Abstract
New correlations to predict the entrainment fraction in horizontal pipes are proposed based on the Pan & Hanratty correlation. The Pan & Hanratty correlation cannot properly predict the entrainment fraction at low liquid flow rates, and this results from too high critical liquid Reynolds numbers for the calculation of the maximum entrainment fraction. To solve this problem, we suggest two new entrainment models by replacing the maximum entrainment model in the original equation with the one from Al-Sarkhi et al. (2012) or from Mantilla (2008). For the Mantilla model, we propose a minor modification so that the correlation can predict the maximum entrainment fraction better. We validate the proposed models with an extensive range of experimental data involving pressure from 1 to 70 bar, pipe diameter from 2.3 to 9.5 cm, and fluid type of air-water and N2-water. The proposed models show good agreement with the experimental measurements by improving the predictions at low liquid flow rates, and their performances are better or similar compared to the other entrainment models. In particular, the Pan & Hanratty correlation with the modified Mantilla model demonstrates satisfactory performance showing root mean square error of 10 % over all data.
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