Numerical simulation method for vortex-induced vibration of deepwater riser considering platform motion

Abstract

A numerical simulation method of vortex-induced vibration of deepwater riser considering platform motion, comprising: constructing spatial point motion equation of deepwater riser and fluid force model based on wake oscillator equation; inputting riser structure parameters, platform motion parameters and background flow field parameters, and dimensionless number and empirical parameters required for vortex-induced vibration simulation; setting calculation total time and time step, discretizing riser into bar elements, setting initial conditions and boundary conditions; synchronously solving spatial point motion equation and wake oscillator equation by using central difference method, cyclically updating displacement, rotation angle and wake variable of each spatial point, and realizing dynamic prediction of vortex-induced vibration response. The method can efficiently and accurately obtain vortex-induced vibration response characteristics such as displacement and velocity of deepwater riser under the combined action of platform motion and background flow field, and provide numerical simulation means and important technical support with high calculation efficiency and strong adaptability for deepwater riser structure analysis, optimization design and performance improvement.

Description

TECHNICAL FIELD

[0001] The present application relates to structural vibration response measurement and numerical simulation technology, and particularly to a vortex-induced vibration numerical simulation method for a deepwater riser considering platform motion. BACKGROUND

[0002] As a typical structural vibration phenomenon, vortex-induced vibration is widely present in the process of interaction between engineering structures and fluids, and its main performance is the vibration response of the structure under the excitation of periodic vortex shedding. When viscous fluid flows around a bluff body (such as a riser, truss or cylinder), positive and negative vortices will alternately shed in the wake region within a certain Reynolds number range, forming a regular Karman vortex street structure. The alternately shed vortices act on the surface of the structure, exciting periodic streamwise and transverse fluid forces, and then inducing mechanical vibration of the structure. This phenomenon has obvious fluid-structure coupling characteristics: on the one hand, the vibration response is modulated by the wake characteristics; on the other hand, the structure motion also affects the shape of the wake, making the whole system present a nonlinear coupling evolution process. Especially when the vortex shedding frequency is close to the natural frequency of the structure, the "lock-in" phenomenon (i.e. frequency lock-in resonance) will be induced, which will lead to significant amplification of the structure amplitude, thus causing fatigue accumulation and structural damage.

[0003] The deepwater riser system carried by the floating platform is prone to strong vortex-induced vibration under the coupling action of marine multi-source loads (wind, wave, current), and its long-term fatigue damage has become a key problem in marine engineering. Therefore, it is urgent to develop a modeling and simulation system that can effectively characterize the vibration response characteristics of flexible structures, extract dynamic characteristics and measure engineering. At present, a large number of studies have proposed various calculation methods for predicting the vibration of deepwater risers based on semi-empirical models or fluid-structure coupling theory frameworks, which are used to assist engineering design, fatigue evaluation and response measurement analysis. However, none of them can consider platform motion. In contrast, high-fidelity computational fluid dynamics simulation has higher accuracy, but the calculation cost is high and it is difficult to adapt to large-scale engineering condition prediction; while the physical test method has high reliability, but the cost of device construction, boundary control and measurement data processing is huge, and its simulation capability for complex loads and platform motion is limited.

[0004] In recent years, engineering practice has put forward higher requirements for the accurate measurement, rapid prediction and expandable simulation of the vibration response of deepwater flexible structures. Under this background, high-efficiency numerical simulation and response extraction methods combined with platform real motion boundary input have gradually attracted attention.

[0005] It should be noted that the information disclosed in the above background section is only for understanding the background of the present application, and therefore can include information that does not constitute the prior art known to those of ordinary skill in the art. SUMMARY

[0006] The main purpose of the present application is to overcome the defects in the background art, and provide a deepwater riser vortex-induced vibration numerical simulation method considering platform motion.

[0007] To achieve the above object, the present application adopts the following technical solutions:

[0008] A deepwater riser vortex-induced vibration numerical simulation method considering platform motion, comprising the following steps:

[0009] Model establishment step: constructing a spatial point motion equation of the deepwater riser, and establishing a fluid force model based on a wake oscillator equation;

[0010] Parameter input step: inputting structural parameters of the deepwater riser, platform motion parameters, background flow field parameters, and dimensionless numbers and empirical parameters required for vortex-induced vibration simulation;

[0011] Solution setting step: setting a total calculation time and a time step, discretizing the riser along the length direction into rod elements, and setting initial conditions and boundary conditions;

[0012] Global spatial point solution step: synchronously solving the spatial point motion equation and the wake oscillator equation by using a central difference method, cyclically updating displacement, angle and wake variables of each spatial point, and realizing dynamic prediction of vortex-induced vibration response.

[0013] Further, the construction of the spatial point motion equation specifically comprises:

[0014] Discretizing the riser into rod elements and spatial points based on a vector finite element method, and the motion variables of each spatial point including displacement and angle;

[0015] Establishing a motion equation in a path unit according to Newton's second law, including a mass balance equation and a moment balance equation;

[0016] Stripping the rigid displacement component of the rod element through virtual reverse motion, and calculating pure deformation internal force and internal moment.

[0017] Further, the establishment of the fluid force model specifically comprises:

[0018] Based on the superposition of background flow field velocity and riser along-flow motion velocity, constructing a relative velocity expression of the riser and the flow field;

[0019] Correlating oscillation drag force coefficients and lift force coefficients to dimensionless wake variables, and introducing an inertia force term generated by platform motion;

[0020] Using a van der Pol type wake oscillator equation, and nonlinearly coupling vortex shedding frequency and riser vibration acceleration through empirical parameters;

[0021] The fluid force component expression including drag force, lift force and inertial force is established by velocity vector decomposition and force projection mapping.

