A numerical prediction method for the vibration response of a cantilevered deep-sea mining pipeline under outflow excitation

Abstract

The application relates to a numerical prediction method for the vibration response of a cantilever type deep sea mining pipeline under external flow excitation, and belongs to the technical field of pipeline lifting type mining. The application aims to solve the problem that a two-end hinged type marine riser model cannot effectively simulate the complex dynamic response of a cantilever type pipeline under real deep sea mining working conditions. The application is directed to a cantilever pipeline end with a concentrated mass block, and vibration control equations of the cantilever pipeline are respectively established in the transverse and flow directions; an external flow field excitation model in the transverse and flow directions is integrated into the vibration control equations; based on vector analysis theory, the cantilever pipeline structure and the external flow field are coupled to establish a numerical prediction model for the vibration of the cantilever pipeline under external flow excitation; and for the numerical prediction model for the vibration of the cantilever pipeline under external flow excitation, a central difference method and a backward difference method with second-order accuracy are used to expand the numerical solution of the coupled model, so that the numerical prediction of the vibration response of the cantilever type deep sea mining pipeline is realized.

Description

Technical Field

[0001] This invention belongs to the field of pipeline lifting mining technology, specifically relating to a numerical prediction method for vibration response of deep-sea mining pipelines. Background Technology

[0002] The ocean is not only a vital component of the global ecosystem but also contains vast resources upon which humanity's future development depends. Recent exploration findings further demonstrate that my country possesses abundant seabed mineral resources with immense development potential. Their efficient development and utilization hold long-term strategic value for safeguarding national resource security and promoting sustainable economic and social development, with extremely broad future prospects. However, these resources are often located thousands of meters deep on the seabed, and the harsh environmental conditions make the extraction process fraught with challenges. Therefore, developing deep-sea mining technology has become a crucial research direction in the field of marine engineering worldwide. Among these, the pipeline lift mining system, due to its structural integrity and high technological maturity, is widely considered internationally to be the most promising development model.

[0003] Pipeline lifting mining systems such as Figure 1 As shown, the vertical lifting pipe, with its high slenderness ratio, is the lifeblood of the entire mining system and also the most technically challenging and vulnerable link requiring breakthroughs. Ensuring that the vertical lifting pipe does not become unstable or vibrate significantly under the influence of external currents is one of the key issues urgently needing resolution in deep-sea mining system research. In actual deep-sea mining operations, the vertical lifting pipe is constantly exposed to external ocean currents. When the current flows around the pipe, it generates vortex shedding behind it. Periodic vortex shedding creates periodic hydrodynamic loads on the structure, inducing vortex-induced vibrations and leading to fatigue damage. If the vertical lifting pipe experiences fatigue fracture, it will not only directly cause the failure of a critical transport channel in the deep-sea mining system, resulting in operational interruptions and equipment damage, but may also trigger slurry leaks, potentially polluting the marine ecosystem.

[0004] Current research on the vortex-induced vibration response characteristics of pipelines under outflow excitation primarily focuses on traditional marine risers with hinged ends used for oil and gas transportation, neglecting the vibration response of cantilevered pipelines used for ore transportation with one end fixed and the other free in real marine environments. Furthermore, previous studies on the coupled vortex-induced vibration response characteristics of marine risers in the cross-current and downstream directions have largely simplified the fluid forces acting on the risers based on the assumption that "the vibration velocity of the marine riser is small compared to the flow velocity." However, in actual deep-sea mining operations, this simplification fails to fully reflect the coupled force characteristics and vibration response mechanisms of the marine riser in the cross-current and downstream directions. Therefore, to accurately assess the dynamic characteristics and vibration response laws of vertical lift pipelines under ocean currents, it is essential to establish a numerical prediction model that fully considers the complete coupling of forces and vibrations in the lateral and downstream directions of cantilevered marine risers, and to study the vibration response characteristics under outflow excitation based on this model. This research can provide important technical support for the preliminary engineering design of cantilever deep-sea vertical lifting pipelines and their safe operation during service.

