Nonlinear response solving method of catenary mooring platform under action of focused wave

Abstract

The invention provides a nonlinear response solving method for a catenary mooring platform under the action of focused waves, and the method comprises the following steps: constructing a pool model and a catenary mooring platform model moored in the pool model, the catenary mooring platform model comprises a floating platform model and a plurality of catenary models, one end of each catenary model is fixed to the water bottom of the water body model, and the other end of each catenary model is fixed to the floating platform model; generating focused wave making data based on a phase focusing method, wherein the focused wave making data comprises an initial wave surface and an initial flow velocity field corresponding to focusing the focused wave on the catenary mooring platform; simulating focused wave propagation in the pool model by using the wave making data; and solving the motion response of the floating platform model under the action of the focused wave and the catenary mooring constraint based on a bidirectional coupling calculation mode. According to the method provided by the invention, the nonlinear response of the floating platform under the extreme sea condition can be accurately solved.

Description

Nonlinear response solution method for catenary mooring platform under focused wave action Technical Field

[0001] This application belongs to the field of marine engineering equipment safety monitoring and assessment technology, specifically providing a method for solving the nonlinear response of a catenary mooring platform under focused wave action. Background Technology

[0002] As marine engineering equipment develops towards deep-sea areas, the dynamic response characteristics of floating platforms under extremely complex sea conditions have become an important research topic for engineering design and safety assessment. In particular, the motion response and accurate solution of anchor chain tension of catenary-moored floating platforms under transient strong nonlinear waves, i.e., focused waves, have become an important issue.

[0003] A focused wave is a massive wave formed by the superposition of multiple wave components of different frequencies and wavelengths at a specific time and spatial location, resulting in concentrated energy. These wave components propagate at different phase velocities. At a focal point and moment, the wave components are in phase, superimposing to form an instantaneous high wave peak. After focusing, due to the difference in phase velocity, the wave components rapidly disperse. When various floating platforms moored by catenaries happen to be located in the focal region of a focused wave, they are severely threatened by the instantaneous high energy and short-duration strong impact of the focused wave. On the one hand, the swaying, rolling, and drifting of the floating platform may exceed the safe operating range, seriously affecting the safety of personnel and equipment on the platform. On the other hand, the nonlinear motion response of the platform acts on the mooring catenary system, causing dragging of the anchor under catenary tension and chain stacking and entanglement after rapid slackening, damaging the structure of the mooring system and the floating platform.

[0004] Existing technologies have the following shortcomings when calculating the motion of floating platforms moored by catenaries under extremely complex sea conditions: (1) Existing extreme wave reconstruction methods are mostly based on potential flow theory. Although they can simulate three-dimensional wave fields, their mathematical models are based on weak nonlinear assumptions and cannot capture key dynamic characteristics such as strong nonlinear free surface deformation, wave steepness increase, and wave breaking during extreme wave processes, resulting in simulation results deviating from real extreme sea conditions; (2) Existing calculation methods generally equate the mooring system to a linear spring or only consider tension changes, and cannot simulate geometric nonlinear behaviors such as anchor chain contact with the seabed, slippage, tension relaxation, etc. This simplification weakens the authenticity of the overall dynamics of the platform-mooring system. Due to insufficient nonlinear description of extreme waves, incomplete platform-mooring coupling, and simplification of mooring models, it is impossible to accurately capture the real nonlinear response of catenary moored platforms under strong nonlinear sea conditions such as extreme focused waves.

[0005] Therefore, there is an urgent need for a method that can accurately reconstruct the focused wave field and achieve a fully coupled solution of the nonlinear hydrodynamic response of an offshore platform and the catenary mooring system. Summary of the Invention

[0006] This application provides a method for solving the nonlinear response of a catenary mooring platform under focused wave action, comprising the following operations: Operation 1, constructing a water tank model and a catenary mooring platform model moored within the water tank model, wherein the water tank model includes a water body model and an air layer model above it, and the catenary mooring platform model includes a floating platform model and several catenary models, with one end of each catenary model fixed to the bottom of the water body model and the other end fixed to the floating platform model; Operation 2, generating focused wave generation data based on a phase focusing method, wherein the focused wave generation data includes the initial wave surface and initial velocity field corresponding to focusing the focused wave onto the catenary mooring platform; Operation 3, simulating focused wave propagation in the water tank model using the wave generation data; Operation 4, solving the motion response of the floating platform model under focused wave action and catenary mooring constraints based on a two-way coupled calculation method.

[0007] The nonlinear response solution method for a catenary mooring platform under focused wave action provided in this application embodiment achieves high-precision reconstruction of extreme focused waves through phase focusing method. At the same time, it optimizes the solution framework for the nonlinear response of the floating platform and the catenary under strong coupling state under focused wave action. Based on the fluid pressure field obtained from simulation under focused wave action, the floating platform model and the catenary model are driven by the velocity field, and the motion response of the floating platform model and the bidirectional coupling solution of the catenary model are performed. Relying on this complete technical framework, the accuracy of motion response and mooring force calculation and analysis of the floating platform under extreme sea conditions can be significantly improved. Attached Figure Description

[0008] Figure 1 is a flowchart of the nonlinear response solution method for a catenary mooring platform under focused wave action according to an embodiment of this application; Figure 2 is a schematic diagram of the layout of the pool model and the catenary mooring platform model according to an embodiment of this application; Figure 3 is a schematic diagram of the specific construction method of the floating platform model and the catenary model according to an embodiment of this application; Figure 4 is a schematic diagram of the focused wave propagation evolution process according to an embodiment of this application; Figure 5 is a wave surface duration curve of the focusing position of the floating platform model according to an embodiment of this application during the period when the focused wave passes; Figure 6 is a flowchart of the bidirectional coupling solution process according to an embodiment of this application; Figure 7 is a flowchart of the implementation of step S422 according to an embodiment of this application; Figure 8 is a schematic diagram of the STAR CCM+, DFBI, MoorDyn and coupling data exchange process according to an embodiment of this application; Figure 9 shows the state change of the floating platform model in the pool model during the focused wave action stage; Figure 10 is a motion response duration curve of the floating platform model under focused wave action according to an embodiment of this application; Figure 11 is a tension change curve of the catenary model according to an embodiment of this application. Detailed Implementation

[0009] The present application will now be further described based on preferred embodiments and with reference to the accompanying drawings.

