Computational fluid dynamics analysis of the circulation characteristics of a binary mixture of particles in an internally circulating fluidized bed

Applied Mathematical Modelling 72 (2019) 1–16

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Computational fluid dynamics analysis of the circulation characteristics of a binary mixture of particles in an internally circulating fluidized bed Muhammad Hassan a,b,∗, Khurshid Ahmad b, Muhammad Rafique a,c, Wenjian Cai a, Huilin Lu a,∗ a

School of Energy Science & Engineering, Harbin Institute of Technology, Harbin 150001, China U.S.–Pakistan Center for Advanced Studies in Energy, University of Engineering and Technology, Peshawar 25000, Pakistan c Mehran University of Engineering and Technology, S.Z.A.B, Campus Khairpur Mir’s, Sindh, Pakistan b

a r t i c l e

i n f o

Article history: Received 7 May 2018 Revised 8 February 2019 Accepted 13 February 2019 Available online 26 February 2019 Keywords: Binary mixture Computational fluid dynamics simulation Internally circulating fluidized bed Mixing Solids circulation rate

a b s t r a c t The process where solids circulate in an internally circulating fluidized bed (ICFB) with two or more chambers can be developed by applying unequal gas velocities in these chambers. In this study, a twin chamber ICFB with a binary mixture (two particles comprising G116 and P275, which differed in terms of their size and density) was simulated using the multifluid Eulerian model. The effects of variations in the gas velocities, mixing of solids, and mixture composition were investigated, and the results were quantified in terms of the solids circulation rate (Gs ). An increase in the gas velocity in the reaction chamber (RC), UR , at a constant gas velocity in the heat exchange chamber (HEC), UH , resulted in an increase in the circulation rate for the binary mixture. Solid particles flowed upward in the RC and downward into the HEC. The ratio of the circulation rate for G116 relative to that for P275 was approximately equal to the ratio of their masses in the ICFB. An increase in UH at constant UR led to a decrease in the circulation rate of the binary mixture. Similar to UR and UH , the mixture composition played a critical role in controlling the circulation rate of the binary mixture in the ICFB. Furthermore, the ICFB exhibited a higher capacity for solids mixing compared with a conventional bubbling fluidized bed. © 2019 Elsevier Inc. All rights reserved.

1. Introduction Fluidized beds are a well-established method and they are employed in a variety of applications throughout the world in many industries. The process where particles circulate in fluidized beds is beneficial for many applications, and it can be either achieved externally such as in the conventional circulating fluidized bed (CFB), or internally such as in the nonconventional internally circulating fluidized bed (ICFB). In CFBs, a cyclone collects particles from the riser and returns them to the base of the riser. By contrast, ICFBs comprise a single vessel, which is divided in an appropriate manner into two or more chambers either by placing a central plate in a baffle type ICFB or a tube in the case of a draft-tube type ICFB. The circulation of the particles can then be developed in a single vessel simply by applying unequal fluidizing velocities in these chambers. The two ICFB chambers are usually referred to as the reaction chamber or fast bed (RC), and the heat ∗

Corresponding authors. E-mail addresses: [email protected] (M. Hassan), [email protected] (H. Lu).

https://doi.org/10.1016/j.apm.2019.02.022 0307-904X/© 2019 Elsevier Inc. All rights reserved.

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M. Hassan, K. Ahmad and M. Rafique et al. / Applied Mathematical Modelling 72 (2019) 1–16

Nomenclature CD d e n g gi and gij Gs Ga Gratio Mratio k I¯

I2D p u Re t UR , UH UBFB

 Ø

drag coefficient diameter (μm) restitution coefficient number of solid phases (n = 2 in this study) gravity (m s–2 ) radial distribution function evaluated at a radius equal to the diameter of the particle solids circulation rate (kg m–2 s–1 ) gas bypassing flux (kg m–2 s–1 ) circulation ratio of the two particles mass ratio of the two particles diffusion coefficient for granular energy (kg m–1 s–1 ) unit tensor second invariant of deviatoric stress tensor pressure (Pa) velocity vector (m s–1 ) Reynolds number time (s) gas velocity to RC and HEC (m s–1 ) gas velocity of BFB (m s–1 ) granular temperature (m2 s–2 ) internal friction angle (°)

