Advances in the Multiphase Vortex-Induced Vibration Detection Method and Its Vital Technology for Sustainable Industrial Production

: Fluid-induced vibration detection technology for the multiphase sink vortex can help achieve efﬁcient, safe, and low-carbon sustainable industrial production in various areas such as the marine, aerospace, and metallurgy industries. This paper systematically describes the basic principles and research status in light of the important issues related to this technology in recent years. The primary issues that occur in practical application are highlighted. The vital technologies involved, such as the vortex-formation mechanism, interface dynamic evolution, the shock vibration response of thin-walled shells, and vortex-induced vibration signal processing algorithms, are analyzed. Based on in-depth knowledge of the technology, some signiﬁcant scientiﬁc challenges are investigated, and further research prospects are suggested. The research results show that this technology can achieve the real-time detection of vortex-induced vibration states. Two future research directions are those of exploring multiphysical ﬁeld coupling under harsh conditions and more accurate modeling methods for multiphase coupling interfaces. Regarding vortex-induced vibration, forced-vibration characters with various restriction conditions, the forced-vibration displacement response of liquid-ﬁlled shells, intrinsic properties inﬂuenced by random excitation forces, and highly effective distortion-detection algorithms will continue to attract more attention. The associated results could give technical support to various ﬁelds, including energy-efﬁciency improvement in manufacturing processes, tidal power generation condition monitoring, and the performance optimization of low-carbon energy components.


Introduction
The fluid-induced vibration detection technology for the multiphase sink vortex is widely used in developing detection systems for process production, such as in energy conversion in hydroelectric generation, supplying stability for liquid rocket fuel systems, and the condition monitoring of nuclear cooling reactors.Various vortices in the abovementioned mechanical-equipment flow channels often appear as complex spatial structures.The vortex flow phases are difficult to forecast because of generated physical phenomena such as multiphase coupling, material transfer, and fluid-structure coupling shock.The surface fluid or solid particles sucked by the vortex are a multiphase and multiphysics field coupling dynamics issue during the vortex formation process.Its intense gas-liquid-solid suction coupling effect can form energy-pulse and nonlinear shock vibration, which can be the cause of many adverse effects in the industrial production process [1][2][3].
In the above industrial process, the issue of vortex gas entrainment for a liquid rocket fuel system is a primary difficulty for safe manufacturing.Vortex gas cores formed by external disturbances can rapidly reduce a system's reliability, and a large number of bubbles can cause an unstable and costly combustion.The vortex generates a sequence of irregular pulsing pressures in the turbine unit of a tidal hydropower facility.These may result in increased pulsing stresses on the pipe connection mechanism, and the resulting shock vibration severely damages hydraulic equipment [4].Some interactions, such as the vortex and wave, can create intense disturbance responses and can damage the purity of molten steel in the steel flow refining process, resulting in industrial production accidents and economic losses [5][6][7].Therefore, it is vital to study the fluid-induced vibration detection technology of the multiphase sink vortex and to realize online detection and active control for its dynamic evolution process.
The above technical applications show that the vortex generation process is the primary cause of fluid-induced vibration, and a vibration distortion feature occurs in the critical transition stage.Vortex modeling and critical transition state detection are difficult to achieve due to the vortex's three-dimensional, unstable, turbulent, nonlinear, and spatiotemporal multiscale coupling as well as due to a lack of precise knowledge of its suction process [8,9].Meanwhile, the flow-control equipment that creates a vortex often includes various mechanical constraints such as pipes, screens, and valves, forming a complicated dynamic system with the flow channel.Due to the fluid, nonlinear excitation acting on the flow channel, the pipeline will have distinct vibration features that can be used to describe its functioning condition.However, in practical engineering applications, detection techniques are often exposed to extreme environmental disturbances such as high temperature (1400 • C), high pressure (15 MPa), and high-frequency shock disturbances (200 dB).As a result, video inputs from industrial monitoring systems make it impossible to observe vortex flow fields directly.The shock vibration caused by vortex energy may reduce the accuracy and service life of a vibration detection system, resulting in a low detection-success rate, poor real-time performance, and unstable operation.This has become a critical technical bottleneck for fluid-induced vibration detection systems.
Countries and institutions around the world, particularly in Western developed countries, have placed a high priority on tackling the issues mentioned above.In the late 1980s, Germany successfully developed vortex-detecting technology based on the electromagnetic induction theory.It has a broad range of applications in the continuous casting process, including steel flow detection [10].However, in the detecting process, this technology is vulnerable to a high-temperature environment, and it has drawbacks such as a short service life, inconvenient installation, and high maintenance costs.To address the above problems, other industrial fluid detection techniques, such as the ultrasonic detection method [11], infrared detection method [12], and vibration detection method [13], have been developed.The vibration detection technique has been extensively applied in the industrial fluid detection due to its benefits of high detection stability and accuracy.It has become one of the most important tools for increasing the detection success rate of flow-field states.This approach, however, must comply with stringent technical standards.The vibration detection sensor needs to have a high sensitivity, good anti-interference performance, and a long service life.The detection sensor may then be mounted in a suitable detecting location, and the vibration signal created by the fluid can be collected and sent to the industrial computer.To determine the liquid-state transition process, an appropriate signal-processing technique must be applied to the vibration signal.This technique is used to determine the state of molten steel.
In light of the method's exceptional performance, this paper describes the underlying concept of vortex-induced vibration detection technology and its research development.The most important scientific concerns are described and assessed, and current issues and research trends are forecasted.It can not only offer a useful theoretical reference for researchers working on multiphase vortex cross-scale modeling, vibration evolution mechanisms, and signal detection methods, but it also has promising application prospects in some industrial fields, such as those of energy-saving process, the vibration-optimization design of thin-walled shells, and the development of new emission energy systems.This paper is organized as follows.In Section 2, the basic principle of vortex state detection technology and the research status of vortex-induced vibration detection are introduced.Section 3 discusses the key technology for vortex-induced vibration detection.The research trend and prospects for this technology are detailed in Section 4. The conclusions are reported in Section 5.

Vortex State Detection Technology
As a fluid drains from a vessel with a drainage hole at the bottom, the accumulated turbulent energy causes the free surface to become unstable.It reaches a specific height and produces a free sink vortex [14,15].If the sink vortex extends to a gaseous vortex core, the flow field forms a gas-liquid two-phase suction flow.When suspended solids or other liquids are involved in the vortex core along the free surface, the flow field becomes a complex gas-liquid-solid or gas-liquid-liquid three-phase flow system.Many industrial operations, including metallurgy pouring, chemical extraction, and hydropower energy conversion, would be adversely affected by this process [16][17][18][19].Meanwhile, the related flow control equipment frequently uses closed and invisible limited physical space to meet the stable and dependable operating requirements.As a result, the real-time detection of flow field states is challenging.
A number of flow state detection technologies, including electromagnetic detection [20], infrared detection [20][21][22], ultrasonic detection [23], and vibration detection [24][25][26][27], have been developed to overcome the aforementioned issues.Figure 1 shows the essential functioning concepts: (1) The electromagnetic detection method works on the idea of installing a transmitting and receiving coil on the container's wall and using the different permeabilities of the fluid and solid to detect the flow status [28].This method, which has nothing to do with the nozzle valve opening, can see the amount of solid content in the fluid in real time.It has a high success rate and a quick response time, but it has various drawbacks in the detecting process, including a high price, a short service life, a complicated installation, and a high maintenance cost.(2) The infrared detection approach is based on pointing an infrared camera at a fluid and detecting it by comparing the thermal radiation properties of the fluid and the solid in the infrared frequency range [29].The technology collects and processes a real-time image of the draining process using a contactless infrared camera.Visualization, vividness, and excellent reliability are all advantages.Due to the high temperature and severe environment, the infrared detection system can only collect a limited number of visible signals at the equipment entrance and is only utilized as a backup to other detection methods.The detection is always delayed, and it can only be noticed when a particular quantity of solid is incorporated into the fluid, limiting the precision and dependability.(3) The ultrasonic detection technique works based on the difference in ultrasonic reflected signals between pure fluid and mixed fluid to determine the solid content in the drainage process [30].Like the infrared and electromagnetic methods, this approach is a posterior detection.It has various flaws, such as a low detecting accuracy and being damaged easily.(4) The concept of the vibration detection method is that when the nozzle pipe and the linked operational arm are subjected to fluid impact during the drainage process they will produce a specified range of vibrations.The flow is greater and the vibration is stronger when the nozzle opening is larger.Hence, the difference in fluid-induced vibration is employed [31][32][33].It belongs to the prior detection category and has the following benefits: long service life, high operating stability, cheap production cost, and simple installation and maintenance.
Scene experiments and related investigations revealed that the above detection technique might enable the online detection and active control of the vortex flow field to some extent.The following advantages are available: (1) improving the quality recovery rate of goods by lowering the critical formation height of the free sink vortex and lowering the residual fluid volume of flow control equipment; (2) the amount of suspended contaminants drawn by the sink vortex is minimized, which improves the purity of the lower fluid medium; (3) the vortex flow status may be monitored in real time, and the valve can be closed in time to prevent clogging; (4) fluid state sensing can regulate valve opening ahead of time, reducing the intensity of the pulsating load and reducing damage to flow control equipment; and (5) reducing suction contaminants can help to reduce equipment lining erosion and extend its service life.

