New method for flow regime identification in a bubble column based on ultrafast x-ray tomography data

Bubble columns (used for absorption, oxidation, chlorination, hydrogenation, waste water treatment, etc.), operate in different hydrodynamic regimes (homogeneous, transition and heterogeneous). It is essential to identify the boundaries between these flow regimes since most of the correlations for prediction of the main design parameters (gas holdup, interfacial area, mass transfer coefficients, etc.) are valid only within a certain flow regime. In the past three decades different methods of data analysis (statistical, spectral, fractal, chaotic, wavelet, etc.) have been developed for flow regime identification. However, they can identify successfully only the first transition velocity (from homogeneous to transition regime). The bubble column hydrodynamics are very complex and usually more than two regime transitions occur. They could be detected by means of some new and more powerful method of data analysis. In this work, we introduce a new dimensionless parameter based on the division of the X-ray tomography data into many state vectors. Some routines from nonlinear chaos analysis (Schouten et al., 1994) are used.
The bubble column had an inner diameter of 0.1 m and was equipped with a perforated plate distributor (55 holes, ø 0.5×10-3 m). The gas-liquid system consisted of air and deionized water. The clear liquid height Ho was set at 0.66 m. Superficial gas velocities Ug ranging from 0.01 up to 0.10 m/s were employed. The data used for the new method were recorded by means of ultrafast X-ray tomography (scan level=0.5 m). The time series consisted of 29,000 points and were sampled with a frequency of 1000 Hz.
Every reconstructed image was divided into the same semi-rings. In this work the pixel values in a specific semi-ring (inner radius=10×10-3 m ; outer radius=15×10-3 m) were used for further analysis. The data were divided into state vectors consisting of 50 elements and then the distance between pre-selected vector pairs was estimated. For this purpose, the maximum norm (Schouten et al., 1994) was used, i.e. the vector distance was equal to the maximum absolute difference between two elements from the vector pair. The number of vector pairs with distance smaller than some pre-selected criterion (three times the average absolute deviation (AAD)) was used as a basis for the new method for flow regime identification in a bubble column.
It was found that the ratio of the number of vector pairs (with a distance smaller than 3AAD) found in the second part of the signal divided by the one in the first part of the signal can be used for identifying three transition velocities Utrans. They correspond to three well-pronounced local minima. At Ug=0.02 m/s the gas maldistribution regime transforms itself into homogeneous (bubbly) regime. This flow regime is stable up to Ug=0.04 m/s. Beyond this critical gas velocity begins the transition flow regime. The onset of the heterogeneous (churn-turbulent) regime occurs at Ug=0.06 m/s.
When the reconstruction entropies (RE) (Nedeltchev, 2015) are extracted from the vector pairs (meeting the criterion about the vector distance) in both the first and second parts of the signal and the ratio between them is calculated, the same three Utrans values are identified. It was illustrated that the three local minima occur at Ug=0.02, 0.04 and 0.06 m/s, respectively.
In the full-length contribution, based on the above-mentioned new approach, the transition velocities Utrans in many different parts from the column’s cross-section will be identified. A comparison between the transition velocities in the column core and annulus will also be shown.