Development of correlations for liquid entrainment through a large-scale inclined branch pipe connected to the main horizontal pipe

Abstract

Many theoretical and experimental studies have been conducted over the years on liquid entrainment through a branch pipe connected to the main horizontal pipe (i.e., entrainment at the T-junction). Several mathematical models have been developed to predict the onset of liquid entrainment and branch quality during the liquid entrainment process with reasonable accuracy. Most of these models are developed based on small-scale branch, where the ratio of the branch diameter to the horizontal pipe diameter is less than or equal to 0.2 (d/D ≤ 0.2). Therefore, these models are not suitable to predict the onset of liquid entrainment through a large-scale branch. In addition, these models are developed for a specific branch angle (typically 0 or 90°) and therefore, are incapable of making good predictions of the onset of liquid entrainment through a large-scale branch inclined at other angles. In order to address these issues, we conducted experiments to investigate the onset of liquid entrainment through a large-scale branch pipe (d/D > 0.6) inclined at three angles (32.2, 47.9, and 62.3°) and we assessed the mass flow quality of the branch. By analyzing the mathematical models for liquid entrainment currently available and by theoretical deduction, we developed new correlations to predict the onset of liquid entrainment and mass flow quality. We found that the values predicted by these correlations fit well with the experimental data with a maximum error of ±35%. Both of these liquid entrainment correlations provide good predictions of liquid entrainment through a large-scale branch inclined at an angle of 32.2, 47.9, and 62.3°. We also obtained some meaningful conclusions based on the experimental data. We found that at the onset of liquid entrainment, under similar experimental conditions, the critical Froude number Frg decreases with an increase in the branch angle. In addition, the larger the branch angle, the lower the effect of the branch scale on the onset of liquid entrainment. There are two primary factors that influence the liquid entrainment process: (1) gas chamber height—the liquid entrainment process is promoted as the gas chamber height decreases, and (2) vertical component of the inertial force—the liquid entrainment process is weakened with a decrease in the vertical component of the inertial force. This indicates that the gas chamber height dominates the liquid entrainment process at relatively large branch angles whereas the vertical component of the inertial force dominates the liquid entrainment process at small branch angles.