Method and system for analyzing wave-current motion response of moored multi-buoy array

Abstract

The application belongs to the technical field of new ocean energy, and provides an anchor line multi-floating body array wave flow motion response analysis method and system, and its technical scheme is that the present research adopts a combined simulation method of multi-body dynamics and computational fluid dynamics to comprehensively model and analyze the mooring type multi-floating body array, designs a universal joint connecting structure for platform connection, and introduces an equivalent concentrated mass-spring unit to simplify the modeling of the mooring chain. The combined simulation is implemented in a numerical wave and current pool, the hydrodynamic force and structural response of the anchor line multi-floating body array system under the conditions of steady current and regular wave are evaluated, the influence of the floating ball size, the mooring chain weight and the flow velocity on the hydrodynamic performance and the platform stability is systematically studied, and the performance requirements under the complex ocean environment are better met.

Description

Technical Field

[0001] This invention belongs to the field of marine new energy technology, and in particular relates to a method and system for analyzing the wave and current motion response of moored multi-buoy arrays. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Moored multi-buoy arrays serve as carriers for floating photovoltaic systems and energy islands at sea, offering advantages such as full utilization of marine energy resources and land conservation. However, the marine environment is complex and harsh, and moored multi-buoy arrays are subjected to continuous dynamic loads from waves and currents. These environmental loads not only affect the life-cycle cost and efficiency of energy production but may also threaten the structural integrity of the multi-buoy array. Therefore, in-depth research on the dynamic response of moored multi-buoy arrays is crucial. In the composition of a moored multi-buoy array system, the mooring system is the core component ensuring its safety and stability, and it accounts for a significant portion of the cost. Mooring design faces optimization challenges: reducing the number of mooring points to lower costs typically requires heavier anchor chains to maintain mooring force, but this increases the draft of the moored platform, thereby increasing the horizontal hydrodynamic loads it experiences, creating an unfavorable cycle.

[0004] A considerable amount of research has been conducted on the dynamic response and environmental loads of moored multi-floating body array systems at sea. These systems need to maintain structural safety under extreme sea conditions and remain stable during long-term operation. Studies have shown that wave loads are often the dominant component of the total environmental load in marine environments. Traditional analytical methods, including semi-empirical methods based on the Morison equation and analyses using specialized software such as HydroDyn and OrcaFlex, have supported previous research to some extent. However, these methods cannot fully reflect the nonlinear flow field characteristics of the multi-floating body array and its interactions. Co-simulation methods using Multibody Dynamics (MBD) and Computational Fluid Dynamics (CFD) can provide high-resolution velocity and pressure fields, making them more suitable for complex multibody-fluid coupling problems; however, traditional grid-based CFD often requires moving overlapping meshes, which leads to significant computational overhead when dealing with strong relative motion among the multibody components. Summary of the Invention

[0005] To address at least one of the technical problems mentioned above, this invention provides a method and system for analyzing the wave and current motion response of moored multi-buoy arrays. This method helps to more comprehensively understand the design trade-offs of mooring systems and improve design accuracy, thereby better meeting the performance requirements in complex marine environments.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of the present invention provides a method for analyzing the wave and current motion response of a moored multi-buoy array, comprising the following steps: Construct a moored multi-floating body array model of the simulated floating body object; wherein, the moored multi-floating body array model includes multiple floating platforms, connectors, mooring systems and buoys; Adjacent floating platforms are connected by the connector, and the connector is provided with universal joints with corner limiting devices at both ends to maintain the desired distance between the platforms and release two relative rotational degrees of freedom. The mooring system comprises multiple mooring chains, each of which is simplified using a lumped mass-spring unit. Specifically, each mooring chain is discretized into multiple chain balls that are equivalent in properties. Adjacent chain balls are connected by springs with axial constraint and torsional freedom characteristics, and the springs are allowed to shorten within a preset range. At least one buoy is installed on each mooring chain to provide upward net buoyancy to counteract the vertical component of the mooring force. Based on the relevant parameters of the moored multi-buoy array obtained, a numerical pool model for simulating wave and current scenarios is constructed. Based on the constructed numerical pool model, a joint simulation was conducted to simulate the dynamic response of the mooring multi-buoy array under preset ocean current and wave conditions, and the dynamic response results were analyzed. Based on the simulation analysis results, an optimized design scheme for the mooring system is generated. Furthermore, a variable stiffness spring model is used to simulate the corner limiting device, and a nonlinear spline curve is used to define the relationship between the spring rotation angle and the generated resisting torque, replacing the contact collision model of the limiting block. The allowable free rotation angle range of the corner limiting device is jointly determined by the floating platform length L, height H, spacing D, and connector installation height P, and their relationship is expressed as: .

[0007] Furthermore, the equivalent radius of the chain ball is determined as follows: first, the initial radius is calculated based on the Morison equation and the actual chain link parameters, and then it is corrected through computational fluid dynamics simulation to ensure that the hydrodynamic resistance of the lumped mass-spring unit under the same motion conditions is consistent with that of the actual mooring chain model.

