A free-surface in-harbor coupled hydrodynamic ship motion prediction method and a prediction system

Abstract

The application discloses a free-surface port in-coupling hydrodynamic ship motion prediction method and a prediction system, which decomposes a flow field of a free-surface port into an internal sub-domain and an external sub-domain of the free-surface port, gives a velocity potential equation and boundary conditions of the flow field based on a linear potential flow theory, and applies matching conditions on the boundary surfaces of the internal and external sub-domains; and boundary integral equations are obtained; the boundaries of the internal and external sub-domains are discretized into units, and the velocity potential is solved; the pressure is obtained through Bernoulli equation according to the obtained velocity potential; the hydrodynamic force acting on the ship body is calculated by integrating the pressure; and the six-degree-of-freedom motion equation of the ship is obtained, so that the ship motion is predicted. Based on the flow field decomposition method, in combination with the Green function method, the hydrodynamic force problem under the coupling action of the ship, the wave and the free-surface port is considered, and the prediction of the hydrodynamic force and the motion of the ship in the free-surface port can achieve high numerical precision in the whole calculation frequency range.

Description

Technical Field

[0001] This invention relates to ship motion prediction, specifically to a ship motion prediction method and system coupled with hydrodynamics in a free-plane harbor. Background Technology

[0002] The movement of ships in free-face ports is far more complex than their movement in open waters because, in addition to the ship's natural frequency, the port itself also possesses a natural frequency. This can cause ships floating in free-face ports to exhibit significant motion responses. This can affect cargo loading and unloading efficiency and even pose a threat to the safety of the port or the ship. Therefore, accurately predicting the motion behavior of ships in free-face ports is of great importance.

[0003] Numerous scholars have conducted extensive research on wave motion within free-face ports, primarily falling into two categories: one focusing on the interaction between waves and the free-face port, and the other employing domain decomposition methods to study the motion of objects floating within the free-face port. Furthermore, the problem of ship-wave interaction within a free-face port mainly focuses on providing accurate solutions for freely floating vessels. However, research on the coupling hydrodynamics between waves and vessels within the port, the mechanisms of vessel motion, and the characteristics of water wave scattering is relatively scarce. Many hydrodynamic phenomena and mechanisms remain unrevealed, and the research also suffers from high computational complexity. Therefore, a simpler domain decomposition method is needed to address the interaction between waves, the free-face port, and freely floating vessels within the port.

[0004] Currently, the single-watershed method based on Green's function Rankine source and free surface Green's function, which is widely used, is a relatively traditional three-dimensional ship motion prediction method. However, its application scenarios are relatively limited. It is not suitable for the analysis of ship hydrodynamic characteristics in large free surface ports, and it cannot effectively predict ship motion in ports. Summary of the Invention

[0005] Purpose of the invention: To address the above problems, this invention provides a method and system for predicting ship motion coupled with hydrodynamics in a free-face harbor to ensure the safety of ships operating within the free-face harbor.

[0006] Technical Solution: To solve the above problems, this invention employs a ship motion prediction method coupled with hydrodynamics in a free-plane harbor, comprising the following steps:

[0007] (1) The watershed of the free-faced port is decomposed into an internal sub-domain and an external sub-domain. Based on the linear potential flow theory, the velocity potential Laplace control equation and boundary conditions that satisfy the entire watershed of the free-faced port are given. Matching conditions are applied on the boundary surfaces of the internal and external sub-domains of the free-faced port to ensure the continuity of velocity and pressure.

[0008] (2) Using Green's formula and Green's function, the boundary integral equations of the inner subdomain and the outer subdomain of the free surface port are constructed respectively;

[0009] (3) Discretize the boundaries of the inner subdomain and the outer subdomain of the free surface port into elements, and solve the velocity potential on all elements at the same time. Obtain the pressure through the linearized Bernoulli equation based on the obtained velocity potential.

[0010] (4) Based on the obtained pressure, the hydrodynamic forces acting on the hull are calculated by integrating the pressure on the wet surface of the hull.

[0011] (5) The six-degree-of-freedom equations of motion of the ship are obtained based on the hydrodynamic forces acting on the hull, and the ship motion is predicted based on the obtained ship motion equations.

