Energy dissipation floating breakwater with resonant cavity and method for analyzing hydrodynamic performance thereof

Abstract

This application relates to the field of marine engineering technology, and discloses a floating breakwater with a resonant cavity and its hydrodynamic performance analysis method. The method includes: constructing a floating breakwater model; determining the target length and target width of the resonant cavity, the wave-facing open-type wave-dissipating chamber, and the wave-repelling open-type wave-dissipating chamber on the leeward side; dividing the entire fluid domain of the floating breakwater into multiple regions; obtaining the velocity potential of each region; calculating the wave force of the floating breakwater; using the velocity potential of each region to express the added mass and radiation damping of the floating breakwater when it undergoes unit forced oscillation, so as to construct the motion response equation of the floating breakwater in the frequency domain under wave action; obtaining the transmission coefficient and energy dissipation coefficient of the floating breakwater through the equation set, and evaluating the shielding performance and wave-dissipating performance of the floating breakwater based on each coefficient. The synergy of the resonant cavity and the open-type wave-dissipating chamber can improve the wave-dissipating efficiency, and the analysis method can provide an efficient and reliable basis for the design of breakwaters.

Description

Technical Field

[0001] This application relates to the field of marine engineering technology, for example to an energy-dissipating floating breakwater with a resonant cavity and a method for analyzing its hydrodynamic performance. Background Technology

[0002] Deep-sea environments are dominated by medium- and long-period waves, with complex, harsh, and highly destructive environmental loads. Offshore engineering structures are expensive, and their failure can cause significant economic losses. Therefore, developing efficient and economical offshore protection facilities is crucial. Breakwaters, as safety barriers for offshore engineering, directly withstand harsh ocean loads and provide cover for subsequent construction operations. Traditional bottom-mounted breakwaters are difficult to meet the needs of deep-sea expansion due to their large size, high cost, demanding seabed foundation requirements, and complex construction. Research shows that over 90% of wave energy is concentrated within three times the wave height below the free surface. Floating breakwaters, developed based on this characteristic, consist of a floating body and a mooring system. They offer advantages such as simple structure, low cost, ease of installation, and low foundation requirements, while not hindering free water exchange and adapting to tidal changes, making them promising for deep-sea engineering. However, floating breakwaters have a short development history and the technology is not yet mature, presenting certain limitations. The core issue is their inability to effectively withstand medium- and long-period waves (the dominant loads in deep-sea engineering).

[0003] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or describe the scope of protection of these embodiments, but rather as a prelude to the detailed description that follows.

[0005] This disclosure provides an energy-dissipating floating breakwater with a resonant cavity and a method for analyzing its hydrodynamic performance, in order to improve the overall wave-dissipating efficiency of the breakwater.

[0006] In some embodiments, the hydrodynamic performance analysis method for the energy-dissipating floating breakwater with resonant cavities includes: S10, constructing a floating breakwater model, the floating breakwater including: a main body of the breakwater, wherein the main body of the breakwater is provided with a resonant cavity, and wave-dissipating chambers with openings on the wave-facing side and the wave-repelling side located on both sides of the resonant cavity; S20, determining the target length and target width of the resonant cavity, the wave-facing side opening wave-dissipating chamber, and the wave-repelling side opening wave-dissipating chamber; S30, dividing the entire fluid domain of the floating breakwater into multiple regions, and representing the total velocity potential of the fluid motion, the velocity potential satisfaction conditions of each region, the velocity potential satisfaction conditions of the diffracted and radiated waves on the non-perforated surface of the floating breakwater, and the scattering and radiating potential satisfaction conditions of the perforated plate of the floating breakwater. S40, based on the velocity potential satisfaction conditions of each region, the velocity potential satisfaction conditions of the diffracted and radiated waves of the non-perforated surface, and the scattering and radiating potentials of the perforated plate of the floating breakwater, the velocity potential of each region is obtained; S50, the wave force of the floating breakwater is calculated, and the additional mass and radiation damping of the floating breakwater when it undergoes unit forced oscillation are expressed using the velocity potential of each region, so as to construct the motion response equation of the floating breakwater in the frequency domain under wave action; S60, based on the motion response equation, the motion response amplitude of the floating breakwater's motion displacement is obtained, and based on the motion response amplitude, the total velocity potential of each region is calculated, thereby obtaining the transmission coefficient and energy dissipation coefficient of the floating breakwater, and the shielding performance and wave-dissipating performance of the floating breakwater are evaluated according to each coefficient.

[0007] In some embodiments, the energy-dissipating floating breakwater with resonant cavities is applicable to the hydrodynamic performance analysis method of the energy-dissipating floating breakwater with resonant cavities as described above; it includes: a main body of the breakwater, provided with a resonant cavity, and wave-dissipating chambers with openings on the wave-facing side and the back-wave side respectively located on both sides of the resonant cavity; the main body of the breakwater has a top opening at the top and a connecting opening at the bottom, the top opening connecting the resonant cavity and the external environment, and the connecting opening connecting the resonant cavity and the external environment; the wave-facing side and the back-wave side of the main body of the breakwater are respectively provided with a wave-facing opening plate and a back-wave opening plate, the openings of the wave-facing opening plate communicating with the wave-facing opening wave-dissipating chamber, and the openings of the back-wave opening plate communicating with the back-wave opening wave-dissipating chamber; both the wave-facing and back-wave opening wave-dissipating chambers have water outlet holes at their bottoms; and an anchoring system is provided at the bottom of the main body of the breakwater.

[0008] The energy-dissipating floating breakwater with resonant cavity and its hydrodynamic performance analysis method provided in this disclosure can achieve the following technical effects:

[0009] 1. Through the synergistic effect of the resonant cavity and the perforated wave-dissipating chamber, the ability to reduce medium and long period waves is specifically enhanced. The resonant cavity efficiently dissipates the energy of specific frequency waves through the resonance effect, while the perforated wave-dissipating chamber further enhances energy dissipation through turbulent flow. The two work together to improve the overall wave-dissipating efficiency of the breakwater.

[0010] 2. The floating breakwater features a rational structural design. The main body of the breakwater adopts a regular rectangular box structure, facilitating prefabrication and assembly, resulting in lower construction difficulty and material costs. The embedded design highly integrates the resonant cavity and the perforated wave-dissipating chamber without increasing the structural volume. The relaxed mooring system reduces requirements on seabed geology and construction equipment, simplifying construction and offering strong adaptability to deep water. This structure has wide applicability; the resonant cavity size, connecting port cross-sectional parameters, perforated plate characteristics, and mooring system parameters can be flexibly adjusted according to wave conditions in different sea areas, meeting the diverse needs of deep-sea engineering construction.

[0011] 3. The hydrodynamic performance analysis method provided in this disclosure establishes a frequency domain analytical model based on two-dimensional potential flow theory, which can quickly calculate the transmission coefficient and energy dissipation coefficient of the breakwater, and realize a quantitative evaluation of its wave-dissipating and shielding performance. This method does not require complex numerical modeling and time-consuming calculations, significantly improving the efficiency of scheme selection in the early design stage and providing convenient theoretical support for engineering applications;

[0012] 4. The analytical method of this disclosure fully considers the influence of key design variables such as breakwater draft, resonant cavity size, opening ratio, and cross-sectional parameters of the connecting opening, enabling rapid analysis for wave conditions in different sea areas. Through the calculation and evaluation of this method, the optimal combination of structural dimensions can be preliminarily determined, significantly reducing computational costs and providing an efficient and reliable optimization method for the engineering design of floating breakwaters.

[0013] The above general description and the description below are exemplary and illustrative only and are not intended to limit this application. Attached Figure Description

[0014] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations and drawings do not constitute a limitation on the embodiments. Elements having the same reference numerals in the drawings are shown as similar elements. The drawings are not to be scaled. And wherein:

[0015] Figure 1 This is a three-dimensional schematic diagram of an energy-dissipating floating breakwater with a resonant cavity provided in an embodiment of this disclosure;

[0016] Figure 2 This is a cross-sectional side view of the energy-dissipating floating breakwater with a resonant cavity provided in an embodiment of this disclosure;

[0017] Figure 3This is a frontal view of the wave-facing side of the energy-dissipating floating breakwater with a resonant cavity provided in an embodiment of this disclosure;

[0018] Figure 4 This is a top view of the energy-dissipating floating breakwater with a resonant cavity provided in an embodiment of this disclosure;

[0019] Figure 5 This is a cross-sectional schematic diagram of an energy-dissipating floating breakwater with a resonant cavity provided in an embodiment of this disclosure;

[0020] Figure 6 This is a schematic diagram of the hydrodynamic performance analysis method for an energy-dissipating floating breakwater with a resonant cavity provided in an embodiment of this disclosure;

[0021] Figure 7 This is a schematic diagram of the partitioning of an energy-dissipating floating breakwater with a resonant cavity provided in an embodiment of this disclosure.

[0022] Figure label:

[0023] 10. Main body of the floating breakwater; 20. Perforated plate on the wave-facing side; 30. Perforated plate on the leeward side; 40. Bottom plate; 50. Connecting opening; 60. Top opening; 70. Wave-facing perforated wave-dissipating chamber; 80. Resonance cavity; 90. Wave-facing perforated wave-dissipating chamber; 100. Anchor chain; 110. Sink block; 120. Mooring system; 130. Water outlet. Detailed Implementation

[0024] To provide a more detailed understanding of the features and technical content of the embodiments of this disclosure, the implementation of the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and are not intended to limit the embodiments of this disclosure. In the following technical description, for ease of explanation, several details are used to provide a full understanding of the disclosed embodiments. However, one or more embodiments may still be implemented without these details. In other cases, well-known structures and devices may be simplified in their depiction to simplify the drawings.

[0025] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion.

[0026] Unless otherwise stated, the term "multiple" means two or more.

[0027] In this embodiment of the disclosure, the character " / " indicates that the objects before and after it are in an "or" relationship. For example, A / B means: A or B.

[0028] The term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0029] The term "correspondence" can refer to an association or binding relationship. The correspondence between A and B means that there is an association or binding relationship between A and B.

[0030] Combination Figures 1 to 5 As shown, this disclosure provides an energy-dissipating floating breakwater with a resonant cavity, including: a floating breakwater body 10 and an anchoring system 120.

[0031] The main body of the floating breakwater 10 forms the foundation of the entire floating breakwater. It is a regular rectangular box structure, and its high degree of regularity facilitates prefabrication on land, transportation at sea, and on-site installation, reducing construction difficulty and project costs. It has a top opening 60 and a connecting opening 50 at the bottom, allowing the draft of the floating breakwater to be determined based on wave conditions and actual water depth in the working area. By adjusting the internal counterweights, it ensures that the main body of the floating breakwater 10 floats stably after being launched and that its draft meets design requirements.

