A method for analyzing umbilical cable motion affected by vortex-induced vibration

Abstract

The invention discloses an umbilical cable motion analysis method affected by vortex-induced vibration, and relates to the technical field of umbilical cable motion. Firstly, a finite volume method is used to model a ship and a fluid domain, and the ship motion combines heave, sway, surge, bow pitch, pitch and roll six-degree-of-freedom motion; then, an immersed boundary method and a lattice Boltzmann method fluid-solid coupling calculation method are used and a turbulence equation is introduced to establish an IB-LBM architecture model of the umbilical cable; the umbilical cable is discretized into umbilical cable particles, which are respectively top particles connected to a mother ship, connection particles connected to a load and intermediate particles of the umbilical cable itself, and the motion law of the umbilical cable particles under the influence of ship motion and vortex-induced vibration is analyzed; then, the slicing principle is used to simplify the umbilical cable particle motion model to a two-dimensional plane, and an interpolation model is used to extend the vortex-induced vibration response at the slice obtained to the entire umbilical cable, and a direct force immersed boundary method umbilical cable dynamics model is constructed to analyze the motion law of the umbilical cable in the fluid domain.

Description

Technical Field

[0001] The invention relates to the technical field of umbilical cable motion, and in particular to a method for analyzing the motion of an umbilical cable affected by vortex-induced vibration. Background Art

[0002] Cabled deep-sea mining and exploration systems usually consist of a mother ship, an umbilical cable, and underwater engineering equipment. The umbilical cable is the main connection device for energy exchange, information transmission, and equipment recovery between underwater engineering equipment and the mother ship, and is the lifeline of underwater engineering equipment. However, the umbilical cable is a slender and flexible structure, and will be subject to various interferences during the umbilical cable retraction and towing process, such as the relative movement between the mother ship and the load, fluid impact, and vortex-induced vibration. When the umbilical cable is working, its internal stress is in a state of continuous change. When the internal stress change of the umbilical cable exceeds a certain critical value, the umbilical cable will suffer irreversible damage or even break, which will cause huge economic losses. Therefore, in order to improve the safety of cabled underwater systems working in complex sea conditions, it is necessary to study the complex dynamic behavior of the umbilical cable under the influence of fluid-solid coupling such as mother ships, load movement, and vortex-induced vibration.

[0003] At present, the dynamic parameters of the umbilical cable are generally studied by establishing an umbilical cable dynamic model for the multi-body motion response of the mother ship-umbilical cable-load. Only the influence of the uniform flow umbilical cable motion is considered, and the influence of vortex-induced vibration, ship motion and turbulence on the stress and strain of the umbilical cable is ignored. The conclusions have limitations in the structural design of the umbilical cable and the speed control of the cable-carrying marine engineering equipment. Summary of the invention

[0004] In view of the above-mentioned technical problems to be solved, the present invention provides a method for analyzing the motion of an umbilical cable affected by vortex-induced vibration, especially the mother ship-umbilical cable-load multi-body motion, to analyze the numerical changes of the complex dynamic characteristics of the umbilical cable when the umbilical cable is disturbed by the mother ship motion and fluid-solid coupling.

[0005] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0006] A motion analysis method for an umbilical cable affected by vortex-induced vibration is disclosed. The method firstly adopts a finite volume method to model a ship and a fluid domain, wherein the ship motion is combined with six degrees of freedom motions, namely, heave, sway, surge, pitch, pitch and roll. Then, an IB-LBM framework model of an umbilical cable system is established by adopting a fluid-solid coupling calculation method of an immersed boundary method and a lattice Boltzmann method and introducing the Spalart-Allmaras turbulence equation. The model discretizes the umbilical cable into umbilical cable particles, wherein the umbilical cable particles are top particles connected to a mother ship, connection particles connected to a load and intermediate particles of the umbilical cable itself, and the motion laws of the umbilical cable particles under the influence of ship motion and vortex-induced vibration are analyzed. Then, the umbilical cable immersed boundary particle model is simplified to a two-dimensional plane by using the slicing principle, and the vortex-induced vibration response at the slice is extended to the entire umbilical cable by using an interpolation model, and a direct force immersed boundary method umbilical cable motion dynamics model is constructed to analyze the motion law of the umbilical cable in the fluid domain.