Greek letters α volume fraction ρ density (kg m–3 ) stress tensor (Pa) τ β inter-phase momentum exchange coefficient (kg m–3 s–1 ) γ collisional energy dissipation (kg m–1 s–3 ) λ bulk viscosity (kg m–1 s–1 ) μ shear viscosity (kg m–1 s–1 ) α s,max maximum solid volume fraction Subscripts a gas phase i, j solid phases Abbreviations CFD computational fluid dynamics CFB circulating fluidized bed BFB bubbling fluidized bed HEC heat exchange chamber RC reaction chamber ICFB internally circulating fluidized bed

exchange chamber (HEC) or slow bed. In the case of coal/biomass gasification, the fast bed chamber acts as a combustor whereas the slow bed is a gasifier. The circulation of the bed material within the reactor allows the transfer of energy from the combustion chamber to the gasification chamber. ICFBs have several advantages compared with CFBs because of their unique features, such as reduced height, compact size, low construction cost, and comparatively lower heat loss. These advantages mean that ICFBs have a wide range of applications, such as in coal combustion and gasification [1,2], biomass gasification [3], solid waste disposal [4–6], flue gas desulfurization [7], and membrane reactors [8]. ICFBs have a much greater capacity for mixing particles compared with conventional fluidized beds [9]. Kim et al. [10] showed that solid recirculation increases as the superficial gas velocity increases, but decreases as the particle diameter increases. Hadley et al. [11] found that the rate of solids circulation depends on the gas velocity ratio between the two chambers in an ICFB. When fluidized separately, the circulation rate of more dense fluidized bed ash particles was greater than that of less dense plastic balls in a twin fluidized bed system [12]. Foscolo et al. [13] found that compared with a conventional fluidized bed, more efficient energetic exchange can be obtained between sand and biomass particles in an ICFB due to internal recirculation, thereby enhancing the mixing and reducing the segregation of biomass particles to the bed surface as well as decreasing the elutriation of fine carbon particles to ultimately improve the yield and quality of

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the gas product. Similarly, the fluidization of particles with a wide size distribution (WSD) was better in an ICFB than the conventional fluidized bed, where segregation of the WSD particles was also minimized considerably due to the continuous solid recirculation process [14]. The solids circulation rate controls the solid residence time, gas–solid contact, and heat and mass transfer rates in the bed, and thus it needs to be determined carefully to facilitate the efficient design of an ICFB reactor [15]. It is difficult to obtain a complete understanding of the complex gas solid dynamics in an industrial ICFB based on experiments, even for a cold state process, and it is even more challenging when chemical reactions or high temperatures need to be considered. To overcome these challenges, it has been demonstrated that computer modeling can complement experiments in extensive evaluations of the effects of the design and operating parameters as well as the solid–fluid physical/chemical properties on complex multiphase gas–solid hydrodynamics such as those encountered in ICFBs. Previously, the effects of different design and operating parameters on the bed performance in a two-dimensional ICFB were evaluated in computational fluid dynamics (CFD) simulations using the two-fluid model by incorporating the kinetic theory of granular flow [16–18]. The results obtained in these studies showed that the solids circulation rate between the two chambers is related to the superficial gas velocities in the RC and HEC, as well as the static bed height and structure of the ICFB. Several studies [9,19,20] used the CFD–discrete element method (CFD–DEM) to investigate the effects of several factors, such as the bed pressure, solid friction coefficient, restitution coefficient, particle diameter and density, superficial gas velocity, bottom slot height, and the inclination angles of the gas distributor, baffle plate, or side wall of the bed, and demonstrated that these parameters can greatly influence the circulation performance of an ICFB. Increasing the particle size decreases the solids circulation rate, whereas the solids circulation rate increases as the density of the solids increases. Similar studies employed the CFD-DEM to investigate the gas and solid behavior in an ICFB [21,22], where they concluded that much better solids mixing can be achieved in an ICFB compared with a conventional fluidized bed, and that the DEM model can provide better details of the flow dynamics in the bed. However, these studies focused mainly on mono-sized particles in ICFBs. Fluidized bed systems generally operate using complex bed materials with different size and density properties, such as mixtures of sand, coal, biomass, sorbents, and bottom ash. Many studies have investigated the behavior of binary materials in bubbling fluidized beds (BFBs) and CFBs [23–30]. However, the hydrodynamic characteristics of binary mixtures in an ICFB have not been reported previously. Therefore, it is necessary to study and describe the gas–solid flow characteristics of a binary mixture of particles in an ICFB. In the present study, we used a multi-fluid Eulerian model to investigate a baffle-type ICFB containing a binary mixture of particles (G116 and P275) with different sizes and densities. We investigated the effects of several parameters such as variations in the superficial velocities in the two chambers, the mixture composition, and solids mixing, and the results were quantified in terms of the solids circulation rate (Gs ).

