A method for constructing a vortex-induced vibration model for a submarine inclined pipeline conveying unsteady internal flow

Abstract

The present invention provides a method for constructing a vortex-induced vibration model for an inclined submarine pipeline conveying a non-constant internal flow. This method comprehensively considers the frictional coupling between the pipe wall and the fluid within the pipe, the coupling of the pipe body's axial and lateral vibrations, and the influence of the internal flow pressure. Based on Timoshenko beam theory, a set of nonlinear partial differential equations for submarine pipeline vibration under internal and external flow excitation is derived, taking into account the frictional coupling between the pipe wall and the internal flow, the axial and lateral vibration coupling of the pipe body, and the vibration response of the internal flow pressure to the pipeline. This system presents the response results of the axial and lateral vibration displacements and the internal flow pressure, thus solving the problem of constructing and mathematically deducing a vortex-induced vibration model for inclined pipelines conveying a non-constant internal flow.

Description

Technical Field

[0001] The present invention belongs to the technical fields of submarine pipelines, modeling and analysis, and particularly relates to a method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow. Background Art

[0002] With the rapid development of marine engineering technology, submarine water pipelines are gradually extending into deeper waters, resulting in an increase in the pipeline's aspect ratio and enhanced nonlinear response. Although these slender pipelines are more convenient for transportation, the highly coupled torsional, axial, and lateral flexibility can easily exacerbate vortex-induced vibrations in the pipeline's free-span sections. In particular, the flow of internal fluids significantly influences the dynamics of slender, flexible submarine pipelines. Compared with studies of steady internal flow, the dynamic response of submarine pipelines under unsteady internal flow excitation is greater.

[0003] However, due to the current vortex-induced vibration method of pipelines being very unclear about their dynamic interaction and mechanical transfer behavior, the load generated by the internal flow is only applied to the pipeline in the form of additional mass, while the coupling between the internal flow and the pipe wall and the influence of the fluid pressure in the pipe are ignored, and the non-steady internal flow-pipe wall dynamic coupling characteristics cannot be reflected. Summary of the Invention

[0004] To address the shortcomings and deficiencies of existing technologies, this paper comprehensively considers the friction coupling between the pipe wall and the fluid inside the pipe, the coupling of the pipe body's axial and lateral vibrations, and the influence of internal flow pressure. Based on Timoshenko beam theory, and taking into account the friction coupling between the pipe wall and the internal flow, the axial and lateral vibration coupling of the pipe body, and the vibration response of the internal flow pressure to the pipeline, a set of nonlinear partial differential equations for submarine pipeline vibration under internal and external flow excitation is derived. The equations present the response results of axial and lateral vibration displacements and internal flow pressure, thus solving the problem of constructing and mathematically deducing a vortex-induced vibration model for inclined pipelines conveying non-steady internal flow.

[0005] To this end, the present invention provides a method for constructing a vortex-induced vibration model for an inclined submarine pipeline conveying unsteady internal flow, comprising the following steps: improving a dual fluid-solid coupling system (ocean current-pipeline-internal flow) model that can effectively simulate unsteady internal flow and an inclined seabed, making assumptions about the new model; performing a force analysis on the new model, establishing motion equilibrium equations for the fluid and pipeline units within the pipeline, and deriving axial and lateral vibration equations; adding consideration of the internal flow fluid pressure to derive the momentum equations for the fluid within the pipeline; introducing a van der Pol wake oscillator model and an ocean hydrodynamic model to analyze the wake vortex effect in the new model; coupling the pipeline structure vibration equation, the internal flow momentum equation, and the wake vortex oscillator equation in the new model; applying boundary conditions at both ends of the pipeline to the new model; and dimensionlessly converting the improved coupled equations. The method of the present invention can derive a set of nonlinear partial differential equations for submarine pipeline vibration under internal and external flow excitation, taking into account the friction coupling between the pipe wall and the internal flow, the axial and lateral vibration coupling of the pipe body, and the vibration response of the internal flow pressure to the pipeline. The method is applicable to inclined pipelines and pipelines conveying unsteady flow.

