Two-phase minor loss due to the 45-degree elbow in horizontal bubbly flow

The present study investigates the geometric effects of a 45-degree 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-degree 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-degree elbow is also utilized as well. The conventional Lockhart-Martinelli correlation with parameter C=30 predicts the overall two-phase frictional pressure loss well for both the 90-degree and 45-degree elbow experiments. 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-degree and 45-degree 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-degree and 45-degree cases, respectively.