Deepwater riser vortex-induced vibration numerical simulation method considering platform motion

Abstract

The invention discloses a deepwater riser vortex-induced vibration numerical simulation method considering platform motion. The method comprises the following steps: constructing a spatial point motion equation of a deepwater riser and a fluid force model based on a wake flow vibrator equation; vertical pipe structure parameters, platform motion parameters and background flow field parameters as well as dimensionless numbers and empirical parameters required by vortex-induced vibration simulation are input; setting and calculating total duration and time step length, dispersing the riser into rod elements, and setting initial conditions and boundary conditions; and synchronously solving a space point motion equation and a wake flow vibrator equation by adopting a central difference method, and circularly updating displacement, rotation angle and wake flow variables of each space point to realize dynamic prediction of vortex-induced vibration response. According to the method, vortex-induced vibration response characteristics such as displacement and speed of the deepwater riser under the combined action of platform motion and a background flow field can be efficiently and accurately obtained, and a numerical simulation means with high calculation efficiency and high adaptability and important technical support are provided for structural analysis, optimization design and performance improvement of the deepwater riser.

Description

Technical Field

[0001] The present invention relates to a structure vibration response measurement and numerical simulation technology, and in particular to a deepwater riser vortex-induced vibration numerical simulation method taking platform motion into account. Background Art

[0002] Vortex-induced vibration (VIV), a typical structural vibration phenomenon, is widely present in the interaction between engineering structures and fluids. Its primary manifestation is the structural vibration response generated by periodic vortex shedding excitation. When a viscous fluid flows around a blunt body (such as a riser, truss, or cylinder), it alternately sheds positive and negative vortices in the wake within a certain Reynolds number range, forming a regular Karman vortex street structure. These alternating vortices act on the structural surface, stimulating periodic downstream and cross-stream fluid forces, which in turn induce mechanical vibration in the structure. This phenomenon exhibits distinct fluid-structure coupling characteristics: on the one hand, the vibration response is modulated by the wake characteristics; on the other hand, the structural motion in turn affects the wake morphology, resulting in a nonlinear coupled evolution of the entire system. In particular, when the vortex shedding frequency approaches the natural frequency of the structure, a "locking" phenomenon (i.e., frequency-locked resonance) is induced, significantly amplifying the structural vibration amplitude, leading to fatigue accumulation and structural damage.

[0003] Deepwater riser systems carried by floating platforms are prone to intense vortex-induced vibrations (VIVs) due to the coupled effects of multiple ocean loads (wind, waves, and currents). Long-term fatigue failure has become a critical issue in marine engineering. Therefore, there is an urgent need to develop a modeling and simulation framework that can effectively characterize the vibration response characteristics of flexible structures, extract dynamic features, and verify their engineering measurability. Currently, numerous studies have proposed various computational methods for predicting deepwater riser vibrations based on semi-empirical models or fluid-structure interaction theoretical frameworks, which are used to assist in engineering design, fatigue assessment, and response measurement analysis. However, these methods fail to account for platform motion. In contrast, high-fidelity computational fluid dynamics simulations, while highly accurate, are computationally expensive and difficult to adapt to the rapid prediction of large-scale operating conditions encountered in engineering. While physical testing methods offer high reliability, they are expensive to construct, control boundaries, and process measurement data, and their ability to simulate complex loads and platform motion is limited.

[0004] In recent years, engineering practice has placed higher demands on the precise measurement, rapid estimation, and scalable simulation of the vibration responses of deepwater flexible structures. Against this backdrop, efficient numerical simulation and response extraction methods that incorporate input from the platform's real-world motion boundaries have gained increasing attention.

[0005] It should be noted that the information disclosed in the above background technology section is only used to understand the background of this application, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0006] The main purpose of the present invention is to overcome the defects existing in the above-mentioned background technology and provide a numerical simulation method of vortex-induced vibration of deepwater risers taking into account platform motion.

[0007] To achieve the above object, the present invention adopts the following technical solutions: A method for numerically simulating vortex-induced vibration of a deepwater riser taking into account platform motion comprises the following steps: Model building steps: Construct the spatial point motion equation of the deep-sea riser and establish a fluid force model based on the wake oscillator equation; Parameter input steps: input the structural parameters of the deep-sea riser, platform motion parameters, background flow field parameters, and dimensionless numbers and empirical parameters required for vortex-induced vibration simulation; Solution setup steps: Set the total calculation time and time step, discretize the riser into rod elements along the length direction, and set initial conditions and boundary conditions; Global spatial point solution steps: Use the central difference method to synchronously solve the spatial point motion equation and the wake oscillator equation, cyclically update the displacement, rotation angle and wake variables of each spatial point to achieve dynamic prediction of vortex-induced vibration response.

[0008] Furthermore, the construction of the spatial point motion equation specifically includes: Based on the vector finite element method, the riser is discretized into rod elements and space points. The motion variables of each space point include displacement and rotation. Establishing the equations of motion within the pathway unit based on Newton's second law, including the mass balance equation and the moment balance equation; The rigid body displacement components of the rod element are stripped off by virtual reverse kinematics, and the pure deformation internal forces and internal moments are calculated.

[0009] Furthermore, the establishment of the fluid force model specifically includes: Based on the superposition of the background flow field velocity and the downstream velocity of the riser, the relative velocity expression between the riser and the flow field is constructed. The oscillating drag and lift coefficients are related to dimensionless wake variables and the inertial force term due to platform motion is introduced. The van der Pol type wake oscillator equation is used to nonlinearly couple the vortex shedding frequency with the riser vibration acceleration through empirical parameters. Through velocity vector decomposition and force projection mapping, the fluid force component expression including drag force, lift force and inertia force is established.