[0008] Furthermore, the construction of the numerical pool model for simulating wave and current scenarios specifically includes: S1: Construct a basic model of a numerical water tank, including a tank representing the water tank, a floating body, a seabed plate representing the seabed, and an anchor mooring submodule; the anchor mooring submodule predefines the connection and contact relationship between the seabed plate and the anchor chain with the buoy, and fixes the end of the anchor chain to the seabed plate; S2: Based on the arrangement of the float array in the multi-float array, copy and arrange multiple floats, and connect the multiple floats into an array using connectors; based on the number and location of the mooring points, copy and arrange multiple anchoring sub-modules, and connect the top of each anchor chain to the corresponding floating platform to form a complete anchoring multi-float system assembly; S3: A stable ocean current environment is simulated by defining the motion of the sliding pair of the seabed plate relative to the box; S4: Based on the physical properties of actual seawater, define the density, dynamic viscosity, and surface tension coefficient of the liquid filling the tank to a set height; S5: Based on the determined target wave parameters, drive the wave-generating plate set inside the box to move and generate the target wave; S6: Execute a multibody dynamics and computational fluid dynamics co-simulation loop until the simulation ends, thereby generating an equivalent virtual ocean scene in the numerical pool.

[0009] Furthermore, the simulation of the dynamic response of the moored multi-buoy array under preset ocean current and wave conditions, and the analysis of the dynamic response results, include: analyzing the influence of the float size and mooring chain weight parameters on the hydrodynamic and structural response of the moored multi-buoy array system under different towing and wave conditions.

[0010] Furthermore, based on simulation analysis, the following design criteria are derived: Under steady-state ocean current conditions, as the size of the buoy increases, both the horizontal and vertical components of the mooring force decrease, and the buoy's load-reducing effect becomes more significant as the current velocity increases. Under regular wave conditions, optimizing the buoy size requires balancing two competing mechanisms: first, buoyancy counteracts the vertical component of mooring force to suppress motion; second, the increased projected area leads to an increase in horizontal hydrodynamic load. The optimal buoy size is related to the weight of the mooring chain. A second aspect of this invention provides a wave and current motion response analysis system for a moored multi-buoy array, comprising: An anchored multi-floating body array model construction module is used to construct an anchored multi-floating body array model of the simulated floating body object. The anchored multi-floating body array model includes multiple floating platforms, connectors, a mooring system, and buoys. Adjacent floating platforms are connected by the connectors, which are equipped with universal joints with corner limiting devices at both ends to maintain the desired spacing between platforms and release two relative rotational degrees of freedom. The mooring system includes multiple mooring chains, each represented by a lumped mass-spring unit for simplification. Specifically, each mooring chain is discretized into multiple chain balls with equivalent properties. Adjacent chain balls are connected by springs with axial constraint and torsional freedom characteristics, and the springs are allowed to shorten within a preset range. At least one buoy is installed on each mooring chain to provide upward net buoyancy to counteract the vertical component of the mooring force. A numerical pool model construction module is used to construct a numerical pool model for simulating wave and current scenarios based on the acquired parameters of the anchored multi-floating body array. The response analysis module is used to perform co-simulation based on the constructed numerical pool model, simulate the dynamic response of the mooring multi-buoy array under preset ocean current and wave conditions, and analyze the dynamic response results; based on the simulation analysis results, an optimized design scheme for the mooring system is generated.

[0011] A third aspect of the present invention provides a computer-readable storage medium.

[0012] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-described method for analyzing the wave and current motion response of a moored multi-buoy array.

[0013] A fourth aspect of the present invention provides a computer device.

[0014] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the above-described method for analyzing the wave and current motion response of a moored multi-buoy array.

[0015] A fifth aspect of the present invention provides a program product, which is a computer program product including a computer program that, when executed by a processor, implements the steps in the above-described method for analyzing the wave and current motion response of a moored multi-buoy array.

[0016] Compared with the prior art, the beneficial effects of the present invention are: This invention employs a joint simulation method combining multibody dynamics and computational fluid dynamics to comprehensively model and analyze an anchored multi-buoy array. A universal joint connection structure for platform connection is designed, and an equivalent lumped mass-spring element is introduced to simplify the modeling of the mooring chain. Joint simulations are conducted in numerical wave generation and ocean current tanks to evaluate the hydrodynamic and structural responses of the anchored multi-buoy array system under steady-state currents and regular wave conditions. The effects of buoy size, mooring chain weight, and flow velocity on hydrodynamic performance and platform stability are systematically studied. This contributes to a more comprehensive understanding of the design trade-offs of mooring systems and improves design accuracy, better meeting the performance requirements of complex marine environments.

[0017] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0018] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0019] Figure 1 This refers to the arrangement of the multi-buoy array and mooring chain provided in the embodiments of the present invention; Figure 2 This is the floating platform provided in the embodiments of the present invention; Figure 3 This is a connector with universal joints at both ends, as provided in the embodiments of the present invention; Figure 4 This describes the relationship between the limiting angle of the float connector and the size and installation position of the float provided in this embodiment of the invention. Figure 5 This is the relationship curve between the rotation angle and the resisting torque of the connector equivalent spring based on the definition of a nonlinear spline curve provided in the embodiments of the present invention; Figure 6 This invention provides a force balance analysis of the anchorage buoy under conditions with and without a buoy, as provided in the embodiments of the present invention. Figure 7 The present invention provides a hybrid mooring chain with buoys; Figure 8 The present invention provides a numerical water tank with a wave generator and a wave-damping structure for simulating ocean wave and current scenarios. Figure 9 The present invention provides a numerical water tank for simulating a drag flow field, including a tank body and a seabed plate model, wherein (a) is the numerical water tank model in multibody dynamics software, and (b) is the numerical water tank model in computational fluid dynamics software. Figure 10The data interaction process during MBD-CFD co-simulation provided in this embodiment of the invention; Figure 11 This invention provides the effect of different buoy sizes on mooring force values ​​at a towing speed of 1.0 m / s; where (a) is the vertical mooring force at the mooring point and (b) is the horizontal mooring force at the mooring point. Figure 12 This is the arrangement of a 2×3 multi-buoy array of four anchorage subsystems obtained by copying in MBD software, as provided in the embodiments of the present invention. Figure 13 The mooring force of the lightweight mooring chain under wave conditions with different buoy radii provided in the embodiments of the present invention is shown in the following: (a) is the mooring force of chain L1 in the X direction in the waves, (b) is the mooring force of chain L1 in the Z direction in the waves, and (c) is the average mooring force of chain L1 in the last 4 cycles. Figure 14 This is the maximum pitch angle of platform Z1 under the conditions of a lightweight mooring chain provided in this embodiment of the invention. Detailed Implementation

