Dynamic state analysis method and equipment for suspended submarine cable based on slicing method

Abstract

The present invention discloses a method and device for analyzing the dynamic state of a suspended submarine cable based on a slicing method. The method comprises: constructing a geometric model and a calculation model for a target submarine cable; performing finite element meshing on the target submarine cable and the surrounding water body according to the geometric model and the calculation model, and dividing the flow field into finite elements by the slicing method; the fluid and the solid are solved by the finite element method, the former constructs a flow field simulation by solving the NS control equation, and the latter constructs a solid simulation model by solving the solid motion equation; the slicing method is used to calculate the flow field simulation model, and the immersed boundary method is used to perform fluid-solid coupling processing on the flow field simulation model and the submarine cable body motion simulation model to generate a dynamic response model of the suspended submarine cable; and the dynamic response characteristics of the suspended submarine cable are analyzed according to the dynamic response model of the suspended submarine cable. The present invention performs approximate calculations by the slicing method, saves calculation amount, and quickly realizes the numerical simulation of vortex-induced vibration of the suspended submarine cable.

Description

Technical Field

[0001] The present invention relates to the technical field of submarine cables, and in particular to a method and device for analyzing the dynamic state of a suspended section of a submarine cable based on a slicing method. Background Art

[0002] Marine energy development is to convert offshore wind energy, wave energy, tidal energy and other energy into electrical energy, and transmit the electrical energy back to land for use through submarine cables. With the rapid development of marine energy, the number of submarine cables in the ocean is increasing. In order to ensure the safe operation of submarine cables, submarine cables are generally buried on the seabed. However, in actual engineering, the mud and sand on the submarine cables are often carried away, and the submarine cables are often suspended on the seabed. Under the action of ocean currents and waves, periodic vortex-induced vibrations will occur. Once vortex-induced vibration occurs, the suspended section of the submarine cable is prone to displacement, causing fatigue damage at both ends of the submarine cable. Therefore, vortex-induced vibration-induced submarine cable breakage or fatigue damage is one of the main failure modes of submarine cables. Accurate analysis of its dynamic response state can provide technical support for submarine cable protection.

[0003] For suspended sections of submarine cables, existing numerical model methods generally use full three-dimensional computational fluid dynamics (CFD) models for calculations. However, full three-dimensional CFD models are very computationally resource-intensive and time-consuming, and cannot meet actual application requirements. Summary of the invention

[0004] In view of this, an embodiment of the present invention provides a method and device for analyzing the dynamic state of a suspended section of a submarine cable based on a slicing method.

[0005] A first aspect of the present invention provides a method for analyzing the dynamic state of a suspended section submarine cable based on a slicing method, comprising the following steps:

[0006] Construct geometric and computational models for target submarine cables;

[0007] According to the geometric model and the calculation model, meshing and slicing the target submarine cable are performed to obtain finite elements;

[0008] The NS control equation is used to simulate the flow field, and the finite element method is used to solve the NS control equation to construct a flow field simulation model;

[0009] The solid motion equation is used to simulate the motion of the submarine cable body, and the finite element method is used to solve the solid motion equation to construct a submarine cable body motion simulation model;

[0010] The slicing method is used to calculate the flow field simulation model, and the immersed boundary method is used to perform fluid-solid coupling between the flow field simulation model and the submarine cable body motion simulation model to generate the dynamic response model of the suspended section submarine cable.

[0011] The dynamic response characteristics of the target submarine cable are analyzed according to the dynamic response model of the suspended section of the submarine cable to obtain an analysis result of the suspended section of the target submarine cable.

[0012] Furthermore, constructing a geometric model and a computational model for the target submarine cable specifically includes the following steps:

[0013] Obtain the state parameters, material parameters and hydrodynamic parameters of submarine cables;

[0014] The calculation area, boundary conditions and initial value conditions are determined according to the state parameters, material parameters and hydrodynamic parameters, and a geometric model and a calculation model are constructed.

[0015] Furthermore, the target submarine cable is meshed and sliced ​​according to the geometric model and the computational model to obtain finite elements, which specifically includes the following steps:

[0016] Performing grid division processing on the suspended section of the target submarine cable along the radial direction of the target submarine cable;

[0017] Slicing the suspended section of the target submarine cable along the axial direction of the target submarine cable to construct a fluid slicing model;

[0018] A multi-grid method is used to locally encrypt the flow field at the intersection of the fluid slice and the suspended section of the target submarine cable.

[0019] Furthermore, the NS control equation is used to simulate the flow field, and the finite element method is used to solve the NS control equation to construct a flow field simulation model, which specifically includes the following steps:

[0020] The NS equation is used to describe the flow law of the flow field near the target submarine cable;

[0021] The NS equations are numerically discretized using a two-step Taylor-Galerkin algorithm to construct a time-discrete form;

[0022] According to the step-by-step method of the momentum equation, the velocity increment in the time discrete equation is divided into an intermediate velocity increment ignoring the pressure gradient and a corrected velocity increment.

