Computational fluid dynamics (CFD)- deep neural network (DNN) model to predict hydrodynamic parameters in rectangular and cylindrical bubble columns

Bubble columns are omnipresent in the chemical, bio-chemical, petrochemicals, petroleum industries, but their design and scale-up is complex owing to its complex hydrodynamics. Liquid velocity and gas holdup is one of the critical hydrodynamic parameters which effects the mixing, heat and mass transfer in bubble columns. CFD is widely recognized as a powerful tool for estimating critical hydrodynamic parameters but requires significant computational resources, time and expertise. These limitations restrict its practical use in hydrodynamic simulations that need real-time processing involving large-scale simulations of bubble columns. To overcome these limitations, CFD-DNN model is developed to predict the time averaged gas holdup and axial liquid velocity at various operating conditions. The DNN model was trained using CFD data that was produced for rectangular (with dimensions L=0.2 m, W=0.05 m, H=1.2 m) and cylindrical (with a diameter of 0.19 m) bubble columns. The data covers a range of operating conditions and various flow regimes. The superficial gas velocity for the rectangle column was selected at 1.33 and 7.3 mm/s, whereas for the cylindrical bubble column, it was fixed at 0.02 and 0.12 m/s. The CFD-DNN model was validated against the experimental and the CFD data from the literature. Further, the model was tested for new data that the CFD-DNN model has not seen with existing literature and showed good agreement with their data and it reflects the excellent generalization ability of the model. The proposed CFD-DNN approach improves current CFD models by providing shorter computing time, decreasing computational expenses, and reducing the expertise in CFD simulations. The accuracy of the developed CFD-DNN model was evaluated using different metrics for gas holdup and axial liquid velocity. For rectangular bubble columns, the model achieved MSE of 0.0001 for gas holdup and 0.0007 for axial liquid velocity. Similarly, for cylindrical bubble columns, the MSE values were 0.0009 for gas holdup and 0.0006 for axial liquid velocity.