Ekman boundary layer mass transfer mechanism of free sink vortex

Abstract The suction-extraction phenomenon occurs in the formation process of free sink vortex, and it is a complex gas-liquid coupling matter. The mass transfer mechanism of the Ekman boundary layer involved in the above matter is with important scientific value and engineering significance. To address the matters, we construct a Rankine-vortex-based fluid mechanic model, and propose a Helmholtz-equation-based solution method to acquire the critical penetration condition of sink vortex. The two-phase mass suction-extraction mechanism of the Ekman boundary layer is discussed. Then, a coupled computational fluid dynamic and discrete element method (CFD-DEM) modeling method is presented to obtain the matter transfer regularities of particles pumped by sink vortex, and the critical condition of particle stability motion is solved by the Laplace transform method. Numerical results show that the critical penetration condition is a data set because of different initial velocity components; the heights of suction/extraction holes form the container bottom have no relation to the initial velocity components; if the initial disturbances are enhanced, the suction-extraction height and Ekman layer thickness increase, but the Ekman suction-extraction intensities grow weaker; a particle aggregation phenomenon exists in the vortex center, and can be stable state until the surface tension broken by the Ekman suction effect, wherein the Ekman resultant force with different positions causes the particle motion trajectory to be complex. A PIV observation experimental platform is developed, and the effectiveness of the proposed method is verified. Then, the vortex core boundary is observed, so the radius of the vortex core can be acquired precisely; there is an energy transition process from potential energy to kinetic energy in the suction and extraction stages, which causes the Ekman boundary vorticity intensities to decline; the particle pumping process induces the aggregation and dissipation of turbulent vortices quickly, accelerating the fluid mass transfer efficiencies. The research works can provide direct guidance for the active control of vortex formation in industrial areas, and supply useful references to related fluids engineering calculation issues.