Array type breakwater and design and test method thereof

Abstract

The invention discloses an array breakwater and a design and test method thereof, and the design method comprises the steps: S100, setting a planar open water area, the depth of which is a constant finite value, arranging an array breakwater in the open water area, and building a first energy band diagram, a second energy band diagram and a third energy band diagram for describing the propagation characteristics of water waves in the array breakwater; s200, obtaining a corrected fourth energy band diagram by considering water wave characteristics, determining a target wave absorption period, and marking the target wave absorption period on the fourth energy band diagram; and S300, based on the fourth energy band diagram, single structure parameters corresponding to the upper limit and the lower limit of the target wave absorbing period are obtained, N single structures with the structure parameters are arranged in an array mode according to the rule given in the S200 in the wave direction, and the array type breakwater is formed. According to the method, the corresponding matching relation between the resonance frequency of each type of wave and each structural characteristic parameter of the array type breakwater is accurately given by drawing the energy band diagram, and each design parameter value of the array type breakwater can be quickly obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of offshore engineering equipment, and more specifically, relates to a design method, a system and a test method for an array breakwater. Background Art

[0002] Traditional breakwaters mainly dissipate waves by using principles such as blocking, reflection, and dissipation, and can be mainly divided into two types according to the structural form: bottom-mounted and floating. The bottom-mounted breakwater has a good wave dissipation effect for waves in the full cycle range, but it consumes a large amount of construction materials and has a high cost. Especially in deep water areas, the construction cost and construction difficulty are further increased. To solve the above problems and considering that the wave energy is mainly concentrated near the water surface, a floating breakwater was developed, that is, the breakwater floats on the sea surface and is fixed to the seabed through a mooring system, etc. Although the floating breakwater has a lower construction cost and construction difficulty, its wave dissipation effect on long-period waves is relatively limited. Based on this, we proposed an array breakwater and its design method. This method can quickly design an array breakwater that meets the engineering requirements by using Bloch theory and the finite element method, thereby eliminating the drawbacks of existing breakwaters and traditional hydrodynamic analysis and design methods.

[0003] The design process of the proposed array breakwater using the traditional hydrodynamic analysis method is as Figure 2 shown. This method includes the following steps: (1) Preset the structural characteristic parameters of the array breakwater (the combination of outer diameter R1 - inner diameter R2 - draft d - opening size ln - array spacing a) according to experience; (2) Consider a series of incident waves with different frequencies and analyze the variation law of the corresponding reflection / transmission coefficients, as Figure 1 shown; (3) Consider a series of different combinations of structural characteristic parameters and analyze the variation law of the corresponding reflection / transmission coefficients in combination with step 2 to obtain a series of different reflection / transmission coefficient curves, as Figure 2 shown; (4) Analyze the series of reflection / transmission coefficient curves and select the coefficient curve that meets the requirements (for example, a wide frequency domain with an effective frequency band range of 6s - 10s and an energy dissipation effect meeting the requirements). Among them, different line types in the figure represent different possible variation trends / patterns; curves of different colors under the same line type represent different situations that may occur under the same variation pattern / trend. Obviously, the best combination strategy for the structural characteristic parameters is combination mode 1.

[0004] From the above analysis, traditional hydrodynamic analysis methods can, to a certain extent, determine the design parameters of the required array breakwaters by considering a series of incident waves with different frequencies, coupling a series of different combinations of structural characteristic parameters, and analyzing the variation laws of the corresponding reflection / transmission coefficients. However, the prerequisite is that calculation examples must be carefully selected / designed to ensure that the combinations of wave frequencies and array structure parameters considered can excite resonances of various types of waves, and the combinations of working conditions considered need to cover all possible situations, which are complex and numerous. Traditional hydrodynamic analysis methods face the defects of unclear working condition combination strategies and low calculation efficiency when applied to the design of the proposed new type of array breakwater. In summary, the existing floating breakwaters have limited effect on reducing long waves, and the proposed array breakwaters cannot be quickly and accurately designed according to the actual situation on site, so their wave dissipation effect cannot match the actual use requirements. Summary of the Invention

[0005] Aiming at the above defects or improvement requirements of the existing technology, the present invention provides a design method and system for an array breakwater that can effectively reduce broadband long waves, and accurately gives the corresponding matching relationship between the resonance frequencies of various types of waves and the structural characteristic parameters of the array breakwater by drawing a band diagram. Among them, waves with frequencies falling within the band / passband range can propagate in the array structure, while waves falling within the band gap / forbidden band between the bands will have their propagation absolutely prohibited, which is the working frequency range of wave resonance or the array breakwater. For different service sea areas, the values of the design parameters of the array breakwater can be directly obtained by referring to the band diagram according to the wave conditions and the target working frequency range of the sea area, greatly reducing the calculation working conditions and simplifying the design process of the array breakwater.

