Evaluation of a Three-Dimensional Numerical Model of a Scaled

Ind. Eng. Chem. Res. 2001, 40, 5081-5086

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Evaluation of a Three-Dimensional Numerical Model of a Scaled Circulating Fluidized Bed Claus H. Ibsen,* Tron Solberg, and Bjørn H. Hjertager Chemical Engineering Laboratory, Aalborg University Esbjerg, Niels Bohrs Vej 8, DK-6700 Esbjerg, Denmark

This work concerns the evaluation of a numerical model of a scaled circulating fluidized bed (CFB) with a square cross section. The evaluation consists of a comparison of the numerical results with measurements achieved using laser Doppler anemometry (LDA) and pressure taps. The CFB is fluidized using metal particles, which enable the laboratory-scale CFB to be operated under scaled conditions of a full-scale CFB. The numerical part is based on a three-dimensional multiphase computational fluid dynamics (CFD) model that uses an Eulerian description for the gas and solid phases. The conservation equations for the solid phases are based on the kinetic theory for granular flow, which provides adequate modeling of the solid phase when the Eulerian approach is used. Three-dimensional simulations are found to be superior to two-dimensional simulations in comparisons to the experimental findings. Introduction Circulating fluidized beds (CFBs) are widely used in industry for the drying and agglomeration of particulate materials, chemical conversions in catalytic reactors, and power generation in boilers. Nevertheless, a better understanding of the hydrodynamics of multiphase flow can improve the design of such systems significantly. Numerical modeling of the hydrodynamics can be an effective tool for optimizing the flow and can supplement or, to some extent, replace the need for experimental analyses. This study deals with a scaled model of a 12MW CFB boiler. Three-dimensional simulations have been presented by Zhang and VanderHeyden,1 Benyahia et al.,2 Kuipers and van Swaaij,3 and Mathiesen et al.4 They all simulated cold nonscale CFB systems in contrast to this study, which is concerned with a scaled system. The cold laboratory-scale CFB model is a 1/9 scale model of a 12MW CFB boiler operated according to simplified scaling laws proposed by Glicksman et al.5 To obey the scaling laws, the CFB system was operated with metal particles, which in this study were chosen to be bronze particles. Velocity measurements were performed with laser Doppler anemometry. In addition, pressure taps provided the pressure drop across the riser. To evaluate the numerical model the numerical results were compared to the experimental findings. Special emphasis is given to a comparison of three-dimensional versus two-dimensional simulations, grid refinement, and mean diameter. Experimental Setup The scaled CFB is shown in Figure 1. The dimensions of the riser are 0.19 × 1.5 × 0.17 m3, corresponding to depth (x) × height (y) × width (z), respectively. The entrance of the cyclone is located at the rear of the riser, 1.2 m above the primary air distributor. No secondary * Author to whom correspondence should be addressed. E-mail: [email protected]. Web address: http:\\hugin.aue.auc.dk.

Figure 1. Photo of the 1/9 scale model of the Chalmers 12-MW CFB boiler.

air was used to simplify the flow pattern. A cyclone was used to separate the solids, which passed a particle seal designed as a bubbling bed, before being reintroduced in the lower part of the riser. The amount of solids recirculated was adjusted to give a pressure drop across the riser equal to 2.7 kPa. The fluidized bronze particles had a mean diameter of 58 µm and a standard deviation of 20 µm. A detailed description of the model is given elsewhere by Johnsson et al.6 LDA/PDA Settings. The measurements were carried out using a two-dimensional laser Doppler anemometer from Dantec Measurements Technology A/S. This sys-

10.1021/ie0010060 CCC: $20.00 © 2001 American Chemical Society Published on Web 08/07/2001

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Mass equation for phase k ∂ ∂ ( F ) + (kFkUi,k) ) 0 ∂t k k ∂xi

(1)

where , F, and U are the volume fraction, density and velocity, respectively.

Momentum equation for phase k ∂ Figure 2. Location of the origin in the xz plane.