[0007] As a further improvement of the above technical solution:

[0008] Preferably, the IB-LBM architecture model for establishing the umbilical cable system is specifically:

[0009] Assuming the fluid is viscous and incompressible, the governing equation of the fluid is:

[0010] ;

[0011] (1)

[0012] in, is the velocity vector; is the density; For pressure; is kinematic viscosity; is the external body force vector; is the gradient operator;

[0013] In the IB-LBM framework, the velocity field in the fluid domain is determined by the discrete grid distribution function and is calculated as follows:

[0014] (3)

[0015] in, is the particle density distribution function; is the equilibrium distribution function of the particle; is the velocity vector; is the volume force at the Euler point, is the grid point position of the current particle, t Indicates the current grid time of the particle, is the relaxation time; and The expressions are:

[0016] (4)

[0017] (5)

[0018] in, is the velocity vector at the current grid point, is the grid speed, is the volume force of the flow field, is the volume force at the Euler point, is the weight coefficient vector in each direction;

[0019] The Spalart-Allmaras turbulence equation is introduced and numerically solved by the difference method, which can be expressed as:

[0020] (6)

[0021] in, Additional terms arising from turbulence; is the turbulent viscosity dissipation due to wall obstruction and liquid viscosity; and is a constant; represents the molecular kinematic viscosity vector, For fluid i Speed ​​in direction;

[0022] In the immersed boundary method, the fluid force on the solid boundary particles is determined by the flow velocity of the flow field around the particles and the relevant weight coefficients. The solid boundary has a feedback fluid force on the fluid domain. The calculation equations of the two are:

[0023] (7)

[0024] (8)

[0025] in, is the velocity of the solid affected by the fluid; is the velocity of the fluid near the solid boundary particles; is the Euler coordinate of the flow field grid; is the Lagrangian coordinates of the solid boundary points; is the Dirac interpolation function, is the volume force of the flow field near the solid boundary particles.

[0026] Preferably, in the motion of the ship, the dynamic equations of the heave, roll and pitch of the ship in the waves are expressed as:

[0027] (9)

[0028] in, , are the ship mass and the additional mass for the ship's heave motion respectively; , are the roll moment of inertia and the roll additional moment of inertia respectively; , are pitch moment of inertia and pitch additional moment of inertia respectively; ~ is the hydrodynamic coefficient of the ship's heave motion; is the roll damping moment coefficient; , is the roll restoring moment coefficient; ~ is the ship pitching hydrodynamic coefficient; , and They are the wave disturbance force in the heave direction, and the wave disturbance moment in the roll and pitch degrees of freedom; is the heave displacement, is the heave speed, is the heave acceleration, is the pitch angle, is the pitch angular velocity, is the pitch angular acceleration, is the roll angle, is the rolling angular velocity, is the pitch angle acceleration.

[0029] Preferably, the analysis of the motion law of the umbilical cable particles under the influence of vortex-induced vibration is specifically as follows:

[0030] The vortex-induced vibration response at the umbilical cable w is obtained through the slice simulation experiment:

[0031] (15)

[0032] In the formula, and are the excitation coefficient and additional mass coefficient at the umbilical cable w, respectively; is the hydrodynamic diameter, is the fluid density, is the fluid velocity, is the frequency of vibration of the umbilical cable;

[0033] The vortex-induced vibration response of nodes other than the high-quality slices is fitted by the Spline interpolation function; the expression of the Spline interpolation function is:

[0034] (18)

[0035] In the formula, For The displacement amplitude of the umbilical cable at ; For the i The displacement of the nodes in the x direction, is the displacement of the i+1th node in the x direction, For the i The second-order derivative at the nodes, For the i The displacement of the nodes in the z direction, is the displacement of the i+1th node in the z direction, is the second-order derivative at the i+1th node.

[0036] Preferably, the equation of motion of the umbilical cable particles is:

[0037] (1) Top particles:

[0038] ;

[0039] ;

[0040] (20)

[0041] (2) Intermediate particles:

[0042] ;

[0043] ;

[0044] (twenty one)

[0045] (3) Connecting particles:

[0046] ;

[0047] ;

[0048] (twenty two)

[0049] in, is the lateral displacement of the umbilical cable; is the axial displacement; is the longitudinal displacement; and are the lateral and axial fluid forces respectively; and are the transverse and axial stress components respectively; and are the lateral and axial displacement increments of the umbilical cable, represents the lateral displacement of the ship, represents the axial displacement of the ship, represents the longitudinal displacement of the ship, represents the lateral acceleration of the particle, represents the lateral displacement increment of the particle, represents the acceleration of the particle in the axial direction, represents the displacement increment of the particle in the axial direction, represents the acceleration of the particle in the longitudinal direction, is the load equivalent gravity.

[0050] The method for analyzing the motion of an umbilical cable affected by vortex-induced vibration provided by the present invention has the following advantages compared with the prior art:

[0051] The umbilical cable motion analysis method affected by vortex-induced vibration of the present invention establishes an IB-LBM architecture model of the umbilical cable system to study the dynamic parameter change law of the umbilical cable under the motion of the mother ship and the interference of vortex-induced vibration. Under the IB-LBM architecture, according to the actual connection characteristics of the umbilical cable, the boundary particles of the umbilical cable are divided into top particles connected to the mother ship, connection particles connected to the load, and intermediate particles of the umbilical cable itself, and a direct force immersed boundary method umbilical cable dynamics model is proposed according to the classification of particles. In addition, according to the characteristic that the immersed boundary method particles have mass, the dynamic characteristics of the umbilical cable under different masses are studied. The vortex-induced vibration model adopts a discrete slicing method to obtain the vortex-induced vibration model of discrete boundary particles, and then expands the Spline interpolation function to obtain the vortex-induced vibration response of the entire umbilical cable particles. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the deep sea mining and exploration system of the present invention.