[0006] To achieve the above object, the present invention proposes a design method for an array breakwater, including:

[0007] S100: Set an open water area on a plane with a constant finite depth, and arrange an array breakwater therein, and establish first, second, and third band diagrams for describing the propagation characteristics of water waves in the array breakwater;

[0008] S200: Based on the first, second, and third band diagrams, obtain a modified fourth band diagram considering the characteristics of water waves, determine the target wave dissipation period according to the actual engineering requirements, and mark it on the fourth band diagram;

[0009] S300: Based on the fourth band diagram, obtain the single - body structure parameters corresponding to the upper and lower limits of the target wave dissipation period, and combine the wave dissipation efficiency and resonance frequency band stacking factors, and arrange N single - bodies with the above - mentioned structure parameters in an array along the wave direction according to the law given in S200 to form an array breakwater.

[0010] Further, the establishment of the first band diagram in step S100 includes:

[0011] S101: Arrange a three - dimensional Cartesian coordinate system at the still water surface. The x - y plane is the mean free water surface, and the z - axis is vertically upward along the water depth direction. Assuming the water body is inviscid, irrotational, and only considering the case of linear small - amplitude wave incidence, the fluid / wave motion is described by the velocity potential function as follows:

[0012] Φ(x,y,z,t)=Re[φ(x,y,z)e -iωt (1)

[0013] In the formula, the velocity potential function φ satisfies the Laplace equation in the fluid domain:

[0014] ▽ 2 φ(x,y,z)=0 (2)

[0015] In the formula, i is the imaginary unit; ω is the wave angular frequency, t is the time; ▽ is the Hamiltonian operator.

[0016] Furthermore, in step S100, the establishment of the first energy band diagram includes:

[0017] S102: The structure surface and the water bottom need to satisfy the solid - wall boundary condition:

[0018] ▽φ·n=0 (3)

[0019] In the formula, n is the unit normal vector of the wall surface;

[0020] The boundary condition at the free surface is:

[0021]

[0022] In the formula, g is the acceleration due to gravity.

[0023] Furthermore, based on Bloch theory, the infinite - period array - type breakwater is divided into a series of array unit structures, and it is considered that the solutions in each array unit show the following periodic variation:

[0024] η(r)=e iq·r ψ(r) (5)

[0025] In the formula, η(r) is the wave surface elevation, r is the position vector of any point in the array; q(=q1i + q2j) is the Bloch wave number in the reciprocal lattice space, i and j are the unit vectors along the x and y directions in the reciprocal lattice space respectively, and ψ is a periodic function.

[0026] Furthermore, the function ψ has the same period as the array, that is:

[0027] ψ(r + R)=ψ(r) (6)

[0028] Wherein, R = m1a1 + m2a2, where m1 and m2 are integers; a1 and a2 are vectors in the x and y directions respectively, and the lengths are the spacing a1 between adjacent single - body structures along the wave incident direction and the spacing a2 between adjacent single - body structures perpendicular to the wave incident direction.

[0029] Further, the solution in each array unit is:

[0030] η(r + R) = T B η(r) (7)

[0031] Wherein, T B (= e iqR ) is the Bloch transmission coefficient, which can be either real or complex in water waves. If q is real, the wave can pass through the infinite - period array smoothly, and the corresponding frequency range is called the passband; if q is complex, the frequency range with no real - valued solution is called the bandgap or forbidden band, which represents the wave - frequency range where resonance occurs.

[0032] Further, the established periodic boundary conditions are:

[0033]

[0034] Wherein: q1a1 ∈ [0, π], q2a2 ∈ [0, π], q1 and q2 are the components of the Bloch wave number q in the x and y directions respectively, and a1 and a2 are the spacing between adjacent single - body structures along the wave incident direction and the spacing between adjacent single - body structures perpendicular to the wave incident direction respectively.

[0035] Further, the establishment of the first band diagram includes:

[0036] S103: Discretize the computational domain, apply boundary conditions, and after assembling the coefficient matrix, transform the calculation of the Bloch wave number into a standard linear eigenvalue problem for solution:

[0037]

[0038] Wherein, the matrix C contains the Bloch wave number q, and g is the acceleration due to gravity.

[0039] Further, the solution also includes: Plotting the eigenvalue k = ω 2 / g versus q1a1 on a graph can obtain the first band diagram, which characterizes the frequencies and intervals where water - wave resonance occurs for a given array - type breakwater.

[0040] Further, based on the first energy band diagram, considering a series of different array breakwaters, a second energy band diagram is obtained, which includes a three-dimensional diagram with the abscissa taken as the inner diameter R2 and the opening ln respectively, and the ordinate as the middle value of the band gap, and a three-dimensional diagram with the abscissa taken as the inner diameter R2 and the opening ln respectively, and the ordinate as the band gap width. The two together constitute the second energy band diagram of the array breakwater, characterizing the corresponding matching relationship between the characteristic dimensions of different array composition structures and the water wave resonance frequency and range.

[0041] Further, based on the second energy band diagram, assuming that the array composition structures all have the same opening, wall thickness and draft, a third energy band diagram is obtained.

[0042] Further, the single structure is an open C-shaped cylinder.

[0043] Further, in step S200, the correction includes:

[0044] By comparing the linear results in S100 with the experimental / high-fidelity numerical simulation results, systematically analyzing and summarizing the rules, and performing parametric post-processing, a fourth energy band diagram is obtained.

[0045] According to the second aspect of the present invention, an array breakwater is provided, which is realized by using the described design method and includes an array structure composed of a plurality of open C-shaped cylinders.

[0046] Further, the effective frequency band range of the array breakwater needs to cover the wide frequency domain with a period of 6s - 10s, and the transmission coefficient is less than 0.5.

[0047] According to the third aspect of the present invention, a test method for an array breakwater is provided, including:

[0048] S600: For the selected sea area water depth, keeping the array spacing, wall thickness, draft, and opening size unchanged, based on the described design method, obtain the corrected energy band diagram of the array breakwater corresponding to this sea area;

[0049] S700: According to the measured joint probability of waves in the corresponding sea area, determine the wave period and effective wave height in this sea area, and determine the wave dissipation target period range of the array breakwater according to the engineering requirements;

[0050] S800: Mark the target period range and its corresponding inner diameter in the corrected energy band diagram, and arrange a plurality of open C-shaped cylinders with the inner diameter changing according to the above given rules along the wave direction to form an array breakwater;

[0051] S900: According to the Froude number similarity criterion, build a test model of the array breakwater through a scale ratio, and place it in a wave flume to carry out a physical model test to verify the wave dissipation performance of the designed array breakwater.

[0052] Furthermore, the scale ratio is 1:5 - 1:20.

[0053] Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0054] 1. The method of the present invention proposes an array breakwater. By constructing a Helmholtz - type marine structure monomer, namely a C - shaped open cylinder, local resonance phenomenon is induced to effectively reduce long - period waves within a single or relatively narrow frequency range with a relatively small structural characteristic size. At the same time, by reasonably arranging the Helmholtz - type marine structure monomers in an array, the multi - type water wave resonance is synergistically utilized to form a new type of array breakwater that continuously dissipates energy within a wide frequency range of long - period waves.

[0055] 2. The method of the present invention, based on a new type of array breakwater with a gradually changing array arrangement of C - shaped structures, significantly enhances the reduction effect on long - period waves within a wide frequency range of the target sea area by inducing multiple wave resonances.

[0056] 3. The method of the present invention provides a specific method for solving the eigenvalue energy band diagram, and the method is universal and can be applied to the design and analysis of various structural forms.

[0057] 4. The method of the present invention introduces the correction of water wave characteristics in the calculation of the energy band diagram, further improving the engineering applicability and accuracy of the results, and better meeting the actual needs.

[0058] 5. The method of the present invention has a simple breakwater structure design, convenient manufacturing and installation processes, and high engineering practicability.

[0059] 6. The method of the present invention gives the specific design process of the C - shaped cylinder array breakwater, and has high application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic diagram of the variation law of the transmission / reflection coefficient of the array breakwater in the embodiment of the present invention with respect to the incident wave frequency;

[0061] Figure 2 It is a schematic diagram of the traditional hydrodynamic analysis design method in the embodiment of the present invention;

[0062] Figure 3 is a schematic diagram of the structure of the array breakwater in the embodiment of the present invention; 3(a) is a schematic diagram of the array breakwater, and 3(b) is a top view of the array breakwater;

[0063] Figure 4 It is a schematic diagram of the periodic boundary conditions of the array breakwater in the embodiment of the present invention;

[0064] Figure 5 It is a schematic diagram of the first energy band diagram in the embodiment of the present invention;

[0065] FIG. 6 is the second energy band diagram of the array breakwater in the embodiment of the present invention; 6(a) shows the change of the middle value of the band gap with the inner diameter and the opening, and 6(b) shows the change of the band gap width with the inner diameter and the opening;

[0066] Figure 7 Schematic diagram of the third energy band in the embodiment of the present invention;

[0067] Figure 8 It is the modified energy band structure diagram of the array breakwater in the embodiment of the present invention, that is, the fourth energy band diagram;

[0068] FIG. 9 is a schematic diagram of the design method of the array breakwater based on the energy band diagram in the embodiment of the present invention; 9(a) marks the wave-damping period according to the target requirements; 9(b) finds the corresponding inner diameter of the C column; 9(c) arranges multiple C columns with gradually changing inner diameters in an array (illustrated with N = 6);

[0069] Figure 10 It is the fourth energy band diagram of the array breakwater in the Shanwei sea area in the embodiment of the present invention;

[0070] Figure 11 Schematic diagram for determining the size of the array breakwater in the Shanwei sea area in the embodiment of the present invention;

[0071] Figure 12 In the embodiment of the present invention, the transmission coefficient and the reflection coefficient change with the incident wave period;

[0072] Figure 13 It is the video screenshot during the test in the embodiment of the present invention;

[0073] Figure 14 Schematic diagram of the design method flow of the array breakwater in the embodiment of the present invention;

[0074] Figure 15 Schematic diagram of the test method flow of the array breakwater in the embodiment of the present invention. Detailed implementation manners

[0075] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0076] As Figure 1 shown, the main performance technical indicators of the array breakwater of the present invention include the transmission / reflection coefficient K t / K r(Ratio of the amplitude of the transmitted or reflected wave to the amplitude of the incident wave) and the effective frequency band range / operating range Δω (the wave frequency range where the transmission coefficient is less than a certain threshold, which is closely related to the wave resonance frequency). Generally speaking, to meet the requirements of engineering construction, the effective frequency band range of the new array breakwater needs to cover the wide frequency domain with a period of 6s - 10s, and the energy dissipation effect reaches more than 50% (the transmission coefficient is less than 0.5; Figure 1 the red dotted line in

[0077] As Figure 14 shown, in order to achieve the main performance and technical index requirements of the array breakwater, the present invention provides a design method for an array breakwater, including:

[0078] S100: Set an open water area on a plane with a constant finite depth, and arrange an array breakwater therein, and establish the first, second, and third band diagrams for describing the propagation characteristics of water waves in the array breakwater;

[0079] S200: Obtain a modified fourth band diagram considering the characteristics of water waves, determine the target wave-damping period according to the actual engineering requirements, and mark it on the fourth band diagram;

[0080] S300: Based on the fourth band diagram, obtain the single-body structure parameters corresponding to the upper and lower limits of the target wave-damping period, and combine the wave-damping efficiency and resonance frequency band stacking factors, and arrange N single-body structures with the above structure parameters in an array along the wave direction according to a given rule to form an array breakwater.

[0081] The present invention realizes effectively reducing long-period waves in a single or relatively narrow frequency range with a relatively small structural characteristic size by constructing a Helmholtz-type marine structure single body, that is, a C-shaped open cylinder, to induce local resonance. By reasonably arranging the Helmholtz-type marine structure single bodies in an array and synergistically utilizing multi-type water wave resonances, a new array breakwater with continuous energy dissipation in the wide frequency domain of long-period waves is formed. Among them, the Bloch theory was initially used to describe the motion state and energy level structure of electrons in a crystal with a periodic structure. This theory believes that the propagation of electron waves in a periodic potential field (i.e., an infinite periodic array) will present a Bloch state, which is a plane wave with an amplitude modulated periodically. If the amplitude is only modulated by the phase, the electrons can move throughout the crystal, which is the pass band; if they experience both amplitude and phase modulation, the electrons can only move within the atoms, which is the forbidden band. Considering the similarity between water waves and electron waves / light waves, the Bloch band theory in solid physics is extended to establish a band diagram for describing the propagation characteristics of water waves in the array breakwater to guide its design.

[0082] Embodiment 1

[0083] As shown in Figure 3, the embodiment of the present invention provides a design method for an array breakwater, including the following steps:

[0084] Step 1: Establish the governing equations

[0085] First, consider an open water area in the x-y plane with a constant finite depth h (defined along the z-axis). The vertical coordinate z-axis is positive upwards, and its origin coincides with the still water surface, so z = -h represents the seabed. The domain is bounded by a flat bottom and a free surface, and an array of breakwaters is arranged within it.

[0086] Assuming the water body is inviscid, irrotational, and only considering linear small-amplitude wave incidence, the fluid / wave motion is described by the velocity potential function as follows:

[0087] Φ(x, y, z, t) = Re[φ(x, y, z)e -iωt (1)

[0088] In the formula, the velocity potential function φ satisfies the Laplace equation within the fluid domain:

[0089] ▽ 2 φ(x, y, z) = 0 (2)

[0090] In the formula, i is the imaginary unit; ω is the wave angular frequency, t is the time; ▽ is the Hamiltonian operator, k is the wave number, which satisfies the linear dispersion relation ω 2 = gktanh(kh), ω is the wave angular frequency, and g is the acceleration due to gravity.

[0091] Step 2: Establish the boundary conditions

[0092] The solid wall boundary conditions need to be satisfied on the structure surface and the seabed:

[0093] ▽φ · n = 0 (3)

[0094] In the formula, n is the unit normal vector of the wall surface.

[0095] The boundary condition at the free surface is:

[0096]

[0097] In the formula, g is the acceleration due to gravity.

[0098] As shown in Fig. 3(b), Bloch theory divides the infinite periodic array into a series of array unit structures (with side lengths of the array pitches a1 and a2), and it is considered that the solutions in each array unit (taking the wave surface elevation as an example) show the following periodic variation law:

[0099] η(r) = e iq·r ψ(r) (5)

[0100] In the formula, η(r) is the wave surface elevation, and r is the position vector of any point in the array; q (=q1i + q2j) is the Bloch wave number in the reciprocal lattice space, where i and j are the unit vectors along the x and y directions in the reciprocal lattice space respectively; ψ is a periodic function, and the function ψ has the same period as the array, that is:

[0101] ψ(r + R) = ψ(r) (6)

[0102] In the formula, R = m1a1 + m2a2, where m1 and m2 are integers; a1 and a2 are the vectors along the x and y directions respectively, and their lengths are the spacing a1 between adjacent C-type cylinders along the wave incident direction and the spacing a2 between adjacent C-type cylinders perpendicular to the wave incident direction. At this time, formula (5) can be equivalent to:

[0103] η(r + R) = T B η(r) (7)

[0104] In the formula, T B (=e iqR ) is the so-called Bloch transmission coefficient, which can be either real or complex in water waves. If q is real, the wave can pass through the infinite periodic array smoothly, and the corresponding frequency range is called the passband; if q is complex, the frequency range with no real solutions is called the band gap or forbidden band, which represents the wave frequency range where resonance occurs.

[0105] For example Figure 4 , formula (7) is equivalent to the following four periodic boundary conditions:

[0106]

[0107] Step 3: Numerical solution

[0108] When solving, theoretically, q1a1 ∈ [0, π] and q2a2 ∈ [0, π]. If only considering the wave incident in the positive direction, then q2 = 0 and q1a1 ∈ [0, π]. q1 and q2 are the components of the Bloch wave number q in the x and y directions respectively, and a1 and a2 are the spacing between adjacent single body structures along the wave incident direction and the spacing between adjacent single body structures perpendicular to the wave incident direction respectively. When the array spacing changes along the wave direction, the value of a1 also changes accordingly. If the array gradient is not considered, a1 is fixed. When applying the finite element method for solving, a single breakwater structure unit (C-type cylinder) is modeled and the computational domain is discretized, that is, the mesh is divided.

[0109] After applying the finite element method to discretize the computational domain, apply the boundary conditions, and assemble the coefficient matrix, the calculation of the Bloch wave number can be transformed into a standard linear eigenvalue problem for solution:

[0110]

[0111] In the formula, the matrix C contains the Bloch wave number q. As described above, at this time, the present invention only cares about when the equation (10) has real solutions, so the eigenvector method is used for solution. Plotting the eigenvalue (k = ω 2 / g) against q1a1 (array structure parameter) on a graph can obtain the first energy band diagram as shown in Figure 5 Figure 6, which characterizes the frequencies and intervals of water wave resonance for a given array breakwater; at this time, the dimensions of the C-type cylinder are known values given in advance (realized by modeling when dividing the grid). The blue shaded area in the figure is the energy gap in the energy band diagram, that is, the region where the eigenvalue has no real solutions and wave resonance occurs.

[0112] Considering a series of different C-type cylinder sizes and jointly plotting the corresponding band gaps on one graph, the second energy band diagram of the array breakwater as shown in Figure 6 can be obtained, which characterizes the corresponding matching relationship between different array composition structure characteristic sizes and water wave resonance frequencies and intervals. Among them, the abscissa of Figure 6(a) is the inner diameter R2 and the opening ln respectively, and the ordinate is the middle value of the band gap, that is, the sum of the lower limit and the upper limit of the band gap divided by 2, which is one of the characterization values of the effective working frequency band of the array breakwater. The abscissa of Figure 6(b) is the inner diameter R2 and the opening ln respectively, and the ordinate is the band gap width, that is, the upper limit of the band gap minus the lower limit of the band gap, which is the second characterization value of the effective working frequency band of the array breakwater. Figure 6(a) and Figure 6(b) together constitute the third energy band diagram of the array breakwater, that is, the corresponding matching relationship diagram between its characteristic size and the effective working frequency band. At this time, it is assumed that the waves are incident normally, and the array spacing, wall thickness, and draft remain unchanged as fixed values. This energy band diagram reveals the matching relationship between the array structure characteristic parameters and the water wave resonance period, providing an important reference basis for the design of the breakwater.

