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Effect of Inlet Boundary Conditions on Computational Fluid Dynamics (CFD) Simulations of GasSolid Flows in Risers Milinkumar T. Shah,† Ranjeet P. Utikar,† Geoffrey M. Evans,‡ Moses O. Tade,† and Vishnu K. Pareek*,† † ‡

Department of Chemical Engineering, Curtin University, GPO Box U1987, Perth, Western Australia 6845 Department of Chemical Engineering, University of Newcastle Callaghan, NSW 2308, Australia ABSTRACT: The effect of type of inlet conditions on the predictions of EulerianEulerian simulations of a circulating fluidized bed riser has been investigated in both 2D and 3D domains. The 2D simulations were conducted using 3 different inlet configurations: (A) solids entering in radial direction from a two-sided inlet and gas entering axially from the bottom inlet, (B) solid entering axially from a two-sided bottom inlet near the wall and gas entering axially from a bottom inlet at the center, and (C) gas phase entering axially from a two-sided bottom inlet near the wall and solids entering axially from a bottom inlet at the center. In 2D simulations, it was found that both time-averaged axial velocity and solids volume fraction radial profiles were functions of the inlet kinetic energy as well as gassolid mixing patterns at the inlet. Whereas 2D simulations using boundary conditions A and C showed significant deviations from experimental profiles, the boundary condition B as well as full-scale 3D simulations gave reasonable agreements with experimental observations.

’ INTRODUCTION A circulating fluidized bed (CFB) reactor has many advantages over conventional chemical reactors due to its enhanced heat and mass transfer characteristics. For these reasons CFB systems have been widely applied in several unit operations such as fluid catalytic cracking, catalytic reforming, coal combustion, and polymerization. The most important section of a CFB unit is a riser where chemical reactions take place. Reactions may be either catalyzed by the solids such as fluid catalytic cracking or occurring between the gas and fluidized solids phases such as combustion of pulverized coal. In a riser, the interaction and flow of gas and solid phases plays an important role in governing the conversions of chemical reactions, and in turn the performance of the CFB unit. Therefore, an in-depth understanding of the hydrodynamics of riser is essential for designing and scaling-up of CFB systems.1 Recently, computational fluid dynamics (CFD) has been extensively used for studying the hydrodynamics of risers.24 In most of the previous studies, 2D EulerianEulerian simulations have been used, essentially to minimize computational requirements. Because a 2D domain cannot directly capture the asymmetric entry of solids to a continuously flowing riser, simulations in previous studies have been conducted using different types of boundary conditions for the inlets and outlets. For example, Pita and Sundaresan5 examined three different boundary conditions: (i) uniform, (ii) core-annulus flow, and (iii) circumferential injection of secondary gas at the inlet. They found that for the uniform and core-annulus cases the segregation of particles toward the wall caused widespread internal recirculation of solids and gas. For the circumferential injection of secondary gas, the authors noted that the segregation of particles toward the wall occurred more slowly and resulted in a substantial reduction in recirculation of solids. Neri and Gidaspow6 used uniform and trapezoidal profiles of gas and solid velocities at the U-tube inlet which was smaller in diameter than the riser. They found that the simulations using trapezoidal inlet profiles predicted denser flows in both core and annular regions than those using the uniform profiles. Moreover, their results for both types of inlet boundary conditions only r 2011 American Chemical Society

showed qualitative agreement with the experimental data. Benyahia et al.3 compared simulations with experimental measurements for both one- and two-sided inlets. The simulations using the one-sided inlet predicted the gas to be flowing toward the opposite side of the solid inlet, which in turn created a nonsymmetric radial distribution of solids throughout the full height of the riser. The core-annular flow regime, which has been widely observed experimentally,7 was not produced with one-sided inlet, but it did appear in the simulations for the two-sided inlet. Vaishali et al.4 also used a two-sided inlet in their riser simulations, which were in qualitative agreement with experimental data8 under dilute phase flow conditions. Almuttahar and Taghipour2 simulated a 2D geometry of the inlet section of a riser. They found that a core-annulus inlet having solids entering vertically upward along the walls and air entering in the core of the riser gave reasonable qualitative and quantitative agreements between simulations and experimental measurements of solids volume fraction and radial profiles of solid velocities. The preceding discussion clearly indicates that there is a lack of agreement on type of boundary conditions in 2D domains, and more research is therefore required for selection of inlet boundary conditions. In this study, three different types of boundary conditions in 2D simulations have been investigated and compared with experimental results of Bhusarapu et al.8 as well as transient 3D simulations. The influence of both no- and partialslip wall boundary conditions has also been investigated.

