Hydrodynamic analysis method for floating structure with multi-body and multi-coupling characteristics

Abstract

The invention discloses a hydrodynamic analysis method for a floating structure with multi-body and multi-coupling characteristics, which comprises the following steps of: acquiring geometric characteristics of each floating body, and dividing boundary element computational grids; wave excitation force, additional mass and radiation damping of each floating body are calculated, and a mass matrix and a rigidity matrix of each floating body are obtained; determining a connection mode and a coupling factor of the floating body; according to a connection mode and coupling characteristics of the system, establishing displacement connection conditions among the floating bodies; constructing a motion constraint matrix according to the displacement continuity condition and the motion constraint relation; determining a frequency domain motion equation of the multi-floating-body system according to a Lagrange multiplier method; and solving the motion equation to obtain the motion response of the multi-floating-body system, and further systematically analyzing the wave energy capture power according to the coupling characteristics of the system. According to the analysis method, the problem that the motion response of each degree of freedom cannot be accurately described when the hydrodynamic response characteristics of the complex multi-body system are obtained through an existing simulation method is solved.

Description

Technical Field

[0001] This invention belongs to the field of marine engineering structure hydrodynamics technology, specifically relating to a hydrodynamic analysis method for floating structures with multi-body and multi-coupling characteristics. Background Technology

[0002] A multi-functional floating platform is a marine engineering equipment that integrates multiple functions. It mainly utilizes the principle of buoyancy to complete tasks such as exploration, energy development, and observation in the marine environment. It features high mobility, strong adaptability to complex sea conditions, and diversified functions.

[0003] In recent years, multifunctional floating platforms based on the concepts of cost sharing and synergistic efficiency have become a research hotspot. Examples include the world's first megawatt-class floating wave energy power generation device, "Nankun," the semi-submersible wave energy aquaculture and tourism platform, "Penghu," and the UK's Blue Growth Farm, a floating aquaculture platform with combined wind and wave power supply.

[0004] Currently, from a mechanical perspective, these multi-functional floating platforms share similar characteristics, namely complex multi-body connections, which are quite different from traditional marine structures (such as offshore oil and gas platforms). The characteristics of this new type of multi-functional platform are as follows: multiple objects are interconnected, and the positions of the hinge points are relatively complex; the structural degrees of freedom are not simply relative motions, but often accompanied by motions of other degrees of freedom; the system's motion is accompanied by additional coupling factors (such as mooring factors, energy output damping, etc.). Therefore, efficient and accurate hydrodynamic analysis methods are crucial for designing this type of multi-functional marine structure. Thus, to adapt to the development of this new type of marine structure, a hydrodynamic analysis method suitable for complex multi-body systems at sea is urgently needed. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by providing a hydrodynamic analysis method for floating structures with multi-body and multi-coupling characteristics. To solve the problem that existing simulation methods cannot accurately characterize the motion response of each degree of freedom when acquiring the hydrodynamic response characteristics of complex multi-body systems, this invention proposes an analytical solution method for the hydrodynamic response of complex multi-body systems. This method involves modeling each floating body of the multi-body floating structure, performing boundary element mesh generation, and determining the connection methods and coupling factors between the floating bodies. Then, by establishing displacement connection conditions between the floating bodies and constructing a motion constraint matrix, the frequency domain equations are determined and solved using the Lagrange multiplier method, enabling a systematic analysis of wave energy capture power.

[0006] The technical solution adopted in this invention: 1. A hydrodynamic analysis method for floating structures with multi-body and multi-coupling characteristics, comprising the following steps: S1. Obtain the geometric features of each floating body and divide the boundary element computation mesh; S2. Calculate the wave excitation force, added mass and radiation damping of each floating body, and obtain the mass matrix and stiffness matrix of each floating body. S3. Determine the connection method and coupling factors of the floating body; S4. Based on the system's connection method and coupling characteristics, establish the displacement connection conditions between each floating body; S5. Construct the motion constraint matrix based on the displacement continuity condition and motion constraint relationship; S6. Determine the frequency domain equations of motion for the multi-buoy system using the Lagrange multiplier method; S7. Solve the equations of motion to obtain the motion response of the multi-floating body system. Based on the coupling characteristics of the system, further analyze the wave energy capture power.

