**5. Results and discussions**

All simulations were performed for 20 s of real flow time and the first 5 s were neglected to reduce the start-up effect. Thus, the results reported were averaged over the last 15 s of real flow time. Bubble properties were calculated from the volume fraction contours produced by the CFD software, Fig. 3.

These volume fraction contours were then analysed by the in-house code. The first step in analysing bubble properties is to discriminate the bubble from the rest of the bed. This was done by setting a solid volume fraction cut-off point to produce discriminated volume

Numerical Simulation of Dense

2 mm 4 mm 5 mm 10 mm

0 0.01 0.02 0.03 0.04 0.05 0.06

> 2 mm 4 mm 5 mm 10 mm

0.0 0.2 0.4 0.6 0.8 1.0 1.2

**Mean bubble rise velocity [m/s]**

**Mean bubble diameter [m]**

Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model 247

**Mean bubble diameter [m]**

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

> 2 mm 4 mm 5 mm 10 mm

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

**Mean bubble rise velocity [m/s]**

2 mm 4 mm 5 mm 10 mm

Fig. 4. Comparison of mean bubble diameter for different grid sizes.

0 0.1 0.2 0.3 0.4 0.5

NT

**Bed height [m]**

NT

Fig. 5. Comparison of mean bubble rise velocity for different grid sizes.

0 0.1 0.2 0.3 0.4 0.5

**Bed height [m]**

**5.2 Two-dimensional versus three-dimensional simulation** 

2D NT 2 96000 70 4 24000 18 5 15300 12 10 3840 5 S6 2 101838 75 4 27694 27 5 18469 16 10 5190 11 3D NT 4 120000 159 5 61440 75 S6 4 145705 219 5 72924 105 Table 2. Computational time requirements for different solution domains, bed geometries

Generally, all practical gas-solid flows are three-dimensional (3D) in nature and numerical simulations in 3D domain should be performed to validate and study these 3D flows.

[mm] Number of cells Simulation time per second

0 0.1 0.2 0.3 0.4 0.5

**Bed Height [m]**

0 0.1 0.2 0.3 0.4 0.5

S6

**Bed height [m]**

S6

of real flow time [h]

Domain Geometry Grid size

and grid sizes.

fraction contours from the CFD code (ANSYS FLUENT 12.1) used. In the results reported in this book, a bubble was assumed to be the area with solid volume fraction of less than or equal to 0.2. There is no uniform definition of bubble boundary in literature with threshold values ranging from 0.15 to 0.30 for the solid volume fraction with 0.2 mostly used. Some sensitivity analyses performed showed that there is no significant difference in rise velocity and bubble shape with the different bubble boundaries used while the mean bubble diameter slightly varied with the threshold values (Asegehegn et al., 2011a). In this work, 50 frames per seconds were sampled to be consistent with the experimental analysis. Therefore, for the total 15 seconds of real flow time 750 frames are analysed for the statistical analysis of bubble properties. Though this was much less than the number of frames in the experimental results, considering the computational effort needed it was found to be sufficient for the statistical analysis of bubble properties.

Fig. 3. Instantaneous volume fraction contour plots.

#### **5.1 Influence of grid size**

It is common practice to perform grid sensitivity analyses in order to ensure grid independent solution during numerical simulations. However, it is usually difficult to achieve grid independent solution using the granular kinetic theory as the granular theory closure equations do not give grid independent solutions with reasonable grid sizes. However, in this work a grid sensitivity analysis was performed at least to ensure the mean bubble properties are not significantly affected by the grid size used. For this purpose simulations were performed for both beds with grid sizes ranging from 2 mm to 10 mm. The results are plotted in Fig. 4 and 5 for the mean bubble diameter and mean bubble rise velocity respectively. With the exceptions of a grid size of 10 mm other sizes (5 mm, 4 mm, 2 mm) provided comparable results hence the grid size of 5 mm was selected taking into account the accuracy and computational time required.