[0006] The technical solution specifically adopted by the present invention to solve the technical problem is:

[0007] A method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow comprises the following steps:

[0008] S1. Establish an overall structural model of the pipeline system and make assumptions about the submarine pipeline, the fluid inside the pipeline, and the ocean current outside the pipeline;

[0009] S2. Introducing the microelement method to analyze the motion and force of the fluid and pipe microelement in the pipe, establishing the motion equilibrium equations of the fluid and pipe units in the pipe, analyzing the axial internal force T and shear force Q, and deriving the axial and lateral vibration equations of the submarine water pipeline structure;

[0010] S3. Considering the coupling mechanism of internal flow and pipe wall friction and the influence of internal flow pressure on the vibration of the pipeline system, the momentum equation of the fluid in the pipe is derived based on the motion equilibrium equation of the fluid and pipe unit, ignoring high-order traces;

[0011] S4. Introduce the wake oscillator model and the ocean current hydrodynamic model, introduce the dimensionless wake oscillator q, regard the interaction between the submarine pipeline structure and the vortex wake as a whole system, analyze the vortex effect in the wake, use the van der Pol oscillator with acceleration coupling term to simulate the drag and lift of ocean current fluctuations, analyze the coupled vortex-induced vibration between the outflow and the pipeline, simplify the alternating force exerted by the wake field on the pipeline, and obtain the external attached fluid force F x 、F z and the external fluid force F f formula;

[0012] S5, combine the pipeline axial vibration equation and pipeline lateral vibration equation obtained in S2, the internal flow axial momentum equation obtained in S3 and the van der Pol wake vortex oscillator equation obtained in S4, and substitute the external pipe attachment fluid force F obtained in S5 x 、F z and the external fluid force F f The formula is used to obtain the nonlinear differential equations for submarine pipeline vibration under the excitation of internal and external flows;

[0013] S6. Analyze the boundary conditions of submarine water pipelines when the boundary conditions are simply supported at both ends, fixedly supported at both ends, and fixedly supported at one end and simply supported at one end;

[0014] S7. By using the similarity criterion to compare the physical phenomena between different systems, the dimensionless form and dimensionless parameters of physical quantities are introduced, and a set of nonlinear dimensionless differential equations for submarine pipeline vibration under the excitation of internal and external flows is obtained.

[0015] Compared with the existing technology, the present invention and its preferred solution can derive a set of nonlinear partial differential equations for submarine pipeline vibration under internal and external flow excitation, taking into account the friction coupling between the pipe wall and the internal flow, the axial and lateral vibration coupling of the pipe body, and the vibration response of the internal flow pressure to the pipeline. It is also suitable for inclined pipes and pipelines conveying non-steady flows. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0017] Figure 1 It is a flow chart of a method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to an embodiment of the present invention.

[0018] Figure 2 It is a three-dimensional schematic diagram of the vortex-induced vibration model of the submarine water pipeline according to an embodiment of the present invention.

[0019] Figure 3 This is a force diagram of a fluid element according to an embodiment of the present invention.

[0020] Figure 4 This is a force diagram of a pipeline microelement according to an embodiment of the present invention.

[0021] Figure 5 This is a bifurcation diagram of the vibration displacement values ​​of a submarine pipeline conveying pulsating flow and steady flow according to an embodiment of the present invention. DETAILED DESCRIPTION

[0022] To make the features and advantages of this patent more clearly understood, the following embodiments are specifically described in detail as follows:

[0023] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by those skilled in the art to which this application belongs.

[0024] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0025] like Figure 1 As shown, an embodiment of the present invention provides a method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow, comprising the following steps:

[0026] S1. Construct the overall structural model of the pipeline system. The overall structure of the pipeline system is as follows: Figure 2 As shown in the figure, the central axis of the pipeline is set as the x-axis (the direction of axial displacement vibration), the direction of the ocean current is set as the y-axis, and the vertical direction of space is the z-axis (the direction of lateral vibration). A submarine pipeline with a length of L and two ends simply supported is laid obliquely on the seabed, and the horizontal inclination angle of the seabed is Bending stiffness is EI p , the lateral displacement of the pipe is w(x, t), the axial displacement is u(x, t), and the wake vortex vibration variable is q(x, t); the outer diameter of the pipe is D p , inner diameter is D i , the internal flow velocity is U i , the ocean current velocity is U e .