[0023] Furthermore, the method of simulating the motion of the submarine cable body by using the solid motion equation and solving the solid motion equation by the finite element method to construct a submarine cable body motion simulation model specifically includes the following steps:

[0024] Large eddy simulation is used to numerically simulate vortex-induced vibration in order to construct the structural vibration control equation of the solid.

[0025] In vortex-induced vibration, the path length of one vibration cycle is related to the model size;

[0026] The ratio of the mass of the solid structure to the mass of the fluid displaced by the solid volume is taken as the mass ratio;

[0027] The ratio of mass ratio and damping factor is taken as reduced damping.

[0028] Furthermore, the slicing method is used to calculate the flow field simulation model, and the immersed boundary method is used to perform fluid-solid coupling processing on the flow field simulation model and the submarine cable body motion simulation model to generate the suspended section submarine cable dynamic response model, which specifically includes the following steps:

[0029] According to the motion boundary condition d f =d s , generating the fluid velocity boundary condition Among them, d f is the fluid displacement on the coupling surface, d s is the solid displacement on the coupling surface;

[0030] According to the dynamic boundary condition n·τ f =n·τ s , on the fluid-solid coupling surface, the force of the solid structure node is obtained by integrating the distributed force of the fluid:

[0031] F(t)=∫h d τ f ·ds

[0032] Among them, τ f is the fluid stress on the coupling surface, τ s is the solid stress on the coupling surface, h d is the displacement of the structural node, and n is the normal vector of the coupling surface.

[0033] Further, the performing of a dynamic response characteristic analysis on the target submarine cable according to the dynamic response model of the suspended section submarine cable to obtain an analysis result of the suspended section of the target submarine cable specifically includes the following steps:

[0034] Considering the underwater gravity, the mid-span deflection of the simply supported beam with fixed supports at both ends is calculated using the material mechanics theory formula:

[0035] ω=ql 4 / 384EI

[0036] Where ω is the deflection, I is the moment of inertia and I = πD 4 / 64,q=(ρ s -ρ w )gl·πD 2 / 4,ρ w is the density of water;

[0037] Simplify the deflection to ω=(ρ s-ρ w )ql 4 / 24ED 2 .

[0038] Furthermore, the performing of a dynamic response characteristic analysis on the target submarine cable according to the dynamic response model of the suspended section submarine cable to obtain an analysis result of the suspended section of the target submarine cable also includes the following steps:

[0039] According to the principle of static-dynamic superposition, the dynamic time history curves of displacement and principal stress of the target submarine cable are obtained through the fluid slice model;

[0040] The dynamic time history curve is compared with the allowable value of the design stress of the target submarine cable to determine the stress state of the target submarine cable.

[0041] Furthermore, the performing of a dynamic response characteristic analysis on the target submarine cable according to the dynamic response model of the suspended section submarine cable to obtain an analysis result of the suspended section of the target submarine cable also includes the following steps:

[0042] Calculate the natural vibration frequency of the suspended section of the target submarine cable:

[0043]

[0044] Among them, f n is the natural frequency of the structure, C is the constant coefficient, L is the suspended length, and M is the mass per unit length of the pipeline;

[0045] According to the SN curve equation, the fatigue stress amplitude corresponding to the i-th sea condition is calculated as S i Fatigue life N i , where N i =(S0 / S i ) m ×10 7 , S0 is the fatigue endurance limit, m is the slope of the SN curve;

[0046] The fatigue cumulative damage D of k sea conditions in one year a It is expressed as:

[0047]

[0048] Where N is the total number of cycles of vibration of the target submarine cable within one year, P i is the probability of occurrence of the ith sea condition, k is the number of sea conditions in a year;

[0049] Calculate the fatigue life T of the target submarine cable:

[0050]

[0051] Where Δc is the fatigue damage tolerance value, D a is the cumulative fatigue damage, S ei is the equivalent stress amplitude of the i-th sea state;

[0052] The remaining life T of the target submarine cable is calculated using the critical analysis method. life :

[0053]

[0054] Where a is a constant.

[0055] A second aspect of the present invention discloses an electronic device, comprising a processor and a memory;

[0056] The memory is used to store programs;

[0057] The processor executes the program to implement a method for analyzing the dynamic state of a suspended section of a submarine cable based on a slicing method.

[0058] The embodiment of the present invention also discloses a computer program product or a computer program, which includes a computer instruction stored in a computer-readable storage medium. A processor of a computer device can read the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the above method.

