CN117252123B - Full-coupling CFD-mooring nonlinear analysis method for floating structure - Google Patents

Abstract

The invention relates to the technical field of predicting large-amplitude motion response of a mooring floating structure, in particular to a fully-coupled CFD-mooring nonlinear analysis method of the floating structure, which comprises the following steps: s1, constructing a nonlinear finite element mooring dynamics module: the dynamic mooring analysis method based on the slender rod theory is realized in the form of six-degree-of-freedom rigid body constraint in OpenFOAM, and is compiled into a single module in the form of a dynamic library so as to be conveniently coupled with different fluid solvers; s2, coupling the mooring module with the overlapped grid CFD solver: the two-phase flow solver overInterDyMFoam with the OpenFOAM overlapped grid function is combined with the open source wave generation library waves2Foam and is coupled with a developed dynamic mooring analysis method based on the slender rod theory, and a new wave-structure-interaction coupling solver is established and named overWaveDyMFoam. The invention can realize accurate simulation and prediction of the obvious motion response of the floating structure under severe sea conditions.

Description

A fully coupled CFD-mooring nonlinear analysis method for floating structures

Technical Field

The invention relates to the technical field of predicting large motion response of a moored floating structure, and in particular to a fully coupled CFD-mooring nonlinear analysis method for a floating structure.

Background technique

The dynamic response of floating structures in marine environments has always been a hot topic in the field of marine engineering. The impact of wave loads affects their stability and service life. In addition, the violent movement of floating structures may cause system failures, while equipment maintenance and component replacement will greatly increase operating costs. Therefore, it is crucial to accurately predict the motion response of floating structures in waves.

At present, the coupled analysis of the motion response of floating structures under wave loads mainly adopts potential flow and computational fluid dynamics (CFD) numerical methods. Among them, the numerical method based on potential flow theory has long been used to study the dynamic response of floating structures in waves due to its high computational efficiency. However, these methods cannot accurately take into account the viscosity and nonlinear effects. With the rapid development of computer technology, many CFD methods based on the nonlinear Navier-Stokes equations have been developed. These methods are more accurate and can provide rich flow field information because they inherently consider the viscosity of the fluid. Therefore, CFD methods are increasingly widely used in the study of the motion response of floating systems. The mooring system plays a vital role in the stability and safety of floating platforms. If the mooring cable is suddenly broken by extreme wind and wave loads during its service life, it will cause the floating platform to move violently, seriously threatening the operational stability and safety of the floating platform. Therefore, it is crucial to accurately predict the dynamic response of the mooring cable. Commonly used mooring analysis models can be divided into three types: static, quasi-static and dynamic. By considering the dynamic effects in the equations of motion of the mooring line, the dynamic analysis model can predict the mooring loads more accurately than the static and quasi-static models, and thus predict the response of the floating structure. In recent years, some researchers have tried to combine the dynamic mooring analysis model with the CFD solver for the response prediction of moored floating structures.

However, the coupled analysis models of moored floating structures established and verified by researchers are mostly for structural responses under normal sea conditions. However, when a moored floating structure is in use, when resonance occurs or it is subjected to extreme wave loads, a large nonlinear motion response will be stimulated. In such dangerous sea conditions, the survivability study of moored floating structures involves strong nonlinear mooring dynamics and significant structural translational and rotational responses, requiring a high-fidelity coupled CFD-mooring model. In order to adapt to the response of floating structures in CFD simulations, the computational grid must be updated. The most commonly used grid update technology is the dynamic grid deformation method, which uses a grid deformation method and does not change the grid topology, but when it involves large structural responses, it may lead to a decrease in grid quality or even simulation failure. However, the overlapping grid technology can overcome this difficulty, and then accurately simulate and predict the large motion response of floating structures.

Summary of the invention

In order to solve the shortcomings of the existing technology, the present invention proposes a fully coupled CFD-mooring nonlinear analysis method for floating structures for the first time, targeting the large motion of moored floating structures. First, a nonlinear finite element mooring dynamic analysis method based on the slender rod theory with large axial extension is developed under the open source CFD framework OpenFOAM, and it is creatively combined with a two-phase flow RANS solver based on overlapping grids and a rigid body six-degree-of-freedom motion solver to achieve accurate simulation and prediction of the significant motion response of floating structures under severe sea conditions.