[0007] Furthermore, in S1, the process of dividing the boundary element computation mesh is as follows: The floating body is geometrically modeled using modeling software to generate a geometric file, which is then imported into external software for boundary element mesh generation to produce a mesh file.

[0008] Furthermore, in S2, the calculation methods for the wave excitation force, added mass, and radiation damping are as follows: Based on linear potential flow theory, for the... A multi-floating body system consisting of several floating bodies, whose respective wetted surfaces are denoted as . ,in Total wet surface area is Total velocity potential It can be decomposed into: (1) In the formula, For the incident potential, For diffraction, The imaginary unit, , For wave frequency, radiation potential and Spatial coordinate system The Middle The first floating body Radiation potential and motion response amplitude for each degree of freedom, incident potential The specific expression is: (2) In the formula, For wave number, Because of the water depth, For the incident wave amplitude, Let be the phase angle between the incident wave direction and the normal incidence direction. It is the acceleration due to gravity. For a fixed spatial coordinate system The coordinates of any point within the area; The above velocity potentials all satisfy the Laplace equation: (3) Free surface SF, satisfying: (4) The surface of the object SB satisfies: (5) The seabed SD boundary satisfies: (6) Sommerfeld condition at infinity: (7) In equations (3) to (7), It is the acceleration due to gravity. Because of the water depth, This represents the horizontal distance between the far-field point and the floating body. Indicates the first an object In the Boundary surface normal vectors under each degree of freedom; The radiation potential and diffraction potential of the floating body surface are calculated using a three-dimensional Green's function, where, in a multi-floating body system, the number of floating bodies is... The source-couple mixed distribution radiation and diffraction equations for the boundary of a multi-floating body system are as follows: (8) (9) In equations (8) to (9), , Let be a variable, where The total number of face elements is denoted as , As the source The element in question, Green's function to satisfy the free surface condition, , These are the coordinates of the field point and the source point, respectively. Specifically, in solving for the added mass and radiation damping matrix, the following formula can be supplemented, namely, since the first... The first object The motion in the first degree of freedom causes the first The first object The additional mass and radiation damping for each degree of freedom are solved as follows: (10) Furthermore, the wave excitation force, added mass, and radiation damping are obtained by solving the boundary integral equations through grid discretization to obtain the radiation potential. and diffraction potential This allows us to obtain wave excitation force, added mass, and radiation damping. Among them, the additional mass array of the multi-floating body system and radiation damping matrix It can be represented as: (11) (12) In the formula , They respectively represent the reason that the first The first object The motion in the first degree of freedom causes the first The first object Additional mass and radiation damping in each degree of freedom; No. The first object The first-order wave excitation force in each degree of freedom includes the Froude-Krylov force and the diffraction force, expressed as follows: (13) Similarly, wave excitation force It can be represented as: (14) The total mass matrix of the multi-floating body system is shown in the following form: (15) For the first The six-degree-of-freedom mass matrix of a floating body ， Its specific form of expression is as follows: (16) In equation (16), Floating body quality , , Floating bodies The coordinate components of the center of gravity on the three coordinate axes. middle , respectively represent The three directions represent the moment of inertia of the floating body, and their specific forms are as follows: (17) when hour, = 1, when hour, = 0; Similarly, The total hydrostatic restoring force matrix of the multi-floating body system is shown in the following form: (18) In equation (18), For the first The six-degree-of-freedom still water restoring force matrix of a floating body, where ， The specific format is as follows: (19) In equation (19), , , Floating bodies The waterline surface area, the distance between the center of buoyancy and the center of gravity, and the volume of water displaced. The density of seawater is 1025 kg / m³. 3 , It is the acceleration due to gravity. Floating body Waterline surface.

[0009] Furthermore, in step S3, the method for determining the connection method and coupling factors of the floating body is as follows: The PTO matrix is ​​obtained through the relative motion between the float and the floating carrier, which captures the directional degree of freedom of wave energy. .