’ GASSOLID FLOW MODELING APPROACHES The gassolid flow models can be broadly classified into two categories, namely the EulerianEulerian (EE) and Eulerian Lagrangian (EL) methods. The selection of a particular approach Special Issue: Nigam Issue Received: May 1, 2011 Accepted: September 2, 2011 Revised: August 31, 2011 Published: September 02, 2011 1721

dx.doi.org/10.1021/ie200940f | Ind. Eng. Chem. Res. 2012, 51, 1721–1728

Industrial & Engineering Chemistry Research

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Table 1. EulerianEulerian GasSolid Flow Model

Table 1. Continued Collisional energy dissipation 12ð1 e2ss Þgo, ss pffiffiffi Fs εs Θ3=2 γθs ¼ s dp π

Continuity equation for gas phase ∂ ðεFg Þ þ ∇ðεFg uBg Þ ¼ 0 ∂t

Diffusion coefficient for the granular energy pffiffiffiffiffiffiffi 15dp Fs εs Θπ 12 2 16 1 þ η ð4η 3Þεs go, ss þ ð41 33ηÞηεs go, ss kθs ¼ 4ð41 33ηÞ 5 15π

Continuity equation for solid phase ∂ ðεs Fs Þ þ ∇ðεs Fs uBs Þ ¼ 0 ∂t

η ¼

Momentum conservation equation for gas phase ∂ ðεFg uBg Þ þ ∇ðεFg uBg uBg Þ ¼ ε∇P ∇τ g þ εFg g βðuBg uBs Þ ∂t Momentum conservation equation for solid phase ∂ ðεs Fs uBs Þ þ ∇ðεs Fs uBs uBs Þ ¼ εs ∇P ∇τ s þ εs Fs g βðuBg uBs Þ ∂t Interphase exchange coefficient Gidaspow drag model 3 εð1 εÞ Fg jug us jCD0 ε 2:7 βWenYu ¼ 4 dp βErgun ¼ 150

ð1 εÞ2 εμg εdp

þ 1:75

for ε > 0:8

ð1 εÞFg jug us jεμg dp

for ε e 0:8

Gas phase stressstrain tensor 2 τg ¼ μg ð∇uBg þ ∇uBTg þ λg μg ∇uBg I Þ 3 Solid phase stressstrain tensor 2 τs ¼ Ps I þ μs ð1 εÞð∇uBs þ ∇uBTs Þ ∇uBs I 3 Solid pressure Ps ¼ εs Fs Θs ð1 þ 2ð1 þ ess Þεs go, ss Þ Solid bulk viscosity

rffiffiffiffi 4 Θ λs ¼ ε2s Fs ds go, ss ð1 þ ess Þ 3 π

Solid shear viscosity μs ¼ μs, col þ μs, kin þ μs, f ri rffiffiffiffi 4 Θ μs, col ¼ ε2s Fs dp go, ss ð1 þ ess Þ 5 π pffiffiffiffiffiffiffi 2 10Fs dp Θπ 4 μs, kin ¼ 1 þ ε2s ð1 þ ess Þgo, ss 5 96es ð1 þ ess Þgo, ss μs, fri ¼

Pf sin ϕ pffiffiffiffiffiffi 2 I2D

Frictional pressure ðεs εs, min Þn Pf ¼ Fr ðεs, max εs Þm Radial distribution factor " # 2:5emax εs go, ss ¼ 1 εs, max Granular temperature 1 Θs ¼ uB2s 3 Granular temperature equation

3 ∂ ðεs Fs Θs Þ þ ∇ðεs Fs uBs Θs Þ ¼ ð Ps I þ τ s Þ : ∇uBs þ ∇ðkθs ∇Θs Þ γθs þ ϕls 2 ∂t