The technical solution of the present invention is:

The present invention provides a fully coupled CFD-mooring nonlinear analysis method for a floating structure, the method comprising the following steps:

S1. Constructing nonlinear finite element mooring dynamics module: The dynamic mooring analysis method based on slender rod theory is implemented in OpenFOAM in the form of six-degree-of-freedom rigid body constraints and compiled into a separate module in the form of a dynamic library to facilitate coupling with different fluid solvers;

S2. Coupling of mooring module with overlapping grid CFD solver: The two-phase flow solver overInterDyMFoam with OpenFOAM overlapping grid function is combined with the open source wave generation library waves2Foam, and coupled with the developed dynamic mooring analysis method based on slender rod theory to establish a new wave-structure-interaction coupling solver named overWaveDyMFoam.

Furthermore, step S1 further includes:

The motion equation of a slender rod model that allows large axial stretching is established in a three-dimensional rectangular coordinate system. The center line of the deformed rod is represented by a space curve r(s, t). The space curve r(s, t) is a function of the arc length s and the time t. In the space curve, t, n, and b are unit vectors in the tangent, normal, and binormal directions, respectively. e _x , e _y , and e _z are unit vectors in the x, y, and z axes, respectively.

The equations of motion and constraint equations for a slender rod that allows large axial tension are defined as:

In equations (1) and (2), the dot above the variable represents the derivative with respect to time t, and the prime sign represents the derivative with respect to arc length s; q is the external force acting on the mooring cable; M is the mass matrix; is the Lagrange multiplier; represents the maximum elongation, which is different from the small deformation ε;

The expressions of the above variables are:

M＝ρ _t A _t I+ρ _f A _f C _Mn (1+ε)N+ρ _f A _f C _Mt (1+ε)T (3)

Where I is the identity matrix;

T and N are transformation matrices;

The transformation matrices T and N are defined as:

N＝I-T

The external forces q acting on the mooring line include gravity, hydrostatic pressure and hydrodynamic force; the hydrodynamic force part includes inertial force, drag force and Froude-Krylov force of seawater, among which the drag force is calculated by Morrison equation;

The expression of external force q is:

Where, C _Mn , C _Mt , C _Dn , and C _Dt represent the normal additional mass coefficient, tangential additional mass coefficient, normal drag coefficient, and tangential drag coefficient, respectively;

ρ _f is the density of seawater;

D _f is the equivalent diameter of the mooring rope;

A _f is the cross-sectional area of the mooring line calculated from D _f ;

ρ _t is the density of the mooring cable material;

A _t is the structural cross-sectional area of the mooring line;

v _f is the flow velocity;

a _f is the flow acceleration;

g is the acceleration due to gravity;

The Galerkin numerical analysis method is used to solve the governing equations of the slender rod theory (i.e., the equation of motion of equation (1) and the constraint equation of equation (2)). The Hermite cubic shape function a _i (ξ) and quadratic shape function p _i (ξ) are introduced to discretize the mooring line into a series of finite elements, which are used to describe the displacement vectors r, Load parameters such as q and M;

Cubic Hermite shape function a _i (ξ):

Quadratic Hermite shape function p _i (ξ):

Where ξ is a dimensionless quantity ξ = s/L, L is the unit length before deformation;

Therefore, the unit displacement vector r and the Lagrange multiplier in the coordinate system The approximate expressions of the distributed load q and mass matrix M are:

Among them, n = 1 to 3, i = 1 to 4 and m = 1 to 3, the main parameters described by the shape function in the equation are:

Where u refers to the unit node displacement;

In order to spatially discretize the motion control equation of the mooring system, the terms on the right side of the motion equation of equation (1) are moved to the left side to obtain:

The Galerkin numerical analysis method is used to simplify the equation of motion of formula (14) into a set of ordinary differential equations: First, both ends of the equation are multiplied by the shape function a _i (ξ) and integrated over [0, L]:

Second, simplify the above formula (15) and integrate it by parts to get:

The right side of equation (16) is the force at the unit endpoint, which can be expressed by the generalized force _fi . The expression of the generalized force _fi is:

Substituting equations (8), (6) and (7) into equation (16), we can obtain a set of ordinary differential equations for the slender rod element:

Where i, k = 1 to 4, j, l, m, n = 1 to 3;

Similarly, substituting equations (8), (6) and (7) into equation (2), we can get the expression of the constraint equation:

Where i, k = 1 to 4, j, l, m, n = 1 to 3;

Where _fin is the generalized internal force at both ends of the unit. Due to the continuity of the structure, the boundary conditions are:

L ⁽ⁿ⁾ and L ⁽ⁿ⁺¹⁾ are the lengths of elements (n) and (n+1) respectively. If there is no concentrated mass, force or moment at the element nodes, the generalized internal forces between two adjacent elements cancel each other out:

For the first and last element, the boundary conditions of the structure should be applied.

