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Numerical Study on the Effect of the Air Jets at the Inlet Distributor in the Gas-Solids Circulating Fluidized-Bed Risers Botao Peng,† Jesse Zhu,*,‡ and Chao Zhang† Department of Mechanical and Materials Engineering and Department of Chemical and Biochemical Engineering, The UniVersity of Western Ontario, London, Ontario, Canada N6A 5B9
This work numerically conducted a comprehensive study on the jet effect of inlet distributor arrangements on the flow structure of gas-solids two-phase flow in circulating fluidized-bed risers. A computational fluid dynamics (CFD) model based on the Eulerian-Eulerian approach coupled with granular kinetics theory was adopted to carry out the simulation. Simulation results were compared with the experimental data. It was found that the inlet distributor has a great effect on the entire flow structure. The numerical results using jet inlet approaches predicted more distinct core-annulus flow structures mimicking the experimental results while the uniform inlet condition predicted a very flat flow structure. The jet effect of the inlet distributor is clearly revealed. A large lateral flow can be seen because of the jet effect. A reasonable CFD model needs to take into account the inlet distributor configuration and consider the jet effect at the inlet. 1. Introduction Fluidization is a phenomenon in which granular materials are converted from a static solidlike state to a dynamic fluidlike state by passing a fluid (liquid or gas) upward with sufficient velocity through the granular materials. When the superficial gas velocity is increased, the system will go through particular bubbling, slugging, turbulent, and circulating fluidization and dilute-phase conveying regimes. In a circulating fluidized-bed (CFB) riser reactor, solids particles are continuously fed into the bed at the bottom to maintain the required solids holdup and are then entrained out of the reactor at the top by highvelocity gas flow. Solids particles captured at the top are sent back to the bottom of the riser through a recirculation system. Because of the advantages of good particle mixing and heat transfer and continuous powder handling ability, CFBs have found applications in a wide range of chemical processes,1,2 including fluid catalytic cracking (FCC), combustion of lowgrade coal, and fluid hydroformation. The hydrodynamic behavior of gas-solids two-phase flow in a riser, which often dominates mass transfer, heat transfer, and the overall chemical reaction, has, in general, played a decisive role in the performance of the CFB. A more efficient design for CFBs relies heavily on our ability to obtain a better understanding of the complex hydrodynamic processes in CFBs. For its importance, the hydrodynamics in the CFB riser has been the subject of a number of studies as reported in the literature.3-7 In general, most experimental results illustrate some kind of core-annulus pattern (center-dilute side-dense profile) in the gas and solids flows in CFBs, with a lower solids concentration in the center than in the wall region at all axial locations along the riser. Experimental studies are considered to be more accurate, but in many cases, computational fluid dynamics (CFD) can provide a simple approach to numerically studying the hydrodynamic behavior in CFBs. In general, there are two approaches when numerically solving such flows according to the different methods dealing with the solids phase: the Eulerian-Lagrangian (E-L) approach and the Eulerian-Eulerian (E-E) approach. * To whom correspondence should be addressed. E-mail: jzhu@ uwo.ca. † Department of Mechanical and Materials Engineering. ‡ Department of Chemical and Biochemical Engineering.