[0027] For the model and method proposed in this invention, the following assumptions are made about the submarine pipeline, the fluid inside the pipeline, and the ocean current outside the pipeline:

[0028] (1) The water in the pipe is incompressible, and the flow velocity is constant across the cross section of the pipe and does not vary along its length;

[0029] (2) The pipe wall material is linear, uniform and isotropic;

[0030] (3) For submarine pipelines with large aspect ratios, the pipe deformation is considered as a Timoshenko beam model;

[0031] (4) Pipeline axial vibration and lateral vibration are considered, but cross-section rotation is not considered.

[0032] S2. Establish the motion balance equations of the fluid in the pipe and the pipe unit, such as Figure 3 and Figure 4As shown in the figure, the micro-element method is used to take a control volume micro-segment of length dx from the pipeline system and separate the pipeline unit body and the internal flow unit body. T is the axial internal force of the pipeline unit body, Q is the cross-sectional shear force, M is the cross-sectional bending moment, and A i is the internal flow cross-sectional area, p i A i is the internal flow pressure, γS is the tangential friction between the pipe wall and the internal flow, N is the normal force between the pipe and the internal flow, F x 、F z is the ocean current hydrodynamic force in the x and z directions caused by wake dynamics, m i is the mass of the internal flow fluid per unit length, m p is the mass of the pipe per unit length, g is the acceleration due to gravity, θ is the angle between the tangent direction of the neutral axis of the unit body and the x-axis, is the horizontal inclination of the seabed.

[0033] Decompose the force of the unit body into the x-direction and z-direction to establish the equilibrium equation. The motion equation of the fluid unit in the tube is:

[0034] Axial:

[0035] Horizontal:

[0036] Where, γS=(f s / 2D i )m i U i |U i |,f s is the Darcy-Weisbach friction coefficient.

[0037] The acceleration of the unsteady flow in the tube in the x and z directions is:

[0038] Axial:

[0039] Horizontal:

[0040] The equation of motion of the pipeline unit is:

[0041] Axial:

[0042] Horizontal:

[0043] Where, the pipeline structure damping c s =2ζ(m p +m i +m a )ω n, ωn is the natural frequency of the pipeline, ζ is the structural damping coefficient; the additional mass per unit length of the pipeline m a =πC a ρ e D p 2 / 4,C a is the additional mass coefficient, which is usually taken as 1 for cylindrical structures.

[0044] When the pipe undergoes a small deformation, cosθ≈1-w′ 2 / 2, sinθ≈w′-u′w′-w′ 3 / 2. The axial internal force T consists of two parts: the initial axial tension T0 of the pipeline and the additional axial internal force generated by the pulsating strain ε.

[0045] The axial internal force T of the pipeline is:

[0046] T=T0+EA p ε (7)

[0047]

[0048] The shear force Q is expressed as:

[0049] Q=-EI p w″′ (9)

[0050] Where, E is the elastic modulus of the pipe; I p is the moment of inertia of the pipe section.

[0051] Substituting Equations (7) to (9) into Equations (5) and (6), and combining Equations (1) to (4), eliminating the forces N and γS between the tube wall and the fluid, and ignoring the high-order micro-arrangements above the second power, the axial and lateral vibration equations are derived as follows: Axial: Horizontal:

[0052] Where: m = m i +m p The partial differential terms in the system of equations represents inertial force; Damping force; Coriolis force representing internal flow; EI p w″″ represents the elastic restoring force; m i U i 2 w″, centrifugal force of internal flow; p i A i w″ represents the internal flow pressure that is added into consideration; Represents the longitudinal resistance of unsteady internal flow, etc.

[0053] That is, Equations (10) and (11) are the axial and lateral vibration equations of the submarine water pipeline structure.