Furthermore, step S2 further includes:

After initializing the mooring system using the static analysis method, the position and velocity of the floating structure are transferred from the six-degree-of-freedom motion solver to the fairlead;

The dynamic mooring analysis solver updates the status of the mooring lines, including tension and node positions;

The mooring forces are applied to the floating structure and fed back into the 6-DOF motion solver to update the motion response of the floating structure.

The beneficial effects achieved by the present invention are:

First, the present invention develops a nonlinear finite element mooring dynamic solution module based on the slender rod theory under the OpenFOAM framework. The significant advantages of this mooring dynamic solution method are that it can handle large axial deformation of the mooring, can consider the nonlinear effect of the mooring, and can converge quickly during calculation. It is the first to solve the problem of large axial deformation of the mooring in extreme environments that conventional mooring dynamic solution methods cannot handle.

Second, the present invention for the first time couples the mooring system dynamic solution module independently developed and solved using the finite element method with the overlapping grid, and integrates the waves2Foam wave-making function to form a two-phase flow solver that can accurately simulate the large-scale motion response of the moored floating body under the action of extreme waves, solving the problem of divergence in the calculation of large-scale motion response of moored floating structures under extreme sea conditions, as well as the problem of large axial deformation of the mooring.

Third, the solver developed in the present invention can accurately predict the motion response of the interaction between the moored floating structure and the extreme waves and the loads acting on the mooring cables and the floating structure, which is beneficial to the study of the survivability of moored floating structures under severe sea conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a slender rod model in a three-dimensional rectangular coordinate system of the present invention.

FIG. 2 is a flow chart of the coupling solver overWaveDyMFoam of the present invention.

FIG. 3 is a comparative RAO of the experimental and simulated surge of the present invention.

Figure 4 is a comparison of the energy spectra of motion responses in irregular waves.

Detailed ways

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

As shown in FIGS. 1 to 4 , the present invention provides a fully coupled CFD-mooring nonlinear analysis method for a floating structure, comprising the following steps:

Step 1: Establishment of nonlinear finite element mooring dynamics module:

The dynamic mooring analysis method based on the slender rod theory is implemented in OpenFOAM in the form of six-degree-of-freedom rigid body constraints and compiled into a separate module in the form of a dynamic library to facilitate coupling with different fluid solvers.

Step 2: Mooring module coupled with overlay grid CFD solver:

The two-phase flow solver overInterDyMFoam with OpenFOAM overlapping grid function is combined with the open source wave generation library waves2Foam, which uses relaxation zone technology to effectively avoid wave reflection at the outlet boundary. It is coupled with the developed dynamic mooring analysis method based on slender rod theory to establish a new wave-structure-interaction coupling solver named overWaveDyMFoam.

Step 1 specifically also includes:

The equation of motion of a slender rod model that allows large axial stretching is established in a three-dimensional rectangular coordinate system. As shown in Figure 1, the center line of the deformed rod can be represented by a space curve r(s, t), which is a function of the arc length s and time t. In Figure 1, t, n, and b are unit vectors in the tangent direction, normal direction, and binormal direction, respectively, and e _x , e _y , and e _z are unit vectors on the x, y, and z axes, respectively.

The equations of motion and constraint equations for a slender rod that allows large axial tension are defined as:

In equations (1) and (2), the dot above the variable represents the derivative with respect to time t, and the prime sign represents the derivative with respect to arc length s; q is the external force acting on the mooring cable; M is the mass matrix; is the Lagrange multiplier; Represents the maximum elongation, which is different from the small deformation ε.

The expressions of the above variables are:

M＝ρ _t A _t I+ρ _f A _f C _Mn (1+ε)N+ρ _f A _f C _Mt (1+ε)T (3)

Where I is the identity matrix;

T and N are transformation matrices;

The transformation matrices T and N are defined as:

N＝I-T

The external forces q acting on the mooring line include gravity, hydrostatic pressure and hydrodynamic force; the hydrodynamic force part includes inertial force, drag force and Froude-Krylov force of seawater, among which the drag force is calculated by Morrison equation;

The expression of external force q is:

Where, C _Mn , C _Mt , C _Dn , and C _Dt represent the normal additional mass coefficient, tangential additional mass coefficient, normal drag coefficient, and tangential drag coefficient, respectively;

ρ _f is the density of seawater;

D _f is the equivalent diameter of the mooring rope;

A _f is the cross-sectional area of the mooring line calculated from D _f ;

ρ _t is the density of the mooring cable material;

A _t is the structural cross-sectional area of the mooring line;

v _f is the flow velocity;

a _f is the flow acceleration;

g is the acceleration due to gravity;

The Galerkin numerical analysis method is used to solve the governing equations of the slender rod theory (i.e., the equation of motion of equation (1) and the constraint equation of equation (2)). The Hermite cubic shape function a _i (ξ) and quadratic shape function _pi (ξ) are introduced to discretize the mooring line into a series of finite elements, which are used to describe the displacement vectors r, Load parameters such as q and M;

Cubic Hermite shape function a _i (ξ):

Quadratic Hermite shape function p _i (ξ):

Where ξ is a dimensionless quantity ξ = s/L, L is the unit length before deformation;

Therefore, the unit displacement vector r and the Lagrange multiplier in the coordinate system The approximate expressions of the distributed load q and mass matrix M are:

Where n = 1 to 3, i = 1 to 4 and m = 1 to 3, the main parameters described by the shape function in the equation are:

Where u refers to the unit node displacement;

In order to spatially discretize the motion control equation of the mooring system, the terms on the right side of the motion equation of equation (1) are moved to the left side to obtain:

The Galerkin numerical analysis method is used to simplify the motion equation of equation (14) into a set of ordinary differential equations:

(1) Multiply both ends of the equation by the shape function a _i (ξ) and integrate over [0,L]:

(2) Simplifying the above formula (15) and integrating by parts, we can obtain:

The right side of equation (16) is the force at the unit endpoint, which can be expressed by the generalized force _fi . The expression of the generalized force _fi is:

Substituting equations (8), (6) and (7) into equation (16), we can obtain a set of ordinary differential equations for the slender rod element:

Where i, k = 1 to 4, j, k, m, n = 1 to 3;

Similarly, substituting equations (8), (6) and (7) into equation (2), we can get the expression of the constraint equation:

Where i, k = 1 to 4, j, l, m, n = 1 to 3;

Where _fin is the generalized internal force at both ends of the unit. Due to the continuity of the structure, the boundary conditions are:

L ⁽ⁿ⁾ and L ⁽ⁿ⁺¹⁾ are the lengths of elements (n) and (n+1) respectively. If there is no concentrated mass, force or moment at the element nodes, the generalized internal forces between two adjacent elements cancel each other out:

For the first and last unit, the boundary conditions of the structure should be applied; if a mooring line in three-dimensional space has N units, there should be 15+8(N-1) independent equations and coefficients in the calculation module.

The advantage of step 1 is that a nonlinear finite element mooring dynamic solution module was developed in OpenFOAM for the first time, which makes up for the defect that the native OpenFOAM does not have a mooring solution module and provides a basis for the subsequent establishment of a moored floating structure coupling model.

Step 2 specifically also includes:

First, the coupling between the mooring module and the floating structure is specifically implemented as follows:

(1) After initializing the mooring system using the static analysis method, the position and velocity of the floating structure are transferred from the six-degree-of-freedom motion solver to the fairlead;

(2) Then, the dynamic mooring analysis solver updates the state of the mooring line, including tension and node positions;

(3) Subsequently, the mooring force is applied to the floating structure and returned to the six-degree-of-freedom motion solver to update the motion response of the floating structure.

Secondly, the moored floating structure coupling model is experimentally verified:

The free decay response of the platform can reflect the natural period under a certain degree of freedom. In the present invention, experimental and numerical free decay tests were carried out on the three most important degrees of freedom of the moored floating structure, namely, sway, heave and pitch. The relative differences between the numerically predicted natural periods of the three degrees of freedom and the experimental results are all less than 3%. In addition, the interaction between regular waves and semi-submersible platforms is simulated, and the numerical predictions are compared with the experimental data. Computational domain: The length of the wave generation/propagation/relaxation zone is equal to 1/0.5/2 times the wavelength, respectively. By comparing the predicted and measured motion responses of the moored platform under five different working conditions, it is found that the moored platform exhibits periodic or quasi-steady-state equal-amplitude motion responses under the action of regular waves, and the three responses of the platform obtained by the coupling model are in good agreement with the experimental measurement results.