[0022] Further, the internal force and internal moment calculation specifically includes:

[0023] The pure deformation quantity including the axis length change, axial torsion and bending deformation is extracted by virtually separating the rigid translation and rotation of the inverse kinematic link element;

[0024] The node internal force and bending moment are calculated based on the material mechanics theory;

[0025] The internal force and internal moment are integrated according to the static force balance condition of the spatial link element and mapped to the spatial point through the forward motion.

[0026] Further, in the global spatial point solving step:

[0027] The spatial point motion equation and the wake oscillator equation are discretized by using the explicit central difference format;

[0028] In each time step, the following steps are sequentially performed:

[0029] The spatial point displacement and rotation angle are updated;

[0030] The internal force and internal moment are calculated based on the pure deformation quantity;

[0031] The wake oscillator equation is solved to update the dimensionless wake variable; wherein the riser vibration acceleration is coupled with the wake oscillator equation as an input item; the wake variable is explicitly updated by the central difference method to drive the real-time calculation of the fluid force model;

[0032] The external force and external moment are calculated according to the fluid force model;

[0033] The synchronous coupling solution of the structure and the flow field is realized through the time step loop.

[0034] Further, the output response data of the dynamic prediction includes:

[0035] The in-line and cross-flow displacement, velocity and acceleration of the riser global spatial point;

[0036] The vortex-induced vibration amplitude based on the displacement response and the frequency characteristics extracted through frequency domain transformation.

[0037] Further, the frequency characteristics are extracted by:

[0038] The displacement response is subjected to fast Fourier transform or wavelet transform;

[0039] The main frequency and the lock-in interval characteristics of the vortex-induced vibration are extracted.

[0040] Further, the vector finite element method:

[0041] Simplify the model by mass concentration on the spatial point and the assumption of no mass of the rod element;

[0042] Directly construct the motion equation based on the second law of Newton, avoid the traditional stiffness matrix assembly;

[0043] Describe the motion trajectory through the path unit, and based on the mass point-unit processing mode of the structure, the internal force calculation method and the motion equation solving method, it is suitable for the vortex-induced vibration problem of large deformation and nonlinearity.

[0044] Further, the boundary condition setting comprises:

[0045] The riser bottom end is fixed and articulated to the wellhead, and all displacements and angles are constrained;

[0046] The riser top end is excited by platform motion, and a time-varying displacement boundary condition is applied.

[0047] The present application has the following beneficial effects:

[0048] The present application provides a deepwater riser vortex-induced vibration response numerical simulation method considering platform motion, first constructs the spatial point motion equation of the deepwater riser, and establishes a fluid force excitation model in combination with the wake oscillator equation, comprehensively considers the nonlinear coupling effect between the fluid wake and the structure. In the parameter input stage, the basic parameters of the deep sea riser structure and environment, and the dimensionless number and empirical parameters required for vortex-induced vibration simulation are systematically introduced, so as to ensure the generality and engineering adaptability of the model. Then set the total calculation time and time step, and divide the riser along the length direction into a plurality of rod elements, set the initial conditions and boundary conditions, and construct a global spatial point solving framework. The central difference method is used to solve the structure response and wake variable, and the spatial point, force and wake information are updated in real time, so as to realize the synchronous feedback of the structure dynamic response and the flow field action. Finally, the in-line and cross-flow displacement responses of any spatial point at any time can be output. Through the method of the present application, the displacement, velocity, acceleration and hydrodynamic response characteristics of the deepwater riser under the action of platform motion and background flow field can be obtained, the vortex-induced vibration response is efficiently and accurately predicted, and a numerical simulation method with high calculation efficiency and strong adaptability is provided for the structural analysis and optimization design of the deepwater riser.

[0049] The present application has significant advantages in the numerical simulation of deepwater risers compared with the prior art. Specifically, the present application can provide efficient and accurate prediction of the vortex-induced vibration response of deepwater risers considering platform motion, as well as in-depth mechanism analysis and research. The advantages of the present application compared with the prior art are:

[0050] 1. In engineering practice, the vortex-induced vibration of a deepwater riser under real marine environment is significantly affected by the motion of the upper platform. The semi-empirical numerical simulation method proposed in the embodiments of the present application can effectively introduce the platform motion parameters, accurately describe the coupling effect of the platform motion on the riser response, and improve the physical authenticity of the simulation.

[0051] 2. The embodiments of the present application adopt the vector finite element method and the wake oscillator equation to construct a numerical model, and combine the central difference format to form a time domain solving framework. The calculation process does not require iterative solution, and can meet the demand of rapid response evaluation under large-scale working conditions, and has high calculation efficiency.

[0052] 3. The method of the embodiments of the present application does not depend on the stiffness matrix assembly in the traditional finite element method, but directly constructs the motion equation based on Newton's second law, and combines the characteristics of the motion equation in the processing of particle motion, internal force calculation and motion equation solving, and is particularly suitable for processing the large deformation and nonlinear problems of vortex-induced vibration of a deepwater riser.

[0053] In summary, the numerical simulation method of vortex-induced vibration of a deepwater riser considering platform motion provided by the present application can efficiently and accurately predict the vortex-induced vibration response of a deepwater riser under the combined action of platform motion and background flow field, thereby providing important technical support for the design improvement and performance improvement of a deepwater riser.

[0054] Other beneficial effects of the embodiments of the present application will be further described below. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 The overall flowchart of the numerical simulation method of vortex-induced vibration of a deepwater riser considering platform motion of the present application.

[0056] Figure 2 The flowchart of the numerical simulation method of vortex-induced vibration of a deepwater riser considering platform motion of the embodiments of the present application.

[0057] Figure 3 The schematic diagrams of (a) vortex-induced vibration of a deepwater riser considering platform motion of the embodiments of the present application and (b) fluid force load of the embodiments of the present application are shown.

