An evaluation of predictive correlations for the terminal rising velocity of a single bubble in quiescent clean liquid

Evaluation work was carried out on widely used correlations for predicting the terminal velocities of single bubbles rising in quiescent liquids against a database with 758 data points. The data were collected from the experiments of air bubbles rising in pure water with diameters covering 0.02-66.97 mm. The correlations are firstly categorized into three groups according to their application ranges: group 1 for spherical and ellipsoidal bubbles with rectilinear paths, group 2 for ellipsoidal bubbles with unstable paths and sphericalcap bubbles and group 3 for bubbles of all sizes. Evaluation results show that among group 1 correlations, the Moore (1965) correlation demonstrates the best MAE of 2.9% within its application range (Re > 50). The Chen et al. correlation and Rastello et al. correlation, with the broadest application range in group 1, yield good overall MAEs of 7.0% and 5.0%, respectively. The Lehrer correlation gives the smallest MAE of 4.3% in group 2. In group 3, the Dijkhuizen et al. correlation and Baz-Rodriguez et al. correlation achieve the highest accuracy against all the experimental data, with global MAEs of 7.7% and 8.7%, respectively. Although present prediction methods have achieved good agreement with the experimental results, predicting the terminal velocity of ellipsoidal bubbles with unstable paths is the most intractable and lacks satisfactory methods, and it still remains challenging to develop a unified correlation.