2. CFD model description The multi-fluid Eulerian model used in the commercial CFD software package ANSYS Fluent 14.5 was employed to model the circulation process for the binary mixture in the ICFB. This multi-fluid model applies the kinetic theory of granular flow to obtain the constitutive equations. Further details of the model equations can be found in the Fluent manual [31,32]. In the following, we summarize the governing equations and the associated constitutive closure equations for the multifluid Eulerian model incorporating the kinetic theory of granular flow [33,34], which we employed in our simulations of an ICFB. The Eulerian–Eulerian model has been successfully implemented and applied widely in previous studies to bidisperse mixtures of particles in BFBs [27,28,35]. The continuity equation for the gas phase can be written as:

∂ (α ρ ) + ∇ .(αa ρa ua ) = 0. ∂t a a

(1)

For a system with n solid phases, the continuity equation for each solid phase i (i = 1, …, n) without any mass transfer is written as:

∂ (α ρ ) + ∇ .(αi ρi ui ) = 0 ∂t i i αa +

n 

αi = 1, where n = 2 in the present study.

(2)

(3)

i=1

The momentum conservation equations for the gas and solid phases are as follows. n  ∂ βai (ui − ua ) (αa ρa ua ) + ∇ .(αa ρa ua ua ) = −αa ∇ p + ∇ .τ a + αa ρa g − ∂t i=1

(4)

4

M. Hassan, K. Ahmad and M. Rafique et al. / Applied Mathematical Modelling 72 (2019) 1–16 n    ∂ βij ui − u j (αi ρi ui ) + ∇ .(αi ρi ui ui ) = −αi ∇ p + ∇ .τ¯ i − ∇ Pi + αi ρi g − βai (ua − ui ) + ∂t i=1,i= j

(5)

Analogous to the thermodynamic temperature of gases, the granular temperature, i = /3, represents a measure of the particle velocity fluctuations in the ith solid phase. The solid phase stress depends on the magnitude of these particle velocity fluctuations, so a balance of the granular energy associated with these particle velocity fluctuations is required to supplement the continuity and momentum balance for both phases. The conservation equation for the fluctuation energy (granular temperature) of the solid particles is written as follows.

3 2



     ∂ (αi ρi i ) + ∇ .(αi ρi ui i ) = −pi I¯ + τ¯ i : ∇ ui + ∇ . ki ∇ i − γi − 3βai i ∂t

(6)

The constitutive sub-model equations used for the Eulerian–Eulerian model include the stress tensors of the gas phase and solids phase [36–39]:



2 τ a = αa μa ∇ ua + (∇ ua )T − αa μa ∇ .ua

(7)

 

2 τ i = αi μi ∇ ui + (∇ ui )T + αi λi − μi (∇ .ui )I

(8)

3

3

The constitutive relationships in the presence of several solid phases are based on the kinetic theory for the mixture of particles. According to different selections of the hydrodynamic parameters, the kinetic theory is derived for the binary mixture of particles and no assumption is required regarding energy equipartition (i.e., different particles have different granular temperatures). The solid viscosity and pressure are expressed as functions of the granular temperatures of the binary particles [26,40,41]. In addition, energy equipartition is assumed when the granular energy balance equation is selected for the mixture [32,34,39]. Jenkins and Mancini [42] used an approximation in the derivation of the constitutive equation for a granular binary mixture, where they defined the granular temperature of the ith solid phase as θ i = mi /3. It is assumed that the mixture is homogenous and that the binary particles have equal granular temperatures in terms of the kinetic theory of the mixture: θ k = θ i = mi /3. The constitutive relationships for the binary granular mixture are expressed as functions of the granular temperatures. The detailed implementation of the granular energy equation described above is still under development. The current model uses expressions proposed by Coroneo et al. [43] based on the kinetic theory of mixtures [32,34]. The frictional pressure is also considered in the current model to account for the high accumulation of solids in the ICFB. The solid shear viscosity is given as:

μi = μi,collision + μi,kinetic + μi,frictional , where:



μi,collision

  4 = αi ρi di gi j 1 + ei j 5

μi,kinetic =

i π

 2 π 4  i  1 + αi gi j 1 + ei j

10ρi di

96αi gi j 1 + ei j

μi,frictional =

Ps, f rictional sin θ i

 Ps,frictional =

5



(10)

(11)

(12)

2 I2D 1025 (αs − αs,max )10 0

(9)

αs > αs,max . αs ≤ αs,max

(13)

The solid bulk viscosity is written as follows.