[0053] Figure 2 It is a schematic diagram of slicing the umbilical cable in the present invention.

[0054] Figure 3 It is a curve diagram of the change of lateral surge, longitudinal surge and heave displacement in the present invention.

[0055] Figure 4 It is a curve diagram of the roll, pitch and yaw angle changes in the present invention.

[0056] Figure 5 It is a schematic diagram of the umbilical cable system model in the present invention.

[0057] FIG. 6 ( a ) is a visualization diagram of the fluid flow rate when the umbilical cable is working in the experimental verification of the present invention.

[0058] FIG6( b ) is a visualization diagram of the watershed density distribution when the umbilical cable is working in the experimental verification of the present invention.

[0059] Figure 7 It is a three-dimensional diagram of the vortex-induced vibration response of each part of the umbilical cable over a period of time in the experimental verification of the present invention.

[0060] Figure 8 It is a summary comparison diagram of the axial displacement of each section of the umbilical cable in the experimental verification of the present invention.

[0061] Fig. 9 It is a comparison diagram of the vortex-induced vibration responses of various sections of the umbilical cable in the experimental verification of the present invention.

[0062] Fig.10 It is a comparison diagram of stress changes in various sections of the umbilical cable in the experimental verification of the present invention. DETAILED DESCRIPTION

[0063] The specific embodiments of the present invention are described in detail below. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0064] like Figure 1 As shown, the umbilical cable motion analysis method affected by vortex-induced vibration of the present invention is aimed at the mother ship-umbilical cable-load multi-body motion. By establishing the IB-LBM architecture model of the umbilical cable system, the dynamic parameter change law of the umbilical cable under the mother ship motion and vortex-induced vibration interference is analyzed. Under the IB-LBM architecture, the umbilical cable is composed of many particles and springs, wherein the particles are movable and have mass, and the springs only provide elastic force. On this basis, according to the actual connection characteristics of the umbilical cable, the present invention divides the boundary particles of the umbilical cable into top particles connected to the mother ship, connection particles connected to the load, and intermediate particles of the umbilical cable itself, and proposes a direct force immersed boundary method umbilical cable dynamics model according to the classification of particles; in addition, according to the characteristic that the immersed boundary method particles have mass, the dynamic characteristics of the umbilical cable under different masses are analyzed; and then the vortex-induced vibration response at the slice is expanded by the Spline interpolation function to obtain the vortex-induced vibration response of the entire umbilical cable particle.

[0065] The IB-LBM architecture is a fluid-solid coupling calculation method that combines the Immersed Boundary Method (IBM) and the Lattice Boltzmann Method (LBM). In the IB-LBM architecture, the solid boundary is embedded in the fluid grid through IBM, and each grid point in the fluid grid is updated according to the position and motion state of the solid boundary. This method can effectively handle the interaction between fluid and solid, and is suitable for problems with complex geometries and dynamic boundary conditions. The NS equation is the basic equation that describes fluid motion. The IB-LBM architecture uses LBM to solve the NS equation. Through the collision and migration process of LBM, physical quantities such as the velocity field and pressure field of the fluid can be simulated, thereby realizing the dynamic simulation of the fluid.

[0066] The method for analyzing the motion of an umbilical cable affected by vortex-induced vibration of the present invention comprises the following steps:

[0067] Step S1, construct fluid control equations and IB-LBM

[0068] The present invention adopts finite volume method to model the ship and fluid domain, the domain is divided into two parts, water and air, and dynamic grid technology is adopted. The turbulence model adopts Spalart-Allmaras turbulence equation.

[0069] Assuming the fluid is viscous and incompressible, the governing equation of the fluid is:

[0070] ;

[0071] (1)

[0072] in, is the velocity vector; is the density; For pressure; is kinematic viscosity; is the external body force vector; is the gradient operator.

[0073] In actual situations, the ocean fluid is in a state of high Reynolds number, and the influence of turbulence needs to be considered. Therefore, a turbulence model needs to be introduced on the basis of equation (1) for calculation. In this embodiment, the Spalart-Allmaras turbulence equation is introduced, which is expressed as follows:

[0074] (2)

[0075] in, Additional terms arising from turbulence; is the turbulent viscosity dissipation due to wall obstruction and liquid viscosity; and is a constant; is the molecular kinematic viscosity; is the self-source term, represents the molecular kinematic viscosity vector, For fluid i The velocity vector in the direction, , , are Cartesian coordinates, is the fluid dynamic viscosity, is the fluid density. The variables are calculated as follows:

[0076] ; ; ; ; ; ; ; ; ; .