[0010] In the description of the embodiments of this application, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationships commonly used when the product of this application is in use, are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. Furthermore, in the description of this application, the terms "first," "second," etc., are used to distinguish different units, but these are not limited by the manufacturing order, nor should they be construed as indicating or implying relative importance. Their names may differ in the detailed description and claims of this application. In addition, for ease of understanding, various components in the drawings have been enlarged or reduced, but this is not intended to limit the scope of protection of this application.

[0011] The vocabulary used in this specification is for illustrative purposes and is not intended to limit the scope of this application. It should also be noted that, unless otherwise expressly specified and limited, the terms "set," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection, a direct connection, or an indirect connection via an intermediate medium; or they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of these terms in this application.

[0012] This application provides a method for solving the nonlinear response of a catenary mooring platform under focused wave action. Figure 1 shows a flowchart of the method in some embodiments. As shown in Figure 1, the method includes the following operations: Operation 1: Constructing a pool model and a catenary mooring platform model moored in the pool model. The pool model includes a water body model and an air layer model above it. The catenary mooring platform model includes a floating platform model and several catenary models, with one end of each catenary model fixed to the bottom of the water body model and the other end fixed to the floating platform model; Operation 2: Generating focused wave generation data based on the phase focusing method. The focused wave generation data includes the initial wave surface and initial velocity field corresponding to the catenary mooring platform that focus the focused wave; Operation 3: Simulating focused wave propagation in the pool model using the wave generation data; Operation 4: Solving the motion response of the floating platform model under focused wave action and catenary mooring constraints based on a two-way coupled calculation method.

[0013] The specific implementation methods of each of the above steps are explained in detail below with reference to the accompanying drawings.

[0014] Operation 1, "Scene and Equipment Modeling," is used to construct and initialize the various numerical models required to solve the nonlinear response of the catenary mooring platform under focused wave action. These numerical models include a pool model to simulate the propagation of the focused wave and a catenary mooring platform model moored in the pool. Figure 2 shows a schematic diagram of the layout of the pool model and the catenary mooring platform model in some optional embodiments.

[0015] A. Water Tank Model: The water tank model provides mooring space for the catenary mooring platform model and generates focused waves along a preset direction in the water section. By adjusting the focusing position of the focused waves to the catenary mooring platform, the nonlinear response of the platform under the action of the focused waves can be solved.

[0016] The construction of the pool model can be achieved using techniques known to those skilled in the art. For example, in some specific embodiments, the pool model consists of a water body model with a finite volume and an air layer model above the water body model. Both the water body model and the air layer model are numerical models. The space occupied by these two numerical models constitutes the computational domain for the propagation of the focused wave and its effect on the catenary mooring platform. The size, mesh type, and density of the computational domain can be determined according to the size of the focused wave to be analyzed and the catenary mooring platform. Generally, the length of the computational domain can be set to 5-10 times the length of the focused wave along the propagation direction, and the width of the computational domain can be set to 3-5 times the width of the floating platform model. The mesh type adopts hexahedral mesh, polyhedral mesh, or cut volume mesh, etc. The mesh number and density division strategy can be flexibly adjusted according to the solution accuracy and the position of the catenary mooring platform. For example, a coarser mesh can be divided in the far field region, and a finer mesh can be divided at the water-air interface. In the area where the floating platform model and the catenary model are located, the mesh is further densified. In addition, by setting no-slip wall boundary conditions on the sides and bottom of the water body computational domain, the constraint effect of the pool wall and bottom on the water body model is simulated.

[0017] The pressure and velocity field distributions in the water model during the propagation and evolution of the focusing wave can be obtained by discretizing and solving the incompressible Navier-Stokes equations using the finite volume method. (1), (2).

[0018] Equation (1) is the continuity equation for the water body, and equation (2) is the momentum equation for the water body, where, , These are the velocity field and the pressure field, respectively. For time variables, For water density, For viscous stress, It is the acceleration due to gravity. Other volume forces, such as surface tension.

[0019] The water-air interface at the junction of the water model and the air layer model can be captured using the VOF (Volume of Fluid) method by solving the VOF transport equations. (3), among which, It represents the volume fraction of the aqueous phase. For water, It is air.

[0020] In some optional embodiments, a pool model can be established based on the above-mentioned grid division strategy, and the above-mentioned finite volume method and VOF (Volume of Fluid) method can be implemented by programming to obtain the velocity field and pressure field distribution in the water body, as well as the wave morphology changes at the water-air interface.