Principle of Multiphase Vortex-Induced Vibration Detection Technology
While several detection methods have shown positive results, the chosen met should first fulfill the fundamental characteristics of high precision, good stability, ea maintenance, and extended equipment life.To prevent a multiphase vortex from form the detection technique must meet the multiphase vortex's necessary real-time detec criteria [34].Vibration detection based on a multiphase vortex has a greater chance o ing used in practice.It can meet the requirements for real-time detection in various in

Principle of Multiphase Vortex-Induced Vibration Detection Technology
While several detection methods have shown positive results, the chosen methods should first fulfill the fundamental characteristics of high precision, good stability, ease of maintenance, and extended equipment life.To prevent a multiphase vortex from forming, the detection technique must meet the multiphase vortex's necessary real-time detection criteria [34].Vibration detection based on a multiphase vortex has a greater chance of being used in practice.It can meet the requirements for real-time detection in various industrial operations [35,36].The mixed fluid creates different frequency shock vibrations on the container or pipe due to the varying density of the fluid coming out of the container or pipe [1].As a result, the real-time flow condition of the interior multiphase vortex may be indirectly determined based on the vibration intensity difference under fluid impact.
The basic principle of the vibration detection method is described in Figure 2, where the vibration sensor is installed on the pipeline or operation arm end away from the container and connected with the industrial computer by a special communication wire.The vibration sensor collects the real-time fluid-induced vibration signal and transmits it to the industrial computer.The computer then uses a signal processing method to identify fluid state transitions.The industrial system's control terminal emits a pulse signal when the content of suspended solids in the fluid reaches or exceeds a predefined threshold.The sliding orifice valve closes, and the draining process comes to a halt as a result of this signal.This detection approach has the benefit of being simple to set up, disassemble, and maintain.It has no impact on the industrial flow field's flow process.Furthermore, the vibration sensor can be placed outside of the flow field.In this method, the sensor consumable problem in high-temperature environments can be effectively handled, and the detection system's operating reliability and service life may be greatly enhanced.signal.This detection approach has the benefit of being simple to set up, disassemble, a maintain.It has no impact on the industrial flow field's flow process.Furthermore, vibration sensor can be placed outside of the flow field.In this method, the sensor c sumable problem in high-temperature environments can be effectively handled, and detection system's operating reliability and service life may be greatly enhanced.

Advances in the Multiphase Vortex-Induced Vibration Technology
Many researchers have selected the vibration detection approach to explore the v tex state detection procedure because of the above advantages.The vibration sensor w originally utilized to detect the occurrence of ladle whirling slag in a Kawasaki factory Japan in the early 1980s.The manufacturer discovered that the vortex pulled certain st slag impurities into the nozzle case.The vibration sensor's signal was altered dram cally, and its detection accuracy needed to be enhanced [2,37].The diverse applicat situations of infrared imaging and vibration detection technologies were described Chakraborty et al. [38].They suggested an image detection approach based on a C camera and discovered that the swirling slag might be spotted when the abrupt incre in light intensity surpasses a specified limit.However, because it is a post hoc detecti it cannot identify slagging in advance.Zhang et al. [39] developed a flow pattern learni based vibration signal processing approach and used a local target space alignm (LTSA) algorithm based on wavelet decomposition to analyze nonstationary vibrat data.This approach extracts the major kind of liquid steel and obtains the anomalo spectral energy distribution generated by a molten steel vortex and slag inclusion usin sliding time window and an incremental LTSA algorithm.They used the vibration signa a 60-ton ladle as an example to show that the approach can detect vortex and slag pheno ena.However, the detection effect is dependent on the sliding time window's paramete To identify the vortex state of steel flow, Tan et al. [40] suggested a simulated anne ing artificial neural network (SA-ANN) approach (Figure 3).The liquid steel vibrat signal is used as the target signal, and the time point of slag carry-over is determin based on the amplitude difference between molten steel and steel slag.The real detect accuracy of vortex slag can reach more than 96%.Chakraborty et al. [41] employed a C camera and image processing technology to detect the vortex suction process, and th highlighted the limits of this approach and the vibration detection method.They fou that the flow rate increased as the slag swirled, and that lots of solid slags had made th way into the lower equipment.While the vision-based detection approach can iden

