 3 mm are used to mesh the ICFBs, resulting in 26,400 hexahedral cells for this simulation. Inlet conditions with constant gas velocity of Uf and Um are assigned to the RC and the HEC, respectively. The pressure outlet boundary condition is imposed at the top of the bed. Meanwhile, the no-slip boundary condition is applied to all side walls and the baffle, while the free-slip boundary condition is used for the front and back walls of the bed. Table 3 lists all gas–solid properties and simulation domain setups of this study. Most of these are exactly the same as those of Müller et al. (2008, 2009). Because most ICFBs operate in the bubbling fluidized regime and in previous research (Fang et al., 2013; Luo et al., 2013, in press) our code predicts flow dynamics very well. Meanwhile, the solids represent biomass material (cf. Müller et al. (2008, 2009)) and this was seldom

ij;f

t

3

ll

in which h ~ i ∂U~ S~ ij ¼ 12 ∂∂xUji þ ∂xij ; …Δ ¼ ðΔxΔyΔzÞ1=3 The interphase momentum exchange, Fp, can be written as: ~ ! ! n¼N V β F p ¼ V 1cell ∑n ¼ 1 p ð1−p ε~gsf Þ ð u − v p Þ in which βgs ¼

18με~ f 2 εp

βgs ¼

18με~ f 2 εp



 F 0 ðεp Þ þ 12 F 3 ðεp ÞRep ;

Rep 440



 F 0 ðεp Þ þ 14 F 1 ðεp ÞRep ; pffiffiffiffiffiffiffi

Rep o 40

2

dp

F 0 ðεp Þ ¼

2

dp

8 > < 1þ3

εp =2þ135=64εp lnðεp Þþ16:14εp 1þ0:681εp −8:48ε2p þ8:16ε3p

> : 10εp =~ε f 3

εp o 0:4 εp ≥0:4

F 1 ðεp Þ ¼ 0:110 þ 5:10  10−4 e11:6εp F 3 ðεp Þ ¼ 0:0673 þ 0:212εp þ 0:0232=~ε f 5 ~ ! ! Rep ¼ ε~ f ρf j u f − v p jdp =μ

DEM ones without the risk of crashing. Hence, the calculation of CFD and DEM occurs at a certain time interval and a relatively nice cost-effectiveness performance can be maintained. The finite volume method is adopted to discretize the equations in Table 1.

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Table 2 The governing equations for the solid-phase. The translational motion equation of solid-phase ! ~ ! V β ! dv mp dt p ¼ −V p ∇p~ þ ð1−p ε~gsf Þ ð u − v p Þ þ mp g þ F C The rotational motion equation of solid phase dω

I p dtp ¼ T p The expression of solid interaction Fc ! ! ! ! ! F C ¼ ∑nj¼ 1 ðkn δ nij −γ n v n ij Þ þ ðkt δ t ij −γ t vr t ij Þ where the normal stiffness coefficient kn and the damping coefficient γn qffiffi pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi Rn δn ; γ n ¼ −2 56β Sn mn ≥0

kn ¼ 43 Y n

and the tangential stiffness coefficient kt and the damping coefficient γt qffiffi pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi kt ¼ 8Gn Rn δn ; γ t ¼ −2 56β St mn ≥0 pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi where Sn ¼ 2Y n Rn δn , St ¼ 8Gn Rn δn , 1=mn ¼ 1=m1 þ 1=m2 , pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1=R ¼ 1=R1 þ 1=R2 , β ¼ lnðeÞ= ln2 ðeÞ þ π 2 , 1=Y n ¼ ð1−ν21 Þ=Y 1 þ ð1−ν22 Þ=Y 2 , 1=Gn ¼ 2ð1−ν21 Þ=Y 1 þ 2ð1−ν22 Þ=Y 2

Table 3 Simulation domain and gas–solid properties. Simulation domain setup Width (x)–depth (y)–height (z) (mm) Grid number (x–y–z) (–) Baffle height (mm) Gap height (mm) Gas properties Density (ρf ) (kg/m3) Viscosity (μ) [kg/(m s)] Solid properties Number of solid particle (–) Density (ρs ) (kg/m3) Diameter (dp ) (mm) Young modulus (Y p ) (Pa) Poisson's ratio (νs ) (–) Restitution coefficient (e) (–) Friction coefficient (μs ) (–) Dynamic friction coefficient (μk ) (–)