[0059] The present invention provides a method and device for analyzing the dynamic state of a suspended section of a submarine cable based on a slicing method. On the one hand, the slicing method is introduced to solve the NS equations by the finite element method, and the momentum equation step-by-step method is used to numerically discretize the NS equations, thereby improving the computational efficiency and computational timeliness and reducing the consumption of computational resources. On the other hand, the present invention uses a large eddy simulation method to calculate turbulence parameters, constructs a motion simulation model of a suspended section of a submarine cable based on a slicing method, and realizes the time domain simulation of the vortex-induced vibration of a long flexible submarine cable. On the other hand, the coupling between the water flow and the foundation structure in the present invention adopts a fluid-solid coupling method, and the fluid transfers the load to the solid by interpolation on the fluid-solid coupling surface, thereby calculating the overall motion response of the submarine cable structure. In summary, the embodiments of the present invention provide a method and device for analyzing the dynamic state of a suspended section of a submarine cable based on a slicing method, which can improve the computational efficiency and computational timeliness and reduce the consumption of computational resources by introducing a slicing method.

[0060] Additional aspects and advantages of the present invention will be given in part in the following description, and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0062] Figure 1 It is a flow chart of an embodiment of a method for analyzing the dynamic state of a suspended section submarine cable based on a slicing method of the present invention;

[0063] Figure 2 It is a schematic diagram of the grid division of the suspended section submarine cable in the present invention;

[0064] Figure 3 It is a schematic diagram of the slicing process of the suspended section submarine cable in the present invention;

[0065] Figure 4 It is a schematic diagram of a slice of a suspended section submarine cable in the present invention;

[0066] Figure 5 It is the SN curve diagram in the present invention. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0068] See also Figure 1 , Figure 1 The flowchart of an embodiment of the method for analyzing the dynamic state of a suspended section submarine cable based on the slicing method of the present invention is shown, which includes:

[0069] S101, constructing a geometric model and a computational model for the target submarine cable;

[0070] Specifically, the steps of constructing a geometric model and a computational model for the target submarine cable include:

[0071] (1) Obtaining the state parameters, material parameters and hydrodynamic parameters of the submarine cable;

[0072] The status parameters of the submarine cable include the actual posture (horizontally placed or tilted), the (x, y, z) coordinates of the points where the submarine cable enters the mud on both sides, and the seabed topography of the submarine cable routing area.

[0073] The material parameters of submarine cables include diameter, cross-sectional area, equivalent elastic modulus, density, Poisson's ratio, etc.

[0074] The hydrodynamic parameters of the routing area of ​​the submarine cable include flow velocity and flow direction.

[0075] (2) Construct a geometric model and a calculation model based on state parameters, material parameters, and hydrodynamic parameters, and determine the calculation area, boundary conditions, and initial conditions.

[0076] In practical applications, appropriate geometric models can be selected according to state parameters, material parameters and hydrodynamic parameters, and a calculation model can be established.

[0077] S102, meshing and slicing the target submarine cable according to the geometric model and the calculation model to obtain finite elements;

[0078] Specifically, according to the geometric model and the computational model, the steps of meshing and slicing the target submarine cable to divide the finite elements include:

[0079] (1) Meshing the suspended section of the submarine cable along the radial direction of the submarine cable;

[0080] like Figure 2 As shown, the terrain and submarine cable are converted into local coordinates, the axis of the submarine cable is along the X-axis direction, the suspended section of the submarine cable is laid flat on the seabed, and both ends are generalized to be fixed, and the suspended section of the submarine cable is divided into a grid.

[0081] (2) Slice the suspended section of the submarine cable along the axial direction of the submarine cable and construct a fluid slice model;

[0082] like Figure 3 As shown, the submarine cable is divided into multiple slices along the axial direction, and the number of slices is related to the axial flow distribution characteristics of the submarine cable, the cable span length, computing resources, computing accuracy and other requirements; if it is a single uniform flow condition, the three-dimensional effect of the axial fluid of the submarine cable is relatively weak, the number of slices is small, and the intervals between slices are large, which can also represent the fluid action of this submarine cable section; if the incoming flow varies greatly along the axial direction of the cable, the three-dimensional effect of the axial fluid of the submarine cable is strong, the number of slices required is large, and the intervals between slices need to be reduced.

[0083] like Figure 4 As shown, a fluid slice model is added on the basis of the static model. The slices are distributed along the longitudinal direction of the submarine cable and are in the YZ coordinate plane. The number of segments is selected and the fluid model is established at the corresponding position.

[0084] It should be noted that the slices and submarine cables are modeled separately, but the slice positions need to be determined to ensure that the slice positions are not exactly at the boundaries of the submarine cable units.

[0085] (3) The multi-grid method is used to locally encrypt the position of the suspended submarine cable.

[0086] The multi-grid method is used for encryption at the submarine cable location to ensure the stability of fluid calculation and the development of vortices.