ð Ps I þ τ s Þ : ∇uBs ¼ generation of energy by solid stress tensor

1 ð1 þ ess Þ 2

ϕls = energy exchange between lth fluid or solid phase and sth solid phase

primarily depends on the scale of the equipment and available computational power.9 The majority of riser simulations have been conducted using the EE approach as it is more amenable to largescale geometries having high solid inventories. In the EE approach, both continuous and dispersed phases are treated as an interpenetrating continuum, and the ensemble averaging of local instantaneous mass, momentum, and energy balances for each phase are used in formulating the governing equations. Due to the continuum assumption, the stress tensor for the solid phase is not explicitly defined and the kinetic theory of granular flow,10 which is based on the kinetic theory of gases, is applied to determine the motion of the particles. In adopting this approach the stress tensor requires additional closures for several other properties such as the granular viscosity, solid pressure, frictional viscosity, and frictional pressure. The governing equations for both phases are coupled with the interphase exchange drag coefficient. A comparative study using different closure relation was conducted by van Wachem et al.,11 and following their recommendations the model equations used in this study are summarized in Table 1.

’ SIMULATION APPROACH All CFD simulations were performed using commercial CFD package FLUENT v 6.3. 2D simulations were conducted using a time step size of 0.0005 s. This time-step size was chosen on the basis of previous studies24,12 which found 0.0005 s to be adequate for 2D riser simulations. However, to minimize computational requirements, 3D simulations were conducted with a time step of 0.0002 s. A second-order discretization scheme was used for the momentum equation, and the QUICK scheme was applied for the volume fraction. The turbulence in the gas phase and its effect on the dispersed secondary phase was modeled using the standard k-ε model. The pressurevelocity coupling was resolved using the SIMPLE algorithm. The physical properties of the gas and solid phases are listed in Table 2. Also included in the table are the simulation parameters, which correspond to the experimental study of Bhusarapu et al.8 All of the simulations were run on a cluster of eight high speed computers, and it took more than three weeks for each of the 3D simulations to complete. Simulations were conducted in both 2D and 3D domains of riser. The 3D simulations were performed using the cylindrical riser with actual dimensions in all three coordinates. In the 2D simulations, only a rectangular slice of the cylindrical riser was used, and with conservation equations were solved only in two coordinates. In FLUENT, the neglected coordinate is assumed to be unity, thus giving a cross-sectional area numerically equal to the diameter of the riser. Consequently, for a flux of solids, the solid mass flow rates in the 2D and 3D simulations are often significantly different (see Table 2). 1722

dx.doi.org/10.1021/ie200940f |Ind. Eng. Chem. Res. 2012, 51, 1721–1728


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Table 2. Physical Properties of Both Phases and Simulation Parameters phase properties

simulation parameters

gas phase

air

riser diameter

152 mm

air density

1.12 kg/m3

riser height

7.9 m

air viscosity

1.18 1005

inlet boundary

velocity inlet pressure outlet

kg/m 3 s air velocity

4.5 m/s

outlet boundary

solid phase

glass beads

discretization

second order

particle diameter

150 μm

turbulent model

k-ε model

solid density

2550 kg/m3

2D simulation

solid flux

37 kg/m2s

restitution factor

grid size

9.5 25 mm

time step

5 104 s

particleparticle

0.95

C/s area of riser

1 0.152 m2

particlewall

0.9

mass flow rate of

5.624 kg/s

max. packing limit

0.6

Figure 3. Simulated mass flow rate at the outlet as a function of time for BC-A inlet.

solids 3D simulation time step

2 104 s

C/s area of riser

0.01814 m2

mass flow rate of

0.6714 kg/s

solids

Figure 1. (a) Experimental and (b) simulated3 solid inlet configurations.

Figure 2. Inlet arrangements used in 2D simulations.

The inlet arrangement configurations were selected to best represent the experimental study of Bhusarapu et al.,8 where the gas entered at the bottom of the riser through a distributor while the solids were introduced via an inclined pipe (see Figure 1a). Previous 2D simulation studies3 have shown, however, that by having a single solid inlet, such as that shown in Figure 1b, it was not possible to produce the experimentally observed core annulus solids density profile. Consequently, inlet arrangements for 2D simulations have been widely tweaked to get desired comparisons with 3D experimental data. Therefore, as shown in

Figure 2, the following three different types of inlet configurations for 2D simulations were investigated in this study: BC-A. (Figure 2a) Solid entering in radial direction from a twosided inlet and gas entering axially from the bottom inlet.3,4,13 BC-B. (Figure 2b) Solid entering axially from two-sided bottom inlet near the wall and gas entering axially from a bottom inlet at the center.2,5 BC-C. (Figure 2c) Axial solid entry from a single bottom inlet at the center and gas entry from two bottom inlets near the walls. The experimental setup in refs 8,14, and 15 comprised a single outlet at the top of the riser through which the gassolid flow entered into the disengagement section. Therefore, a single top outlet was adopted for this study.

