Equivalent bubble diameter

The simulation results on bubble velocities, bubble shapes, and their fluctuation shown in Fig. 3 are consistent with the existing correlations (Fan and Tsuchiya, 1990) and experimental results obtained in this study. Bubble rise experiments were conducted in a 4 cm x 4 cm Plexiglas bubble column under the same operating conditions as those of the simulations. Air and tap water were used as the gas and liquid phases, respectively. Gas is introduced through a 6 mm nozzle. Note that water contamination would alter the bubble-rise properties in the surface tension dominated regime. In ambient conditions, this regime covers the equivalent bubble diameters from 0.8 to 4mm (Fan and Tsuchiya, 1990). All the air-water experiments and simulations of this study are carried out under the condition where most equivalent bubble diameters exceed... 

Figure 9 Scaling of equivalent bubble diameter with gravity (Fluid water).

For particular bubble Reynolds and Eotvos numbers, Rei, = PgdgUhi rise/ Pg > 150 and Eo = gApd /aj > 40, the data on spherical cap bubbles indicate that a semi-empirical relation for the terminal velocity expressed in terms of the volume equivalent bubble diameter is appropriate [54] ... 

The equivalent bubble diameter d, defined as the diameter of a spherical bubble with a volume equal to the average bubble volume, is often used as a measure of bubble size. A representative relation for the equivalent bubble diameter in a three-dimensional bed with B particles supported by a perforated plate distributor was given by [134] ... 

A more general relation for the equivalent bubble diameter in three-dimensional beds was derived by Barton et al [27] ... 

Figure 4.6 Selection of processing steps of the digital image analysis (DIA) script (A) original image, (B) imported image by DIA, (C) corrected and smoothed image with freeboard removed, (D) bubble detection, and (E) representation of the equivalent bubble diameter of all bubbles found. Reprinted from De Jong et al. (2013) with permission from Elsevier.

Second, DIA data files were compared for the reference series in terms of equivalent bubble diameter. However, contrary to the PIV data files (which always have the same amount of data), the deviation in the bubble diameter... 

Figure 4.8 Equivalent bubble diameter as a function of axial position in the fluidized bed for (A) two series based on 1350 independent images each and (B) six series based on 50 independent images each. Reprinted from De Jong et al. (2011) with permission from Elsevier.

In this equation, Aq represents the catchment area and t the depth of the bed. Fig. 4.22 shows a graph of the equivalent bubble diameter of the reference series as a function of the bed height the reference without gas... 

Subsequently, we will first compare the cases where the background fluidization velocity was kept constant and the amount of gas added or extracted was varied. The equivalent bubble diameter as a function of the height for these series is shown in Fig. 4.23A. In the lower part of the fluidized bed, the bubbles remain approximately the same size, irrespective of the amount of gas extraction or addition. Only from a height of approximately 20 cm, a difference becomes apparent. However, mdike what would be expected intuitively, extracting gas leads to larger bubbles, while adding gas results in smaller bubbles. 

The bubble rise velocity (Fig. 4.23B) as a function of the equivalent bubble diameter appears to be quite similar for all cases. The graphs of the lateral profile of the equivalent bubble diameter and the axial profile of the bubble holdup (Fig. 4.23C and D) provide more insight into the bubble behavior. 

The most striking aspect is the fact that the average equivalent bubble diameter in a system with internals is much smaller compared to the system without internals, despite the fact that the other bubble properties (bubble aspect ratio and number of bubbles) are relatively similar. Compared to this difference in bubble size, the influence of the permeation of gas through the membrane tubes is of minor importance. The increased bubble breakup due to the presence of the membrane tubes can clearly be distinguished from the local decrease in bubble size. 

Fig. 4.45 shows the equivalent bubble diameter as a function of lateral and axial positions, as well as the number of bubbles per frame for the different membrane configurations investigated. 

Figure 4.45 Equivalent bubble diameter of the four different membrane arrangements as a function of lateral position (top) and axial position (center) for 40% gas extraction (left), no permeation (center), and 40% gas addition (right), all with constant background fluidization velocity. The bottom row shows the number of bubbles per frame as a function of the axial position. Reprinted from De Jong et al. (2013) with permission from Eisevier.

The most obvious trend that can be inferred from Fig. 4.52 is the fact that the equivalent bubble diameter remains small in the presence of the membrane tubes compared to the wall simulation series even without permeation (graphs B and E), the average bubble size is significantly reduced. 

Equivalent bubble diameter (mm) Equivalent bubble diatneter (mm) Equivalent bubble diameter (mm)... 

The next step in the DIA technique is to average the concentration inside the whole bubble as well as to determine the equivalent bubble diameter. The snapshots of concentration profiles (Fig. 4.58E) show some dark spots caused by the presence of some particles inside the bubble, which will not be taken into account for when determining the averaged concentration. 

Figure 4.60 Averaged CO2 concentration inside the bubble (A), the equivalent bubble diameter as a function of time (B), and the linearity correlation for mass transfer coefficient (C). Reprinted from Dang et al. (2013) with permission from Elsevier. 

From the experiments, the averaged CO2 concentration in the bubble < 002,b and the equivalent bubble diameter have been determined and fitted as a function of time. It should be noted that this is a simplification used to be able to compute a gas exchange coefficient and compare it with... 

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