**6. Conclusion**

252 Computational Simulations and Applications

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

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

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.

0.1

0 0.1 0.2 0.3 0.4 0.5

dp = 347 m Umf = 0.144 m/s

**Bed height [m]**

0.3

0.5

0.7

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

0.9

1.1

1.3

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

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

resembled a similar trend as in the case of the bed without immersed tubes.

largely associated with the wall effect as discussed above.

dp = 246 m Umf = 0.0876 m/s

0 0.1 0.2 0.3 0.4 0.5

**Bed height [m]**

small daughters (Asegehegn et al. 2011a).

**5.3.3 Bubble rise velocity** 

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

0.1

0.3

0.5

0.7

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

0.9

1.1

1.3

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 conclusions can be drawn:

