Two-phase flow in straight pipes and across 90 degrees sharp-angled mitre elbows

Pressure drop of single-phase flow across 90 ◦ sharp-angled mitre elbows connecting straight circular pipes is studied in a bespoke experimental facility by using water and air as working fluids flowing in the range of bulk Reynolds number 500<Re<60000. To the best of our knowledge, the dependence on the Reynolds number of the pressure drop across the mitre elbow scaled by the dynamic pressure, i.e. the pressure-loss coefficient K, is reported herein for the first time. The coefficient is shown to decrease sharply with the Reynolds number up to about Re=20000 and, at higher Reynolds numbers, to approach mildly a constant K=0.9, which is about 20% lower than the currently reported value in the literature. We quantify this relation and the dependence between K and the straight-pipe friction factor at the same Reynolds number through two new empirical correlations, which will be useful for the design of piping systems fitted with these sharp elbows. The pressure drop is also expressed in terms of the scaled equivalent length, i.e. the length of a straight pipe that would produce the same pressure drop as the elbow at the same Reynolds number. Air-water flow in horizontal and vertical straight pipes and through 90 ◦ sharp-angled mitre elbows, is investigated visually by using high-speed high-resolution camera. The flow is studied in pipes with three diameters for about 600 conditions of air-water flows, characterized by superficial velocities in the ranges of jL =0.297-1.015 m/s for water and jG =0.149-33.99 m/s for air. The portion of the pipe upstream of the elbow is always positioned horizontally, while the portion of the pipe downstream of the elbow is oriented horizontally or vertically with the flow moving upward. Plug, slug, slug-annular and annular flows are observed in horizontal straight pipes, while slug, churn and annular regimes are recorded in vertical straight pipes. These flow patterns are well predicted by the Mandhaneet al. [1] map for horizontally oriented straight pipes and by the Hewitt and Roberts [2] map for vertically oriented straight pipes. The prediction of the flow patterns along the straight portions of the pipe improves by expressing the maps in non-dimensional form. The changes of the flow patterns as the fluids pass through the mitre elbows are thoroughly discussed. A multiple membrane flow structure is observed in the vertical upward flow at much higher Reynolds numbers, based on the water superficial velocity, than in the vertical downward case previously reported in the literature. The flow patterns through the elbows are expressed for the first time in terms of rescaled Mandhane et al. [1] maps, which simultaneously represent the flow patterns both upstream and downstream of the elbows. The dimensional analysis proves that a rigorous way to present the flow regimes of an incompressible isothermal air-water flow for a given geometry is a map in the space of the Reynolds numbers based on the superficial velocities of air and water for fixed Froude number. The pressure drop generated by air-water flows was measured in horizontal and vertical straight pipes and across 90◦ sharp-angled mitre elbows for the same flow conditions of visual investigations.Two new pattern-based values of the Lockhart-Martinelli parameter C are found for the pressure drop in horizontal pipes with the presence of mitre elbows. A dimensional analysis is employed to scale the pressure drop data for straight pipes and across the elbows. New pattern-based empirical correlations are proposed to fit the scaled frictional pressure drops for the flows through the straight portions of the pipe and across the elbows. The flow perturbation length upstream of the elbow is located at less than 32.5D for single-phase and two-phase flows, while the flow recovery length downstream of the lbow was less than 32.5D ∗ and 60D ∗ for single-phase and two-phase flows, respectively. The peripheral pressure upstream and downstream of the elbow is found to be axially symmetric farther than 7D upstream and downstream of the elbow for horizontal orientation in single-phase and two-phase flows.