Comparison Between the Boundaries of the Main Flow Regimes Identified by Ultrafast X-Ray Tomography in Different Parts from the Cross-Section of a Bubble Column

Bubble columns are characterized by an effective phase contact, high heat and mass transfer coefficients, low maintenance and operating costs due to the absence of moving parts and low column pressure drop. Due to their numerous advantages bubble columns are used extensively in many applications (oxidation, chlorination, waste water treatment, etc.). Therefore, it is essential to have detailed knowledge about the hydrodynamic behavior of these gas-liquid contactors. The identification of the boundaries of the main hydrodynamic regimes is important for improvement of the design, operation and control of bubble columns. The main objective of our work is to apply a new identification method (based on the modified Shannon entropy) to x-ray tomography data for accurate determination of the boundaries of the main hydrodynamic regimes (homogeneous, transition and heterogeneous).
The time series (extracted from reconstructed raw images) were measured by means of ultrafast x-ray tomography (sampling frequency=1000 Hz) in a bubble column (0.1 m in ID) and they were subsequently treated by the modified Shannon entropy algorithm developed by Nedeltchev et al. (2016). The raw time series give very good information about the x-ray attenuation and they are measure for the density distribution and the fraction of gas phase in different regions from the column’s cross-section. The column was equipped with a perforated plate distributor (55 holes, Ø 0.5×10-3 m) and operated with an air-deionized water system at ambient conditions. The tomographic scans were performed at an axial height of 0.5 m.
The data were organized in groups of 100 points and their sums were calculated. These sums were needed for the calculation of the probabilities of appearance of a particular value in the time series and the local Shannon entropies. It was found that the maximum sum can be used as a flow regime identifier. It was shown that two well-pronounced minima can be distinguished in the maximum sum values extracted at different superficial gas velocities Ug in the central part of the column’s cross-section. The first local minimum occurs at Ug=0.03 m/s and identifies the end of the homogeneous regime. The onset of the heterogeneous regime occurs at Ug=0.07 m/s. It was illustrated that the information entropy extracted from the data in the entire cross-section is capable of identifying the two main transition velocities at 0.025 m/s and 0.085 m/s. So, it was concluded that the heterogeneous regime starts somewhat earlier in the center of the cross-section. The homogeneous regime in the center and the entire cross-section ends at practically the same Ug value (0.025-0.03 m/s). It is noteworthy that for air-water system the theoretical prediction (0.029 m/s) by the correlation of Reilly et al. (1994) is very close to our experimental results.
Such a comparison has been performed at 20 different segments of the column’s cross section. The approach enables the preparation of a radial profile of the transition velocities. Flow regime identification results based on the maximum sums, information amounts and Shannon entropies are compared and discussed.