λi

  4 = αi ρi di gi j 1 + ei j 3



i π

(14)

The collision energy dissipation is written as follows.



γi =



12 1 + ei j 2 gi j ρi αi 2 i 3 √ di π

The solid pressure is written as follows.

(15)

M. Hassan, K. Ahmad and M. Rafique et al. / Applied Mathematical Modelling 72 (2019) 1–16

 Pi = αi ρi i 1 + 2

3 2   di + d j  2 di

i=1

1 + ei j

5





α j gi j

(16)

The radial distribution function coefficients gij and gi have been explained explicitly in many previous studies such as that by Coroneo et al. [43], and they can be written as:



di g j + d j gi gi j = di + d j

where gi = 1 −

 3

αs

−1

αs,max

1  αi di , di 2 2

+

(17)

i=1

where α s is the total solid volume fraction and α s ,max is the maximum packing limit, which can be calculated for a binary mixture according to the empirical method described by Fedors and Landel [44], and it is well documented for ANSYS Fluent [32]. The diffusivity of the granular temperature is given as:

ki

  2   i i π 6 2   1 + αi gi j 1 + ei j + 2αi ρi di gi j 1 + ei j = . 5 π 384 1 + ei j gi j 150ρi di



(18)

For the gas–particle and particle–particle interphase interactions, the exchange coefficient is calculated using the Syamlal et al. [39] drag models. It is recognized that bubbles play a critical role in the mixing/segregation dynamics of particle mixtures in fluidized beds [45]. The solid–solid exchange coefficient β ij and gas–solid drag coefficient β ai can be written as follows.



3 1 + ei j

βi j =

 π 2



 αi ρi α j ρ j (di + d j )2 gi j  ui − u j   3 2 π ρi d i + ρ j d j + C f r,i j π8

2



3

(19)

The gas–solid drag coefficient can be written as:

3 4

βai = CD βai = 150 where:



CD =

Rei =

24 Rei

αi αa ρa |ua − ui | di

αa −2.65 for αa ≥ 0.8

αi (1 − αa )μa αs ρa |ua − ui | + 1.75 for αa < 0.8, 2 di αa di

1 + 0.15(Rei )0.687 0.44

αa ρa |ua − ui |di . μa



for for

Rei ≤ 10 0 0 Rei > 10 0 0

(20)

(21)

(22)

(23)

3. Simulation setup The ICFB considered in this study comprised two inter-connected fluidized bed chambers called the RC and the HEC separated by a vertical baffle, as shown in Fig. 1. The length and width of the central baffle were 200 mm and 2 mm, respectively, where a 20 mm slot was formed beneath. The gap or slot under the baffle allowed the solids to return from the HEC to the RC. The simulations were performed using two-dimensional geometry to reduce the computational effort required by the large number of cases considered. Complete descriptions of the gas and solid properties (adopted from Joseph et al. [46]) as well as the geometrical specifications of the simulated ICFB are presented in Table 1. Table 2 shows the simulation strategy and the objectives of the present study. G116 comprised glass particles and P275 were polystyrene particles. The velocity inlet condition was specified for the gas phase with no solids flow at the inlet and a uniform gas flow was applied at the gas distributor for simplicity. An atmospheric pressure boundary condition was applied at the gas outlet. In multiphase flows, several different wall boundary conditions can be defined for the solid phase, such as no slip, free slip, and partial slip. In our simulations, we applied a no slip boundary condition to the gas phase at the walls, whereas the Johnson and Jackson [47] slip wall boundary condition was used for each granular phase. The particle–particle and particle–wall coefficients for restitution were set to 0.99 and 0.9, respectively, and the specularity coefficient was 0.5 according to the study by Zhong et al. [28]. The model equations were solved using the commercial CFD software ANSYS Fluent with UDF [31]. To ensure the accuracy of the results, the pressure-based second order implicit unsteady solver was selected and the phase coupled SIMPLE algorithm was used for the pressure–velocity coupling together with the high order discretization scheme QUICK. All of the simulations were performed for a total time period of 20 s with a time step size of 0.001 and time-averaged values for the desired variables were obtained for the last 15 s across the slot below the baffle.