(kFkUj,k) +

∂t

∂

(kFkUi,kUj,k) ) -k

∂xi

∂P ∂xj

+

∂τij,k

+

∂xi

M

tem provides information about the mean and RMS velocities at the measurement point. By traversing the system in the horizontal x and z directions, horizontal solids velocity profiles can be obtained. Such profiles were taken at three different heights (y) above the air distributor. The location of the measurement point over the cross section of the riser is defined by coordinates x and z according to Figure 2. The vertical coordinate y is related to the height above the air distributor (y ) 0). The data presented in this work were recorded along the two profiles shown in Figure 3. Two sets of profiles are compared. For profile 1, x/width ) 0, y/heightexp ) 0.5, z/depth ) -0.5 to 0, and for profile 2, x/depth ) -0.5 to 0.5, y/heightexp ) 0.5, z/depth ) -0.3. For each measuring point, one of two criteria was fulfilled: 15 000 samples (minimum 200 s sampling time) or a sampling time of 900 s (minimum of 8000 samples). These settings for the acquisition time are considered sufficient to capture both small- and largescale fluctuations in the CFB system. Measurements of the u and v components were performed with the laser Doppler anemometry (LDA) system operated in backscatter mode using a lens with a focal length of f ) 160 mm. The wavelength of the laser light is 514.5 nm for the axial component and 488 nm for the spanwise component. Numerical Model The numerical model is based on a three-dimensional Eulerian multiphase computational fluid dynamics (CFD) model, FLOTRACS-MP-3D. The conservation equations for the solid phases are based on the kinetic theory for granular flow. A large eddy simulation (LES) technique is used to describe the turbulence in the continuous phase. The governing equations for the multiphase gas-solid model can be written as

Figure 3. Location of profiles 1 and 2.

kFkgj +

∑ Φkm(Uj,m - Uj,k) m)1,m*k

(2)

where P and g are pressure and gravitational acceleration, respectively. Φkm is the drag coefficient between phases k and m. The gas phase stress tensor is given by

[(

τij,g ) µeff,g

)

]

∂Uj ∂Ui 2 ∂Uk + - δij ∂xi ∂xj 3 ∂xk

(3)

g

where δij is the Kroenecker delta. The gas-phase turbulence is modeled by the subgrid scale (SGS) model proposed by Deardorf7

µeff,g ) g(µlam,g + µturb,g) ) gµlam,g + gFg(ct∆)2xSij,g:Sij,g (4) where ∆ ) (∆x∆y∆z)1/3 and Sij ) 1/2(∂Uj/∂xi + ∂Ui/∂xj). The SGS model constant ct is set to 0.079. The stress tensor for the solid phase is given by

τij,s ) -Psδij + ξsδij

∂Uk,s + ∂xk ∂Uj ∂Ui 2 ∂Uk + - δij µs ∂xi ∂xj 3 ∂xk

[(

)

]

(5)

s

where the solid-phase pressure Ps, the bulk viscosity ξs, and the shear viscosity µs are derived from the kinetic theory for granular flow.

Turbulent kinetic energy equation for solid phase k

[

] ( )

3 ∂ ∂ ( F θ ) + (kFkUi,kθk) ) 2 ∂t k k k ∂xi ∂θs ∂Uj,k ∂ + κ - γk - 3Φkgθk (6) τij,k ∂xi ∂xi ∂xi where θ is the turbulent kinetic energy. κ and γ are the

Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5083 Table 1. Specification of the Grids ∆x (m) case 15 0.01 case 50 0.007 case 80 0.007 case 105 0.005 case 1052D -

∆y (m)

∆z (m)