132–10–600 44–3–200 90 12 1.225 1.8  10−5 92,000 1000 1.20 1.20  105 0.33 0.97 0.10 0.05

reported in previous studies. Furthermore, the solids properties (especially the small Young modulus) imply that a relatively larger DEM time step can be chosen, making extensive numerical simulation studies better affordable. Table 4 lists all operational and design parameters involved in this study. The design in Fig. 1a is used to investigate the effect of two parameters: superficial gas velocities of the RC (Uf) and HEC (Um). The Uf is less than seven times the solid minimum fluidization velocity (Umf, 0.3 m/s) to avoid particle blow-off, and the range of fluidizing velocity is rarely discussed in aforementioned research (Feng et al., 2012; Kim et al., 2002; Song et al., 1997; Xie et al., 2009; Zhang et al., 2012). Moreover, Fig. 1b–d shows the bed geometries used for evaluating the effect of the inclination angle of the gas distributor, baffle plate, and the HEC side wall on the flow dynamics, respectively. In addition, a study of different gap height is also involved. In all simulations the initial static bed is amassed by 92,000 free-falling solid particles. After that, the bed is aerated at Umf to eliminate the initially uneven packing. Simulation of each case persists for 13 s, and the data of the last 10 s are used to generate time-averaged results.

3. Results and discussions 3.1. Numerical validation Although our code has been successfully applied to investigate different aspects of the ICFBs (Fang et al., 2013;

Luo et al., 2013, in press), validation is still carried out, referring to the combined experimental and numerical work of Müller et al. (2008, 2009). The static bed has a dimension of 44  10  30 mm3 and the gas–solid properties are those listed in Table 3. The solid particles are fluidized at two superficial velocities, 0.6 and 0.9 m/s, corresponding to two and three times the minimum fluidization velocity (Umf, 0.3 m/s) of this system, respectively. These processes are numerically reproduced using the aforementioned approach and the results are shown in Fig. 2. The predicted value of the minimum fluidization velocity exactly matches with experimental data provided by Müller et al. (Fig. 2a). As shown in Fig. 2b and c, the timeaveraged voidage (7.2 mm above the gas distributor with superficial velocity of 0.6 m/s) and the time-averaged solids axial velocity (10 mm above the gas distributor with superficial velocity of 0.9 m/s) agree well with the experimental results. After this validation, comprehensive parameter sensitivity analyses were performed and appropriate values of these parameters were chosen for this study. Considering the great resemblance between these two studies (similar gas–solid properties and flow patterns) and the simulation results, this numerical study is able to reproduce the actual dynamics of the ICFB qualitatively and quantitatively. 3.2. Gas and solid flow dynamics The foremost feature distinguishing ICFBs from other fluidized facilities is the unique solids circulation behavior within the bed. The gas–solid flow dynamics of the prototype bed (with Uf ¼1.2 m/ s, Um ¼0.6 m/s, and 90 mm static bed height, hereafter refers to as “representative case”) is discussed in this section. Fig. 3 shows snapshots of gas velocity, particle position and velocity, bed voidage and pressure distribution at a simulation time of 5.2 s. Different flow patterns emerge with different aeration rates to the two baffle-separated chambers. Particles in the RC are sparged vigorously with voids and bubbles clearly observed, while solids are smoothly fluidized in the HEC, as shown in Fig. 3b. Generally, the flow pattern in the RC is intense bubbling, slugging or even turbulent fluidization, while the HEC hosts a moving bed (Song et al., 1997). Hence, the different solid fractions of the two chambers (Fig. 3c) produce a pressure difference (Fig. 3d) driving the solids of the HEC into the RC through the gap. Above the baffle, solids are lifted and scattered around by bubble breakup (Fig. 3b) and gas diversion (Fig. 3a). This carry-over balances the bottom flux of solids through the gap and sustains the internal circulation. In a gas–solid fluidized system, the presence of solid particles modifies the gas flow pattern to some extent. Fig. 4 exhibits snapshots of the solids spatial distribution (colored by its horizontal velocity) and the gas streamline at different times of the representative case. Particles with high velocity occur where gas streamlines are densely distributed, while the channeling flow of gas emerges together with a sparse cluster of solids. Near the gas distributor, the particles of the two chambers possess transverse velocities in opposite directions, indicating strong back-mixing along the RC side wall. In the upper region above the baffle, gas flow deviates toward the HEC and particles are cascading due to bubble dynamics. Interestingly, transverse velocities of the solids above the static bed height can be generally distinguished by the horizontal location of the baffle. Compared with the previous study (Feng et al., 2012), the local recirculation of gas flow in the HEC is obviously weak even at Um ¼2Umf. This may be associated with the solid properties and the relatively low aspect ratio of the chamber. Fig. 5 presents the time-averaged properties of the gas–solid flow for the last 10 s of the simulation. The time-averaged solids transverse velocity in the vicinity of gas distributor is just contrary