[0087] S103, simulating the flow field by using the NS control equation, and solving the NS control equation by using the finite element method to construct a flow field simulation model;

[0088] It should be noted that the finite element method is used to solve the NS (Navier-Stokes equations) control equations to calculate the unit velocity, pressure, temperature and other parameters of the flow field;

[0089] Specifically, the steps of simulating the flow field by using the NS control equation and solving the NS control equation by the finite element method to construct the flow field simulation model include:

[0090] (1) The NS equation is used to describe the flow law of the flow field near the submarine cable;

[0091] The flow field near the submarine cable is a complex three-dimensional unsteady incompressible turbulent flow, and its flow law can be described by the incompressible viscous flow NS equation:

[0092]

[0093]

[0094] Where u is velocity, t is time, ρ is fluid density, P is pressure, τ is fluid viscous stress, μ is fluid dynamic viscosity coefficient, and f b is the body force of the fluid (including the force exerted by the solid structure on the fluid), and d represents the total derivative.

[0095] (2) The NS equations are numerically discretized using the step-by-step method of the momentum equation to construct a time-discrete form;

[0096] Introducing time parameters θ1 and θ2 into the NS equation, equations (1) and (2) are rewritten into a time-discrete form:

[0097]

[0098]

[0099] Among them, the range of θ1 and θ2 is [0,1]; when 1 / 2≤θ1≤1 and 1 / 2≤θ2≤1, it is a semi-implicit time discrete format, when 1 / 2≤θ1≤1 and θ2=0, it is an explicit time discrete format, and n is the time step.

[0100] (3) According to the step-by-step method of the momentum equation, the velocity increment in the time discrete equation is divided into an intermediate velocity increment that ignores the pressure gradient and a corrected velocity increment.

[0101] According to the two-step Taylor-Galerkin algorithm, the velocity increment Δu can be divided into the intermediate velocity increment Δu ignoring the pressure gradient: * and the correction speed increment Δu ** :

[0102] Δu=Δu * +Δu ** (5)

[0103]

[0104]

[0105] Furthermore, the discretization of the NS equation is divided into three steps:

[0106] (1) Explicit calculation of the intermediate velocity field increment Δu * ;

[0107] definition G = -τ / ρ and Q = -f b , rewrite equation (6) into the conventional conservation equation form:

[0108]

[0109] Applying the two-step Taylor-Galerkin method (TSTG), the increment Δu * It can be calculated in two steps:

[0110]

[0111]

[0112] F in formula (10) n+1 / 2 and Q n+1 / 2 By using u in formula (9) n+1 / 2 calculate.

[0113] Using the standard Galerkin approximation, the spatial discretization form of equation (10) is:

[0114]

[0115] In the formula M = ∫N T NdΩ, and N represent the nodal variables and shape functions of the velocity field, respectively.

[0116] (2) According to Δu * Calculation of pressure increment Δp n ;

[0117] Introduced in formula (3) To calculate the pressure:

[0118]

[0119] In the formula and N p denote the nodal increments and shape functions of pressure, respectively.

[0120] (3) According to Δp n Calculate the correction value Δu of the velocity field increment ** Following this step, we can get the velocity field u for the next time step: n+1 .

[0121] Correct Δu in equation (7) using the pressure value obtained in the previous step:

[0122]

[0123] In the formula,

[0124] The symmetric stepwise over-relaxation preconditioned conjugate gradient method (SSORPCG) is used as the inner iterative solver for the fluid.

[0125] S104, using a solid motion equation to simulate the motion of the submarine cable body, and using a finite element method to solve the solid motion equation to construct a submarine cable body motion simulation model;

[0126] The equation of motion for solid mechanics is as follows:

[0127] (14)

[0128] Among them, M, C and K are the mass matrix, damping matrix and stiffness matrix of the system respectively. and δ are the nodal acceleration vector, velocity vector and displacement vector of the system respectively, and F is the nodal load vector of the system, which includes the load acting on the solid structure by the fluid at the fluid-solid coupling surface.

[0129] The present invention uses a large eddy simulation method to perform numerical calculations on vortex-induced vibrations, and uses a finite element method to solve the solid motion equation to calculate parameters such as solid displacement, strain, and stress. The specific steps include:

[0130] (1) The large eddy simulation method is used to numerically simulate vortex-induced vibration to construct the structural vibration control equation of the solid;

[0131] For incompressible viscous fluid, the above NS equation is used to describe its motion law, and the large eddy simulation method is used to numerically simulate the vortex-induced vibration; the structural vibration control equation of the solid is:

[0132]

[0133] Where m is the mass of the solid structure, c is the damping of the vibrating solid system, k is the solid stiffness, i=1,2,3, respectively representing the x, y, z directions, and xi is the displacement of the solid structure in the i direction. i is the fluid force acting on the structure in the i-th direction.

[0134] (2) In vortex-induced vibration, the path length of one vibration cycle is related to the model size;

[0135] In vortex-induced vibration, the path length in one vibration cycle is U / f, where U is the incoming flow velocity and f is the vibration frequency. Relating this value to the model size and taking the vibration frequency as the natural frequency yields:

[0136]

[0137] Among them, f n is the structural natural frequency, D is the structural characteristic length, U r is the reduced speed.