The results of model experimental verification show that the relative differences between the numerical prediction results and the experimental results are less than 5%.

Finally, the verified moored floating structure coupling model is used to predict the large-amplitude motion response of the moored floating structure:

The JONSWAP spectrum was used to generate irregular waves, and the shape parameter was set to γ = 3.3. The significant wave height was 0.12m and the spectrum peak period was 1.6s. In order to ensure that the numerical model can accurately generate irregular waves, a single wave simulation without considering any structure was first performed. The simulation time was 160s or 100 times the spectrum peak period, and a wave meter was set 0.5m away from the wave generation area. The results show that the effective wave height obtained by numerical simulation is comparable to the experimental measurement results.

Then, the energy spectrum analysis was performed to compare the numerical and experimental data in the frequency domain. The energy spectrum calculated from the measured wave surface elevation is bell-shaped, with most of the energy distributed near 0.625 Hz or near the specified spectral peak period of 1.6 s, indicating that the simulated energy spectrum is in good agreement with the experimental energy spectrum. Several important characteristic parameters defining the spectrum were further extracted, including significant wave height, spectral peak period and spectral peak. Comparison of the experimental data with the numerical data showed that the difference in spectral characteristic parameters between the measured and simulated values was less than 3%. The total energy of the irregular wave was obtained by integrating the energy spectrum density in the frequency range of 0 to 1.4 Hz, and the difference between the experiment and the simulation did not exceed 5%. Therefore, the current numerical wave tank can generate the required irregular waves with good accuracy.

The verified irregular waves were applied to moored floating structures, and their simulated motion responses were compared with experimental data. In order to eliminate the influence of the initial disturbance, the response data in the time range of 40-200s were selected for FFT analysis, and two different spectral peaks appeared in the predicted energy spectrum and the experimental energy spectrum. One peak corresponds to the incident wave frequency (0.625Hz), and the other is close to the natural frequency of the three-degree-of-freedom semi-submersible platform. The resonant energy of the longitudinal and pitching motions is significantly greater than the energy distributed near the wave (main) frequency, indicating that the significant response amplitude appears at the resonant frequency and should not be underestimated. For the vertical motion, the energy distribution of the two peaks is similar.

Several important characteristic parameters of longitudinal sway, vertical sway and pitching motion were extracted, including significant response height, spectral peak period and spectral peak. The maximum error of the characteristic parameters of the experimental response and numerical response of the three degrees of freedom is no more than 6.4%. At the same time, the energy spectrum density of the three degrees of freedom is integrated in the frequency range of 0 to 1.4 Hz to obtain the total energy of each degree of freedom. The difference between the experiment and the simulation does not exceed 8%. The peak energy of the resonance spectrum of longitudinal sway, vertical sway and pitching motion does not differ by more than 10% compared with the experiment, which is acceptable considering the many factors that affect the measurement accuracy in the experiment.

For a floating structure moored with a catenary, the stiffness of the mooring system plays a key role in its surge response. When the floating structure undergoes large horizontal motions, the mooring line may be stretched to a certain extent, making the mooring stiffness nonlinear. The resonant frequencies of heave and pitch motions are around 0.46 Hz and 0.19 Hz, respectively, corresponding to their natural frequencies, and the motions in these two directions are less affected by the mooring system.

The prediction results show that the established coupled numerical model can not only accurately capture the wave frequency response of the moored floating structure under surge, heave and pitch motion, but also capture the resonant response of the moored floating structure in three degrees of freedom.

The advantages of step 2 are: for the first time, a two-phase flow coupling solver overWaveDyMFoam using overlapping grid technology was developed in OpenFOAM, and coupled with the nonlinear finite element mooring dynamics solution module developed in step 1; the accuracy of the developed numerical coupling method is significantly improved compared with the traditional method (the traditional method generally has an acceptable error of less than 15%); the established coupled numerical model solves the problem of divergence in the calculation of large motions of moored floating structures by the traditional dynamic grid CFD method. At the same time, the verification results fully demonstrate the ability of the full nonlinear coupling method to predict the motion response of moored floating structures in a strongly nonlinear marine environment.