[0032] The main body 10 of the floating breakwater is equipped with a wave-dissipating chamber 70 with an opening on the wave-facing side, a resonant cavity 80, and a wave-dissipating chamber 90 with an opening on the back wave side. The wave-dissipating chamber 70 with an opening on the wave-facing side and the wave-dissipating chamber 90 with an opening on the back wave side are located on both sides of the resonant cavity 80.

[0033] The resonant cavity 80 is the core wave-dissipating component, specifically designed for dissipating energy from medium- and long-period waves. Embedded in the middle of the main body 10 of the floating dike, it mainly consists of the inner wall of the main body 10, the connecting opening 50, and the top opening 60. The resonant cavity 80 is a rectangular sealed chamber, its boundary being the inner wall of the main body 10. The connecting opening 50 is located on the bottom plate 40 of the main body 10 and is evenly distributed along its length. The top opening 60 is evenly distributed along the top of the resonant cavity 80, with both ends connecting to the resonant cavity 80 and the external atmosphere, providing a flow path for air within the resonant cavity 80. The natural frequency of the resonant cavity 80 is designed to match the dominant medium- and long-period wave frequency of the working sea area. Frequency matching is achieved through precise calculation of the cavity dimensions and connecting opening parameters, utilizing the resonance effect between external waves and the fluid within the cavity to dissipate wave energy.

[0034] The wave-facing and back-wave-facing perforated wave-dissipating chambers 70 and 90, as important components of the composite wave-dissipating system, work synergistically with the resonant cavity 80 to further dissipate wave energy. Each chamber is composed of the outer wall of the main body 10 and the wave-facing perforated plate 20, and the outer wall of the main body 10 and the back-wave-facing perforated plate 30, respectively. The wave-facing and back-wave-facing perforated plates 20 and 30 are fixed to the outer wall of the main body 10 using anchor bolts. The perforations can be circular, rectangular, or strip-shaped. Water outlet holes 130 are provided at the bottom of the wave-dissipating chambers to ensure water balance inside and outside the chambers, guaranteeing the overall stability of the breakwater. This system guides waves into the wave-dissipating chambers through the perforated plates, creating strong turbulent flow. Utilizing mechanisms such as vortex generation and shedding, and turbulent kinetic energy dissipation, it efficiently reduces wave energy, lowers the intensity of transmitted waves, and enhances the overall protection effect behind the breakwater.

[0035] The mooring system 120 is located at the bottom of the floating breakwater body. It employs a parallel, relaxed mooring system, comprising multiple sets of mooring systems 120 consisting of anchor chains 100 and sinkers 110. One end of the anchor chain 100 is connected to the sinker 110, and the other end is connected to the floating breakwater body 10. The working principle of the floating breakwater is as follows: This breakwater achieves efficient wave energy dissipation through the synergistic effect of the resonant cavity 80, the wave-facing perforated wave-dissipating chamber 70, and the wave-repelling perforated wave-dissipating chamber 90. Simultaneously, the floating breakwater body 10 and the mooring system 120 ensure overall structural stability. When waves propagate towards the breakwater, they first act on the wave-facing side. The wave-facing perforated plate 20 initially blocks and diverts the waves. Some waves pass through the wave-facing perforated plate 20 and enter the wave-facing perforated wave-dissipating chamber 70, colliding with the inner wall of the chamber and forming a strong turbulent flow. Vortices are continuously generated and detached in the water flow, and the wave energy is initially reduced. After initial energy dissipation by the wave-facing perforated wave-dissipating chamber 70, the waves enter the resonant cavity 80 through the connecting port 50. Because the natural frequency of the resonant cavity 80 is pre-matched with the dominant medium-to-long-period wave frequency of the working sea area, the fluid inside the cavity undergoes intense resonant motion. During this resonant motion, frictional loss occurs between the fluid and the cavity wall, converting some wave energy into internal energy. Simultaneously, the air inside the cavity is repeatedly compressed and expanded, exchanging energy with the external atmosphere through the top opening 60. At this point, some of the energy of the medium-to-long-period waves is efficiently reduced. The waves, after being dissipated by the resonant cavity 80, continue to propagate towards the leeward side, entering the leeward-side perforated wave-dissipating chamber 90. The leeward-side perforated wave-dissipating chamber 90 adopts the same structural design as the wave-facing side. The remaining waves enter the leeward-side perforated wave-dissipating chamber 90 through the leeward-side perforated plate 30, and then undergo another process of guidance, disturbance, and turbulent dissipation, further reducing wave energy. Finally, after two perforation-based wave dissipation processes and one resonant wave dissipation process, the wave energy transmitted behind the breakwater is significantly reduced, achieving effective reduction of medium-to-long-period waves. Throughout the wave dissipation process, the floating breakwater 10 ensures its buoyancy and stability through reasonable size design and draft control. The parallel-type relaxed anchoring structure of the anchoring system 120 prevents the floating breakwater 10 from drifting significantly horizontally through the gravity fixation of the sinkers and the tension constraint of the anchor chains. At the same time, the relaxed anchor chains can buffer the instantaneous load brought by wave impact, avoid excessive stress on the anchor chains and breakage, and ensure the safety and stability of the floating breakwater in complex deep-water environments.