[0138] (3) The ratio of the mass of the solid structure to the mass of the fluid displaced by the solid volume is taken as the mass ratio;

[0139] The ratio of the mass of a solid structure to the mass of the fluid that can be displaced by the solid volume is called the mass ratio, which is also an important dimensionless parameter affecting vortex-induced vibration:

[0140]

[0141] The mass ratio is a measure of the buoyancy factor of the fluid and the model inertia corresponding to the fluid inertia. It is used to detect the sensitivity of lightweight structures with small mass to flow-induced vibrations. When the mass ratio increases, the possibility of fluid-induced vibrations will also increase. The mass ratio has a great influence on the correlation between the flow direction and the lateral vibration response of the structure that undergoes vortex-induced vibrations. When the mass ratio is small, the lateral amplitude of the vibrating structure with both flow and lateral degrees of freedom will be larger. When the mass ratio is large, the lateral displacement of the vibrating structure with only lateral movement freedom is not much different from that of the vibrating structure with both lateral and flow degrees of freedom. This critical mass ratio is about 3.5. The mass ratio of a general structure must be greater than 3.5. Therefore, it can be seen that the influence of flow vibration can be ignored when studying lateral vortex-induced vibrations.

[0142] (4) The ratio of mass ratio and damping factor is taken as the reduced damping:

[0143]

[0144] Where ξ is the damping ratio of the solid structure. The vibration of the structure during vortex-induced vibration is very sensitive to the influence of damping. In order to reduce the vibration displacement and locking range of the structure, it can be achieved by increasing the damping of the structure.

[0145] S105, using a slicing method to calculate a flow field simulation model, and using an immersed boundary method to perform fluid-solid coupling processing on the flow field simulation model and the submarine cable body motion simulation model, so as to generate a dynamic response model of the suspended section submarine cable;

[0146] The present invention couples the forces between fluid and solid through the immersed boundary method, and calculates the fluid-solid coupling effect, including the interaction between flow velocity and solid displacement, and the interaction between flow pressure and solid stress. The movement of the submarine cable is caused by the movement of water flow. The fluid transmits fluid force to the solid through interpolation on the fluid-solid coupling surface. The fluid force acts on the solid structure through the immersed boundary point. The displacement of the solid structure is obtained by solving the solid motion equation, and the feedback is used as the boundary of the fluid domain to realize the bidirectional coupling between the fluid and the solid.

[0147] It should be noted that the movement of submarine cables is mainly caused by water flow, and the immersed boundary method is used to calculate the fluid-solid coupling scheme. The focus of the immersed boundary method is to accurately calculate the coupling force between the fluid and the solid. The momentum equation considering the gravity body force term is:

[0148]

[0149] in I is the unit tensor.

[0150] We can use Fs to represent the force of the solid on the fluid, and F to represent the concentrated force on the immersed boundary point. Fs is the reaction force of the integral of the stress tensor σ on the solid surface Sb, that is, n is the external normal vector of Sb, pointing from the solid to the fluid.

[0151] If the momentum equation without additional body forces is integrated along the computational region Ω, and considering that the momentum equation is balanced in any control volume, then

[0152]

[0153] Converted into area Where Sout is the surface of Ω, Sb is the solid surface, and for the fluid region, the outer normal of Sb is from the fluid to the solid. Since Sb is the object surface, whether it is no slip or slip, it satisfies n·uu=0, so it can be simplified to

[0154]

[0155] From this we get

[0156]

[0157] The fluid transfers load to the solid through interpolation on the fluid-solid coupling surface. The motion boundary conditions and dynamic boundary conditions should be met on the fluid-solid coupling surface:

[0158]

[0159] Among them, d f is the fluid displacement on the coupling surface, d s is the solid displacement on the coupling surface, τ f is the fluid stress on the coupling surface, τ s is the solid stress on the coupling surface, is the normal vector of the coupling surface.

[0160] Specifically, the steps of using the slicing method to perform fluid-solid coupling processing on the flow field simulation model and the submarine cable body motion simulation model to generate the suspended section submarine cable dynamic response model include:

[0161] (1) According to the motion boundary condition d f =d s , generate the fluid velocity boundary condition:

[0162] (Non-slip solid wall)

[0163] Among them, d f is the fluid displacement on the coupling surface, d s is the solid displacement on the coupling surface;

[0164] (2) According to the dynamic boundary condition n·τ f =n·τ s , on the fluid-solid coupling surface, the force of the solid structure node is obtained by integrating the distributed force of the fluid:

[0165] F(t)=∫h d τ f ·ds

[0166] Among them, τ f is the fluid stress on the coupling surface, τ s is the solid stress on the coupling surface, h d is the displacement of the structural node, and n is the normal vector of the coupling surface.