Model Information

A specific example model is used for illustration. The scaling ratio of the semi-submersible model in this example is set to λ=1:100, and the main parameters are shown in Table 1. The water depth of the wave tank is 1m, the model draft is 0.251m, and the center of mass of the model is 0.013m from the water surface. The origin of the coordinate system is defined at the center of the model on the free surface. The mooring system of the semi-submersible model consists of 8 catenaries, each of which consists of a steel chain and a spring. The mooring parameters are shown in Table 2. The mooring lines are arranged symmetrically, and the angles between the two mooring lines at each corner and the x-axis are 37.5° and 60° respectively.

Table 1 Main scale parameters of semi-submersible model

Table 2 Mooring parameters

First, according to the coordinate system shown in Figure 1, a finite element mooring dynamic solution module is developed in OpenFOAM according to step 1; secondly, according to the flowchart of Figure 2, step 2 is completed: developing a moored floating structure coupling solver; then the effectiveness and accuracy of the moored floating structure coupling numerical model are verified; finally, the large amplitude motion response of the moored floating structure is predicted, demonstrating the ability of the full nonlinear coupling method of the present invention to predict the motion response of the moored floating structure in a strong nonlinear marine environment. This example is only an implementation example of the present invention and does not represent the final implementation scheme of the present invention.

Calculation results

The response amplitude operator (RAO) can better reflect the motion characteristics of the interaction between the moored floating body and the wave than the motion response. RAO is calculated from the time history curve by normalizing the response amplitude (from maximum to minimum) with the incident wave height. Figure 3 shows the variation of the pitch RAO with the incident wave period. It can be seen from the figure that with the increase of the wave period, the surge RAO increases almost linearly. The simulation results are very close to the model experimental results, with a relative difference of less than 5%, indicating that the solution accuracy of the coupling analysis method proposed in the present invention is higher than that of the traditional method (the traditional method generally has an acceptable error of less than 15%).

The resonant energy of the pitch motion in Figure 4 is significantly greater than the energy distributed near the wave (main) frequency, indicating that a significant response amplitude occurs at the resonant frequency and should not be underestimated. In order to further investigate the resonant frequency and spectral peak of the pitch motion in Figure 4, the incident wave frequency and the corresponding natural frequency are also plotted. The predicted and measured resonant frequencies of the pitch motion in Figure 4 are both close to 0.09 Hz, while the natural frequency of the surge is close to 0.139 Hz. The reason for this frequency mismatch may be the nonlinear effect of the mooring line. For a floating body moored with a catenary, the stiffness of the mooring system plays a key role in its longitudinal surge response. When the floating structure undergoes large horizontal motions, the mooring line may be stretched to a certain extent, making the mooring stiffness nonlinear.

It can be seen that the calculation results of the fully coupled-moored nonlinear analysis method for moored floating structures proposed in the present invention are better than those of traditional coupled analysis methods and have higher accuracy. At the same time, the proposed coupling method can not only accurately capture the wave frequency response of the moored floating structure under longitudinal sway, heave and pitch motion, but also capture the resonant response of the moored floating structure under three degrees of freedom, solving the problem of divergence of the traditional dynamic grid CFD method for large-scale motion calculation of moored floating structures. At the same time, the nonlinear finite element mooring solution module developed by the present invention can well capture the nonlinear effect of mooring and its influence on the pitch motion of floating structures, significantly improving the accuracy of numerical simulation. The above calculation results fully demonstrate the effectiveness of the fully coupled analysis method for moored floating structures proposed in the present invention, as well as the engineering significance of the study on the survivability of moored floating structures under severe sea conditions.