In the E-L approach, Navier-Stokes equations are solved for the gas phase (continuous phase). The solids phase is solved as a discrete phase, and each particle is tracked based on a Lagrangian force balance. This method has many advantages, such as a clear and simple physical mechanism and an escape from false numerical diffusion. However, its biggest drawbacks are the high computational cost and neglect of the solids pressure and solids viscosity, resulting from particle random motion and particle-particle interaction. With an increased number of particles, the calculation time will increase exponentially, and a huge computer memory is required. Moreover, interparticle collision is often neglected. Therefore, at present this method is mainly applied to some engineering cases where the solids are dilute enough. Some researchers have applied this method to simulate some specific cases. For example, certain researchers8-14 have numerically simulated the production and disaggregation of floc, bubbling, and slugging phenomena inside the gas-solids fluidized beds. If the particle number is low, the simulation results seem to agree well with the experimental trend qualitatively, but quantitatively there are still some apparent deviations from the experimental data. In the E-E approach, both phases are treated as interpenetrating continua, and the concept of the phasic volume fraction is introduced. Mass and momentum conservation equations for both phases are solved. These equations are closed by constitutive relations that are obtained from empirical information or, in the case of granular flows, by application of the kinetic theory of the granular phase. The E-E approach has been widely used in the simulations of gas-solids two-phase flows in the fluidized beds, for example, the works by certain researchers.15-27 Generally, for gas-solids two-phase flows under the E-E frame, a phase-coupled SIMPLE algorithm is often employed to solve the flow. As known to all, the solids phase volume fraction is an unknown to be solved. The governing equation for the solids volume fraction is implicit in the mass conservation equation for the solids phase. The solids concentration is not directly under constraint at the wall boundary; that is, the solids concentration on the wall is not specified. Therefore, the inlet boundary condition of the solids distribution is of crucial importance to the numerical simulation results. In addition, note that in the momentum equations the solids concentration is tightly coupled with solids and gas velocities, so the approach
10.1021/ie901902j 2010 American Chemical Society Published on Web 04/19/2010
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to specify the inlet boundary conditions is of crucial importance for numerical results. Surprisingly, very few researchers have reported in the open literatures their detailed settings of inlet boundary conditions, especially the reason why they adopted such conditions if ever reported. The most commonly used expression for inlet boundary conditions is “velocities and concentrations of both phases were specified”, “the solids volume fraction at inlet is determined by experimental measurements”, or “inlet conditions are taken from the experiment”. The detailed value and profile are usually not provided, let alone the detailed reasons to employ such conditions. Noting the importance of inlet boundary conditions on the simulation, it requires a more comprehensive and thorough analysis and discussion on how to specify the inlet boundary conditions and how the inlet boundary conditions affect the gas-solids two-phase flow in CFB risers. The main objectives of the present work are to conduct comparative analysis of the jet effect of the inlet distributor on the simulation results and to numerically investigate the detailed flow field and the solids distribution and their relationship. The E-E approach with the standard k-ε turbulence model for each phase is applied to solve the gas-solids two-phase flow in the CFB riser. 