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Table 4 Simulation conditions. Uf (m/s)

Um (m/s)

Gap height (mm)

Gas distributor angle (1)

Baffle angle (1)

HEC side wall angle (1)

0.6; 0.2

12

0

0

0

Values of Um

0.9, 1.2, 1.5, 1.8, 2.1; 0.3, 0.4, 0.5, 0.6; 1.2

12

0

0

0

Gap height Gas distributor angle Baffle angle HEC side wall angle

1.2 1.2 1.2 1.2

0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 0.6 0.6 0.6 0.6

6, 9, 12, 15 12 12 12

0 3, 6, 9, 12 0 0

0 0 3, 6, 9, 12 0

0 0 0 3, 6, 9, 12, 18, 24

Values of Uf

to that in the upper region (Fig. 5a) establishing and sustaining the particles circulation pattern of the bed. Besides this main circulating flow, local recirculation/back-mixing of solids can be clearly witnessed along the side walls of both chambers (Fig. 5b). This is less mentioned in previous research, and may be related to the small aspect ratio of the chambers and the low superficial gas velocities. Besides back-mixing of solids, channeling flow is also obvious in the RC. Due to the effect of particles back-mixing along the side walls, the main flow of the RC is pushed towards the baffle. Moreover, a void with low gas velocity can be spotted in the RC due to the encounter of back-mixing solids and circulating solids (Fig. 5c). The solid volume fraction is almost uniform in the HEC and a bed expansion can be clearly detected (compared with the initial bed height of 90 mm); while in the RC, it is higher in the region near the side wall than that in the vicinity of the baffle. Meanwhile, a void with very low solid fraction can be spotted just at the bottom of the baffle (Fig. 5d). The solids circulation flux (SCF) and gas bypassing flux (GBF) are important indicators in evaluating the operation of ICFBs. The SCF is calculated following the method similar to Song et al. (1997) and Jeon et al. (2008), but the instantaneous average of the voidage and solids transverse velocity at the gap is used. To determine the GBF, the same calculation method is applied as for the SCF. The time evolution of SCF and GBF for the representative case is plotted in Fig. 6. Obviously, the SCF varies strongly with time, and reverse circulation (gas/solid flow from RC to HEC) can only be spotted at the initial launch stage of the system ( 0.2 s). However, regular circulation from HEC to RC dominates the remainder of the simulation. The same feature can also be identified for the GBF and further observations show that the SCF and GBF are remarkably similar, not only in the concurrence of their extreme values, but also in their variation with time. These correlations are justified by considering the driving force of gas–solid flow, e.g. the pressure difference between the two chambers (Fig. 3d). SCF and GBF are still adopted to characterize the performance of the system in the following discussion, but their time-averaged results (calculated by the time-averaged gas–solid velocities and voidage at the gap) are adopted to represent the net circulation flow statistically. Furthermore, the solids residence time (SRT, for the last 10 s of each simulation) between the chambers of the bed is figured out by judging consecutive positions of solid particles relative to the baffle, to clarify the variations of solids residence time with different design and operating parameters. Before analyzing the influence of different parameters on the circulation, a grid sensitivity analysis is carried out. Four sets of grid are involved in this study and the simulation results of SCF and GBF using these grid systems are listed in Table 5. As one can see, the outcomes are insensitive to the grid used and the default setting (44  3  200) is appropriate and reliable for this study. 3.3. Effect of the fluidizing velocity Uf Uf, representing the aeration to the RC, is a key parameter regulating the gas–solid flow patterns in ICFBs (Feng et al., 2012;