[0167] Since the solid only transmits rigid displacement to the fluid and ignores the effect of solid elastic deformation on the fluid, only one iteration is required between the fluid and the solid. In addition, since the relative position of the fluid and the solid does not change basically, the interpolation information processing only needs to be performed once at the beginning on the fluid-solid coupling surface, and the interpolation conditions will not change in the subsequent calculation process. This can greatly reduce the calculation time and cost, and can also improve the convergence of numerical calculations and increase the reliability of calculations.

[0168] S106, analyzing the dynamic response characteristics of the suspended section submarine cable according to the dynamic response model of the suspended section submarine cable.

[0169] It should be noted that the present invention can perform dynamic response characteristic analysis of the suspended section of the submarine cable according to the dynamic response model of the suspended section of the submarine cable, including analysis of the flow field and the movement of the submarine cable body, analysis of the fluid-solid coupling effect, analysis of specific problems (such as vibration, strength, etc.), data visualization, result output, static analysis, vortex-induced vibration characteristic analysis and fatigue life analysis, etc.

[0170] The following is a further detailed description of static analysis, vortex-induced vibration characteristic analysis and fatigue life analysis:

[0171] 1. Static analysis

[0172] For the underwater static force calculation of different suspended submarine cables, the constraint conditions can be given as fixed-end constraints at both ends (i.e., constraining the displacements in the X, Y, and Z directions at both ends of the submarine cable), and the static deflection under the action of deadweight is calculated under the premise of only considering the underwater gravity.

[0173] Specifically, the steps of performing static analysis on the suspended section submarine cable according to the dynamic response model of the suspended section submarine cable include:

[0174] (1) Using the material mechanics theory formula ω = ql 4 / 384EI, calculate the mid-span deflection ω of a simply supported beam with clamped supports at both ends.

[0175] It should be noted that the mid-span deflection ω of a simply supported beam with both ends fixed can be calculated using the material mechanics theory formula ω=ql 4 / 384EI calculation, where: I is the moment of inertia, I=πD 4 / 64; q is the concentration force, q=(ρ s -ρ w )glπD 2 / 4,ρ w is the density of water, ρ w =1000kg / m 3 , g is the acceleration due to gravity; ρ s is the density of the submarine cable material; l is the length of the suspended section of the submarine cable.

[0176] (2) Simplify the deflection to ω = (ρ s -ρ w )ql 4 / 24ED 2 .

[0177] Substituting the moment of inertia I and concentrated force q into the material mechanics theory formula, the deflection formula can be obtained after simplification:

[0178] ω=(ρ s -ρ w )ql 4 / 24ED 2

[0179] 2. Vortex-Induced Vibration Characteristics Analysis

[0180] Specifically, the steps of analyzing the vortex-induced vibration characteristics of the suspended section submarine cable according to the dynamic response model of the suspended section submarine cable include:

[0181] (1) According to the principle of static-dynamic superposition, the dynamic time history curves of submarine cable displacement and principal stress are obtained through the fluid slice model;

[0182] The calculation of vortex-induced vibration needs to take the fluid effect into consideration. The fluid slice model is established by the slice method. The principle of static and dynamic superposition is considered to obtain the dynamic time history curves of submarine cable displacement and principal stress.

[0183] (2) Compare the dynamic time history curve with the allowable value of the submarine cable design stress to determine the stress state of the submarine cable.

[0184] 3. Fatigue life analysis

[0185] Specifically, the steps of performing fatigue life analysis on the suspended section submarine cable according to the dynamic response model of the suspended section submarine cable include:

[0186] (1) Calculate the natural vibration frequency of the suspended span:

[0187]

[0188] Among them, f n is the natural frequency of the structure; C is a constant coefficient, C=1; L is the span length; M is the mass per unit length of the pipeline; K is an empirical coefficient, K=4.73 when both ends are fixed.

[0189] (2) According to the SN curve equation, the fatigue stress amplitude corresponding to the i-th sea condition is calculated as S i Fatigue life N i ;

[0190] like Figure 5As shown, in the SN curve diagram, the horizontal axis is the number of stress cycles, and the vertical axis is the stress amplitude; for different pipeline structural characteristics, the corresponding SN curve is different.

[0191] The fatigue stress amplitude corresponding to the i-th sea condition is calculated as S according to the SN curve equation. i Fatigue life N i :

[0192] N i =(S0 / S i ) m ×10 7 ,

[0193] Among them, S0 is the fatigue endurance limit. When the fatigue stress amplitude is equal to S0, the fatigue life is 10 7 ; m is the slope of the SN curve.

[0194] (3) The fatigue cumulative damage D of k sea conditions in one year a It is expressed as:

[0195]

[0196] Where N is the total number of cycles of pipeline vibration in one year; P i is the probability of occurrence of the ith sea condition; k is the number of sea conditions in a year.

[0197] (4) When the cumulative fatigue damage D a When it reaches a certain value, fatigue failure will occur; the fatigue life of the pipeline T (year) can be expressed as:

[0198]

[0199] Wherein, Δc is the fatigue damage tolerance value, which varies under different standards; D a is the cumulative fatigue damage; S ei is the equivalent stress amplitude of the ith sea state.

