Wake acceleration effect on spherical bubbles aligned in-line

• Proposal of drag force model with a new reference fluid velocity to estimate the wake acceleration effect.
• Investigation of velocity profile around a bubble immersed in the wake to avoid artificial parameters in the modeling.
• Validation of the proposed drag force model with experimental and DNS results.

The hydrodynamic behaviors of multi-bubble in a gas–liquid system which differs from that of a single bubble are found to be dependent on the complex hydrodynamic interactions between neighboring bubbles. It is observed that wake effect which leads to an increased rising velocity is responsible for bubble–bubble interactions. In this paper, a new drag force model was proposed to consider the wake acceleration effect on spherical bubbles. Key relation of the new model is the modeling of the relationship between the reduced drag force and the wake velocity, for which the concept of define a proper reference fluid velocity is applied. No artificial coefficient is employed in the current analysis. The proposed model was validated against experimental and numerical studies in which spherical bubble pairs are aligned in line vertically. It is illustrated that the performance of the proposed model in predicting the wake acceleration effect are promising for 3 ≤ Reb ≤ 200 and 2 ≤ s/d ≤ 15. The small discrepancies may be related to the wake velocity profile predicted by laminar boundary layer theory.