(231d) Numerical Simulation of the Bubble Column with a CFD-PBM Coupled Model: Importance of the Drag Force of Bubble Swarms

Introduction

The drag coefficient of bubble swarms is different from that of single
bubbles for the existence of the bubble interaction [1-3]. Some researchers
[3-4] studied the rising of bubbles in bubbly flow and found that the velocity
of small bubbles decreased in the bubble swarms due to hindering effect.
Meanwhile, some other researchers [5-6] found the rising velocity of large
bubbles increased due to wake accelerating effect. To account for these
effects, some correlations were proposed for the relatively velocity or drag
coefficient of bubble swarms. Actually, both the hindering effect of small
bubbles and wake accelerating effect of large bubbles exist in bubble swarms
[1-2], and the drag coefficient should be related to both the bubble diameter
and local gas holdup. However, the applicable condition range of the existing
drag models and correlations are still limited. The present work aimed to
propose a drag model applicable in a wider range of conditions by correlating
with the bubble size distribution and local gas holdup and including both the hindering
effect and wake accelerating effect. The performance of this drag model was
investigated in the numerical simulations of a bubble column with a CFD-PBM
(population balance model) coupled model.

Model Development

The numerical
simulations were carried out with the CFD-PBM coupled model, which was similar
to that used in our previous work [7], except that a new drag model was
employed, as shown in Figure 1. The average drag coefficient of single bubbles
was first calculated based on the local gas holdup and bubble size
distribution. Then the lumped quantity of bubble swarms effect was modified
with a drag correction factor C_D/C_D0, which based on the bubble size distribution
and local gas holdup and included both hindering effect of small bubbles and
wake accelerating effect of large bubbles in bubble swarms.

Figure 1. Schematic of the CFD-PBM coupled
model with drag force of bubble swarms.

Results
and Discussion

The calculated drag correction factor was plotted as a function of the
local gas holdup for different superficial gas velocities, as shown in Figure
2(a). With increasing local gas holdup, C_D/C_D0 increased linearly in the low gas holdup
range, then increased to its maximum (1.5 at 0.06 m/s), and significantly
decreased in the high gas holdup range. This complex variation was attributed
to the change of the governing factor from the hindering effect of small
bubbles to the wake accelerating effect of large bubbles. Although the variation
trend for the drag correction factor was similar at different superficial gas
velocities, the value of C_D/C_D0 depended on the gas velocity, especially at low
local gas holdup. The reason was that the drag correction factor depended not
only the local gas holdup, but also the bubble size distribution that can be
significantly different even at a certain local gas holdup.

To provide a
concise diagram, we chose the simulated data of U_g = 0.06 m/s to compare with the experimental results
from literatures [2-3]. Note that the data of Roghair et al. [3] were from
numerical experiments for d_b
= 4 mm. The complex variation trend of C_D/C_D0 was similar, as shown in
Figure 2(b). The slight deviation was attributed to the different bubble size
distributions.

Figure 2. (a) Simulated drag correction factors at
different superficial gas velocities; (b) Comparison of simulated and
experimental drag correction factors.

Conclusions

Both the hindering effect and wake accelerating effect exist for bubble
swarms in a bubble column. With increasing local gas holdup, the drag
correction factor increased and then decreased, which was attributed to the
change in the governing factor from the hindering effect of small bubbles to
the wake accelerating effect of large bubbles. The drag
model based on the bubble size distribution and local gas holdup was applicable
to a wider range of conditions.

Acknowledgement

The authors thank the financial supports by the National Natural Science
Foundation of China (No. 21476122).

References

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