Wave load calculation method for near-free-surface cylindrical structure in marine environment

Abstract

The invention relates to the technical field of ocean engineering, in particular to a wave force estimation method which can accurately predict a circular rod piece and the like in an ocean structure located in an area near a free surface, and is particularly suitable for wave force estimation of a cylindrical structure horizontally arranged in an extreme wave environment under the action of transient strong nonlinear waves. The wave load calculation method for the near-free-surface cylindrical structure in the marine environment specifically comprises the steps that a wave force calculation model is established based on a classical Morrison equation, a focused wave field is constructed, focused waves are constructed by superposing a plurality of regular wave components, and the focused wave field is constructed by superposing a plurality of regular wave components; compared with the prior art, the method has the advantages that the applicability is wider, broadband multi-component focused wave field modeling can be effectively processed, and the method is particularly suitable for being applied to engineering early-stage design and parameter sensitivity analysis.

Description

Technical Field

[0001] The present invention relates to the field of marine engineering technology, and specifically to a method for calculating wave loads on cylindrical structures near the free surface in marine environments, based on a modified Morrison equation that focuses on wave characteristics and can accurately predict the forces acting on circular rods in marine structures near the free surface. The method is particularly suitable for estimating wave forces on horizontally arranged cylindrical structures (such as cylindrical horizontal buoys, horizontal pipelines, and floating bridge foundations) under transient strong nonlinear waves in extreme wave environments, thereby improving the accuracy of structural force prediction and the safety of engineering design. Background Art

[0002] With the development of marine engineering, renewable energy, and underwater structure construction, a large number of horizontally arranged cylindrical structures are widely used in complex sea conditions. These structures are usually located near the free surface and are significantly disturbed by waves. In extreme wave conditions, such as focused waves, they exhibit strong nonlinear response characteristics, such as concentrated hydrodynamic forces and localized impacts. Traditional empirical models often have difficulty accurately characterizing these characteristics.

[0003] The Morrison equation is currently the most widely used model for estimating wave forces. Based on the local response to flow field velocity and acceleration, it characterizes wave forces through inertia and drag terms. Its form is simple and its physical meaning is clear. However, the traditional Morrison equation is mostly established for regular waves, solitary waves, or internal waves. Its applicability and accuracy are significantly limited for focused wave fields with strong dispersion and high local concentration. This is particularly evident when wave forces near the free surface are strongly asymmetric and experience sudden transient increases.

[0004] Although existing studies have attempted to introduce CFD data or high-order potential flow corrections into the Morrison equation to improve accuracy, there is a lack of universal modeling methods in engineering. In particular, when considering issues such as structural exposure, uneven wave propagation direction, and changes in the force integration area, there is no complete Morrison equation correction scheme that is suitable for focused wave environments. Summary of the Invention

[0005] In response to the shortcomings and deficiencies in the existing technology, the present invention proposes a wave load calculation method for near-free-surface cylindrical structures in marine environments by modifying the Morrison equation and introducing structural layered modeling and wave group decomposition mechanisms to effectively capture the horizontal and vertical hydrodynamic responses of the cylindrical structure under the action of irregular waves.

[0006] The present invention is achieved by the following measures: A method for calculating wave loads on a near-free-surface cylindrical structure in a marine environment is characterized in that a wave force calculation model is established based on the classical Morrison equation as follows: (1), (2), Among them, the horizontal wave force F x Consists of two parts: horizontal inertia force F ix , horizontal resistance F dx ; Vertical wave force F z It consists of three parts: vertical inertia force F iz , vertical resistance F dz and still water buoyancy F b , where ρ is the water density, in kg / m³; the inertia coefficient C m and drag coefficient C d They are C m =2.0 and C d =1.2, V ( t ) represents the submerged volume of the cylinder at time t, V 0 is the initial submerged volume under static water conditions; A x ( t ) and A z ( t ) represents the instantaneous horizontal projection area and vertical projection area of ​​the cylinder under the action of waves at time t, u x ( t ) and u z ( t ) are the horizontal and vertical velocities of the flow field at the cylindrical position, ∂ u x / ∂ t and ∂ u x / ∂ t are the horizontal and vertical accelerations at the cylinder position, u x ( t ) 、 u z ( t ) 、∂ u x / ∂ t and ∂ u x / ∂ t Calculated by linear wave theory.