[0058] Figure 4a And Figure 4b Figures are respectively comparison and verification diagrams of the root mean square amplitude of the in-line and cross-flow vibration of a deepwater riser calculated based on experimental example one by the method of the present application and the test results.

[0059] Figure 5a And Figure 5b Figures are respectively time history curve diagrams of the in-line and cross-flow vibration displacement of a deepwater riser calculated based on experimental example two by the method of the present application.

[0060] Figure 6a AndFigure 6b respectively are the variation cloud maps of the in-line and cross-flow vibration displacement responses of the deepwater riser calculated by the method of the present application based on Experimental Example Two. DETAILED DESCRIPTION

[0061] The embodiments of the present application are described in detail below. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present application and its applications.

[0062] The present application aims to provide a numerical simulation method for vortex-induced vibration of deepwater riser considering platform motion, which can efficiently and accurately predict the vortex-induced vibration response of deepwater riser under the combined action of platform motion and background flow field, thereby providing key technical support for structural design optimization and performance improvement.

[0063] Referring to Figure 1 , the present application provides a numerical simulation method for vortex-induced vibration of deepwater riser considering platform motion, comprising the following steps:

[0064] Model establishment step: constructing the spatial point motion equation of the deepwater riser and establishing the fluid force model based on the wake oscillator equation;

[0065] Parameter input step: inputting the structural parameters of the deepwater riser, platform motion parameters, background flow field parameters, and dimensionless numbers and empirical parameters required for vortex-induced vibration simulation;

[0066] Solution setting step: setting the total calculation time and time step, discretizing the riser along the length direction into rod elements, setting the initial conditions and boundary conditions;

[0067] Global spatial point solving step: synchronously solving the spatial point motion equation and the wake oscillator equation by using the central difference method, cyclically updating the displacement, angle and wake variables of each spatial point, and realizing dynamic prediction of the vortex-induced vibration response.

[0068] In some embodiments, the construction of the spatial point motion equation specifically comprises: discretizing the riser into rod elements and spatial points based on the vector finite element method, the motion variables of each spatial point including displacement and angle; establishing the motion equation within the path element according to Newton's second law, including mass balance equation and moment balance equation; calculating the pure deformation internal force and internal moment by stripping the rigid body displacement component of the rod element through virtual inverse motion.

[0069] In some embodiments, the establishment of the fluid force model specifically comprises: based on the superposition of the background flow field velocity and the riser in-line motion velocity, constructing the relative velocity expression of the riser and the flow field; correlating the oscillation drag force coefficient and the lift force coefficient to the dimensionless wake variable, and introducing the inertial force term generated by the platform motion; using the van der Pol type wake oscillator equation to nonlinearly couple the vortex shedding frequency and the riser vibration acceleration through an empirical parameter; through velocity vector decomposition and force projection mapping, establishing the fluid force component expression including the drag force, the lift force and the inertial force.

[0070] In some embodiments, the internal force and internal moment calculation specifically comprises: through virtual inverse motion separation of the rigid body translation and rotation of the bar element, extracting the pure deformation quantity including the axis length change, the axial twist and the bending deformation; based on the material mechanics theory, calculating the node internal force and the bending moment; according to the spatial bar element static force balance condition, integrating the internal force and the internal moment, and mapping to the spatial point through the forward motion.

[0071] In some embodiments, in the global spatial point solving step: using the explicit central difference format to discretize the spatial point motion equation and the wake oscillator equation; in each time step, sequentially performing: updating the spatial point displacement and the rotation angle; calculating the internal force and the internal moment based on the pure deformation quantity; solving the wake oscillator equation to update the dimensionless wake variable; wherein, the riser vibration acceleration is coupled with the wake oscillator equation as an input term; the wake variable is explicitly updated through the central difference method to drive the real-time calculation of the fluid force model; the external force and the external moment are calculated according to the fluid force model; through the time step cycle, the synchronous coupling solving of the structure and the flow field is realized.

[0072] In some embodiments, the output response data of the dynamic prediction includes: the in-line and cross-flow displacement, velocity and acceleration of the riser global spatial point; the vortex-induced vibration amplitude based on the displacement response and the frequency characteristics extracted through frequency domain transformation. The frequency characteristics are extracted by: performing fast Fourier transform or wavelet transform on the displacement response; extracting the main frequency and the lock-in interval characteristics of the vortex-induced vibration.

[0073] In some embodiments, the vector finite element method: simplifies the model through the mass concentration in the spatial point and the massless assumption of the bar element; directly constructs the motion equation based on Newton's second law, avoiding the traditional stiffness matrix assembly; through the way element description of the motion trajectory, based on its mass point-element processing mode of the structure, internal force calculation method and motion equation solving method, it is suitable for the vortex-induced vibration problem of large deformation and nonlinearity.

[0074] In some embodiments, the boundary condition setting comprises: the riser bottom end is fixedly hinged to the wellhead, constraining all displacements and rotation angles; the riser top end is excited by the platform motion, and a time-varying displacement boundary condition is applied.

[0075] This invention provides a numerical simulation method for vortex-induced vibration of deep-water risers that takes into account the influence of platform motion. By constructing the spatial point motion equations of the deep-sea riser and establishing a hydrodynamic model based on the wake oscillator equations, the method solves for the global spatial points using the central difference method. This enables efficient and accurate prediction of the vortex-induced vibration response of deep-water risers under the combined effects of platform motion and background flow field, obtaining its displacement, velocity, acceleration, and hydrodynamic response characteristics. As a numerical modeling and simulation method with high computational efficiency, adaptability to complex boundaries, and the ability to extract response features, it is suitable for simulation analysis and response measurement of structural vibration behavior in complex environments. It can be used to evaluate and extract vibration characteristics of deep-water flexible risers. It can not only simulate response characteristics and obtain vibration signals at key structural points, but also, in conjunction with experimental verification systems, serve applications such as vibration monitoring, frequency domain analysis, and fatigue life prediction of mechanical structures. It provides a computationally efficient and adaptable numerical simulation method and key technical support for the structural analysis, optimization design, and performance improvement of deep-water risers, and has good engineering application prospects and research value.