[0054] S3. Derive the momentum equation of the fluid in the pipe. Unlike conventional submarine pipeline vortex-induced vibration models, the method of the present invention considers the coupling mechanism of internal flow and pipe wall friction and the influence of internal flow pressure on pipeline system vibration.

[0055] Substituting Equations (3) and (4) into Equations (1) and (2), eliminating N and γS, and ignoring higher-order traces, we can further obtain the axial momentum equation for the flow in the submarine pipeline:

[0056]

[0057] S4. Introduce the wake oscillator model. The vortex shedding in the wake is like an oscillator. The drag and lift of ocean current fluctuations can be simulated using a van der Pol oscillator with acceleration coupling. By introducing the wake variable, the interaction between the submarine pipeline structure and the vortex shedding wake is analyzed as a whole system. The model has a clear physical meaning and requires fewer empirical parameters. The numerical prediction results are close to the wake vortex characteristics in actual conditions. The van der Pol wake oscillator model is as follows:

[0058]

[0059] Where ε and Λ are empirical coefficients, which can be adjusted by model calibration and experimental results and are taken as 0.3 and 12; q is the dimensionless wake oscillator, Ω f is the vortex shedding angular frequency, and its expressions are:

[0060]

[0061]

[0062] Where C L is the instantaneous vortex lift coefficient, Re<10 4 It is stable between 0.4 and 0.6, 10 4 <Re<10 8 gradually increases; C L0 is the vortex lift coefficient when the structure is stationary; St is the Strouhal number, which is closely related to the Reynolds number. <Re<2×10 5 In the subcritical region, the St value is relatively stable, about 0.2.

[0063] The ocean current hydrodynamic model is introduced. When external ocean currents pass through a submarine pipeline, vortices alternately shed along the pipeline surface, generating pulsating pressure. The outer wall of the pipeline deforms under stress, exerting a reaction force on the vortices, thereby forming coupled vortex-induced vibrations between the external current and the pipeline.

[0064] The ocean current hydrodynamic model is introduced to simplify the alternating force exerted by the wake field on the pipeline, that is, the external fluid force F x 、F z for:

[0065] F x =0 (16)

[0066]

[0067] External fluid force F f Including: ocean current additional damping force, ocean current additional mass force and lift:

[0068]

[0069] Where p o is the hydrostatic pressure at both ends of the pipeline; the additional damping of the ocean current c f =C D ρ e D p U e / 2;C D is the drag coefficient, which is usually 1.2 for water depths of 0 to 150 m and 0.7 for water depths greater than 150 m. The lift F generated by the ocean current flowing through the pipeline L =C L0 ρ e U e 2 D p q / 4,ρ e is the density of the ocean current fluid.

[0070] S5. By coupling the vibration equation, momentum equation, and wake vortex oscillator equation, that is, combining Equations (10) to (13) and (8) to (18), we can obtain the nonlinear differential equations for submarine pipeline vibration under internal and external flow excitation:

[0071] Pipe axial vibration equation:

[0072]

[0073] Pipe lateral vibration equation:

[0074]

[0075] Van der Pol wake vortex oscillator equation:

[0076]

[0077] The axial momentum equation of the internal flow is:

[0078]

[0079] From equations (19) to (22), it can be seen that the axial displacement u, lateral displacement w, ocean current wake oscillator q, and internal flow pressure p i A i , the four variables are fully coupled. Therefore, once the fluid velocity U in the tube is determined i , the four physical quantities can be solved jointly. Equations (19) and (20) reflect the coupling of the axial and lateral vibrations of the pipeline system; Equation (21) reflects the coupling between the pipeline structure and the ocean current; and Equation (22) reflects the coupling between the internal flow pressure fluctuations and the internal flow motion caused by the internal flow pulsation. This model includes the coupling of friction coupling and pipe vibration deformation and is applicable to inclined pipes and pipelines conveying unsteady flows.

[0080] S6. Analyze the boundary conditions of the equation group when the boundary conditions of the submarine water pipeline are different.