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0022] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0023] Example 1 This embodiment provides a method for analyzing the wave and current motion response of a moored multi-buoy array, including the following steps: Step 1: Construct an anchored multi-floating body array model of the simulated floating object; The anchored multi-floating body array model includes multiple floating platforms, connectors, a mooring system, and buoys. Adjacent floating platforms are connected by connectors with universal joints at both ends to maintain a safe distance between platforms and release two relative rotational degrees of freedom. The mooring system includes multiple mooring chains, each represented by a lumped mass-spring unit. Each chain is simplified into several chain balls that are equivalent to the original chain in terms of mass, buoyancy, and hydrodynamic resistance. These chain balls are connected by springs with axial constraint and torsional freedom, and the springs can be shortened within a certain range. Each mooring chain is equipped with a buoy to provide upward net buoyancy to reduce the vertical component of the mooring force. This embodiment uses one assembly method as an example to illustrate the specific construction process, including 6 floating platforms. The 6 floating platforms are connected by connectors to form a 3×2 array, and 4 mooring lines are used at the four corners. Figure 1 As shown, the specific steps include the following: In this embodiment, each floating platform uses a lightweight cylindrical float assembly, which possesses good buoyancy and resistance to seawater corrosion. The float assemblies are assembled into a rigid frame via connectors, such as... Figure 2 As shown in Table 1, the platform parameters for each floating platform are as follows: Table 1 Parameters of Floating Platform

[0024] To prevent adjacent floating platforms from colliding in waves, in this embodiment, the connector includes a connecting rod and universal joints at both ends of the connecting rod. Each universal joint includes a mounting base, a rotating base, and a cross pin. The rotating base is fixed to the end of the connecting rod, and the mounting base is fixed to the platform frame. The cooperation between the connecting rod and the universal joints maintains a safe distance and releases two relative rotational degrees of freedom. The length of the connecting rod is adjustable to maintain the desired distance, such as... Figure 3 As shown; like Figure 4 As shown, the universal joint has corner limiting devices at both ends, and the allowed free rotation angle range of the corner limiting devices is... The dimensions are determined by the length L, height H, spacing D of the floating platform, and the installation height P of the connector, and are expressed as follows: , like Figure 5As shown, the dynamic model corresponding to the connector uses a variable stiffness spring to simulate the connector's angle limiting device. A nonlinear spline curve is used to define the relationship between the spring angle and the resisting torque. The unconstrained angle of the universal joint allows the floats to freely float and rotate under the action of waves; the angle limiting torque prevents collisions between adjacent floats caused by excessive angles. This nonlinear spring replaces the contact collision model of the limiting block, improving computational efficiency. It avoids the contact collision model of the limiting block, improving computational efficiency, and limits the rotation range of the universal joint, preventing collisions between adjacent floats caused by excessive angles. The unconstrained universal joint angle allows the floats to freely float and rotate within a certain range under the action of waves. The constraints are based on the length of the connecting rods (float spacing) and their placement position in the connector, preventing float collisions.

[0025] Mooring chains are primarily used to resist the horizontal hydrodynamic forces generated by waves and currents. Typically, mooring chains are quite heavy, and their restoring force comes from the horizontal component of gravity caused by the chain's weight. Real mooring chains have multiple degrees of freedom, and their motion is constrained by the geometric contact between the links. Since each mooring chain often contains hundreds to thousands of links, the computational complexity of simulating each geometric contact is extremely high.

[0026] To facilitate dynamic analysis of the mooring system, this embodiment simplifies the mooring chain using the lumped mass-spring method, proposing an efficient lumped mass-spring unit (LMSU) to characterize the dynamic properties of the mooring chain. Furthermore, the hydrodynamic loads of the LMSU are calculated using computational fluid dynamics (CFD), achieving higher accuracy compared to semi-empirical methods. Therefore, each chain is simplified into several chain balls equivalent to the original chain in terms of mass, buoyancy, and hydrodynamic drag. These chain balls are connected by springs with axial constraint and torsional freedom, and the springs can shorten within a certain range. The equivalent distance between two adjacent chain balls is defined as follows:

[0027] in, This represents the axial force between two adjacent chain balls. Indicates the spring stiffness. and This represents the reference point at the center of mass of the nth and (n+1)th chain balls. This represents the equivalent distance (initial distance) between the two chain balls. Indicates the damping coefficient. This represents the actual distance between the centers of mass of the nth and (n+1)th chain balls. This represents the relative velocity of the two centers of mass along the line connecting them; Some of the chain balls are suspended in the water, while others lie on the seabed. The catenary morphology makes positioning these chain balls even more difficult. The radius of the anchor point is known.R anchor , water depth D depth With mooring chain total length L total Subsequently, LMSU divided the entire mooring chain into two straight sections: one section being the mooring chain on the seabed, with a length expressed as... L seabed The other section is a mooring chain suspended in the water, the length of which is expressed as... L water At the same time, it is necessary to determine the number of hammers on these two straight segments. N seabed and N water Subsequently, the distance between two adjacent hammers is expressed as: , , in, This represents the distance between two adjacent hammers when they are on the seabed. This indicates the distance between two adjacent hammers when they are suspended in water.