[0021] In other alternative embodiments, various multiphysics simulation software platforms known to those skilled in the art can also be used to construct the aforementioned pool model and solve multiple physics fields. For example, the STAR-CCM+ simulation software platform can be used to generate the pool model. This simulation software platform is mainly used for computational fluid dynamics (CFD) and related multiphysics analysis. The processes, including CAD import of the model, mesh generation, and solving, can be uniformly implemented within its integrated environment. Specifically, during the mesh generation stage, mesh generation can be automated, and the mesh can be automatically optimized based on the flow field characteristics. During the multiphysics solving stage, flow field calculations for incompressible / compressible flow, laminar / turbulent flow, and multiphase flow, as well as free surface capture, can be performed. Those skilled in the art can flexibly select the appropriate solver according to the needs of solving the nonlinear response of the catenary mooring platform under focused wave action, to obtain the velocity and pressure field data required for subsequent calculations.

[0022] B. Catenary Mooring Platform Model The catenary mooring platform model includes a floating platform model and at least two catenary models for mooring the floating platform model. It is understood that both the floating platform model and the catenary models are numerical models. In the embodiment shown in Figure 2, the floating platform model is moored by four catenaries, meaning one floating platform model and two catenary models need to be constructed. In other optional embodiments, two, three, five, or more catenary models can also be used for mooring the floating platform model; correspondingly, two, three, five, or more corresponding catenary models need to be established.

[0023] Figure 3 illustrates the specific construction method of the floating platform model and the catenary model. As shown in Figure 3, the floating platform model floats in the pool model, with its lower part located in the water body model and its upper part located in the air layer model. The shape, size, and mass distribution of the floating platform model can be set with reference to the equipment parameters of a real offshore operating platform. The entire platform is treated as a rigid body to establish a numerical model and perform corresponding mesh generation.

[0024] As shown in Figure 3, each catenary model includes alternating connections. Each node unit and One rod unit, of which The value is a positive integer greater than or equal to 3, and each member element can have an equal length. (or of unequal length), its mass is distributed to the node elements at both ends, and adjacent rod elements are hinged through shared node elements, allowing relative rotation in all directions, thereby simulating the flexible bending characteristics of the mooring structure of floating platforms such as anchor chains and cables.

[0025] Obviously, The appropriate value should be determined based on a comprehensive consideration of the total length of the catenary, the solution accuracy, and the computational complexity. For example, one can first determine the appropriate range of values ​​for the length of the member element, and then determine the appropriate value based on the length of the member element and the total length of the catenary. The range of values ​​for this value. For example, when the total length of the catenary is 50m, if a higher accuracy solution is required, the length of the rod element can be set to approximately 0.5m or shorter. The value can be greater than or equal to 100; for example, when only a rough verification or analysis is required, the length of the rod element can be set to 2m or longer. The value can be less than or equal to 25.

[0026] Furthermore, any first Each node unit The position can be determined by the global vector. express, , Representing the first The x, y, and z coordinates of each node element are shown in Figure 3. The z-axis is perpendicular to the water surface, the x-axis is the direction of focused wave propagation, and the y-axis is perpendicular to both the x and z axes. The bottommost node element is fixed to the bottom of the water model, and the topmost node element... Each node unit is fixedly connected to the floating platform model, i.e., the position of the first node. The position of the last node relative to the fixed underwater surface. It will always remain consistent with a certain point on the floating platform model (corresponding to the position of the cable guide).

[0027] Accordingly, any number individual rod units tangential direction It can be represented by the direction of the line connecting its two adjacent node elements: (4), of which, Indicates the first The node unit and the first The distance between node units. vertical direction Then it is defined as the first The lateral direction of each bar element.

[0028] Solving the nonlinear response of the catenary mooring platform under the action of focusing waves involves generating a focusing wave in the water body model after completing the construction of the above-mentioned pool model and catenary mooring platform model, focusing the wave on the location of the catenary mooring platform, and then solving the motion state of the floating platform model under the driving force of the focusing wave and the mooring force constraints of each catenary.

[0029] For the floating platform model, the gravity and buoyancy acting on it can be considered as balanced. Therefore, the floating platform will be affected by the wave forces generated by the water. and the mooring forces of each catenary Under the influence of [something], it performs six degrees of freedom motion.

[0030] For each catenary model, the position and motion of each node element and member element are constantly changing under the influence of their own gravity / buoyancy, fluid loads, tension forces from adjacent node elements, and constraints from the fixed positions on the seabed and the floating platform. This causes a corresponding change in the overall shape of the catenary, which in turn is transmitted to the uppermost node element, causing mooring forces. The corresponding changes.

[0031] It can be seen that under the action of the focused wave, the dynamic states of the floating platform model and each catenary model are coupled with each other. In Operation 4, which will be described later, the solution process of the dynamic states of the floating platform model and the catenary model will be explained in detail.

[0032] Operation 2, "Determining Wave Generation Data for Focused Waves Based on Real Wave Characteristics," is used to determine focused wave generation data that matches real wave characteristics and can be focused on the location of the catenary mooring platform model. In some optional embodiments, Operation 2 further includes the following steps: Step S21, determining the target wave spectrum.

[0033] The target wave spectrum is used to describe the wave energy distribution characteristics satisfied by the generated focused wave. For example, the JONWSWAP wave spectrum can be used as the target wave spectrum. The format is: (5), among which, For the angular frequency variable of the wave, The frequency of the spectral peak. It is the acceleration due to gravity. As an energy-scale parameter, it can be determined based on the meaningful wave height. It is the peak enhancement factor. These are the peak shape parameters. The values ​​of the above parameters can be determined statistically based on historical wave measurement data of the sea area where focused waves need to be generated.

[0034] Step S22: Determine the wave-generating target of the focused wave. The wave-generating target includes the wave-generating time, wave-generating position, focusing time, focusing position, target wave height at the focusing time, and the number and frequency range of wave components constituting the focused wave.

