Statistical Validation of the Mixing Length Concept in Bubble Columns Operated in the Transition Flow Regime

A new statistical parameter was defined in order to determine the range of applicability of the mixing length concept (Kawase and Tokunaga, 1991) in two bubble columns. Gas holdup time series (60 000 points) were measured in two bubble columns (0.15 and 0.4 m in ID) by a conductivity wire-mesh sensor. The new statistical parameter Φ was defined as a ratio of the mean value of the signal to three times the average absolute deviation (3AAD) and it was correlated to the mixing length equation derived by Kawase and Tokunaga (1991). It was found that this new correlation was not valid in all flow regimes. It is applicable only in the transition flow regime. Such a clarification has not been provided in the literature hitherto. In the narrow bubble column the results were also confirmed on the basis of the Kolmogorov entropy and another statistical parameter.
The new parameter Φ was also used for flow regime identification. In the narrow bubble column the first transition velocity Utrans was identified at 0.034 m/s, whereas the second Utrans occurred at 0.112 m/s. In the large bubble column the two Utrans values were identified at 0.045 and 0.101 m/s, respectively.