On the radial interface profile of the non-circular hydraulic jump

Abstract

The radial interface profile of the non-circular hydraulic jump is analyzed based on the time-averaged film thickness profile of the liquid film formed by a round jet obliquely impinging on a horizontal plate. The influence of many factors, including the jet velocity, impingement angle, azimuthal angle, liquid viscosity, and surface tension, on the radial interface profile is considered. The interface profile is like a quasi-spherical crown when the azimuthal angle is small but is like a sewing needle when the azimuthal angle is larger than 100°. Six parameters, including the inner and outer tangential angles, width, maximum thickness, radial position of maximum thickness, and area are defined to describe the interface profile. Then, six empirical equations are developed to fit the variation of the six parameters. As the azimuthal angle increases, the inner tangential angle decreases, but the outer tangential angle increases. As the jet velocity increases to 20.3 m/s, both the maximum thickness and the area increase suddenly. All empirical equations have a prediction accuracy of about 10%, except for the empirical equation of the radial position of maximum thickness. The bubble trajectory indicates that the liquid flows radially in the thin-layer zone, deflects the flow direction within a relatively short distance in the inner half of the non-circular hydraulic jump, and then flows tangentially. The normal bulk velocity in the radial section of the non-circular hydraulic jump increases from zero at first and then decreases as the azimuthal angle increases.