[0012] Furthermore, in step (1): the velocity potential of the entire free-faced harbor basin is:

[0013]

[0014] Where Re is the real part; i is the imaginary unit; ω is the original frequency; (x,y,z) is a coordinate system with the origin at a point on the interface between the free surface port subdomain and the free surface port external subdomain; t is time; (x′,y′,z′) is a coordinate system with the origin at the ship's center; It is the scattering potential; The radiation potential is represented by j = 1, 2, and 3, which correspond to the translational motion of the hull in the x′, y′, and z′ directions, respectively; and j = 4, 5, and 6, which correspond to the rotational motion of the hull around the x′, y′, and z′ directions, respectively. Let J be the complex amplitude of the j-th mode of the ship's motion;

[0015] The velocity potential satisfies Laplace's equations throughout the entire free-face port basin:

[0016] .

[0017] Furthermore, the boundary conditions in step (1) include:

[0018] Boundary conditions S of free surface F for:

[0019]

[0020] Where ν=ω 2 / g, where g is the acceleration due to gravity;

[0021] Boundary condition S at the bottom of the fluid B for:

[0022] .

[0023] Furthermore, within the free-faced port subdomain, the port wall's impenetrability condition S... W for:

[0024]

[0025] Where n represents the outward unit normal vector of the surface;

[0026] Boundary conditions S on the hull surface H Represented as:

[0027]

[0028] in Let be the unit normal vector of the hull surface.

[0029] (n1,n2,n3)=(n x′ ,n y′ ,n z′ )and(n4,n5,n6)=(x′,y′,z′)×(n x′ ,n y′ ,n z′ );

[0030] In the subdomain outside the free surface harbor, the boundary condition S of the free surface is satisfied. F Boundary conditions S of the coastal wall y To extend along the y-axis to infinity, it is represented as:

[0031]

[0032] At this point, the velocity potential also satisfies the radiation condition S at infinity. R , is represented as:

[0033]

[0034] Among them, R 2 =x 2 +y 2 k0 is a pure real root of the following dispersion equation:

[0035] k0tanh(k0h)=v

[0036] Where h is the water depth. The interface S between the inner subdomain and the outer subdomain of the free-faced port. a At x=0, the continuity condition that guarantees the continuity of velocity and pressure is:

[0037]

[0038] in, The radiation potential of the subdomain within the free-faced port; The radiation potential of the free-faced port's external subdomain.

[0039] Furthermore, within the free-face subdomain, the Laplace equation in the watershed is transformed into a boundary integral equation using the Green's function, i.e.:

[0040]

[0041] Where, α (1) (p) is the solid angle at the midpoint p(x,y,z) in the subdomain inside the free surface harbor, integrated at the source point q(ξ,η,ζ), G (1) (p,q) is the Green function in the subdomain inside the free surface harbor.

[0042] Furthermore, in the free-faced port subdomain, the boundary integral equation obtained from the Green's function is:

[0043]

[0044] Where, α (2) (p a ) is the midpoint p in the free-face port external subdomain. a The fixed angle coefficient, field point p a Located at interface S a superior.

[0045] Furthermore, the boundary integral equation of the subdomain within the free-face harbor, discretized into elements, is as follows:

[0046]

[0047] Where N is the total number of units, S m It is the surface of unit m;

[0048] The boundary integral equation of the outer subdomain of the free-face harbor, after being discretized into elements, is as follows:

[0049]

[0050] Where, N a It represents the total number of units.

[0051] Furthermore, the hydrodynamic forces acting on the hull in step (4) include wave excitation force and radiation force; the wave excitation force f j The calculation formula is:

[0052]

[0053] Where ρ0 represents the fluid density;

[0054] Radiative force can be written as the additional mass Ajk and damping coefficient B jk The formula is:

[0055]

[0056] Furthermore, the three-dimensional complex amplitude η of ship motion j The following can be obtained from the six-degree-of-freedom equations of motion of the floating body:

[0057]

[0058] Where k represents the k-th degree of freedom, M jk C is the quality coefficient. jk This is the static water restoring force coefficient.