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Fig. 1. Geometry of 2D ICFB.

Table 1 System specifications. Solid properties

Unit

G116

P275

Diameter Density Minimum fluidization velocity Particles mass fraction Relative solid volume fraction Maximum packing of particles Packed bed void fraction ICFB Height (y) ICFB width (x) Initial static bed height Gas density Gas viscosity

μm kg/m3 m/s –

116 2476 0.018 0.70 0.50 0.564 0.41 0.80 0.37 0.220 1.2 1.83 × 10−5

275 1064 0.040 0.30 0.50 0.574

m m m kg/m3 kg/m-s

4. Simulation results and discussion 4.1. Grid study Evaluating the grid sensitivity is a crucial step when conducting numerical simulations. To ensure that the CFD calculations were grid independent, we tested three different mesh schemes comprising: fine grid = 18,550 cells, medium grid = 11,960 cells, and coarse grid = 8346 cells, which yielded total solids circulation rates of 263, 269, and 300 kg m–2 s–1 , respectively. The solids circulation rates of the constituent particles G116/P275 were 185.5/77.7, 190/79, and 212/88 kg m–2 s–1 for the fine, medium, and coarse grids, respectively. Moreover, the ratio of the solids circulation rate for the G116 particles relative to that for the P275 particles remained constant and it was equal to 2.39 regardless of the mesh size. Thus, the medium grid scheme was selected for the simulations to ensure the accuracy of the calculations and to reduce the computational effort required.

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Table 2 Simulation objectives.

1. 2. 3. 4.

Purpose

UR (m/s)

UH (m/s)

Effect of UR Effect of UH Effect of the mixture composition Mixing performance of ICFB

0.08, 0.10, 0.15, 0.25 0.084 0.15 Specified

0.05 0.034, 0.048, 0.056, 0.078 0.05 Specified

4.2. Gas–solid flow dynamics Fig. 2 shows instantaneous contour plots of the solid volume fraction, gas and solid velocities, and bed pressure when the gas velocity in the RC (UR ) = 0.25 and the gas velocity in the HEC (UH ) = 0.05 m s–1 . The gas–solids flow patterns in the ICFB indicated the effects of the unequal gas velocities in the two chambers. The bubbling in the RC was more intense compared with that in the HEC. In contrast to the HEC, high gas hold-up developed in the RC due to its high gas velocity (Fig. 2(a) and (b)). Relatively small bubbles were initially generated in the bottom of each chamber and they rose upward to coalesce and form large bubbles, which finally burst at the bed surface. Due to the bubbles bursting, particles were thrown from the RC above the central baffle into the HEC, where they were mixed, cooled, or heated. The particles fell down along the column walls and the baffle. The particles in the HEC were recirculated into the RC through the slot under the baffle, as shown in Fig. 1, and thus a continuous circulation process developed comprising the particles above and below the baffle. Despite the different properties of G116 and P275, the two particles were distributed well within the ICFB and no dead zones formed due to the continuous recirculation process. Snapshots of the gas and solid velocity vectors in the ICFB are also shown in Fig. 2(c), (d), and (e) to illustrate the gas and solid flow behavior in the vessel. The bed particles moved upward in the RC and downward in the HEC. In addition to the solids that circulated between the chambers, other solids circulated within each chamber due to the motions of bubbles and this greatly enhanced the mixing process in the reactor. The bed pressure in the fluidized beds was directly related to the concentration of solids, and Fig. 2(a), (b), and (f) clearly shows this phenomenon, where the particle concentration in the HEC, particularly in the lower part, was higher than that in the RC, and thus the pressure was higher in the HEC compared with the RC. The higher gas hold-up in the RC compared with the HEC led to a difference in density in the ICFB, so a pressure gradient developed between the two chambers, as shown in Fig. 2(f). This pressure gradient facilitated the gas–solid flow from the high pressure region (i.e., the HEC) to the low pressure region (i.e., RC) through the slot below the baffle. Thus, the baffle that separated the two chambers was a key component in the circulation process. The instantaneous gas pressures near the gas distributors in the RC and HEC chambers in the ICFB at UR = 0.25 and UH = 0.05 m s–1 are plotted in Fig. 3(a). Initially, both pressure curves overlapped with each other but after some time when the beds become fully fluidized, a consistently higher pressure developed in one chamber and this situation persisted subsequently. Fig. 3 shows that the gas pressures in the chambers fluctuated greatly over time, where the pressure in the HEC was higher than that in the RC, which led to solid recirculation from the HEC to the RC through the slot below the baffle. The pressure curves obtained for the two chambers are consistent with the pressure contour plot shown in Fig. 2(f). Fig. 3(b) plots the instantaneous solids circulation rates for the G116 and P275 particles through the slot in the ICFB at specific gas velocities. The solids circulation rate (Gs ) was calculated for both particle types (G116 and P175) based on the simulated solid velocity and voidage at the slot below the baffle. The same method was applied to calculate the gas bypassing rate (Ga ).

