Two-phase minor loss in horizontal bubbly flow with elbows: 45° and 90° elbows

The present study investigates the geometric effects of a 45° elbow on the pressure drop due to the minor loss in horizontal bubbly flow. A round glass tube with inner diameter of 50.3 mm is employed as a test section, along which a 45° elbow is installed at L/D = 353.5 from the two-phase mixture inlet. In total, 15 different flow conditions are examined. The local static pressures are measured at four axial locations at L/D = 197, 342, 363 and 419 from the two-phase mixture inlet. The effect of the elbow is clearly demonstrated in the pressure data along the axial direction. In the data analysis, the pressure data previously acquired with a 90° elbow is also utilized as well. The conventional Lockhart–Martinelli correlation with parameter C = 30 predicts the overall two-phase frictional pressure loss between the inlet and exit of the test section relatively well for both the 90° and 45° elbow experiments. However, it fails to predict the pressure loss across the elbows, because the existing model does not account for the additional loss due to the flow restrictions. In view of this, a new correlation analogous to Lockhart and Martinelli’s is developed for the two-phase frictional pressure loss across the elbows. The new correlation with the parameter C = 65 and the minor loss factors of k = 0.58 and k = 0.35 for the 90° and 45° elbows, respectively, yields the best fit to the data. The average percent differences between the predictions made by the new correlation and the data are ±2.1% and ±1.3% for 90° and 45° cases, respectively.