Method for calculating wave load of near-free surface cylindrical structure in marine environment

Abstract

The application relates to the technical field of ocean engineering, in particular to a wave load calculation method for a near-free-surface cylindrical structure in a marine environment, which can accurately predict a circular rod and the like in a marine structure located in a region near a free surface, is especially suitable for wave force estimation of a horizontally arranged cylindrical structure under the action of transient strong nonlinear waves in an extreme wave environment, and improves the precision of structure stress prediction and the safety of engineering design, and specifically comprises the following steps: a wave force calculation model is established based on a classic Morison equation, a focused wave field is constructed, wherein the focused wave is constructed by superimposing multiple regular wave components, so that an idealized free liquid surface profile is formed, and then horizontal wave force and vertical wave force are respectively calculated in the focused wave field, compared with the prior art, the method has wider applicability, can effectively process wide-frequency multi-component focused wave field modeling, and is especially suitable for application of engineering early design and parameter sensitivity analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ocean engineering, in particular to a wave load calculation method for a near-free-surface cylindrical structure in a marine environment, which can accurately predict the circular rod and the like in the ocean structure located in the vicinity of the free surface based on the correction of the Morison equation according to the characteristics of focused waves, and is especially suitable for the wave force estimation of the horizontally arranged cylindrical structure (such as cylindrical horizontal buoy, horizontal pipeline, floating bridge foundation and the like) under the action of transient strong nonlinear waves in the extreme wave environment, thereby improving the accuracy of structural stress prediction and the safety of engineering design. BACKGROUND

[0002] With the development of ocean 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, especially in the case of focused waves and the like, which exhibit strong nonlinear, hydrodynamic concentration and local impact response characteristics, and traditional empirical models often cannot accurately depict them.

[0003] The Morison equation is the most widely used wave force estimation model at present, which is based on the local response of the flow field velocity and acceleration, and represents the wave force through the inertia term and the resistance term, and has the advantages of simple form and clear physical meaning. However, the traditional Morison equation is mostly established under the condition of regular waves, solitary waves or internal waves, and its applicability and accuracy have great limitations for focused wave fields with strong frequency dispersion and high local concentration, especially when the wave force near the free surface is strongly asymmetric and transiently steep.

[0004] Although existing researches have tried to introduce CFD data or high-order potential flow correction into the Morison equation to improve the accuracy, there is still a lack of a general modeling method in engineering, especially when considering the structure exposure, the non-uniformity of wave propagation direction, and the change of force integration area, and there is no complete Morison equation correction scheme suitable for focused wave environment. SUMMARY

[0005] The present application proposes a wave load calculation method for a near-free-surface cylindrical structure in a marine environment by modifying the Morison equation and introducing structure layered modeling and wave group decomposition mechanism, which can effectively capture the horizontal and vertical hydrodynamic response of the cylindrical structure under the action of irregular waves.

[0006] The present application achieves the following measures:

[0007] A wave load calculation method for a near-free-surface cylindrical structure in a marine environment, characterized in that a wave force calculation model is established based on the classical Morison equation as follows:

[0008] (1),

[0009] (2),

[0010] where the horizontal wave force F x is composed of two parts: the horizontal inertial force F ix and the horizontal drag force F dx ; the vertical wave force F z is composed of three parts: the vertical inertial force F iz , the vertical drag force F dz and the hydrostatic buoyancy force F b , where p is the water density with unit of kg / m3; the inertial coefficient C m and the drag coefficient C d are C m = 2.0 and C d = 1.2, respectively, V ( t ) denotes the submerged volume of the cylinder at time t, V 0 is the initial submerged volume under the static water condition; A x ( t ) and A z ( t ) denote the instantaneous horizontal and vertical projected areas of the cylinder under the wave action at time t, u x ( t ) and u z ( t ) are the horizontal and vertical velocities of the flow field at the position of the cylinder, u x ∂ t x / ∂ t are the horizontal and vertical accelerations at the position of the cylinder, u x ( t ), u z ( t ), u x ∂ t x and ∂​u x / ∂ t Calculated by linear wave theory.