Gs =

 1 n i=1 A

Ga =

1 A



ρi αi ui dA

ρa αa ua dA



(24)

(25)

Initially, the particles flowed from the RC to the HEC according to the negative Gs values, but the regular recirculation of particles from the HEC to the RC was then established and maintained subsequently. This behavior is consistent with the pressure curves shown in Fig. 3(a), as mentioned above. The circulation rate was higher for the G116 particles (also called jetsam) compared with the P275 particles (also called flotsam) because of their different masses (i.e., mass of G116 = 70% and mass of P275 = 30%) in the mixture in the ICFB. The gas bypassing rate calculated in a similar manner to the solids circulation rate is also shown in the Fig. 3. In addition, Fig. 3 shows that the solids circulation rates for both particles and the gas bypassing rate fluctuated greatly over time. The solids circulation rates for G116 and P275 as well as Ga fluctuated in a synchronous manner, where an increase in Ga corresponded to an increase in Gs for both particle types and vice versa. The granular temperature is a measure of the random oscillations of particles and it is the basic feature considered in the kinetic theory of granular flow. This feature is analogous to the thermal temperature in the kinetic theory of gases. Previous studies [26,48–50] of the granular temperature in binary mixtures of particles have shown that the constituent

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Fig. 2. Contours of the simulated gas and solids volume fraction, velocities and bed pressure in the ICFB at UR = 0.25 and UH = 0.05 m/s.

particles have unequal granular temperatures, and this phenomenon was also observed in our simulations. The instantaneous granular temperatures determined for G116 and P275 in the ICFB through the gap beneath the baffle are shown in Fig. 3(c). The granular temperatures fluctuated greatly over time because the particles flowed continuously from the HEC to the RC under the influence of the pressure difference between the two chambers. The two particle types had unequal granular temperatures and the energy fluctuations were higher for the P275 particles than the G116 particles.

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Fig. 3. Instantaneous gas pressure, solids circulation rate, gas bypassing rate and granular temperatures in the ICFB.

4.3. Effect of the gas velocity UR The gas velocities introduced into RC and HEC, i.e., UR and UH , have critical effects on the gas–solid dynamics in an ICFB [51]. Therefore, the effects of both these velocities on the performance of an ICFB should be carefully evaluated. Fig. 4 shows the effects of UR on the time-averaged bed pressures near the gas distributor in the two chambers (RC and HEC) of the ICFB as a function of the velocity ratio UR /UH . We mentioned earlier that the pressure in a fluidized bed is directly related to the bed concentration. We found that when the velocity ratio UR /UH was increased, the pressure in the RC decreased due to the high gas hold-up whereas the pressure in the HEC increased due to the high solids hold-up. This trend is also consistent with the results obtained in previous studies [16] of ICFBs with particles of a single size and density, i.e., monodispersed particles. In baffle-type ICFBs, the eruption of bubbles at the surface generally throws the solid particles from the RC to the HEC above the baffle, and these particles recirculate from the HEC to the RC through the slot beneath the baffle due to the pressure difference that develops across the slot. Fig. 5 shows the time-averaged solid circulating rate and pressure difference between the chambers as a function of the velocity ratio UR /UH . The gas velocity in the RC (UR ) plays a crucial role in the gas solid dynamics in all types of ICFBs. After increasing UR , the solids circulation rate Gs increased regardless of the particle type (Fig. 5(a)) because the solid hold-up decreased in the RC chamber whereas it increased in the HEC to generate a pressure gradient between the two chambers (Fig. 5(b)). Hence, the pressure difference between the chambers was the driving force responsible for the recirculation of particles through the slot. This finding is consistent with the results obtained in a previous study [16] of an ICFB system with monodispersed particles. The circulation rate was higher for G116 compared with that for P275 because of their different concentrations (i.e., the mass of G116 = 70% and the mass of P275 = 30%) in the mixture in the ICFB. Fig. 5(b) shows that decreasing the velocity ratio UR /UH also reduced the pressure difference between the two chambers, thereby leading to a drop in the solids circulation rate. Fig. 6 shows the solids circulation rate for the binary mixture as a function of the pressure difference between the two chambers in the ICFB, which demonstrates that an increase in the pressure difference across the gap between the two chambers corresponded to an increase in the solids circulation rate for the binary mixture and vice versa.