[0059] This invention also employs a ship motion prediction system, comprising a first mechanism unit, a second mechanism unit, and a prediction mechanism unit. The first mechanism unit decomposes the free-faced harbor's watershed into an internal free-faced harbor sub-domain and an external free-faced harbor sub-domain. Based on linear potential flow theory, it derives the velocity potential Laplace governing equation and boundary conditions satisfying the entire free-faced harbor watershed, and applies matching conditions on the boundary surfaces of the internal and external free-faced harbor sub-domains to ensure the continuity of velocity and pressure. Furthermore, using Green's formula and Green's function, it constructs boundary integral equations for the internal and external free-faced harbor sub-domains, respectively. The second mechanism unit discretizes the boundaries of the internal and external free-faced harbor sub-domains into elements, simultaneously solving for the velocity potential on all elements. Based on the obtained velocity potential, it obtains the pressure using a linearized Bernoulli equation. Based on the obtained pressure, it calculates the hydrodynamic forces acting on the hull by integrating the pressure on the wetted surface of the hull, and obtains the ship's six-degree-of-freedom motion equations based on the hydrodynamic forces acting on the hull. The prediction mechanism unit predicts the ship's motion based on the obtained ship motion equations.

[0060] Beneficial effects: Compared with existing technologies, the significant advantage of this invention is that it is based on the watershed decomposition method and combined with the Green's function method, considering the hydrodynamic problem under the coupled effects of ships, waves, and free-face ports. It can achieve high numerical accuracy in predicting the hydrodynamics and motion of ships within free-face ports across the entire computational frequency range. At the same time, the use of this prediction method also greatly improves computational efficiency. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating the ship motion prediction method of this invention.

[0062] Figure 2 This is a structural block diagram of the ship motion prediction system in this invention. Detailed Implementation

[0063] Example 1

[0064] like Figure 1 As shown in this embodiment, a method for predicting ship motion in a free-face harbor coupled with hydrodynamics firstly decomposes the flow field into two subdomains: the free-face harbor interior and the free-face harbor exterior. Using Green's function, boundary integral equations are constructed for the internal and external waters of the free-face harbor, respectively. Matching conditions are applied at their interface to ensure the continuity of velocity and pressure. The influence of the coastline is eliminated, thus establishing an approximately effective solution program for the coupled interaction between the ship, waves, and the free-face harbor. This program can numerically solve for the ship's added mass, damping coefficient, and wave excitation force. Specifically, the method includes the following steps:

[0065] (1) Based on linear potential flow theory, the Laplace governing equation and boundary conditions for the velocity potential of the entire free-face port are given, and matching conditions are applied on the boundary surfaces of the subdomains inside and outside the free-face port to ensure the continuity of velocity and pressure. The linearized potential flow theory assumes that the fluid is inviscid, incompressible, and homogeneous, and that the fluid motion is non-rotational. When the amplitude and wavelength of the wave motion and ship motion are smaller than the ship size, the total velocity potential Φ is written as:

[0066]

[0067] Where Re is the real part; i is the imaginary unit; ω is the original frequency; the x-axis points to the open water and is perpendicular to the y-axis, the y-axis is along the interface between the two subdomains, the z-axis is vertically upward, the x′-axis is along the ship's length, the y′-axis is along the ship's crossbeam, and the z′-axis is vertically upward. It is the scattering potential. η represents the radiation potential; j = 1, 2, 3 correspond to the translational motion of the hull in the x′, y′, z′ directions, respectively; j = 4, 5, 6 correspond to the rotational motion of the hull around the x′, y′, z′ directions, respectively. j Let be the complex amplitude of the j-th mode of the ship's motion.

[0068] This method is for solving boundary value problems, where mass conservation requires the velocity potential to satisfy Laplace's equations throughout the fluid:

[0069]

[0070] All boundary conditions within this flow field are as follows:

[0071] Boundary conditions S of free surface F It can be represented as:

[0072]

[0073] Where ν=ω 2 / g, where g is the acceleration due to gravity.