[0028] The contact force between the hammer and the seabed is defined to accurately calculate the length of the chain segment lying on the seabed and the contact force. F seabed Represented as: , in, K seabed and C seabed This indicates the stiffness and damping of the seabed. D chainball and H seabed represents the vertical position of the chain ball in the global coordinate system and the depth of the seabed, respectively, and exp is the power exponent in the contact force model; Let be the velocity component of the chain ball along the seabed in the normal direction.

[0029] Initial radius of the hammer According to the definition of the Morison equation, it can be expressed as: , in, Indicates the equivalent radius of the chain link; The number of chain balls used to correct the true radius in CFD simulation; and These are the drag coefficients of the chain link and the sphere, respectively.

[0030] Subsequently, the equivalent density of the chain link is defined as "total weight of the chain links / total volume of the chain link", expressed as: , in, This represents the actual total length of the anchor chain. This represents the actual density of the anchor chain material. Subsequently, the chain ball radius was corrected using CFD simulation to ensure that the hydrodynamic drag of the LMSU was consistent with that of the real mooring chain. The real mooring chain consists of chain links connected by contact forces; while the LMSU, with the same length as the real chain model, is connected by equivalent spring forces. Initially, both chains were suspended in the water with their bottom ends free. Then, the top of the chain moved horizontally, accelerating to 1.0 m / s, and the horizontal hydrodynamic drag and vertical tension at the top were compared. After determining a suitable chain ball radius, the density was adjusted accordingly.

[0031] In this embodiment, the mooring chain adopts an R3-class stopless chain. The geometric structure of the R3-class stopless chain is shown in Table 2. Table 2 Mooring Chain Parameters

[0032] Horizontal component T of mooring force x Used to limit the horizontal movement of the frame; while the downward component T z This will increase the draft of the moored platform. To reduce this downward component, spherical buoys are installed near the guide wire to provide net upward buoyancy F. bb The mooring force T reaches its maximum value when the guide wire is far from the anchor point. Therefore, a force balance analysis of the "mooring chain-buoy-platform" system is required, such as... Figure 6 As shown, the mooring force T is decomposed into a horizontal component T x and vertical component T z In the absence of a float, T x The combined horizontal load F on the platform p Balance, T z Due to the platform's buoyancy F bf Cancel; but in the case of a float, T z Due to the buoyancy F of the buoy bb With platform buoyancy F bf After mutual cancellation and calculation, the parameters of LMSU and float are shown in Table 3: Table 3 Parameters of LMSU and float

[0033] Each mooring chain is divided into a set number of chain balls, such as 25; the spherical buoys combined with the LMSU are shown in... Figure 7The mooring forces acting on the platform are almost horizontal, thus generating a smaller downward load when resisting horizontal movement of the platform.

[0034] Step 2: Based on the articulation and anchoring relationship and inertial parameters of the anchored multi-buoy array, construct a numerical water tank for simulating wave and current scenarios; Based on calculations and existing research on the motion response of multi-buoy systems, the arrangement of the array's long side relative to the dominant wave direction affects the hydrodynamic response. To examine more demanding conditions, this embodiment sets the dominant wave direction perpendicular to the array's long side. The numerical tank uses a box with a wave-damping structure and a rotatable wave generator to produce periodic linear waves, such as... Figure 8 ; A rotating wave generator rotates around its base, with wave height and period controlled by rotational speed and rotation angle. To ensure flow field stability, the wave generator is not activated for a set time (e.g., 3 seconds) before the simulation, subsequently generating regular waves with set parameters. For example, a regular wave with a height of 2.0 m and a period of 8 s is represented as: , Under conditions of a water depth of 7.6m, the wave generator can produce regular waves with target parameters of 2.0m wave height and 8s period after pre-running and stabilization. Table 4 shows the modeling parameters for the numerical water tank. Table 4 Modeling parameters for the numerical water tank

[0035] In this embodiment, to study the dynamic response of a multi-buoy array under ocean current and wave conditions in a numerical tank, a moored platform was first towed to characterize the ocean current; subsequently, the dynamic response of the moored 2×3 multi-buoy array was studied in waves generated by a wave generator. The multi-buoy array was modeled using the multibody dynamics software RecurDyn, while the numerical tank was modeled using Particleworks—a CFD software based on a meshless, semi-implicit moving particle method.

[0036] like Figure 9 The figure shows a numerical water tank for simulating a drag flow field, including a tank body and a seabed model. (a) is the numerical water tank model in multibody dynamics software, and (b) is the numerical water tank model in computational fluid dynamics software. like Figure 10 As shown, the specific steps include the following: Specifically, the steps include the following: Step 201. Construct a basic numerical water tank model in multibody dynamics software; In this embodiment, the basic model includes a tank representing a pool, a float, a seabed plate representing the seabed, and an anchoring subsystem module. The anchoring subsystem module consists of a seabed plate and an anchor chain with a buoy attached. The contact relationship between the seabed plate and the anchor chain ball is predefined in the multibody dynamics software, and the end of the anchor chain ball is fixedly connected to the seabed plate. The seabed plate is set at the same height as the bottom surface of the tank. The anchoring subsystem module is an independent functional unit, and the seabed plate, anchor chain, buoy, and their connections and contact relationships are fully defined within it.