[0077] , , , , , , , is the closure constant, is the turbulent viscosity, , , is the empirical function of the turbulence model, is the deformation tensor, is the strain rate tensor, is the distance to the wall, is the intermediate variable, for j Direction velocity vector, is the velocity vector in the k direction; the default values ​​are as follows:

[0078] ; ; ; ; ; ; ; .

[0079] In the IB-LBM framework, the velocity field in the fluid domain is determined by the discrete grid distribution function and is calculated as follows:

[0080] (3)

[0081] in, is the particle density distribution function; is the equilibrium distribution function of the particle; is the velocity vector; is the volume force at the Euler point, is the grid point position of the current particle, t Indicates the current grid time of the particle, is the relaxation time; and The expressions are:

[0082] (4)

[0083] (5)

[0084] in, is the velocity vector at the current grid point, is the grid speed, is the volume force of the flow field, is the volume force at the Euler point, is the weight coefficient vector of each direction. In the two-dimensional case, D2Q9 is the most widely used model for solving the flow field part of the IB-LBM model. The D2Q9 model refers to the lattice Boltzmann model using nine velocity directions in two-dimensional space. The velocity distribution function on each grid describes the velocity and density of the fluid at that location, and the velocity distribution function is updated through collision and migration processes. In D2Q9, . Velocity vector .

[0085] The Spalart-Allmaras turbulence equation introduced is numerically solved by the difference method and is expressed as follows:

[0086] (6)

[0087] in, Additional terms arising from turbulence; is the turbulent viscosity dissipation due to wall obstruction and liquid viscosity; and is a constant; represents the molecular kinematic viscosity vector, For fluid i Speed ​​in direction.

[0088] In the immersed boundary method, the fluid force on the solid boundary particles is determined by the flow velocity of the flow field around the particles and the related weight coefficients, and the solid boundary also has a feedback volume force on the fluid domain. The calculation equations for the flow field velocity and volume force of the solid boundary particles are as follows:

[0089] (7)

[0090] (8)

[0091] in, is the velocity of the solid affected by the fluid; is the velocity of the fluid near the solid boundary particles; is the Euler coordinate of the flow field grid; is the Lagrangian coordinates of the solid boundary points; is the Dirac interpolation function; is the volume force of the flow field near the solid boundary particles.

[0092] Step S2: constructing a numerical model of the mother ship's motion

[0093] In complex sea conditions, the mother ship will produce six degrees of freedom motions such as heave, sway, surge, pitch, pitch and roll under the influence of sea conditions, which will drive the umbilical cable to produce complex motion underwater. Among them, heave, roll and pitch are the main factors causing the ship's motion. The dynamic equations of heave, roll and pitch of the ship in waves can be expressed as:

[0094]

[0095] ;

[0096] (9)

[0097] in, , are the ship mass and the additional mass for the ship's heave motion respectively; , are the roll moment of inertia and the roll additional moment of inertia respectively; , are pitch moment of inertia and pitch additional moment of inertia respectively; ~ is the hydrodynamic coefficient of the ship's heave motion; is the roll damping moment coefficient; , is the roll restoring moment coefficient; ~ is the ship pitching hydrodynamic coefficient; , and They are the wave disturbance force in the heave direction, and the wave disturbance moment in the roll and pitch degrees of freedom; is the heave displacement, is the heave speed, is the heave acceleration, is the pitch angle, is the pitch angular velocity, is the pitch angular acceleration, is the roll angle, is the rolling angular velocity, is the pitch angle acceleration.

[0098] Step S3, constructing a vortex-induced vibration model of the umbilical cable

[0099] The umbilical cable vortex-induced vibration exists in two directions, namely the In-Line (IL) direction and the Cross Flow (CF) direction. The vortex-induced vibration in the IL direction coincides with the influence of the flow-solid coupling and is not considered here. In the CF direction, the umbilical cable model can be simplified to a two-dimensional plane using the slicing principle. The simplification process is as follows: Figure 2 shown.

[0100] Assume that each slice simplified to two dimensions can be regarded as a cylindrical model supported by elastic force, and there is only one degree of freedom in the CF direction. On this basis, assume that the vibration in the CF direction is a single-frequency harmonic response, then the function of the vortex-induced vibration response in time and space is expressed as:

[0101] (10)

[0102] in, coordinate The displacement amplitude at ; is the frequency of the vortex-induced vibration response of the umbilical cable. According to the conditions of formula (10), the lift in the z direction is It is expressed as:

[0103] (11)

[0104] in, is the displacement amplitude in the z direction, is the phase angle.

