Different Identification Methods for Studying the Radial Distribution of the Transition Velocities in a Bubble Column

The identification of the boundaries of the main transition velocities in a bubble column is a very important research topic since it is related to the bubble column design and scale-up. The degrees of mixing, heat and mass transfer depend on the prevailing flow regime. In the literature hitherto, very different results (even for air-water system) about the main transition velocities Utrans have been reported. A good explanation for that is the fact that different signals (differential or absolute pressure fluctuations, bubble frequency, radioactive particle trajectories, photon counts, etc.) have been recorded and further analyzed by different methods (statistical analysis, fractal analysis, chaos analysis, etc.). The main objective of this work was to perform a comparison among the transition velocities (at different radial positions) identified by different entropies (information entropy, Kolmogorov entropy, Shannon entropy, etc.). The latter were extracted from gas holdup fluctuations recorded by a conductivity wire-mesh sensor. Recently, Nedeltchev et al. (2014) have shown that this data can be used for flow regime identification.

The data were recorded in a small (0.15 m in ID) bubble column equipped with a perforated plate gas distributor (14 holes, hole diameter: ø 4×10-3 m, open area=1 %). The local gas holdup fluctuations were measured at five different dimensionless radial positions (r/R): 0.88, 0.63, 0.39, 0.14 and 0.00. It was found that there were differences between the transition velocities identified by the information entropy (IE) and the Kolmogorov entropy (KE). The KE profile at r/R=0.88 was capable of identifying (based on a well-pronounced local minima) two Utrans values at 0.045 and 0.101 m/s. The IE profiles at the same radial position distinguished almost the same Utrans values: 0.045 and 0.112 m/s. The two transition velocities discriminate the boundaries of the three main flow regimes. Nedeltchev et al. (2014) visualized the flow patterns and documented the existence of strong gas maldistribution.

The KE profiles at r/R=0.63 revealed the existence of three Utrans values: 0.034, 0.067 and 0.124 m/s. In comparison with the wall region, at this radial position the transition regime was split into two sub-regimes. They were observed by Olmos et al. (2003). The IE profile at r/R=0.63 was difficult for interpretation due to the observed multiple local minima. However, taking into account the KE results the following three Utrans values were identified: 0.034, 0.067 and 0.112 m/s. So, only the last Utrans value was somewhat lower. Our results show that the transition is only a deviation (a sharp decrease) of a single point in the entropy profiles.

Such a detailed comparison between the IE and KE values was also performed at the other three radial positions. The IE values were derived from different initial information and compared with the Shannon entropies. Such a comparison has not been performed in the literature hitherto. We have found an effect of the radial position on the Utrans values.