’ RESULTS AND DISCUSSION Preliminary 2D simulations were carried out using the boundary condition BC-A to determine the approximate time required for the system to attain a “dynamic” steady state. A mass flux of 37 kg/m2 and superficial gas velocity of 4.5 m/s were used, which corresponded to experimental conditions of Bhusarapu et al.8 As shown in Figure 3, the solids mass flow rate at the outlet was plotted for the first 40 s of a simulation. It is clear that after an initial period of about 5 s the solids mass flow rate fluctuated around an average solid flow rate of about 5.4 kg/s. A further check on the time required for dynamic steady state was carried out by comparing the radial profiles of solids velocity and volume fraction at an arbitrary riser height of 5.5 m, which were time-averaged at a sampling frequency of 2 kHz over the previous 10, 15, and 20 s of the 40 s simulation. This comparison is shown in Figure 4. It can be seen that there was negligible difference between the solid velocity profiles for all three time-averaging periods. In all cases, the maximum velocity was observed at the center with a zero value near the wall, which was consistent with the core-annulus flow structure reported in previous simulation studies.6,16,17 Only minor differences were observed between the mean solids volume fraction profiles averaged over different time periods. This analysis for the effect of time-averaging was also performed for simulations with all different types of boundary conditions, and it was found that the averaging period of 20 s, corresponding to the time interval 1030 s was sufficient for all further quantitative analysis. Effect of Solid Inlet Boundary Conditions. Time-averaged radial profiles of mean solid velocity and volume fraction in the fully developed zone for the three simulation conditions were 1723



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Figure 4. Time-averaged radial profiles of (a) solids axial velocity and (b) solid volume fraction (at a riser height of 5.5 m).

Figure 5. Time-averaged radial profiles for (a) solids axial velocity and (b) solid volume fraction (at a riser height of 5.5 m).

Figure 6. Solids axial velocity vector and volume fraction contours in the riser entrance region.

compared with the experimental measurements of Bhusarapu et al.8 as shown in Figure 5. It can be seen that the simulations using the boundary condition BC-B were in good agreement with the experimental measurements, while simulations using both BC-A and BC-C under-predicted the mean solid velocity and over-predicted the

volume fraction. The differences between the simulation predictions can be attributed to differences in the mixing of the gas and solid phases at the inlet as shown in Figure 6, which shows a set of time-averaged velocity vector plots (a, c, e) and solid volume fraction contours (b, d, f) near the inlets for the three different inlet configurations. 1724


Industrial & Engineering Chemistry Research For the BC-A configuration (Figure 6a and b), it can be seen that as the solids entered in the radial direction, they were thoroughly mixed with the gas entering from the bottom in the axial direction. The mixing between the solids and gas phases led to a relatively higher dissipation of the kinetic energy, and thus a lower solids velocity than configuration BC-B (Figure 6c and d), where the solids moved upward with a higher velocity and higher volume fractions near the wall, and the gas moved along the center part. Consequently, there was less mixing between the two phases, which then rapidly assisted in the formation of a core-annular flow structure. For the boundary condition BC-C (Figure 6e and f), even the axial entry of both phases did not adequately prevent the mixing between the

Figure 7. Kinetic energies of gas and solid phases in the riser entrance region.