[0005] Currently, there is a technological gap in numerical prediction of the vibration response of cantilevered riser pipelines used for ore transportation in deep-sea mining. Existing methods mostly rely on traditional models of articulated marine risers used for oil and gas transportation, which are difficult to effectively simulate the complex dynamic response of cantilevered pipelines under real deep-sea mining conditions. Furthermore, existing technologies do not perform a complete coupled analysis of the forces and structural vibration responses of real marine risers in both cross-current and downstream directions, making it even more difficult to simulate the complex dynamic response under real deep-sea mining conditions. Summary of the Invention

[0006] The present invention aims to solve the problem that the two-end articulated marine riser model is difficult to effectively simulate the complex dynamic response of cantilevered pipelines under real deep-sea mining conditions.

[0007] A numerical prediction method for the vibration response of a cantilevered deep-sea mining pipeline under outflow excitation includes the following steps: Step 1: For the coupled vortex-induced vibration model of the cantilever pipe with a concentrated mass block at the end, the cantilever vertical lifting pipe is regarded as an Euler-Bernoulli beam, and the vibration control equations of the cantilever pipe are established in the transverse and flow directions respectively. Step 2: Based on the wake oscillator model, establish external flow field excitation models in the transverse and flow directions, and integrate the external flow field excitation models in the transverse and flow directions into the vibration control equations of the cantilever pipe established in the transverse and flow directions, respectively; and based on vector analysis theory, couple the cantilever pipe structure and the external flow field to establish a numerical prediction model of cantilever pipe vibration under external flow excitation. Step 3: For the numerical prediction model of cantilever pipeline vibration under external excitation, the coupled model is numerically solved based on the central difference method and backward difference method with second-order accuracy to realize the numerical prediction of vibration response of cantilever deep-sea mining pipeline.

[0008] Furthermore, the vibration control equations for the cantilever pipe, established in the lateral and flow directions respectively, are as follows: (1) (2) In the formula, m The mass of the cantilever pipe vibration system per unit length, R s and R f These represent the structural damping coefficient and the fluid damping coefficient, respectively. The local Støhal vortex shedding frequency is calculated based on the Støhal relation. It is the viscosity coefficient; X , Y , Z They represent the pipes along X , Y , Z Displacement in the axial direction, T O represents time; O-XYZ represents the world coordinate system. Z Perpendicular to XOY flat; , For cantilever pipes X , Y The force acting along the axial direction, i.e., the fluid force; EI For bending stiffness; This indicates the partial derivative; For arbitrary coordinates Z Axial tension at the location.

[0009] Furthermore, the mass per unit length of the cantilever pipe vibration system m for: (3) In the formula, , as well as These are the density of the pipe material, the density of the fluid inside the pipe, and the density of the fluid outside the pipe, respectively. C M For additional quality coefficients; and These are the inner and outer diameters of the pipe.

[0010] Furthermore, arbitrary coordinates Z Axial tension at the point ,M b This represents the concentrated mass at the lower free boundary, where g is the acceleration due to gravity. L The length of the cantilever pipe; W r This indicates the wet weight per unit length of the structure.

[0011] Furthermore, the wet weight per unit length of the structure .

[0012] Furthermore, the external flow field excitation models in the transverse and flow directions, established based on the wake oscillator model, are as follows: (17) (18) in, The density of the fluid outside the pipe; The outer diameter of the pipe; C D0 and C L0 These represent the oscillating drag force coefficient and lift coefficient on a stationary pipe, respectively. p ( Z , T )as well as q ( Z , T ) respectively characterize the pipe at X as well as Y The motion state of the wake oscillator in the direction of the vortex shedding, that is, the oscillation state of the wake oscillator variable of the fluid force generated by the vortex shedding; U ( Z () indicates the incoming flow velocity along the pipe axis, i.e., the Z direction; , , For a dimensionless parameter related to velocity, T For time; This represents the average drag coefficient.