[0113] If the opening ln = ln1 is further set, then make a cross-section of X = ln1 in the energy band diagram 6(a) and project it onto the Y-Z plane to obtain the variation law of the middle value of the band gap with the inner diameter R2 as shown in Figure 7 Figure 7. Similarly, the variation law of the band gap width with the inner diameter R2 when ln = ln1 can be obtained in Figure 6(b), and by coupling the middle value of the band gap in Figure 7(a), the third energy band diagram as shown in Figure 7 Figure 8 can be obtained.

[0114] Step Four: The modified energy band structure diagram considering the characteristics of water waves, that is, the fourth energy band diagram.

[0115] The above Bloch theory is based on the energy band structure obtained under the linear potential flow assumption and assumes that the breakwater is an infinite periodic array structure. However, in actual engineering applications, the influence mechanisms of the viscous effect of the fluid, the nonlinear characteristics of the waves, the number of array elements, etc. on the energy band diagram must be considered and necessary corrections must be made, such as Figure 8As shown in the figure. The two closed regions formed by the black dotted lines in the figure are the linear energy band structure before correction (the same as Figure 7 ), and the two blue shaded regions are the energy band structures after correction. By comparing the linear results with the experimental / high-fidelity numerical simulation results, summarizing the rules through systematic analysis, and performing parametric post-processing, the fourth energy band diagram is obtained.

[0116] Step Five: Implement the design of the array breakwater based on the energy band diagram

[0117] 1. Assuming that the array spacings a1 and a2, the opening ln, the wall thickness, and the draft remain unchanged, the corrected fourth energy band structure diagram as shown in Figure 8 is obtained.

[0118] 2. According to the actual engineering requirements, the target wave dissipation period is [T1, T2], and it is marked on the energy band diagram, as shown in Fig. 9(a).

[0119] 3. Check the energy band diagram to find the inner diameter R2 of the C column corresponding to T1 1 , and the inner diameter R2 of the C column corresponding to T2 2 , as shown in Fig. 9(b).

[0120] 4. Considering the cost, wave dissipation efficiency, and resonance frequency band stacking (the effective working frequency range is continuous), consider arranging N C columns with an inner diameter R2 ∈ [R2 1 , R2 2 along the wave direction in an array. The increase value of the inner diameter of adjacent C columns is △R = (R2 2 - R2 1 ) / (N - 1) to form an array breakwater, as shown in Fig. 9(c). Note that at this time, except for the inner diameter R2, other structural parameters remain unchanged.

[0121] The present invention realizes the effective reduction of long-period waves in a single or relatively narrow frequency range with a relatively small structural characteristic size by constructing a Helmholtz-type marine structure monomer, namely a C-shaped open cylinder, to induce local resonance. At the same time, by reasonably arranging the Helmholtz-type marine structure monomers in an array and synergistically utilizing multi-type water wave resonance, a new type of array breakwater with continuous energy dissipation in a wide frequency range of long-period waves is formed.

[0122] Example 2

[0123] As shown in Figure 15 , in order to verify the effectiveness of the design method of the present invention, in another embodiment of the present invention, an experimental method for an array breakwater is provided, including:

[0124] S600: For the selected water depth in the sea area, keeping the array spacing and the opening size unchanged, obtain the fourth energy band structure diagram of the array breakwater corresponding to the sea area based on the design method described in any one of claims 1-13;

[0125] S700: Determine the wave period and significant wave height of the corresponding sea area according to the measured joint probability of waves in the sea area, and determine the target wave dissipation period range of the array breakwater according to the engineering requirements;

[0126] S800: Mark the target period range and its corresponding inner diameter in the fourth energy band diagram, and arrange multiple open-type C cylinders with different inner diameters along the wave direction according to a specified rule to form a breakwater;

[0127] S900: According to the Froude number similarity criterion, construct a test model of the array breakwater through a scale ratio, and place it in a wave flume to conduct a physical model test to verify the wave dissipation performance of the designed array breakwater.