2. Configuration of the CFB Riser System The riser is 15.1 m in height with 0.1 m i.d. Both gas and solids particles enter the riser from the bottom and exit from the top of the riser. The particulate materials in the CFB riser are spent FCC particles with Sauter mean diameter dp ) 67 µm and particle density Fp ) 1500 kg/m3. The local solids concentrations and velocities in the riser are measured at different radial positions and at different height levels. All experiments were conducted under ambient temperature (25 °C) and pressure (101.3 kPa) by Huang et al.5,6 in our group. 3. Gas-Solids Two-Phase Flow Model Description 3.1. Governing Equations. In order to simulate the flow in a CFB riser, a CFD model based on the transient E-E approach coupled with the kinetic theory of granular phases is used. The governing equations consist of mass and momentum conservation equations for both phases, as follows:28 Mass Conservation Equation of Gas Phase g ∂ (R F ) + ∇ · (RgFgF W g) ) 0 ∂t g g Mass Conservation Equations of Solids Phase s ∂ (R F ) + ∇ · (RsFsF W s) ) 0 ∂t s s
(1)
(2)
(3)
Momentum Conservation Equation of Gas Phase g ∂ (R F F W g) ) -Rg∇p + W ) + ∇ · (RgFgF W gF ∂t g g g m + c ∇ · (Rg(τc τRe g + Ksg(F Ws - F W g) (4) g g )) + RgFgb where 2 τcmg ) - µg,m∇ · F W g + ∇F W gT) W gcI + µg,m(∇F 3 2 FT F c F c τRe g ) - (Fkg + µg,t∇ · W g)I + µg,t(∇ W g + ∇ W g ) 3
Momentum Conservation Equation of Solids Phase s ∂ (R F F W ) + ∇ · (RsFsF W sF W s) ) -Rs∇p - ∇ps + ∂t s s s m Re F F F c ∇ · (Rs(τc s + τs )) + RsFs g + Kgs( W g - W s) (5) where 2 m FT Fc F τc s ) (λs - µs)∇ · W s I + µs(∇ W s + ∇ W s ) 3 2 Re F c F FT τc s ) - (Fks + µs,t∇ · W s) I + µs,t(∇ W s + ∇ W s ) 3 The solids pressure, ps, solids shear viscosity, µs, and solids bulk viscosity, λs, in eqs 4 and 5 are related to the granular temperature, Θs, based on the kinetic theory. The granular temperature, Θs, is obtained by solving its transport equation. Granular Temperature Equations 3 ∂ (F R Θ ) + ∇ · (FsRsF W sΘs) ) (-pscI + τcs):∇F Ws + 2 ∂t s s s ∇ · (kΘs∇Θs) - γΘs + φgs (6)
[
]
where φgs ) -3KgsΘs. The collisional energy dissipation, γΘs, can be obtained from ref 29: γΘs )
12(1 - ess2)g0,ss ds√π
FsRs2Θs3/2
(7)
k-ε Turbulence Model for the Gas Phase µg,t ∂ (R F k ) + ∇ · (RgFgF W gkg) ) ∇ · Rg ∇kg + ∂t g g g σk (RgGg,k - RgFgεg) + Ksg(Csgks - Cgskg) µs,t µg,t Ws - F W g) · ∇Rs + Ksg(F Ws - F W g) · ∇R (8) Ksg(F Rsσs Rgσg g
(
)
(
)
µg,t ∂ (RgFgεg) + ∇ · (RgFgF W gεg) ) ∇ · Rg ∇εg + ∂t σε εg C R G - C2εRgFgεg + C3ε Ksg(Csgks - Cgskg) kg 1ε g g,k µs,t µg,t Ws - F W g) · ∇Rs + Ksg(F Ws - F W g) · ∇R (9) Ksg(F Rsσs Rgσg g
[
(
)]
where turbulent viscosity µg,t ) FgCµ(kg2/εg).
with the constraint Rg + R s ) 1
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k-ε Turbulence Model for the Solids Phase µs,t ∂ (RsFsks) + ∇ · (RsFsF W sks) ) ∇ · Rs ∇ks + ∂t σk
(
)
(
)
(RsGs,k - RsFsεs) + Kgs(Cgskg - Csgks) - Kgs(F Wg - F W s) · µg,t µs,t ∇R + Kgs(F Wg - F W s) · ∇R (10) Rgσg g Rsσs s µs,t ∂ (RsFsεs) + ∇ · (RsFsF W sεs) ) ∇ · Rs ∇εs + ∂t σε εs C R G - C2εRsFsεs + C3ε Kgs(Cgskg - Csgks) ks 1ε s s,k µg,t µs,t Wg - F W s) · ∇Rg + Kgs(F Wg - F W s) · ∇R (11) Kgs(F Rgσg Rsσs s
[
(
where turbulent viscosity µs,t ) FsCµ(ks2/εs).