Song et al., 1997). In this section, two different sets of Uf are appraised (Fig. 7), based on different aeration rates to the HEC (Um ¼0.2 m/s and 0.6 m/s). Although the SCF and GBF are small, solids circulation is still established when Uf ¼ 2Umf ( 25.87 kg m−2 s−1). This implies, at least for this specific system, that a wider operating range of fluidizing gas velocity can be obtained, compared with the draft-tube-type ICFBs for which solids cannot circulate when Uf o2Umf (Kim et al., 2002) or even Uf o2.5Umf (Choi and Kim, 1991). When the gas velocity is low, the solids circulate in such a way that particles from the RC overflow to the HEC as a consequence of bed expansion, and then the denser receiving bed pushes the particles through the gap, back into the RC. In such conditions, only about 65% of the total solids is involved in overall circulation (Uf ¼2Umf), while all others remain in the chambers they were originally located in. Hence, the SRT standard derivation is large when Um ¼ 0.2 m/s (Fig. 7d). The SCF and GBF increase almost linearly with Uf when Um is low (0.2 m/s), and the difference between the SRT of the two chambers becomes larger (Fig. 7d). Particles circulation is not restricted by solids motion in the HEC when the HEC is aerated with Um ¼0.6 m/s, and thus Uf becomes the determining factor. The SCF and GBF continuously increase, then reach a maximum at Uf ¼ 6Umf (1.8 m/s with SCF 179.39 kg m−2 s−1 and GBF 1.11 kg m−2 s−1), and finally levels off due to the strong back-mixing of particles (Song et al., 1997). This indicates saturation of increasing Uf on the intensity of solids circulation. This trend agrees well with previous investigations (Ahn et al., 1999; Feng et al., 2012; Jeon et al., 2008; Kim et al., 2002; Song et al., 1997). The SRT in the HEC is larger than that of the RC, and this difference becomes larger and larger as Uf increases. However, their standard deviations become smaller ( 1.3 s with Uf ¼6Umf) as Uf increases and post-processing of the simulation results illustrates that all particles are actively involved in circulation. Although the pressure difference between the two chambers is small, owing to the particle properties and shallow bed height, it can still be adopted as an indicator for the circulation of solids. Its variation nicely explains the time evolution of SCF and GBF, and its role as the driving force for the solids circulation is justified once again. 3.4. Effect of the fluidizing velocity Um As Uf, Um also plays an important role in controlling the circulation in ICFBs (Jeon et al., 2008; Shih et al., 2003; Song et al., 1997). This influence of Um on the circulation is presented in Fig. 8. In addition to GBF, the gas bypassing fraction (GBFn, defined as GBF divided by the gas flow rate of the HEC) is also plotted. It is commonly used (Jeon et al., 2008; Shih et al., 2003; Song et al., 1997) and may be more appropriate as the gas flow rate of the HEC varies with Um. Obviously, the general trends of the SCF, GBFn, and the pressure differences between the two chambers are almost the same: first they increase, and then they decrease almost linearly with increasing Um. This increasing trend of GBFn when Um o1.6Umf agrees with the previous studies of Song et al. (1997) and Shih et al. (2003), but not with Jeon

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(2008). When Um 41.6Umf, the formation of bubbles suppresses circulation and then diminishes the SCF (Kim et al., 2002). However, to draw a universal rule for the effect of Umf on the bed performance, more comprehensive studies are still needed. As Um increases, the SRT also rises in the RC and decreases in the HEC. Meanwhile, the standard deviation of the SRT initially increases and then diminishes with increasing Um (minimum value is 1.63 s with Um ¼ 0.5 m/s): solids in the HEC cannot be fully fluidized when Um is low, while the back-mixing of solids of the HEC to the RC above the baffle is more pronounced when Um is high. As a conclusion, the solids circulation of the unit seems more sensitive to Um than to Uf. 3.5. Effect of gap height Although the effect of gap height on solids circulation is important, it was rarely discussed in previous studies. To the best of our knowledge, there are no design rules allowing determining this key parameter. The influence of gap height is quantified in Fig. 9. No consistent trend is found between solids circulation and gas bypassing, no matter the variation of the gap area is considered (using solids circulation rate (SCR) and gas bypassing rate (GBR) calculated by multiplication of SCF and GBF with gap area, respectively) or not (using SCF and GBF). The first rising and then decreasing trend of SCF (Fig. 9a) partially agrees with that found by Song et al. (1997), while the continuous increase of SCR (Fig. 9a) with increasing gap height matches that of Shih et al. (2003). Meanwhile, gas bypassing also exhibits a different trend: the GBR is first rising and then decreasing as gap height increases, while the GBF keeps decreasing (Fig. 9b). Considering the variation of the gap dimensions at varying gap height, the flow rate may be more suitable to quantify solids circulation than the flux information. The decrease of GBF illustrates that the time-averaged gas velocity at the gap is decreasing. This agrees well with the downtrend pressure difference between the chambers as the gap height increases (Fig. 9c). Meanwhile, the increase of SCR indicates that the rising gap height lowers the flow resistance (Milne et al., 1992; Shih et al., 2003) and enhances solids circulation by compensating the reduced solids velocity with the enlarged flow area. Both the mean value and the standard derivation of the SRT are insensitive to variations of gap height, especially when it is larger than 9 mm. As a conclusion, increasing gap height presents nice regulation abilities to control the operation of the bed (enhancing solids circulation, suppressing gas bypassing, while leaving SRT nearly untouched). This may be favorable to some industries, e.g. pyrolysis and gasification, and it needs further exploration. 3.6. Effect of the inclination angle of the gas distributor