0.02-0.04 0.01-0.03 0.01 0.01-0.02 0.01-0.02

0.01 0.0068 0.0068 0.005 0.005

number of cells 14 535 47 250 81 000 105 944 2788

(19 × 45 × 17) (27 × 70 × 25) (27 × 120 × 25) (38 × 82 × 34) (1 × 82 × 34)

conductivity of granular temperature and collisional energy dissipation, respectively. Φkg is the gas-particle drag. The interphase momentum transfer coefficient is modeled as proposed by Gidaspow.8 For g e 0.8, the Ergun equation is used (Ergun9)

Φsg ) 150

s(1 - g)µlam,g g(ψsds)

2

+ 1.75

sFg|u bg - b u s| (7) ψsds

where ψs is equal to unity for a sphere. For g > 0.8, the drag coefficient is based on Wen and Yu’s approach10

{

bg - b us| -2.65 3 sgFg|u g Φsg ) Cd 4 ψsds

24 (1 + 0.15Re0.687) for Res e 1000 Re Cd ) s for Res > 1000 0.44 Res )

dsFgg |u bg - b u s| µlam,g

Figure 4. Pressure drop as a function of riser height. Table 2. Net Solids Flux Gs (kg/m2s)

(8)

}

case 15 case 50 case 80 case 105 case 1052D case 50dp70 experiment

(9)

(10)

A full description of the model can be found in Mathiesen et al.11 Numerical Configuration. As the riser section of the CFB is rectangular, a three-dimensional Cartesian geometry is chosen with dimensions 0.19 × 1.20 × 0.17 m3, width (x) × heightnum (y) × depth (z). The inlet is located at the bottom, and the outlet is located at the top, thereby leading to neglect of the effects of the inlet and the exit, which are placed at the side on the actual riser. Four three-dimensional grids with increasing numbers of grid cells were constructed and compared with one two-dimensional grid. For all grids, the grid cells are uniformly distributed in the x and z directions, whereas in the y direction, the grid cells are nonuniformly distributed (except case 80). The specification of the grids can be seen in Table 1. A uniform plug flow is assumed for the gas phase at the inlet, with a superficial velocity of 1.0 m/s. The inlet flux of the solid phase is assumed to be equal to the outlet flux. To ensure that the overall continuity condition is satisfied, the gas-phase velocities are calculated from a total mass balance at the outlet. No-slip boundary conditions are adopted along the walls for all phases. As initial conditions, the solid phase is evenly distributed in the lower half of the riser with zero velocity. In previous work,12 it has been found that up to 60 s of simulated real time is necessary to have time-independent average profiles in two-dimensional simulations. Considering the larger number of grid cells used in this study, however, the simulations were run for 30 s of real time, and the average results were obtained from the last 20 s, which was been found to be adequate. The density was set to 1.20 kg/m3 for the gas phase and 7800 kg/m3 for the solid phase. The mean volumelength diameter was used for the solid phase,13 which

105 101 84 69 74 1.6 2

was dp ) 45 µm. In addition to the primary case studies, one case, case 50dp70, was examined that used a mean diameter for the solid phase of dp ) 70 µm. The amount of solid in the numerical model was 9 kg. This value was determined by adjusting the amount of solid in the riser to give a pressure drop over the riser height comparable to that observed in the experiment. The laminar gas viscosity was set to 1.8 × 10-5 kg/m3. The solid form factor and restitution coefficient were set to 1.0 and 0.95, respectively. Maximum packing of the solid phase was set to 0.64. The time stepping was controlled by a Courant number of 1.0. Results Mean Diameter. To evaluate the numerical results, the predicted net solids flux out of the riser is compared to the measured net outlet flux in Table 2. As seen, the flux is overpredicted in the numerical simulations when compared to the experimental findings. When case 50 was run with a representative diameter for the solid phase of 70 µm, case 50dp70, the flux for this case is close to the experimental findings, as shown in Table 2. Figures 4 and 5 present plots of the pressure as a function of riser height. Again, case 50dp70, with a higher representative particle diameter, gives the best agreement with the experiments. Neglecting friction and acceleration, a solids volume concentration can be derived from the pressure drop and is shown in Figure 6. Clearly, the representative particle diameter of 45 µm results in a solids volume concentration that is too high in the upper part of the riser, and therefore, the dense bottom bed that can be visually observed is not present in these simulations (see Figures 12 and 13). Peirano and Leckner13 argue that, for this kind of CFB system with a small particle Reynolds number, the mean volume-length diameter is the appropriate diameter to use for characterization of the flow structure. Also, as can be seen in the section Particle Velocity, the

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Figure 5. Pressure drop as a function of riser height.