)]
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The interaction between gas and solids has been mainly expressed in the form of drag force, which is used to model the momentum exchange between the gas and solids phases. The drag force has been studied extensively, and the drag coefficient is related to the flow regime and the properties of the two phases. The Syamlal and O’Brien correlation,30 which is based on measurements of the particle terminal velocity in fluidized or settling beds, is commonly used to estimate the drag coefficient for fluidized beds. Therefore, it is used in the present work. Vr,s ) 0.5(A - 0.06Res +
√(0.06Res)2 + 0.12Res(2B - A) + A2)
Ksg )
1.28
3RsRgFg 2
4Vr,s ds
(
0.63 +
2.65
4.8
√Res /Vr,s
)( ) 2
Res |F Ws - F W g | (13) Vr,s
From ref 31, the solids pressure can be calculated as ps ) 2Fs(1 + ess)Rs2g0,ssΘs
(14)
The solids shear viscosity can be obtained from ref 31:
( )
Θs 1/2 4 µs ) RsFsdsg0,ss(1 + ess) + 5 π RsFsds√Θsπ 2 1 + (1 + ess)(3ess - 1)Rsg0,ss (15) 6(3 - ess) 5
[
]
The solids bulk viscosity accounts for the resistance of the granular particles to compression and expansion. It can be calculated using the following:29
( )
Θs 4 λs ) RsFsdsg0,ss(1 + ess) 3 π
1/2
(16)
3.2. Boundary Conditions. To carry out the numerical simulations, the boundary conditions at the inlet, wall, and outlet of a CFB riser need to be specified. Boundary Conditions at the Inlet. The profiles of the solids volume fraction and velocities for both phases need to be specified according to the inlet distributor configuration, which will be thoroughly discussed later in a separate section in this work. Boundary Conditions at the Wall. No-slip boundary condition is used for the gas phase; i.e., the tangential and normal velocities are zero at the wall. For the solids phase, the velocity normal to the wall is also set as zero, i.e., no solids mass flow across the wall, while the solids phase is allowed to slip on the wall. The tangential velocity for the solids phase, i.e., the solids slip velocity parallel to the wall, Vt,w, is calculated by24 Vt,w ) -
6µsRs,max
∂Vs,w πφFsg0,ssRs√3Θs ∂n
Rs Rs π π √3φ F g Θ V 2 - √3 (1 - esw2)Fsg0Θs3/2 6 Rs,max s 0√ s t,w 4 Rs,max (18)
Here φ is the specularity coefficient between the solids and the wall and g0 is the radial distribution function. Boundary Conditions at the Outlet. Fully developed exit conditions (outflow) are employed for both phases because the riser is long enough. 4. Mesh and Solver
(12)
where A ) Rg , B ) 0.8Rg for Rg e 0.85 and B ) Rg for Rg > 0.85, and Res ) (Fgds|F Ws - F W g|)/µg. Then 4.14
qs )
(17)
where Rs,max is the volume fraction for the particles at maximum packing. The general boundary condition for the granular temperature at the wall takes the following form:32
To reduce the computational time, a two-dimensional model is employed to simulate the gas-solids two-phase flow in the CFB riser because a comparison indicated that the difference between the simulation results of the two-dimensional model and of the axisymmetric model is very small. The mesh for the simulation is generated using Gambit.33 A quad grid system is used with finer mesh near the wall, as shown in Figure 1. The mesh in the inlet region is also refined because the change in the flow parameters is great at the inlet region. The doubleprecision, segregated, implicit formulation and unsteady solver is used in this study. The governing equations are solved using a finite-volume approach. The phase-coupled SIMPLE algorithm34 is employed in s pressure-velocity coupling. Power law schemes35 are used to discretize the governing equations for all unknowns except the volume fraction, for which QUICK35 is used. The commercial CFD software Fluent 6.328 is used to carry out the simulations. 5. Approach to Specify the Inlet Boundary Conditions Some researchers employed uniform profiles for all parameters at the riser inlet, including the solids concentration and velocities for both phases. However, the results shown in Figure 2 illustrate that when a uniform inlet condition (the all-flat profiles approach) is employed, the predicted solids concentration profile does not show a very distinct center-dilute sidedense profile. A fairly flat result for the solids concentration profile is predicted instead. The predicted solids concentration does increase slightly when the wall is approached, but the socalled core-annulus structure for the solids concentration is not markedly seen. Similar findings have also been reported in ref 36. They predicted near-flat radial (lateral) profiles for solids holdup in the CFB riser when the uniform inlet condition is employed.36 However, the experimental data clearly show a very steep center-dilute side-dense profile of the lateral solids concentration.5,6 To enable more accurate predictions, one needs to more carefully define the boundary condition at the riser inlet. In the practical operation of CFB risers, the main air always enters the riser either through a number of nozzles or through a number of holes on the plate, generating a number of highvelocity air jets, as shown in Figure 3. For example, in the experimental work in refs 5-7, rows of air jets were employed at the riser inlet. Those high-velocity air jets can change the inlet flow field and affect the solids fluidization significantly. Therefore, adopting the uniform inlet condition is not able to grasp the major characteristics of the flow and results in a discrepancy between the simulation and the practical situation. On the basis of the practical CFB riser operating situation, the inlet gas-solids mixture flowing through a certain number of jets will be specified as the inlet boundary condition. The air flow rate in all jets is assumed to be the same and is determined based on the total air flow
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Figure 1. Mesh for the calculation domain in the testing riser.