[0013] Furthermore, the numerical prediction model for the vibration of the cantilever pipe under the external excitation is as follows: (twenty three) (twenty four) (25) (26) in, As an intermediate variable to be converted into a dimensionless form, Based on reference flow rate U refThe calculated frequency of the Sturhart vortex emission; Based on The result obtained by dimensionless transformation , For based on , The result obtained by dimensionless conversion; , For based on , The result obtained by dimensionless conversion; ω f ( z () indicates different flow profiles; , , A x as well as A y These are empirical parameters. It is the viscosity coefficient; It is the mass ratio; , , , , For dimensionless parameters, , C D ( Z , T )as well as C L ( Z , T The figures () represent the average drag coefficient, the oscillating drag coefficient, and the lift coefficient, respectively. C D0 and C L0 These represent the oscillating drag force coefficient and lift coefficient on a stationary pipe, respectively. For Stochár numbers, EI For bending stiffness, m For the overall quality of the pipeline, This refers to axial tension.

[0014] Furthermore, flow profile ω f ( z )= U ( z ) / U ref , U ref For reference flow rate, U ( z ( ) represents the inflow velocity along the axial direction of the pipe. U ( Z )go through The result after conversion.

[0015] Preferably, the reference flow rate U ref The maximum flow velocity in the flow profile.

[0016] Furthermore, based on the central difference method and backward difference method with second-order accuracy, the process of numerically solving the coupled model includes: Assuming the dimensionless total length of the cantilever pipe is divided into: M Segment, after being discretized M +1 spatial point is represented as: z = z i , i =0, 1, 2, …, M ; Calculate the dimensionless total time t total Divided into N Segment, after being discretized N +1 time point is represented as: t = t j , j =0, 1, 2,.., N ; Assumption t n time z m The dimensionless parameter x corresponding to the location y , p and q Represented as , , and And then according to , , and The partial derivative terms in (23)-(26) are represented by second-order central difference, and at the same time, the terms are expressed as follows: and The partial derivative terms are expressed in a second-order backward difference scheme, then substituted into equations (23)-(26) and rearranged, and then the initial time... x , y , p , q Substitute to get t = t 1 time x , y , p , q The value; in t = tAfter time 2, combine the boundary conditions to... y and q The solution is obtained through repeated iterations. x , y , p as well as q .

[0017] Beneficial effects: The method of this invention enables rapid evaluation of the vibration response mechanical characteristics of cantilevered deep-sea mining pipelines under external excitation, effectively simulating the complex dynamic response of cantilevered pipelines under real deep-sea mining conditions, and providing key assurance for the long-term stable service of deep-sea mining pipelines. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of a pipeline lifting mining system.

[0019] Figure 2 This is a simplified diagram of the coupled lateral and directional vortex-induced vibration model of a cantilever pipe with a concentrated mass block at the end.

[0020] Figure 3 This is a schematic diagram of the forces acting on a vibrating cantilever pipe.

[0021] Figure 4 Phase diagrams of the cantilever pipe at different axial positions in the x-direction and Poincaré mappings at the end are shown for different velocities.

[0022] Figure 5 Phase diagrams of the cantilever pipe at different axial positions in the y-direction and Poincaré mapping at the end are shown for different speeds. Detailed Implementation