[0010] Furthermore, the calculation of internal forces and internal moments specifically includes: Separate the rigid body translation and rotation of the rod element through virtual inverse kinematics to extract pure deformation, including axial length change, axial torsion and bending deformation; Calculate the internal forces and bending moments of nodes based on the theory of material mechanics; The internal forces and internal moments are integrated according to the static equilibrium conditions of spatial rod elements and mapped to spatial points through forward kinematics.

[0011] Furthermore, in the step of solving the global space point: The explicit central difference scheme is used to discretize the spatial point motion equations and the wake oscillator equations; Execute sequentially in each time step: Update spatial point displacement and rotation angle; Calculate internal forces and internal moments based on pure deformation; Solve the wake oscillator equations and update the dimensionless wake variables. The riser vibration acceleration is coupled to the wake oscillator equations as an input. The wake variables are explicitly updated using the central difference method to drive real-time calculations of the fluid force model. Calculate external forces and moments based on the fluid force model; The synchronous coupling solution of structure and flow field is achieved through time step cycle.

[0012] Furthermore, the output response data of the dynamic prediction includes: The displacement, velocity and acceleration of the riser's global spatial point in the downstream and cross-stream directions; Vortex-induced vibration amplitude based on displacement response and frequency characteristics extracted through frequency domain transformation.

[0013] Furthermore, the frequency characteristics are extracted in the following manner: Perform fast Fourier transform or wavelet transform on the displacement response; Extract the main frequency and locking range characteristics of vortex-induced vibration.

[0014] Furthermore, the vector finite element method: The model is simplified by concentrating the mass at a point in space and assuming that the rod element is massless; Construct the equation of motion directly based on Newton's second law, avoiding the traditional stiffness matrix assembly; The motion trajectory is described by path units. Based on its particle-unit processing method for the structure, internal force calculation method and motion equation solution method, it is suitable for large deformation and nonlinear vortex-induced vibration problems.

[0015] Furthermore, the boundary condition setting includes: The bottom end of the riser is fixedly hinged to the wellhead to constrain all displacements and rotations; The top of the riser is excited by the platform motion and a time-varying displacement boundary condition is imposed.

[0016] The present invention has the following beneficial effects: The present invention provides a numerical simulation method for the vortex-induced vibration response of a deepwater riser taking into account the platform motion. First, the spatial point motion equation of the deepwater riser is constructed, and the fluid force excitation model is established in combination with the wake oscillator equation, comprehensively considering the nonlinear coupling effect between the fluid wake vortex and the structure. In the parameter input stage, the basic structural and environmental parameters of the deep-sea riser, as well as the dimensionless numbers and empirical parameters required for vortex-induced vibration simulation, are systematically introduced to ensure the versatility and engineering adaptability of the model. Subsequently, the total calculation time and time step are set, and the riser is divided into multiple rod elements along the length direction, the initial conditions and boundary conditions are set, and a solution framework for global spatial points is constructed. The structural response and wake variables are solved by the central difference method, and the spatial point, force and wake information are updated in real time to achieve synchronous feedback of the structural dynamic response and the flow field effect. Ultimately, the downstream and cross-stream displacement responses of any spatial point at any time can be output. The method of the present invention can obtain the displacement, velocity, acceleration and hydrodynamic response characteristics of the deepwater riser under the action of platform motion and background flow field, realize efficient and accurate prediction of vortex-induced vibration response, and provide a numerical simulation method with high computational efficiency and strong adaptability for the structural analysis and optimization design of deepwater risers.

[0017] This invention demonstrates significant advantages over existing technologies in numerical simulation of deepwater risers. Specifically, it can provide efficient and accurate prediction of the vortex-induced vibration response of deepwater risers, taking into account platform motion, as well as in-depth mechanism analysis. The advantages of this invention over existing technologies include: In engineering practice, the vortex-induced vibration of deepwater risers in real marine environments is significantly affected by the motion of the upper platform. The semi-empirical numerical simulation method proposed in this embodiment effectively incorporates platform motion parameters, accurately describing their coupling effects on the riser response, and enhancing the physical realism of the simulation.

[0018] 2. The embodiment of the present invention adopts the vector finite element method and the wake oscillator equation to construct a numerical model, and combines it with the central difference format to form a time domain solution framework. The calculation process does not require iterative solution, can meet the needs of rapid response evaluation under large-scale working conditions, and has high computational efficiency.

[0019] 3. The method of the embodiment of the present invention does not rely on the stiffness matrix assembly in the traditional finite element method. By directly constructing the motion equation based on Newton's second law and combining its characteristics in particle motion processing, internal force calculation and motion equation solution, it is particularly suitable for dealing with large deformation and nonlinear problems of vortex-induced vibration of deepwater risers.

[0020] In summary, the numerical simulation method for vortex-induced vibration of deepwater risers taking into account platform motion provided by the present invention can efficiently and accurately predict the vortex-induced vibration response of deepwater risers under the combined action of platform motion and background flow field, thereby providing important technical support for the design improvement and performance enhancement of deepwater risers.

[0021] Other beneficial effects of the embodiments of the present invention will be further described below. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is an overall flow chart of the numerical simulation method for vortex-induced vibration of deepwater risers taking platform motion into account according to the present invention.