[0081] When the boundary conditions of the submarine water pipeline are simply supported at both ends, we have:

[0082] w(0,t)=w(L,t)=w″(0,t)=w″(L,t)=0 (23)

[0083] u(0,t)=u(L,t)=u″(0,t)=u″(L,t)=0 (24)

[0084] q(0,t)=q(L,t)=q″(0,t)=q″(L,t)=0 (25)

[0085] For a submarine water pipeline with fixed supports at both ends, the boundary conditions are:

[0086] w(0,t)=w(L,t)=w′(0,t)=w′(L,t)=0 (26)

[0087] u(0,t)=u(L,t)=u′(0,t)=u′(L,t)=0 (27)

[0088] q(0,t)=q(L,t)=q′(0,t)=q′(L,t)=0 (28)

[0089] For a submarine water pipeline with one end fixed and the other simply supported, the boundary conditions are:

[0090] w(0,t)=w(L,t)=w′(0,t)=w″(L,t)=0 (29)

[0091] u(0,t)=u(L,t)=u′(0,t)=u″(L,t)=0 (30)

[0092] q(0,t)=q(L,t)=q′(0,t)=q″(L,t)=0 (31)

[0093] S7. Use similarity criteria to compare physical phenomena between different systems so as to apply them to the qualitative analysis of actual submarine water pipeline engineering problems. Introduce the dimensionless forms and dimensionless parameters of the following physical quantities:

[0094]

[0095] Substituting formula (32) into formulas (19) to (22), the dimensionless equations for pipeline vibration are:

[0096] Pipe axial vibration equation:

[0097]

[0098] Pipe lateral vibration equation:

[0099]

[0100] Van der Pol wake vortex oscillator equation:

[0101]

[0102] The axial momentum equation of the internal flow is:

[0103]

[0104] To simulate the phenomenon of non-constant internal flow pulsation in submarine pipelines caused by compressors or pumps, it is assumed that the periodic pulsation of the flow velocity in the pipeline is as follows:

[0105] U i =U i0 (1+μcosωt) (37)

[0106] Where ω represents the internal flow pulsation frequency, μ represents the internal flow pulsation amplitude, and U i0 is the pulsating average flow velocity.

[0107] In a specific application example of the present invention, a 100-meter-long APIX65-grade steel pipeline system is used as an example. The specific parameter 1, whose aspect ratio is 307.69, can better reflect the modal characteristics of the vortex-induced vibration of the submarine pipeline with a large aspect ratio.

[0108] Table 1 Numerical example parameters

[0109] parameter Numerical parameter Numerical Pipe length L / m 100 <![CDATA[Initial lift coefficient C L0 > 0.3 <![CDATA[Outer diameter D ap / m]]> 0.325 <![CDATA[Drag coefficient C D > 1.2 <![CDATA[Inner diameter D i / m]]> 0.305 <![CDATA[Added mass coefficient C a > 1 Young's modulus E / (Gpa) 210 Seabed inclination angle α 0° <![CDATA[Pipe density ρ p / (kg / m 3 )]]> 7850 Strouhal number 0.2 <![CDATA[Seawater density ρ e / (kg / m 3 )]]> 1025 Vortex-induced vibration coupling coefficient Λ 12 <![CDATA[Inward flow density ρ i / (kg / m 3 )]]> 1000 Vortex-induced vibration coupling coefficient ε 0.3 <![CDATA[Aspect ratio L / D p > 307.69 <![CDATA[Mass ratio β = m i / (m i +m p )]]> 0.4584 <![CDATA[Axial tension T0 / N]]> 0 Pipeline structure damping 0.005

[0110] Figure 5The bifurcation diagram of the transverse vibration displacement value at x = L / 2 of the submarine pipeline conveying pulsating flow and steady flow is given. The gray hollow circle represents the average internal flow velocity U i0 = 2.0, pulsation frequency ω = 10, pulsation amplitude μ = 0, the black hollow circle represents the internal flow velocity U i0 =2.0, pulsation frequency ω = 0, and pulsation amplitude μ = 0. Overall, the bifurcation diagram of the pipeline system when conveying pulsating flow differs significantly from that when conveying steady flow. This inventive method further demonstrates that the flow of internal fluid significantly influences the dynamics of slender, flexible submarine pipelines. Compared to steady internal flow, the dynamic response of submarine pipelines under the excitation of unsteady internal flow is greater. Furthermore, the resulting equations accurately describe the vibration and mechanical characteristics of a vortex-induced vibration model of an inclined submarine pipeline conveying unsteady internal flow.