The above-described embodiments of the present invention do not constitute a limitation on the protection scope of the present invention. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims (1)

1. A fully coupled CFD-mooring nonlinear analysis method for a floating structure, characterized in that the method comprises the following steps: S1. Constructing nonlinear finite element mooring dynamics module: The dynamic mooring analysis method based on slender rod theory is implemented in OpenFOAM in the form of six-degree-of-freedom rigid body constraints and compiled into a separate module in the form of a dynamic library to facilitate coupling with different fluid solvers; S2. Coupling of mooring module with overlay grid CFD solver: The two-phase flow solver overInterDyMFoam with OpenFOAM overlay grid function is combined with the open source wave generation library waves2Foam, and coupled with the developed dynamic mooring analysis method based on slender rod theory to establish a new wave-structure-interaction coupling solver named overWaveDyMFoam; Step S1 also includes: The equation of motion of a slender rod model that allows large axial stretching is established in a three-dimensional rectangular coordinate system. The center line of the deformed rod is represented by a space curve r(s, t), which is a function of arc length s and time t. The equations of motion and constraint equations for a slender rod that allows large axial tension are defined as: In equations (1) and (2), the dot above the variable represents the derivative with respect to time t, and the prime sign represents the derivative with respect to arc length s; q is the external force acting on the mooring cable; M is the mass matrix; is the Lagrange multiplier; represents the maximum elongation, which is different from the small deformation ε; The expressions of the above variables are: M＝ρ _t A _t I+ρ _f A _f C _Mn (1+ε)N+ρ _f A _f C _Mt (1+ε)T (3) Where I is the identity matrix; T and N are transformation matrices; The transformation matrices T and N are defined as: N＝I-T The external forces q acting on the mooring line include gravity, hydrostatic pressure and hydrodynamic force; the hydrodynamic force part includes inertial force, drag force and Froude-Krylov force of seawater, among which the drag force is calculated by Morrison equation; The expression of external force q is: Where, C _Mn , C _Mt , C _Dn , and C _Dt represent the normal additional mass coefficient, tangential additional mass coefficient, normal drag coefficient, and tangential drag coefficient, respectively; ρ _f is the density of seawater; D _f is the equivalent diameter of the mooring rope; A _f is the cross-sectional area of the mooring line calculated from D _f ; ρ _t is the density of the mooring cable material; A _t is the structural cross-sectional area of the mooring line; v _f is the flow velocity; a _f is the flow acceleration; g is the acceleration due to gravity; The Galerkin numerical analysis method is used to solve the governing equations of the slender rod theory, namely the equation of motion of equation (1) and the constraint equation of equation (2). The Hermite cubic shape function a _i (ξ) and quadratic shape function _pi (ξ) are introduced to discretize the mooring line into a series of finite elements to describe the displacement vectors r, q and M load parameters; Cubic Hermite shape function a _i (ξ): Quadratic Hermite shape function p _i (ξ): Where ξ is a dimensionless quantity ξ = s/L, L is the unit length before deformation; Therefore, the displacement vector r and the Lagrange multiplier in the coordinate system are The approximate expressions of the external force q acting on the mooring cable and the mass matrix M are: Among them, n = 1 to 3, i = 1 to 4 and m = 1 to 3, the main parameters described by the shape function in the equation are: Where u refers to the unit node displacement; In order to spatially discretize the motion control equation of the mooring system, the terms on the right side of the motion equation of equation (1) are moved to the left side to obtain: The Galerkin numerical analysis method is used to simplify the equation of motion of formula (14) into a set of ordinary differential equations: First, both ends of the equation are multiplied by the shape function a _i (ξ) and integrated over [0, L]: Second, simplify the above formula (15) and integrate it by parts to get: The right side of equation (16) is the force at the unit endpoint, which is expressed by the generalized force _fi . The expression of the generalized force _fi is: Substituting equations (8), (6) and (7) into equation (16), we can obtain a set of ordinary differential equations for the slender rod element: Where i, k = 1 to 4, j, l, m, n = 1 to 3; Similarly, substituting equations (8), (6) and (7) into equation (2), we can get the expression of the constraint equation: Where i, k = 1 to 4, j, k, m, n = 1 to 3; Where _fin is the generalized internal force at both ends of the unit. Due to the continuity of the structure, the boundary conditions are: L ⁽ⁿ⁾ and L ⁽ⁿ⁺¹⁾ are the lengths of elements (n) and (n+1) respectively. If there is no concentrated mass, force or moment at the element nodes, the generalized internal forces between two adjacent elements cancel each other out: For the first and last element, the boundary conditions of the structure should be applied; Step S2 also includes: After initializing the mooring system using the static analysis method, the position and velocity of the floating structure are transferred from the six-degree-of-freedom motion solver to the fairlead; The dynamic mooring analysis solver updates the status of the mooring lines, including tension and node positions; The mooring forces are applied to the floating structure and fed back into the 6-DOF motion solver to update the motion response of the floating structure.