Advances in the Multiphase Vortex-Induced Vibration Technology
Many researchers have selected the vibration detection approach to explore the vortex state detection procedure because of the above advantages.The vibration sensor was originally utilized to detect the occurrence of ladle whirling slag in a Kawasaki factory in Japan in the early 1980s.The manufacturer discovered that the vortex pulled certain steel slag impurities into the nozzle case.The vibration sensor's signal was altered dramatically, and its detection accuracy needed to be enhanced [2,37].The diverse application situations of infrared imaging and vibration detection technologies were described by Chakraborty et al. [38].They suggested an image detection approach based on a CCD camera and discovered that the swirling slag might be spotted when the abrupt increase in light intensity surpasses a specified limit.However, because it is a post hoc detection, it cannot identify slagging in advance.Zhang et al. [39] developed a flow pattern learningbased vibration signal processing approach and used a local target space alignment (LTSA) algorithm based on wavelet decomposition to analyze nonstationary vibration data.This approach extracts the major kind of liquid steel and obtains the anomalous spectral energy distribution generated by a molten steel vortex and slag inclusion using a sliding time window and an incremental LTSA algorithm.They used the vibration signal of a 60-ton ladle as an example to show that the approach can detect vortex and slag phenomena.However, the detection effect is dependent on the sliding time window's parameters.
To identify the vortex state of steel flow, Tan et al. [40] suggested a simulated annealing artificial neural network (SA-ANN) approach (Figure 3).The liquid steel vibration signal is used as the target signal, and the time point of slag carry-over is determined based on the amplitude difference between molten steel and steel slag.The real detection accuracy of vortex slag can reach more than 96%.Chakraborty et al. [41] employed a CCD camera and image processing technology to detect the vortex suction process, and they highlighted the limits of this approach and the vibration detection method.They found that the flow rate increased as the slag swirled, and that lots of solid slags had made their way into the lower equipment.While the vision-based detection approach can identify slag layer variation, its efficiency is limited by the computation of the cursor location with a fixed standard deviation, and detection accuracy must be increased.Tan et al. [42] suggested an improved nonlinear vibration identification technique based on a wavelet packet to determine the ladle pouring state in recent years, as illustrated in Figure 4a,b.The empirical mode decomposition endpoint continuation approach is used to reduce endpoint effects during the reconstruction fitting phase.Experiments reveal that the accuracy of slag identification in common casting states may reach more than 98 percent, providing a useful benchmark for recognizing the fluid condition of unseen vessels.Takács et al. [43] used a cumulative sum control graph to perform a real-time analysis of vibration acceleration data and implemented it in an integrated microcontroller.Experiments revealed that the system benefits from simplicity, low cost, mobility, and a lack of immersion.However, it can only detect a small quantity of steel slag change.Yenus et al. [44] analyzed the mechanism of the sensor monitoring position, the slag phase depth, and the vibration sound signal in the vortex detection process of continuous casting steel.The control technology of vibration acoustic signals is widely employed in vortex detection.It was found that noise sources could be solved, and irrelevant signals could be deleted using advanced analytic techniques.Tan et al. [42] suggested an improved nonlinear vibration identification technique based on a wavelet packet to determine the ladle pouring state in recent years, as illustrated in Figure 4a,b.The empirical mode decomposition endpoint continuation approach is used to reduce endpoint effects during the reconstruction fitting phase.Experiments reveal that the accuracy of slag identification in common casting states may reach more than 98 percent, providing a useful benchmark for recognizing the fluid condition of unseen vessels.Takács et al. [43] used a cumulative sum control graph to perform a real-time analysis of vibration acceleration data and implemented it in an integrated microcontroller.Experiments revealed that the system benefits from simplicity, low cost, mobility, and a lack of immersion.However, it can only detect a small quantity of steel slag change.Yenus et al. [44] analyzed the mechanism of the sensor monitoring position, the slag phase depth, and the vibration sound signal in the vortex detection process of continuous casting steel.The control technology of vibration acoustic signals is widely employed in vortex detection.It was found that noise sources could be solved, and irrelevant signals could be deleted using advanced analytic techniques.Tan et al. [42] suggested an improved nonlinear vibration identification techniq based on a wavelet packet to determine the ladle pouring state in recent years, as ill trated in Figure 4a,b.The empirical mode decomposition endpoint continuation approa is used to reduce endpoint effects during the reconstruction fitting phase.Experime reveal that the accuracy of slag identification in common casting states may reach mo than 98 percent, providing a useful benchmark for recognizing the fluid condition of u seen vessels.Takács et al. [43] used a cumulative sum control graph to perform a real-ti analysis of vibration acceleration data and implemented it in an integrated microcontr ler.Experiments revealed that the system benefits from simplicity, low cost, mobility, a a lack of immersion.However, it can only detect a small quantity of steel slag chan Yenus et al. [44] analyzed the mechanism of the sensor monitoring position, the slag pha depth, and the vibration sound signal in the vortex detection process of continuous casti steel.The control technology of vibration acoustic signals is widely employed in vor detection.It was found that noise sources could be solved, and irrelevant signals could deleted using advanced analytic techniques.Vortex-induced vibration detection technology offers several benefits in terms of investment cost, product quality, detection accuracy, and service life: (1) the vibration detection technique can assess and realize the previous vortex slag condition during the vortex generation process by using the amplitude difference of vibration signals; (2) the vibration sensor does not have to be installed inside the high-temperature flow control system; however, it can be located in a low-temperature region away from the industrial environment to ensure that the detection system's service life is reliably assured and has no negative influence on typical industrial productivity; (3) the vortex-induced vibration detection platform has a basic design, is simple to install and maintain, and does not require changes to existing industrial production equipment; and (4) the cost of producing the equipment is minimal, and it is simple to popularize.
While the vibration detection approach has had a lot of success, there are still a few issues that need to be addressed in real-world engineering applications: (1) When the sliding door is opened, the flow control equipment is set to low-flow, reducing the fluid level.Impurities cannot be recognized if a vortex does not develop.(2) The fluid impact force is restricted and susceptible to external noise influences, resulting in erroneous judgments by the fluid-induced vibration system.Its detection rate and consistency need to be improved.(3) A nonlinear pulse with unpredictability characterizes the fluid impact signal.Many experimental data and field practical experience must be used to identify the signal's characteristics.As a result, in order to satisfy the actual industrial applications, the detection software must spend a long time debugging to meet the premise of system identification real-time performance.The primary problem is a scarcity of comprehensive studies on the multiphase sink vortex's transport characteristics and fluid-induced vibration dynamics.Further investigation on how to solve the issues above is required.As a result, the technical theories for multiphase vortex-induced vibration detection technology should be further developed

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, Odgaard [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.Marcu 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.Tan 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.
Mazzaferro 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.Yang 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.As shown in Figure 5a, the oil and water distribution follows a precise pattern from the start of the vortex at the free surface through a continual downward extension, eventually attaining stability.Khoshkalam et al. [60] investigated the water draining from a tank to establish why an air-core vortex forms, obtaining the tangential vorticity contours for surface vortices at different intervals, as shown in Figure 5b, and discovered that angular momentum is essential to the formation of an air-core vortex.Tan et al. [56] used the Helmholtz equation to calculate the ideal critical conditions for vortex generation, as illustrated in Figure 5c.The axial disturbance velocity was discovered to have a significant impact on vortex formation, and its variation pattern is similar to that of z, with a monotonically growing connection.The magnitude of the axial disturbance velocity reaches its maximum when the vortex penetrates the pipe.The development of the Rankine vortex was studied by Xie et al. [61] using the enhanced interphase slip moment technique.Under the droplet slip effect, it was discovered that as droplet particles are introduced into the Rankine vortex, the Rankine vortex structure undergoes a sequence of alterations.
The critical condition of vortex suction occurs during the sink vortex generation process, resulting in concentrated energy release in the flow field.The formation and dissipation of a turbulent vortex cloud, which is fundamentally connected to fluid-induced vibration, exhibits nonlinear characteristics.Koria and Kanth demonstrated that the multiphase fluid medium was not synchronized while entering the drainage hole due to various physical features [62].The main issue with the procedure mentioned above is that the motion laws become nonlinear due to the viscous friction of the multiphase interface and the trans-scale asynchronous transport of the Ekman layer.
According to the above study, there is no mature theoretical model for the correct quantitative analysis of the vortex formation process and motion law.Still, the restricted local features may be derived only under specific ideal assumptions or combined with experimental research.In computational fluid engineering, flow features with accurate modeling of multiphase sink vortices appear to be a difficult task.Research on the vortex generation process focuses on ideal critical conditions, velocity distribution, the laminar flow state, and other factors.However, the formation mechanisms of multiphase flow under vortex turbulence and the associated dynamic features such as heat/mass transfer remain unknown and require additional research.
The Ekman boundary layer flow theory has been widely used in oceanography [63], meteorology [64], engineering fluid calculation [65,66] In the dual-pulse PIV system, Wei et al. [69] discovered that the fluid field is controlled by a reverse vortex driven by elastic forces, and inertial-driven local vortices are positioned at the corner between the bottom and the column wall.Youngwoo et al. [70] discovered that vortex diffusion improves the mass transfer rate between the flow zone and vortices as the flow Reynolds number rises.In Figure 6c,d, Park et al. [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.Yokoyama et al. [72] found that the vortex has an Ekman transport-ascending two-cell structure.Aravind 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.
Mazzaferro et al. [58] investigated the link between nozzle diameter, geomet shape, bottom tilt, and vortex formation in recent years.The nozzle diameter was show to significantly impact the vortex's critical submerged height.Moreover, other physi characteristics are directly related to the essential submerged height, and the volume p tion of the residual fluid may be lowered properly with a tilt of 25 degrees.Yang et al. [ used the volume of the fluid model to obtain the oil-gas-water three-phase eddy curr field, yielding the flow structure and evolution process of the free surface vortex.shown in Figure 5a, the oil and water distribution follows a precise pattern from the st of the vortex at the free surface through a continual downward extension, eventually taining stability.Khoshkalam et al. [60] investigated the water draining from a tank establish why an air-core vortex forms, obtaining the tangential vorticity contours for s face vortices at different intervals, as shown in Figure 5b, and discovered that angu momentum is essential to the formation of an air-core vortex.Tan et al. [56] used Helmholtz equation to calculate the ideal critical conditions for vortex generation, as lustrated in Figure 5c.The axial disturbance velocity was discovered to have a signific impact on vortex formation, and its variation pattern is similar to that of z, with a mon tonically growing connection.The magnitude of the axial disturbance velocity reaches maximum when the vortex penetrates the pipe.The development of the Rankine vor was studied by Xie et al. [61] using the enhanced interphase slip moment technique.U der the droplet slip effect, it was discovered that as droplet particles are introduced in the Rankine vortex, the Rankine vortex structure undergoes a sequence of alterations.In recent years, Tan 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].Kim 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 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.The introduction of the Ekman layer suction idea and the accompanying theoretical model analysis of sink vortices can give critical value in analyzing the physical factor interaction of the vortex flow.The multiphase vortex development model may be described in a more understandable mathematical form.A precise and reliable physical model can be developed for the numerical analysis of the sink vortex.As a result, more theoretical study on the multiphase vortex transport effect, cross-scale vortex coupling, boundary layer measurement, and other relevant dynamic features is required, in conjunction with the Ekman boundary layer theory.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.The introduction of the Ekman layer suction idea and the accompanying theoretical model analysis of sink vortices can give critical value in analyzing the physical factor interaction of the vortex flow.The multiphase vortex development model may be described in a more understandable mathematical form.A precise and reliable physical model can be developed for the numerical analysis of the sink vortex.As a result, more theoretical study on the multiphase vortex transport effect, cross-scale vortex coupling, boundary layer measurement, and other relevant dynamic features is required, in conjunction with the Ekman boundary layer theory.