Figure 3. Inlet distributors with different jet arrangements.
is assumed to be uniform within the specific jet, can be calculated. The solids lateral (radial) velocity is set as zero at the inlet. 6. Results and Discussion
Figure 2. Comparison between the experimental data and simulation using uniform inlet conditions.
rate. The air velocity outside of the air jets is specified as zero, as shown in Figure 3. For each air jet, it is assumed that the air velocity is in the axial direction and is uniform within the specific jet. Six different inlet distributors in the CFB riser are considered and simulated in this study, from a 1-jet approach to an 11-jet inlet approach, as shown in Figure 3. Each approach has the same total open area. For the solids phase, it is assumed that all solids enter the riser bottom through the jet with a volume fraction of 0.3 within the specific inlet jet. This value of “0.3” is taken because the very bottom region of the CFB riser is often shown to have bubbling-bed behavior and “0.3” is a typical value for the solids concentration in bubbling beds. Then, with a given solids circulation rate, Gs, the solids axial velocity at the inlet jet, which
6.1. Solids Accelerating-Diluting Process at the Riser Entrance Region Using Different Inlet Conditions. Uniform Inlet Condition. Figure 4 shows the flow and concentration fields at the entrance region using the uniform inlet condition. The operating conditions are Ug ) 5.5 m/s and Gs ) 100 kg/m2 · s. One can see that the streamlines for both phases are nearly straight lines. Under this condition, the gas-solids flow can be regarded as the so-called plug flow. The flow is almost all in the axial direction, and the lateral flow is almost neglegible. The solids concentration contour shows that the solids distribution is also quite uniform in the lateral direction and that the solids concentration is decreasing in the axial direction along the riser. In general, the solids diluting process along the riser is quite laterally uniform, although the solids diluting process is slightly slowed near the wall, and this fairly flat profile at the entrance region leads to the very flat profile in the fully developed region (see Figure 2). The slowdown of the solids diluting process near the wall might result from the slowdown of the solids accelerating process because the no-slip condition of the gas phase leads to a lowvelocity region therein. It should be mentioned that the uniform inlet condition is merely an ideal condition, and it is not very likely to be completely realized in the practical operation of CFB risers. Inlet Distributor with the 1-Jet Approach. The solids concentration contour and flow streamlines at the riser
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Figure 4. Flow and concentration fields near the inlet using a uniform inlet condition.