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two phases, which then along with the rapid motion of gas along the wall prevented the formation of the core annular structure. The kinetic energies of the solids and gas phases at the entrance for the three different inlet configurations are compared with the experimental measurements of Bhusarapu et al.8 in Figure 7. It can be seen that for all three inlet configurations the simulated kinetic energies for the gas phase were approximately an order of magnitude higher than those determined—for experimental inlets. For the solids phase the BC-B and BC-C simulations were similar and higher in value than the experimental results. Conversely, the BC-A simulation reported a lower value. An interesting observation is that while BC-B and BC-C have similar solids kinetic energy terms, the resultant radial profiles for the solids axial velocity and volume fraction are considerably different, as shown in Figure 5a and b, respectively. Similarly, while the solids kinetic energy for BC-A is similar to that for experimental solid inlet the corresponding solids axial velocity and volume fraction profiles are considerably different from the measured values (see Figure 5). In summary, the discrepancies between 2D simulation results and experimental data, for the same mass flux and superficial gas velocity, highlight the challenges in correctly establishing appropriate boundary conditions for 2D simulations. Effect of Type of Wall Boundary Condition. The effect of type of wall boundary condition was investigated by configuring the wall as either “no-slip” or “partial-slip” for the solid phase. In the EE model, the conservation of the granular temperature can be modeled using two types of equations, i.e., (i) algebraic and (ii) partial differential equations. In the algebraic equation, convection and diffusion of the granular temperature are

Figure 8. Effect of type of wall boundary conditions on mean solid velocity and fraction profiles. 1725



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Figure 9. (a) Schematic of 3D riser. (b) Profiles of solids volume fraction. (c) Radial profiles of axial solid velocities.

neglected, and the wall can only be configured as a no-slip for both phases. Conversely, the partial differential equation accounts for the dissipation terms such as the conduction of granular temperature, dissipation of granular temperature due to the inelastic granular collisions, and the rate of transfer of fluctuating energy between the gas and solid phases. Using the partial differential equation approach, the wall can be configured using a partial-slip boundary condition as derived by Johnson and Jackson.18 In this type of wall boundary condition, the solid tangential velocity and granular temperature at the wall are calculated using a specularity coefficient and particlewall restitution coefficient, respectively. The specularity coefficient is a measure of fraction of collisions, which transfers momentum to the wall, and the restitution coefficient specifies the collision dissipation rate between particle and wall. The specularity coefficient and particlewall restitution factor were set as 0.6 and 0.9, respectively, using previous simulation studies.3,19 Simulations using BC-A and BC-B inlet configurations were conducted to investigate the effect of the wall boundary conditions on the time-averaged mean solid velocity and volume fraction. The results are shown in Figure 8. For BC-A (Figure 8a and b), the partial-slip wall boundary condition resulted in poor agreement for both solids velocity and volume fraction. The higher solid segregation near the wall using the partial-slip wall can be attributed to dissipation of energy due to collisions between solids and wall, which are neglected in the noslip wall boundary condition. Conversely, the no-slip wall boundary condition was generally in reasonable agreement with

the measured solid velocity and volume fraction profiles, especially near the wall. This improvement can be attributed to the exclusion of dissipation caused by the particlewall collisions, which is a reasonable assumption for the dilute phase transport. Figure 7c and d shows the effect of wall type on the radial profiles using the inlet type BC-B. Unlike that for BC-A, only a minor effect of the wall boundary condition on both solids velocity and volume fractions profiles was observed. 3D Full-Scale Simulations. Figure 9a shows a schematic of the 3D geometry of the riser, which was meshed with a total of over 210 000 cells. A cluster of eight processors was used to conduct these CFD simulations. Since a small time step size of 0.0002 s was used to carry out the simulation, it took more than three weeks for \30 s of real flow time simulation. Figure 9b and c shows the time-averaged radial profiles of the solid volume fraction and axial velocity, respectively. The predicted values showed a reasonable qualitative agreement with the experimental values. However, near the center, the simulation slightly over-predicted solid volume fractions and underpredicted solid velocities, and an opposite trend was predicted near the wall. Vaishali et al.4 conducted simulations using a 2D riser, in which the authors evaluated two drag correlations by comparing not only the radial profiles of the solid velocity and volume fraction but also the fluctuating solid velocity (granular temperature). Although the authors successfully compared their predictions with the experimental data for the fast fluidization of solids they could not even predict the basic core-annulus nature of the riser flow for the dilute phase transport. They had emphasized a need 1726



