Correlation of drag coefficient between rising bubbles in chain

Abstract

Bubbles-in-chain is a two-phase fluid flow phenomenon in natural environments and engineering practices with unique bubble–bubble interactions. The interactions among bubbles lead to a periodically varying local drag coefficient, which has been rarely studied. Here, we report a numerical investigation of rising bubbles in a chain using large eddy simulation and coupled volume-of-fluid and level-set methods to examine the local drag coefficient and its predicting models. We first validated the bubble diameter and rise velocity with an experimental dataset. The local drag coefficient was then calculated and compared with the traditional Weber number based model. We propose a modified Weber number model with a trigonometric relation, defining the upper and lower limits of the drag coefficient as a result of bubble–bubble interactions. With the proposed model, the predicted drag coefficient shows an acceptable accuracy with errors less than 7%. The resolved flow field in the bubble wake confirms the correlation among the drag coefficient, wake velocity, and rising velocity. This mechanism provides a stable and periodical variation of the drag coefficient in the bubbles-in-chain system.