[0036] In summary, the floating breakwater of this embodiment enhances the ability to reduce medium- and long-period waves through the synergistic effect of the resonant cavity and the perforated wave-dissipating chamber. The resonant cavity efficiently dissipates specific frequency wave energy through the resonance effect, while the perforated wave-dissipating chamber further enhances energy dissipation through turbulent flow. Together, they improve the overall wave-dissipating efficiency of the breakwater.

[0037] Furthermore, the floating breakwater features a rational structural design. The main body of the breakwater adopts a regular rectangular box structure, facilitating prefabrication and assembly, resulting in lower construction difficulty and material costs. The embedded design highly integrates the resonant cavity and the perforated wave-dissipating chamber without increasing the structural volume. The relaxed mooring system reduces requirements on seabed geology and construction equipment, simplifying construction and offering strong adaptability to deep water. This structure has wide applicability, allowing for flexible adjustment of the resonant cavity size, connecting port cross-sectional parameters, perforated plate characteristics, and mooring system parameters according to wave conditions in different sea areas, meeting the diverse needs of deep-sea engineering construction.

[0038] Based on the above-mentioned floating breakwater, combined with Figure 6 As shown in the figure, this disclosure provides a method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity, including:

[0039] S10, Construct a floating breakwater model. The floating breakwater includes: a main body of the breakwater, which is equipped with a resonant cavity, and wave-dissipating chambers with openings on the wave-facing side and the wave-dissipating chambers with openings on the back side, respectively located on both sides of the resonant cavity.

[0040] S20, determine the target length and target width of the resonant cavity, the wave-facing side opening wave-dissipating chamber, and the wave-repelling side opening wave-dissipating chamber, respectively.

[0041] S30 divides the entire fluid domain of the floating breakwater into multiple regions and represents the total velocity potential of the fluid motion, the conditions for satisfying the velocity potential of each region, the conditions for satisfying the velocity potential of the diffracted and radiated waves on the non-perforated surface of the floating breakwater, and the conditions for satisfying the scattering and radiating potentials of the perforated plate of the floating breakwater.

[0042] S40. Based on the conditions for satisfying the velocity potential of each region, the conditions for satisfying the velocity potential of the diffracted and radiated waves on the unperforated surface, and the scattering and radiating potentials of the perforated plate of the floating breakwater, the velocity potential of each region is obtained.

[0043] S50 calculates the wave force on the floating breakwater, using the velocity potential of each region to express the additional mass and radiation damping of the floating breakwater when it undergoes unit forced oscillation, so as to construct the motion response equation of the floating breakwater in the frequency domain under wave action.

[0044] S60, based on the motion response equation, the motion response amplitude of the floating breakwater is obtained, the total velocity potential is calculated based on the motion response amplitude, and then the transmission coefficient and energy dissipation coefficient of the floating breakwater are obtained. The shielding performance and wave dissipation performance of the floating breakwater are evaluated according to each coefficient.

[0045] First, execute S10, according to Figures 1 to 5 The structure shown is used to construct a floating breakwater model.

[0046] Then, execute S20 to determine the target length and target width of the resonant cavity, the wave-facing side opening wave-dissipating chamber, and the wave-repelling side opening wave-dissipating chamber, respectively. Specifically, this includes:

[0047] S21, Determine the target length and target width of the resonant cavity, including:

[0048] Assuming the boundaries of the resonant cavity are impenetrable, and the length of the resonant cavity is... Width is 2 c The nonzero solution of the Laplace equation within the resonant cavity is expressed as:

[0049] ,

[0050] In the formula, n and m It can be any integer, and not all of them can be 0 at the same time; k The wave number of the water wave motion within the resonant cavity; k , n and m The following conditions must be met:

[0051] ;

[0052] Draft d Or, the target length of the resonant cavity. c and target width This allows the resonant cavity to reach its desired natural frequency.

[0053] From the above formula, it can be seen that the adjustment c and The value of affects the wavenumber of water wave motion within the resonant cavity. k Combining the dispersion equation By adjusting the draft d Or design a suitable c and It can achieve the desired natural frequency of the resonant cavity. When the wave approaches the natural frequency of the resonant cavity, a strong fluid resonance phenomenon will occur inside the resonant cavity. The fluid inside and outside the resonant cavity will freely exchange through the bottom opening, forming a strong turbulent flow, thereby achieving the effect of cavity resonance and energy dissipation.

[0054] S22, determine the target length and target width of the wave-dissipating chamber with openings on the wave-facing side and the wave-dissipating chamber with openings on the wave-receiving side, including:

[0055] Assuming the boundaries of the perforated wave-damping chamber are all impermeable, and the length is... , width is b - a Then the nonzero solution of the Laplace equation in the open-aperture wave-damping chamber can be expressed as:

[0056] ,

[0057] In the formula, n and m It can be any integer, and not all of them can be 0 at the same time; β The wave number of the water wave motion in the perforated wave-damping chamber; β , n and m The following conditions must be met:

[0058] ;

[0059] Draft d Alternatively, the target length and target width of the perforated wave-damping chamber are determined so that the corresponding perforated wave-damping chamber reaches its desired natural frequency.

[0060] From the above formula, it can be seen that adjusting the width of the opening of the wave-damping chamber and The value of affects the wave number of water wave motion within the cavity. β Combining the dispersion equation The draft of the breakwater can be adjusted. d Or the length of the wave-dissipating chamber and width ( b - a The desired natural frequency of the perforated wave-dissipating chamber is reached. When the wave frequency approaches the natural frequency of the perforated wave-dissipating chamber, a significant fluid resonance phenomenon will be induced inside the wave-dissipating chamber, thereby improving the energy dissipation performance of the entire floating breakwater.