[0037] Step 202. Based on the number and spatial distribution of anchor chains in the moored multi-floating body system to be simulated, copy and rotate the moored floating body model constructed in step 201 in the multibody dynamics software to arrange multiple moored subsystems around the floating body array, and fix the top of each anchor chain to the corresponding floating body to form a complete moored multi-floating body system assembly; when copying and rotating the moored subsystem model, its operation reference point is the design position of the corresponding floating body in the array.

[0038] Step 203. In the multibody dynamics software, based on the direction and velocity of the target ocean current, the motion of the seabed plate relative to the box is defined using a sliding joint to simulate a stable ocean current environment; The speed and direction of the moving pair are set according to the constant or time-varying ocean current profile to be simulated.

[0039] Step 204. Import the box model and the mooring multi-buoy system assembly obtained in step 202 into a computational fluid dynamics software based on particle dynamics, wherein the seabed plate model is not imported; fill the box with liquid of a set height, and define the density, dynamic viscosity and surface tension coefficient of the liquid in the computational fluid dynamics software according to the physical properties of actual seawater; the height of the liquid is lower than the top of the box to form a free liquid surface.

[0040] Step 205. Based on the period and wave height of the target ocean wave, a joint simulation is performed between the multibody dynamics software and the computational fluid dynamics software. The wave-generating plate installed in the tank is driven by the multibody dynamics software to generate the corresponding wave in the numerical water tank. The wave-generating plate is a single-plate pusher plate, and its motion law is controlled by the multibody dynamics software according to the target wave parameters.

[0041] Step 206. Execute the co-simulation loop: The computational fluid dynamics software calculates the fluid forces between the hull, wave generator, anchor chain, and float, based on the current position and velocity of the hull, wave generator, anchor chain, and float, and feeds these forces back to the multibody dynamics software. The multibody dynamics software, based on the received fluid forces, calculates the acceleration and constraint forces of each component in the system, solves for the position and velocity of each component in the next time step, and then sends the updated position and velocity information back to the computational fluid dynamics software. This data interaction and iterative calculation between the multibody dynamics software and the computational fluid dynamics software continues until the simulation ends, thereby generating a virtual ocean scene in the numerical simulation pool equivalent to the specified ocean currents and waves. The co-simulation loop is advanced using a fixed time step or an adaptive time step.

[0042] Step 3: Based on the constructed numerical pool model, perform joint simulation to simulate the dynamic response of the mooring multi-buoy array under preset ocean current and wave conditions, and analyze the dynamic response results. In this embodiment, the specific analysis includes analyzing the influence of the float size on the platform attitude angle and mooring force under different towing conditions, and the influence of different mooring chain weights and float sizes on the platform attitude angle and mooring force under wave conditions; A moored platform was towed at varying constant speeds within a numerical tank to characterize ocean current conditions. The bottom end of the mooring chain was fixed to a seabed model, which moved relative to the numerical tank at a given towing speed. In the MBD software, all chain balls were established in contact with the seabed model, allowing some chains to lie flat on the surface. To avoid disturbing the flow field, the geometry of the seabed model was not imported into the CFD software; therefore, the motion of the seabed did not directly affect the surrounding fluid, and the hydrodynamic loads acting on the chain balls were solved using Particleworks. To verify the aforementioned force balance analysis, two simulations were conducted at a towing speed of 2.0 m / s: one with "no buoy" and the other with "buoy with an installation radius of 800 mm". The results show that installing a buoy can significantly suppress the platform's pitching motion.

[0043] For a mooring chain without buoys, the submerged volume of its platform is almost equivalent to the total submerged volume of "platform + buoy" in a "mooring chain with buoys." Since the drag coefficient of a sphere is much lower than that of a cylinder, the buoy can effectively reduce the hydrodynamic load on the entire system.

[0044] The results show that, without a float, F bf Less than F in the case of a float bb With F bf The sum of the values, and when there is a buoy, is expressed as F. bbThe buoy is the primary contributor. It is the reduction in the submerged volume of the platform that decreases the overall horizontal hydrodynamic drag, thereby reducing the mooring force and its vertical component T. z This reduces the total buoyancy required to achieve balance.

[0045] Subsequently, to investigate the effect of the buoy, two sets of towing simulations were conducted: First, the influence of buoy size was analyzed at a constant towing speed of 1.0 m / s, with buoy radii set to 400, 600, 800, and 1000 mm, respectively; second, with an 800 mm buoy installed, the speed effect was evaluated at towing speeds of 0.5, 1.0, 1.5, and 2.0 m / s, respectively. The corresponding "no buoy" scenario was also analyzed to demonstrate the advantages of the buoy.

[0046] Influence of float size at a towing speed of 1.0 m / s Numerical results include the platform's pitch angle and mooring force, with the mooring force further decomposed into horizontal and vertical components for detailed analysis. Figure 11 As can be seen, (a) represents the vertical mooring force at the mooring point, and (b) represents the horizontal mooring force at the mooring point. Both the horizontal and vertical mooring forces decrease as the float size increases; the decrease is most significant when the float radius increases from 0 mm to 800 mm, while the difference between the 800 mm and 1000 mm cases is relatively small. This trend is more pronounced in the vertical component. Combined with the pitch angle results, the pitch decreases as the float size increases, and its trend is consistent with the vertical mooring force. Overall, under this operating condition, a float with a radius of 800 mm is the optimal configuration.