[0007] The present invention also includes constructing a focused wave field, wherein the focused wave is constructed by superimposing multiple regular wave components to form an idealized free liquid surface profile. x and time t The free surface lift at is expressed as: (3), in, Respectively represent the amplitude, angular frequency, wave number and initial phase of the nth wave component, so that it can be focused at the preset focus position. x f and focus moments t f A high-amplitude wave group is generated at point ( x 0 , z 0 ) represents the global coordinate of the cylinder center. To calculate the horizontal wave force, the cylinder is discretized along the vertical direction as N z The unit in the horizontal direction of each layer is dz =2 R / N z , the center height of each layer is recorded as z j , accordingly, to calculate the vertical wave force, the cylinder is discretized in the horizontal direction as N x vertical slices, each slice is dx =2 R / N x , the bottom height of each slice is recorded as z j ,In order to simplify the geometric processing in the integration process, the middle layer except the arc segments at both ends is geometrically approximated as a trapezoid.

[0008] The present invention calculates the horizontal wave force and the vertical wave force in the focused wave field. To calculate the horizontal wave force, the cylinder is discretized along the vertical z direction into N z The unit in the horizontal direction of the layer, the center coordinates of each layer z j The calculation is as follows: (4), In formula (4), z0 is the global vertical coordinate of the cylinder center, R is the cylinder radius, and j is the number of each layer. For each layer unit, if its center is below the instantaneous free liquid surface, that is, z j < η ( t ), it is considered to be in a submerged state. In the focused wave field, the horizontal velocity and acceleration of each layer are at point ( x 0 , z j ) and is obtained by superimposing all linear wave components. Specifically, the velocity u x ( x 0 , z j , t ) and acceleration ∂u x / ∂t ( x 0 , z j , t ) is expressed as follows: (5), (6), Structure at the moment t The total horizontal wave force is obtained by summing the contributions of all submerged layer elements and is expressed as: (7), in, A j represents the horizontal projection area of ​​the jth layer. Depending on the position of the layer in the cylinder, its area is estimated using different approximate methods: For the trapezoidal area in the middle, its horizontal projection area is approximately ; For the arc segment area of ​​the edge, the area is: ; To determine each layer at time t Is it in a flooded state? A logic switch function δ( z j < η ( t )): (8), The cross-sectional area of ​​each horizontal slice A j and bottom elevation z j It is obtained by geometric decomposition of the function, which is consistent with the method used in the horizontal force calculation.

[0009] In the calculation process of vertical wave force, the inertia term depends on the submerged area of ​​each layer. Given the instantaneous free liquid surface height η ( t ), the flooding depth of the jth layer is , only when h j ( t )>0, the layer is considered to be in a submerged state and is included in the summation of vertical wave forces; Submergence ratio ratioj ( t ) represents the extent to which the jth layer is covered by waves, and the estimation formula is: (9), in, z j represents the elevation of the bottom of layer j, ensuring the flooding ratio ratioj(t) Always restricted to the interval [0,1]; In the focused wave field, the vertical velocity and acceleration are calculated at each sampling point ( x j , z 0 ) by adding all the linear wave components, which is as follows: (10), (11), Obtain the total vertical wave force F z ( t ) ， Total vertical wave force F z ( t ) is in time t The force acting on the submerged horizontal cylinder at any moment is obtained by summing the vertical hydrodynamic forces of all layers covered by water, including inertia and resistance terms, and the final expression is: (12), product ratioj ( t ) ⋅A j Indicates that the jth layer is at time t The instantaneous flooded area, function δ ( h j ( t )>0) is a logical indicator function defined as: (13).

[0010] Compared with the existing technology, the present invention has a wider applicability, can effectively handle broadband multi-component focused wave field modeling, and can adapt to the calculation requirements of structures under arbitrary segmented exposure or burial depth fluctuations. The model has a clear form and can be implemented through programming, which is suitable for rapid prediction in engineering. Compared with CFD simulation, the present invention has higher computational efficiency and stronger scalability, and is particularly suitable for applications in early engineering design and parameter sensitivity analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Attachment Figure 1 Schematic diagram of cylindrical wave action in an embodiment of the present invention.