In Table 2 the different computational times needed per one second of real flow time is presented for the different grid sizes as well as 2D and 3D simulations. All simulations were performed on a Quad-Core Intel Xeon processor (3 GHz each) workstation and a time step of 2.5×10-5 s was used. It can be clearly seen that the simulation time significantly increased as the grid size reduced. The difference between the NT and S6 can be attributed to the increase in number of cells in S6 as a result of the refinement near the tube surfaces.

fraction contours from the CFD code (ANSYS FLUENT 12.1) used. In the results reported in this book, a bubble was assumed to be the area with solid volume fraction of less than or equal to 0.2. There is no uniform definition of bubble boundary in literature with threshold values ranging from 0.15 to 0.30 for the solid volume fraction with 0.2 mostly used. Some sensitivity analyses performed showed that there is no significant difference in rise velocity and bubble shape with the different bubble boundaries used while the mean bubble diameter slightly varied with the threshold values (Asegehegn et al., 2011a). In this work, 50 frames per seconds were sampled to be consistent with the experimental analysis. Therefore, for the total 15 seconds of real flow time 750 frames are analysed for the statistical analysis of bubble properties. Though this was much less than the number of frames in the experimental results, considering the computational effort needed it was found to be

It is common practice to perform grid sensitivity analyses in order to ensure grid independent solution during numerical simulations. However, it is usually difficult to achieve grid independent solution using the granular kinetic theory as the granular theory closure equations do not give grid independent solutions with reasonable grid sizes. However, in this work a grid sensitivity analysis was performed at least to ensure the mean bubble properties are not significantly affected by the grid size used. For this purpose simulations were performed for both beds with grid sizes ranging from 2 mm to 10 mm. The results are plotted in Fig. 4 and 5 for the mean bubble diameter and mean bubble rise velocity respectively. With the exceptions of a grid size of 10 mm other sizes (5 mm, 4 mm, 2 mm) provided comparable results hence the grid size of 5 mm was selected taking into

In Table 2 the different computational times needed per one second of real flow time is presented for the different grid sizes as well as 2D and 3D simulations. All simulations were performed on a Quad-Core Intel Xeon processor (3 GHz each) workstation and a time step of 2.5×10-5 s was used. It can be clearly seen that the simulation time significantly increased as the grid size reduced. The difference between the NT and S6 can be attributed to the

increase in number of cells in S6 as a result of the refinement near the tube surfaces.

sufficient for the statistical analysis of bubble properties.

Fig. 3. Instantaneous volume fraction contour plots.

account the accuracy and computational time required.

**5.1 Influence of grid size** 

Fig. 4. Comparison of mean bubble diameter for different grid sizes.

Fig. 5. Comparison of mean bubble rise velocity for different grid sizes.


Table 2. Computational time requirements for different solution domains, bed geometries and grid sizes.

#### **5.2 Two-dimensional versus three-dimensional simulation**

Generally, all practical gas-solid flows are three-dimensional (3D) in nature and numerical simulations in 3D domain should be performed to validate and study these 3D flows.

Numerical Simulation of Dense

u=2.0Umf.

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

> 0.0 0.2 0.4 0.6 0.8 1.0 1.2

**Mean bubble rise velocity [m/s]**

**Mean bubble diameter [m]**

m, u=2.0Umf.

parametric studies, 2D simulations remain indispensable.

NT

Experiment 3D 2D

Experiment 3D 2D

0 0.1 0.2 0.3 0.4 0.5

**Bed height [m]**

NT

0 0.1 0.2 0.3 0.4 0.5

**Bed height [m]**

Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model 249

was believed that neglecting the front and back walls in the 2D simulations resulted in higher bubble rise velocities. In the experiment as well as 3D simulations, as a result of small bed thickness, the down flowing particles along the front and back walls increased the drag experienced by the bubbles, thus slowed the bubbles. On the other hand these walls were neglected in the 2D simulations and bubbles could move freely in the bed without experiencing the drag of down flowing particles as well as the friction of walls. Others also reported similar results, e.g. Krishna et al. (2000) and Li et al. (2010). Krishna et al. (2000) studied the influence of walls on bubble rise velocity for both gas-liquid and gas-solid systems and they reported that the rise velocity of single gas bubbles was significantly reduced as the ratio of bubble to bed width increased. Though 2D simulations have certain limitations and are physically different form the 3D flow exit in practical applications, they can provide quiet satisfactory results compared to experimental observations. It is clear that 3D simulations are more realistic and should be preferred, but with current, even in the near future, computer capacity these are far from reaching. Comparing the computational time needed for 2D and 3D simulations as shown in Table 2 above, it was found that 3D simulations are 5 to 9 times more expensive than their 2D equivalents. As an example in order to simulate 20 s of real flow time in the 2D grid with a mesh size of 5 mm using the no tube geometry 240 h (approx. 10 days) of simulation time were necessary while this was increased to 1500 h (approx. 62 days) in the case of 3D simulations. Therefore, as also deduced by Xie et al. (2008) and Cammarata et al. (2003), especially for conducting extensive