[0047] This indicates that installing buoys can reduce the platform's pitch motion. As pitch decreases, the draft at the platform's bow becomes shallower, thereby reducing the horizontal hydrodynamic forces at the mooring point. An 800 mm radius buoy can effectively reduce the overall hydrodynamic load under a 1 m / s current; therefore, the next operating condition will continue to use an 800 mm buoy to study the effect of towing speed.

[0048] The effect of an 800 mm radius buoy at different towing speeds A comparative study was conducted on platforms without buoys and with buoys of 800 mm radius at towing speeds of 0.5, 1.0, 1.5, and 2.0 m / s. Simulations were performed over a period of 20.0–25.0 s. The results showed that the horizontal and vertical mooring forces of the platform without buoys increased almost linearly with increasing towing speed. After installing buoys, both the overall mooring force and pitch angle of the platform decreased significantly. At all speeds, the vertical mooring force was reduced to almost zero, while the reduction in horizontal mooring force became more pronounced with increasing speed. The simulations indicate that at low towing speeds, buoys do not introduce additional hydrodynamic loads; and their load-reduction effect becomes increasingly significant with increasing speed. At 2.0 m / s, the horizontal and vertical mooring forces decreased by approximately 50% and 96%, respectively, a significant increase compared to the case without buoys. These towing conditions also demonstrate that buoys can effectively counteract downward loads in ocean currents, and their compensatory effect is more pronounced at higher current velocities.

[0049] To analyze the influence of different mooring chain weights on the motion response and mooring force of a floating platform array under wave conditions, MBD-CFD co-simulation was used to study the dynamic response of a 2×3 array constrained by four mooring chains under regular wave action. The CFD software provided the forces exerted by the fluid on the mooring array; the MBD software provided the constraint forces between the platforms in the array, such as... Figure 12 As shown.

[0050] For lightweight mooring chains (chain ball radius 150mm): The lightweight mooring chain consists of chain balls with a radius of 150 mm. The horizontal and vertical mooring forces at the mooring point are represented by X-axis and Z-axis components, respectively. The X-axis and Z-axis mooring forces of chain L1 both exhibit obvious periodicity, such as... Figure 13 As shown in (a) and (b). Figure 13 Figure (c) shows the average Poisson force during the last four steady-state cycles after the system reaches dynamic equilibrium.

[0051] As the buoy size increases, the mooring force in the X direction increases; when the buoy radius is 1000 mm, the X-direction mooring force is 2.718 kN higher than that without a buoy. Increasing the buoy radius from 0 to 400 mm significantly reduces the mooring force in the Z direction. A buoy with a radius of 400 mm has a significant effect on reducing mooring force during the trough phase, but its effect is weaker during the crest phase because the buoy is completely submerged; when the buoy radius increases to 600 mm, the Z-direction mooring force is significantly reduced even during the crest phase (see...). Figure 13 (b)). When the buoy radius exceeds 600 mm, the mooring force in the Z direction begins to increase. Therefore, a 600 mm buoy is a better choice for reducing mooring force. It should be noted that the buoy increases the projected area along the wave direction, thereby enhancing the horizontal hydrodynamic load.

[0052] like Figure 14 As shown, the maximum pitch angle of platform Z1 in each of the last four oscillation cycles is given for different float sizes. Since the pitch angle includes both positive and negative values, the absolute values ​​of all negative values ​​are taken before extracting the peak value.

[0053] It can be observed that when a buoy with a radius of 400 mm is installed, the pitch amplitude decreases significantly; as the buoy radius further increases, the maximum pitch angle continues to decrease. When the buoy radius increases from 0 mm to 600 mm, the pitch amplitude gradually decreases; after further increasing the radius, the pitch angle tends to stabilize, remaining between approximately 5.6° and 6°. This indicates that the buoy effectively suppresses the platform's pitch motion by offsetting part of the downward mooring force through buoyancy.

[0054] For a medium mooring chain (equivalent mass sphere radius = 200 mm): To evaluate the impact of mooring chain weight on the optimal buoy size, the radius of the equivalent mass sphere of the mooring chain was increased to 200 mm (for a heavier chain), and simulations were performed under various buoy sizes to evaluate response changes and verify the aforementioned mechanism.

[0055] For medium-sized mooring chains, buoys with radii of 400 mm and 600 mm are insufficient to effectively counteract the vertical component of mooring tension; they can only reduce minimum tension during wave troughs, while peak tension increases slightly. When the buoy radius reaches 800 mm, the buoyancy is sufficient to counteract most of the vertical component, the "buoyancy reduction" mechanism dominates, and peak tension decreases significantly. At 1000 mm, the lateral (horizontal) hydrodynamic increment becomes more pronounced, causing mooring tension to gradually increase again. In summary, for medium-sized mooring chains (equivalent mass sphere radius 200 mm), 800 mm is the optimal buoy radius.

[0056] For heavy-duty mooring chains (equivalent mass sphere radius = 250 mm): For heavy-duty mooring chains, the buoyancy provided by an 800 mm radius buoy is still insufficient to effectively counteract the longitudinal load on the chain. Correspondingly, as the buoy radius increases from 0 to 400, 600, and 800 mm, its main function is to reduce minimum tension during wave troughs, while the peak mooring tension remains essentially unchanged. Furthermore, when using an 800 mm buoy, the lateral (horizontal) hydrodynamic force generated at wave crests is significant, which can actually increase the overall peak tension. When the buoy radius increases to 1000 mm, the buoyancy is sufficient to counteract most of the vertical component of the mooring tension; the "buoyancy reduction" mechanism dominates, and both the vertical peak and minimum tension decrease significantly.