[0012] Attachment Figure 2 Schematic diagram of cylindrical layering process in an embodiment of the present invention, wherein Figure 2 (a) is a schematic diagram of horizontal layered processing, and (b) is a schematic diagram of vertical layered processing.

[0013] Attachment Figure 3 is the submerged depth in the embodiment of the present invention S = 0.1 m, where (a) is the wave force calculation method and the test results. x (b) Comparison of wave forces in the z direction; (c) Comparison of wave forces in the z direction.

[0014] Attachment Figure 4 is the submerged depth in the embodiment of the present invention S = 0.0 m, where (a) is the wave force calculation method and the test results. x (b) Comparison of wave forces in the z direction; (c) Comparison of wave forces in the z direction. DETAILED DESCRIPTION

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0016] This paper proposes a method for obtaining wave force loads on cylindrical structures near the water surface in a marine environment. Based on the traditional Morrison equation, a wave force calculation model for dynamic evaluation of submerged state is established as follows: (1), (2), The submerged volume and projected area of ​​a two-dimensional cylinder are calculated separately for each layer; The value of the focused wave at a specified location and time is based on the theoretical solution of the focused wave in an empty tank; the dynamic evaluation is performed by the wave surface and the cylindrical coordinates after stratification, and the vertical wave force is calculated by the submergence ratio. ratioj ( t ) represents the extent to which the jth layer is covered by waves, and the total wave force is determined by the judgment function δ (h j ( t )>0) for control.

[0017] Taking a two-dimensional cylinder as an example, the radius of the cylinder is 0.05 meters, and the submergence depths of 0.1 meters and 0.0 meters are selected for calculation and verification. The incident wave frequency is f p =0.6Hz, the amplitude is A max =0.043 meters and A max =0.104 m, focus position x f =13 meters, focusing time t f = 25 seconds, and substituting into formulas 5, 6, 10, and 11, we can calculate the velocity and acceleration of the focused wave at the specified position; Furthermore, the above wave velocity and acceleration can be substituted into formula (7) and formula (12) to calculate the horizontal wave force and vertical wave force, where the water density is taken as ρ= 1000kg / m³, acceleration due to gravity g =9.81m / s²; In order to verify the accuracy of the method of the present invention, the calculation results of this method are compared with the test results of wave action with the same frequency and amplitude. In order to make the comparison more general, only the wave force after dimensionless processing is compared. The comparison results are as follows: Figure 3 、 Figure 4 ,in, Figure 3 and Figure 4 (a) in x Directional wave force comparison; (b) z Comparison of directional wave forces; it can be seen that the wave force calculation method of the present invention is in good agreement with the test results and can accurately calculate the wave force acting on the cylindrical structure.

[0018] Compared with the existing technology, the present invention has the following advantages: (1) It is applicable to broadband multi-component focused wave field modeling; (2) It is adaptable to the exposure of arbitrary sections of the structure and the fluctuation of the buried depth; (3) The model form is clear and programmable, which is suitable for rapid engineering prediction; (4) Compared with CFD simulation, it has higher efficiency and scalability, and is suitable for early engineering design and parameter sensitivity analysis applications.

Claims

1. A method for calculating wave loads on a near-free-surface cylindrical structure in a marine environment, characterized in that: The wave force calculation model based on the classic Morrison equation is as follows: （1）， （2）， Among them, the horizontal wave force F x Consists of two parts: horizontal inertia force F ix , horizontal resistance F dx ; Vertical wave force F z It consists of three parts: vertical inertia force F iz , vertical resistance F dz and still water buoyancy F b , ρ is the water density, in kg / m³; the inertia coefficient C m and drag coefficient C d They are C m =2.0 and C d =1.2, V ( t ) represents the submerged volume of the cylinder at time t, V 0 is the initial submerged volume under static water conditions; A x ( t ) and A z ( t ) represents the instantaneous horizontal projection area and vertical projection area of ​​the cylinder under the action of waves at time t, u x ( t ) and u z ( t ) are the horizontal and vertical velocities of the flow field at the cylindrical position, ∂ u x / ∂ t and ∂ u x / ∂ t are the horizontal and vertical accelerations at the cylinder position, u x ( t ) 、 u z ( t ) 、∂ u x / ∂ t and ∂ u x / ∂ t Calculated by linear wave theory.