Interface Dynamic Evolution of Vortex and Flow Pattern Tracking
The vortex interface shape and flow pattern evolution exhibit highly nonlinear characteristics during the sink vortex suction creation process due to the suction force change

Interface Dynamic Evolution of Vortex and Flow Pattern Tracking
The vortex interface shape and flow pattern evolution exhibit highly nonlinear characteristics during the sink vortex suction creation process due to the suction force change and the viscous friction of the interphase interface.The multidimensional parameters of the vortex core scale, vorticity distribution, and flow trajectory are challenging to characterize adequately.As a result, studying the vortex dynamics model is challenging because of the interface dynamic evolution of multiphase viscous coupling and the flow pattern tracing approach.CFD technology has greatly aided in understanding physical phenomena as science and technology have progressed.Computer discrete numerical simulation techniques, such as the labeled grid method [76,77], fluid volume method [78,79], and level set method [80,81], are used to simulate, track, locate, and even restore the sink vortex formation process, which can reveal the flow field's internal dynamic evolution law.
Tan et al. [82] used the level set method to track the interface evolution process of the two-phase vortex and obtained the energy shock phenomenon generated with coupling, as shown in Figure 9a; however, they discovered that the technique is insufficient to capture the broken features of the two-phase interface.In Figure 9b, Ann et al. [83] studied the vortex generation during the turbine operation of a tidal power plant using a simplified reservoir model and the SST-CC turbulence model.It was found that the two-phase vortex flow in the reservoir has a significant impact on the inlet flow, and the intense vorticity and air content produce pipeline flow inhomogeneity.The effect of the surface vortex on pipeline flow grows exponentially as the level drops or the water level differential rises.
Tan et al. [82] used the level set method to track the interface evolution process of two-phase vortex and obtained the energy shock phenomenon generated with coupl as shown in Figure 9a; however, they discovered that the technique is insufficient to c ture the broken features of the two-phase interface.In Figure 9b, Ann et al. [83] stud the vortex generation during the turbine operation of a tidal power plant using a sim fied reservoir model and the SST-CC turbulence model.It was found that the two-ph vortex flow in the reservoir has a significant impact on the inlet flow, and the inte vorticity and air content produce pipeline flow inhomogeneity.The effect of the surf vortex on pipeline flow grows exponentially as the level drops or the water level dif ential rises.In recent years, Son et al. [84,85] developed a numerical simulation of the vortex core phenomena using the finite volume approach and the fluid volume interface track method.They analyzed the dynamic evolution of the free interface and vortex interact process, as illustrated in Figure 10, and successfully reproduced three-dimensional f patterns, such as the spiral free surface waves of the ring Taylor vortex core.Tan et al. developed a turbulent dynamics model of a two-phase vortex using a volume of fl model and a piecewise linear interface reconstruction method, effectively simulated critical penetration process, and showed the evolution law of the gas-liquid interface.spite positive outcomes from related research, the free sink vortex is a typical two-ph or multiphase flow with more complex and random motion characteristics.Momentu mass, and energy transmission processes emerge from the interaction of the medium w various physical properties between the liquid surfaces of two phases [87].The interf thickness of two-phase fluids in a multiphase flow system is typically thin, measurin few molecules or thicker in diameter, and the interface between the two fluids is in In recent years, Son et al. [84,85] developed a numerical simulation of the vortex gas core phenomena using the finite volume approach and the fluid volume interface tracking method.They analyzed the dynamic evolution of the free interface and vortex interaction process, as illustrated in Figure 10, and successfully reproduced three-dimensional flow patterns, such as the spiral free surface waves of the ring Taylor vortex core.Tan et al. [86] developed a turbulent dynamics model of a two-phase vortex using a volume of fluid model and a piecewise linear interface reconstruction method, effectively simulated its critical penetration process, and showed the evolution law of the gas-liquid interface.Despite positive outcomes from related research, the free sink vortex is a typical two-phase or multiphase flow with more complex and random motion characteristics.Momentum, mass, and energy transmission processes emerge from the interaction of the medium with various physical properties between the liquid surfaces of two phases [87].The interface thickness of two-phase fluids in a multiphase flow system is typically thin, measuring a few molecules or thicker in diameter, and the interface between the two fluids is in the mixture of the two-state transition area.With a single medium, the density and concentration of the mixture change greatly, increasing the simulation difficulties.The interface dynamic evolution of the sink vortex, as shown in the literature, c centrates on the free surface development, distribution features of the flow field, a phase interaction law and is primarily concerned with the gas-liquid interface.The re tionship between the morphology of single-layer surfaces and vortex production is exa ined without considering surface tension.The microdynamics characteristics of gasuid interfaces break down during vortex suction and are difficult to capture using tra tional interface evolution modeling approaches.There are no publications on the visco coupling process's interface dynamic evolution of multilayer multiphase flow.As a res it is necessary to improve numerical simulation methods in real-world engineering ap cations, improve numerical calculation methods through experiments, improve the sim lation accuracy of two-phase or multiphase gas-liquid interfaces, and achieve an accur simulation of a multiphase sink vortex.Some relevant methods for studying the fluid medium of the vortex flow field w developed to detect the flow pattern of the free sink vortex.Zhao  The Euler-Euler and Euler-Lagrange techniques [91] are two types of particle fl methods.The fluid and particle phases are supposed to constitute an interpenetrat continuum in the former framework, with the Navier-Stokes equations describing pa cle motion.The method, however, lacks a theoretical basis since numerous changed eq tions are required to replicate the inconsistent qualities between particle and fluid f The interface dynamic evolution of the sink vortex, as shown in the literature, concentrates on the free surface development, distribution features of the flow field, and phase interaction law and is primarily concerned with the gas-liquid interface.The relationship between the morphology of single-layer surfaces and vortex production is examined without considering surface tension.The microdynamics characteristics of gas-liquid interfaces break down during vortex suction and are difficult to capture using traditional interface evolution modeling approaches.There are no publications on the viscous coupling process's interface dynamic evolution of multilayer multiphase flow.As a result, it is necessary to improve numerical simulation methods in real-world engineering applications, improve numerical calculation methods through experiments, improve the simulation accuracy of two-phase or multiphase gas-liquid interfaces, and achieve an accurate simulation of a multiphase sink vortex.Some relevant methods for studying the fluid medium of the vortex flow field were developed to detect the flow pattern of the free sink vortex.Zhao et al. studied the flow process of the two-phase sink vortex using a volume of fluid model and a Reynolds stress turbulence model and found that it is a type of Rankine vortex formed by the local accumulation of circumferential energy and that the flow field has two character regions, which are defined as the suction hole and extraction hole [88].Zhang et al. [89] used a large eddy simulation to undertake numerical investigations of turbulent vortex generation, combining the traditional Smagorinsky stress model with the Boltzmann technique and proposing a lattice Boltzmann approach.This approach was shown to obtain typical flow patterns in the vortex development process, confirming the involvement of the Coriolis force in sink vortex creation and revealing velocity distribution rules.Ruan et al. [90] used a multiphase mathematical model to study vortex formation and slag entrainment in tundishes, as illustrated in Figure 11a.The critical height of the vortex formation was greatly lowered by adjusting the position of the diversion hole on the dam near the outflow.
The Euler-Euler and Euler-Lagrange techniques [91] are two types of particle flow methods.The fluid and particle phases are supposed to constitute an interpenetrating continuum in the former framework, with the Navier-Stokes equations describing particle motion.The method, however, lacks a theoretical basis since numerous changed equations are required to replicate the inconsistent qualities between particle and fluid features.Wu et al. used the discrete vortex technique to investigate the liquid and solid action law in solid-liquid flow and found the critical characteristics of vortex evolution [92].Huang et al. [93] studied the flow track, physical properties, and vortex structure of solid particles in the vortex field and the flow mode of solid particles in the vortex field.Some aspects of the turbulent vortex aggregation and dissipation mechanisms, such as particle collision, rotation, sedimentation, and collision, frequently affect the vortex pumping process.As a result, the contact force between particles and fluids cannot be overlooked.The multiphase coupling tracking process, however, is difficult to handle with a single modeling technique.It cannot capture the flow state change process in real time, which is the critical state for detecting vortex-induced vibrations.As a result, more research into the flow pattern tracking law of multiphase coupling is required to precisely measure the vibration features and capture the vortex transition state.According to the literature, the real-time tracking technique of vortex flow pattern mostly analyzes the flow pattern evolution law of gas-liquid or solid-liquid two-pha flow fields, whereas the flow pattern tracking method of the gas-liquid-solid multipha coupling flow field is not ideal.In recent years, Li et al. [94] studied the dynamic law particle flow patterns and suggested a primary CFD-DEM coupled gas-liquid-solid vo tex transport modeling technique, as illustrated in Figure 11b,c.They found that the pa ticle flow pattern has complicated nonlinear turbulence characteristics.The gas-liquid solid three-phase coupling modeling method used in the preceding study presents a con cept for achieving the vortex flow field under high-speed turbulent conditions.As a resu the real-time tracking method of multiphase vortex flow patterns is investigated furth According to the literature, the real-time tracking technique of vortex flow patterns mostly analyzes the flow pattern evolution law of gas-liquid or solid-liquid two-phase flow fields, whereas the flow pattern tracking method of the gas-liquid-solid multiphase coupling flow field is not ideal.In recent years, Li et al. [94] studied the dynamic law of particle flow patterns and suggested a primary CFD-DEM coupled gas-liquid-solid vortex transport modeling technique, as illustrated in Figure 11b,c.They found that the particle flow pattern has complicated nonlinear turbulence characteristics.The gas-liquid-solid three-phase coupling modeling method used in the preceding study presents a concept for achieving the vortex flow field under high-speed turbulent conditions.As a result, the real-time tracking method of multiphase vortex flow patterns is investigated further in order to accurately track the flow pattern of the particle phase, reveal the flow pattern evolution law driven by various potential areas, such as thermal, pressure, and magnetic fields, and provide useful guidance for the active control of multiphase sink vortices.