Fig. 6. Comparison of mean bubble diameter between 2D and 3D simulations, dp = 347 m,

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

**Mean bubble diameter [m]**

Experiment 3D 2D

Experiment 3D 2D

0 0.1 0.2 0.3 0.4 0.5

S6

**Bed height [m]**

S6

0 0.1 0.2 0.3 0.4 0.5

**Bed height [m]**

Fig. 7. Comparison of mean bubble rise velocity between 2D and 3D simulations, dp = 347

0.0 0.2 0.4 0.6 0.8 1.0 1.2

**Mean bubble rise velocity [m/s]**

However, even with improved computational facilities, 3D simulations are still computationally prohibitive even for engineering-scale fluidized beds. Therefore, the majority of simulation studies encountered in the literature are limited to two-dimensional (2D) coordinate system to simulate 3D fluidized beds. However, there are no studies proving that 2D computations are sufficient for validation and parametric study of fluidized beds. 2D simulations are most likely to be successful in cases where the flow is presumed to be 2D, that is in cases where the variations in space and time in a given direction of the physical space are negligible compared to the variations encountered in the other directions. This is typically in the case of pseudo-2D beds, which have small depth compared to the height and width. In such cases, the particle motion can be effectively suppressed in the depth direction thus resembling 2D motion of the particles in the axial and radial directions only. Many researchers have applied 2D Cartesian simulations to model such rectangular pseudo-2D beds and found reasonable agreement between model prediction and experimental results. However, such comparisons leave an important difference between the pseudo-2D experimental beds and 2D numerical models. The front and back walls, which are neglected in the numerical model, could have considerable influence on the hydrodynamics of the fluidized beds. So far, only Li et al. (2010) have performed both 2D and 3D simulations of a pseudo-2D and compared the results with experimental measurements. They found considerable difference in the bubble rise velocity predicted by the 2D and 3D simulations while the bubble diameter predicted by both domains is generally comparable. Cammarata et al. (2003) performed simulations using 2D and 3D domains of a rectangular bed and the results of bubble diameter were compared with correlation from the literature. These authors found considerable difference of the bubble diameter predicted by the simulations. On the other hand, Peirano et al. (2001) analysed and compared simulation results of the power spectra of pressure fluctuations, bed height, and probability density function of particle volume fraction with experimental measurements. They observed a significant difference between 2D and 3D simulations and concluded that 2D simulations should be used with caution and only for sensitivity analysis. Though all the above authors concluded that 3D simulations should be preferably performed except maybe in cases where the flow is by nature 2D, they also indicate that 2D simulations could be used to conduct sensitivity analyses.

In this work, simulations were performed for two different particle sizes and two bed geometries with and without immersed horizontal tubes using 2D and 3D domains and the results were compared to experimental data obtained from pseudo-2D bed. The mean bubble diameter and rise velocity are shown in Fig. 6 and 7 respectively for the particle with mean diameter of 347 m. Similar results were obtained for the other particle size as well but the results are not presented here to reduce redundancy. As shown in Fig. 6 the mean bubble diameter predicted by both 2D and 3D simulations are generally in very good agreement with the experimental though the 2D simulations predicted slightly smaller bubbles than the 3D. This was consistent with the results of Li et al. (2010) while Cammarata et al. (2003) reported otherwise. The results obtained from 2D simulations showed greater divergence from the experimental data with increasing bed height. Though not shown here, this was more pronounced with increasing superficial velocity. A significant difference between 2D and 3D simulations was observed in mean bubble rise velocity, Fig. 7. 2D simulations predicted much higher rise velocity than 3D simulations and significantly deviate from the experiment measurements. This was largely attributed to the wall effect. It

