Data-Driven Bubble Tracking DMD Method for Predicting Bubble Rising Behaviors in a Hele-Shaw Cell

The dynamic mode decomposition (DMD) is a promising data-driven modeling method for flow field prediction with adequate accuracy but much less computational burden than traditional computational fluid dynamics (CFD) methods. However, the DMD remains incapable of predicting complicated traveling wave problems such as bubble rising in liquid. Therefore, an improved bubble tracking DMD (BT-DMD) method is proposed in this paper to predict both the deformation and movement of a rising bubble in a Hele-Shaw confined space. Three gas-liquid boundary processing methods, namely, threshold segmentation, level-set, and Lagrangian frame, were also designed to reduce the noise on the bubble boundary shape. The data required for BT-DMD training and testing were generated experimentally from a bubble rising process in a Hele-Shaw cell. By comparing the predicted results with the experimental data, the proposed BT-DMD method is shown to be effective in reconstructing and predicting the deformation and motion of bubbles with different typical shapes. The average mean-square error of the predictions obtained by the proposed BT-DMD method is less than 1%.