Thin-Walled Shell Vibration Evolution Mechanism with Liquid-Solid Coupling
The equipment flow channel in real engineering applications generally has complicated mechanical boundary limitations, such as valves and screen mesh, as well as certain harsh condition restrictions, such as high-temperature, high-pressure, and high-frequency restrictions.It is difficult to correctly quantify the fluid random excitation force operating on the flow channel.Under liquid impact, the vibration response of the flow channel component is very nonlinear.The vibration characteristics of the nozzle case have a direct impact on the vibration detection result.As a result, studying the dynamic properties of shell components, such as the vibration response and natural frequency analysis, is critical.The characteristics of liquid-solid coupling vibration can be viewed as a driving force acted on the shell by a multiphase fluid coupling and exhibiting nonlinear characteristics as the driving force changes [95].
Fuller et al. studied the vibration characters of shell structures, obtaining the Flügge equations under fluid-solid coupling, modifying the radial displacement component of the equations with the hydrodynamic term, and proposing the energy expression of a shell vibration wave [96].Based on the above results, Fuller investigated the forced vibration of cylindrical shells under liquid-solid coupling using the combined Fourier transform and residue theorem to solve the forced displacement response of cylindrical shells.However, a detailed solution process was not provided [97].Xu et al. [98] investigated the energy flow propagation characteristics of liquid-filled cylindrical shells under forced vibration based on Fuller's study.The dynamic features of vibration waves with frequency were shown by the relative value of energy flow between fluid vibration waves in the shell.Li et al. [99] systematically studied the shell vibration energy flow with the wave propagation method, suggested a reasonably efficient numerical calculation method, and analyzed the natural frequencies and modes of shell vibration under various limitations.Bochkarev et al. [100] studied circular cylindrical shells partially filled with an ideal liquid and analyzed the influence of the fluid level in the shell on the critical values of external pressure with and without the consideration of gravitational effects on the fluid's free and lateral surfaces, as shown in Figure 12a.It was found that the gravitational field can significantly affect the dynamic characteristics of the structure.Munoz et al. [101] employed numerical methods to investigate the solid interaction between fluid elasticity and surface tension.This resulted in fewer spurious pressure oscillations at the fluid-solid interface.Romero et al. designed and validated a hybrid technique for studying liquid-solid coupling vibration in the frequency domain [102].Zheng et al. [103] used the wave propagation technique to investigate the vibration response of the cylindrical shell system using the Flügge shell theory and Helmholtz equation, as shown in Figure 12b, and found that the external excitation causes the shell stress to propagate as waves.In Figure 12c, Abdollahi et al. [104] explored the nonlinear dynamic characteristics of annular cylinders that were linked to determine the effective parameters on stability margins at various rotation speeds.As the circumferential wave number grew, it was discovered that an increase follows a decrease in natural frequencies.The rotation speed, rather than the mass ratio, is more sensitive to forward and backward frequencies.Zhang et al. [105] investigated the fluid-solid coupling process in a gas-liquid slug flow and discovered that the vibration peak value was higher in the intense slug flow.L. Li et al. [106] proposed a bidirectional coupling method to study vortex-induced vibration characteristics in recent years, adopted dynamic grid technology to solve the distortion problem induced by the vortex-induced vibration, and conducted a preliminary study on the vibration dynamics characteristics.Wang et al. [107] created a fluid transport cylindrical shell model and investigated the nonlinear vibration characteristics of the linked model using the Hamilton principle and von Karman geometric nonlinearity.To study the dynamic response of two-phase flow, Mohmmed et al. [108] used the unidirectional fluid-solid coupling model, as illustrated in Figure 13a,b, and found the two-phase flow mode and its maximum produced stress law.Keramat et al. [109] investigated the pressure signal of an oil pipeline with an axial stop and found that the stiffness and location of support had the greatest impact on the signal change law, as illustrated in Figure 13c,d.The nature of the structural boundary was discovered to modify the amplitude according to the system's inherent frequency.According to the aforementioned study, current research on thin-walled shell vib tion focuses mostly on natural frequency analysis, dispersion characteristics, and ener flow propagation law.The research on the liquid-solid coupling vibration response so tion method and the calculation example are not perfect.Previous research has focus on the liquid-filled tube shell with a single-phase flow as the fluid medium, avoiding complexities of nonlinear energy impact, multiphase coupling, pressure pulsation, a other physical phenomena.The intrinsic relationship between the above phenome caused by an unstable vortex and fluid-solid coupling vibration has not been thoroug investigated.The research by Fuller et al. on the vibration characteristics of liquid-so coupling systems in shells gives an important concept for this technology's research.Ev though a basic calculation notion for shell displacement was presented, no precise d placement response solution was offered, and the complicated boundary limitations w not considered.As a result, it is critical to perfect the propagation mechanism of sh fluid-induced vibration under the complex boundary constraint condition.