[0011] The application also includes constructing a focused wave field, wherein the focused wave is constructed by superimposing multiple regular wave components, thereby forming an idealized free surface profile, the free surface elevation at a position x and time t is expressed as:

[0012] (3),

[0013] wherein, respectively represent the amplitude, angular frequency, wave number and initial phase of the nth wave component, thereby being able to generate a high-amplitude wave group at a preset focusing position x f and focusing time t f ; point x 0 , z 0 represents the global coordinates of the cylinder center, for calculating the horizontal wave force, the cylinder is discretized into N z horizontal units, and the height of each layer is dz =2 R / N z , and the center height of each layer is recorded as z j , and correspondingly, for calculating the vertical wave force, the cylinder is discretized into N x vertical slices, and the width of each slice is dx =2 R / N x , and the bottom height of each slice is recorded as z j , for simplifying the geometric processing in the integration process, the middle layer is approximately trapezoidal in geometry, except for the two end arc segments.

[0014] The application calculates the horizontal wave force and the vertical wave force in the focused wave field, wherein, for calculating the horizontal wave force, the cylinder is discretized into N z horizontal units along the vertical z direction, and the center coordinates of each layer are z j calculated as follows:

[0015] (4),

[0016] In formula (4), z0 is the global vertical coordinate of the cylinder center, R is the cylinder radius, and j is the layer number; for each layer unit, if the center is below the instantaneous free surface, i.e. z j η t , it is considered to be in the submerged state. In the focused wave field, the horizontal velocity and acceleration of each layer are calculated at point x 0 z j , and are obtained by superimposing all linear wave components. Specifically, the velocity u x x 0 z j t and the acceleration ∂u x / ∂t x 0 z j t are expressed as follows:

[0017] (5),

[0018] (6),

[0019] The total horizontal wave force on the structure at time t is obtained by summing the contributions of all layer units in the submerged state, and its expression is:

[0020] (7),

[0021] where A j represents the horizontal projection area of the jth layer, which is estimated in different ways according to the different positions of the layer in the cylinder:

[0022] For the middle trapezoidal region, its horizontal projection area is approximately ; for the edge circular arc segment region, the area is: ;

[0023] To determine whether each layer is in the submerged state at time t , a logical switch function δ( z j η t ​​​​​​​​​​​)):

[0024] (8),

[0025] cross-sectional area of each horizontal slice A j and bottom elevation z j Obtained by geometric decomposition function, the method is consistent with the way adopted in horizontal force calculation.

[0026] In the calculation process of vertical wave force, the inertial term depends on the submerged area of each layer, given the instantaneous free surface height η ( t ), the submerged depth of the jth layer is , only when h j ( t )>0, the layer is considered to be in a submerged state, and is counted in the summation of vertical wave force;

[0027] The submerged ratio ratioj ( t ) represents the degree of the jth layer covered by the wave, and the estimation formula is:

[0028] (9),

[0029] wherein, z j represents the elevation of the bottom of the jth layer, which ensures that the submerged ratio ratioj(t) is always limited between the interval [0, 1];

[0030] In the focused wave field, the vertical velocity and acceleration are calculated at the sampling point x j , z 0 of each layer, which is to superimpose all linear wave components, and the specific form is as follows:

[0031] (10),

[0032] (11),

[0033] Obtain the total vertical wave force F z ( t ) ， The total vertical wave force F z ( t ) is at time tThe force acting on the submerged horizontal cylinder at all times is obtained by summing the vertical hydrodynamic forces over all water-covered layers, including inertial and drag terms. The final expression is:

[0034] (12)

[0035] product ratioj ( t ) ⋅A j Indicates the time of the j-th layer t The instantaneous flooded area, function δ ( h j ( t `)>0)` is a logical indicator function, defined as:

[0036] (13).

