Velocity profiles in bathtub vortices: validation of analytical models

Free surface vortices in water are often observed around a drain outlet in sinks and bathtubs, and different researchers deal with the problem of how the bathtub vortex is generated. In a previous work [1], some analytical free surface vortex models were discussed and analyzed, and their limits were underlined. In the present paper, the vortex models of Burgers, Hite and Chen are considered. Burgers’ model was derived as a result of purely analytical hypotheses, while the other two were developed modifying the Burgers’ vortex model according to experimental observations. In all these models, two parameters - the circulation Γ and the vortex core radius rm - have to be defined. In order to validate these analytical models, experimental measurements have been carried out for different horizontal and vertical planes by means of optical methods (Particle Image Velocimetry - PIV), reproducing free surface vortex formation in the GETS (Gas Entrainment Test Section) experimental facility. The two main parameters to be used in the models have been derived from experimental measures. Velocity profiles and vorticity distribution, calculated from the analytical models, have been compared with experimental velocity and vorticity fields. As a result, it is showed that Hite’s model seems to be the most accurate model compared to experimental data.