[0035] Specifically, let each wave component be in Moment occurs at The location, i.e., the time and position of wave generation. Then the focus position can be adjusted. Set the x-coordinate to be the same as the location of the floating platform model, and determine the focusing time when the focused wave arrives at that location. The lower and upper frequency limits of the wave components constituting the focused wave are respectively and In the frequency range shared within Each wave component, further, will Divided into equal intervals There are intervals, and the frequency of the wave component in each interval is . At the moment of focus ,this Each wave component will be at the focal position. Reach the target wave height .

[0036] Step S23: Determine the wave number of each wave component using the dispersion equation.

[0037] Specifically, the wave number of each wave component Satisfy the dispersion equation We can use Newton's iteration method to solve iteratively and obtain the solution. The wave number corresponding to each wave component .

[0038] Step S24: Determine the amplitude of each wave component based on energy conservation.

[0039] Specifically, the superposition of the wave components should satisfy energy conservation; therefore, the amplitude of each wave component can be determined based on the following formula: (6), among which, For the first The amplitude of each wave component For the first The frequency of each wave component Wave spectrum value at that location, For the target wave height, This represents the frequency interval of each wave component.

[0040] Step S25: Based on the wave generation position, wave generation time, focusing time, and focusing position of each wave component, determine the initial phase of each wave component at the wave generation position.

[0041] Specifically, as mentioned above, each wave component at the wave generation time and wave generation location Generate the wave surface expressions for each wave component. for: (7), among which, For the first The initial phase of each wave component at the wave generation position and time; the initial phase of each wave component at the focusing time and position. They reach the same phase, therefore satisfying the following equation: (8), among which, The phase of each wave component when it is focused.

[0042] Then, according to equation (8), the initial phase of each wave component can be determined. .

[0043] Step S26: Based on the amplitude and initial phase of each wave component, determine the initial wave surface and initial velocity field at the wave generation time and wave generation location.

[0044] Specifically, the result obtained through equation (6) and obtained through equation (8) Substituting into equation (7) and superimposing the results, we can obtain the wave generation time and wave generation location. Initial wavefront at the location : (9).

[0045] The velocity potential expression for each wave component is denoted as: (10), among which, Given the water depth, when each wave component propagates along the x-axis, the partial derivatives of equation (10) in the x and z directions are taken and superimposed to obtain the horizontal velocity field of the focused wave. and vertical velocity field The expression: (11), (12) will Substituting into equations (11) and (12), we can obtain the initial velocity field at the wave-generating time and location.

[0046] In the embodiments of this application, the initial wave surface and initial velocity field at the aforementioned wave-generating time and location are referred to as focused wave generation data. Using the aforementioned focused wave generation data as initial conditions, the propagation process of each wave component according to these initial conditions is simulated in the water model. This allows the catenary mooring platform model to be subjected to focused waves at the expected focusing time. Furthermore, since the spectral composition of each wave component of the focused wave in this method is determined by the actual ocean wave spectrum characteristics, it better matches the energy distribution characteristics of waves at different frequencies in the real ocean environment, thereby improving the reliability of the nonlinear response solution results of the catenary mooring platform.

[0047] <Simulation of Focused Wave Propagation and Evolution> After obtaining the initial wave surface and initial velocity field at the wave generation time and location through Operation 2, Operation 3 can be executed. Using the aforementioned wave generation data, the simulation of the focused wave propagation and evolution process is performed using numerical calculation methods known to those skilled in the art.

[0048] As mentioned above, in some optional embodiments, the simulation process can be performed on the STAR CCM+ simulation platform: the wave generation data is compiled using Visual Studio to generate wave.dll (dynamic link library), which is then imported into the pool model in STAR CCM+, and the initial wave surface and velocity field are generated at the wave generation location (also known as the inlet); boundary damping is set at the outlet to clip the waves and reduce the impact of wave reflections at the outlet.

[0049] Furthermore, the built-in fluid model of STAR CCM+ can be directly used to simulate the pressure and velocity fields of the water body during the propagation and evolution of the focused wave. For example, the water flow is characterized by the SST k-ω turbulence model, and the pressure and velocity fields are obtained by using the SIMPLE method (Semi-Implicit Method for Pressure-Linked Equations) to solve the incompressible Navier-Stokes equations. The time discretization adopts an implicit unsteady time-progression scheme. The water-wall interaction at the pool boundary is processed using the full y+wall treatment model. The VOF method and high-resolution interface capture (HRIC) technique are used to capture the changes of the free surface at the water-air interface with high precision.

[0050] Figure 4 shows a schematic diagram of the focused wave propagation evolution process in a specific embodiment. Part (a) of Figure 4 shows that before the focusing moment, each wave component moves toward the floating platform model and the phase gradually focuses; part (b) shows that at the focusing moment, each wave component focuses at the floating platform model to form the maximum amplitude; and part (c) shows that after the focusing moment, each wave component moves away from the floating platform model and the phases between them gradually separate.

[0051] Figure 5 shows the wavefront duration curve at the focal position of the floating platform model during the period of the focused wave in a specific embodiment.

[0052] As can be seen from Figures 4 and 5, by performing operations two and three above, the focused wave that conforms to the real wave energy distribution can be effectively reproduced, and its propagation and evolution process can be accurately simulated. At the same time, by controlling the initial conditions, it can be ensured that the focusing position of the focused wave is located at the catenary mooring platform model.