[0023] To address the issue that existing technologies do not provide a complete coupled analysis of the forces and structural vibration responses of real marine risers in both transverse and longitudinal directions, this method fully considers the complete mutual coupling of forces and vibrations in the transverse and longitudinal directions of cantilevered vertical lifting pipelines. A three-dimensional theoretical analysis and numerical prediction model for the vortex-induced vibration response of cantilevered vertical lifting pipelines is established. Based on this model, the characteristics of the vortex-induced vibration response of cantilevered vertical lifting pipelines under different flow velocities are systematically analyzed and discussed, effectively supporting the structural design and operational safety assessment of deep-sea mining pipeline systems. Specific implementation method one: This embodiment is a numerical prediction method for the vibration response of a cantilevered deep-sea mining pipeline under outflow excitation, mainly including the following steps: Step 1: Based on D'Alembert's principle, establish a three-dimensional theoretical analysis model for the vortex-induced vibration of a cantilever pipe that is coupled laterally and in the flow direction. For example Figure 2The coupled vortex-induced vibration model of the cantilever pipe with a concentrated mass block at its end is shown below. Treating the cantilevered vertical lifting pipe as an Euler-Bernoulli beam, the vibration control equations for the cantilever pipe are established in both the transverse and flow directions, as follows: (1) (2) In the formula, m The mass of the cantilever pipe vibration system per unit length, R s and R f Let represent the structural damping coefficient and the fluid damping coefficient, respectively. Here, we assume the structural damping coefficient is... R s When the value is 0, the fluid damping coefficient can be expressed as: , The local Støhal vortex shedding frequency calculated based on the Støhal relation. ,in St For Sturhart number, U ( Z () indicates along the axial direction of the pipe. Z (The velocity of the incoming flow in the direction of flow) The viscosity coefficient, , This represents the average drag coefficient. X , Y , Z They represent the pipes along X , Y , Z Displacement in the axial direction, T O represents time. O-XYZ is the world coordinate system. XOY The plane is sea level. Z Perpendicular to XOY flat; , For cantilever pipes X , Y The force acting along the axial direction, i.e., the fluid force; EI For bending stiffness; This indicates the partial derivative.

[0025] in m It consists of three parts: the mass of the pipe structure, the mass of the fluid inside the pipe, and the additional mass of the fluid outside the pipe, which can be expressed as: (3) In the formula, , as well as These are the density of the pipe material, the density of the fluid inside the pipe, and the density of the fluid (seawater) outside the pipe. C M To add a mass factor, for cylindrical pipes, C M 1.0 is acceptable; and These are the inner and outer diameters of the pipe; Any coordinate in equation (2) Z Axial tension at the point Q ( Z It can be written as: (4) In formula (4) M b This represents the concentrated mass at the lower free boundary, where g is the acceleration due to gravity. L The length of the cantilever pipe; W r The wet weight per unit length of the structure can be expressed as: (5) Step 2: Based on the wake oscillator model, establish external flow field excitation models in both the transverse and directional directions. Then, based on vector analysis theory, couple the cantilever pipe structure with the external flow field to establish a numerical prediction model for cantilever pipe vibration under external excitation. For a stationary pipe, the action on the pipe F X as well as F Y The directions are respectively related to the drag force F D and lift F L The directions are consistent. However, for oscillating pipes, the relative velocity between the structure and the fluid increases due to structural vibration. The direction is no longer along X The direction further leads to: F X Will no longer be with F D Consistent direction F Y Will no longer be with F L They are in the same direction.

