February 26, 2010

Entrainment fraction is one of the crucial variables in many cases in multiphase flow. Very few mechanistic models (with reasonable accuracy) exist for entrainment rate. Understanding the basic physics of these phenomena is essential to model situations of practical interest to the industry. For example, the pressure gradient in an annular flow is contributed by three parameters, the hydrostatic, the interfacial friction at the interface and the entrainment fraction. The wave characteristics and the pipe diameter and its inclination angle are all affecting the entrainment fraction.

A new entrainment fraction model was proposed by Xianghui Chen (TUFFP ABM October 2005) which is claimed to be applicable for all inclination angles. Reasonable agreement was obtained between the new model predictions and published entrainment data. It has been noticed that for horizontal and inclined pipeline and at a large liquid film Reynolds number the entrainment fraction is under-predicted. In addition to the previous mentioned disadvantage of this model, the model uses implicit parameters as an input which needs another models or closure relationships. This procedure most likely carries uncertainties of the other closure relationships.

The only inclined data available in literature is presented in a paper by Ousaka 1996 in a small 26-mm pipe diameter and on which the Chen model was formulated. More data are needed at larger pipe diameter and different pipe inclination.

Kyle Magrini (2009) conducted numerous tests to investigate the effect of pipe inclination on entrainment fraction in air-water annular flow. Inclination angles of 0, 10, 20, 45, 60, 75, and 90 degrees from horizontal were analyzed. Two techniques were used to measure the entrainment fraction: film removal and isokinetic sampling. Pressure drop, liquid holdup, film thickness, and wave characteristics were also measured to better understand the inclination effect and the physics of the droplet entrainment. The data of Magrini will be used to enrich and support the future modeling front.

Several dimensionless groups correlating the entrainment fraction for all inclination angles has been identified and verified with the experimental data from the open literature. A number of correlations have been tested against Magrini data. The best predicting methods were determined for vertical, horizontal, and inclined flow orientations with reasonable to low uncertainty. Based on the statistical analysis for vertical annular flow, the Oliemans et al. (1986) correlation most accurately predicts entrainment fraction. For horizontal annular flow entrainment prediction, the Pan and Hanratty (2002b) horizontal correlation most accurately predicts entrainment. Based on the statistical analysis for inclined annular flow, the Paleev and Filippovich (1966) correlation prediction is most accurate.

Finally, the focus will be on the modeling side and the effective use of Magrini's data. A new reliable model for all inclination angles or a modification of an existing model will be the target of the future work.

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