[0037] Compared with existing technologies, this invention has a wider range of applicability, can effectively handle broadband multi-component focused wave field modeling, and can adapt to the calculation needs of structures exposed in arbitrary segments or with burial depth fluctuations. The model has a clear form and can be implemented through programming, making it suitable for rapid prediction in engineering. Compared with CFD simulation, this invention has higher computational efficiency and stronger scalability, and is particularly suitable for applications in early engineering design and parameter sensitivity analysis. Attached Figure Description

[0038] Appendix Figure 1 This is a schematic diagram of the cylindrical wave effect in an embodiment of the present invention.

[0039] Appendix Figure 2 This is a schematic diagram of the cylindrical layering process in an embodiment of the present invention, wherein... Figure 2 (a) is a schematic diagram of horizontal layering, and (b) is a schematic diagram of vertical layering.

[0040] Appendix Figure 3 The flooding depth in this embodiment of the invention S Comparison of wave force calculation method and experimental results at a wave height of 0.1 m, where (a) is... x (a) Comparison of wave forces in the z-direction; (b) Comparison of wave forces in the z-direction.

[0041] Appendix Figure 4 The flooding depth in this embodiment of the invention S Comparison of wave force calculation method and experimental results at 0.0 m, where (a) is... x (a) Comparison of wave forces in the z-direction; (b) Comparison of wave forces in the z-direction. Detailed Implementation

[0042] The application will be further described below with reference to the accompanying drawings and examples.

[0043] The application provides a method for obtaining wave force load of a near-water cylindrical structure in a marine environment, and the method is based on a traditional Morison equation and establishes a dynamic evaluation submerged state wave force calculation model as follows:

[0044] (1),

[0045] (2),

[0046] The calculation method of the submerged volume and the projected area of the two-dimensional cylinder is separately calculated in layers;

[0047] The value of the focused wave at the specified position and time is based on a theoretical solution of the focused wave in an empty water tank; the wave surface and the layered cylinder coordinates are dynamically evaluated, and the submerged ratio is used in the vertical wave force calculation ratioj ( t ) represents the degree of the jth layer covered by the wave, and the total wave force is controlled by judging the function δ ( h j ( t )>0.

[0048] Taking a two-dimensional cylinder as an example, the radius of the cylinder is 0.05 meters, and the submerged depths of 0.1 meters and 0.0 meters are selected for calculation and verification, the incident wave frequency is f p =0.6 Hz, the wave amplitude is A max =0.043 meters and A max =0.104 meters, the focusing position x f =13 meters, and the focusing time t f =25 seconds, the wave speed and acceleration of the focused wave at the specified position are calculated by substituting the formulae 5, 6, 10 and 11;

[0049] Further, the wave speed and acceleration can be brought into the formula (7) and the formula (12) to calculate the horizontal wave force and the vertical wave force, wherein the water density is taken as p = 0.5 1000 kg / m³, and the gravity acceleration g =9.81 m / s².

[0050] Further, in order to verify the accuracy of the method of the application, the calculation results of the method are compared with the test results of the wave with the same frequency and wave amplitude, in order to make the comparison more general, only the dimensionless wave forces are compared, and the comparison results are as follows Figure 3 ,Figure 4 wherein, Figure 3 and Figure 4 (a) in x directional wave force contrast; (b) is z directional wave force contrast; it can be seen that the wave force calculation method of the application is in good agreement with the test results, and the wave force acting on the cylindrical structure can be accurately calculated.

