Comparison between the transition velocities in both core and annulus of bubble columns based on a modified Shannon entropy

Bubble columns (BC) are frequently used in chemical, petroleum and biochemical industries due to their simple construction, ease of temperature control and good heat and mass transfer characteristics. Their hydrodynamics depend on the prevailing flow patterns (regimes) which in turn depend mainly on the superficial gas velocity Ug, the gas distributor design and column diameter. At low Ug values the bubbly flow (homogeneous) regime prevails, which is characterized with relatively small and uniform bubbles and a gentle agitation of the gas-liquid dispersion. The bubble size distribution (BSD) is very narrow and it is only influenced by the gas distributor. A relatively uniform gas holdup profile and a rather flat liquid velocity profile are observed. When the gas distributor is not effective, a gas maldistribution instead of the bubbly flow is observed. The transition regime is characterized by large eddies and a widened BSD due to bubble coalescence. It has been found that the occurrence and the persistence of the transition regime depend largely on the quality of the aeration. The transition from the homogeneous to the heterogeneous (churn-turbulent flow) regime is a gradual process.
In the churn-turbulent flow regime large bubbles start to form whose wakes cause gross circulation patterns. This flow regime is characterized by a wide BSD, vigorous mixing and by the existence of a radial gas holdup profile, which causes liquid circulation, as well. Both bubble coalescence and break-up occur. The gas sparger has little effect on the hydrodynamics.
In particular, the circulation zones give rise to the assumption that regime transitions in different regions occur at different operating conditions. Thus, the primary objective of this work is to compare the main transition velocities Utrans in both the core and annulus of two different BCs based on the modified Shannon entropy (SE). The ratio of the minimum-to-maximum SE in a time-dependent signal can be used successfully for position-dependent flow regime identification in BCs.
The modified SE algorithm has been applied to gas holdup time series data obtained by means of a conductivity wire-mesh sensor (fs=2000 Hz, sensor’s axial position: 1.3 m). Two different BCs operated with an air-deionized water (clear liquid height: 2.0 m) system were used. Both facilities were equipped with perforated plate distributors having the same opening diameter (Ø 4.0×10-3 m). The gas sparger in the small BC (0.15 m in ID) consisted of 14 holes, while the one in the large BC (0.4 m in ID) consisted of 101 holes. In both cases the open area was 1 %.
The SE quantifies the degree of uncertainty involved in predicting the output of a probabilistic event. In the case of fully predictable outcome of an event, the SE will be zero. The definition of the probability in the SE algorithm (Zhong et al., 2009) was modified. Then, the total number of points (60,000) in the signal was divided into six segments (each consisting of 10,000 points) and the modified SE in each of them was calculated. It was found that the ratio of the minimum-to-maximum (SEmin/SEmax) modified SE in every time series at various Ug values can be used for the flow regime identification.
It was found that the dimensionless SEmin/SEmax ratio in the annulus (r/R=0.88) of the small BC (0.15 m in ID) was characterized with two local minima, which corresponded to the two main Utrans values (0.045 and 0.089 m/s). These two boundaries delineated the ranges of the three main hydrodynamic regimes: gas maldistribution (Ug≤0.045 m/s), transition (0.0450.089 m/s). The existence of the gas maldistribution regime in both BCs has been visualized by Nedeltchev et al. (2015).
The SEmin/SEmax in the core (r/R=0) of the small BC (0.15 m in ID) was also capable of identifying the two main Utrans values. At Ug=0.034 m/s the onset of the transition flow regime was identified, whereas at Ug=0.089 m/s the second minimum in the SE ratio distinguished the formation of the churn-turbulent flow regime. The same Utrans values for the whole cross-section of the small BC have been reported by Nedeltchev et al. (2015). It is noteworthy that the minima in the core are much deeper and very well pronounced.
The results in Figure 2 exhibit further that the gas maldistribution ends at lower Ug value in the core of the small BC. The second Utrans value is independent of the radial position. A similar comparison between the Utrans values in both zones of the large BC will be presented. The effect of the radial position on the Utrans values will be studied since it will give an information about the BSD.