## 3 Key Technology in Multiphase Vortex-Induced Vibration Detection
### Formation and Evolution Mechanism of Free Sink Vortex
[71] investigated the Taylor vortex and Ekman vortex, as well as their interaction process, and confirmed the influence of the Ekman layer suction effect on the gas core. [PERSON] et al. [72] found that the vortex has an Ekman transport-ascending two-cell structure. [PERSON] et al. [73] investigated the compressible flow field's transport mechanism and discovered that when the sweep angle increases the size of the wake region shrinks (Figure 7). The secondary flow provides an intense temperature and density gradient in the flow. The increase in the temperature gradient causes the mass jet flow to grow, which improves the mass transfer process of neighboring surfaces. Based on the preceding description, contemporary sink vortex research focuses mostly on two-phase flow, gas core development, and convection mass transfer. In multiphase viscous fluid vortices, the energy development of local vortex clusters, vorticity polymerization and dissipation processes, and trans-scale suction and transport phenomena of the Ekman layer are yet unknown. [PERSON], [PERSON], and [PERSON] only demonstrated the presence of the Ekman boundary layer and its nonlinear turbulent properties, and their findings were limited to a set rotation speed and could not attain a complete turbulent state. Figure 5: Flow features of the free surface vortex. (**a**) Fluid volume fraction and tangential velocity. (Reprinted with permission from Ref. [56]. 2020, Elsevier). (**b**) Tangential vorticity contours. Reproduced with the permission of Springer Nature. (Reprinted with permission from Ref. [59]. 2019, Springer Nature). (**c**) Axial disturbance velocity. Reproduced with the permission of Elsevier. (Reprinted with permission from Ref. [60]. 2019, Springer Nature). The above research work can provide a reference for Ekman layer theory in studying the suction transport mechanism of the multiphase sink vortex. In recent years, [PERSON] et al. set up a gas-liquid two-phase vortex dynamics model and discussed the internal relationship between the initial velocity component and the Ekman boundary layer. The results revealed that when the initial disturbance velocity is different, the vortex's suction hole is consistent with the liquid level at the bottom of the container, as illustrated in Figure 8a. However, the thickness and critical height of the Ekman layer rise as the circumferential velocity increases. Then, as shown in Figure 8c, the vorticity evolution process of the flow field and particle at the suction and extraction stages was investigated, and it was found that a turbulent energy transition happens in this process [74]. [PERSON] et al. [75] studied the characters of free-surface vortex formation processes in a self-ingested reactor, as shown in Figure 8b, and found that the Ekman layer affects the bubble flow and the separation process of the eddy vortex. The presence of the Ekman boundary layer influences vortex generation significantly. The mechanism of the Ekman boundary layer on vortex generation has only been examined qualitatively in  
Figure 6: Ekman layer evolution characters of free sink vortex. (**a**) Laminar flow phenomenon. (**b**) Lundgren’s equations with surface tension and without surface tension. Reproduced with the permission of the Cambridge University Press. (Reprinted with permission from Ref. [68]. 2006, Cambridge University Press). (**c**) Generation and progression of the air cone. (**d**) Progression of the vorticity distribution. Reproduced with the permission of Elsevier. (Reprinted with permission from Ref. [71]. 2011, Elsevier). previous research. They still did not have a good grasp of the intrinsic link between local vortex development and the Ekman number. The suction mechanism of the free vortex becomes more complex due to the presence of a multiphase material. Momentum approximation theory is used to examine Ekman layer theory, which has crucial implications for analyzing the interplay of physical factors in the vortex generation process.