[0051] Compared with the prior art, the application has the following advantages: (1) applicable to wideband multi-component focused wave field modeling; (2) adaptive to any segmented outcrop, buried depth fluctuation; (3) clear model form, programmable implementation, suitable for engineering rapid prediction; (4) compared with CFD simulation, higher efficiency and scalability, 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 by, The wave force calculation model is established based on the classical Morison equation as follows: （1）， （2）， where, horizontal wave force F x consists of two parts: horizontal inertial force F ix , horizontal drag force F dx ; vertical wave force F z consists of three parts: vertical inertial force F iz , vertical drag force F dz , and hydrostatic buoyancy force F b , ρ where, ρ is the water density, with unit of kg / m³; inertial coefficient C m and drag coefficient C d are C m = 2.0 and C d = 1.2, respectively; V ( t ) is the submerged volume of the cylinder at time t, V 0 is the initial submerged volume under the static water condition; A x ( t ) and A z ( t ) are the instantaneous horizontal and vertical projected areas of the cylinder under the wave action at time t, u x ( t ) and u z ( t ) are the horizontal and vertical velocities of the flow field at the position of the cylinder, u x / ∂ t and u Z / ∂ t are the horizontal and vertical accelerations at the position of the cylinder, u x ( t ), u z ( t ), u x / ∂ t and u Z / ∂ t are calculated by the linear wave theory. Also included is constructing a focused wave field, wherein the focused wave is constructed by superimposing a plurality of regular wave components to form an idealized free surface profile, the free surface elevation at a certain position x and time t is expressed as: （3）， wherein, respectively represent the amplitude, angular frequency, wave number and initial phase of the n-th wave component, so that a wave group with a high amplitude can be generated at the preset focusing position x f and the focusing moment t f at the focusing position Point x 0 , z 0 represents the global coordinate of the cylinder center, for the calculation of the horizontal wave force, the cylinder is discretized into N z elements in the horizontal direction, and the height of each layer is dz =2 R / N z , R is the radius of the cylinder, and the center height of each layer is recorded as z j , and correspondingly, for the calculation of the vertical wave force, the cylinder is discretized into N x vertical slices, and the width of each slice is dx =2 R / N x , and the bottom height of each slice is recorded as z j , to simplify the geometric processing in the integration process, the middle layer is trapezoidal in geometry, except for the arc segments at both ends The horizontal wave force and the vertical wave force are calculated in the focused wave field, respectively, wherein, for calculating the horizontal wave force, the cylinder is discretized into N z The horizontal direction of the layer unit, the center coordinates of each layer z j The calculation is as follows: （4）， In equation (4), z0 is the global vertical coordinate of the cylinder center, and j is the number of each layer. For each layer cell, if its center is below the instantaneous free surface, i.e. 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 calculated at points x 0 , z j , and obtained by superimposing all linear wave components. Specifically, the velocity u x x 0 , z j , t and the acceleration ∂u x / ∂t x 0 z j t are expressed as follows:​​​​​ （5）， （6）， The structure at time t The total horizontal wave force experienced is obtained by summing the contributions from all the layer elements that are in the flooded state, which is expressed as: （7）， where A j denotes the horizontal projected area of the jth layer, which is estimated in different ways depending on the position of the layer in the cylinder: For the middle trapezoidal region, the horizontal projection area is ; for the edge circular arc segment region, the area is: ; To determine whether each layer is submerged at time t, a logical switch function δ( t is introduced: z j <η ( t )) : （8）， Cross-sectional area of each horizontal slice A j And bottom elevation z j Obtained by geometric decomposition functions, consistent with the way adopted in the calculation of horizontal forces; In the calculation of the vertical wave force, the inertia term depends on the submerged area of each layer, given the instantaneous free surface height η ( t ), the submerged depth of the jth layer is , this layer is considered to be in a submerged state and is counted in the summation of the vertical wave force only when h j ( t )>0. submergence ratio ratio j ( t ) represents the degree to which the jth layer is covered by the wave, and is estimated by the formula: （9）， wherein, z j denotes the elevation of the bottom of the jth layer, ensuring the submergence ratio ratio j ( t ) is always limited between the interval [0,1]; In the focused wavefield, the vertical velocity and acceleration are computed at the sample points (x, z) of each layer by superimposing all the linear wave components, in the form x j , z 0 ) （10）， （11）， Total vertical wave force F z ( t ) ， Total vertical wave force F z ( t ) is the force acting on a submerged horizontal cylinder at time t t, obtained by summing the vertical hydrodynamic forces of all the water-covered layers, including the inertia and drag terms, and is finally expressed as: （12）， Product ratioj ( t ) ⋅A j denotes the instantaneous inundated area of the jth layer at time t , the function δ ( h j ( t )>0) is a logical indicator function defined as: （13）。

Images