entrance region are shown in Figure 5 when using the 1-jet approach (Figure 3a). The same operating conditions of Ug ) 5.5 m/s and Gs ) 100 kg/m2 · s are employed for the 1-jet approach (and also for the multijet inlet approaches to be discussed later). From Figure 5, one can see that the velocity of the gas phase changes its direction to a very large angle at the corner between the inlet and the wall. A large lateral flow is produced, resulting from the so-called “jet effect”. The jet effect due to abrupt expansion can be clearly observed from the gas streamlines. The lateral gas flow resulting from
the air jet effect pushes the solids particles also to move toward the wall. Correspondingly, the solids phase velocity pattern is similar to the gas velocity pattern because the particles are driven by the air flow. It can be seen from the solids concentration contour that the solids diluting process is very fast in the core region. However, the lateral solids flow leads to a solids densifying process in the near-wall region to fill up the solids-free side part. That is, the solids concentration near the wall is increased by the lateral flow toward the wall. When a
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Figure 5. Flow and concentration fields at the entrance region using a 1-jet distributor.
considerable amount of solids particles arrive at the wall, the solids concentration thereafter becomes much higher than that in the core region, and a very distinct center-dilute sidedense profile can be seen from the solids concentration contour. Compared with the uniform inlet condition in Figure 4, this reveals that the solids distribution is greatly affected by the inlet flow profiles. Inlet Distributor with Multijet Approaches. Figures 6-10 illustrate the flow and concentration fields at the riser entrance region using the multijet inlet approach.
Results for the 3-jet inlet approach (see Figure 3b) are shown in Figure 6. It can be seen from the streamlines that each air jet flows in a diverging manner, and there exists a “converging zone” where two adjacent jets meet together. In the “converging zone”, the flow branches produced by the two adjacent jets are not just exactly neutralized, and it seems that the center air jet pushes the side air jet to flow slightly further toward the wall. From the solids phase streamlines, one can also see that, in the near-wall region, the lateral flow drives the solids particles to move toward
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Figure 6. Flow and concentration fields at the entrance region using a 3-jet distributor.
the wall. Therefore, a dense near-wall region is formed, as shown in the solids concentration contour in Figure 6. Compared with a 1-jet approach, the lateral flow for a 3-jet inlet approach is much smaller because the gap between the wall and the most adjacent jet becomes much smaller. Physically, a larger gap allows the jet to expand more dramatically and thus produces a larger lateral flow.
The results using the 5-jet to 11-jet inlet approaches are also illustrated in Figures 7-10 separately. In general, all of the results show the phenomena similar to that of a 3-jet inlet approach. For example, a “converging zone” where two adjacent jets meet can be revealed; the center jet pushes the side jets to flow slightly further toward the wall, the lateral flow pushes the particles to move toward the wall, and finally
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Figure 7. Flow and concentration fields at the entrance region using a 5-jet distributor.
a center-dilute side-dense solids distribution is produced. A comparison between the uniform inlet condition and different jet inlet approaches revealed that different inlet profiles result in different flow and concentration fields in the riser entrance region. 6.2. Solids Concentration Profile in the Fully Developed Region for Different Inlet Conditions. Figure 11 shows the radial solids concentration profiles (experimental vs numerical) in the fully developed region at a height of 10 m from the riser inlet for different jet arrangements.
In general, the fully developed solids concentration profiles using jet inlet approaches are distinctly different from the results using the uniform inlet condition. One can see that the predicted solids volume fraction profile is quite flat when the uniform inlet condition is used. The typical center-dilute side-dense pattern (core-annulus structure) cannot be clearly seen, although the solids concentration profile goes up slightly when the wall is approached. Differently, when the jet inlet approaches are used, a very distinct core-annulus structure can be seen. The solids concentration is quite low in the
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Figure 8. Flow and concentration fields at the entrance region using a 7-jet distributor.