[0026] like Figure 3 As shown, take the coordinates as Z The pipe cross-section at point [location] is assumed to have a vibration velocity of [value]. Its vector expression can be written as: (6) In equation (6), and They are respectively X , Y Unit vectors on the axis. For example... Figure 3 As shown, based on the incoming flow velocity and the vibration velocity of the pipeline itself The relative velocity between the pipe and the incoming flow can be obtained. , means as follows: (7) like Figure 3 As shown, the resultant hydrodynamic force per unit length of pipe at coordinate Z is... It consists of three parts: lift Average drag force and oscillating drag force , F X as well as F Y It can be represented as the resultant force of hydrodynamics. exist X and Y The projection onto the axis is as follows: (8) (9) In equations (8) and (9), the average drag force Direction of action and incoming flow velocity The directions coincide; while the oscillating drag force Direction of action and relative incoming flow velocity Since the directions coincide, and therefore, combining this with the formula for calculating the magnitude of the drag force, we can... as well as The vector expression is written as: (10) Combining the Rodrigues formula, the lift in equations (8) and (9) can be expressed as... Unit vectors in a direction are written as follows: (11) In equation (11), Let Z represent the unit vector in the Z direction. Based on equation (11) and combined with the expression for calculating the magnitude of lift, the lift can be... The vector expression is written as: (12) In equations (10) and (12), , C D ( Z ,T )as well as C L ( Z , T The figures () represent the average drag coefficient, the oscillating drag coefficient, and the lift coefficient, respectively. A value of 1.2 is usually acceptable. C D ( Z , T )and C L ( Z , T ) can be represented as: , ,in, C D0 and C L0 These represent the oscillating drag force coefficient and lift coefficient on a stationary pipe, respectively. C D0 and C L0 Typically, these values ​​can be taken as 0.2 and 0.3 respectively; p ( Z , T )as well as q ( Z , T ) respectively represent the position of the cylinder at X as well as Y The motion of the wake oscillator in the direction of the current. It should be noted that: p ( Z , T )and q ( Z , T It is not a traditional physical variable, but an intermediate variable describing the oscillating state of the fluid forces (lift / drag) generated by vortex shedding, namely the wake fluid variable, which is a dimensionless number.

[0027] Substituting equations (10) and (12) into equations (8) and (9), we obtain the coordinates as follows: Z A cylinder of unit length at X and Y The expression for the magnitude of the force in the direction is as follows: (13) (14) To further determine the relative magnitude of the incoming flow velocity Expressed as the magnitude of the incoming flow velocity U ( Z The relational expression introduces the following three dimensionless parameters related to velocity: (15) Substituting equation (15) into equation (7), we can further obtain the relative inflow velocity. The expression is as follows: (16) Substituting equation (16) into equations (13) and (14), and combining it with equation (15), we can obtain F X as well as F Y The expression for (i.e., the expression for fluid force) is as follows: (17) (18) Incorporate (17) and (18) into formulas (1) and (2) respectively.

[0028] The modified Van der Pohl equation is used to satisfy the nonlinear characteristics of the wake oscillator, and the expression is as follows: (19) (20) In equations (19) and (20) , , A X as well as A Y These are empirical parameters. A X = A Y =12; ; Convert equations (1), (19), (2) and (20) into dimensionless form, let: (twenty one) In equation (21), Based on reference flow rate U ref The calculated Sturhar vortex emission frequency, .

[0029] Substituting equation (21) into equation (15), we can obtain expressions for the two dimensionless parameters: (twenty two) Substituting the four equations in equation (21) into equations (1), (19), (2), and (20) respectively, we obtain the dimensionless equation: (twenty three) (twenty four) (25) (26) In equations (22)-(26), Based on The result obtained by dimensionless conversion; ω f ( z Different flow profiles can be represented as follows: ; , These are the empirical parameters in the Van der Pohl equation; here, U ref Maximum flow velocity in the flow profile U max Therefore, at the upper end of the pipe ω f ( z () = 1. Mass ratio μ and system dimensionless parameters , M D , c , b , M L It is expressed as follows: (27) in, This refers to axial tension.

[0030] In fact, from (17) and (18), we can obtain the two terms on the right side of formulas (1) and (2). At this time, all terms of formulas (1) and (2) can be expressed. After performing a series of dimensionless processing on formulas (1) and (2), we obtain formulas (23) and (25). At the same time, we make formulas (19) and (20) dimensionless to obtain formulas (24) and (26). Thus, by combining formulas (23) and (26), we obtain a complete set of equations. We then solve these four equations (23) and (26) using the finite difference method.

[0031] Step 3: Based on the central difference method and backward difference method with second-order accuracy, numerically solve the coupled model: The equations (23)-(26) are discretized in space and time using the second-order precision central difference pair, and the equation (22) is discretized using the second-order precision backward difference pair, and the solution is obtained iteratively.