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Fig. 4. Effect of UR on the bed pressure of the two chambers in the ICFB.

Fig. 5. Effect of UR on the solids circulation rate and pressure difference between the HEC and RC in the ICFB.

4.4. Effect of the gas velocity UH Next, we determined the effect of UH on the gas–solid flow behavior in the ICFB in terms of the solids circulation rate. Fig. 7 shows the time-averaged solids circulation rate through the slot under the baffle and the pressure difference between the chambers as a function of UH /UR at UR = 0.084 m s–1 . Similar to the gas velocity UR , UH played a critical role in controlling

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Fig. 6. Correlation of the total solids circulation rate as a function of the pressure difference between the two chambers.

the solids circulation rate in the ICFB. Thus, variations in the gas velocities (UR or UH ) in the RC and HEC had significant effects on the pressure drop across the slot to affect the solids circulation rate in the ICFB. As the value of UH increased and gradually approached UR , the gas hold-up in the HEC chamber increased due to bubble formation. Thus, there was also a decrease in the pressure difference between the two chambers, which was the driving force responsible for the recirculation of particles through the slot (Fig. 7(b)). As a consequence, the criterion for solids circulation where one chamber should be fluidized and the other should be in a moving state no longer applied. Ultimately, the solids circulation rate in the ICFB started to decrease and approached zero as UH increased (Fig. 7(a)). Despite this decrease, the circulation rate was still larger for G116 compared with that for P275 because of the uneven mixture composition, as discussed in the previous section. 4.5. Effect of the mixture composition Interestingly, the relative ratio of the circulation rate (Gratio ) for the two particles (G116 and P275) had an almost linear relationship with the ratio of their respective masses (Mratio ) in the mixture within the ICFB under all conditions (i.e., various values for UR /UH , UH /UR , or mass ratios), as shown in Fig. 8. For example, when the mixture had an even composition (i.e., when the mass of G116 equaled the mass of P275), both particles had almost the same circulation rates, i.e., Mratio = 1.0 and Gratio = 1.0. Similar trends in Mratio = Gratio were observed under all of the other conditions tested in this study. Thus, similar to the fluidization velocities UR and UH , the relative ratio of the concentrations of the two particles or the composition of the mixture also played a critical role in predicting and controlling the circulation behavior of the binary mixture in the ICFB. This unique feature of the ICFB has never been studied and discussed previously. 4.6. Particle mixing performance: ICFB vs. BFB Solid mixing has important effects on the product quality, yield, and homogeneity in several industries related to granular materials. ICFBs possess excellent mixing capabilities and they can achieve an appropriate mixing status in a relatively short time compared with conventional fluidized beds, provided that the reactor has sufficient aeration [9,14]. For example, Foscolo et al. [13] used an ICFB for biomass gasification and found that compared with a conventional BFB, more efficient energetic exchange was obtained between sand and biomass particles in an ICFB, thereby leading to better mixing as well as reducing the segregation of biomass particles on the bed surface and the elutriation of fine carbon particles to ultimately improve the yield and quality of the gas product. The excellent mixing quality obtained using ICFBs is due to the continuous circulation of the internal solids between different zones in the reactor. Moreover, as explained in Section 4.2, in addition to the solids circulation between the chambers, further solids circulation occurs within each chamber because the motion of bubbles enhances the mixing process in the reactor. Figs. 9–11 compare the mixing performance in the ICFB with that reported in a conventional BFB by Joseph et al. [46] in terms of the jetsam (G116) mass fraction under different aeration levels, where the results indicate that an ICFB can provide

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Fig. 7. Effect of UH on the solids circulation rate and pressure difference between the HEC and RC in the ICFB.

Fig. 8. Correlation of the ratio of the circulation rate of the two particle types to their mass ratio in the ICFB.