center region and dramatically increases toward the wall in the near-wall region. The results using different jet inlet approaches are also different. The 1-jet approach provides the steepest lateral solids concentration profile. The peak value of the solids concentration is over 0.23, and this may result from the large lateral solids flow produced by the abrupt expansion of the jet. The large gap between the wall and the adjacent jet allows a very intensive lateral expansion, the solid particles are pushed toward the wall, and thus a very dense near-wall region is produced. When the number of jets
is increased to “3”, the solids concentration profile is flattened significantly, and the peak value is reduced to about 0.15. The gap between the wall and the adjacent jet for the 3-jet inlet approach is much narrower than that for the 1-jet approach, and thus the lateral flow due to the jet effect is less intensive. As a result, the solids concentration profile is flattened and its peak value is largely reduced compared with the 1-jet approach. If we further increase the number of jets, the peak values of the solids concentration profile are further decreased slightly. The peak values for the 5-jet to 11-jet
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Figure 9. Flow and concentration fields at the entrance region using a 9-jet distributor.
inlet approaches are quite close, and all of them are around 0.12. If we zoom in on the core region of the solids concentration profile, to gain better observation in Figure 11b, one can see that the uniformity of the lateral solids concentration profile is increased with an increase in the number of jets. The results for approaches using a fewer number of jets show a certain wiggly lateral solids concentration profile, but such wiggling starts to disappear when the 11-jet inlet approach is used, leading to a more uniform solids concentration in the core region. The radial profiles
with a greater number of jets agree better with the experimental results obtained by Huang et al.,5,6 as shown in Figure 11. 6.3. Solids Velocity Profile in the Fully Developed Region for Different Inlet Conditions. Figure 12 shows the radial profile of the solids axial velocity in the fully developed region at a height of 10 m from the riser inlet for different jet arrangements. Again, the fully developed solids velocity profiles using jet inlet approaches are clearly different from the results using a
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Figure 10. Flow and concentration fields at the entrance region using an 11-jet distributor.
uniform inlet condition. One can see that the predicted solids velocity profile is quite flat when the uniform inlet condition is used. Differently, when the jet inlet approaches are used, much steeper solids velocity profiles can be seen. Again, the simulation results using jet inlet approaches agree better with the experimental data than the predicted results using the uniform inlet condition. It should be noticed that there still exists a deviation between the experimental data and the predicted results using the jet approach, especially in the near-wall region. This deviation might result from the modeling assumption that
particles are spherical with uniform size and the solids agglomeration is ignored. 7. Conclusion The present work numerically conducted a comprehensive study on the jet effect of inlet distributor arrangements on the flow structure of gas-solids two-phase flow in CFB risers. The CFD model using the Eulerian-Eulerian approach with the standard k-ε turbulence model for each phase is adopted to
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predicted more distinct core-annulus flow structures mimicking the experimental results while the uniform inlet condition predicted a very flat flow structure. (2) The jet effect of the inlet distributor is clearly revealed. A large lateral flow can be seen because of the jet effect. A reasonable CFD model needs to take into account the inlet distributor configuration and consider the jet effect at the inlet. The results obtained from this study may provide useful information and a helpful reference to CFB designs and operations. Appendix Nomenclature ds ) solids particle diameter (m) g ) gravitational acceleration ) 9.81 (m/s2) I ) unit tensor H ) height of the CFB riser Kgs ) gas-solids momentum exchange coefficient p ) pressure (kPa) R ) radial of the CFB riser Re ) Reynolds number t ) time (s) u ) velocity (m/s) b V ) velocity vector (m/s) x ) axial coordinate (m) y ) lateral coordinate (m) Greek Letters R ) volume fraction µ ) viscosity (kg/m · s) F ) density (kg/m3) τ ) stress tensor (Pa) Subscripts g ) gas phase s ) solids phase Figure 11. Comparison of the solids concentration (volume fraction) profiles in the fully developed region (x ) 10 m) for different jet inlet approaches.
Figure 12. Comparison of the solids axial velocity (volume fraction) profiles in the fully developed region (x ) 10 m) for different jet inlet approaches.
carry out the simulation. The following conclusions can be drawn from the results: (1) The inlet distributor has a great effect on the entire flow structure. The numerical results using jet inlet approaches
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ReceiVed for reView December 2, 2009 ReVised manuscript receiVed March 16, 2010 Accepted March 18, 2010 IE901902J