[0057] In summary, for heavy-duty mooring chains, a 1000mm float size is the optimal choice.

[0058] Based on the above analysis, the following conclusions are drawn: First, under steady-state towing conditions, the buoy does not introduce additional hydrodynamic loads at low flow velocities. As the buoy size increases, both the horizontal and vertical components of the mooring force decrease, reaching their minimum values ​​when the buoy radius is 800 mm. The load-reducing effect of the buoy becomes more significant with increasing flow velocity: at U = 2.0 m / s, the horizontal and vertical forces at the mooring point decrease by approximately 50% and 96%, respectively, while the pitch angle remains below 0.5°, demonstrating excellent stability. Although the relative reduction ratio decreases due to the rapid increase in total mooring load, the absolute difference in force expands with increasing velocity, indicating that the beneficial effect of the buoy is stronger at higher flow velocities.

[0059] Second, under regular wave conditions (wave height H = 2m, period T = 8 s), the buoy affects the mooring point reaction force through two competing mechanisms: (i) Buoyancy counteracts the longitudinal (vertical) load in the chain, thereby effectively suppressing platform motion (sway). (ii) Increasing the projected area increases lateral (horizontal) hydrodynamic forces. The importance of these two mechanisms depends on the size of the buoy and the weight of the mooring chain (characterized in this embodiment by equivalent mass sphere diameters of 150, 200, and 250 mm). When the buoy is relatively small compared to the chain weight, it mainly reduces the tension trough while the peak value is similar to that without a buoy; when the buoy size is appropriate, it can effectively counteract the vertical load, reduce the overall tension, and suppress pitch; if the buoy is too large, the lateral load dominates, and the mooring tension slightly increases. Considering both mooring tension and pitch performance, for equivalent mass sphere diameters of 150, 200, and 250 mm (density 3466 kg·mm²), - For the three cases (³), the optimal float radii are 600, 800, and 1000 mm, respectively.

[0060] The MBD-CFD co-simulation method of this invention for the design of floating platform mooring systems has advantages such as high accuracy, convenient parameter adjustment, intuitive and rapid model modification, and accurate response output. It helps to understand the design trade-offs of mooring systems more comprehensively and improve design accuracy, so as to better meet the performance requirements of complex marine environments.

[0061] Example 2 This embodiment provides a wave and current motion response analysis system for a moored multi-floating body array, including: An anchored multi-floating body array model construction module is used to construct an anchored multi-floating body array model of the simulated floating body object; wherein, the anchored multi-floating body array model includes multiple floating platforms, connectors, mooring systems and buoys; adjacent floating platforms are connected by the connectors, and the connectors are provided with universal joints with rotation limit devices at both ends to maintain the desired spacing between the platforms and release two relative rotational degrees of freedom; The mooring system includes multiple mooring chains, each of which is simplified using lumped mass-spring units. Specifically, each mooring chain is discretized into multiple chain balls that are equivalent in properties. Adjacent chain balls are connected by springs with axial constraint and torsional freedom characteristics, and the springs are allowed to shorten within a preset range. At least one buoy is installed on each mooring chain to provide upward net buoyancy to counteract the vertical component of the mooring force. A numerical pool model construction module is used to construct a numerical pool model for simulating wave and current scenarios based on the relevant parameters of the mooring multi-buoy array. The response analysis module is used to perform co-simulation based on the constructed numerical pool model, simulate the dynamic response of the mooring multi-buoy array under preset ocean current and wave conditions, and analyze the dynamic response results; based on the simulation analysis results, an optimized design scheme for the mooring system is generated.

[0062] It should be noted that the specific implementation of the moored multi-buoy array wave and current motion response analysis system in this embodiment of the invention is similar to the specific implementation of the anchored multi-buoy array wave and current motion response analysis method in this embodiment of the invention. For details, please refer to the description in the method section. To reduce redundancy, it will not be repeated here.

[0063] Example 3 This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the above-described method for analyzing the wave and current motion response of a moored multi-buoy array.

[0064] Example 4 This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the above-described method for analyzing the wave and current motion response of a moored multi-buoy array.

[0065] Example 5 This embodiment provides a program product, which is a computer program product, including a computer program. When the computer program is executed by a processor, it implements the steps in the above-described anchored multi-floating body array wave and current motion response analysis method.

[0066] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage and optical storage) containing computer-usable program code.

[0067] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0068] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0069] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0070] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0071] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the wave and current motion response of a multi-buoy array anchored mooring, characterized in that, Includes the following steps: Construct a moored multi-floating body array model of the simulated floating body object; wherein, the moored multi-floating body array model includes multiple floating platforms, connectors, mooring systems and buoys; Adjacent floating platforms are connected by the connector, and the connector is provided with universal joints with corner limiting devices at both ends to maintain the desired distance between the platforms and release two relative rotational degrees of freedom. A variable stiffness spring model is used to simulate the corner limiting device, and a nonlinear spline curve is used to define the relationship between the spring rotation angle and the generated resisting torque to replace the contact collision model of the limiting block. The allowable free rotation angle range of the corner limiting device is jointly determined by the floating platform length L, height H, spacing D, and connector installation height P, and their relationship is expressed as follows: ; The mooring system comprises multiple mooring chains, each of which is simplified using a lumped mass-spring unit. Specifically, each mooring chain is discretized into multiple chain balls that are equivalent in properties. Adjacent chain balls are connected by springs with axial constraint and torsional freedom characteristics, and the springs are allowed to shorten within a preset range. At least one buoy is installed on each mooring chain to provide upward net buoyancy to counteract the vertical component of the mooring force. Based on the relevant parameters of the moored multi-buoy array, a numerical pool model for simulating wave and current scenarios is constructed. Based on the constructed numerical pool model, a joint simulation was conducted to simulate the dynamic response of the mooring multi-buoy array under preset ocean current and wave conditions, and the dynamic response results were analyzed. Based on the simulation analysis results, an optimized design scheme for the mooring system is generated.