Water Model Experiment Platform for Vortex-Induced Vibration Detection
It is difficult to directly see and quantify the physical parameters associated with industrial process's flow field because of significant environmental disturbances, such a high temperature, a high pressure, and high-frequency noise.As a result, a simulat experiment platform should be created in accordance with the study objectives.Mu According to the aforementioned study, current research on thin-walled shell vibration focuses mostly on natural frequency analysis, dispersion characteristics, and energy flow propagation law.The research on the liquid-solid coupling vibration response solution method and the calculation example are not perfect.Previous research has focused on the liquid-filled tube shell with a single-phase flow as the fluid medium, avoiding the complexities of nonlinear energy impact, multiphase coupling, pressure pulsation, and other physical phenomena.The intrinsic relationship between the above phenomena caused by an unstable vortex and fluid-solid coupling vibration has not been thoroughly investigated.The research by Fuller et al. on the vibration characteristics of liquid-solid coupling systems in shells gives an important concept for this technology's research.Even though a basic calculation notion for shell displacement was presented, no precise displacement response solution was offered, and the complicated boundary limitations were not considered.As a result, it is critical to perfect the propagation mechanism of shell fluid-induced vibration under the complex boundary constraint condition.

Water Model Experiment Platform for Vortex-Induced Vibration Detection
It is difficult to directly see and quantify the physical parameters associated with the industrial process's flow field because of significant environmental disturbances, such as a high temperature, a high pressure, and high-frequency noise.As a result, a simulation experiment platform should be created in accordance with the study objectives.Multiphase vortex-induced vibration detection is based on this study.Due to water being easy to regulate and observe, research on sink vortices in industrial processes is primarily accom-plished using a water model experiment that has a low experimental cost [110,111].Because elements such as the initial disturbance, boundary feature, and operating state may readily change the flow characteristics of the vortex, experimental measurement cannot correctly characterize the flow mode of an industrial application.In most experiment research, the original model was abstracted from difficult conditions, such as a high temperature, a restricted space, and a hazardous environment.The experimental model was created using the scale and the principle of fluid similarity, and the particular physical quantity of the target object was measured.The geometric proportion and other physical parameter relationships between the water model and prototype were then calculated using the fluid criteria calculation rule [112].
Many types of experimental research on vortex motion have been conducted recently by academics.The free sink vortex's formation process, evolution mechanism, and affecting factors are statistically or qualitatively studied.Then, the critical submergence parameters, disturbance components, and free sink vortex flow patterns are investigated.Park et al. [71] conducted an experiment with rotating cylindrical liquid-filled storage tanks and analyzed the gaseous vortex core phenomenon using a speed control system, a diode laser, and a high-speed CCD camera.Li et al. [113] employed particle image velocimetry and flow visualization technologies to determine the vortex state and found that the critical submergence was discovered to be connected to the Froude number and the flume boundary effect, and the tangential velocity distribution was found to be comparable to the Rankine vortex.As illustrated in Figure 14a-d, Cristofano et al. [114] built an experimental device for a gas entrainment test section using cold water as the working fluid and determined the average velocity field for various Reynolds numbers and measurement planes.It was found that when the radial velocity approaches the outlet hole, it exhibits a potential behavior that is proportional to the average outlet velocity.As demonstrated in Figure 14e,f, Ezure et al. [115] used PIV measurement to observe the entrained argon phenomena in the sodium coolant design process.The quantitative link between the circulation, vertical velocity gradient, and core length was determined using the velocity distribution attribute, demonstrating that the evaluation approach based on the vortex model was an appropriate way to determine the gas ratio.As shown in Figure 15, Mulligan et al. [116] used planar laser-induced fluorescence technology to investigate the Taylor-Couette eddy system of a turbulent vortex.The instability phenomena comparable to the Taylor-Couette vortex were obtained under the centrifugal action of a wall-bounded free vortex, and several stability states of the free surface vortex core were validated by the Rayleigh stability criterion.
The experimental platform serves as the material carrier for the multiphase vortexinduced vibration detection system and serves as a vital research link [117,118].Because vortex generation is nonlinear, it is critical to conduct experimental observation and precise detection in order to develop related theories.At the moment, water-model experimental research focuses on determining the essential height of vortex formation, gas core development, and velocity distribution under steady input and exit circumstances.The established numerical model is optimized and changed with necessary simulation calculations.The water-model experiment platform, however, is relatively straightforward in design.Some complicated turbulent mechanical phenomena, such as the accurate quantitative analysis of a vortex core under high-speed vortex rotation, the multiphase flow transition pattern, and the turbulent cross-scale vortex growth, are unknown.The vibration detection of the multiphase vortex with a liquid-solid interaction study has to be improved.As a result, developing a multiphase vortex cross-scale vibration test platform is crucial for enhancing multiphase vortex-induced vibration detection technology.
was an appropriate way to determine the gas ratio.As shown in Figure 15, Mulligan et al. [116] used planar laser-induced fluorescence technology to investigate the Taylor-Couette eddy system of a turbulent vortex.The instability phenomena comparable to the Taylor-Couette vortex were obtained under the centrifugal action of a wall-bounded free vortex, and several stability states of the free surface vortex core were validated by the Rayleigh stability criterion.The experimental platform serves as the material carrier for the multiphase vortexinduced vibration detection system and serves as a vital research link [117,118].Because vortex generation is nonlinear, it is critical to conduct experimental observation and precise detection in order to develop related theories.At the moment, water-model experi-

Flow-Induced Vibration Signal Processing Algorithm
In the actual industrial field environment, the data capture of a vibration signal is subject to high-frequency interference in the field environment, and the data, after interference removal and signal separation processing, still contain a large number of irrelevant signals.The fluid-induced vibration signal has a low energy and a high-frequency distortion nonlinear vibration component linked to the vortex generation process's critical state transition.These interference factors bring great difficulties to the design of a distortion detection and recognition algorithm for vortex-induced vibration signals.As a result, simple or single signal identification methods (such as FFT, cepstrum, etc.) are insufficient to meet the requirements, and it is necessary to optimize and integrate fluid-induced vibration signals according to their characteristics in order to ensure system detection effectiveness [119].Li et al. [120] used the hidden Markov model to identify steel flow vibration signals and obtained beneficial results in field experiments.Tan et al. [121] adopted the discrete wavelet transform to detect the vibration signals in the casting process, which could identify the typical pouring state and achieved good results.In recent years, Li et al. [1] carried out a preliminary study on the fluid-solid coupling vibration characters of multiphase vortices and analyzed the distortion features of vibration signals with time spectrum and cepstrum.In the critical penetration condition, especially in large flows, the vibration signal contains a nonlinear pulse component due to multiphase coupling, which is represented in an apparent step growing and reducing that is characteristic of the vibration wave.The discrete wavelet transform method is used to identify the signal distortion feature; however, it has to be enhanced in terms of recognition stability and judgment reaction time.
The last link in the vortex-induced vibration detection technology is detecting and identifying vibration signals, which is directly connected to the efficacy of the vibration detection system.The information presented above is undoubtedly beneficial.However, the success of the vibration signal processing algorithm is primarily determined by an examination of the physical development of the multiphase vortex and the flow-induced vibration detection technique.The key concept will be to find a suitable signal processing technique to detect the critical transition stage of the multiphase vortex based on the relevant study results of the multiphase vortex formation mechanism and flow-induced vibration features.