[0010] Furthermore, in S4, the displacement connection conditions between the various floating bodies are established as follows: Based on the kinematic relationship between the float and the floating carrier, the relative motion direction degree of freedom is released, and the other degrees of freedom satisfy the displacement continuity condition at the hinge point. The displacement continuity condition and the corresponding displacement constraint matrix are then determined. .

[0011] The present invention has the following beneficial effects: This invention, after confirming the complex connection and coupling factors between floating bodies, calculates the wave energy capture efficiency based on solving the motion response, thereby evaluating the wave power generation performance of multiple systems; it features high computational efficiency and high accuracy. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the structure of Embodiment 1 of the present invention.

[0013] In the diagram: 1. Floating carrier; 2. Hemispherical float; 3. Connecting rod; 4. Hinge joint. Detailed Implementation

[0014] The technical solution of the present invention will be clearly and completely described below through embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] Example 1 In this embodiment, as Figure 1 The structure shown is a floating structure with multi-body and multi-coupling characteristics, which is composed of multiple floating bodies hinged together. The floating bodies are divided into floating body carriers 1 and hemispherical floats 2. The two floating bodies 1 are hinged together by hinge parts 4, and the floating bodies 1 can rotate relative to each other. Each floating body 1 is provided with a hemispherical float 2, which is hinged to the floating body 1 by connecting rods 3, so that the hemispherical float 2 and the floating body 1 can rotate relative to each other. That is, there is also a relative roll motion between the hemispherical float 2 and the floating body 1. Wave energy capture is achieved by using the relative roll motion between the hemispherical float 2 and the floating body 1, while releasing the roll motion between the hemispherical float 2 and the floating body 1 as well as the pitch motion between the floating bodies 1.

[0016] The geometric parameters of many floating bodies in the ocean are complex and diverse, with common shapes including box-shaped, cylindrical, and spherical. Due to the diverse types of floating structures in complex multibody systems, this embodiment focuses on... Figure 1 The multi-floating body system structure shown is composed of an oscillating float and a floating carrier. An example is given using the hydrodynamic analysis method for floating structures with multi-body, multi-coupling characteristics disclosed in this invention. The method includes the following steps: S1. Obtain the geometric features of each floating body and divide the boundary element computation mesh, specifically: Using modeling software Figure 1 The oscillating float and floating carrier in the multi-floating body system structure shown are geometrically modeled, and after generating the geometric file, they are imported into external software for boundary element mesh generation to generate the mesh file. S2. Calculate the wave excitation force, added mass, and radiation damping of each floating body, and obtain the mass matrix and stiffness matrix of each floating body. The algorithm is as follows: Based on linear potential flow theory, for the... A multi-floating body system consisting of several floating bodies, whose respective wetted surfaces are denoted as . ,in Total wet surface area is The total velocity potential can be decomposed into: (1) In the formula, For the incident potential, For diffraction, The imaginary unit, , For wave frequency, radiation potential and Spatial coordinate system The Middle The first floating body Radiation potential and motion response amplitude for each degree of freedom, incident potential The specific expression is: (2) In the formula, For wave number, Because of the water depth, For the incident wave amplitude, Let be the phase angle between the incident wave direction and the normal incidence direction. It is the acceleration due to gravity. For a fixed spatial coordinate system The coordinates of any point within the area; The above velocity potentials all satisfy the Laplace equation: (3) Free surface SF, satisfying: (4) The surface of the object SB satisfies: (5) The seabed SD boundary satisfies: (6) Sommerfeld condition at infinity: (7) In equations (3) to (7), It is the acceleration due to gravity. Because of the water depth, This represents the horizontal distance between the far-field point and the floating body. Indicates the first an object In the Boundary surface normal vectors under each degree of freedom; The radiation potential and diffraction potential of the floating body surface are calculated using a three-dimensional Green's function, where, in a multi-floating body system, the number of floating bodies is... The source-couple mixed distribution radiation and diffraction equations for the boundary of a multi-floating body system are as follows: (8) (9) In equations (8) to (9), Let be a variable, where The total number of face elements is denoted as , As the source The element in question, Green's function to satisfy the free surface condition, These are the coordinates of the field point and the source point, respectively. Specifically, in solving for the added mass and radiation damping matrix, the following formula can be supplemented, namely, since the first... The first object The motion in the first degree of freedom causes the first The first object The additional mass and radiation damping for each degree of freedom are solved as follows: (10) The wave excitation force, added mass, and radiation damping are obtained by solving the boundary integral equations through grid discretization to obtain the radiation potential. and diffraction potential This allows us to obtain wave excitation force, added mass, and radiation damping. Among them, the additional mass array of the multi-floating body system and radiation damping matrix It can be represented as: (11) (12) In the formula , They respectively represent the reason that the first The first object The motion in the first degree of freedom causes the first The first object Additional mass and radiation damping in each degree of freedom; No. The first object The first-order wave excitation force in each degree of freedom includes the Froude-Krylov force and the diffraction force, expressed as follows: (13) Similarly, wave excitation force It can be represented as: (14) The total mass matrix of the multi-floating body system is shown in the following form: (15) For the first The six-degree-of-freedom mass matrix of a floating body ， Its specific form of expression is as follows: (16) In equation (16), Floating body quality , , Floating bodies The coordinate components of the center of gravity on the three coordinate axes. middle , respectively represent The three directions represent the moment of inertia of the floating body, and their specific forms are as follows: (17) when hour, = 1, when hour, =0; Similarly, The total hydrostatic restoring force matrix of the multi-floating body system is shown in the following form: (18) In equation (18), For the first The six-degree-of-freedom still water restoring force matrix of a floating body, where ， The specific format is as follows: (19) In equation (19), , , Floating bodies The waterline surface area, the distance between the center of buoyancy and the center of gravity, and the volume of water displaced. The density of seawater is 1025 kg / m³. 3 , It is the acceleration due to gravity. Floating body Waterline surface.