Figure 8. Axial particle velocity, profile 1.

Figure 6. Solid volume fraction as a function of riser height.

Figure 9. Spanwise particle velocity, profile 1.

Figure 7. Axial particle velocity, profile 1.

Figure 10. Axial particle velocity, profile 2.

mean volume-length diameter gives good agreement with the experimental findings when particle velocity profiles are considered. Grid-Independent Solution. Zhang and VanderHeyden1 define a grid-independent solution as when the flux in the simulation matches the flux in the experiments. When the mean volume-length diameter is used, it is questionable whether such a criterion can be satisfied at all. Zhang and VanderHeyden1 simulated a

CFB with the dimensions of 0.2 × 2.0 × 0.2 m3 (depth × height × width) that was fluidized with glass particles with a mean diameter of 120 µm, which is comparable in size to the riser used in this study. They achieved a grid-independent resolution with grid cell dimensions of 0.645 × 1.333 × 0.645 cm3 (x y z)cell. In this study, a comparable resolution is used in case 105. The velocity profiles in Figure 7 show that case 80, which, compared to case 50, has a finer resolution in the vertical direction

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Figure 11. Spanwise particle velocity, profile 2.

and the same resolution in the horizontal direction, gives different results than case 105, which, compared to case 50, has a finer grid resolution in the horizontal direction and approximately the same resolution in the vertical direction. This indicates that combining the grid resolutions of cases 80 and 105 would yield new results and, therefore, that a grid-independent solution has not yet been achieved. A comparison of the ratio between the particle diameter and the width of the grid cell from the work of Zhang and VanderHeyden,1 dp/xgridcell ≈ 1%, with that from case 105, dp/xgridcell ≈ 2%, also indicates that further refinement might be necessary. This would

be practically unachievable, however, because of computational limitations. Particle Velocity and Volume Fraction. Axial particle velocities are shown in Figures 7, 8, and 10 for profile 1 and profile 2. As can be seen, cases 15, 50, 80, and 105 all compare relatively well with the experimental findings. Figure 7 shows that the agreement between the measurements and the predictions improves in the wall region when the grid resolution is increased. The numerical profiles shown in Figure 10 are not symmetric about the center line, which might indicate that the averaging time was too short. In Figure 8, the line labeled case 1052D shows the results from the two-dimensional simulation. The velocity profile is noted to be more parabolic than those observed for the experiments and the three-dimensional simulations and to not show a constant velocity in the center of the riser. Spanwise particle velocities are shown in Figures 9 and 11 for profile 1 and profile 2, respectively. The numerical model compares relatively well with the experimental findings. Figures 12 and 13 present instantaneous (t ) 30 s) and mean contour plots of solids volume fractions, respectively, for cases 15, 50, 105, and 50dp70. A comparison of cases 15, 50, and 105 shows that finer structures are captured in flow when a finer grid resolution is used. A comparison of cases 50 and 50dp70 shows that a denser bottom bed is obtained when a higher representative particle diameter is used for the

Figure 12. Instantaneous contour plot (t ) 30 s) of solids volume fraction. From left to right: case 15, case 50, case 105, and case 50dp70. x/depth ) 0.

Figure 13. Mean contour plot of solids volume fraction. From left to right: case 15, case 50, case 105, and case 50dp70. x/depth ) 0.