Research Trends and Prospects
Flow-induced vibration detection technology of the multiphase vortex has played an increasingly important role in flow-field state identification and has received much attention.It is crucial for realizing energy-saving in-process manufacturing and for optimizing the design of low-carbon energy devices.The vital scientific challenges involved in multiphase vortex-induced vibration-sensing technologies are discussed in this paper.The research directions and opinions described and summarized below are discussed and summarized.It is worth noting that a free sink vortex is a complex turbulent mechanical phenomenon involving multiphase trans-scale transport, thermal/pressure/magnetic multiphysical field coupling, vorticity aggregation and dissipation, pressure pulsation, fluid-solid coupling shock, and other complex multiscale coupling phenomena.This current study focuses on analyzing the dynamic features of a gas-liquid two-phase vortex.However, the development process of multiphysical field coupling under extreme circumstances such as high temperature, high pressure, and intense radiation remains unknown.Related flow-field dynamics modeling approaches and fluid-induced vibration features in extreme settings have not been fully described for more complicated multi-gas-liquid-solid or gas-liquid-liquid multiphase flows.According to an overview of the fundamental challenges, this technological study may be carried out from the following perspectives: (1) An investigation of the transport mechanism of the multiphase sink vortex in extreme environments.A multiphase-temperature-pressure multifield coupling mechanical model of vortex trans-scale suction transport motion should be set up to analyze the distribution characteristics of temperature, pressure, and other physical quantities, taking into account the vortex distribution characteristics with high temperatures and high pressures.The heat/pressure coupling drive mechanism of the turbulent structure of the vortex flow field should then be investigated, with the heat transfer and the coupling transport processes described as related to various potential fields.
(2) To investigate the self-similar nesting features of vortex clusters in a turbulent environment, a transport mechanical model of the multiphase sink vortex based on the Ekman boundary-layer theory should be constructed.The dynamic features and trans-scale transport rule of the Ekman boundary layer may be shown, along with the cross-scale spatial and temporal distribution aspects of multiphase vortex clusters.Then, the highprecision image acquisition and processing technology of the vortex flow field should be studied to extract a high-speed continuous image-frame sequence of the vortex core, flow mode, and vorticity distribution attributes and to reveal the characteristics of energy aggregation and dissipation in the flow field.
(3) A modeling-solving approach for the multiphase coupling interface evolution process should be provided based on the fracture and deformation characteristics of the multiphase viscous coupling interface.A high-precision interface reconstruction of the vortex flow field should be created to derive the dynamic development of the multiphase viscous coupling interface shape in real time.
(4) A flow-pattern tracking dynamic model of the gas-liquid-solid vortex based on bidirectional coupling should be constructed to study the particle-particle and particle-wall contact effects, aiming at the rotational and nonlinear character of the gas-liquid-solid three-phase vortex in a critical transition state.It is possible to perform phase interface coupling calculations on a larger scale than the grid and discrete phase calculations on a subgrid scale.The evolution of flow patterns, such as particle distribution, rotation, and motion trajectory, may be found in the critical transition stage of the vortex flow field.
(5) Based on the theory of the bidirectional liquid-solid interaction and the principle of the vibration wave and flow-field coupling, a forced vibration model of the thin shell under a fluid-structure interaction with random uncertain excitation at two or more ends should be built to study the relationship between the forced-displacement character vector and the vibration wave property.It is possible to study the effects of hydraulic pressure and random excitation force on a system's natural mode, dispersion features, and energy flow propagation.The internal relationships between nonlinear energy shock, multiphase coupling, pressure pulsation, and fluid-solid coupling vibration need to be examined, along with the displacement response of a liquid-filled thin-walled shell under nonlinear fluid stimulation.
(6) Given the nonlinear transient distortion of vibration signals caused by vortex flow, the transient distortion features of vibration signals in the multiphase coupling process should be analyzed to construct the character parameter sequence of forced vibration under the impact of fluid-solid coupling.A multiphase vortex-induced vibration detection algorithm suitable for extreme working conditions should be proposed to achieve the online detection and recognition of liquid-filled shells and the coupling transition state under complex boundary conditions.

Conclusions
Fluid-induced vibration detection technology for the multiphase sink vortex has vital scientific research value and engineering application prospects for improving hydropower station energy conversion, emission reduction in the continuous casting process, and the stable supply of liquid rocket fuel systems.The electromagnetic technique, infrared test, ultrasonic test-flow field condition, and the basic concept of testing technology and its application features are all covered in this article.The benefits of these detecting technologies are summarized, including those of lowering the critical height of the vortex, improving product quality yield and the purity of the lower fluid medium, lowering the strength of the pulse load, reducing the damage caused by convection control equipment, and ensuring the equipment's service life.
Based on the difference in the intensity of impact vibration induced by the difference in density of the fluid medium, the vibration detection technique may indirectly acquire the real-time flow condition of a multiphase sink vortex.This technology has the advantages of being simple to install, disassemble, and maintain as well as having no effect on the flow process, thus increasing the detection system's reliability and service life.Furthermore, the challenges that the detection technique must overcome are listed, including low flow detection, restricted impact force, and intense nonlinearity.Also listed are the enhanced detection success rate and stability.
In vortex-state detection, vibration detection technique has several drawbacks, such as a poor identification rate and a long debugging time.We studied the related scientific issues and offer the following proposals: (1) The suction transport mechanism of the multiphase vortex in an extreme environment should be investigated.The heat/pressure coupled mechanism of the turbulent flow field should be explored to examine the coupling transport mechanism under different potential driving fields.(2) A transport mechanical model of the multiphase vortex based on the Ekman layer theory should be set up to investigate the self-similar nesting properties of the vortex, and the dynamic characters and cross-scale transport law of the Ekman boundary layer should be obtained.(3) With highprecision flow-field image acquisition and processing technology, the energy aggregation and dissipation of vortex clusters should be explored.Modeling and solving methods for the morphological evolution dynamic model of the multiphase coupling interface should be proposed to solve the problem of the high-precision interface with an intense shear attribute.After this, the dynamic evolution of the multiphase coupling interface can be investigated.(4) The gas-liquid-solid vortex's flow pattern tracking dynamics model should be investigated to analyze particle-particle and particle-wall contact effects.The flow pattern evolution law of the critical transition state should be studied.(5) Based on twoway solid-liquid coupling theory and the principle of vibration wave coupling, the forcedvibration model of the thin shell with the random uncertain excitation of two (multiple) ends should be investigated as well as the mechanism of hydrodynamic pressure and an excitation force on the system's natural characteristics.Then, the internal relationship between vortex formation and fluid-induced vibration can be investigated, as can the impact vibration of vortex formation and evolution.(6) A transient distortion-detection algorithm for multiphase vortex-induced vibration under extreme conditions should be further proposed to realize the online detection and recognition of a liquid-filled shell and the multiphase coupling transition state.

Figure 2 .
Figure 2. Basic principle of the vibration detection method.