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Fig. 9. Solids mixing comparison of ICFB and BFB when masses (%) of the constituent particle types (G116 / P275) are 50/50.

Fig. 10. Solids mixing comparison of ICFB and BFB when masses (%) of the constituent particle types (G116 / P275) are 70/30.

much better mixing than BFBs. Instead of the minimum fluidization velocity Umf , the concept of the Ufc (complete fluidization velocity at which all particles are fluidized) is generally applied for binary mixtures. For the mixture shown in Fig. 9, the value of Ufc was 0.041 m s–1 , whereas it was equal to 0.024 m s–1 for that in Figs. 10 and 11. According to Fig. 9, the gas velocity in the BFB was about 1.2Ufc , whereas the gas velocities in the RC and HEC in the ICFB were about 1.2Ufc and 3.6Ufc , respectively. The aeration of the RC in the ICFB was comparatively higher than that in the BFB, but the gas velocity in the HEC was similar to that in the BFB, and the mixing in both the RC and HEC were much better than that in the BFB, where clear segregation was observed. As shown in Fig. 10, the gas velocities in the RC and HEC in the ICFB were 2Ufc and 3.3Ufc ,

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Fig. 11. Solids mixing comparison of ICFB and BFB at same gas velocities when masses (%) of the constituent particle types (G116 / P275) are 70/30.

respectively, but 1.9Ufc , 2.3Ufc , and 3.2Ufc in the BFB. At the specified gas velocities, better mixing was observed in the ICFB compared with the BFB. Segregation occurred in the BFB, except at 3.2Ufc , and thus better mixing could be achieved in the ICFB than the BFB, although at the expense of higher fluidization velocities. Furthermore, both the ICFB and BFB were fluidized under almost the same aeration conditions, i.e., at 1.6Ufc and 1.9Ufc in the RC and HEC in the ICFB, respectively, and at 1.6Ufc and 1.9Ufc in the BFB, but the mixing was still comparatively better in the ICFB than the BFB. Some segregation was observed in the bottom section of the ICFB but this can be minimized (Figs. 9 and 10) because ICFBs are usually operated at relatively higher gas velocities. These results support our predictions and confirm the findings of the previous experimental studies [9,13,14] mentioned earlier. Compared with conventional BFBs, the enhanced solids mixing performance makes ICFBs highly suitable for various applications, such as in biomass gasification, to avoid the segregation of biomass particles on the bed surface and to facilitate energetic exchange between the bed material and biomass particles.

5. Conclusion The solids circulation process in an ICFB with two or more chambers can be developed by applying unequal gas velocities in these chambers. We performed Eulerian–Eulerian simulations to study the gas–solid flow dynamics in an ICFB containing a binary mixture by using ANSYS Fluent combined with the kinetic theory of granular flow. The binary mixture comprised two particles (G116 and P275) with different sizes and densities. We investigated the effects of several parameters on the performance of the ICFB, such as variations in the gas velocities in the two chambers, the mass ratios of the constituent particles, and solids mixing, and the results were quantified in terms of the solids circulation rate (Gs ). Variations in the superficial velocities in the chambers significantly affected the performance of the ICFB. The circulation of the binary mixture involved two main processes in the ICFB. The bursting of bubbles in the RC was responsible for the solids circulating from the RC to the HEC above the baffle. In addition, the pressure difference between the two chambers was responsible for the recirculation of solids through the slot under the baffle from the HEC to the RC. The gas velocities comprising UR and UH strongly influenced the solids circulation rate and the pressure drop across the slot. An increase in the gas velocity in the RC, UR , with a constant velocity in the HEC, UH , resulted in an increase in the circulation rate of the binary mixture. The relative ratio of the circulation rates of the G116 and P275 particles was approximately equal to the ratio of their respective masses in the mixture within the ICFB. An increase in the gas velocity in the HEC, UH , under constant aeration in the RC, UR , resulted in a decrease in the circulation rate of the binary mixture. The particles in the mixture had unequal granular temperatures and the fluctuating energy of the P275 particles was higher than that of the G116 particles. The continuous internal solids circulation process resulted in much better solids mixing in the ICFB compared with conventional BFBs. Our simulations showed that the multi-fluid Eulerian model could capture the main features of the behavior of the gas and the mixture of binary particles. This proof-of-concept study focused on the effects of the fluidizing gas velocity in the

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