However, even with improved computational facilities, 3D simulations are still computationally prohibitive even for engineering-scale fluidized beds. Therefore, the majority of simulation studies encountered in the literature are limited to two-dimensional (2D) coordinate system to simulate 3D fluidized beds. However, there are no studies proving that 2D computations are sufficient for validation and parametric study of fluidized beds. 2D simulations are most likely to be successful in cases where the flow is presumed to be 2D, that is in cases where the variations in space and time in a given direction of the physical space are negligible compared to the variations encountered in the other directions. This is typically in the case of pseudo-2D beds, which have small depth compared to the height and width. In such cases, the particle motion can be effectively suppressed in the depth direction thus resembling 2D motion of the particles in the axial and radial directions only. Many researchers have applied 2D Cartesian simulations to model such rectangular pseudo-2D beds and found reasonable agreement between model prediction and experimental results. However, such comparisons leave an important difference between the pseudo-2D experimental beds and 2D numerical models. The front and back walls, which are neglected in the numerical model, could have considerable influence on the hydrodynamics of the fluidized beds. So far, only Li et al. (2010) have performed both 2D and 3D simulations of a pseudo-2D and compared the results with experimental measurements. They found considerable difference in the bubble rise velocity predicted by the 2D and 3D simulations while the bubble diameter predicted by both domains is generally comparable. Cammarata et al. (2003) performed simulations using 2D and 3D domains of a rectangular bed and the results of bubble diameter were compared with correlation from the literature. These authors found considerable difference of the bubble diameter predicted by the simulations. On the other hand, Peirano et al. (2001) analysed and compared simulation results of the power spectra of pressure fluctuations, bed height, and probability density function of particle volume fraction with experimental measurements. They observed a significant difference between 2D and 3D simulations and concluded that 2D simulations should be used with caution and only for sensitivity analysis. Though all the above authors concluded that 3D simulations should be preferably performed except maybe in cases where the flow is by nature 2D, they also indicate that 2D simulations could be used

In this work, simulations were performed for two different particle sizes and two bed geometries with and without immersed horizontal tubes using 2D and 3D domains and the results were compared to experimental data obtained from pseudo-2D bed. The mean bubble diameter and rise velocity are shown in Fig. 6 and 7 respectively for the particle with mean diameter of 347 m. Similar results were obtained for the other particle size as well but the results are not presented here to reduce redundancy. As shown in Fig. 6 the mean bubble diameter predicted by both 2D and 3D simulations are generally in very good agreement with the experimental though the 2D simulations predicted slightly smaller bubbles than the 3D. This was consistent with the results of Li et al. (2010) while Cammarata et al. (2003) reported otherwise. The results obtained from 2D simulations showed greater divergence from the experimental data with increasing bed height. Though not shown here, this was more pronounced with increasing superficial velocity. A significant difference between 2D and 3D simulations was observed in mean bubble rise velocity, Fig. 7. 2D simulations predicted much higher rise velocity than 3D simulations and significantly deviate from the experiment measurements. This was largely attributed to the wall effect. It

to conduct sensitivity analyses.

was believed that neglecting the front and back walls in the 2D simulations resulted in higher bubble rise velocities. In the experiment as well as 3D simulations, as a result of small bed thickness, the down flowing particles along the front and back walls increased the drag experienced by the bubbles, thus slowed the bubbles. On the other hand these walls were neglected in the 2D simulations and bubbles could move freely in the bed without experiencing the drag of down flowing particles as well as the friction of walls. Others also reported similar results, e.g. Krishna et al. (2000) and Li et al. (2010). Krishna et al. (2000) studied the influence of walls on bubble rise velocity for both gas-liquid and gas-solid systems and they reported that the rise velocity of single gas bubbles was significantly reduced as the ratio of bubble to bed width increased. Though 2D simulations have certain limitations and are physically different form the 3D flow exit in practical applications, they can provide quiet satisfactory results compared to experimental observations. It is clear that 3D simulations are more realistic and should be preferred, but with current, even in the near future, computer capacity these are far from reaching. Comparing the computational time needed for 2D and 3D simulations as shown in Table 2 above, it was found that 3D simulations are 5 to 9 times more expensive than their 2D equivalents. As an example in order to simulate 20 s of real flow time in the 2D grid with a mesh size of 5 mm using the no tube geometry 240 h (approx. 10 days) of simulation time were necessary while this was increased to 1500 h (approx. 62 days) in the case of 3D simulations. Therefore, as also deduced by Xie et al. (2008) and Cammarata et al. (2003), especially for conducting extensive parametric studies, 2D simulations remain indispensable.