[0023] Figure 2 This is a flow chart of a method for numerically simulating vortex-induced vibration of a deepwater riser taking platform motion into account according to an embodiment of the present invention.

[0024] Figure 3 Schematic diagrams showing (a) vortex-induced vibration of a deepwater riser taking into account platform motion according to an embodiment of the present invention and (b) fluid force loads according to an embodiment of the present invention.

[0025] Figure 4a and Figure 4b They are comparative verification diagrams of the RMS amplitudes of the downstream and transverse vibrations of the deepwater riser calculated using the method of the present invention based on Experimental Example 1 and the test results.

[0026] Figure 5a and Figure 5b They are respectively time history curves of the vibration displacement of the deepwater riser in the downstream direction and the cross-stream direction calculated by the method of the present invention based on Experimental Example 2.

[0027] Figure 6a and Figure 6b They are respectively the cloud diagrams of the vibration displacement response changes of the deepwater riser in the downstream and transverse directions calculated by the method of the present invention based on Experimental Example 2. DETAILED DESCRIPTION

[0028] The following is a detailed description of the embodiments of the present invention. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present invention and its application.

[0029] The present invention aims to provide a numerical simulation method for vortex-induced vibration of deepwater risers taking into account platform motion, which can efficiently and accurately predict the vortex-induced vibration response of deepwater risers under the combined action of platform motion and background flow field, thereby providing key technical support for its structural design optimization and performance improvement.

[0030] See Figure 1 The embodiment of the present invention provides a method for numerically simulating vortex-induced vibration of a deepwater riser taking platform motion into account, comprising the following steps: Model building steps: Construct the spatial point motion equation of the deep-sea riser and establish a fluid force model based on the wake oscillator equation; Parameter input steps: input the structural parameters of the deep-sea riser, platform motion parameters, background flow field parameters, and dimensionless numbers and empirical parameters required for vortex-induced vibration simulation; Solution setup steps: Set the total calculation time and time step, discretize the riser into rod elements along the length direction, and set initial conditions and boundary conditions; Global spatial point solution steps: Use the central difference method to synchronously solve the spatial point motion equation and the wake oscillator equation, cyclically update the displacement, rotation angle and wake variables of each spatial point to achieve dynamic prediction of vortex-induced vibration response.

[0031] In some embodiments, the construction of the spatial point motion equation specifically includes: discretizing the riser into rod elements and spatial points based on the vector finite element method, and the motion variables of each spatial point include displacement and rotation; establishing the motion equation within the path unit based on Newton's second law, including the mass balance equation and the torque balance equation; stripping off the rigid body displacement component of the rod element through virtual reverse motion, and calculating the pure deformation internal force and internal moment.

[0032] In some embodiments, establishing the fluid force model specifically includes: constructing a relative velocity expression between the riser and the flow field based on the superposition of the background flow field velocity and the downstream motion velocity of the riser; associating the oscillating drag force coefficient and the lift coefficient with the dimensionless wake variables, and introducing the inertial force term generated by the platform motion; using the van der Pol type wake oscillator equation, nonlinearly coupling the vortex shedding frequency and the riser vibration acceleration through empirical parameters; and establishing a fluid force component expression including the drag force, lift force and inertial force through velocity vector decomposition and force projection mapping.

[0033] In some embodiments, the calculation of internal forces and internal moments specifically includes: separating the rigid body translation and rotation of the rod element through virtual reverse motion, extracting pure deformation, including axial length change, axial torsion and bending deformation; calculating the node internal forces and bending moments based on material mechanics theory; integrating the internal forces and internal moments according to the static equilibrium conditions of the spatial rod element, and mapping them to spatial points through forward motion.

[0034] In some embodiments, in the global space point solution step: the space point motion equations and wake oscillator equations are discretized using an explicit central difference format; in each time step, the following are performed in sequence: updating the space point displacement and rotation angle; calculating the internal force and internal torque based on the pure deformation; solving the wake oscillator equation and updating the dimensionless wake variable; wherein, the riser vibration acceleration is coupled to 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; the external force and external torque are calculated according to the fluid force model; and the synchronous coupling solution of the structure and the flow field is achieved through a time step cycle.

[0035] In some embodiments, the dynamic prediction output response data includes: the downstream and cross-stream displacement, velocity, and acceleration of the global spatial point of the riser; the vortex-induced vibration amplitude based on the displacement response; and frequency characteristics extracted through frequency domain transformation. The frequency characteristics are extracted by performing a fast Fourier transform or wavelet transform on the displacement response and extracting the dominant frequency and locked range characteristics of the vortex-induced vibration.

[0036] In some embodiments, the vector finite element method: simplifies the model by concentrating the mass at a point in space and assuming that the rod element is massless; constructs the motion equation directly based on Newton's second law to avoid traditional stiffness matrix assembly; describes the motion trajectory through path units, and is suitable for large deformation and nonlinear vortex-induced vibration problems based on its point-to-unit processing method for the structure, internal force calculation method and motion equation solution method.

[0037] In some embodiments, the boundary condition setting includes: the bottom end of the riser is fixedly hinged to the wellhead to constrain all displacements and rotations; the top end of the riser is excited by the platform movement to apply time-varying displacement boundary conditions.