Fig. 2. Numerical validation against relevant experimental measurements (cf. Müller et al. 2008, 2009): (a) predicted minimum fluidization velocity (Umf ¼ 0.3 m/s); (b) predicted time-averaged bed voidage (evaluated at a position of 7.2 mm above the gas distributor with 0.6 m/s superficial gas velocity); (c) predicted time-averaged solid vertical velocity (evaluated at a position of 10 mm height above the gas distributor with 0.9 m/s superficial gas velocity).

et al. (2008). However, a decreasing trend of GBFn and SCF is barely reported. The continuous increase of SCF (Um o1.6Umf) agrees well with the reports of Song et al. (1997), Shih et al. (2003) and Jeon et al.

Inclined gas distributors have been applied in practice to avoid particles accretions and promote particles motion above the gas distributor (Hirota et al., 1990). As an important design parameter, it may influence the rotary motion of particles. Fig. 10 reveals the results as a function of different gas distributor inclination angles. Increasing the gas distributor inclination angle, the SCF, GBF, and pressure difference of the two chambers all decrease. However, the SRT of the two chambers are almost unchanged (about 4.5 s and 5.5 s for RC and HEC, respectively). Because both bed height and solids inventory of the two chambers vary with the inclination angle of gas distributor, crippling the pressure difference between the two chambers and thus gas–solid circulation. Therefore, the inclination angle of the gas distributor should be determined cautiously when using large particle diameter, low density bed material together with a relatively shallow bed height. Feng et al. (2012) investigated the inclination angle in a two-dimensional unit and only slight increase

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Fig. 3. Gas–solid spatial distribution at a simulation time of 5.2 s for the representative case (ICFB base-case with Uf ¼ 1.2 m/s, Um ¼ 0.6 m/s, and static bed height of 90 mm): (a) gas velocity of the central slice at y¼ 5 mm, (b) particles position colored by their velocity (between the slices of y¼ 4.5 mm and y ¼5.5 mm), (c) voidage distribution, and (d) pressure distribution of the bed central slice.

of the SCF was found. However, the variation of the gas distributor inclination angle in their study is limited. 3.7. Effect of the inclination angle of the baffle Compared with the draft tube, the baffle provides additional convenience since it can be installed with different inclination

angles. This may change the solids inventory, affect the pressure difference and modify the flow dynamics of the two chambers. In this study, the baffle is inclined at different angles towards the HEC, and its influence on the circulation is presented in Fig. 11. The intensity of particle exchange is first rising then decreasing with increasing baffle inclination angle, and the correlation among SCF, GBF and pressure difference of the two chambers is obvious. As the

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Fig. 4. Snapshots of the spatial distribution of particles (colored by their horizontal velocity) and gas streamlines (colored with the magnitude of gas velocity) between the slices of y¼ 4.5 mm and y ¼5.5 mm at different times of the representative case: (a) 1.6 s, (b) 4.5 s, (c) 9.0 s, (d) 12.7 s. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