[0017] S3. Determine the connection method and coupling factors of the floating body; The PTO matrix is ​​obtained through the relative motion between the float and the floating carrier, which captures the directional degree of freedom of wave energy. ,exist Figure 1 In the multi-buoy system structure shown, for the two floating bodies and Wave energy capture using relative roll, corresponding to relative roll displacement It can be represented as , The expressions are as follows: (20) The local force at the constrained location can be expressed as: , For PTO damping.

[0018] Convert local forces into force vectors acting in each floating body coordinate system. Therefore, its PTO matrix The expression is as follows: (twenty one) S4. Based on the system's connection method and coupling characteristics, establish the displacement connection conditions between each floating body; Based on the kinematic relationship between the float and the floating carrier, only the degree of freedom in the relative motion direction is released, while the other degrees of freedom satisfy the displacement continuity condition at the hinge point. This determines the displacement continuity condition and the corresponding displacement constraint matrix. .

[0019] exist Figure 1 In the structure shown, there are two displacement constraint relationships: on the one hand, there is a relative pitching motion between the floating carriers, and on the other hand, the wave energy is captured by the PTO damping system driven by the relative rolling motion between the float and the floating carrier. At the hinge point, a floating carrier is only allowed to rotate relative to the other direction in the pitch direction, while restricting the freedom of movement in other directions. Therefore, a floating carrier... and floating carrier The displacement continuity condition is satisfied at the hinge point, and its specific expression is as follows: (twenty two) In equation (22), , and Floating carriers in the global coordinate system Hinge point coordinates and floating carrier The center of rotation, and Floating bodies and floating body Each constrained degree of freedom corresponds to the motion response in sway, heave, roll, and pitch, respectively. In addition, due to the use of a roll float With floating carrier (or The relative roll motion between the two sides drives the PTO damping to achieve wave energy capture, thus the hemispherical float in the roll direction... With floating carrier There is relative motion between them, and other degrees of freedom are constrained at the hinge points, as specifically expressed below: (twenty three) In formula (23) , and These are the lateral floats in the global coordinate system. Hinge point coordinates and floating carrier The center of rotation, and Hemispherical floating bodies and floating carrier Each constrained degree of freedom corresponds to the motion response in sway, heave, pitch, and yaw, respectively. S5. Construct the motion constraint matrix based on the displacement continuity condition and motion constraint relationship; By shifting the right side of equation (22) to the left side and transforming it into a matrix form, the floating carrier can be obtained. and floating carrier Release the constraint matrix for pitch: (twenty four) (25) Similarly, by shifting the right side of equation (23) to the left side and transforming it into matrix form, we can obtain the hemispherical float. and floating carrier Release the constraint matrix for roll: (26) (27) Then, based on the actual hinge relationship, the matrix is... , , , By combining these components, a displacement constraint matrix can be obtained. ; S6. Determine the frequency domain equations of motion for the multi-buoy system using the Lagrange multiplier method; When a regular wave is incident, for a multi-floating body system, each floating body is considered a rigid body. Assuming the total external force is applied to the center of gravity of each sub-module, and