[0038] The present invention provides a numerical simulation method for vortex-induced vibration of deepwater risers that takes into account the influence of platform motion. By constructing the spatial point motion equations of the deepwater riser, establishing a fluid force model based on the wake oscillator equation, and solving the global spatial points using the central difference method, the method can efficiently and accurately predict the vortex-induced vibration response of the deepwater riser under the combined effects of platform motion and background flow field, and obtain its displacement, velocity, acceleration, and hydrodynamic response characteristics. As a numerical modeling and simulation method with efficient computing capabilities, adaptability to complex boundaries, and the ability to extract response characteristics, 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 deepwater flexible risers. It can not only simulate response characteristics and obtain vibration signals at key structural points, but also cooperate with experimental verification systems to serve applications such as vibration monitoring, frequency domain analysis, and fatigue life prediction of mechanical structures. It provides a highly efficient and adaptable numerical simulation method and key technical support for the structural analysis, optimization design, and performance improvement of deepwater risers, and has good engineering promotion prospects and research value.

[0039] The following further describes specific embodiments of the present invention, its algorithm examples and experimental verification.

[0040] A method for numerically simulating vortex-induced vibration of a deepwater riser taking platform motion into account comprises the following steps: The model building step includes constructing the spatial point motion equation of the deep-sea riser and establishing a fluid force model based on the wake oscillator equation. The spatial point motion equation of the deep-sea riser is constructed, and the deep-sea riser is divided into N rod elements, and N+1 spatial point connected. Any spatial point in the riser system i The position vector is a time function. In the analysis method of vector structural mechanics, a set of point values ​​at time points are used to describe the motion trajectory of a space point. A space point moves from a position at a certain time point to another position after a period of time. If the motion of the space point during this period of time satisfies the standard governing equation, then this period of time is a path unit. i The motion of satisfies Newton's second law, which is used to construct the equation of motion of a point in space:

[0041] Where, N is the number of divided units; m i is the total mass of the space point; I i is the total mass moment of inertia, which is a symmetric matrix; g is the damping ratio; F i ext and F i int The spatial points i The net external and internal forces; M i ext and M i int The spatial points i The total external and internal moments; is the rotation angle of the space point, is the displacement of a space point, t For time.

[0042] The fluid force model based on the wake oscillator equation is established according to the velocity of the background flow field. and the downstream movement speed of the riser The relative velocity between the riser and the background flow field is constructed by combining the riser velocity driven by the platform movement and the unknown downstream vibration velocity. The expression:

[0043] is the velocity component.

[0044] The relative velocity expression is combined with the dimensionless wake variable to describe the oscillating drag coefficient and the oscillating lift coefficient Build drag force separately Expressions and lift The expression:

[0045] Where, r e is the density of the background flow field, C DM is the Morrison drag coefficient of the stationary riser, is the outer diameter of the riser.

[0046] Since the movement of the top platform will drive the movement of the riser, additional inertial force will be generated in the downstream direction. , whose expression is:

[0047] Where, C M is the inertia coefficient of the stationary riser, a x is the acceleration of the riser in the downstream direction.

[0048] The drag force F D and lift F L Projection to x and y direction, and superimposing the inertial force, we can get x and y Fluid force in direction F x and F y The expression is:

[0049] Where, f is the relative speed V rel and x The angle between the directions can be obtained:

[0050] Oscillation drag coefficient C D and the oscillating lift coefficient C L The dimensionless wake variable v and w describe:

[0051] Where, C D0 and C L0 are the drag coefficient and lift coefficient of the stationary riser, respectively.

[0052] The van der Pol equation, which includes dimensionless wake variables and riser velocity and satisfies the nonlinear characteristics of the wake oscillator, is used as the wake oscillator equation:

[0053] Where, e x 、 e y , Λ x and Λ y is an empirical parameter estimated through experiments, and the vortex shedding circular frequency Expressed as:

[0054] Where, St is the Strouhal number.

[0055] From this arrangement, the fluid force model based on the wake oscillator equation can be obtained:

[0056] Parameter input step: first input the basic structural and environmental parameters of the deep-sea riser, including the length of the riser L , outer diameter D , inner diameter d , mass per unit length m s , pretension T 0. Damping ratio g , Young's modulus E , Poisson's ratio n and natural frequency f n , the oscillation amplitude of the platform motion A o and oscillation frequency f o , the density of the background flow field r e and flow rate U e ; Secondly, input the dimensionless numbers and empirical parameters required for vortex-induced vibration simulation, including the Strouhal number St , Additional mass coefficient of static riser C a , drag coefficient C D0 , lift coefficient C L0 , Morrison drag coefficient C DM and the coefficient of inertia C M and the empirical parameters in the wake oscillator equation e x 、 e y 、 L x and L y .

[0057] Solution setting steps: First, set the total calculation time of the numerical simulation t and the time step of the solution h , which is used to control the time accuracy and stability of the iterative solution. Then the riser is divided into N The spatial discretization is completed by using segmented rod elements. After completing the discretization settings, the initial conditions for the riser vibration and the initial values ​​of the wake oscillator variables are set to define the system state at the initial time. Finally, the boundary conditions at both ends of the riser are set, including the motion excitation at the top platform and the hinged fixation at the bottom end. This provides complete boundary information for the subsequent solution of the vortex-induced vibration response.

[0058] The global spatial point solution step solves the time-domain response of each spatial point on the riser. The constructed riser spatial point motion equations and wake oscillator equations are solved using the central difference method, gradually increasing the time step and cyclically updating the displacement and wake variables of each spatial point. This numerical method can obtain the downstream and cross-stream vibration displacements of the global spatial point of the riser at future times, enabling dynamic prediction of the vortex-induced vibration response of deepwater risers.