[0032] Assuming the cantilever pipe has a dimensionless total length L / D Can be divided intoM Segment; Calculate the dimensionless total time t total Can be divided into N The segment. Therefore, the computational space step size is... ; Calculate the time step Discretized M +1 spatial point can be represented as: z = z i ( i =0, 1, 2, …, M Discretized N The +1 time point can be represented as: t = t j ( j =0, 1, 2,.., N For ease of representation, ). , Abbreviated as p , q ; Assumption t n time z m The dimensionless parameter x corresponding to the location y , p and q It can be represented as , , and Then, the second-order central difference scheme of each partial derivative term in equations (23)-(26) can be expressed as: (28) (29) (30) The second-order backward difference scheme of the partial derivative terms in equation (22) can be expressed as: (31) Substituting equations (28)-(31) into equations (23)-(26) and rearranging, we get: (32) (33) (34) (35) Assumption x and y initial conditions ( t =t 0) means that both displacement and velocity are 0, that is: ; p and q The initial condition is set to a wavelength with a small amplitude, and Combining equation (28), we get: (36) In this embodiment p and q The initial condition is set to 1*10 (-3) However, it should be noted that, according to the initial irrelevance verification, p and q As long as the amplitude is small, it will not have a significant impact on the simulation results.

[0033] Substituting equation (36) into equations (35), (34), (33), and (32) in turn, we obtain... t = t 1 time x , y , p as well as q The value is represented as follows: (37) The solution is thus obtained. t = t 0 with t 1 moment y as well as q The value of .

[0034] exist t = t Two hours later, y and q Solving this problem requires the use of boundary conditions. When n ≥ 2 and When, it can be solved directly through iteration (32)-(35), when n ≥ 2 and m When the values ​​are 0 or 1, a fixed boundary condition is required at the upper end of the pipe, with zero displacement and zero rotation, as shown below: (38) In the combined formula (29) , The expression yields: (39) when n ≥ 2 and m = M -1、 MAt this time, the lower end of the pipe needs to use free boundary conditions, and there is an attached mass of M b The lumped mass at the end can be simplified to a point mass, and its lower boundary condition can be written as: (40) The boundary conditions given in equation (40) can be written in dimensionless form as follows: (41) In equation (41) α、β All are dimensionless coefficients, represented as follows: (42) Substituting equation (29) into equation (41), we get: (43) Substituting equations (39) and (43) into equations (33) and (35), we can obtain as well as The value at the boundary of the cantilever pipe ( m = 0, 1,……, M - 1 and M Then, according to equations (32) and (34), we can obtain as well as The value, and so on, for x , y , p as well as q The solution is obtained through repeated iterations.

[0035] Step 4: Select design parameters and perform calculations and analyses on the cantilever pipe model based on the above analysis methods. The parameter values ​​during the analysis process are shown in Table 1. Table 1 Calculation parameters for the cantilever deep-sea mining pipeline model

[0036] To fully understand the vibration dynamic response characteristics of cantilever pipes caused by outflow, based on the numerical model proposed earlier, and selecting the design parameters in Table 1, we focused on discussing the cantilever pipes at different velocities. x , y Phase diagrams for the four axial positions and the Poincaré map corresponding to the end of the pipe. Figure 4 (in) a The data shows that when the flow velocity is 0.4 m / s, the cantilever pipe... xPhase diagrams at different axial positions and Poincaré mappings at the end: The phase diagrams at the 1 / 4, 1 / 2, 3 / 4 and end positions of the pipe all show compact and approximately elliptical closed trajectories with stable trajectory shapes and small amplitudes; the Poincaré mapping points at the end have low dispersion, mainly concentrated near a few isolated points, and exhibit overall chaotic vibration characteristics. Figure 4 (in) b The following gives the cantilever pipe at a flow velocity of 1.0 m / s. x Phase diagrams and end-poincaré maps at different axial positions: As the outflow velocity increases, the phase diagram expands significantly and exhibits a more complex multi-turn winding structure. The trajectory at the end position shows obvious trajectory diffusion, indicating that the system enters a strongly nonlinear vibration state after the energy input increases. The end-poincaré map becomes even more chaotic at this point, exhibiting strong nonlinear and chaotic characteristics overall. This phenomenon suggests that under high flow velocity conditions, the pipeline... x The dynamic behavior of the direction is highly unstable, and the uncertainty and fatigue risk brought about by strong nonlinearity and chaos must be considered in the design.