[0105] When the umbilical cable is working in the deep sea, there are differences in the vortex-induced vibration responses at different depths. A single slice experiment cannot show the vortex-induced vibration responses of the umbilical cable at all depths. However, if a slice simulation experiment is performed at each depth on the umbilical cable model in fluid-solid coupling, the experimental calculation amount will be too large. Therefore, in order to save computing resources, this embodiment uses a segmented method to segment the umbilical cable. The vortex-induced vibration response is closely related to the curvature of the umbilical cable during operation. For this reason, this embodiment obtains a curve of the change of the curvature of the umbilical cable with increasing depth in fluid-solid coupling through a separate simulation experiment. The change in curvature is similar to the measured data of the curvature of the umbilical cable. According to the curve, this embodiment uses four linear relationships to linearly couple the curve. The specific fitting is as follows: Figure 2 shown.

[0106] Through the simulation experiment of slices, the lift can be obtained According to the numerical model, the lift and vortex-induced vibration response of the umbilical cable have the following nonlinear relationship:

[0107] (12)

[0108] in, is the hydrodynamic diameter, is the fluid velocity, and are the excitation coefficient and additional mass coefficient at the umbilical cable w, is the acceleration in the z direction at coordinate w, is the velocity in the z direction at coordinate w.

[0109] Substituting equations (10) and (11) into equation (12), we obtain:

[0110] (13)

[0111] in, is the amplitude at coordinate w, is the hydrodynamic diameter, is the fluid density, is the fluid velocity, is the vortex-induced vibration response frequency of the umbilical cable, The phase angle of the umbilical cable vibration, is the displacement amplitude at coordinate w. By simplifying formula (13) by sub-items, we can obtain:

[0112] (14)

[0113] Substituting equation (14) into equation (10), the vortex-induced vibration response at the umbilical cable w can be obtained through the slice simulation experiment:

[0114] (15)

[0115] In the formula, and are the excitation coefficient and additional mass coefficient at the umbilical cable w, respectively, which are expressed by equations (16) and (17) in the calculation process as follows:

[0116] (16)

[0117] (17)

[0118] In the formula, represents the fluid velocity, It represents the integral number of vibration cycles in the cross-flow direction or downstream direction. is the length of the umbilical cable.

[0119] In actual situations, the changes of the umbilical cable in time and space have the characteristics of continuity. Therefore, the interpolation model can be used to extend the vortex-induced vibration response at the slice obtained by the discrete slice experiment to the entire umbilical cable. The cubic Spline interpolation function is a constrained piecewise cubic function. The function is smooth at the nodes and its first-order and second-order derivatives are continuous variables, which is consistent with the continuity characteristics of the umbilical cable in time and space. The vortex-induced vibration response of the nodes outside the high-quality slices is fitted by the Spline interpolation function. The expression of the Spline interpolation function is:

[0120] (18)

[0121] In the formula, For The displacement amplitude of the umbilical cable at ; For the i The displacement of the nodes in the x direction, is the displacement of the i+1th node in the x direction, For the i The second-order derivative at the nodes, For the i The displacement of the nodes in the z direction, is the displacement of the i+1th node in the z direction, is the second-order derivative at the i+1th node.

[0122] Step S4: constructing a direct force immersed boundary method umbilical cable dynamics model

[0123] The coupling between solid structures and fluids is not only due to the mechanical interaction between the two, but also due to physical constraints on the solid structure, and other force fields and limitations of the material itself must also be considered.

[0124] In this embodiment, a direct force immersed boundary method umbilical cable particle motion dynamics model is designed according to the working characteristics of the umbilical cable. The principle is as follows: according to the immersed boundary method, the umbilical cable particles are divided into three types. The first type is the particle connected to the ship at the head end. The motion law of this particle is consistent with the pulley of the ship's umbilical cable retracting rack; the second type is the connected particle connected to the load at the tail end. The characteristic is that the upper end of the particle is the umbilical cable, and the lower end is directly connected to the load, and it moves under the influence of both; the third type is the intermediate particle, which produces dynamic motion due to the fluid force and the internal stress of the upper and lower umbilical cables. The motion equations of the three particles affected by ship motion, fluid impact and vortex-induced vibration are as follows:

[0125] (1) Top particles:

[0126] ;

[0127] ;

[0128] (20)

[0129] (2) Intermediate particles:

[0130] ;

[0131] ;

[0132] (twenty one)

[0133] (3) Connecting particles:

[0134] ;

[0135] ;

[0136] (twenty two)

[0137] in, is the lateral displacement of the umbilical cable; is the axial displacement; is the longitudinal displacement; and are the lateral and axial fluid forces respectively; and are the transverse and axial stress components respectively; and are the lateral and axial displacement increments of the umbilical cable, represents the lateral displacement of the ship, represents the axial displacement of the ship, represents the longitudinal displacement of the ship, represents the lateral acceleration of the particle, represents the displacement increment of the k+1th particle in the lateral direction, represents the acceleration of the particle in the axial direction, represents the displacement increment of the k+1th particle in the axial direction, represents the acceleration of the particle in the longitudinal direction, is the load equivalent gravity.