[0111] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0112] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0113] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0114] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0115] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other manner. Any person skilled in the art may utilize the above-disclosed technical content to modify or modify the present invention into equivalent embodiments. However, any simple modifications, equivalent variations, and modifications to the above embodiments that do not depart from the technical content of the present invention and are based on the technical essence of the present invention remain within the scope of protection of the present invention.

[0116] This patent is not limited to the above-mentioned optimal implementation method. Anyone can derive various other forms of methods for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying non-constant internal flow under the inspiration of this patent. All equal changes and modifications made within the scope of the patent application of this invention should be covered by this patent.

Claims

1. A method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow, characterized in that: The following steps are involved: S1. Establish an overall structural model of the pipeline system and make assumptions about the submarine pipeline, the fluid inside the pipeline, and the ocean current outside the pipeline; S2. Introducing the microelement method to analyze the motion and force of the fluid and pipe microelement in the pipe, establishing the motion equilibrium equations of the fluid and pipe units in the pipe, analyzing the axial internal force T and shear force Q, and deriving the axial and lateral vibration equations of the submarine water pipeline structure; S3. Considering the coupling mechanism of internal flow and pipe wall friction and the influence of internal flow pressure on the vibration of the pipeline system, the momentum equation of the fluid in the pipe is derived based on the motion equilibrium equation of the fluid and pipe unit, ignoring high-order traces; S4. Introduce the wake oscillator model and the ocean current hydrodynamic model, introduce the dimensionless wake oscillator q, regard the interaction between the submarine pipeline structure and the vortex wake as a whole system, analyze the vortex effect in the wake, use the van der Pol oscillator with acceleration coupling term to simulate the drag and lift of ocean current fluctuations, analyze the coupled vortex-induced vibration between the outflow and the pipeline, simplify the alternating force exerted by the wake field on the pipeline, and obtain the external attached fluid force F x 、F z and the external fluid force F f formula; S5, combine the pipeline axial vibration equation and pipeline lateral vibration equation obtained in S2, the internal flow axial momentum equation obtained in S3 and the van der Pol wake vortex oscillator equation obtained in S4, and substitute the external pipe attachment fluid force F obtained in S4 x 、F z and the external fluid force F f The vibration equation, momentum equation and wake vortex oscillator equation are coupled to obtain the nonlinear differential equations for submarine pipeline vibration under internal and external flow excitation: In the nonlinear differential equations of submarine pipeline vibration, the axial displacement u, the lateral displacement w, the ocean current wake oscillator q, the internal flow pressure p i A i The four variables are fully coupled; by determining the fluid velocity U in the tube i , so that the four physical quantities are obtained by simultaneous solution; the pipeline axial vibration equation and the pipeline lateral vibration equation are used to reflect the coupling between the axial and lateral vibrations of the pipeline system; the van der Pol wake vortex oscillator equation is used to reflect the coupling between the pipeline structure and the ocean current; the internal flow axial momentum equation is used to reflect the coupling between the internal flow pressure fluctuation caused by the internal flow pulsation and the internal flow motion; S6. Analyze the boundary conditions of submarine water pipelines when the boundary conditions are simply supported at both ends, fixedly supported at both ends, and fixedly supported at one end and simply supported at one end; S7. By using the similarity criterion to compare the physical phenomena between different systems, the dimensionless form and dimensionless parameters of physical quantities are introduced, and a set of nonlinear dimensionless differential equations for submarine pipeline vibration under the excitation of internal and external flows is obtained.