[0059] In the equation of motion of a spatial point, the motion variables of any spatial point include three displacements X i = [ x i y i z i ] T and three corners i i = [ i xi i yi i zi ] T , and construct the mass, damping and torque balance equations respectively.

[0060] The wake oscillator equation introduces dimensionless wake variables v i and w i , and can be combined with empirical parameters e x 、 e y , Λ xand Λ y Perform vortex shedding and fluid force modeling.

[0061] During the vector finite element processing, the rigid body motion of the rod element is stripped away to obtain the true deformation response.

[0062] The central difference format can be used in the finite difference solution.

[0063] The output structural response data can include transverse and longitudinal displacements, velocities, accelerations, etc., which can be used for further fatigue assessment or design optimization analysis.

[0064] Preferably, in the step of constructing the spatial point motion equation of the deep-sea riser, the mass of the rod element is evenly distributed at the two connected spatial points, the internal and external forces are equivalently applied to the spatial points at both ends, and the movement and force of the riser structure are reflected by the spatial points.

[0065] 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+ 1 spatial point, the movement of the platform can drive the N+ The motion of a spatial point to take into account the influence of platform motion.

[0066] Preferably, in the step of constructing the spatial point motion equation of the deep-sea riser, the effects of the riser's gravity and buoyancy may be considered to more accurately reflect the stress state and vibration characteristics of the riser in water.

[0067] Preferably, in the step of establishing the fluid force model based on the wake oscillator equation, the dimensionless wake variables are included in x Dimensionless wake variables of direction v and in y Dimensionless wake variables of direction w , based on the dimensionless wake variable v Describes the oscillatory drag coefficient, based on the dimensionless wake variable w The oscillating lift coefficient is described, and the drag force expression is constructed based on the relative velocity, oscillating drag force coefficient and Morrison drag force coefficient. The inertia force expression is constructed based on the riser vibration acceleration and inertia coefficient.

[0068] Preferably, in the step of solving the global space point, an explicit central difference method is used to solve the problem, thereby avoiding the iteration and convergence problems existing in the implicit integration method.

[0069] Preferably, in the global space point solving step, the vibration displacements of the global space point of the deep-sea riser in the downstream and transverse directions at the initial moment are first solved, and then calculations are performed at different times to obtain the vibration displacements of the global space point in the downstream and transverse directions at future times after the time-space transformation.

[0070] Preferably, in the global space point solution module, after obtaining the vibration displacement of the deep-sea riser global space point in the downstream and cross-stream directions at a future time, the vortex-induced vibration response amplitude of the riser is calculated based on the vibration displacement, and the frequency characteristics are calculated by fast Fourier transform and wavelet transform, so as to realize the prediction of the vortex-induced vibration response of the deep-water riser.

[0071] The following further describes a specific embodiment of the numerical simulation method of vortex-induced vibration of deepwater risers taking into account platform motion. Figure 2 The process shown includes the following steps: 1. Model establishment steps, specifically including the steps of constructing the spatial point motion equation of the deep-sea riser and the steps of establishing the fluid force model based on the wake oscillator equation.

[0072] The step of constructing the spatial point motion equation of the deep-sea riser is to construct the spatial point motion equation of the deep-sea riser for the deep-sea riser.

[0073] According to the vector finite element method, the deep-sea riser is first discretized by finite element, and the riser is decomposed into a series of alternately distributed space points and rod elements. Each adjacent space point is connected by a rod element, and each space point has mass while each rod element has no mass. Figure 3 The schematic diagram of the vortex-induced vibration of the deepwater riser and the fluid force loads taking into account the platform movement is shown in the figure. The connection between the riser and the wellhead is taken as the coordinate origin. O Establish a domain coordinate system and establish the first spatial point here. The spatial points are gradually increased to the point where the top of the riser is connected 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 displacement X i = [ x i y i z i ] T and three corners i i = [ i xi i yi i zi ] T Then, the spatial point i In a pathway unit t The equation of motion of a space point at time is:

[0074] Where,N is the number of divided units; m i is the total mass of the space point; I i is the total mass moment of inertia, which is a symmetric matrix; g is the damping ratio; F i ext and F i int The spatial points i The net external and internal forces; M i ext and M i int The spatial points i The total external moment and the total internal moment.

[0075] The step of establishing a fluid force model based on the wake oscillator equation is used to establish a fluid force model based on the wake oscillator model.

[0076] According to the speed of the background flow field U e and the downstream movement speed of the riser V x The relative velocity between the riser and the background flow field is constructed by combining the riser velocity driven by the platform movement and the unknown downstream vibration velocity. V rel The expression of the relative speed V rel The expression of the dimensionless wake variable v 、 w The oscillatory drag coefficient described by C D and the oscillating lift coefficient C L Build drag force separately F D Expressions and lift F L The expression of drag force F D and lift F L The projection mapping relationship in the downstream and cross-flow directions respectively obtains the fluid forces in two directions F x and F y and uses the expression including the dimensionless wake variable v 、 wThe van der Pol equation, which is coupled with the riser motion acceleration on the right side of the equal sign and satisfies the nonlinear characteristics of the wake oscillator, is used as the wake oscillator equation (the expression of the vortex shedding frequency includes the riser downstream motion velocity), and then a comprehensive fluid force model is constructed.

[0077] Specifically, if Figure 3 As shown in (b), consider the position z At a certain cross section at the vertical pipe, the velocity of the vertical pipe in the downstream and cross-flow directions are V x and V y The relative motion speeds of the riser and the background flow field in 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 V rel :

[0078] Thus, the drag force can be obtained F D and lift F L The expression is:

[0079] Where, r e is the density of the background flow field, C DM is the Morrison drag coefficient of the stationary riser.

