Analyses and modified models for bubble shape and drag coefficient covering a wide range of working conditions

Abstract

In this paper, the dynamics and dominant parameters of bubble shape deformation and drag coefficient during bubble rising were theoretically analyzed based on fundamental insights into bubble motion. Modified models for the aspect ratio and drag coefficient applying to a wide range including saturate vapor-water conditions under high pressure (6.9–15.5 MPa) were finally proposed based on theoretical analyses and comprehensive evaluations on previous correlations of aspect ratio and drag coefficient. Results showed that the combination of Weber number and Morton number can reasonably characterize the bubble shape deformation, while the combination of Reynolds number, Eötvös number and Morton number can reasonably characterize the drag coefficient. The proposed aspect ratio correlation in this paper predicts 90% of the existing experimental and numerical data within ±20% with a relative mean error of 8.2% for bubble rising in both two-component systems at atmospheric pressure and mono-component vapor-water systems at 6.9–15.5 MPa, while the proposed drag coefficient correlation predicts 93.5% of the data within ±35% with a relative mean error of 13.8% covering a wide range of 10−3 ≤ Re ≤ 105, 10−2 ≤ Eo ≤ 103 and 10−14 ≤ Mo ≤ 107.