Free sink vortex Ekman suction-extraction evolution mechanism

The suction-extraction phenomenon occurs in the formation process of free sink vortex (bathtub vortex), and it is a complex gas-liquid coupling matter. The Ekman layer coupling and its evolution mechanism involved in the above matter possess important scientific value and practical engineering significance. To address the above issue, a modeling and analytical method for the Ekman suction-extraction evolution mechanism of free sink vortex is proposed. Based on the multiphase volume of fluid model and turbulent kinetic energy-dissipation (k-epsilon) model, a gas-liquid two-phase fluid dynamic model for free sink vortex Ekman suction-extraction is set up. Considering the rotating and shearing characteristics of sink vortex, a two-phase surface is reconstructed by piecewise linear interface construction method. Based on the above models, the internal relations between initial rotation velocity component, drainage capacity and Ekman suction-extraction are investigated, and the corresponding flow field profile regularities are revealed. According to the results of a series of numerical instances, some regularities are obtained as follows. 1) If the initial velocity disturbance is variable, the distances of the suction and extraction holes from the container bottom both keep constant. In the suction stage, the suction hole is located at a fixed position above the container bottom surface, and the extraction hole is in the plane of the bottom surface. 2) If the initial disturbance is enhanced, the rotation velocity of the suction stage increases, and the suction and extraction heights and Ekman layer thickness become larger, while Ekman suction-extraction intensities of suction, extraction and penetration stages turn weaker. 3) If the initial disturbance is invariable, the heights of Ekman suction and extraction remain unchanged, and are independent of drainage capacity. 4) The small-scale vortexes separated from the large-scale ones in the bottom corner of container take on a phenomenon of flow around by a right-angle, which is caused by the viscosity of Ekman boundary layer and the potential flow of the sink hole. 5) Considering the stream line profiles of suction and extraction stages, the dispersion of stream lines keeps constant with the time going by, and the stream lines near the central region of vortex tend to be converged by increasing the gas-liquid coupling. In general, the results can offer useful reference to the research work of free sink vortex formation mechanism, and provide technical supports for vortex suppression control of the areas of metallurgy pouring, chemistry separation and hydraulic drainage. The subsequent researches of the fractal based sink vortex evolution mechanism and lattice Boltzmann based phase surface tracing will be carried out.