Investigation of the radial effect on the transition velocities in a bubble column based on the modified Shannon entropy

Abstract

A new parameter for flow regime identification in a bubble column based on the calculation of the Shannon entropy (SE) from different parts of the signal was developed. The bubble column (0.15m in ID) was equipped with a perforated plate distributor (14 holes, Ø 4×10−3m) and operated with an air-deionized water system at ambient conditions. The newly introduced dimensionless ratio of minimum SE to maximum SE was capable of identifying the main transition velocities Utrans at three different dimensionless radial positions (r/R): 0.0 (core), 0.63 (inversion point of axial liquid velocity) and 0.88 (annulus).In the column’s core the new dimensionless SE ratio identified successfully three Utrans values at 0.034, 0.089 and 0.134m/s. They marked the end of the gas maldistribution regime, the onset and the end of the churn-turbulent flow regime, respectively. Three Utrans values (at 0.045, 0.089 and 0.124m/s) were also identified in the annulus. However, the second Utrans value identified the boundary between the first and second transition sub-regimes. The third Utrans value distinguished the onset of the churn-turbulent flow regime. It was found that in the core both the transition and churn-turbulent flow regimes started earlier.At r/R=0.63 the end of the gas maldistribution regime was shifted to a somewhat higher Utrans value (0.067m/s). The second transition sub-regime began at 0.101m/s, whereas the onset of the churn-turbulent regime occurred at 0.124m/s.