each floating body is simplified to a generalized concentrated mass acting at its center of gravity, the articulated multi-floating body system, in addition to considering the interactions between floating bodies due to wave radiation and diffraction, must also consider the influence of the connecting forces between the floating bodies. Therefore, the equation of motion for the articulated multi-floating body system can be written as: (28) Applying Hamiltonian theory and Lagrange multiplier method from structural mechanics, the equations of motion for complex multi-floating body systems are as follows: (29) In equation (29): The number of hinge points. The number of floating bodies The overall stiffness matrix of the multi-floating body system is expressed in the following form: , , , , , and These correspond to the mass matrix (Formula (15)), the additional mass matrix and the radiation damping matrix (Formulas (11), (12)), the PTO damping matrix (Formula (21)), the still water stiffness matrix (Formula (18)), and the mooring stiffness matrix, respectively. This indicates the connecting force between the floating bodies. This is the displacement constraint matrix; Displacement vector The forms are as follows: (30) In the formula: Represented as the first The floating body in the first Motion response in one degree of freedom; S7. Solve the equations of motion to obtain the motion response of the multi-floating body system. Based on the coupling characteristics of the system, further analyze the wave energy capture power.

[0020] The motion response of each float in the multi-body system can be obtained by solving formula (29). Figure 1 Taking the case shown as an example, the power of the float and the The power generation of each float It can be represented as: (31) Corresponding relative roll displacement The expression is .

[0021] The above description is not intended to limit the invention, nor is the invention limited to the examples given above. Modifications to the displacement conditions and the PTO matrix can also be used. It can also be applied to other complex multi-body articulation situations, such as: coupling of ultra-large floating bodies with array floats, array-type floating breakwaters, offshore installation vessels, crane vessel hoisting, etc. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention are also within the protection scope of the present invention.

Claims

1. A hydrodynamic analysis method for floating structures with multi-body and multi-coupling characteristics, characterized in that: Includes the following steps: S1. Obtain the geometric features of each floating body and divide the boundary element computation mesh; S2. Calculate the wave excitation force, added mass and radiation damping of each floating body, and obtain the mass matrix and stiffness matrix of each floating body. S3. Determine the connection method of the floating body and obtain the PTO damping and coupling factors; S4. Based on the system's connection method and coupling characteristics, establish the displacement connection conditions between each floating body; S5. Construct the motion constraint matrix based on the displacement continuity condition and motion constraint relationship; S6. Determine the frequency domain equations of motion for the multi-buoy system using the Lagrange multiplier method; S7. Solve the equations of motion to obtain the motion response of the multi-floating body system. Based on the coupling characteristics of the system, further determine the wave energy capture power of the system.

2. The hydrodynamic analysis method for the interaction between waves and floating multibody systems according to claim 1, characterized in that: In S1, the process of dividing the boundary element computation mesh is as follows: The floating body is geometrically modeled using modeling software to generate a geometric file, which is then imported into external software for boundary element mesh generation to produce a mesh file.