[0076] The following further describes specific embodiments of the present invention, algorithm examples, and experimental verification.

[0077] A numerical simulation method for vortex-induced vibration of a deep-water riser considering platform motion includes the following steps:

[0078] The model establishment steps include constructing the spatial point motion equations of the deep-sea riser and establishing a hydrodynamic model based on the wake oscillator equations. The construction of the spatial point motion equations of the deep-sea riser involves dividing the deep-sea riser into sections using the vector finite element method. N Each rod element, and together with N+ Connected by one spatial point. Any spatial point in the riser system. i The position vector is a time function. In vector structural mechanics analysis, a set of time points is used to describe the trajectory of a spatial point. A spatial point moves from one position at a certain time point to another over a time interval. If the motion of the spatial point within that time interval satisfies the standard governing equations, then that time interval is considered a path unit. Within any path unit, the riser spatial point... i The motion of a point in space satisfies Newton's second law, and the equations of motion for that point can be constructed accordingly:

[0079]

[0080] In the formula, N The number of units to be divided; m i The total mass of the point in space; I i Let be the total mass moment of inertia, which is a symmetric matrix; ζ The damping ratio; F iext and F i int are the spatial points i experienced by the combined external force and the combined internal force; M i ext and M i int are the spatial points i experienced by the combined external moment and the combined internal moment; is the rotation angle of the spatial point, is the displacement of the spatial point, t is the time.

[0081] The fluid force model based on the wake oscillator equation is established, and the velocity of the background flow field and the velocity of the riser in the flow direction (the superposition of the riser motion caused by the platform motion and the unknown vibration velocity in the flow direction) together constitute the expression of the relative velocity between the riser and the background flow field:

[0082]

[0083] is the velocity component.

[0084] The relative velocity expression is combined with the oscillation drag coefficient and the oscillation lift coefficient described by the dimensionless wake variable to respectively construct the expression of the drag force and the expression of the lift force :

[0085]

[0086] In the formula, ρ e is the density of the background flow field, C DM is the Morison drag coefficient of the static riser, is the outer diameter of the riser.

[0087] Since the motion of the top platform will drive the motion of the riser, an additional inertial force in the flow direction will be generated, and its expression is:

[0088]

[0089] In the formula, C M is the inertia coefficient of the static riser, a xThe acceleration of the riser in the streamwise direction.

[0090] The drag force F D and the lift force F L are projected into x and y directions, and superimposed with the inertial force, to obtain the fluid forces in x and y directions F x and F y The expressions are:

[0091]

[0092] where φ is the relative velocity V rel and the angle between x directions, and further obtain:

[0093]

[0094] The oscillating drag coefficient C D and the oscillating lift coefficient C L can be described by the dimensionless wake variables v and w

[0095]

[0096] where C D0 and C L0 are the drag and lift coefficients of the stationary riser, respectively.

[0097] The van der Pol equation, which contains the dimensionless wake variables and the riser motion velocity and satisfies the nonlinear characteristics of the wake oscillator, is used as the wake oscillator equation:

[0098]

[0099] where ε x , ε y , x and y are empirical parameters estimated by experiments, and the vortex shedding circular frequency is expressed as:

[0100] ​

[0101] where, St is the Strouhal number.

[0102] Thus, the fluid force model based on the wake oscillator equation is:

[0103]

[0104] The parameter input step firstly inputs the basic parameters of the deepwater riser structure and environment, including the length L , outer diameter D , inner diameter d , mass per unit length m s , pretension T 0, damping ratio ζ , Young's modulus E , Poisson's ratio ν and natural frequency f n , oscillation amplitude A o and oscillation frequency f o of the platform motion, density ρ e and flow velocity U e of the background flow field; secondly, the dimensionless numbers and empirical parameters required for the vortex-induced vibration simulation are input, including the Strouhal number St , additional mass coefficient of the static riser C a , drag coefficient C D0 , lift coefficient C L0 , Morison drag coefficient C DM and inertia coefficient C M as well as the empirical parameters in the wake oscillator equation ε x , ε y , Λ x and Λ y .

[0105] The solution setting step firstly sets the total length of time for the numerical simulation t and the time step for the solution h , which is used to control the time accuracy and stability of the iterative solution. Subsequently, the riser is divided into NSegmented rod element, complete spatial discretization. After the completion of the discretization setting, set the initial conditions of the riser vibration and the initial value of the wake oscillator variable, which is used to define the state of the system at the initial time. Finally, set the boundary conditions of the riser at both ends, including the motion excitation at the top platform and the bottom end hinged fixed, which provides complete boundary information for subsequent vortex-induced vibration response solution.

[0106] Global spatial point solving step, the time domain response of each spatial point of the riser is solved. The central difference method is used to solve the constructed riser spatial point motion equation and wake oscillator equation, and the time step is gradually advanced, and the displacement and wake variable of each spatial point are updated. Through this numerical method, the in-line and cross-flow vibration displacement of the global spatial point of the riser at future time can be obtained, and the dynamic prediction of the vortex-induced vibration response of the deepwater riser is realized.

[0107] In the spatial point motion equation, the motion variables of any spatial point include three displacements X i = [ x i y i z i ] T And three rotation angles θ i = [ θ xi θ yi θ zi ] T And the mass, damping and moment balance equations are constructed respectively.

[0108] The wake oscillator equation introduces dimensionless wake variables v i And w i And can be combined with empirical parameters ε x , ε y ,Λ x AndΛ y Vortex shedding and fluid force modeling.