[0138] Adding equations (20), (21), and (22) to the umbilical cable fluid-solid coupling model, the discretized displacement calculations of the three particles can be expressed as follows:

[0139] ;

[0140] ;

[0141] (twenty three)

[0142] ;

[0143] ;

[0144] (twenty four)

[0145] ;

[0146] ;

[0147] (25)

[0148] in, The displacement of the load particle in the y direction is calculated for the n+1 time step, The displacement of the load particle in the y direction for n calculation time steps, is the displacement increment of the ship, The displacement of the load particle in the x direction is calculated for the n+1 time step, The displacement of the load particle in the x direction is calculated for n time steps, The displacement of the load particle in the z direction is calculated for the n+1 time step, Calculate the y-direction displacement of the intermediate particle in the n+1 time step, Calculate the y-direction displacement of the particle in the nth time step, Calculate the x-direction displacement of the intermediate particle in the n+1 time step, The x-direction displacement of the particle in the middle of the calculation time step is n, Calculate the z-direction displacement of the intermediate particle in the n+1 time step, Calculate the y-direction displacement of the top particle for the n+1 time step, The y-direction displacement of the top particle is calculated for n time steps, The displacement increment of the top particle in the y direction is calculated for n time steps, Calculate the x-direction displacement of the top particle for time step n+1, The x-direction displacement of the top particle is calculated for n time steps, The displacement increment of the top particle in the x direction is calculated for n time steps, Calculate the z-direction displacement of the top particle for time step n+1, , is the displacement increment of the axial and horizontal items of the intermediate particles, which can be calculated by the following formula:

[0149] (26)

[0150] (27)

[0151] (28)

[0152] (29)

[0153] (30)

[0154] ;

[0155] (31)

[0156] in, Calculate the stress between particle k and particle k+1 for time step n; Calculate the stress between node k and node k+1 for time step n-1, Calculate the stress between particle k and particle k-1 for time step n-1, is the relative quality of k nodes; is the Lagrangian coordinate of particle k; is the Lagrangian coordinate of the k+1 particle, is the initial Lagrangian coordinate of particle k+1, is the initial Lagrangian coordinate of particle k; and are the acceleration vector and velocity vector of particle k, and their internal components are and ; Calculate the acceleration vector of particle k at time step n-1, Calculate the velocity vector in the y direction for particle k in time step n, Calculate the acceleration vector in the y direction of particle k for n time steps, Calculate the stress in the y direction of the initial particle for time step n-1, Calculate the fluid force on the initial particle in the y direction for time step n-1, Calculate the fluid force in the y direction for particle k in time step n-1, is the static load, is the phase difference vector between particle k and particle k+1, and the calculation formula is:

[0157] (32)

[0158] in, is the phase difference vector between particle k and particle k+1, is the displacement of particle k in the y direction, is the displacement of particle k-1 in the y direction, is the displacement of particle k in the x direction. is the displacement of particle k-1 in the x direction.

[0159] In the present invention, according to the particle dynamics model, the top particles are affected by the ship motion. Therefore, the coordinates of the top particles are updated according to the ship dynamics equation (9). The z direction of the middle particles is considered as the displacement under the influence of the vortex-induced force. The x and y directions are affected by the fluid force. Therefore, according to equations (3) to (5) in the IB-LBM framework, the fluid domain parameter values ​​are determined and a slice experiment simulation is performed. The fluid force and the external force acting on the particles are solved using equation (26). The particle displacement increment is calculated by combining equations (23) to (32) and the particle coordinates are updated. Then, the dynamic response displacement and motion trajectory of the umbilical cable affected by the vortex-induced vibration in the x, y and z directions are obtained.

[0160] Experimental verification

[0161] The fluid domain in the simulation system architecture is set according to the seawater parameters. The specific parameters of the umbilical cable system model are shown in Table 1.

[0162] Table 1 Umbilical cable system model parameters

[0163]

[0164] 1) Numerical results and analysis of ship motion response

[0165] Figure 3 , Figure 4The following are the response curves of the six degrees of freedom of the ship under the fourth level of sea conditions. It can be seen from the figure that the response of the ship's heave motion varies in the range of -1~1m, the surge motion response varies in the range of -0.05~0.05m, and the sway displacement is almost 0; the bow motion is almost 0, the pitch angle varies in the range of -0.1~0.15°; the roll response is almost 0. From the above data analysis, it can be seen that the movement of the ship is mainly determined by the three degrees of freedom of heave, pitch and surge.