[0080] Since the movement of the top platform will drive the movement of the riser, additional inertial force will be generated along the flow direction, which is expressed as:

[0081] Where, C M is the inertia coefficient of the stationary riser, a x is the acceleration of the riser in the downstream direction.

[0082] according to Figure 3 The deflection relationship in (b) is the drag force F D and lift F L Projection to x and y direction, and superimposing the inertial force, we can getx and y Fluid force in direction F x and F y The expression is:

[0083] Where, f is the relative speed V rel and x The angle between the directions can be obtained:

[0084] Oscillation drag coefficient C D and the oscillating lift coefficient C L The dimensionless wake variable v and w describe:

[0085] Where, C D0 and C L0 are the drag coefficient and lift coefficient of the stationary riser, respectively. v and w The van der Pol equation that satisfies the nonlinearity of the wake oscillator is used as the wake oscillator equation:

[0086] Where, e x 、 e y , Λ x and Λ y As an empirical parameter estimated through experiments, the vortex shedding circular frequency is expressed as:

[0087] Where, St is the Strouhal number.

[0088] From this arrangement, the fluid force model based on the wake oscillator equation can be obtained:

[0089] Couple the above equation into the spatial point motion equation, specifically, F x and F y The corresponding external force can be obtained by equivalence of the space point Fi ext and M i ext .

[0090] 2. Parameter input steps, specifically including the steps of inputting basic structural and environmental parameters of the deep-sea riser and the steps of inputting dimensionless numbers and empirical parameters required for vortex-induced vibration simulation.

[0091] The step of inputting the basic parameters of the structure and environment of the deep-sea riser is to first input the length of the riser. L , outer diameter D , inner diameter d , mass per unit length m s , pretension T 0. Damping ratio g , Young's modulus E , Poisson's ratio n and natural frequency f n , then input the parameters of the platform motion, including the oscillation amplitude A o and oscillation frequency f o , then input the background flow parameters, including density r e and flow rate U e The values ​​of the above parameters will be given in the specific experimental examples.

[0092] The dimensionless numbers and empirical parameters required for the vortex-induced vibration simulation, including the 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, Morrison drag coefficient C DM = 2.0 and the coefficient of inertia C M = 1.0 and the empirical parameters in the wake oscillator equation e x 、 e y 、 L x and L y They are 0.3, 0.3, 12 and 38 respectively.

[0093] 3. Solution setting steps, specifically including time and space discretization steps and solution condition setting steps.

[0094] The time and space discrete steps first set the total calculation time of the numerical simulation t = 200 seconds, and the solution time step h = 0.0001 seconds, which is used to control the time accuracy and stability of the iterative solution. N = 100 segments of bar elements, completing spatial discretization.

[0095] The step of setting the fixed solution condition is to first set the initial condition of the standpipe vibration, and let any space point i Displacement X i =[0 0 z i ] T , Linear speed V i =[0 0 0] T and angular velocity oh i =[0 0 0] T , then the initial value of the wake oscillator variable dv i / dt =dw i / dt= 0. v i =w i =2. Finally, set the boundary conditions at both ends of the riser. The bottom end of the riser is hinged to the wellhead, so the displacement X 1=[00 0] T , corner i 1 = [0 0 0] T The top of the riser is hinged to the platform, considering its x The direction is stimulated by the platform motion, so t The moving boundary condition at time is .

[0096] At this point, the state of the system at the initial moment and the complete boundary information have been obtained, and all conditions for further solution are in place.

[0097] 4. Global spatial point solution steps, specifically including the steps of solving the spatial point motion equation, calculating the internal force and internal torque, solving the wake oscillator equation, and calculating the external force and external torque.

[0098] The step of solving the spatial point motion equation is to discretize the spatial point motion equation using the central difference method to obtain:

[0099] Where, the damping coefficient C 1=1 / (1+ zhh / 2), C 2=C1 / (1- zhh / 2). Thus we can find the spatial point i Position at the next moment X i n+1 and corners i i n+1 .

[0100] The calculation steps of internal forces and internal moments first need to eliminate the rigid body translation and rigid body rotation of the rod element in a path unit through virtual reverse motion, so as to obtain the pure deformation of the rod element. Then, according to the flexure theory of material mechanics, the deformation and internal forces described in the principal axis coordinates, including the change of the axis length, are calculated. , axial twist And two sets of bending deformation , we can do independent calculations and then superimpose them to get the following node internal forces and moments

[0101] Where, is the change in axial force, is the torque change, is the shear force variation at the two nodes, E is Young's modulus, A is the cross-sectional area of ​​the riser, G is the shear modulus, is the calculation parameter, the torsional moment of inertia and axial moment of inertia Expressed as

[0102] 、 are the axial moments of inertia in the y-axis and z-axis directions respectively;

[0103] Then, according to the six static equilibrium conditions of the spatial rod element, the other six force components are obtained

[0104] is the sum of the forces in the x-direction, is the sum of the moments about the x-axis, is the total moment about the Z axis, is the sum of the moments about the y-axis, is the sum of the forces in the y direction, is the sum of the forces in the z direction, 、 For two nodes at x The change in the directional force component, 、 is the change of the force component of the two nodes in the y direction, 、 is the change in the force components of the two nodes in the z direction, 、 is the change in the moment component of the two nodes around the x-axis, 、 is the change in the moment component of the two nodes around the z-axis, 、 is the change in the moment component of the two nodes around the y-axis;

[0105] Finally, the rod element is made to move forward and return to its original position to perform internal force. F i int and internal torque M i int Integration.