[0109] In the process of vector finite element, the rigid body motion of the stripped rod element is obtained, and the true deformation response is obtained.

[0110] In the finite difference solution, the central difference format can be used.

[0111] The output response data of the structure can include cross-flow and in-line displacement, velocity, acceleration, etc., which can be used for further fatigue evaluation or design optimization analysis.

[0112] Preferably, in the step of constructing the spatial point motion equation of the deep-sea riser, the mass of the rod element is uniformly distributed on two connected spatial points, and the internal and external forces are applied equivalently to the two spatial points. The motion and force of the riser structure are reflected by the spatial points.

[0113] Preferably, in the step of constructing the spatial point motion equation of the deep-sea riser, the bottom end of the riser is placed at the wellhead, which is the first spatial point, and the top end is connected to the platform, which is the second spatial point. N+ At a single spatial point, the movement of the platform can drive the... N+ The motion of a single spatial point is considered to account for the influence of platform motion.

[0114] Preferably, in the step of constructing the spatial point motion equation of the deep-sea riser, the effects of gravity and buoyancy of the riser can be considered to more accurately reflect the force state and vibration characteristics of the riser in the water.

[0115] Preferably, in the step of establishing the hydrodynamic model based on the wake oscillator equation, the dimensionless wake variables include... x dimensionless wake variable in direction v and in y dimensionless wake variable in direction w Based on dimensionless wake variables v Describes the oscillating drag force coefficient based on the dimensionless wake variable. w The oscillatory lift coefficient is described, and the drag force expression is constructed based on the relative velocity, the oscillatory drag force coefficient, and the Morrison drag force coefficient. The inertial force expression is constructed based on the riser vibration acceleration and the inertia coefficient.

[0116] Preferably, the global spatial point solution step uses the explicit central difference method to avoid the iteration and convergence problems that exist in the implicit integration method.

[0117] Preferably, in the global spatial point solution step, the downstream and transverse vibration displacements of the global spatial point of the deep-sea riser at the initial moment are first solved, and then calculations are performed at different times to obtain the downstream and transverse vibration displacements of the global spatial point in the future time under spatiotemporal transformation.

[0118] Preferably, in the global spatial point solving module, after obtaining the downstream and cross-current vibration displacements of the global spatial points of the deep-sea riser in the future time, the amplitude of the riser's vortex-induced vibration response is calculated based on the vibration displacement, and the frequency characteristics are calculated through fast Fourier transform and wavelet transform, thereby realizing the prediction of the deep-water riser's vortex-induced vibration response.

[0119] The following further describes a numerical simulation method for vortex-induced vibration of a deep-water riser that takes into account platform motion, such as... Figure 2 The process shown includes the following steps:

[0120] I. Model establishment steps, specifically including the steps of constructing the spatial point motion equations of the deep-sea riser and the steps of establishing the hydrodynamic model based on the wake oscillator equation.

[0121] The steps for constructing the spatial point motion equations of the deep-sea riser are as follows: For the deep-sea riser, construct the spatial point motion equations of the deep-sea riser.

[0122] Based on the vector finite element method, the deep-sea riser is first discretized using finite element methods, decomposing it into a series of alternating spatial points and rod elements. Each adjacent spatial point is connected by a rod element, and each spatial point has mass while each rod element has no mass. For example... Figure 3 The diagram illustrates the vortex-induced vibration of the deep-water riser and the fluid loads involved in its movement, with the connection point between the riser and the wellhead as the origin of the coordinate system. O Establish a domain coordinate system and create the first spatial point within it. Sequentially increase the number of spatial points until the top of the riser connects to the platform. N+ 1. For any spatial point on the riser. i Its motion variables can be decomposed into motion components along the three coordinate axes of the domain coordinate system, including three displacements. X i = [ x i y i z i ] T and three corners θ i = [ θ xi θ yi θ zi ] T So, spatial point i Within a pathway unit t The equation of motion of the spatial point at time t is:

[0123]

[0124] In the formula, N The number of units to be divided; m i The total mass of the point in space; I i Let be the total mass moment of inertia, which is a symmetric matrix; ζ The damping ratio; F i ext and F i intrespectively i the resultant external force and the resultant internal force; M i ext and M i int respectively i the resultant external moment and the resultant internal moment.

[0125] The step of establishing the fluid force model based on the wake oscillator equation is used to establish a fluid force model based on a wake oscillator model.

[0126] According to the velocity of the background flow field U e and the velocity of the riser in the flow direction V x The expression of the relative velocity between the riser and the background flow field is composed of the velocity of the riser in the flow direction driven by the platform motion and the unknown velocity of the vibration in the flow direction. V rel The expression of the relative velocity V rel The expression of the relative velocity v 、 w The oscillation drag coefficient C D and the oscillation lift coefficient C L respectively construct the expression of the drag force F D and the expression of the lift force F L According to the projection mapping relationship of the drag force F D and the lift force F L in the flow direction and the transverse direction, the expressions of the fluid forces F x and F y in two directions are obtained, and the van der Pol equation which contains the dimensionless wake variable v 、 w and the right side of the equation is coupled with the acceleration of the riser motion and satisfies the nonlinear characteristics of the wake oscillator is used as the wake oscillator equation (where the expression of the vortex shedding frequency contains the velocity of the riser in the flow direction), and then the fluid force model is comprehensively constructed.

[0127] Specifically, as shown in (b) of Figure 3 , considering a certain cross section at position z , the velocity of the riser in the flow direction and the transverse direction are V x and Vy , the relative velocity of the riser to the background flow field in the two directions are U e - V x and- V y In the domain coordinate system, the relative velocity between the riser and the background flow field can be calculated as V rel :

[0128]

[0129] Thus, the expression of the drag force F D and the lift force F L

[0130]

[0131] wherein, ρ e is the density of the background flow field, C DM is the Morison drag force coefficient of the static riser.