[0166] 2) Umbilical cable fluid-solid coupling and slice simulation analysis

[0167] Figure 5 Figure 6 shows the umbilical cable system and its visualization during the simulation. In this experiment, the basic metric parameters of the umbilical cable simulation are as follows: Figure 5 As shown in the figure, D is the depth of the fluid domain; L is the length of the umbilical cable; W is the width of the fluid domain, and the fluid domain simulation area size is 200 100. Figure 6 (a) shows the visualization of the fluid flow velocity when the umbilical cable is working. It can be seen that due to the non-streamlined structure of the load, the fluid flow velocity is almost zero in the back flow direction of the load, while on both sides of the back flow area, the fluid flow velocity is greater than that of other fluid domains. This is because the fluid from the positive flow direction of the load is squeezed into this area. According to the continuity equation in formula (1), the amount of fluid flowing in and out is the same. Therefore, when the inflow increases, the flow velocity is bound to increase. Figure 6 (b) is a density distribution diagram of the flow domain, from which it can be seen that in the back flow area of ​​the load, the density is smaller than that of other flow domains due to the slow flow velocity.

[0168] Figure 7 The figure is a three-dimensional surface diagram of the vortex-induced vibration response of the umbilical cable over a period of time, where the axial direction is the vortex-induced vibration response, the transverse coordinate is the time series, and the longitudinal coordinate is the discrete segment of the umbilical cable. It can be seen that at the same time, as the depth of the umbilical cable decreases, the changes in the vortex-induced vibration of each part of the umbilical cable fluctuate. Under the same section of the umbilical cable, the vortex-induced vibration of this section also fluctuates with the increase of time. This part shows that the umbilical cable fluctuates in space and time.

[0169] 3) Influence of vortex-induced vibration and mother ship motion on dynamic characteristics of umbilical cable

[0170] Figures 8 to 10 The axial displacement, vortex-induced vibration response and stress response are summarized and compared respectively. Figure 8 It can be seen that the axial displacement caused by the movement of the mother ship is weakened in each section. When the mother ship produces an axial displacement of -0.8~0.6m, the axial displacement response transmitted to the load is weakened to ±0.1~±0.4m. Fig. 9 The vortex-induced vibration response changes of each section of umbilical cable. Fig.10This is a summary of stress response. It can be seen from the figure that when H=0.1L, the internal stress change of the umbilical cable is the largest. This is because this part is the connection between the mother ship and the umbilical cable. The downward tension of the umbilical cable in this section is the largest, and the displacement response of the mother ship is the largest. The tension change at this point is the most obvious. As the depth decreases, the stress change amplitude of the umbilical cable will decrease and there will be a delay. During the delay time, the stress change will be affected by the vortex-induced vibration. Fig.10 It can be seen from the enlarged figure that when H=L, there is a small fluctuation in the stress change curve, indicating that with the increase of depth, the influence of vortex-induced vibration on the internal stress and load of the umbilical cable tends to increase.

[0171] From the above analysis, it can be seen that when the umbilical cable is working, the vortex-induced vibration and the movement of the mother ship have a greater impact on the umbilical cable. Figure 8 At H=L, the axial displacement response of the mother ship's motion transmitted to this point reaches ±0.4m, while Fig.10 The stress value of the umbilical cable affected by vortex-induced vibration here reaches 1.05×10 5 , the umbilical cable is prone to fatigue damage during long-term operation. Therefore, when engineering equipment is operating in deep sea, the impact of vortex-induced vibration on load positioning needs to be considered. A spoiler can be installed at a deeper position of the umbilical cable to balance the pressure around the umbilical cable and the load as much as possible, so as to achieve the effect of suppressing vortex-induced vibration, thereby stabilizing the tail end trajectory of the umbilical cable.

[0172] Experiments show that due to the elastic characteristics of the umbilical cable, there will be a delay and amplitude weakening when the axial displacement caused by the movement of the mother ship is transmitted to the load. During the delay time, the vortex-induced vibration will affect the change of the internal stress of the umbilical cable, and this effect will increase with increasing depth; the unit mass of the umbilical cable has a significant influence on the maximum deformation and maximum stress difference of the umbilical cable.