[0037] Figure 5 (in) a The data shows that when the flow velocity is 0.4 m / s, the cantilever pipe... y Phase diagrams and Poincaré mappings at different axial positions: The phase diagram trajectories at the four positions of the pipe all show a near-circular closed loop structure, indicating that the vibration is relatively stable and mainly controlled by a single dominant frequency; the Poincaré mapping at the end shows a highly concentrated cluster of isolated points, indicating that the structure is in a stable periodic vibration state. Figure 5 (in) b The following gives the cantilever pipe at a flow velocity of 1.0 m / s. y Phase diagrams and Poincaré mappings at different axial positions: As flow velocity increases, the trajectory shapes at other locations in the pipe become more regular and the vibration more stable. However, the phase diagram trajectory at the pipe end shows significant diffusion, with slight eccentricity and multiple overlapping loops. The trajectory shape becomes more irregular, and the Poincaré mapping at the end is more loosely distributed, exhibiting a quasi-periodic vibration state. Simultaneously, it can be observed that as flow velocity increases, the cantilever pipe… y The location with the greatest directional vibration energy has undergone a significant "migration": from the 3 / 4 length and end of the pipe at low flow rates to the 1 / 2 and 3 / 4 lengths at high flow rates.

[0038] By applying the above methods, it is possible to quickly assess the vibration response mechanical characteristics of cantilevered deep-sea mining pipelines under outflow excitation, providing a key guarantee for the long-term stable service of deep-sea mining pipelines.

[0039] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A numerical prediction method for the vibration response of a cantilevered deep-sea mining pipeline under outflow excitation, characterized in that: Includes the following steps: Step 1: For the coupled vortex-induced vibration model of the cantilever pipe with a concentrated mass block at the end, the cantilever vertical lifting pipe is regarded as an Euler-Bernoulli beam, and the vibration control equations of the cantilever pipe are established in the transverse and flow directions respectively. Step 2: Based on the wake oscillator model, establish external flow field excitation models in the transverse and flow directions, and integrate the external flow field excitation models in the transverse and flow directions into the vibration control equations of the cantilever pipe established in the transverse and flow directions, respectively; and based on vector analysis theory, couple the cantilever pipe structure and the external flow field to establish a numerical prediction model of cantilever pipe vibration under external flow excitation. Step 3: For the numerical prediction model of cantilever pipeline vibration under external excitation, the coupled model is numerically solved based on the central difference method and backward difference method with second-order accuracy to realize the numerical prediction of vibration response of cantilever deep-sea mining pipeline. The vibration control equations for the cantilever pipe established in the transverse and flow directions are as follows: ； In the formula, The mass of the cantilever pipe vibration system per unit length, These represent the structural damping coefficient and the fluid damping coefficient, respectively. The local Støhal vortex shedding frequency is calculated based on the Støhal relation. Viscosity coefficient; They represent the pipes along Displacement in the axial direction, For time; Using the world coordinate system, Perpendicular to flat; For cantilever pipes The force acting along the axial direction, i.e., the fluid force; EI For bending stiffness; This indicates the partial derivative; For arbitrary coordinates Z Axial tension at the location.