Figure 2 .
Figure 2. Basic principle of the vibration detection method.
, and other domains as a key tool in fluid boundary layer study.The Coriolis force, pressure gradient force, and friction in the fluid boundary layer are all taken into account by Ekman's dynamic equilibrium boundary layer model.With a tiny vortex model, Lamont et al. [67] investigated viscous dissipative vortices.They found that low-energy vortices increased the mixing degree on the big vortex and boosted vortex mass transfer at various scales.Based on the Ekman layer hypothesis, Andersen et al. used a fluorescent fluid experiment to examine the Ekman layer upward flow zone at the bottom of a container.In Figure 6a,b, the dynamic evolution features of the Ekman layer were observed [68].

Figure 5 .Figure 5 . 27 Figure 6 .Figure 6 .
Figure 5. Flow features of the free surface vortex.(a) Fluid volume fraction and tangential veloc (Reprinted with permission from Ref. [56].2020, Elsevier.)(b) Tangential vorticity contours.Rep duced with the permission of Springer Nature.(Reprinted with permission from Ref. [59].20 Springer Nature.)(c) Axial disturbance velocity.Reproduced with the permission of Elsevier.( printed with permission from Ref. [60].2019, Springer Nature.) 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).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.Andersen, Park, and Yokoyama 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 6 .
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 core.(d) Progression of the vorticity distribution.Reproduced with the permission of Elsevier.(Reprinted with permission from Ref. [71].2011, Elsevier.)

Figure 7 .
Figure 7. Influence of temperature gradient on the transport process.(a) Flow field velocity.(b) Relative vorticity and Sherwood number.(c) Changes in relative vorticity.(d) Mass transfer distribution.Reproduced with the permission of Elsevier.(Reprinted with permission from Ref. [73].2017, Elsevier).

Figure 9 .
Figure 9. Interface evolution of a two-phase vortex.(a) Vortex evolution with different nozzle ameters.Reproduced with the permission of the General Iron and Steel Research Institute.printed with permission from Ref. [82].2017, Springer Nature.)(b) Vortex core, flow model, vorticity distribution of the flow field.Reproduced with the permission of Elsevier.printed/adaptedwith permission from Ref.[83].2017, Elsevier.)

Figure 9 .
Figure 9. Interface evolution of a two-phase vortex.(a) Vortex evolution with different nozzle diameters.Reproduced with the permission of the General Iron and Steel Research Institute.(Reprinted with permission from Ref. [82].2017, Springer Nature).(b) Vortex core, flow model, and vorticity distribution of the flow field.Reproduced with the permission of Elsevier.(Reprinted/adapted with permission from Ref. [83].2017, Elsevier).
l. Sci.2022, 12, x FOR PEER REVIEW 14 o mixture of the two-state transition area.With a single medium, the density and conc tration of the mixture change greatly, increasing the simulation difficulties.

Figure 10 .
Figure 10.Spiral Taylor vortex core and spiral surface waves.(a) Vorticity streamline distribut (Reprinted with permission from Ref. [84].2018, Springer Nature.)(b) Axial velocity of gas c surface.(Reprinted/adapted with permission from Ref. [85].2019, Springer Nature.) et al. studied the fl process of the two-phase sink vortex using a volume of fluid model and a Reynolds str turbulence model and found that it is a type of Rankine vortex formed by the local ac mulation of circumferential energy and that the flow field has two character regio which are defined as the suction hole and extraction hole [88].Zhang et al. [89] use large eddy simulation to undertake numerical investigations of turbulent vortex gene tion, combining the traditional Smagorinsky stress model with the Boltzmann techniq and proposing a lattice Boltzmann approach.This approach was shown to obtain typi flow patterns in the vortex development process, confirming the involvement of the C iolis force in sink vortex creation and revealing velocity distribution rules.Ruan et al. [ used a multiphase mathematical model to study vortex formation and slag entrainmen tundishes, as illustrated in Figure 11a.The critical height of the vortex formation was grea lowered by adjusting the position of the diversion hole on the dam near the outflow.
pl. Sci.2022,12,  x FOR PEERREVIEW  15 of    particles in the vortex field and the flow mode of solid particles in the vortex field.Som aspects of the turbulent vortex aggregation and dissipation mechanisms, such as partic collision, rotation, sedimentation, and collision, frequently affect the vortex pumping pr cess.As a result, the contact force between particles and fluids cannot be overlooked.Th multiphase coupling tracking process, however, is difficult to handle with a single mod eling technique.It cannot capture the flow state change process in real time, which is th critical state for detecting vortex-induced vibrations.As a result, more research into th flow pattern tracking law of multiphase coupling is required to precisely measure the v bration features and capture the vortex transition state.

Figure 11 .
Figure 11.Flow pattern tracking of multiphase vortex.(a) Typical flow patterns.Reproduced wi the permission of John Wiley and Sons.(Reprinted with permission from Ref. [90].2020, John Wile and Sons.)(b) Force acting on particles in the Ekman pumping process.(c) Kinetic energy acting o particles.(Reprinted with permission from Ref. [90,94].2020, Elsevier.)

Figure 11 .
Figure 11.Flow pattern tracking of multiphase vortex.(a) Typical flow patterns.Reproduced with the permission of John Wiley and Sons.(Reprinted with permission from Ref. [90].2020, John Wiley and Sons).(b) Force acting on particles in the Ekman pumping process.(c) Kinetic energy acting on particles.(Reprinted with permission from Refs.[90,94].2020, Elsevier).

Figure 12 .
Figure 12.Vibration characters of the fluid-solid-based thin-walled shell.(a) Dependencies of n ural frequencies and external pressures.(Reprinted with permission from Ref. [100].2012, Jo Wiley and Sons.)(b) Cylindrical shell model and its stress feature.(Reprinted with permission fro Ref. [103].2021, Elsevier.)(c) Frequency response of the cylindrical shell under excitation.Rep duced with the permission of Elsevier.(Reprinted with permission from Ref. [104].2022, Elsevie

Figure 12 .
Figure 12.Vibration characters of the fluid-solid-based thin-walled shell.(a) Dependencies of natural frequencies and external pressures.(Reprinted with permission from Ref. [100].2012, John Wiley and Sons).(b) Cylindrical shell model and its stress feature.(Reprinted with permission from Ref. [103].2021, Elsevier).(c) Frequency response of the cylindrical shell under excitation.Reproduced with the permission of Elsevier.(Reprinted with permission from Ref. [104].2022, Elsevier).

Figure 13 .
Figure 13.Vibration characters of the fluid-solid-based thin-walled shell.(a) Dependencies of n ural frequencies and external pressures.(b) Cylindrical shell model and its stress feature.(Reprin with permission from Ref. [108].2020, Elsevier.)(c) Pipe with complex constraints.(d) Freque response of the cylindrical shell under excitation.(Reprinted with permission from Ref. [109].20 Elsevier).

Figure 13 .
Figure 13.Vibration characters of the fluid-solid-based thin-walled shell.(a) Dependencies of natural frequencies and external pressures.(b) Cylindrical shell model and its stress feature.(Reprinted with permission from Ref. [108].2020, Elsevier).(c) Pipe with complex constraints.(d) Frequency response of the cylindrical shell under excitation.(Reprinted with permission from Ref. [109].2020, Elsevier).

Figure 14 . 27 Figure 14 .Figure 15 .
Figure 14.Flow characters of free sink vortex over time.(a) Experimental apparatus of gas entrainment.(b) Different development stages.(c) Normalized radial velocity of section P1.(d) Normalized radial velocity of stage S1.(Reprinted with permission from Ref. [114].2016, Elsevier).(e) Velocity distribution in the intermediate plane.(f) Relationship between the downward velocity gradient and the gas core length.(Reprinted with permission from Refs.[114,115].2019, Elsevier).