2. The method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to claim 1, characterized in that: In step S1, the central axis of the pipeline is set as the x-axis to represent the direction of axial displacement vibration, the direction of ocean current is set as the y-axis, and the vertical direction of space is set as the z-axis to represent the direction of lateral vibration; a simply supported submarine pipeline with a length of L at both ends is laid obliquely on the seabed, and the horizontal inclination angle of the seabed is Bending stiffness is EI p , the lateral displacement of the pipe is w(x, t), the axial displacement is u(x, t), and the wake vortex vibration variable is q(x, t); the outer diameter of the pipe is D p , inner diameter is D i , the internal flow velocity is U i , the ocean current velocity is U e ; The following assumptions are made about the submarine pipeline, the fluid inside the pipeline, and the ocean current outside the pipeline: (1) The water in the pipe is incompressible, and the flow velocity is constant across the cross section of the pipe and does not vary along its length; (2) The pipe wall material is linear, uniform and isotropic; (3) For submarine pipelines with large aspect ratios, the pipe deformation is considered as a Timoshenko beam model; (4) Pipeline axial vibration and lateral vibration are considered, but cross-section rotation is not considered.

3. The method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to claim 2, characterized in that: In step S2, the micro-element method is used to extract a control volume micro-segment of length dx from the pipeline system and separate the pipeline unit body and the internal flow unit body; T is the axial internal force of the pipeline unit body, Q is the cross-sectional shear force, M is the cross-sectional bending moment, and A is the internal force of the pipeline unit body. i is the internal flow cross-sectional area, p i A i is the internal flow pressure, γS is the tangential friction between the pipe wall and the internal flow, N is the normal force between the pipe and the internal flow, F x 、F z is the ocean current hydrodynamic force in the x and z directions caused by wake dynamics, m i is the mass of the internal flow fluid per unit length, m p is the mass of the pipe per unit length, g is the acceleration due to gravity, θ is the angle between the tangent direction of the neutral axis of the unit body and the x-axis, is the horizontal inclination of the seabed; The force of the unit body is decomposed into the x-direction and z-direction to establish the equilibrium equation. The motion equation of the fluid unit in the tube is: Axial: Horizontal: Where, γS=(f s / 2D i )m i U i |U i |,f s is the Darcy-Weisbach friction coefficient; The acceleration of the unsteady flow in the tube in the x and z directions is: Axial: Horizontal: The equation of motion of the pipeline unit is: Axial: Horizontal: Where, the pipeline structure damping c s =2ζ(m p +m i +m a )ω n ,ω n is the natural frequency of the pipeline, ζ is the structural damping coefficient; the additional mass per unit length of the pipeline m a =πC a ρ e D p 2 / 4,C a is the additional mass coefficient; When the pipe undergoes a small deformation, cosθ≈1-w′ 2 / 2, sinθ≈w′-u′w′-w′ 3 / 2; the axial internal force T consists of two parts: the initial axial tension T0 of the pipeline and the additional axial internal force generated by the pulsating strain ε; The axial internal force T of the pipeline is: T=T0+EA p ε (7) The shear force Q is expressed as: Q=-EI p in″′ (9) Where, E is the elastic modulus of the pipe; I p is the moment of inertia of the pipe section; Substituting Equations (7) to (9) into Equations (5) and (6), and combining Equations (1) to (4), eliminating the forces N and γS between the tube wall and the fluid, and ignoring the high-order micro-arrangements above the second power, the axial and lateral vibration equations are derived as follows: Axial: Horizontal: Where: m = m i +m p ; Partial differential terms in the system of equations represents inertial force; Damping force; Coriolis force representing internal flow; EI p w″″ represents the elastic recovery force; Centrifugal force of inflow; p i A i w″ represents the internal flow pressure that is added into consideration; represents the resistance along the unsteady internal flow; That is, Equations (10) and (11) are the axial and lateral vibration equations of the submarine water pipeline structure.