Fig. 6. Comparison of mean bubble diameter between 2D and 3D simulations, dp = 347 m, u=2.0Umf.

Fig. 7. Comparison of mean bubble rise velocity between 2D and 3D simulations, dp = 347 m, u=2.0Umf.

Numerical Simulation of Dense

observed from the experiment.

Experiment\_NT Simulation\_NT Experiment\_S6 Simulation\_S6

Experiment\_2Umf Experiment\_3Umf Experiment\_4Umf Simulation\_2Umf Simulation\_3Umf Simulation\_4Umf

0 0.1 0.2 0.3 0.4 0.5

dp = 246 m Umf = 0.0876 m/s

**Bed height [m]**

NT

0 0.1 0.2 0.3 0.4 0.5

**Bed height [m]**

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.00

0.02

0.04

0.06

**Mean bubble diameter [m]**

0.08

0.10

0.12

**Mean bubble diameter [m]**

mm and Umf = 0.0876 m/s.

Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model 251

sizes. For beds without immersed tubes the simulation and experimental results were in very good agreement until a certain height near the eruption zone. After this height the simulation predicted no growth of bubbles while a continuous growth of bubbles was

Fig. 9. Comparison of mean bubble diameter between simulation results and experimental data for beds with and without immersed tubes and two different particle sizes, u=2Umf.

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

**Mean bubble diameter [m]**

Experiment\_NT Simulation\_NT Experiment\_S6 Simulation\_S6

Experiment\_2Umf Experiment\_3Umf Experiment\_4Umf Simulation\_2Umf Simulation\_3Umf Simulation\_4Umf

0 0.1 0.2 0.3 0.4 0.5

dp = 347 m Umf = 0.144 m/s

**Bed height [m]**

S6

0 0.1 0.2 0.3 0.4 0.5

**Bed height [m]**

Fig. 10. Comparison of mean bubble diameter between simulation results and experimental data for beds with and without immersed tubes and different superficial velocities, dp= 246

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

**Mean bubble diameter [m]**

In the case of beds with horizontal tubes good qualitative agreement was achieved between the simulation and experimental results for both particle sizes. However, the simulation slightly underpredicted bubble diameter in the tube bank region. This was partially attributed to the wall effect that was neglected in the numerical simulation while the experiments were performed using pseudo-2D beds. From both simulation and experiment it can be concluded that the presence of tubes resulted in higher bubble splitting and coalescence which eventually reduced the mean bubble size. Small bubbles formed at the distributor rose and grew by coalescence until they reached the first row of tubes. Upon

#### **5.3 Influence of immersed horizontal tubes 5.3.1 Bubble aspect ratio**

Aspect ratio is an important characteristics of a bubble since it strongly influence the bubble's hydrodynamics. Fig. 8 shows the mean bubble aspect ratio for the two bed geometries (NT and S6) and different superficial velocities. Similar results were obtained for the second particle size and the graphs are not shown here to reduce redundancy. In general, the simulation showed good agreement with the experimental data for all geometries. For the bed without internal tubes both the simulation and experimental results predicted an increase in aspect ratio with bed height. This indicated the flattening and vertical stretching of bubbles with increasing bubble size. Generally, for beds without internal obstacles, the bubble shape was found to be nearly circular when the bubble was smaller and flattened, distorted and elongated when the bubble was bigger. Similar results were reported by Hatano et al. (1986) from experimental observations.

In the case of beds with internal horizontal tubes bubble aspect ratio was found to depend more strongly on tube geometry rather than bubble size or bed height. Bubbles were seen to elongate vertically when they moved between the tubes in a row and retained their original shape and became nearly circular when they were away from the tube rows. This resulted in oscillation of the aspect ratio in the tube bank region as shown in Fig. 8. The elongation of bubbles in the vertical direction was mainly seen as a result of the reduction in flow area and bubbles squeezed and deformed to fit the space between the tubes. As a bubble squeezed it stretched and elongated vertically as the area/volume of the bubble should at least remain the same provided that no splitting has occurred during the process. Qualitatively the simulation predicted a similar trend for fluctuations in the aspect ratio in the tube bank region, however, it predicted bubbles that were relatively circular as opposed to the corresponding experimental data. This could be associated with the no-slip boundary condition imposed on the walls for the gas phase.