baffle inclination angle increases, the restrictions of the baffle on bubble expansion and solids transverse motion are reduced in the RC. Meanwhile, the gradually expanded flow channel reduces the gas velocity and thus solids entrainment. This enhances the moment of solids from the RC to the HEC above the baffle. While in the HEC, the gradually narrowed flow channel suppresses bubble formation and provides higher pressure, pushing more solids into the RC through the gap. However, when the baffle inclination angle is too large, stronger back-mixing occurs among particles sustained by the inclined baffle, exerting a negative effect on the circulation. Although further intensification of solids circulation is restricted, the SRT distributions of the two chambers are greatly modified: it can be larger in the RC than that in the HEC when the baffle inclination angle is larger than 81 (Fig. 11d), and this trend continues with increasing baffle inclination angle. This provides a

convenient (and may be unique) way to effectively regulate the SRT distribution without the risk of greatly changing the flow patterns of the chambers and solids circulation. 3.8. Effect of the inclination angle of the HEC side wall Inclined side walls are often applied in traditional fluidized bed reactors to improve solids mixing and temperature uniformity (Hirota et al., 1990; Kim et al., 1997; Lee et al., 1998; Milne et al., 1999). Meanwhile, it may enhance the solids transverse motion and modify the gas–solid flow dynamics. Its influence on solids circulation is presented in Fig. 12, and a great resemblance can be detected among the variation of SCF, GBF and the pressure difference of the two chambers. They first rise and then decrease as the inclination angle of the side wall increases, and the maximums emerge at about 121. A small inclination angle seems

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Fig. 5. Spatial distribution of time-averaged hydrodynamic properties at the central slice (y¼5 mm) of the representative case: (a) particle horizontal velocity, (b) particle vertical velocity, (c) gas velocity, and (d) solid fraction of the bed.

to intensify circulation only slightly, while a large one somewhat suppresses particles circulation. The HEC geometry is adjusted according to the different inclination angles of side wall to accommodate the same solids inventory as that of the representative case. Therefore, the higher the inclination angle is, the smaller the HEC gas distributor appears. As a result, solids of HEC are hard to fully fluidize and local circulation is observed when the

inclination angle of the side wall is large. Meanwhile, the continuous increase of SRT in the HEC (Fig. 12d) is well explained. Although increasing the side wall inclination angle may promote solids circulation by means of enhancing their transverse motion, this effect is entirely counterbalanced by the local circulation of solids in the HEC. Considering the influence of the side wall inclination angle on the gas–solid circulation is not such

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Fig. 6. Variations of solid circulation flux (SCF) and gas bypassing flux (GBF) with time of the base case.

Table 5 Simulation results for the grid sensitivity analysis. Grid

SCF (kg m−2 s−1)

GBF (kg m−2 s−1)

44  3  200 (default) 40  3  200 44  4  200 44  3  150

143.97 136.21 140.93 141.03

0.86 0.79 0.87 0.83

pronounced, more attention should be paid to its effects on other characteristics, e.g. the solids mixing, of the bed.

4. Conclusions Gas–solid flow characteristics of a baffle-type ICFB are numerically investigated using the CFD-DEM approach. The gas flow is resolved using LES while the dynamics of solid phase is handled by the soft-sphere model. The simulation results demonstrate the key features of a baffle-type ICFB: intensely bubbling in the RC, smoothly bubbling in the HEC and solids circulation between them. The pressure difference between the two chambers is the driving force for the solids circulation through the gap, while the bubble evolution, breakup and gas flow diversion above the bed surface promote solids striding over the baffle. Solids circulation and gas bypassing show strong correlation, hence the ideal state of enhanced particles circulation combined with minimal gas bypassing seems hard to attain. Both operating parameters, Uf and Um, show good abilities for controlling the operation of the ICFB. Solids circulation can still be established at low aeration values (e.g. Uf ¼0.6 m/s with Um ¼0.2 m/s), showing better flexibility than the draft-tube ICFBs. Meanwhile, the nearly linear variation of solids circulation flux and gas bypassing fraction with the increase of Um indicates that the flow dynamics in the HEC than that of the RC plays a more important role in the whole process of the bed. The design parameters differently influence upon the operation of the system. Increasing gap height enhances particles circulation while it suppresses the gas bypassing. This may be favorable to certain applications, e.g. coal gasification. Increasing the inclination angles of baffle plate or HEC side wall first increases and then decreases particles circulation and gas bypassing, and it seems that an optimum value can be found for these two parameters. However, increasing the inclination angle of the gas distributor continuously suppresses particles circulation.