[0061] In this way, by designing the dimensions of the resonant cavity, the wave-dissipating chamber with openings on the wave-facing side, and the wave-dissipating chamber with openings on the wave-repelling side, the floating breakwater can selectively absorb wave energy of specific frequencies, thereby achieving the effect of reducing medium and long period waves.

[0062] Then, S30 is executed to divide the entire fluid domain of the floating breakwater into multiple regions, and to represent the total fluid velocity potential and its satisfying conditions, the satisfying conditions of the velocity potentials of diffracted and radiated waves from the non-perforated surface of the floating breakwater, and the satisfying conditions of the scattering and radiating potentials of the perforated plate of the floating breakwater. Specifically, this includes:

[0063] S31, combined Figure 7 As shown, the water depth is h The total width of the breakwater is B ( B = 2 b The width of the connector is 2. r The resonant cavity width is 2 c The width of both open-aperture wave-damping chambers is ba The draft of the breakwater is dAssuming the length of the floating breakwater is much greater than the wavelength of the incident wave, the interaction between the wave and the floating breakwater can be simplified to a two-dimensional hydrodynamic problem. Establish a rectangular coordinate system with the origin at the still water surface. x Axis to the right is positive. z The axis coincides with the perpendicular bisector of the floating breakwater and points vertically upwards. The entire fluid domain is divided into nine zones:

[0064] Area 1: Water area on the wave-facing side of the breakwater, coordinates are ( x ≤- b - h ≤ z ≤ 0);

[0065] Area 2: x The negative half-axis is the water area at the bottom of the breakwater, with coordinates (- b ≤ x ≤- r - h ≤ z ≤- c );

[0066] Area 3: The water area at the breakwater connection point, with coordinates (- r ≤ x ≤ r - h ≤ z ≤ 0);

[0067] Area 4: x The water area at the bottom of the breakwater along the positive half-axis is located at ( r ≤ x ≤ b - h ≤ z ≤- c );

[0068] Area 5: Water area on the back side of the breakwater, coordinates are ( x ≥ b - h ≤ z ≤ 0);

[0069] Area 6: The internal water area of ​​the wave-dissipating chamber on the wave-facing side, with coordinates (- b ≤ x ≤- a - c ≤ z ≤ 0);

[0070] Area 7: The internal water area of ​​the wave-dissipating chamber on the back side, with coordinates ( a ≤ x ≤ b - c ≤ z ≤ 0);

[0071] Area 8: x The water area inside the negative half-axis resonant cavity is located at coordinates (- c ≤ x ≤- r - c ≤ z ≤ 0);

[0072] Area 9: x The water area inside the positive half-axis resonant cavity is located at ( r ≤ x ≤ c - c ≤ z ≤ 0);

[0073] in, c It is half the width of the resonant cavity. r =0.5 c , a It is half the width of the main body of the floating breakwater. b It is half the total width of the floating breakwater. h The water is deep.

[0074] Under the assumption of an ideal fluid, the velocity potential can be used. Φ ( x , z , t To describe the entire fluid motion, for a linear harmonic problem, the velocity potential is expressed as...

[0075] (1)

[0076] In the formula, Re represents taking the real part of the variable; i is the imaginary unit; ( x , z ) represents the spatial complex velocity potential; t Indicates time; ω It is the angular frequency of wave motion.

[0077] S32. Considering the interaction between a regular wave and a cavity-resonant, open-pore, energy-dissipating floating breakwater, wave diffraction occurs during wave propagation due to the obstruction effect of the breakwater. In the wave diffraction problem, the velocity potential satisfies the Laplace equation, free surface boundary conditions, bottom boundary conditions, structure surface conditions, and far-field radiation boundary conditions. Under the action of wave excitation force, the floating breakwater undergoes a kinematic response, thereby generating radiated waves (wave radiation problem). The total velocity potential of the fluid motion is... Represented as:

[0078] (2)

[0079] In the formula, 4 is the velocity potential of the scattered wave (the sum of the incident wave and the diffracted wave); s It is the potential of the radiated wave velocity generated by the movement of the breakwater; ξ s It is the amplitude of the structural motion response; subscript s = 1, 2 and 3 represent the three degrees of freedom: sway, heave and roll, respectively.

[0080] The velocity potential in each region satisfies the Laplace equation, the free surface condition, the bottom condition, and the far-field radiation condition:

[0081] (3)

[0082] (4)

[0083] (5)

[0084] (6)

[0085] (7)

[0086] In the formula, the superscript "( j ")" indicates a region j ; g It is gravitational acceleration; 0 is the velocity potential of the incident wave; k 0 is the wave number of the incident wave, which satisfies the dispersion equation. .

[0087] On the unperforated surface of a floating breakwater, the velocity potentials of diffracted and radiated waves satisfy:

[0088] (8)

[0089] (9)

[0090] In the formula, The normal derivative of the scattering potential; The normal derivative of the radiation potential; n 1 and n 2 represents the unit outward normal vector of the breakwater surface at... x direction and z Component of direction; n 3= n 1( xx 0) + n 2( zz 0); ( x 0, z0) is the coordinate value of the rotation center of the structure.