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“core-annular”, whereas in the other two inlet types, the solid and gas phases were nearly completely mixed. These mixing patterns were then observed to be directly correlated to the radial distribution of the solids, even to the top part of the riser. The kinetic energies of both phases at the inlets (Figure 7) were significantly different from the 3D experimental case for either of the 2D boundary conditions. Thus, using an arbitrary boundary condition in 2D simulations, the energy balances inside the domain may not reflect the experimental values. The effect of the type of wall boundary condition was also investigated by considering it as either partial or no-slip. Using BC-A type inlet boundary condition, a change in the wall condition from the partial to no-slip, gave results closer to the experimental data (figure 8). This could be attributed to exclusion of the dissipation caused by particlewall collisions. Interestingly, the effect of wall configuration on the radial profiles using the BC-B was negligible. This could also be attributed to predicted lower solid volume fractions using this boundary condition. Thus, the effect of type of wall boundary conditions was strongly dependent on inlet configurations. Therefore, the selection of boundary conditions in 2D simulations was found to be challenging task, and the use of an arbitrary type of boundary conditions could mislead in judging the validation of the EE model. 3D full-scale simulations were also conducted by implementing the inlet and outlet boundary conditions similar to the experimental setup. The 3D simulations showed a reasonable qualitative with the experimental data, but quantitatively there were disagreements (Figure 9) near the central region and walls.

’ AUTHOR INFORMATION Figure 10. Comparison between experimental and simulation results. (a) Profiles of axial velocities of solids. (b) Profiles of volume fraction of solids.

Corresponding Author

*E-mail: [email protected]. Tel: (08) 9266 4687. Fax: (08) 9266 2681.

for a better combination of solid phase closure models and 3D full-scale simulation to eliminate the reported discrepancies. A comparison between the predictions from current study with that of Vaishali et al.4 is also shown in Figure 10. It is evident from the comparison that both 2D and 3D simulations in the current study consistently predicted a qualitative trend of the coreannulus flow with some quantitative discrepancies.

’ ACKNOWLEDGMENT We are thankful to Prof. Mike Dudukovic for his encouragement as well as for providing experimental data of S. Bhusarapu (2005) of CREL-WUSTL. We also wish to acknowledge the financial support from the Australian Research Council (Grants LP0882958, LP110100717).

’ CONCLUSIONS In this work, the effect of boundary conditions on gassolid flows in riser was investigated by conducting both 2D and 3D simulations. In 2D simulations, three different types of inlet configurations: (i) BC-A (Figure 2a), (ii) BC-B (Figure 2b), and (iii) BC-C (Figure 2c) were investigated, and found to have profound effect on the radial profiles of solid velocity and volume fractions even in the top section of riser which has been generally described as the fully developed region and believed to be immune to any entry effect. Furthermore, boundary type BC-B gave more reasonable agreement with the experimental data than BC-A and BC-C. This profound effect of inlet arrangements was attributed to two possible causes, i.e., (i) mixing and (ii) kinetic energies of two phases at the entrance. The contour plots of solid volume fractions (Figure 6) at the entrance clearly indicated that the mixing of two phases was inadequate in boundary type BC-B, which then eventually assisted the solid holdup profile to

’ NOMENCLATURE CD0 = Standard drag coefficient, kg 3 m3 3 s1 dp = Solid diameter, m ess = Coefficient of restitution Fr = Empirical material constant, kg 3 m2 3 s2 g = Gravitational acceleration, m 3 s2 go,ss = Radial distribution function I = Unit stress tensor I2D = Second invariant of the deviatoric stress tensor kθs = Diffusion coefficient for the granular energy m = empirical material constant in frictional pressure model n = empirical material constant in frictional pressure model P = Pressure, kg 3 m1 3 s2 Ps = Solids pressure, kg 3 m1 3 s2 Pf = Frictional pressure, kg 3 m1 3 s2 r = Radial position, m R = Radius of riser, m u = Velocity, m 3 s1 1727


Industrial & Engineering Chemistry Research Greek Letters

ε = Volume fraction β = Drag coefficient, kg 3 m3 3 s1 F = Density, kg 3 m3 τ = Stress tensor, kg 3 m1 3 s2 μ = Viscosity, kg 3 m1 3 s1 λs = Solid bulk viscosity, kg 3 m1 3 s1 γθs = Collisional energy dissipation Θs = Granular temperature, m2 3 s2 ϕ = Angle of internal friction ϕls = energy exchange between lth fluid or solid phase and sth solid phase Subscripts

Col = Collisional fri = Frictional g = Gas phase kin = Kinetic max = Maximum min = Minimum s = Solid phase Abbreviations

BC = Boundary condition CFB = Circulating fluidized bed CFD = Computational fluid dynamics KTGF = Kinetic theory of granular flows QUICK = Quadratic upstream interpolation for convective kinetics SIMPLE = Semi-implicit method for pressure-linked equations