Fig. 8. Comparison of mean bubble aspect ratio between simulation results and experimental data for beds with and without immersed tubes and different superficial velocities, dp= 246 mm and Umf=0.0876 m/s.

#### **5.3.2 Bubble size**

Fig. 9 and 10 present the simulation results and comparisons with experimental data of mean bubble diameter for the two bed geometries (NT and S6) and two different particle

Aspect ratio is an important characteristics of a bubble since it strongly influence the bubble's hydrodynamics. Fig. 8 shows the mean bubble aspect ratio for the two bed geometries (NT and S6) and different superficial velocities. Similar results were obtained for the second particle size and the graphs are not shown here to reduce redundancy. In general, the simulation showed good agreement with the experimental data for all geometries. For the bed without internal tubes both the simulation and experimental results predicted an increase in aspect ratio with bed height. This indicated the flattening and vertical stretching of bubbles with increasing bubble size. Generally, for beds without internal obstacles, the bubble shape was found to be nearly circular when the bubble was smaller and flattened, distorted and elongated when the bubble was bigger. Similar results

In the case of beds with internal horizontal tubes bubble aspect ratio was found to depend more strongly on tube geometry rather than bubble size or bed height. Bubbles were seen to elongate vertically when they moved between the tubes in a row and retained their original shape and became nearly circular when they were away from the tube rows. This resulted in oscillation of the aspect ratio in the tube bank region as shown in Fig. 8. The elongation of bubbles in the vertical direction was mainly seen as a result of the reduction in flow area and bubbles squeezed and deformed to fit the space between the tubes. As a bubble squeezed it stretched and elongated vertically as the area/volume of the bubble should at least remain the same provided that no splitting has occurred during the process. Qualitatively the simulation predicted a similar trend for fluctuations in the aspect ratio in the tube bank region, however, it predicted bubbles that were relatively circular as opposed to the corresponding experimental data. This could be associated with the no-slip boundary

Fig. 8. Comparison of mean bubble aspect ratio between simulation results and experimental data for beds with and without immersed tubes and different superficial velocities, dp= 246

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

**Mean bubble aspect ratio [-]**

0 0.1 0.2 0.3 0.4 0.5 0.6

S6

Experiment\_2Umf Experiment\_3Umf Experiment\_4Umf Simulation\_2Umf Simulation\_3Umf Simulation\_4Umf

**Bed height [m]**

Experiment\_2Umf Experiment\_3Umf Experiment\_4Umf Simulation\_2Umf Simulation\_3Umf Simulation\_4Umf

Fig. 9 and 10 present the simulation results and comparisons with experimental data of mean bubble diameter for the two bed geometries (NT and S6) and two different particle

were reported by Hatano et al. (1986) from experimental observations.

**5.3 Influence of immersed horizontal tubes** 

condition imposed on the walls for the gas phase.

NT

0 0.1 0.2 0.3 0.4 0.5 0.6

**Bed height [m]**

mm and Umf=0.0876 m/s.

**5.3.2 Bubble size** 

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

**Mean bubble aspect ratio [-]**

**5.3.1 Bubble aspect ratio** 

sizes. For beds without immersed tubes the simulation and experimental results were in very good agreement until a certain height near the eruption zone. After this height the simulation predicted no growth of bubbles while a continuous growth of bubbles was observed from the experiment.

Fig. 9. Comparison of mean bubble diameter between simulation results and experimental data for beds with and without immersed tubes and two different particle sizes, u=2Umf.

Fig. 10. Comparison of mean bubble diameter between simulation results and experimental data for beds with and without immersed tubes and different superficial velocities, dp= 246 mm and Umf = 0.0876 m/s.

In the case of beds with horizontal tubes good qualitative agreement was achieved between the simulation and experimental results for both particle sizes. However, the simulation slightly underpredicted bubble diameter in the tube bank region. This was partially attributed to the wall effect that was neglected in the numerical simulation while the experiments were performed using pseudo-2D beds. From both simulation and experiment it can be concluded that the presence of tubes resulted in higher bubble splitting and coalescence which eventually reduced the mean bubble size. Small bubbles formed at the distributor rose and grew by coalescence until they reached the first row of tubes. Upon

Numerical Simulation of Dense

Experiment\_2Umf Experiment\_3Umf Experiment\_4Umf Simulation\_2Umf Simulation\_3Umf Simulation\_4Umf

and Umf = 0.0876 m/s.

conclusions can be drawn:

**7. Acknowledgment** 

of Economics and Technology.

losing much of the information.