[0106] The steps for solving the wake oscillator equation are to discretize the wake oscillator equation using the central difference method to obtain:

[0107] From this we can get the spatial point i The tail variables in the x and y directions at the next moment v i n+1 and w i n+1 , 、 are the external and internal forces acting on the spatial point in the x direction, 、 are the external and internal forces acting on the space point in the y direction, is the vortex shedding circular frequency at the spatial point, are the corresponding empirical parameters.

[0108] The external force and external torque calculation steps are based on the wake variables obtained in the previous step. v i n+1 and w i n+1 , the spatial point is obtained from the above fluid force model i External force F i ext and external torqueM i ext .

[0109] Based on the above steps, the time step is gradually advanced, and the displacement and wake variables of each spatial point are cyclically updated. Ultimately, the downstream and cross-stream vibration displacements of the global spatial point of the riser at future moments can be obtained, realizing the dynamic prediction of the vortex-induced vibration response of the deepwater riser.

[0110] Experimental Example 1 With respect to the values ​​of the parameters shown in Table 1, the method of the present invention is used to realize the numerical simulation of vortex-induced vibration of deepwater riser taking into account the platform motion.

[0111] Table 1

[0112] like Figure 4a and Figure 4b The figure shows a comparison of the root mean square amplitude of the deepwater riser vibration in the downstream and transverse directions calculated based on the numerical simulation method of the deepwater riser vortex-induced vibration taking into account the platform motion of the present invention and the test results based on Experimental Example 1. The horizontal axis is the maximum dimensionless amplitude A xmax / D and A ymax / D The vertical axis is the normalized length of the riser. z / L The range is 0 to 1. The comparison results can verify the accuracy and applicability of the numerical simulation method of vortex-induced vibration of deepwater risers taking into account platform motion in dynamic response prediction. Therefore, the present invention can be used to efficiently and accurately predict the vortex-induced vibration response of deepwater risers taking into account platform motion.

[0113] Experimental Example 2 With respect to the values ​​of the parameters shown in Table 2, the method of the present invention is used to realize the numerical simulation of vortex-induced vibration of deepwater riser taking into account the platform motion.

[0114] Table 2

[0115] The response data calculated based on the vortex-induced vibration numerical simulation method of the deepwater riser taking into account the platform motion in Experimental Example 2 was post-processed. The time history curves of the calculated vibration displacement of the deepwater riser in the downstream and cross-stream directions are shown as follows: Figure 5a and Figure 5b The calculated vibration displacement response changes of deepwater riser in the downstream and transverse directions are shown in the following cloud diagrams: Figure 6a and Figure 6b As shown, the long bar on the right is a displacement color card comparison display.

[0116] In summary, the present invention provides a method for numerically simulating the vortex-induced vibration of deepwater risers that takes platform motion into account. The method of the present invention obtains the displacement, velocity, acceleration, and hydrodynamic characteristics of the deepwater riser, thereby enabling efficient and accurate prediction of the vortex-induced vibration response of the deepwater riser under the influence of platform motion and background flow. This provides a computationally efficient and adaptable numerical simulation method for the structural analysis and optimization design of deepwater risers, thereby providing important technical support for the design improvement and performance enhancement of deepwater risers. The embodiments of the present invention exhibit significant differences and advantages over the prior art in numerical simulation of deepwater risers. Specifically, the present invention can provide efficient and accurate prediction of the vortex-induced vibration response of deepwater risers that takes platform motion into account, as well as in-depth mechanism analysis and research. The advantages of the present invention over the prior art include: 1. In engineering practice, the vortex-induced vibration of deepwater risers in real marine environments is significantly affected by the motion of the upper platform. The semi-empirical numerical simulation method proposed in the embodiments of the present invention can effectively introduce platform motion parameters, accurately describe their coupling effect on the riser response, and enhance the physical authenticity of the simulation. 2. The embodiment of the present invention uses a vector finite element method to construct a numerical model, and combines it with a finite difference format to form a time-domain solution framework. The calculation process does not require iterative solution, can meet the needs of rapid response evaluation under large-scale working conditions, and has high computational efficiency. 3. The method of the embodiment of the present invention does not rely on the stiffness matrix assembly in the traditional finite element method. By directly constructing the motion equation based on Newton's second law and combining its characteristics in particle motion processing, internal force calculation and motion equation solution, it is particularly suitable for dealing with large deformation and nonlinear problems of vortex-induced vibration of deepwater risers.

[0117] In summary, the numerical simulation method for vortex-induced vibration of deepwater risers taking into account platform motion provided by the present invention can efficiently and accurately predict the vortex-induced vibration response of deepwater risers under the combined action of platform motion and background flow, thereby providing important technical support for the design improvement and performance enhancement of deepwater risers.

[0118] An embodiment of the present invention further provides a storage medium for storing a computer program, which at least performs the above method when executed.

[0119] An embodiment of the present invention further provides a control device, comprising a processor and a storage medium for storing a computer program; wherein the processor is configured to execute at least the method described above when executing the computer program.

[0120] An embodiment of the present invention further provides a processor, which executes a computer program and at least performs the method described above.