[0132] Since the motion of the top platform will drive the motion of the riser, an additional inertial force will be generated in the flow direction, and the expression is:

[0133]

[0134] wherein, C M is the inertial coefficient of the static riser, a x is the acceleration of the riser in the flow direction.

[0135] According to the deflection relationship in (b) of Figure 3 , the drag force F D and the lift force F L are projected to x and y directions, and the inertial force is superimposed, so that the expressions of the fluid forces x and y in the F x and F y directions are:

[0136]

[0137] wherein, φ is the relative velocity V ​rel With x The angle between the direction of the flow and the direction of the flow, and then can be obtained:

[0138]

[0139] Oscillating drag coefficient C D And oscillating lift coefficient C L The dimensionless wake variable v And w Description:

[0140]

[0141] In the formula, C D0 And C L0 The drag coefficient and lift coefficient of the static riser, respectively. The dimensionless wake variable v And w The van der Pol equation satisfying the wake oscillator nonlinearity is used as the wake oscillator equation:

[0142]

[0143] In the formula, ε x , ε y , Λ x And Λ y The empirical parameters estimated by experiment, the vortex shedding circular frequency is expressed as:

[0144]

[0145] In the formula, St The Strouhal number.

[0146] Thus, the fluid force model based on the wake oscillator equation can be obtained:

[0147]

[0148] Coupling the above formula into the spatial point motion equation, specifically, F x And F y The corresponding F i ext And M i ext .

[0149] II. Parameter inputting step, specifically including structure and environmental basic parameter inputting step of deep-sea riser and dimensionless number and experience parameter inputting step required by vortex-induced vibration simulation.

[0150] The structure and environmental basic parameter inputting step of deep-sea riser firstly inputs the length of riser L D d m s T ζ E ν f n , and then inputs the parameters of platform motion, including oscillation amplitude A o f o and oscillation frequency ρ e U e , and then inputs the parameters of background flow field, including density

[0151] The dimensionless number and experience parameter inputting step required by vortex-induced vibration simulation includes Strouhal number St = 0.2, additional mass coefficient of static riser C a = 1.0, drag coefficient C D0 = 0.2, lift coefficient C L0 = 0.3, Morison drag coefficient C DM = 2.0 and inertia coefficient C M = 1.0, and experience parameters in wake oscillator equation ε x , ε y , Λ x and Λ y are respectively 0.3, 0.3, 12 and 38.

[0152] III. Solution setting step, specifically including time and space discretization step and definite solution condition setting step.

[0153] The time and space discretization step firstly sets the total calculation time length of numerical simulation t = 200 seconds, and the time step of solution​​​​​​​​​​h = 0.0001 seconds, for controlling the time accuracy and stability of the iterative solution. Then the riser is divided into N = 100 rod elements for spatial discretization.

[0154] The solution condition setting step first sets the initial conditions of the riser vibration, i.e. the displacement i X i = [0 0 z i ] T , linear velocity V i = [0 0 0] T and angular velocity ω i = [0 0 0] T , and the initial value of the wake oscillator variable dv i / dt =dw i / dt= 0, v i =w i = 2. Finally, the boundary conditions of the riser at both ends are set. The bottom end of the riser is hinged to the wellhead, so the displacement X 1= [0 0] T and the rotation angle θ 1= [0 0 0] T . The top end of the riser is hinged to the platform, and the excitation in the x direction is considered due to the platform motion, so the dynamic boundary condition at the time t is .

[0155] At this point, the state of the system at the initial time and the complete boundary information have been obtained, and all conditions for further solution have been met.

[0156] Four, the global spatial point solving step, specifically including the spatial point motion equation solving step, the internal force and internal moment calculation step, the wake oscillator equation solving step, and the external force and external moment calculation step.

[0157] The spatial point motion equation solving step uses the central difference method to discretize the spatial point motion equation to obtain:

[0158]

[0159] In the formula, the damping coefficient C 1=1 / (1+ ζh / 2)、 C 2=C1 / (1-​ζh / 2). This yields the spatial point. i Position at the next moment X i n+1 and corner θ i n+1 .

[0160] The calculation steps for internal forces and moments first require eliminating the rigid body translations and rotations of the member element within a single path element through a virtual reverse motion, thereby obtaining the pure deformation of the member element. Then, based on the deflection theory of mechanics of materials, the deformation and internal forces, including changes in axis length, are described using principal axis coordinates. Axial torsion and two sets of bending deformation The internal forces and bending moments at the nodes can be obtained by performing independent calculations and then superimposing them.

[0161]

[0162] In the formula, It is the change in axial force. It is the change in torque. It is the change in shear force at the two nodes. E It is Young's modulus. A It is the cross-sectional area of ​​the riser. G It is the shear modulus. It is a calculation parameter, the torsional moment of inertia. and axial moment of inertia Represented as

[0163]

[0164] , These are the axial moments of inertia in the y-axis and z-axis directions, respectively;

[0165] Subsequently, based on the six static equilibrium conditions of the spatial rod element, the other six force components were obtained.

[0166]

[0167] Let x be the sum of forces in the x-direction. Let x be the sum of the torques about the x-axis. This represents the sum of torques about the Z-axis. Let be the sum of the torques about the y-axis. Let be the sum of forces in the y-direction. Let Z be the sum of the forces in the z-direction. , For two nodes at x

[0168] the change of force component in the y direction of the two nodes, the change of force component in the z direction of the two nodes, the change of torque component around the x axis of the two nodes, the change of torque component around the z axis of the two nodes, the change of torque component around the y axis of the two nodes, the change of torque component around the y axis of the two nodes;

[0169] Finally, the bar element is made to move forward to return to the original position to make the internal force F i int and the integration of the internal torque M i int .