4. The method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to claim 3, characterized in that: In step S3, Equations (3) and (4) are substituted into Equations (1) and (2), N and γS are eliminated, and high-order traces are neglected. The axial momentum equation of the flow in the submarine pipeline is further obtained as follows:

5. The method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to claim 4, characterized in that: In step S4, the van der Pol wake oscillator model is as follows: Where ε and Λ are empirical coefficients, which are selected and adjusted through model calibration and experimental results; q is the dimensionless wake oscillator, Ω f is the vortex shedding angular frequency, and its expressions are: Where C L is the instantaneous vortex lift coefficient; C L0 is the vortex-induced lift coefficient when the structure is stationary; St is the Strouhal number; The ocean current hydrodynamic model is introduced, that is, the external attached fluid force F x 、F z for: External fluid force F f Including: ocean current additional damping force, ocean current additional mass force and lift: Where p o is the hydrostatic pressure at both ends of the pipeline; the additional damping of the ocean current c f =C D ρ e D p U e / 2;C D is the drag coefficient; the lift F generated when the ocean current flows through the pipe L =C L0 ρ e U e 2 D p q / 4,ρ e is the density of the ocean current fluid.

6. The method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to claim 5, characterized in that: The nonlinear differential equations for submarine pipeline vibration under internal and external flow excitation are specifically: Pipe axial vibration equation: Pipe lateral vibration equation: Van der Pol wake vortex oscillator equation: The axial momentum equation of the internal flow is: Where: m = m i +m p ; Partial differential terms in the system of equations represents inertial force; Damping force; Coriolis force representing internal flow; EI p w″″ represents the elastic restoring force; m i U i 2 w″ represents the centrifugal force of the internal flow; p i A i w″ represents the internal flow pressure that is added into consideration; represents the resistance along the unsteady internal flow; ε and Λ are empirical coefficients, which are selected and adjusted through model calibration and experimental results; q is the dimensionless wake oscillator, Ω f is the vortex shedding angular frequency; T is the axial internal force of the pipe unit, Q is the cross-sectional shear force, M is the cross-sectional bending moment, A i is the internal flow cross-sectional area, p i A i is the internal flow pressure, γS is the tangential friction between the pipe wall and the internal flow, N is the normal force between the pipe and the internal flow, F x 、F z is the ocean current hydrodynamic force in the x and z directions caused by wake dynamics, m i is the mass of the internal flow fluid per unit length, m p is the mass of the pipe per unit length, g is the acceleration due to gravity, θ is the angle between the tangent direction of the neutral axis of the unit body and the x-axis, is the horizontal inclination of the seabed; E is the elastic modulus of the pipeline; I p is the moment of inertia of the pipe section; EI p is the bending stiffness; L is the length of the pipe; the outer diameter of the pipe is D p , inner diameter is D i , the internal flow velocity is U i , the ocean current velocity is U e ; C L0 is the vortex lift coefficient when the structure is stationary; ρ e is the density of the ocean current fluid; c f Add damping to ocean currents.

7. The method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to claim 6, characterized in that: In step S6, the boundary conditions of the equation group when the boundary conditions of the submarine water pipeline are different are as follows: When the boundary conditions of the submarine water pipeline are simply supported at both ends, we have: w(0,t)=w(L,t)=w″(0,t)=w″(L,t)=0 (23) u(0,t)=u(L,t)=u″(0,t)=u″(L,t)=0 (24) q(0,t)=q(L,t)=q″(0,t)=q″(L,t)=0 (25) For a submarine water pipeline with fixed supports at both ends, the boundary conditions are: w(0,t)=w(L,t)=w′(0,t)=w′(L,t)=0 (26) u(0,t)=u(L,t)=u′(0,t)=u′(L,t)=0 (27) q(0,t)=q(L,t)=q′(0,t)=q′(L,t)=0 (28) For a submarine water pipeline with one end fixed and the other simply supported, the boundary conditions are: w(0,t)=w(L,t)=w′(0,t)=w″(L,t)=0 (29) u(0,t)=u(L,t)=u′(0,t)=u″(L,t)=0 (30) q(0,t)=q(L,t)=q′(0,t)=q″(L,t)=0 (31).

8. The method for constructing a vortex-induced vibration model of a submarine inclined pipeline conveying a non-steady internal flow according to claim 7, characterized in that: In step S7, the dimensionless forms and dimensionless parameters of the following physical quantities are introduced: Substituting formula (32) into formulas (19) to (22), the dimensionless equations for pipeline vibration are: Pipe axial vibration equation: Pipe lateral vibration equation: Van der Pol wake vortex oscillator equation: The axial momentum equation of the internal flow is:

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