The solids residence time (SRT) in the HEC is commonly larger than that of the RC, and it can be effectively regulated by adjusting aeration rates. The difference between SRT in the HEC and RC can be enlarged by increasing the difference in superficial gas velocity between the chambers, decreasing the inclination angle of the gas distributor and increasing the inclination angle of the HEC side wall. Moreover, changing the inclination angle of the baffle fundamentally modifies the RST distribution within the bed without the risk of greatly changing the performance of the bed.

Nomenclature dp e Fc Fp F0, F1, F3 g Gn Ip kn, kt mp, mn Np nij p Rn Rep Sn, St Sij t tij Tp U f , Um Ui, Uj, Uk Umf Vp ! vp xi, xj, xk Yp, Yn

particle diameter, m coefficient of restitution, dimensionless solid–solid interaction force, N interphase momentum exchange, N m−3 s−1 coefficient of Koch–Hill model, dimensionless gravitational acceleration, m s−2 coefficient of solid tangential stiffness, Pa rational inertia of solid, kg m2 normal and tangential stiffness of solid, N m−1 solid actual mass and effective mass, kg number of solids in a fluid cell, dimensionless normal vector of collision pair, dimensionless pressure, Pa effective particle radius, m solid particle Reynolds number, dimensionless normal and tangential damp coefficient, dimensionless tensor of fluid strain rate, N m−2 time, s tangential vector of collision pair, dimensionless torque on the solid particle, N m superficial gas velocity to RC and HEC, m s−1 three components of fluid velocity vector, m s−1 minimum fluidization velocity, m s−1 solid volume, m3 solid velocity, m s−1 coordinate components, dimensionless actual and effective Young modulus, Pa

Greek letters εf ,εp ρf ,ρp

volume fraction of fluid and solid, dimensionless density of fluid and solid, kg m−3

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223

Fig. 7. Influence of the fluidizing velocity Uf on bed performance: (a) solid circulation flux, (b) gas bypassing flux, (c) pressure difference, and (d) solid residence time between the two chambers.

Fig. 8. Influence of the fluidizing velocity Um on bed performance: (a) solid circulation flux, (b) gas bypassing flux and gas bypassing fraction, (c) pressure difference, and (d) solid residence time between the two chambers.

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Fig. 9. Influence of the gap height on bed performance: (a) solid circulation flux and solid circulation rate, (b) gas bypassing flux and gas bypassing rate, (c) pressure difference, and (d) solid residence time between the two chambers.

Fig. 10. Influence of the inclination angle of the gas distributor on bed performance: (a) solid circulation flux, (b) gas bypassing flux, (c) pressure difference, and (d) solid residence time between the two chambers. (Geometry as represented in Fig. 1b).

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225

Fig. 11. Influence of the baffle inclination angle on bed performance: (a) solid circulation flux, (b) gas bypassing flux, (c) pressure difference, and (d) solid residence time between the two chambers. (Geometry as represented in Fig. 1c).

Fig. 12. Influence of the inclination angle of the HEC side wall on bed performance: (a) solid circulation flux, (b) gas bypassing flux, (c) pressure difference, and (d) solid residence time between the two chambers. (Geometry as represented in Fig. 1d).

226

τf μ,μt βgs vp ωp γ n ,γ t νs

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fluid viscosity stress tensor, N m−2 fluid laminar and turbulent viscosity, Pa s interphase momentum exchange coefficient translational velocity of solid, m s−1 angular velocity of solid, rad s−1 normal and tangential damping coefficient, dimensionless Poisson's ratio, dimensionless

Operators 

filtering operator in LES

Subscripts f p s t gs n i, j, k

fluid (gas phase) particle (solid phase) solid tangential gas–solid interaction normal index of three coordinates

Acronyms CFB CFD DEM EEM GBF GBFn GBR HEC ICFB LES RC SCF SCR SRT

circulating fluidized bed computational fluid dynamics discrete element method Eulerian–Eulerian model gas bypassing flux, kg m−2 s−1 gas bypassing fraction, % gas bypassing rate, kg s−1 heat exchange chamber internally circulating fluidized bed large eddy simulation reaction chamber solids circulation flux, kg m−2 s−1 solids circulation rate, kg s−1 solids residence time, s

Acknowledgments Financial support from the National Natural Science Foundations of China (Grant nos. 51222602 and 51176170) and from the Zhejiang Provincial Natural Science Foundation of China (Grant no. LR12E06001) is sincerely acknowledged. Meanwhile, authors express their gratitude to Prof. Alfons Buekens for his work on this paper.

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