[0128] Taking a certain sea area in Shanwei as the research object, a typical design case of an array breakwater is presented. First, by analyzing the wave characteristics and engineering requirements of the sea area, the target wave dissipation range is clarified, and the structural characteristic parameters of each part of the array breakwater are designed using the energy band diagram. Subsequently, a model test is carried out in a wave flume to verify the feasibility and effectiveness of the design. The specific steps are as follows:

[0129] (1) The water depth of a certain sea area in the selected Shanwei area is 12.4 meters. Considering the bottom-sitting structure form (draft = water depth) and keeping the array spacing and opening size unchanged, based on the above design method, the fourth energy band diagram of the corresponding array breakwater in this sea area can be obtained, as Figure 10 shown.

[0130] (2) According to the measured joint probability of waves, the wave period in this sea area is concentrated between 4 seconds and 10 seconds, and the significant wave height is between 0.6 meters and 2.0 meters. According to the engineering application requirements, the target wave dissipation period range is determined to be the wave period range of 6 seconds to 8 seconds.

[0131] (3) Mark the target wave dissipation range and its corresponding inner diameter R2 in the energy band diagram. Considering arranging 4 C-columns with inner diameters R2 ∈ [R2 1 , R2 4 along the wave direction to form a breakwater, as specifically shown in Figure 11 shown. According to the energy band diagram, 4 C-columns with different sizes can be obtained and are listed in Table 1.

[0132] Table 1 C-column size parameters under the prototype and model

[0133]

[0134] (4) Conduct a physical model experiment to verify the wave dissipation performance of the designed new type of array breakwater

[0135] Physical model tests were carried out in the wave-current flume of the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology to verify the wave dissipation performance of the designed new type of array breakwater. The Froude number similarity criterion was adopted, and the model scale was 1:20. Unless otherwise specified, the results in this patent description are all prototype results.

[0136] Figure 12 It is the variation law of the experimentally measured wave reflection / transmission coefficient with the incident wave period. As can be seen from the figure, within the target effective working range (i.e., the 6 - 8 s period range; the gray area), the transmission coefficient is less than 0.5, meeting the requirement of broadband continuous effective energy dissipation, and verifying the effectiveness and correctness of the proposed new type of array breakwater and its design method.

[0137] Figure 13 It is a video screenshot at a typical moment during the test. It can be observed from the figure that the water surface behind the breakwater is stable, indicating that the breakwater shows good effects in wave dissipation.

[0138] It is easy for those skilled in the art to understand that the above description is only a preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A design method for an array breakwater, characterized in that, Including: S100: Set an open water area on a plane with a constant finite depth, arrange an array of breakwaters therein, and establish the first, second, and third band diagrams for describing the propagation characteristics of water waves in the array of breakwaters. S200: Obtain a modified fourth band diagram considering the characteristics of water waves, determine the target wave dissipation period according to the actual engineering requirements, and mark it on the fourth band diagram. S300: Based on the fourth band diagram, obtain the single - body structure parameters corresponding to the upper and lower limits of the target wave dissipation period, and combine the wave dissipation efficiency and resonance frequency band stacking factors to arrange N single - body structures with the above - mentioned structure parameters in an array along the wave direction according to a given rule to form an array of breakwaters.

2. The design method of an array breakwater according to claim 1, characterized in that, The establishment of the first band diagram in step S100 includes: S101: Arrange a three - dimensional Cartesian coordinate system at the still water surface, with the x - y plane as the mean free water surface and the z - axis vertically upward along the water depth direction. Assuming that the water body is inviscid, irrotational, and only considering the linear small - amplitude wave incidence, the fluid / wave motion is described by the velocity potential function as: Φ(x, y, z, t) = Re[φ(x, y, z)e -iωt (1) In the formula, the velocity potential function φ satisfies the Laplace equation in the fluid domain: In the formula, i is the imaginary unit; ω is the wave angular frequency, t is the time; ▽ is the Hamiltonian operator.

3. The design method of an array breakwater according to claim 2, characterized in that In step S100, the establishment of the first band diagram includes: S102: The structure surface and the water bottom need to satisfy the solid - wall boundary condition: In the formula, n is the unit normal vector of the wall surface. The boundary condition at the free surface is: In the formula, g is the acceleration due to gravity.

4. A design method of an array breakwater according to any one of claims 1-3, characterized in that Based on Bloch theory, divide the infinite - period array of breakwaters into a series of array unit structures, and assume that the solutions in each array unit show the following periodic variation: η(r) = e iq·r ψ(r) (5) In the formula, η(r) is the wave surface elevation, r is the position vector of any point in the array; q(=q1i + q2j) is the Bloch wave number in the reciprocal lattice space, i and j are the unit vectors in the reciprocal lattice space along the x and y directions respectively, and ψ is a periodic function.