[0173] The above implementation cases are only preferred embodiments of the present invention and are not intended to limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, they are not intended to limit the present invention. Therefore, any simple modification, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for analyzing the motion of an umbilical cable affected by vortex-induced vibration, characterized in that: The analysis method first uses the finite volume method to model the ship and the fluid domain, and the ship motion is combined with the six-degree-of-freedom motion of heave, sway, surge, pitch, pitch and roll; then the fluid-solid coupling calculation method of the immersed boundary method and the lattice Boltzmann method is used and the Spalart-Allmaras turbulence equation is introduced to establish the IB-LBM architecture model of the umbilical cable system; the model discretizes the umbilical cable into umbilical cable particles, and the umbilical cable particles are the top particles connected to the mother ship, the connecting particles connected to the load and the intermediate particles of the umbilical cable itself, and the motion law of the umbilical cable particles under the influence of ship motion and vortex-induced vibration is analyzed; then the slicing principle is used to simplify the umbilical cable particle motion model to a two-dimensional plane, and the interpolation model is used to extend the vortex-induced vibration response at the slice to the entire umbilical cable, and the direct force immersed boundary method umbilical cable dynamics model is constructed to analyze the motion law of the umbilical cable in the fluid domain; The analysis of the movement law of umbilical cable particles under the influence of vortex-induced vibration is specifically as follows: The vortex-induced vibration response at the umbilical cable w is obtained through the slice simulation experiment: (15) In the formula, and are the excitation coefficient and additional mass coefficient at the umbilical cable w, respectively; is the hydrodynamic diameter, is the fluid density, is the fluid velocity, is the frequency of vibration of the umbilical cable; The vortex-induced vibration response of nodes other than the high-quality slices is fitted by the Spline interpolation function; the expression of the Spline interpolation function is: (18) In the formula, For The displacement amplitude of the umbilical cable at ; For the i The displacement of the nodes in the x direction, For the i +1 node displacement in x direction, For the i The second-order derivative at the nodes, For the i The displacement of the nodes in the z direction, For the i +1 node displacement in z direction, For the i+ Second derivative at 1 node.

2. The method for analyzing umbilical cable motion affected by vortex-induced vibration according to claim 1, characterized in that: In the motion law of the umbilical cable particles, the fluid control equation of the umbilical cable particles is: Assuming the fluid is viscous and incompressible, the governing equation of the fluid is: ； (1) in, is the velocity vector; is the density; For pressure; is kinematic viscosity; is the external body force vector; is the gradient operator; In the IB-LBM framework, the velocity field in the fluid domain is determined by the discrete grid distribution function and is calculated as follows: （3） in, is the particle density distribution function; is the equilibrium distribution function of the particle; is the velocity vector; is the volume force at the Euler point, is the grid point position of the current particle, t Indicates the current grid time of the particle, is the relaxation time; and The expressions are: (4) (5) in, is the velocity vector at the current grid point, is the grid speed, is the volume force of the flow field, is the volume force at the Euler point, is the weight coefficient vector in each direction; The Spalart-Allmaras turbulence equation is introduced and numerically solved by the difference method, which can be expressed as: (6) in, Additional terms arising from turbulence; is the turbulent viscosity dissipation due to wall obstruction and liquid viscosity; and is a constant; represents the molecular kinematic viscosity vector, For fluid i Speed ​​in direction; In the immersed boundary method, the fluid force on the solid boundary particles is determined by the flow velocity of the flow field around the particles and the relevant weight coefficients. The solid boundary has a feedback fluid force on the fluid domain. The calculation equations of the two are: (7) (8) in, is the velocity of the solid affected by the fluid; is the velocity of the fluid near the solid boundary particles; is the Euler coordinate of the flow field grid; is the Lagrangian coordinate of the solid boundary point; is the Dirac interpolation function, is the volume force of the flow field near the solid boundary particles.

3. The method for analyzing umbilical cable motion affected by vortex-induced vibration according to claim 2, characterized in that: In the ship motion, the dynamic equations of the heave, roll and pitch of the ship in the waves are expressed as: ； ； （9） in, , are the ship mass and the additional mass for the ship's heave motion respectively; , are the roll moment of inertia and the roll additional moment of inertia respectively; , are pitch moment of inertia and pitch additional moment of inertia respectively; ~ is the hydrodynamic coefficient of the ship's heave motion; is the roll damping moment coefficient; , is the roll restoring moment coefficient; ~ is the ship pitching hydrodynamic coefficient; , and They are the wave disturbance force in the heave direction, and the wave disturbance moment in the roll and pitch degrees of freedom; is the heave displacement, is the heave speed, is the heave acceleration, is the pitch angle, is the pitch angular velocity, is the pitch angular acceleration, is the roll angle, is the rolling angular velocity, is the pitch angle acceleration.

4. The method for analyzing umbilical cable motion affected by vortex-induced vibration according to claim 1, characterized in that: The equation of motion of the umbilical cable particle is: 1) Top particles: ； ； (20) (2) Intermediate particles: ； ； (21) (3) Connecting particles: ； ； （22） in, is the lateral displacement of the umbilical cable; is the axial displacement; is the longitudinal displacement; and are the lateral and axial fluid forces respectively; and are the transverse and axial stress components respectively; and are the lateral and axial displacement increments of the umbilical cable, represents the lateral displacement of the ship, represents the axial displacement of the ship, represents the longitudinal displacement of the ship, represents the lateral acceleration of the particle, represents the lateral displacement increment of the particle, represents the acceleration of the particle in the axial direction, represents the displacement increment of the particle in the axial direction, represents the acceleration of the particle in the longitudinal direction, is the load equivalent gravity.

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