[0053] <Two-way Coupled Solution of Nonlinear Response of Catenary Mooring Platform under Focused Wave Action> In the simulation of focused wave propagation and evolution, as the focused wave enters the area where the catenary mooring platform is located, the pressure field and velocity field will act on the floating platform model and the catenary model: the floating platform model will undergo six degrees of freedom motion under the action of gravity, buoyancy, wave force caused by the focused wave, and mooring force of each catenary; the motion of the floating platform will in turn cause corresponding changes in the shape of each catenary. At the same time, when the velocity field of each rod element in the catenary model changes due to the action of the focused wave in the water model, the load caused by the velocity field will also change accordingly. Superimposed with the gravity, buoyancy, and tension between them, they will undergo complex motion under the action of the above forces, thus reconstructing the overall shape of the catenary and causing changes in the mooring force on the floating platform.

[0054] As mentioned above, in some optional embodiments, the rigid body model of the floating platform can be established in the STAR-CCM+ simulation platform, and its built-in DFBI solver (Dynamic Fluid-Body Interaction, DFBI) can be used to determine the six-degree-of-freedom motion response by solving the fluid-structure interaction problem. However, the DFBI solver does not consider the mooring force term exerted by the catenary on the floating platform.

[0055] Furthermore, in some alternative embodiments, the MoorDyn solver can be used to solve for the spatial morphology and mooring forces of the catenary model. MoorDyn is an open-source software specifically designed for calculating the dynamic response of mooring systems (anchor chains, cables). It can solve for the motion state and morphological changes of each node element in the catenary model, as well as the resulting tension at each node and the changes in mooring forces on the floating platform, based on the loads acting on each node element. However, the MoorDyn solver is generally used for solving the morphology and motion response of mooring systems in still water, and does not consider the additional loads and masses caused by focusing waves.

[0056] It is evident that although DFBI and MoorDyn in STAR-CCM+ can independently calculate the motion response of rigid floating platforms and the motion response and morphology of flexible mooring systems, there is currently no nonlinear motion response solution that can simultaneously consider the bidirectional coupling of the interaction factors between the rigid model of the floating platform and the flexible model of the catenary under the action of the fluid pressure field and velocity field caused by the focused wave.

[0057] Therefore, in the embodiments of this application, through operation four, a process is provided to bidirectionally couple and solve the six-degree-of-freedom motion response of the floating platform model with the overall shape and mooring force of each catenary model under the action of focused waves. Figure 6 shows a flowchart of the bidirectional coupled solution process implemented through Operation 4. As shown in Figure 6, in Operation 4, for each time step to be solved, the following steps are performed: Step S41, update the pressure field and velocity field of the water model under the action of the focused wave corresponding to the time step; Step S42, based on the updated pressure field and velocity field of the water model, iteratively execute steps S421 and S422 until the solution result converges or the number of iterations reaches a preset value: Step S421, based on the wave force exerted by the water model on the floating platform model under the action of the focused wave, and the mooring force exerted by each catenary model on the floating platform model, calculate the motion response of the floating platform model; Step S422, based on the velocity field of the water model at the location of each catenary model under the action of the focused wave, and the motion response of the floating platform model, calculate the mooring force exerted by each catenary model on the floating platform model.

[0058] Specifically, for each time step that needs to be calculated, firstly, step S41 is used to obtain the distribution of the pressure field and velocity field of the water model caused by the propagation and evolution of the focused wave at that time step. Then, steps S421 and S422 are executed iteratively. Combining the pressure field and velocity field data under the action of the focused wave obtained from the simulation, the two-way coupling calculation of the motion response of the floating platform model and the mooring force of each catenary is performed.

[0059] In step S421, the mooring force and wave force required to calculate the motion response of the floating platform model are obtained from the calculation results of step S422 and the pressure field information of the water model obtained through simulation in operation three, respectively. The motion of the floating platform model obtained from the solution in step S421 is passed to step S422, causing the shape of each catenary model to change accordingly. At the same time, the change in the velocity field generated by the water model under the action of the focusing wave obtained through simulation in operation three also further affects the shape of each catenary model and causes the mooring force generated by the uppermost node of the catenary model on the floating platform model to change. The changed mooring force is returned to step S422 to provide mooring force information for the new round of floating platform model motion response solution.

[0060] The bidirectional coupling solution process in steps S421 and S422 will be performed iteratively until the solution results for the motion response of the floating platform model, the mooring force of each catenary model, and the corresponding catenary shape converge (e.g., less than or equal to a preset deviation threshold), or the number of iterations reaches a preset upper limit. At this point, the time step can be updated and the process can return to step S41 to perform the bidirectional coupling solution process for the next time step.

[0061] The specific implementation methods of steps S421 and S422 are described in detail below.

[0062] <Solution of the Motion Response of the Floating Platform Model> In some optional embodiments, as described above, the calculation of the motion response of the floating platform in step S421 can be achieved in the STAR-CCM+ simulation platform by the DFBI solver. This solver uses a second-order accuracy trapezoidal scheme to solve the motion response. When there is a focusing wave in the water model, an additional custom coupling force term needs to be added to the DFBI solver to receive the mooring force updated in step S422. If the gravity and buoyancy of the floating body under still water conditions are considered to be canceled out, then the solver can determine the motion response of the floating platform model by solving equations (13) and (14): (13) (14), among which, , , , These are the mass, inertia tensor, velocity, and angular velocity of the floating platform, respectively. This refers to the wave force generated by the water model on the floating platform, which is generally the resultant force of the wave forces at all locations on the wetted surface of the floating platform model. This represents the resultant force of the mooring forces exerted on the floating platform by each catenary model. This refers to the wave moment generated by the water model on the floating platform model, which is generally the sum of the wave force moments experienced at all locations on the wetted surface of the floating platform model. This is the sum of the mooring torques generated by each catenary model on the floating platform.