[0121] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. Among them, the non-volatile 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 magnetic random access memory (FRAM), a flash memory (Flash Memory), a magnetic surface memory, an optical disc or a read-only optical disc (CD-ROM); the magnetic surface memory can be a magnetic disk memory or a magnetic tape memory. The storage medium described in the embodiments of the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0122] In the several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as: multiple units or components can be combined, or can be integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the components shown or discussed can be through some interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.

[0123] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units; some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0124] In addition, all functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately used as a unit, or two or more units may be integrated into one unit; the above-mentioned integrated units may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0125] Those skilled in the art will appreciate that all or part of the steps of the above-mentioned method embodiments may be implemented by hardware associated with program instructions, and the aforementioned program may be stored in a computer-readable storage medium. When the program is executed, the program executes the steps of the above-mentioned method embodiments. The aforementioned storage medium includes various media that can store program codes, such as mobile storage devices, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0126] Alternatively, if the above-mentioned integrated unit of the present invention is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as mobile storage devices, ROM, RAM, magnetic disks or optical disks.

[0127] The methods disclosed in the several method embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0128] The features disclosed in several product embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0129] The features disclosed in several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments or device embodiments.

[0130] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. Those skilled in the art will recognize that, without departing from the scope of the present invention, several equivalent substitutions or obvious variations can be made, and the performance or use of the same should be considered to fall within the scope of protection of the present invention.

Claims

1. A numerical simulation method for vortex-induced vibration of deepwater risers taking into account platform motion, characterized in that: The following steps are involved: Model building steps: Construct the spatial point motion equation of the deep-sea riser and establish a fluid force model based on the wake oscillator equation; Parameter input steps: input the structural parameters of the deep-sea riser, platform motion parameters, background flow field parameters, and dimensionless numbers and empirical parameters required for vortex-induced vibration simulation; Solution setup steps: Set the total calculation time and time step, discretize the riser into rod elements along the length direction, and set initial conditions and boundary conditions; Global spatial point solution steps: Use the central difference method to synchronously solve the spatial point motion equation and the wake oscillator equation, cyclically update the displacement, rotation angle and wake variables of each spatial point to achieve dynamic prediction of vortex-induced vibration response.

2. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 1, characterized in that: The construction of the spatial point motion equation specifically includes: Based on the vector finite element method, the riser is discretized into rod elements and space points. The motion variables of each space point include displacement and rotation. Establishing the equations of motion within the pathway unit based on Newton's second law, including the mass balance equation and the moment balance equation; The rigid body displacement components of the rod element are stripped off by virtual reverse kinematics, and the pure deformation internal forces and internal moments are calculated.

3. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 1 or 2, characterized in that: The establishment of the fluid force model specifically includes: Based on the superposition of the background flow field velocity and the downstream velocity of the riser, the relative velocity expression between the riser and the flow field is constructed. The oscillating drag and lift coefficients are related to dimensionless wake variables and the inertial force term due to platform motion is introduced. The van der Pol type wake oscillator equation is used to nonlinearly couple the vortex shedding frequency with the riser vibration acceleration through empirical parameters. Through velocity vector decomposition and force projection mapping, the fluid force component expression including drag force, lift force and inertia force is established.

4. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 2, characterized in that: The internal force and internal moment calculation specifically includes: Separate the rigid body translation and rotation of the rod element through virtual inverse kinematics to extract pure deformation, including axial length change, axial torsion and bending deformation; Calculate the internal forces and bending moments of nodes based on the theory of material mechanics; The internal forces and internal moments are integrated according to the static equilibrium conditions of spatial rod elements and mapped to spatial points through forward kinematics.

5. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 1 or 2, characterized in that: In the global space point solving step: The explicit central difference scheme is used to discretize the spatial point motion equations and the wake oscillator equations; Execute sequentially in each time step: Update spatial point displacement and rotation angle; Calculate internal forces and internal moments based on pure deformation; Solve the wake oscillator equations and update the dimensionless wake variables. The riser vibration acceleration is coupled to the wake oscillator equations as an input. The wake variables are explicitly updated using the central difference method to drive real-time calculations of the fluid force model. Calculate external forces and moments based on the fluid force model; The synchronous coupling solution of structure and flow field is achieved through time step cycle.

6. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 1 or 2, characterized in that: The output response data of the dynamic prediction includes: The displacement, velocity and acceleration of the riser's global spatial point in the downstream and cross-stream directions; Vortex-induced vibration amplitude based on displacement response and frequency characteristics extracted through frequency domain transformation.

7. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 6, characterized in that: The frequency characteristics are extracted in the following way: Perform fast Fourier transform or wavelet transform on the displacement response; Extract the main frequency and locking range characteristics of vortex-induced vibration.

8. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 2, characterized in that: The vector finite element method: The model is simplified by concentrating the mass at a point in space and assuming that the rod element is massless; Construct the equation of motion directly based on Newton's second law, avoiding the traditional stiffness matrix assembly; The motion trajectory is described by path units. Based on its particle-unit processing method for the structure, internal force calculation method and motion equation solution method, it is suitable for large deformation and nonlinear vortex-induced vibration problems.

9. The method for numerical simulation of vortex-induced vibration of deepwater riser according to claim 1 or 2, characterized in that: The boundary condition setting includes: The bottom end of the riser is fixedly hinged to the wellhead to constrain all displacements and rotations; The top of the riser is excited by the platform motion and a time-varying displacement boundary condition is imposed.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for numerical simulation of vortex-induced vibration of a deepwater riser according to any one of claims 1 to 9 is implemented.

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