[0200] Accordingly, S ei The calculation formula is:

[0201]

[0202] (5) Calculate the remaining life of the pipeline T using the critical analysis method life :

[0203]

[0204] in, is a constant, The values ​​can be obtained from the SN curve table (Table 1) and Figure 4 It was found in the following:

[0205] Table 1

[0206]

[0207] As can be seen from the above, the basic processing idea of ​​the dynamic state analysis method of the suspended section submarine cable based on the slicing method of the present invention is: first, the suspended span submarine cable is divided into a certain number of control nodes in the axial direction by the finite element method, and the fluid motion is approximated as a two-dimensional plane problem at each control node; then, the fluid force at each control node is calculated by the two-dimensional discrete hydrodynamic model; then, the fluid force calculated at all control nodes is transferred to the finite element model of the submarine cable structure in a bilinear interpolation manner, so that the overall motion response of the submarine cable structure can be calculated; after updating the position of the submarine cable structure at each time step, the instantaneous fluid force at each control node on the two-dimensional plane is calculated by the two-dimensional discrete hydrodynamic model, and the calculation is carried out sequentially step by step, so as to realize the numerical simulation calculation of the vortex-induced vibration of the suspended span submarine cable. When the number of control nodes is large enough and the segmentation is dense enough, the quasi-three-dimensional numerical calculation method using slicing can be used to simulate the vortex-induced vibration problem of the suspended span submarine cable, and the calculation amount of the numerical simulation of the vortex-induced vibration of the submarine cable is greatly reduced under the premise of meeting the accuracy.

[0208] Correspondingly, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein when the processor executes the computer program, the steps of the above-mentioned method for analyzing the dynamic state of a suspended section of a submarine cable based on the slicing method are implemented.

[0209] The embodiment of the present invention also discloses a computer program product or a computer program, wherein the computer program product or the computer program includes a computer instruction, and the computer instruction is stored in a computer-readable storage medium. A processor of a computer device can read the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes Figure 1 The method shown.

[0210] In some selectable embodiments, the function / operation mentioned in the block diagram may not occur in the order mentioned in the operation diagram. For example, depending on the function / operation involved, the two boxes shown in succession can actually be executed substantially simultaneously or the boxes can sometimes be executed in reverse order. In addition, the embodiment presented and described in the flow chart of the present invention is provided by way of example, for the purpose of providing a more comprehensive understanding of technology. The disclosed method is not limited to the operation and logic flow presented herein. Selectable embodiments are expected, wherein the order of various operations is changed and the sub-operation of a part for which is described as a larger operation is performed independently.

[0211] In addition, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise specified, one or more of the functions and / or features described may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in separate physical devices or software modules. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the present invention. More specifically, in view of the properties, functions, and internal relationships of the various functional modules in the device disclosed herein, the actual implementation of the module will be understood within the conventional skills of the engineer. Therefore, those skilled in the art can implement the present invention set forth in the claims without excessive experimentation using ordinary techniques. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present invention, which is determined by the full scope of the appended claims and their equivalents.

[0212] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0213] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0214] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0215] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

[0216] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the described embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for analyzing the dynamic state of a suspended submarine cable based on a slicing method, characterized in that: The following steps are involved: Construct geometric and computational models for target submarine cables; According to the geometric model and the calculation model, meshing and slicing the target submarine cable are performed to obtain finite elements; Based on the slicing method, the NS control equations are used to simulate the flow field, and the finite element method is used to solve the NS control equations to construct the flow field simulation model; The solid motion equation is used to simulate the motion of the submarine cable body, and the finite element method is used to solve the solid motion equation to construct a submarine cable body motion simulation model; The immersed boundary method is used to perform fluid-solid coupling processing on the flow field simulation model and the submarine cable body motion simulation model to generate the dynamic response model of the suspended submarine cable. Performing a dynamic response characteristic analysis on the target submarine cable according to the dynamic response model of the suspended section submarine cable to obtain an analysis result of the suspended section of the target submarine cable; According to the geometric model and the calculation model, the target submarine cable is meshed and sliced ​​to obtain finite elements, which specifically includes the following steps: Performing grid division processing on the suspended section of the target submarine cable along the radial direction of the target submarine cable; Slicing the suspended section of the target submarine cable along the axial direction of the target submarine cable to construct a fluid slicing model; A multi-grid method is used to locally encrypt the flow field at the intersection of the fluid slice and the suspended section of the target submarine cable.

2. According to the method for analyzing the dynamic state of a suspended section submarine cable based on the slicing method in claim 1, it is characterized in that: The geometric model and the calculation model are constructed for the target submarine cable, specifically including the following steps: Obtain the state parameters, material parameters and hydrodynamic parameters of submarine cables; The calculation area, boundary conditions and initial value conditions are determined according to the state parameters, material parameters and hydrodynamic parameters, and a geometric model and a calculation model are constructed.

