Flow Regime Identification in a Bubble Column Based on Both Statistical and Chaotic Parameters Applied to Computed Tomography Data

A novel recurrence-based approach for investigating multiphase flow dynamics in bubble column reactors

In chemical industries, multiphase flows in a bubble column reactor are frequently observed. The nonlinearity associated with bubble hydrodynamics, such as bubble-bubble and bubble-liquid interactions, gives rise to complex spatiotemporal patterns with increased gas or liquid velocities, which are extremely difficult to model and predict. In the current study, we propose a new, computationally efficient recurrence-based approach involving the angular separation between suitably defined state vectors and implement it on the experimental multiphase flow variables. The experimental dataset that consists of image frames obtained using a high-speed imaging system is generated by varying air and water flow rates in a bubble column reactor setup. The recurrence plots using the new approach are compared with those derived from conventional recurrence, considering standard benchmark problems. Further, using the recurrence plots and recurrence quantification from the new recurrence methodology, we discover a transition from a high recurrence state to a complex regime with very low recurrence for an increase in airflow rate. Determinism exhibits a rise for the decrease in airflow rate. A sharp decline in determinism and laminarity, signifying the quick shift to complex dynamics, is more prominent for spatial recurrence than temporal recurrence, indicating that the rise in airflow rate significantly impacts the spatial location of bubbles. We identify three regimes that appeared as distinct clusters in the determinism-laminarity plane. The bubbly regime, characterized by high values of determinism and laminarity, is separated by an intermediate regime from the slug flow regime, which has low determinism and laminarity.

Exploring the Relationships between Gas Dispersion Parameters and Differential Pressure Fluctuations in a Column Flotation

Flotation separation, which is the most important mineral beneficiation technique, is dependent on gas dispersion (hydrodynamic conditions). Thus, many investigations have focused on the precise determination of hydrodynamic conditions such as Reynolds number of the bubbles, bubble velocity, and bubble diameter. However, few studies have examined their relationships with pressure fluctuations in a column flotation. This study introduced the differential pressure fluctuations as an actual variable that could be considered to determine the collection zone's hydrodynamic conditions in a cyclonic microbubble flotation column. In general, the outcomes indicated that superficial gas velocity had the most substantial relationship with the differential pressure fluctuations among other flotation factors (such as pump speed, superficial gas velocity, superficial water velocity, and frother dosage). Furthermore, a high coefficient of determination (R ² > 0.77) for the equation generated to assess the relationships demonstrated that differential pressure fluctuations could be used as a promising tool to determine the hydrodynamic parameters' characteristics in the flotation columns.

A New Statistical Parameter for Identifying the Main Transition Velocities in Bubble Columns

The identification of the main flow regime boundaries in bubble columns is essential since the degrees of mixing and mass and heat transfer vary with the flow regime. In this work, a new statistical parameter was extracted from the time series of the cross-sectional averaged gas holdup. The measurements were performed in bubble columns by means of conductivity wire-mesh sensors at very high sampling frequency. The columns were operated with an air/deionized water system under ambient conditions. As a flow regime indicator, a new dimensionless statistical parameter called “relative maximum number of visits in a region” was introduced. This new parameter is a function of the difference between the maximum numbers of visits in a region, calculated from two different division schemes of the signal range.