Prediction of the profile of a vertical air-entraining vortex

Air-core vortices occurring at intakes cause efficiency losses, vibrations, operational difficulties, and erosion at affiliated water-conveying structures. Air-core vortices are in the forms of non-air entraining vortex (air-core vortex in suspension) and air-entraining vortex. The profile of an air-core vortex is considered to be one of the main characteristics of the vortex. There are available semi-empirical formulas for the profile of a vertical non-air entraining vortex (air-core vortex in suspension) occurring at a vertically-flowing downward intake. However, there is no available developed formula relating to the profile of a vertical air-entraining vortex occurring at a vertically-flowing downward intake because the height, radii, and other physical quantities of the imaginary section of the air-entraining vortex downstream of the intake entrance are not measurable. Therefore, the profile of a vertical air-entraining vortex needs to be predicted. In the present study, by modifying the available formula relating to the profile of a non-air-entraining vortex and incorporating available test data, a practical methodology is developed for predicting the profile of a vertical air-entraining vortex. This study provides a practical formula and a chart to determine the necessary parameters to predict the profile of a vertical air-entraining vortex. The validation of the proposed methodology is examined and checked with available test data relating to the profile of a vertical air-entraining vortex occurring at a vertically-flowing downward intake. The results of the present study are in good agreement with available test data relating to the profile of vertical air-entraining vortices (the coefficient of determination is between 0.976 and 0.995).