2. The wave and current motion response analysis method for anchored multi-buoy arrays as described in claim 1, characterized in that, The equivalent radius of the chain ball is determined as follows: first, the initial radius is calculated based on the Morison equation and the actual chain link parameters, and then it is corrected through computational fluid dynamics simulation to ensure that the hydrodynamic resistance of the lumped mass-spring unit under the same motion conditions is consistent with that of the actual mooring chain model.

3. The wave and current motion response analysis method for anchored multi-buoy arrays as described in claim 1, characterized in that, The construction of the numerical pool model for simulating wave and current scenarios specifically includes: S1: Construct a basic model of a numerical water tank, including a tank representing the water tank, a floating body, a seabed plate representing the seabed, and an anchor mooring submodule; the anchor mooring submodule predefines the connection and contact relationship between the seabed plate and the anchor chain with the buoy, and fixes the end of the anchor chain to the seabed plate; S2: Based on the arrangement of the float array in the multi-float array, copy and arrange multiple floats, and connect the multiple floats into an array using connectors; based on the number and location of the mooring points, copy and arrange multiple anchoring sub-modules, and connect the top of each anchor chain to the corresponding floating platform to form a complete anchoring multi-float system assembly; S3: A stable ocean current environment is simulated by defining the motion of the sliding pair of the seabed plate relative to the box. S4: Based on the physical properties of actual seawater, define the density, dynamic viscosity, and surface tension coefficient of the liquid filling the tank to a set height; S5: Based on the determined target wave parameters, drive the wave-generating plate set inside the box to move and generate the target wave; S6: Execute a multibody dynamics and computational fluid dynamics co-simulation loop until the simulation ends, thereby generating an equivalent virtual ocean scene in the numerical pool.

4. The wave and current motion response analysis method for anchored multi-buoy arrays as described in claim 1, characterized in that, The simulation of the dynamic response of the moored multi-buoy array under preset ocean current and wave conditions, and the analysis of the dynamic response results, include: analyzing the influence of the float size and mooring chain weight parameters on the hydrodynamic and structural response of the moored multi-buoy array system under different towing and wave conditions.

5. The wave and current motion response analysis method for anchored multi-buoy arrays as described in claim 1, characterized in that, The following design criteria are derived based on simulation analysis: Under steady-state ocean current conditions, as the size of the buoy increases, both the horizontal and vertical components of the mooring force decrease, and the buoy's load-reducing effect becomes more significant as the current velocity increases. Under regular wave conditions, optimizing the buoy size requires balancing two competing mechanisms: first, buoyancy counteracts the vertical component of mooring force to suppress motion; second, the increased projected area leads to an increase in horizontal hydrodynamic load; the optimal buoy size is related to the weight of the mooring chain.

6. A wave and current motion response analysis system for an anchored multi-buoy array, characterized in that, include: An anchored multi-floating body array model construction module is used to construct an anchored multi-floating body array model of the simulated floating body object; wherein, the anchored multi-floating body array model includes multiple floating platforms, connectors, mooring systems and buoys; adjacent floating platforms are connected by the connectors, and the connectors are provided with universal joints with rotation limit devices at both ends to maintain the desired spacing between the platforms and release two relative rotational degrees of freedom; A variable stiffness spring model is used to simulate the corner limiting device, and a nonlinear spline curve is used to define the relationship between the spring rotation angle and the generated resisting torque to replace the contact collision model of the limiting block. The allowable free rotation angle range of the corner limiting device is jointly determined by the floating platform length L, height H, spacing D, and connector installation height P, and their relationship is expressed as follows: ; The mooring system includes multiple mooring chains, each of which is simplified using lumped mass-spring units. Specifically, each mooring chain is discretized into multiple chain balls that are equivalent in properties. Adjacent chain balls are connected by springs with axial constraint and torsional freedom characteristics, and the springs are allowed to shorten within a preset range. At least one buoy is installed on each mooring chain to provide upward net buoyancy to counteract the vertical component of the mooring force. A numerical pool model construction module is used to construct a numerical pool model for simulating wave and current scenarios based on the relevant parameters of the mooring multi-buoy array. The response analysis module is used to perform joint simulation based on the constructed numerical pool model, to simulate the dynamic response of the mooring multi-buoy array under preset ocean current and wave conditions, and to analyze the dynamic response results. Based on the simulation analysis results, an optimized design scheme for the mooring system is generated.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the wave and current motion response analysis method for anchored multi-floating body arrays as described in any one of claims 1-5.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the wave and current motion response analysis method for anchored multi-floating body arrays as described in any one of claims 1-5.

9. A program product, said program product being a computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps in the wave and current motion response analysis method for anchored multi-floating body arrays as described in any one of claims 1-5.

Images