5. The design method of an array breakwater according to claim 4, characterized in that, The function ψ has the same period as the array, that is: ψ(r + R)=ψ(r) (6) In the formula, R = m1a1 + m2a2, m1 and m2 are integers; a1 and a2 are vectors along the x and y directions respectively, and their lengths are the spacing a1 between adjacent single - body structures along the wave incidence direction and the spacing a2 between adjacent single - body structures perpendicular to the wave incidence direction.

6. The design method of an array breakwater according to claim 5, characterized in that The solutions in each array unit are: η(r + R) = T B η(r) (7) where, T B (= e iqR ) is the Bloch transmission coefficient, which can be either real or complex in water waves. If q is real, the wave can pass smoothly through the infinite periodic array, and the corresponding frequency range is called the passband; if q is complex, the frequency range with no real solutions is called the energy gap or bandgap, which represents the wave frequency range where resonance occurs.

7. A design method of an array breakwater according to claim 6, characterized in that, The established periodic boundary condition is: In the formula: q1a1 ∈ [0, π], q2a2 ∈ [0, π], q1 and q2 are the components of the Bloch wave number q in the x and y directions respectively, and a1 and a2 are the spacing between adjacent single - body structures along the wave incidence direction and the spacing between adjacent single - body structures perpendicular to the wave incidence direction respectively.

8. A design method of an array breakwater according to claim 7, characterized in that, The establishment of the first band diagram includes: S103: Discretize the computational domain, apply the boundary conditions, and after assembling the coefficient matrix, transform the calculation of the Bloch wave number into a standard linear eigenvalue problem for solution: In the formula, the matrix C contains the Bloch wave number q, and g is the acceleration due to gravity.

9. A design method for an array breakwater according to claim 8, characterized in that, The solution further includes: taking the eigenvalue k = ω 2 / g and plotting its variation with q1a1 on a graph to obtain the first energy band diagram, which characterizes the frequencies and intervals at which water wave resonance occurs for a given array breakwater.

10. A design method of an array breakwater according to claim 9, characterized in that Based on the first energy band diagram, considering a series of different array breakwaters, a second energy band diagram is obtained, which includes a three-dimensional diagram with the abscissa taken as the inner diameter R2 and the opening ln respectively, and the ordinate as the middle value of the band gap, and a three-dimensional diagram with the abscissa taken as the inner diameter R2 and the opening ln respectively, and the ordinate as the band gap width. The two together constitute the second energy band diagram of the array breakwater, characterizing the corresponding matching relationship between the characteristic dimensions of different array composition structures and the water wave resonance frequency and range.

11. A design method of an array breakwater according to claim 10, characterized in that, Based on the second energy band diagram, assuming that the array composition structures all have the same opening, wall thickness and draft, a third energy band diagram is obtained.

12. A design method for an array breakwater according to any one of claims 1-3, characterized in that The single structure shown is an open-type C-shaped cylinder.

13. A design method of an array breakwater according to any one of claims 1-3, characterized in that In step S200, the correction includes: By comparing the linear results with the test / high-fidelity numerical simulation results, systematically analyzing and summarizing the laws, and performing parametric post-processing, a fourth energy band diagram is obtained.

14. An array breakwater, characterized in that, It is implemented by using the design method described in any one of claims 1-13, including an array structure composed of a plurality of open-type C-shaped cylinders.

15. An array breakwater according to claim 14, wherein, The effective frequency band range of the array breakwater needs to cover a wide frequency domain with a period of 6s - 10s, and the transmission coefficient is less than 0.

5.

16. A test method for an array breakwater, characterized in that, Including: S600: For the selected sea area water depth, keeping the array spacing, wall thickness, draft, and opening size unchanged, obtaining the corrected energy band diagram of the array breakwater corresponding to this sea area based on the design method described in any one of claims 1-13; S700: According to the joint probability of the measured waves in the corresponding sea area, determining the wave period and the significant wave height in this sea area, and determining the target wave dissipation period range of the array breakwater according to the engineering requirements; S800: Marking the target period range and its corresponding inner diameter in the corrected energy band diagram, and arranging a plurality of open-type C-shaped cylinders with the inner diameter changing according to the above given law along the wave direction to form an array breakwater; S900: According to the Froude number similarity criterion, building a test model of the array breakwater through a scale ratio and placing it in a wave flume to carry out a physical model test to verify the wave dissipation performance of the designed array breakwater.

17. The test method of an array breakwater according to claim 16, characterized in that, The scale ratio is 1:5 - 1:20.

Images