[0063] <Calculation of Mooring Force for Catenary Model> After updating the calculation results of the motion response of the floating platform model, they will be passed to step S422 along with the velocity field information of the water body model under the action of focused waves, so as to calculate and update the mooring force of each catenary model.

[0064] Compared to calculating the motion response of a rigid floating platform model, the calculation of mooring forces for a catenary model is more complex. This is because during the period of focused wave action, the displacement and attitude changes of the floating platform model are much greater than in still water, directly causing significant changes in the morphology of the catenary. Simultaneously, the changes in the velocity field in the water model caused by the focused wave also affect the individual members of the catenary, making the relative velocity changes between them and the flow field more complex. Consequently, the loads exerted by the fluid on each member will also change significantly, causing motion in each member and further changes in the morphology of the catenary (the fluid loads on the members can be determined using the Morrison equation). Clearly, the above process is itself a coupled process of flexible structure morphology change, force distribution change, and further morphological change.

[0065] Existing solutions for solving the morphology and mooring forces of catenary models, such as the MoorDyn solver, are generally suitable for solving in still water scenarios. In this process, the floating platform model moves at a relatively low speed, the uppermost part of the catenary model can be considered stationary or undergoing low-speed uniform motion, and the water flow velocity is not high. The fluid load on the part of the catenary model moving in the water is also relatively small. In this case, even if the catenary model is continuously updated in a loop of motion response update-morphology update-force update-motion response update, the solution results can be converged relatively quickly.

[0066] However, when the floating platform model and the catenary model are within the range of focused waves, as the above analysis shows, the violent motion of the floating platform model and the drastic changes in the velocity field in the water model will be transmitted to the morphology and force calculations of the catenary model. If the conventional iterative solution method for the catenary state is still used, the convergence speed will obviously be greatly slowed down. Therefore, for the solution of the catenary state under the action of focused waves and simultaneously affected by the motion response of the floating platform, a new processing flow is needed to ensure the accuracy of the solution while avoiding excessive complexity in the calculation process of the catenary morphology and force, so as to improve the overall efficiency of the bidirectional coupled calculation of the floating platform model and the catenary model.

[0067] Therefore, in the embodiments of this application, the implementation process of step S422 is a linear calculation process, which uses a phased application of action terms and focused wave correction terms to calculate the catenary shape, motion response and mooring force.

[0068] Specifically, in step S422, for any catenary model, as shown in Figure 7, its mooring force can be determined through the following steps: First, based on the motion response of the floating platform model obtained in step S421, the shape of the catenary model is updated for the first time.

[0069] Specifically, the movement of the floating platform model will cause the synchronous movement of the uppermost node units of each catenary model. With the position of the lowermost node unit fixed, the remaining node units and rod units will move accordingly under the drive of the uppermost node unit and reach a new position.

[0070] The second step is to obtain the flow velocity field information of the water model corresponding to the position of each link unit after the first morphological update, and to correct the relative velocity between the fluid and the link unit at the position of each link unit after the first morphological update.

[0071] Specifically, in the catenary model, apart from the uppermost node element moving synchronously with the floating platform model and the lowermost node element remaining fixed, the overall shape of the other node elements and rod elements is mainly determined by gravity, buoyancy, and the loads exerted by the fluid on the rod elements. Among these, the fluid load is essentially caused by the velocity difference between the slender rod elements and the fluid nodes that constitute the water body model. The greater the relative velocity between the rod element and the fluid node at its location, the greater the fluid load it experiences. Its specific value can be obtained by solving the Morrison equation.

[0072] When any link unit When in still water, a rod unit is provided. To achieve the first update of the shape, the velocity relative to the pool coordinate system is: Then the fluid node and the rod element at its location The relative velocity can be expressed as When the focused wave acts on the rod element At that time, it is obvious that the bar elements need to be calculated. For fluid loads, rod elements are required. The flow velocity at the location caused by the focused wave relative velocity in still water Make corrections to obtain the bar element. After the first morphological update, the fluid particles at its location affect the rod element. Correction value of relative velocity : (15), of which, Through rod unit Nodes at both ends , Fluid particle velocity at the location and The representation indicates: (16).

[0073] For all bar elements By performing the above steps, the relative velocity of the fluid to each link element at its location can be corrected.

[0074] The third step is to calculate the fluid load (i.e., fluid resistance) on each link element based on the corrected relative velocity of the fluid to the link element.

[0075] Still using bar units For example, the corrected result Projected onto bar unit The tangential and transverse directions can be obtained tangential component and horizontal components : (17); (18).

[0076] Then the bar element The fluid load experienced, i.e., the tangential component of fluid resistance. and horizontal components It can be represented as: (19) (20), among which, and These are the tangential drag coefficient and the lateral drag coefficient of the fluid, respectively. The diameter of the rod element. For the first The length of each member element, when the length of each member element is... hour, .

[0077] By performing the above steps on all member elements, the fluid load on each member element can be obtained.

[0078] The fourth step is to distribute the fluid load on each member element to the node elements at both ends, and to determine the fluid load on each node element.

[0079] Since the mass of the catenary model is concentrated at each node element, after obtaining the fluid load on the rod element, it needs to be further distributed to the nodes at both ends of each rod (e.g., using a uniform distribution method) to solve the motion response of the catenary model under the action of the focused wave and to update the catenary shape a second time. Accordingly, after each node element receives the distributed fluid load from the two rod elements it is connected to, vector synthesis is performed to obtain the fluid load on each node element. .