0 0.1 0.2 0.3 0.4 0.5

NT

**Bed height [m]**

**6. Conclusion** 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

**Mean bubble rise velocity [m/s]**

data.

Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model 253

Experiment\_2Umf Experiment\_3Umf Experiment\_4Umf Simulation\_2Umf Simulation\_3Umf Simulation\_4Umf

Fig. 12. Comparison of mean bubble rise between simulation results and experimental data for beds with and without immersed tubes and different superficial velocities, dp= 246 mm

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

**Mean bubble rise velocity [m/s]**

0 0.1 0.2 0.3 0.4 0.5

S6

**Bed height [m]**

Numerical simulations using the Eulerian-Eulerian TFM were performed for pseudo-2D gas-solid fluidized beds with and without immersed horizontal tubes. The simulation results of bubble characteristics were compared and validated with experimental data obtained by a digital image analysis technique. From the results of this work the following

The two-fluid model is capable of predicting the main bubble characteristics such as bubble aspect ratio, diameter and rise velocity with and without immersed tubes. The calculated bubble properties were in general in good agreement with the experimental

3D simulations gave better results than 2D simulations compared with experiments. However, they are computationally expensive and 2D simulations can be successfully used for parametric study of gas-solid fluidized beds of engineering scale without

The major difference between 2D and 3D simulations was observed in predicting the bubble rise velocity where 2D simulations overpredicted the bubble rise velocity compared to

As a result of higher bubble splitting and coalescence as well as additional drag, the bubble diameter and rise velocity were lower for beds with horizontal tubes than beds without tubes. Moreover, bubble diameter and rise velocity were found to strongly depend on the tube bank geometry rather than the superficial velocity in the case of beds with dense immersed tubes while these bubble properties strongly vary with superficial

The authors gratefully acknowledge the funding of this research project by the "Entrepreneurial Regions"-Initiative established by the German Federal Ministry of Education and Research and Research and COORETEC-Initiative from the Federal Ministry

the corresponding 3D simulations and experimental data.

velocity in the case of beds without immersed tubes.

reaching the first row of tubes they split then grew by coalescence until they reached the second row of tubes. This continued until the last row of tubes after which bubbles rapidly grew without restriction until they finally reached the top of the bed and erupted. As shown in Fig. 10 both the simulation and experiment showed that the growth of bubbles in the tube bank region was mainly dictated by tube bank geometry rather than superficial velocity or bed height. In the tube free region, below and above the tube bank, bubble growth resembled a similar trend as in the case of the bed without immersed tubes.

#### **5.3.3 Bubble rise velocity**

Fig. 11 and 12 illustrate comparisons between simulation and experimental results for bubble rise velocities for the two bed geometries and particle sizes. For beds both with and without immersed tubes the simulation overpredicted rise velocity as compared to the experimental results and it was more pronounced at the upper part of the beds. This was largely associated with the wall effect as discussed above.

Fig. 11. Comparison of mean bubble rise velocity between simulation results and experimental data for beds with and without immersed tubes and two different particle sizes, u=2Umf.

In the tube bank region the rise velocity was highly influenced by the presence of tubes. The reduction in bubble size due to frequent splitting in the tube bank region caused a decrease in bubble rise velocity compared to beds without internal obstacles. Both the experiment and the simulation showed higher rise velocity at the upper part of the tubes and lower rise velocity at the lower part of the tubes. The higher rise velocity seen at the upper part of the tube rows can be explained mainly due to the elongation of bubbles. As a result of elongation of a bubble and stretching the centroid of the bubble moved further in distance than it would if it were circular. This caused the centroid of the bubbles to move further in the vertical direction than they usually do. It was observed that bubbles with higher aspect ratios had higher rise velocities than those with lower aspect ratios. Hatano et al. (1986) also reported similar results for beds without internal obstacles. The reason for the lower mean rise velocity at the bottom of the tubes was due to the semi-stagnant bubbles that occurred at this location as a result of small bubble formation and splitting of bubbles into large and small daughters (Asegehegn et al. 2011a).

Fig. 12. Comparison of mean bubble rise between simulation results and experimental data for beds with and without immersed tubes and different superficial velocities, dp= 246 mm and Umf = 0.0876 m/s.