3. The hydrodynamic analysis method for the interaction between waves and floating multibody systems according to claim 1, characterized in that: In S2, the calculation methods for wave excitation force, added mass, and radiation damping are as follows: Based on linear potential flow theory, for the... N A multi-floating body system consisting of several floating bodies, whose respective wetted surfaces are denoted as . ,in Total wet surface area is Total velocity potential Decomposed into: （1） In the formula, For the incident potential, For diffraction, The imaginary unit, , For wave frequency, radiation potential and Spatial coordinate system The Middle The first floating body Radiation potential and motion response amplitude for each degree of freedom, incident potential The specific expression is: （2） In the formula, For wave number, Because of the water depth, For the incident wave amplitude, Let be the phase angle between the incident wave direction and the normal incidence direction. It is the acceleration due to gravity. For a fixed spatial coordinate system The coordinates of any point within the area; The above velocity potentials all satisfy the Laplace equation: （3） Free surface SF, satisfying: （4） The surface of the object SB satisfies: （5） The seabed SD boundary satisfies: （6） Sommerfeld condition at infinity: （7） In equations (3) to (7), It is the acceleration due to gravity. Because of the water depth, This represents the horizontal distance between the far-field point and the floating body. Indicates the first n an object In the p Boundary surface normal vectors under each degree of freedom; The radiation potential and diffraction potential of the floating body surface are calculated using a three-dimensional Green's function, where, in a multi-floating body system, the number of floating bodies is... The source-couple mixed distribution radiation and diffraction equations for the boundary of a multi-floating body system are as follows: （8） （9） In equations (8) to (9), , Let be a variable, where The total number of face elements is denoted as , As the source The element in question, Green's function to satisfy the free surface condition, , These are the coordinates of the field point and the source point, respectively. Specifically, in solving for the added mass and radiation damping matrix, the following formula is supplemented, namely, due to the... The first object The motion in the first degree of freedom causes the first The first object The additional mass and radiation damping for each degree of freedom are solved as follows: （10） Then, the grid data is used as the initial condition to input the boundary element calculation program to obtain the wave excitation force, added mass, and radiation damping.

4. The hydrodynamic analysis method for the interaction between waves and floating multibody systems according to claim 3, characterized in that: The wave excitation force, added mass, and radiation damping are obtained by solving the boundary integral equations through grid discretization to obtain the radiation potential. and diffraction potential This allows us to obtain wave excitation force, added mass, and radiation damping; Among them, the additional mass array of the multi-floating body system and radiation damping matrix It can be represented as: （11） （12） In the formula , They respectively represent the reason that the first The first object The motion in the first degree of freedom causes the first The first object Additional mass and radiation damping in each degree of freedom; No. The first object The first-order wave excitation force in each degree of freedom includes the Froude-Krylov force and the diffraction force, expressed as follows: （13） Similarly, wave excitation force It can be represented as: （14） The total mass matrix of the multi-floating body system is shown in the following form: （15） For the first The six-degree-of-freedom mass matrix of a floating body ， Its specific form of expression is as follows: （16） In equation (16), Floating body quality , , Floating bodies The coordinate components of the center of gravity on the three coordinate axes. middle = 1, 2, 3, represent respectively The three directions represent the moment of inertia of the floating body, and their specific forms are as follows: （17） when hour, = 1, when hour, = 0; Similarly, The total hydrostatic restoring force matrix of the multi-floating body system is shown in the following form: （18） In equation (18), For the first The six-degree-of-freedom still water restoring force matrix of a floating body, where ， The specific format is as follows: （19） In equation (19), , , Floating bodies The waterline surface area, the distance between the center of buoyancy and the center of gravity, and the volume of water displaced. The density of seawater is 1025 kg / m³. 3 , It is the acceleration due to gravity. Floating body Waterline surface.

5. The hydrodynamic analysis method for the interaction between waves and floating multibody systems according to claim 1, characterized in that: In step S3, the method for determining the connection method and coupling factors of the floating body is as follows: The PTO matrix is ​​obtained through the relative motion between the float and the floating carrier, which captures the directional degree of freedom of wave energy. .

6. The hydrodynamic analysis method for the interaction between waves and floating multibody systems according to claim 1, characterized in that: In step S4, the displacement connection conditions between the various floating bodies are established as follows: Based on the kinematic relationship between the float and the floating carrier, the relative motion direction degree of freedom is released, and the other degrees of freedom satisfy the displacement continuity condition at the hinge point. The displacement continuity condition and the corresponding displacement constraint matrix are then determined. .

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