Extraction of information and reconstruction entropies from ultrafast X-ray tomography data in a bubble column
Abstract Due to the complex hydrodynamics of bubble columns, there are currently no reliable methods for identification of the main transition velocities. In addition, it is not clear, which type of signal is most suitable for flow regime identification. In this work, both the information entropy ( IE ) and reconstruction entropy ( RE ) have been extracted for the first time from tomographic raw images obtained by means of ultrafast X-ray tomography. The time series have been recorded with a sampling frequency of 1000 Hz in a bubble column (0.1 m in ID) operated with an air-deionized water system under ambient conditions. The main transition velocities U trans in two semi-rings (from the cross-section of the bubble column) have been identified based on both the IE and RE values as well as a new parameter, which has been calculated from each signal reconstruction. In the centrally located smaller semi-ring from the reconstructed raw X-ray images, the two U trans values have been successfully identified at 0.04 and 0.11 m/s. In the surrounding larger semi-ring the first and second U trans values occurred slightly earlier at 0.03 and 0.09 m/s, respectively. Although they do not play an important role for the determination of the degrees of mixing, mass and heat transfer, the boundaries of additional sub-regimes have been also identified. It has been found that when all newly developed identification methods are compared, they yield slightly different U trans values. In summary, this work demonstrates for the first time that the ultrafast X-ray tomography data measured at various superficial gas velocities can be used for flow regime identification in a bubble column provided that the hidden information in the time series is quantified by both the IE and RE algorithms.