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solid phase. A larger diameter results in a smaller drag and, thereby, less fluidization. Simulation Time. The simulations were run on one node of an SGI Origin 2000, 195-MHz processor. The time for simulating 30 s of real time was 1 day for case 1502D and 1 month for case 150. In comparison, Zhang and VanderHeyden1 used 101 days to simulate 21 s with their fine grid on a SGI Origin 200 processor. Conclusion Although a rather fine grid resolution was used, it was not possible to obtain a grid-independent resolution. The three-dimensional simulations were found to be superior to the two-dimensional simulation except in terms of simulation time. Indications were found that further grid refinement is necessary before a grid-independent solution can be obtained. In addition, simulations using multiple solid phases would improve the hydrodynamic modeling of the riser flow, and to have symmetry about the center line, average results should be obtained from longer simulations of real time. A major obstacle to taking advantage of these improvements is the time a simulation would require. Acknowledgment The authors acknowledge the Lida and Oscar Nielsens Fond, Fabrikant Mads Clausens Fond, Esbjerg Seminarie Fond, Direktør Ib Henriksens Fond, Fabrikant P. A. Fiskers Fond, and DONG’s Jubilæumslegat for their financial support in establishing a laser-based laboratory. Literature Cited (1) Zhang, D. Z.; VanderHeyden, W. B. High-resolution threedimensional numerical simulation of a circulating fluidized bed. Powder Technol. 2001, 116, 133-141. (2) Benyahia, S.; Arastoopour, H.; Knowlton, T. M. Threedimensional transit numerical simulation of solids and gas flow in the riser section of a circulating fluidized bed. In Fluidization

and Fluid-Particle Systems, AIChE 1999 Annual Meeting, Dallas, TX, Oct 31-Nov 5, 1999; Glicksman, L. R., Ed.; American Institute of Chemical Engineers: New York, 1999; pp 33-40. (3) Kuipers, J. A. M.; van Swaaij, W. P. M. Simulation of threedimensional (3D) riser flow using kinetic theory of granular flow. In 6th International Conference on Circulating Fluidized Beds, Wu¨ rzburg, Germany, August 24-27, 1999; Werther, J., Ed.; DECHEMA e.V.: Frankfurt am Main, Germany, 1999; pp 267273. (4) Mathiesen, V.; Solberg, T.; Hjertager, B. H. A numerical study of three-dimensional multiphase flow pattern in a riser. In 6th International Conference on Circulating Fluidized Beds, Wu¨ rzburg, Germany, August 24-27, 1999; Werther, J., Ed.; DECHEMA e.V.: Frankfurt am Main, Germany, 1999; pp 249254. (5) Glicksman, L. R.; Hyre, M.; Woloshun, K. Simplified scaling relationships for fluidized beds. Powder Technol. 1993, 77, 177199. (6) Johnsson, F.; Vrager, A.; Leckner, B. Solids flow pattern in the exit region of a CFB furnacesInfluence of exit geometry. In 15th International Conference on Fluidized Bed Combustion, Savannah, GA, May 16-19, 1999; ASME: New York, 1999. (7) Deardorf, J. W. On the magnitude of the subgrid scale eddy coefficient. J. Comput. Phys. 1971, 7, 120-133. (8) Gidaspow, D. Multiphase Flow and Fluidization; Academic Press: New York, 1994. (9) Ergun, S. Fluid flow through packed columns. Chem. Eng. Prog. 1952, 48, 89-94. (10) Wen, C. Y.; Yu, Y. H. Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser. 1966, 62, 100-111. (11) 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, 387419. (12) Ibsen, C. H.; Solberg, T.; Hjertager, B. H. The influence of the number of phases in Eulerian multiphase simulations. Presented at the 14th International Congress of Chemical and Process Engineering, Praha, Czech Republic, Aug 27-31, 2000. (13) Peirano, E.; Leckner, B. A diameter for numerical computations of polydispersed gas-solid suspensions in fluidization. Chem. Eng. Sci. 2000, 55, 1189-1192.

Received for review November 29, 2000 Revised manuscript received June 6, 2001 Accepted June 6, 2001 IE0010060