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(12) Yang, N.; Wang, W.; Ge, W.; Li, J. CFD simulation of concurrent-up gas-solid flow in circulating fluidized beds with structure-dependent drag coefficient. Chem. Eng. J. 2003, 96 (13), 71–80. (13) Yang, N.; Wang, W.; Ge, W.; Wang, L.; Li, J. Simulation of heterogeneous structure in a circulating fluidized-bed riser by combining the two-fluid model with the EMMS approach. Ind. Eng. Chem. Res. 2004, 43 (18), 5548–5561. (14) Bhusarapu, S.; Al-Dahhan, M.; Dudukovic, M. P. Quantification of solids flow in a gassolid riser: Single radioactive particle tracking. Chem. Eng. Sci. 2004, 59 (2223), 5381–5386. (15) Bhusarapu, S.; Al-Dahhan, M. H.; Dudukovi, M. P. Solids flow mapping in a gassolid riser: Mean holdup and velocity fields. Powder Technol. 2006, 163 (12), 98–123. (16) Nieuwland, J. J.; Annaland, S.; Kuipers, J. A. M.; Swaaij, W. P. M. Hydrodynamic modelling of gas-particle flows in riser reactors. AIChE J. 1996, 42 (6), 1569–1582. (17) Mathiesen, V.; Solberg, T.; Hjertager, B. H. An experimental and computational study of multiphase flow behavior in a circulating fluidized bed. Int. J, Multiphase Flow 2000, 26 (3), 387–419. (18) Johnson, P. C.; Jackson, R. Friction akollisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 1987, 176. (19) Jiradilok, V.; Gidaspow, D.; Damronglerd, S.; Koves, W. J.; Mostofi, R. Kinetic theory based CFD simulation of turbulent fluidization of FCC particles in a riser. Chem. Eng. Sci. 2006, 61 (17), 5544–5559.

’ REFERENCES (1) Dudukovic, M. P. Frontiers in Reactor Engineering. Science 2009, 325 (5941), 698. (2) Almuttahar, A.; Taghipour, F. Computational fluid dynamics of high density circulating fluidized bed riser: Study of modeling parameters. Powder Technol. 2008, 185 (1), 11–23. (3) Benyahia, S.; Arastoopour, H.; Knowlton, T. M.; Massah, H. Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase. Powder Technol. 2001, 112 (12), 24–33. (4) Vaishali, S.; Roy, S.; Bhusarapu, S.; Al-Dahhan, M. H.; Dudukovic, M. P. Numerical Simulation of GasSolid Dynamics in a Circulating Fluidized-Bed Riser with Geldart Group B Particles. Ind. Eng. Chem. Res. 2007, 46 (25), 8620–8628. (5) Pita, J. A.; Sundaresan, S. Developing flow of a gas-particle mixture in a vertical riser. AIChE J. 1993, 39 (4), 541–552. (6) Neri, A.; Gidaspow, D. Riser hydrodynamics: Simulation using kinetic theory. AIChE J. 2000, 46 (1), 52–67. (7) Knowlton, T.; Geldart, D.; Matsen, J.; King, D. Comparison of CFB Hydrodynamic Models; PSRI challenge problem at the Eighth international fluidization conference 1995, France. (8) Bhusarapu, S.; Al-Dahhan, M. H.; Dudukovic, M. P.; Trujillo, S.; O’Hern, T. J. Experimental Study of the Solids Velocity Field in GasSolid Risers. Ind. Eng. Chem. Res. 2005, 44 (25), 9739–9749. (9) Van der Hoef, M. A.; van Sint Annaland, M.; Deen, N. G.; Kuipers, J. A. M. Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy; Annual review of fluid mechanics 2008, 70, 4070. (10) Lun, C. K. K.; Savage, S. B. Kinetic theories for granular ow: Inelastic particles in Couette ow and slightly inelastic particles in a general ow eld. J. Fluid Mech. 1984, 140, 223–256. (11) Van Wachem, B. G. M.; Schouten, J. C.; Van den Bleek, C. M.; Krishna, R.; Sinclair, J. L. Comparative analysis of CFD models of dense gassolid systems. AIChE J. 2001, 47 (5), 1035–1051. 1728


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