[0091] To account for energy dissipation in the waters near the perforated breakwater, a linear pressure loss boundary condition is applied at the perforated plate. At the perforated plate of the floating breakwater, the scattering potential and radiation potential satisfy the following conditions:

[0092] (10)

[0093] (11)

[0094] In the formula, G These are parameters affecting the porosity of the perforated plate; This represents the scattering potential difference across the perforated plate; This represents the radiation potential difference across the perforated plate; δ s,n = 1 ( s = n ), δ s,n = 0 ( s ≠ n ).

[0095] In this way, by dividing the entire fluid domain into multiple sub-regions and establishing boundary conditions for each region, a mathematical description of the flow field structure can be achieved, thus providing a framework for the expansion of the velocity potential in each region.

[0096] Then, S40 is executed to calculate the velocity potential of each region based on the conditions for satisfying the velocity potential of each region, the conditions for satisfying the velocity potential of diffracted and radiated waves on the unperforated surface, and the scattering and radiating potentials of the perforated plate of the floating breakwater. Specifically, this includes:

[0097] S41, based on equations (3) to (9), using the method of separation of variables, the velocity potential expressions for each region can be obtained:

[0098] (12)

[0099] (13)

[0100] (14)

[0101] (15)

[0102] (16)

[0103] (17)

[0104] (18)

[0105] (19)

[0106] (20)

[0107] In the formula, the subscript s = 1, 2, 3 and 4 represent the radiation potential and scattering potential of the wave in the three degrees of freedom of sway, heave and roll, respectively; R n , T n , J n , I n , A n , V n , E n , W n , C n , D n , , , , , and These are the undetermined expansion coefficients; κ 0 = -i k 0, κ n = k n ( n ≥ 1); Eigenvalue k n ( n ≥ 0) satisfies ; q 0 = -i p 0, q n = p n ( n ≥ 1); Eigenvalue p n ( n ≥ 0) satisfies ; l n = nπ / ( h - d ) ( n ≥ 1).

[0108] In equations (12) to (20), Ys , , Z n ( z ), L n ( z )and P n ( z The expression for ) is:

[0109] (twenty one)

[0110] (twenty two)

[0111] (twenty three)

[0112] (twenty four)

[0113] (25)

[0114] (26)

[0115] S42, by using the boundary conditions (8) and (9) of the side surface of the floating breakwater and the transfer boundary conditions (10) and (11) of the interface between adjacent regions, the expansion coefficients in the velocity potential expressions (12) to (20) can be obtained, and then the velocity potential of each region can be obtained.

[0116] In this way, by combining the fluid control equations with various boundary conditions, the accurate analytical solution of the velocity potential of the complex flow field around and inside the breakwater was achieved, which serves as the basis for subsequent wave force calculations of floating breakwaters.

[0117] Then, S50 is executed to calculate the wave force on the floating breakwater. The velocity potential of each region is used to express the additional mass and radiation damping of the floating breakwater during unit forced oscillation, in order to construct the motion response equation of the floating breakwater in the frequency domain under wave action, and to obtain the motion response amplitude of the floating breakwater's displacement. Specifically, this includes:

[0118] S51, Once the scattered wave velocity potential and the radiated wave velocity potential of the fluid motion are determined through S40, the incident potential can be known. and diffraction potential By integrating the dynamic water pressure along the surface of the structure, the wave force acting on the floating breakwater can be calculated. (Horizontal wave force on the floating breakwater) F 1. Vertical wave force F 2 and about y Torque of the shaft F 3 is calculated using the following formula:

[0119] (27)

[0120] In the formula, S B This refers to the surface of a floating breakwater; 0 represents the velocity potential of the incident wave; 7 represents the velocity potential of the diffracted wave.

[0121] S52, using the velocity potential of each region of the radiated wave to express the added mass of the floating breakwater during unit forced oscillation. μ sj and radiation damping λ sj :

[0122] (28)

[0123] S53, the kinematic response equation of a floating breakwater in the frequency domain under wave action is:

[0124] (29)

[0125] In the formula, M is the mass matrix of the floating breakwater; μ is the additional mass matrix; B is the system damping matrix; λ is the radiation damping matrix; K is the mooring system stiffness matrix; C is the restoring force coefficient matrix; ξ is the structural displacement amplitude vector; and F is the wave excitation force vector.

[0126] In this way, the dynamic characteristics of the flow field are transformed into the governing equations of the structural motion, which makes it possible to quantitatively predict the motion response amplitude of the breakwater under wave action, and the total velocity potential of the floating breakwater can be obtained based on the motion response amplitude.

[0127] Then, S60 is executed, and the reflection coefficient, transmission coefficient, and energy dissipation coefficient of the floating breakwater are obtained by substituting the scattered wave velocity potential, the radiated wave velocity potential, and the motion response amplitude into equation (2). The shielding performance and wave-dissipating performance of the floating breakwater are evaluated based on the transmission coefficient and the energy dissipation coefficient, respectively. Specifically, this includes:

[0128] S61, the motion response amplitude of the floating breakwater displacement is obtained by equation (29). ξ s .

[0129] S62, motion response amplitude ξ s Substituting the velocity potential of the scattered wave and the velocity potential of the radiated wave into equation (2), we can obtain the total velocity potential of the interaction between the wave and the cavity resonant open-type energy dissipation floating breakwater. Total velocity potential The medium coefficient reflects the reflection coefficient, transmission coefficient, and energy dissipation coefficient of the floating breakwater.