[0080] The fifth step is to correct the tangential and lateral additional mass of each member element and distribute the correction results to the node elements at both ends.

[0081] When calculating the motion response of the catenary model, the additional mass of each node element is required. Based on a similar approach to steps three and four, the tangential additional mass of each member element can be determined first using the following formula. and lateral added mass : (twenty one), (22), among which, and These are the tangential additional mass coefficient and the transverse additional mass coefficient, respectively, which can be determined based on the material, mass, and size parameters of the catenary model.

[0082] Then, similarly, each member unit... and The tangential and lateral additional masses received by each node element are then combined to obtain the vector form of the additional mass of each node element. .

[0083] The sixth step is to solve the motion response of each node element and update the shape of the catenary model a second time based on the solution results.

[0084] Specifically, after obtaining the updated fluid load and additional mass of each node, the dynamic equations of each node element can be solved simultaneously under the constraint of the distance between adjacent node elements, thereby obtaining the motion response of each node element.

[0085] The form of the dynamic equations is determined specifically according to the force conditions of different nodal elements. For example, for nodal elements that do not contact the bottom of the water... Its dynamic equation is in the form of: (23), among which, , They are node elements. mass and acceleration, , , , They are node elements. It is subjected to gravity, buoyancy, fluid loads, and internal forces (such as tension from other node elements).

[0086] For node elements in contact with the bottom of the water, it is also necessary to add terms such as the vertical reaction force from the bottom of the water and the friction force when moving on the bottom of the water.

[0087] Clearly, the solution performed in step six is ​​used to determine the motion of each node element of the catenary caused by the focusing wave. Using the solution results, the catenary morphology can be updated a second time.

[0088] The seventh step is to determine the mooring force of the catenary model on the floating platform model based on the motion response of each node unit and the shape of the catenary model.

[0089] Using the solution results from step six and the new shape achieved by the catenary after the second shape update, the tension between each node element is sequentially transmitted along the direction of the rod element, thus obtaining the mooring force exerted by the uppermost node element on the floating platform.

[0090] By superimposing two parameter corrections between two morphological updates, the conventional method of iteratively calculating the catenary state at each time step can be transformed into a sequential execution method. This avoids the drawbacks of drastic changes in the floating platform position caused by the focusing wave and the large computational load and slow convergence speed of the iterative solution when the fluid load of the focusing wave on the catenary is large. It greatly improves the solution speed of the catenary state while ensuring the calculation accuracy. At the same time, the floating platform model and the catenary model are treated as a two-way coupled system and iterated as a whole under the action of the focusing wave to ensure the convergence of the calculation results at each time step.

[0091] Due to the special properties of the focused wave field, the focused wave only causes drastic changes in the velocity field near the focusing position. In order to reduce the computation time caused by data transmission, in some preferred embodiments, the relative velocity between the fluid and the rod element can be corrected only when the maximum amplitude of the focused wave passes through the floating platform model.

[0092] For example, a window triggering mechanism could be added, utilizing the known focus time t. f The relative velocity of each fluid element with respect to each rod element is determined according to the following formula: (twenty four).

[0093] in, To construct the peak period of the wave spectrum of the focused wave, this window can be set to perform relative velocity correction during the period when the focused wave acts on the catenary mooring platform model, and during the non-acting period, it is treated as a normal still water condition.

[0094] In some optional embodiments, steps S421 and S422 of the bidirectional coupled iterative solution described above can be performed in the aforementioned STAR CCM+ simulation platform by calling the DFBI and MoorDyn solvers, respectively. The data exchange process between STAR CCM+, DFBI, MoorDyn, and the coupled data is shown in Figure 8, mainly including: during the iterative solution process at each time step, the water model pressure field data obtained from the STAR CCM+ simulation is transmitted to the DFBI. The DFBI uses this data to determine the wave force and obtains the mooring force from the previous time step from MoorDyn, solves the motion equations, and updates the position and velocity of the floating platform model. The updated floating platform motion response results and the velocity field data obtained from the STAR CCM+ simulation are transmitted to MoorDyn, which determines the updated mooring force based on the process in Figure 7 and returns it to the DFBI solver. This bidirectional coupled process iterates within one time step until the solution converges or the upper limit of the number of iterations is reached.

[0095] Understandably, the DFBI solver needs adaptive improvements to incorporate the updated mooring force term during the six-DOF motion response calculation. Similarly, the MoorDyn solver requires adaptive improvements, with parameter adjustments performed sequentially at each stage during the motion response calculation of nodal elements, as shown in Figure 7. Aside from these adaptive improvements, the parameter settings and initialization operations for both the DFBI and MoorDyn solvers—such as setting the mass, center of mass, and dimensions of the floating platform, as well as setting the structural properties, length, anchor point location, cable hole location, and solution parameters of the catenary—are the same as the conventional calculation process and will not be elaborated upon here.

[0096] Figure 9 illustrates the state changes of the floating platform model in the pool model during the focusing wave action phase, obtained by the method provided in this application, in a specific embodiment. Parts (a), (b), and (c) show the states of the floating platform before, during, and after the focusing moment, respectively. Figure 10 shows the motion response time-history curve of the floating platform model under the focusing wave action obtained by synchronous calculation. Figure 11 shows the tension change curve of the catenary model obtained by synchronous calculation, where parts (a) and (b) are the tension calculation results of the catenary on the wave-facing side and the wave-avoiding side, respectively.