2. The method for calculating wave loads on a near-free-surface cylindrical structure in a marine environment according to claim 1, characterized in that: It also includes constructing a focused wave field, wherein the focused wave is constructed by superimposing multiple regular wave components to form an idealized free liquid surface profile at a certain position. x and time t The free surface lift at is expressed as: （3）， in, Respectively represent the amplitude, angular frequency, wave number and initial phase of the nth wave component, so that it can be focused at the preset focus position. x f and focus moments t f A high-amplitude wave group is generated at point( x 0 , z 0 ) represents the global coordinate of the cylinder center. To calculate the horizontal wave force, the cylinder is discretized along the vertical direction as N z The unit in the horizontal direction of each layer is dz =2 R / N z , the center height of each layer is recorded as z j , accordingly, to calculate the vertical wave force, the cylinder is discretized in the horizontal direction as N x vertical slices, each slice is dx =2 R / N x , the bottom height of each slice is recorded as z j ,In order to simplify the geometric processing in the integration process, the middle layer except the arc segments at both ends is geometrically approximated as a trapezoid.

3. The method for calculating wave loads on a near-free-surface cylindrical structure in a marine environment according to claim 2, characterized in that: The horizontal wave force and vertical wave force are calculated in the focused wave field. To calculate the horizontal wave force, the cylinder is discretized along the vertical z direction as N z The unit in the horizontal direction of the layer, the center coordinates of each layer z j The calculation is as follows: （4）， In formula (4), z0 is the global vertical coordinate of the center of the cylinder, R is the radius of the cylinder, and j is the number of each layer; For each layer unit, if its center is below the instantaneous free liquid surface, that is, z j < η ( t ), it is considered to be in a submerged state. In the focused wave field, the horizontal velocity and acceleration of each layer are at point ( x 0 , z j ) and is obtained by superimposing all linear wave components. Specifically, the velocity u x ( x 0 , z j , t ) and acceleration ∂u x / ∂t ( x 0 , z j , t ) is expressed as follows: （5）， （6）， Structure at the moment t The total horizontal wave force is obtained by summing the contributions of all submerged layer elements and is expressed as: （7）， in, A j represents the horizontal projection area of ​​the jth layer. Depending on the position of the layer in the cylinder, its area is estimated using different approximate methods: For the trapezoidal area in the middle, its horizontal projection area is approximately ; For the arc segment area of ​​the edge, the area is: ; To determine each layer at time t Is it in a flooded state? A logic switch function δ( z j <η ( t )): （8）， The cross-sectional area of ​​each horizontal slice A j and bottom elevation z j It is obtained by geometric decomposition of the function, in the same way as used in the horizontal force calculation.

4. The method for calculating wave loads on a near-free-surface cylindrical structure in a marine environment according to claim 3, characterized in that: In the calculation of vertical wave forces, the inertia term depends on the submerged area of ​​each layer, given the instantaneous free surface height η ( t ), the flooding depth of the jth layer is , only when h j ( t )>0, the layer is considered to be in a submerged state and is included in the summation of vertical wave forces; Submergence ratio ratioj ( t ) represents the extent to which the jth layer is covered by waves, and the estimation formula is: （9）， in, z j represents the elevation of the bottom of layer j, ensuring the flooding ratio ratioj ( t ) is always limited to the interval [0,1]; In the focused wave field, the vertical velocity and acceleration are calculated at each sampling point ( x j , z 0 ) by adding all the linear wave components, which is as follows: （10）， （11）， Obtain the total vertical wave force F z ( t ) ， Total vertical wave force F z ( t ) is in time t The force acting on the submerged horizontal cylinder at any moment is obtained by summing the vertical hydrodynamic forces of all layers covered by water, including inertia and resistance terms, and the final expression is: （12）， product ratioj ( t ) ⋅A j Indicates that the jth layer is at time t The instantaneous flooded area, function δ ( h j ( t )>0) is a logical indicator function defined as: （13）。

Images