[0130] S63. The protective performance and wave-dissipating performance of floating breakwaters are evaluated based on the transmission coefficient and energy dissipation coefficient, respectively. The lower the transmission coefficient, the better the protective performance of the floating breakwater; the higher the energy dissipation coefficient, the better the wave-dissipating performance of the floating breakwater.

[0131] In this way, the transmission coefficient and energy dissipation coefficient of the floating breakwater can be obtained, and its shielding performance and wave dissipation performance can be evaluated, providing a reliable method for hydrodynamic performance analysis.

[0132] In summary, the hydrodynamic performance analysis method provided in this embodiment has the following beneficial effects:

[0133] 1. The hydrodynamic performance analysis method provided in this disclosure establishes a frequency domain analytical model based on two-dimensional potential flow theory, which can quickly calculate the reflection coefficient, transmission coefficient, and energy dissipation coefficient of breakwaters, thereby achieving a quantitative evaluation of wave-dissipating and shielding performance. This method eliminates the need for complex numerical modeling and time-consuming calculations, significantly improving the efficiency of scheme selection in the early stages of design and providing convenient theoretical support for engineering applications.

[0134] 2. The analytical method of this disclosure fully considers the influence of key design variables such as breakwater draft, resonant cavity size, opening ratio, and cross-sectional parameters of the connecting opening, enabling rapid analysis for wave conditions in different sea areas. Through the calculation and evaluation of this method, the optimal combination of structural dimensions can be preliminarily determined, significantly reducing computational costs and providing an efficient and reliable optimization method for the engineering design of floating breakwaters.

[0135] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0136] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity, characterized in that, include: S10, Construct a floating breakwater model, the floating breakwater comprising: a floating breakwater body, wherein the floating breakwater body is provided with a resonant cavity, and wave-dissipating chambers with openings on the wave-facing side and the wave-dissipating chambers with openings on the back side located on both sides of the resonant cavity respectively; S20, determine the target length and target width of the resonant cavity, the wave-facing side opening wave-dissipating chamber, and the wave-repelling side opening wave-dissipating chamber respectively; S30, the entire fluid domain of the floating breakwater is divided into multiple regions, and the total velocity potential of the fluid motion, the conditions for satisfying the velocity potential of each region, the conditions for satisfying the velocity potential of the diffracted and radiated waves on the non-perforated surface of the floating breakwater, and the conditions for satisfying the scattering and radiating potentials of the perforated plate of the floating breakwater are represented; wherein, The conditions for satisfying the total velocity potential of fluid motion, the velocity potential of each region, the velocity potential of the diffracted and radiated waves on the non-perforated surface of the floating breakwater, and the scattering and radiating potentials of the perforated plate of the floating breakwater include: The total velocity potential of the fluid motion Represented as: ， In the formula, 4 is the velocity potential of the scattered wave; s It is the potential of the radiated wave velocity generated by the movement of the breakwater; ξ s It is the amplitude of the structural motion response; subscript s = 1, 2 and 3 represent the three degrees of freedom: sway, heave and roll, respectively; The velocity potential of each region satisfies the Laplace equation, the free surface condition, the bottom condition, and the far-field radiation condition. The velocity potentials of the diffracted and radiated waves on the non-perforated surface of the floating breakwater satisfy the following: ， ， In the formula, The normal derivative of the scattering potential; The normal derivative of the radiation potential; n 1 and n 2 represents the unit outward normal vector of the breakwater surface at... x direction and z Component of direction; n 3 = n 1( xx 0) + n 2( zz 0); ( x 0, z 0) is the coordinate value of the structure's rotation center; The scattering potential and radiation potential of the perforated plate of the floating breakwater satisfy the following: ， ， In the formula, G These are parameters affecting the porosity of the perforated plate; This represents the scattering potential difference across the perforated plate; This represents the radiation potential difference across the perforated plate; δ s,n = 1 ( s = n ), δ s,n = 0 ( s ≠ n ); S40, based on the velocity potential satisfaction conditions of each region, the velocity potential satisfaction conditions of the diffracted and radiated waves from the non-perforated surface, and the scattering and radiating potentials of the perforated plate of the floating breakwater, the velocity potential of each region is calculated; wherein, The process of determining the velocity potential of each region based on the velocity potential satisfaction conditions of each region, the velocity potential satisfaction conditions of the diffracted and radiated waves from the non-perforated surface, and the scattering and radiating potentials of the perforated plate of the floating breakwater includes: Based on the conditions for satisfying the velocity potential of each region and the conditions for satisfying the velocity potential of the diffracted and radiated waves on the unperforated surface, the expression for the velocity potential of each region is obtained using the method of separation of variables. By utilizing the velocity potentials of the diffracted and radiated waves on the non-perforated surface and the scattering and radiating potentials of the perforated plate of the floating breakwater, the expansion coefficients in the expressions for the velocity potentials of each region are obtained, so as to obtain the velocity potentials of each region. S50, calculate the wave force of the floating breakwater, and use the velocity potential of each region to express the additional mass and radiation damping of the floating breakwater when it undergoes unit forced oscillation, so as to construct the motion response equation of the floating breakwater in the frequency domain under wave action. S60, based on the motion response equation, the motion response amplitude of the floating breakwater is obtained, the total velocity potential is calculated based on the motion response amplitude, and then the transmission coefficient and energy dissipation coefficient of the floating breakwater are obtained. The shielding performance and wave-dissipating performance of the floating breakwater are evaluated according to each coefficient.