[0097] As can be seen from Figures 9 to 11, the solution method provided in this application uses the fluid pressure field and velocity field information generated under the action of focused waves to drive the floating platform model and the catenary model respectively, and couples the solution processes of the two in a two-way manner, thereby effectively obtaining the nonlinear response of the catenary mooring platform under the action of focused waves.

[0098] The specific embodiments of this application have been described in detail above. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A method for solving the nonlinear response of a catenary mooring platform under focused wave action, characterized in that, The process includes the following operations: Operation 1: Constructing a pool model and a catenary mooring platform model moored within the pool model. The pool model includes a water body model and an air layer model above it. The catenary mooring platform model includes a floating platform model and several catenary models, with one end of each catenary model fixed to the bottom of the water body model and the other end fixed to the floating platform model. Operation 2: Generating focused wave generation data based on the phase focusing method. The focused wave generation data includes the initial wave surface and initial velocity field corresponding to focusing the focused wave onto the catenary mooring platform. Operation 3: Simulating focused wave propagation in the pool model using the wave generation data. Operation 4: Solving the motion response of the floating platform model under the action of focused waves and catenary mooring constraints using a two-way coupled calculation method.

2. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 1, characterized in that, The floating platform model floats in the pool model, with its lower part located in the water body model and its upper part located in the air layer model. Each catenary model includes multiple alternating node units and multiple rod units. The lowermost node unit is fixed to the bottom of the water body model, and the uppermost node unit is fixedly connected to the floating platform model. The mass of each rod unit is distributed to the node units at both ends, and adjacent rod units are hinged through shared node units. The water body model, air layer model, floating platform model, and catenary model are all numerical models.

3. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 1, characterized in that, Operation 2 includes the following steps: Step S21, determine the target wave spectrum; Step S22, determine the wave-generating target of the focused wave, wherein the wave-generating target includes the wave-generating time, wave-generating position, focusing time, focusing position, target wave height at the focusing time, and the number and frequency range of wave components constituting the focused wave; Step S23, determine the wave number of each wave component using the dispersion equation; Step S24, determine the wave amplitude of each wave component based on energy conservation; Step S25, determine the initial phase of each wave component at the wave-generating position based on the wave-generating position, wave-generating time, focusing time, and focusing position of each wave component; Step S26, determine the initial wave surface and initial velocity field at the wave-generating time and wave-generating position based on the wave amplitude and initial phase of each wave component.

4. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 1, characterized in that, In the simulation of focused wave propagation in Operation 3, the pressure field and velocity field distribution of the water body model during the focused wave propagation and evolution process are obtained by discretizing and solving the incompressible Navier-Stokes equations; the water-air interface at the junction of the water body model and the air layer model is captured by solving the VOF transport equations.

5. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 1, characterized in that, In Operation 4, for each time step to be solved, the following steps are performed: Step S41, update the pressure field and velocity field of the water model under the action of the focused wave corresponding to the time step; Step S42, based on the updated pressure field and velocity field of the water model, iteratively execute steps S421 and S422 until the solution converges or the number of iterations reaches a preset value: Step S421, based on the wave force exerted by the water model on the floating platform model under the action of the focused wave, and the mooring force exerted by each catenary model on the floating platform model, calculate the motion response of the floating platform model; Step S422, based on the velocity field of the water model at the location of each catenary model under the action of the focused wave, and the motion response of the floating platform model, calculate the mooring force exerted by each catenary model on the floating platform model.

6. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 5, characterized in that, In step S421, the motion response of the floating platform model is determined by solving the following equation: ， ,in, 、 、 、 These are the mass, inertia tensor, velocity, and angular velocity of the floating platform, respectively. The wave force generated by the water model on the floating platform. This represents the resultant force of the mooring forces exerted on the floating platform by each catenary model. The wave moment generated by the water model on the floating platform model. This is the sum of the mooring torques generated by each catenary model on the floating platform.

7. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 5, characterized in that, The implementation process of step S422 is a linear calculation process, which uses a segmented application of action terms and a focused wave correction term to calculate the catenary morphology, motion response and mooring force.

8. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 7, characterized in that, In step S422, for any catenary model, its mooring force is determined through the following steps: First, based on the motion response of the floating platform model obtained in step S421, the shape of the catenary model is updated for the first time; Second, the velocity field information of the water model corresponding to the position of each member element after the first shape update is obtained, and the relative velocity between the fluid and the member element at the position of each member element after the first shape update is corrected; Third, based on the corrected relative velocity between the fluid and the member element, the mooring force of each member element is calculated. The steps are as follows: 1) Obtain the fluid load; 2) Distribute the fluid load on each member element to the node elements at both ends to determine the fluid load on each node element; 3) Correct the tangential and lateral additional masses of each member element and distribute the correction results to the node elements at both ends; 4) Solve the motion response of each node element and update the shape of the catenary model a second time based on the solution results; 5) Determine the mooring force of the catenary model on the floating platform model based on the motion response of each node element and the shape of the catenary model.

9. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 8, characterized in that, The correction of the relative velocity between the fluid and the link unit at the position of each link unit after the first morphological update is specifically as follows: for any link unit Using rod units The flow velocity at the location caused by the focused wave relative velocity in still water Make corrections to obtain the bar element. After the first morphological update, the fluid particles at its location affect the rod element. Correction value of relative velocity 。 10. The method for solving the nonlinear response of a catenary mooring platform under focused wave action according to claim 8, characterized in that, The process of correcting the tangential and lateral additional masses of each member element and distributing the correction results to the node elements at both ends involves: first, determining the tangential additional mass of each member element. and lateral added mass Then, each member unit and The tangential and lateral additional masses received by each node element are then combined to obtain the vector form of the additional mass for each node element. 。

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