[0170] The wake oscillator equation solving step adopts a central difference method to discretize the wake oscillator equation to obtain:

[0171]

[0172] Thus, the spatial point i at the next moment x direction and y direction wake variable v i n+1 and w i n+1 , 、 is the external force and internal force suffered by the spatial point in the x direction, 、 is the external force and internal force suffered by the spatial point in the y direction, is the vortex shedding circle frequency at the spatial point, is the corresponding empirical parameter.

[0173] The external force and external torque calculating step obtains the external force v i n+1 and w i n+1 suffered by the spatial point from the above fluid force model. i F i ext and the external torque M i ext . ​​​​​​

[0174] Based on the above steps, the time step is gradually advanced, and the displacement and wake variable of each spatial point are cyclically updated, so that the in-line and cross-flow vibration displacements of the global spatial points of the riser at the future time can be finally obtained, and the dynamic prediction of the vortex-induced vibration response of the deepwater riser is realized.

[0175] Experimental Example One

[0176] For the numerical values of the parameters shown in Table 1, the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion is realized by using the method of the present application.

[0177] Table 1

[0178]

[0179] As shown in Figs. 1 and 2, the root mean square amplitudes of the in-line and cross-flow vibration of the deepwater riser calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example one using the present application are compared with the test results. Figure 4a Figure 4b As shown in Figs. 1 and 2, the root mean square amplitudes of the in-line and cross-flow vibration of the deepwater riser calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example one using the present application are compared with the test results. A xmax / D As shown in Figs. 1 and 2, the root mean square amplitudes of the in-line and cross-flow vibration of the deepwater riser calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example one using the present application are compared with the test results. A ymax / D As shown in Figs. 1 and 2, the root mean square amplitudes of the in-line and cross-flow vibration of the deepwater riser calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example one using the present application are compared with the test results. z / L As shown in Figs. 1 and 2, the root mean square amplitudes of the in-line and cross-flow vibration of the deepwater riser calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example one using the present application are compared with the test results.

[0180] Experimental Example Two

[0181] For the numerical values of the parameters shown in Table 2, the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion is realized by using the method of the present application.

[0182] Table 2

[0183]

[0184] The response data calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example two using the present application are post-processed. The time history curves of the in-line and cross-flow vibration displacements of the deepwater riser calculated are shown in Figs. 3 and 4, respectively. Figure 5a Figure 5b The response data calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example two using the present application are post-processed. The time history curves of the in-line and cross-flow vibration displacements of the deepwater riser calculated are shown in Figs. 3 and 4, respectively. Figure 6a Figure 6b The response data calculated by the vortex-induced vibration numerical simulation method of the deepwater riser considering platform motion based on experimental example two using the present application are post-processed. The time history curves of the in-line and cross-flow vibration displacements of the deepwater riser calculated are shown in Figs. 3 and 4, respectively.

[0185] ​​​In summary, the present application provides a deepwater riser vortex-induced vibration numerical simulation method considering platform motion, which can efficiently and accurately predict the vortex-induced vibration response of the deepwater riser under the combined action of platform motion and background flow, thereby providing important technical support for the design improvement and performance improvement of the deepwater riser.

[0186] In summary, the present application provides a deepwater riser vortex-induced vibration numerical simulation method considering platform motion, which can efficiently and accurately predict the vortex-induced vibration response of the deepwater riser under the combined action of platform motion and background flow, thereby providing important technical support for the design improvement and performance improvement of the deepwater riser.

[0187] The present application also provides a storage medium for storing a computer program, which is executed to perform at least the method described above.

[0188] The present application also provides a control device comprising a processor and a storage medium for storing a computer program; wherein the processor is used to execute the computer program to perform at least the method described above.

[0189] The present application also provides a processor for executing a computer program to perform at least the method described above.

[0190] The storage medium can be implemented by any type of nonvolatile storage device, or a combination thereof. The nonvolatile memory can be a Read Only Memory (ROM), a Programmable Read-Only Memory (PROM), an Erasable Programmable Read-Only Memory (EPROM), an Electrically Erasable Programmable Read-Only Memory (EEPROM), a Ferromagnetic Random Access Memory (FRAM), a Flash Memory, a magnetic surface storage, an optical disc or a Compact Disc Read-Only Memory (CD-ROM). The magnetic surface storage can be a magnetic disc memory or a magnetic tape memory. The storage medium described in the embodiments of the present application is intended to include, but is not limited to, these and any other suitable type of memory.

[0191] In several embodiments provided by the present application, it should be understood that the disclosed system and method can be implemented in other manners. The described device embodiments are merely schematic, and the division of the units is merely a logical function division. For example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed coupling or direct coupling or communication connection between the components can be indirect coupling or communication connection through some interface, device or unit, and can be electrical, mechanical or other forms.

[0192] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e., can be located in one place or distributed on a plurality of network units; some or all of the units can be selected according to actual needs to achieve the purpose of the embodiments.

[0193] In addition, each functional unit in the embodiments of the present application can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in the form of hardware, or in the form of hardware plus software functional units.

[0194] Those skilled in the art can understand that all or part of the steps of the above-mentioned method embodiments can be completed by program instruction related hardware, and the foregoing program can be stored in a computer readable storage medium, and the program performs the steps of the above-mentioned method embodiments when executed; and the foregoing storage medium includes a mobile storage device, a read-only memory (ROM), a random access memory (RAM), a magnetic disc or an optical disc and various storage medium capable of storing program codes.