2. The method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity according to claim 1, characterized in that, Determining the target length and target width of the resonant cavity includes: Assuming the boundaries of the resonant cavity are impenetrable, the length of the resonant cavity is... l Width is 2 c The nonzero solution of the Laplace equation within the resonant cavity is expressed as: ， In the formula, n and m It can be any integer, and not all of them can be 0 at the same time; k The wave number of the water wave motion within the resonant cavity; k , n and m The following conditions must be met: ； Draft d Or, the target length of the resonant cavity. c and the target width l This allows the resonant cavity to reach its desired natural frequency.

3. The method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity according to claim 1, characterized in that, Determining the target length and target width of the wave-dissipating chamber with openings on the wave-facing side and the wave-dissipating chamber with openings on the wave-repelling side includes: Assuming the boundaries of the perforated wave-damping chamber are all impermeable, and the length is... l , width is b -a Then the nonzero solution of the Laplace equation in the open-aperture wave-damping chamber can be expressed as: ， In the formula, n and m It can be any integer, and not all of them can be 0 at the same time; β The wave number of the water wave motion in the perforated wave-damping chamber; β , n and m The following conditions must be met: ； Draft d Alternatively, the target length and target width of the perforated wave-damping chamber are determined so that the corresponding perforated wave-damping chamber reaches its desired natural frequency.

4. The method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity according to claim 3, characterized in that, The process of dividing the entire fluid domain of the floating breakwater into multiple zones includes: Establish a rectangular coordinate system with the center of the resonant cavity as the origin located on the still water surface. x Axis to the right is positive. z The axis coincides with the perpendicular bisector of the floating breakwater and points vertically upward, dividing the entire fluid domain into nine regions: Area 1 is the water area on the wave-facing side of the breakwater, with coordinates ( x ≤ - b - h ≤ z ≤ 0); Area 2 is x The negative half-axis is the water area at the bottom of the breakwater, with coordinates (- b ≤ x ≤ - r - h ≤ z ≤ - c ); Area 3 is the water area at the breakwater connection point, with coordinates (- r ≤ x ≤ r - h ≤ z ≤ 0); Area 4 is x The water area at the bottom of the breakwater along the positive half-axis is located at ( r ≤ x ≤ b - h ≤ z ≤ - c ); Area 5 is the water area on the back side of the breakwater, with coordinates ( x ≥ b - h ≤ z ≤ 0); Area 6 is the internal water area of ​​the wave-dissipating chamber on the wave-facing side, with coordinates (- b ≤ x ≤ - a - c ≤ z ≤ 0); Area 7 is the internal water area of ​​the wave-dissipating chamber on the back side, with coordinates ( a ≤ x ≤ b - c ≤ z ≤ 0); Area 8 is x The water area inside the negative half-axis resonant cavity is located at coordinates (- c ≤ x ≤ - r - c ≤ z ≤ 0); Area 9 is x The water area inside the positive half-axis resonant cavity is located at ( r ≤ x ≤ c - c ≤ z ≤ 0); in, c It is half the width of the resonant cavity. r =0.5 c , a It is half the width of the main body of the floating embankment. b It is half the total width of the floating breakwater. h The water is deep.

5. The method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity according to claim 1, characterized in that, The calculation of the wave force of the floating breakwater, using the velocity potential of each region to express the additional mass and radiation damping of the floating breakwater during unit forced oscillation, includes: The wave force, including horizontal wave force, is calculated by integrating the dynamic water pressure along the surface of the structure and integrating the dynamic water pressure. F 1. Vertical wave force F 2 and about y Torque of the shaft F 3: ； The added mass μ sj and radiation damping λ sj for: 。 6. The method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity according to claim 1, characterized in that, The motion response equation is: ， In the formula, M is the mass matrix of the floating breakwater; μ is the additional mass matrix; B is the system damping matrix; λ is the radiation damping matrix; K is the mooring system stiffness matrix; C is the restoring force coefficient matrix; ξ is the structural displacement amplitude vector; and F is the wave excitation force vector.

7. The method for analyzing the hydrodynamic performance of an energy-dissipating floating breakwater with a resonant cavity according to any one of claims 1 to 6, characterized in that, The evaluation of the protective and wave-dissipating performance of the floating breakwater based on various coefficients includes: The lower the transmission coefficient, the better the shielding performance of the floating breakwater; The higher the energy dissipation coefficient, the better the wave-dissipating performance of the floating breakwater.

8. A floating breakwater with a resonant cavity, applicable to the hydrodynamic performance analysis method of a floating breakwater with a resonant cavity as described in any one of claims 1 to 7; characterized in that, include: The main body of the floating breakwater is equipped with a resonant cavity, and wave-dissipating chambers with openings on the wave-facing side and the wave-repelling side located on both sides of the resonant cavity, respectively. The floating embankment has a top opening at the top and a connecting opening at the bottom. The top opening connects the resonant cavity to the external environment, and the connecting opening connects the resonant cavity to the external environment. The main body of the floating dike is provided with a wave-facing perforated plate and a wave-repellent plate on the wave-facing side and the wave-repellent side, respectively. The openings of the wave-facing perforated plate are connected to the wave-facing perforated wave-dissipating chamber, and the openings of the wave-repellent plate are connected to the wave-repellent wave-dissipating chamber. Both the wave-facing and wave-dissipating chambers on the opposite side and the wave-repelling chamber on the opposite side are provided with water outlet holes at their bottoms. An anchoring system is installed at the bottom of the main body of the floating breakwater.

Images