## 3 Key Technology in Multiphase Vortex-Induced Vibration Detection  
### Formation and Evolution Mechanism of Free Sink Vortex  
The bathtub vortex is another name for the free sink vortex. The initial disturbance velocity, the geometric size of the container and flow passage section, the surface roughness, and other elements all play a role in its development. The rotation direction is consistent with the initial disturbance after the velocity reaches a certain magnitude [45]. In engineering applications, the vortex interface morphology and flow mode take on complex and varied properties due to the boundary of a complex structure and the initial condition of the fluid. The fluctuating position of the gas vortex core makes it challenging to examine the vortex formation mechanism, especially when it evolves into a stable suction vortex due to the gas-liquid coupling interaction. Early scholars and researchers investigated the generation process of the free sink vortex. Based on the fundamental equations of conservation of mass, momentum, and energy, they merely made simplified assumptions about the complicated structure's boundaries. Analytic or approximation analytical solutions are produced by solving the preceding equations, and a typical vortex theoretical model, such as the Rankine vortex [46], Oseen vortex [47], Taylor vortex [48], and Burgess vortex [49], is established. Then, a basic grasp of physical phenomena is gained. Researchers are constantly improving and revising the vortex theory model as well as conducting qualitative or quantitative analyses on the sink vortex formation process, critical conditions, and influencing factors through field tests or model experiments to provide a theoretical foundation for the industrial production process technology. Relevant research results [50; 51; 52] show that a free sink vortex is the main reason that surface fluid is sucked in the drainage process. Its suction characteristics are directly connected to the transient distortion attribute of fluid-structure vibration signals. Under the assumption of vortex viscosity, [PERSON] [53; 54] found that the Froude number and cycles are the key parameters that impact the critical submerged height. In laminar flow, however, the simplified N-S equation solution of the vortex tangential velocity expression is not universal. [PERSON] et al. [55] used the Burgess vortex model to study the motion of solid particles in a rotating flow field. They found that the solid particles sucked by the free sink vortex are closely connected to the particle characters (such as density and size) and the vortex core radius. [PERSON] et al. [56] adopted the Rankine vortex theory model to analyze the vortex formation mechanism and motion law and found that the angular velocity towards the vortex core grows linearly. The velocity and circular intensity at the vortex center point is zero, which are key features of a rigid vortex core. However, a free sink vortex is a combination vortex that is part of a more complicated viscous turbulent process. Its production necessitates transforming both initial kinetic and gravitational potential energy, necessitating energy supplementation and maintenance [56; 57]. Hence, the vortex radius cannot be controlled by theory but must be determined by experiment and experience. [PERSON] et al. [58] investigated the link between nozzle diameter, geometric shape, bottom tilt, and vortex formation in recent years. The nozzle diameter was shown to significantly impact the vortex's critical submerged height. Moreover, other physical characteristics are directly related to the essential submerged height, and the volume portion of the residual fluid may be lowered properly with a tilt of 25 degrees. [PERSON] et al. [59] used the volume of the fluid model to obtain the oil-gas-water three-phase eddy current field, yielding the flow structure and evolution process of the free surface vortex.