2. The numerical prediction method for vibration response of a cantilevered deep-sea mining pipeline under outflow excitation as described in claim 1, characterized in that: Mass per unit length of cantilever pipe vibration system m for: ; In the formula, These are the density of the pipe material, the density of the fluid inside the pipe, and the density of the fluid outside the pipe, respectively. C M For additional quality coefficients; and These are the inner and outer diameters of the pipe.

3. The numerical prediction method for vibration response of a cantilevered deep-sea mining pipeline under outflow excitation as described in claim 2, characterized in that: arbitrary coordinates Z Axial tension at the point , M b This represents the end-concentrated mass attached at the lower free boundary. It is the acceleration due to gravity. The length of the cantilever pipe; This indicates the wet weight per unit length of the structure.

4. The numerical prediction method for vibration response of a cantilevered deep-sea mining pipeline under outflow excitation as described in claim 3, characterized in that: wet weight per unit length of structure .

5. A numerical prediction method for the vibration response of a cantilevered deep-sea mining pipeline under outflow excitation according to any one of claims 1 to 4, characterized in that: The external flow field excitation models for the transverse and flow directions, established based on the wake oscillator model, are as follows: ； in, The density of the fluid outside the pipe; The outer diameter of the pipe; These represent the oscillating drag force coefficient and lift coefficient on a stationary pipe, respectively. Each characterizes the position of the pipeline. X as well as Y The motion state of the wake oscillator in the direction of vortex shedding, that is, the oscillation state of the wake oscillator variable of the fluid force generated by vortex shedding; U ( Z () indicates the incoming flow velocity along the pipe axis, i.e., the Z direction; , , Here, T is a dimensionless parameter related to velocity, and T is time. This represents the average drag coefficient.

6. The numerical prediction method for vibration response of a cantilevered deep-sea mining pipeline under outflow excitation as described in claim 5, characterized in that: The numerical prediction model for cantilever pipe vibration under external excitation is as follows: ； （26）； in, As an intermediate variable to be converted into a dimensionless form, Based on reference flow rate The calculated frequency of the Sturhart vortex emission; Based on The result obtained by dimensionless transformation For based on The result obtained by dimensionless conversion; For based on The result obtained by dimensionless conversion; Indicates different flow profiles; as well as These are empirical parameters. Viscosity coefficient; It is the mass ratio; , , , For dimensionless parameters, , as well as These represent the average drag coefficient, the oscillating drag coefficient, and the lift coefficient, respectively. C D0 and C L0 These represent the oscillating drag force coefficient and lift coefficient on a stationary pipe, respectively. For Stochár numbers, EI For bending stiffness, For the overall quality of the pipeline, This refers to axial tension.

7. The numerical prediction method for vibration response of a cantilevered deep-sea mining pipeline under outflow excitation as described in claim 6, characterized in that: Flow profile , U ref For reference flow rate, U ( z ( ) represents the inflow velocity along the axial direction of the pipe. The result after conversion.

8. The numerical prediction method for vibration response of a cantilevered deep-sea mining pipeline under outflow excitation as described in claim 7, characterized in that: Reference flow rate U ref The maximum flow velocity in the flow profile.

9. The numerical prediction method for vibration response of a cantilevered deep-sea mining pipeline under outflow excitation as described in claim 6, characterized in that: The process of numerically solving the coupled model based on the central difference method and backward difference method with second-order accuracy includes: Assuming the dimensionless total length of the cantilever pipe is divided into: M Segment, after being discretized M +1 spatial point is represented as: , ; Calculate the dimensionless total time t total Divided into N Segment, after being discretized N +1 time point is represented as: , ; Assumption time Dimensionless parameter corresponding to the location Represented as and And then according to and The partial derivative terms in (23)-(26) are represented by second-order central difference, and at the same time, the terms are expressed as follows: The partial derivative terms are expressed in a second-order backward difference scheme, then substituted into equations (23)-(26) and rearranged, and then the initial time... Substitute to get time The value; in After time, combine the boundary conditions to and The solution is obtained through repeated iterations. .

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