[0195] Alternatively, the integrated unit of the present application can be stored in a computer readable storage medium if it is realized in the form of a software function module and sold or used as an independent product. Based on such understanding, the technical solutions of the embodiments of the present application can be embodied in the form of a software product, and the computer software product is stored in a storage medium, includes several instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the methods described in the embodiments of the present application. The foregoing storage medium includes a mobile storage device, a ROM, a RAM, a magnetic disc or an optical disc and various storage medium capable of storing program codes.

[0196] The methods disclosed in the several method embodiments of the present application can be combined arbitrarily without conflict to obtain new method embodiments.

[0197] The features disclosed in the several product embodiments of the present application can be combined arbitrarily without conflict to obtain new product embodiments.

[0198] The features disclosed in the several method or device embodiments of the present application can be combined arbitrarily without conflict to obtain new method or device embodiments.

[0199] The above is a further detailed description of the present application in combination with specific preferred embodiments, and the specific implementation of the present application cannot be limited to these descriptions. For those skilled in the art, without departing from the concept of the present application, a number of equivalent substitutions or obvious modifications can be made, and the performance or use is the same, which should be regarded as belonging to the protection scope of the present application.

Claims

1. A numerical simulation method of vortex-induced vibration of a deepwater riser considering platform motion, characterized in that, The method comprises the following steps: a model establishing step of constructing a spatial point motion equation of the deep-sea riser and establishing a fluid force model based on a wake oscillator equation; the construction of the spatial point motion equation specifically comprises: discretizing the riser into a bar element and a spatial point based on a vector finite element method, the motion variables of each spatial point including displacement and rotation angle; establishing a motion equation in a passage unit according to Newton's second law, including a mass balance equation and a moment balance equation; calculating pure deformation internal force and internal moment by separating the rigid body displacement component of the bar element through virtual reverse motion; the internal force and internal moment calculation specifically comprises: separating the rigid body translation and rotation of the bar element through virtual reverse motion, and extracting pure deformation; calculating node internal force and bending moment based on the theory of material mechanics; integrating the internal force and internal moment according to the static force balance condition of the spatial bar element, and mapping to the spatial point; a parameter input step of inputting the structural parameters of the deep-sea riser, the platform motion parameters, the background flow field parameters, and the dimensionless numbers and empirical parameters required for vortex-induced vibration simulation; a solution setting step of setting the total calculation time and the time step, discretizing the riser into bar elements along the length direction, and setting the initial conditions and boundary conditions; a global spatial point solution step of synchronously solving the spatial point motion equation and the wake oscillator equation by using the central difference method, and cyclically updating the displacement, rotation angle and wake variable of each spatial point to realize dynamic prediction of the vortex-induced vibration response; in the global spatial point solution step: the spatial point motion equation and the wake oscillator equation are discretized by using the explicit central difference format; in each time step, the following operations are sequentially performed: updating the spatial point displacement and rotation angle; calculating the internal force and internal moment based on the pure deformation; solving the wake oscillator equation to update the dimensionless wake variable; wherein the riser vibration acceleration is coupled with the wake oscillator equation as an input item; the wake variable is updated explicitly to drive the real-time calculation of the fluid force model; the external force and external moment are calculated according to the fluid force model; the synchronous coupling solution of the structure and the flow field is realized through the time step cycle.

2. The deepwater riser vortex-induced vibration numerical simulation method of claim 1, wherein, the establishment of the fluid force model specifically comprises: constructing a relative velocity expression of the riser and the flow field based on the superposition of the background flow field velocity and the in-line motion velocity of the riser; relating the oscillation drag force coefficient and the lift coefficient to the dimensionless wake variable, and introducing the inertial force term generated by the platform motion; using the van der Pol type wake oscillator equation to nonlinearly couple the vortex shedding frequency and the riser vibration acceleration through empirical parameters; establishing the fluid force component expression including the drag force, the lift force and the inertial force through velocity vector decomposition and force projection mapping.

3. The deep water riser vortex-induced vibration numerical simulation method of claim 1, wherein the pure deformation includes axial length change, axial twist and bending deformation; when the spatial point motion equation is constructed, the internal force and the internal moment are mapped to the spatial point through forward motion.

4. The deepwater riser vortex-induced vibration numerical simulation method of claim 1, wherein, the wake variable is updated explicitly through the central difference method in the global spatial point solution step.

5. The deepwater riser vortex-induced vibration numerical simulation method of claim 1, wherein, the output response data of the dynamic prediction includes: the in-line and cross-flow displacements, velocities and accelerations of the global spatial points of the riser; the vortex-induced vibration amplitude based on the displacement response and the frequency characteristics extracted through frequency domain transformation.

6. The deepwater riser vortex-induced vibration numerical simulation method of claim 5, wherein, The frequency characteristics are extracted by: Performing fast Fourier transform or wavelet transform on the displacement response; Extracting the main frequency and lock-in range characteristics of vortex-induced vibration.

7. The deepwater riser vortex-induced vibration numerical simulation method of claim 1, wherein, The vector finite element method: Simplifying the model by assuming that mass is concentrated at spatial points and that a rod element has no mass; Directly constructing a motion equation based on Newton's second law to avoid assembling a traditional stiffness matrix; Describing a motion trajectory by a path element, and based on its mass-point-element processing mode of a structure, internal force calculation method and motion equation solving method, the method is suitable for vortex-induced vibration problems with large deformation and nonlinearity.

8. The deepwater riser vortex-induced vibration numerical simulation method of claim 1, wherein, The boundary condition setting includes: Fixing the bottom end of the riser to the wellhead by a hinge to constrain all displacements and angles; Applying a time-varying displacement boundary condition to the top end of the riser excited by platform motion.

9. A computer program product comprising a computer program, characterized in that, The computer program, when executed by a processor, implements the deepwater riser vortex-induced vibration numerical simulation method according to any one of claims 1 to 8.

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