3. The method for analyzing the dynamic state of a suspended section submarine cable based on a slicing method according to claim 1 is characterized in that: The method of simulating the flow field by using the NS control equation and solving the NS control equation by the finite element method to construct a flow field simulation model specifically includes the following steps: The NS equation is used to describe the flow law of the flow field near the target submarine cable; The NS equations are numerically discretized using a two-step Taylor-Galerkin algorithm to construct a time-discrete form; According to the step-by-step method of the momentum equation, the velocity increment in the time discrete equation is divided into an intermediate velocity increment ignoring the pressure gradient and a corrected velocity increment.

4. The method for analyzing the dynamic state of a suspended section submarine cable based on a slicing method according to claim 1 is characterized in that: The method of simulating the motion of the submarine cable body by using the solid motion equation and solving the solid motion equation by the finite element method to construct a submarine cable body motion simulation model specifically includes the following steps: Large eddy simulation is used to numerically simulate vortex-induced vibration in order to construct the structural vibration control equation of the solid. In vortex-induced vibration, the path length of one vibration cycle is related to the model size; The ratio of the mass of the solid structure to the mass of the fluid displaced by the solid volume is taken as the mass ratio; The ratio of mass ratio and damping factor is taken as reduced damping.

5. The method for analyzing the dynamic state of a suspended submarine cable based on a slicing method according to claim 1 is characterized in that: The flow field simulation model is calculated by using the slicing method, and the flow field simulation model and the submarine cable body motion simulation model are subjected to fluid-solid coupling processing by using the immersed boundary method to generate a dynamic response model of the suspended section submarine cable. Specifically, the following steps are included: According to the motion boundary condition d f =d s , generating fluid velocity boundary conditions Among them, d f is the fluid displacement on the coupling surface, d s is the solid displacement on the coupling surface; According to the dynamic boundary condition n.τ f =n·τ s , on the fluid-solid coupling surface, the force of the solid structure node is obtained by integrating the distributed force of the fluid: F(t)=∫h d τ f ·ds Among them, τ f is the fluid stress on the coupling surface, τ s is the solid stress on the coupling surface, h d is the displacement of the structural node, and n is the normal vector of the coupling surface.

6. The method for analyzing the dynamic state of a suspended submarine cable based on a slicing method according to claim 1 is characterized in that: The step of performing a dynamic response characteristic analysis on the target submarine cable according to the dynamic response model of the suspended section submarine cable to obtain an analysis result of the suspended section of the target submarine cable specifically includes the following steps: Considering the underwater gravity, the mid-span deflection of the simply supported beam with fixed supports at both ends is calculated using the material mechanics theory formula: ω=ql 4 / 384EI Where ω is the deflection, I is the moment of inertia and I = πD 4 / 64,q=(ρ s -ρ w )glπD 2 / 4,ρ w is the density of water; Simplify the deflection to ω=(ρ s -ρ w )ql 4 / 24ED 2 .

7. The method for analyzing the dynamic state of a suspended submarine cable based on a slicing method according to claim 1 is characterized in that: The step of performing a dynamic response characteristic analysis on the target submarine cable according to the dynamic response model of the suspended section submarine cable to obtain an analysis result of the suspended section of the target submarine cable further includes the following steps: According to the principle of static-dynamic superposition, the dynamic time history curves of displacement and principal stress of the target submarine cable are obtained through the fluid slice model; The dynamic time history curve is compared with the allowable value of the design stress of the target submarine cable to determine the stress state of the target submarine cable.

8. The method for analyzing the dynamic state of a suspended submarine cable based on a slicing method according to claim 1 is characterized in that: The step of performing a dynamic response characteristic analysis on the target submarine cable according to the dynamic response model of the suspended section submarine cable to obtain an analysis result of the suspended section of the target submarine cable further includes the following steps: Calculate the natural vibration frequency of the suspended section of the target submarine cable: Among them, f n is the natural frequency of the structure, C is the constant coefficient, L is the suspended length, and M is the mass per unit length of the pipeline; According to the SN curve equation, the fatigue stress amplitude corresponding to the i-th sea condition is calculated as S i Fatigue life N i ,in, N i =(S0 / S i ) m ×10 7 , S0 is the fatigue endurance limit, m is the slope of the SN curve; The fatigue cumulative damage D of k sea conditions in one year a It is expressed as: Where N is the total number of cycles of vibration of the target submarine cable within one year, P i is the probability of occurrence of the ith sea condition, k is the number of sea conditions in a year; Calculate the fatigue life T of the target submarine cable: Where Δc is the fatigue damage tolerance value, D a is the cumulative fatigue damage, S ei is the equivalent stress amplitude of the i-th sea state; The remaining life T of the target submarine cable is calculated using the critical analysis method. life : in, is a constant.

9. An electronic device, characterized in that: including a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method according to any one of claims 1 to 8.

Images