[0074] Condition S at the bottom of the fluid B for:

[0075]

[0076] In the inner subdomain, the impenetrability condition S of the harbor wall W for:

[0077]

[0078] Boundary conditions S on the hull surface H It can be represented as:

[0079]

[0080] in Represents the outward unit normal vector of the surface, and

[0081] (n1,n2,n3)=(n x′ ,n y′ ,n z′ )and(n4,n5,n6)=(x′,y′,z′)×(n x′ ,n y′ ,n z′ (7)

[0082] In the external domain, the same free surface boundary conditions as in equation (3) should be satisfied. Coast wall S y In the case where the y-axis extends to infinity, it can be written as:

[0083]

[0084] At this point, the velocity potential should also satisfy the condition at infinity S. R Radiation conditions on:

[0085]

[0086] To ensure the outward propagation of the wave, R 2 =x 2 +y 2 k0 and k0 are the pure real roots of the following dispersion equation:

[0087] k0tanh(k0h)=v (10)

[0088] h represents the water depth. Regarding the diffraction problem, where... This ensures that the incident wave originates from the outer subdomain Ω2 of the free-plane harbor. At the interface S between the inner and outer domains... a At x=0, a continuity condition is applied to ensure the continuity of velocity and pressure:

[0089]

[0090] The superscripts 1 and 2 indicate the inside and outside of the port, respectively.

[0091] (2) Using Green's formula and Green's function, the boundary integral equations of the inner subdomain and the outer subdomain of the free surface port are constructed respectively;

[0092] In the subdomain inside the port, the Laplace equation in the fluid domain is transformed into an integral equation on the boundary using the Green's function:

[0093]

[0094] Where α (1) (p) is the fixed angle coefficient of the midpoint p(x,y,z) in the subdomain Ω1 within the free-face port. The Green's function G(p,q) used in the above equation can be chosen to satisfy all boundary conditions except for the quay wall, the wetted surface of the ship, and the interface within the free-face port, and can be written as:

[0095]

[0096] Where r 2 =(x-ξ) 2 +(y-η) 2 +(z-ζ) 2 J0(kR) represents the distance between the field point p and the source point q. J0(kR) refers to the zeroth-order Bessel function of the first kind.

[0097] In the external waters, the boundary integral equation obtained using the Green's function is:

[0098]

[0099] Where α (2) (p) is the solid angle emanating from midpoint p in Ω2. q and Symmetric about the plane x = 0. 'a' indicates that p lies in S. a Up. When j=0, the diffraction potential can be... Represented as:

[0100]

[0101] in

[0102]

[0103] (3) Discretize the boundaries of the inner subdomain and the outer subdomain of the free surface port into elements, and solve the velocity potential on all elements at the same time. Obtain the pressure through the linearized Bernoulli equation based on the obtained velocity potential.

[0104] Discretize the boundary equations into a finite number of elements, assuming the velocity potential in each element is constant. The boundary equations for the subdomain within the harbor can be discretized as follows:

[0105]

[0106] Where N is the total number of units, N H On the floating body, N W On the harbor wall, N B On a non-flat seabed, N a At the interface, S m It is the surface of unit m.

[0107] The boundary equation of the external water area can be discretized as:

[0108]

[0109] To solve for the velocity potential on all elements simultaneously, the above formulas are written in matrix form:

[0110]

[0111] The subscripts H and A represent the floating body and the interface, respectively, and W represents the harbor wall and the uneven seabed. Replace with By repeating the same process, the combined matrix equation can be derived as follows:

[0112]

[0113] (4) Based on the obtained pressure, the hydrodynamic force acting on the hull is calculated by integrating the pressure on the wetted surface of the hull; after obtaining the velocity potential, the pressure can be obtained through the linearized Bernoulli equation. Then, the hydrodynamic force acting on the hull can be calculated by integrating the pressure on its wetted surface. The total hydrodynamic force is divided into three parts, namely the wave excitation force f. j :

[0114]

[0115] The radiation force generated by the vibration and motion of a ship can be written as the additional mass A. jk and damping coefficient B jk ,Right now

[0116]

[0117] (5) After solving the ship hydrodynamic problem, the three-dimensional complex amplitude η of the ship's motion is obtained. j The following can be obtained from the six-degree-of-freedom equations of motion of the floating body:

[0118]

[0119] Where M jk C is the quality coefficient. jk This is the static water restoring force coefficient.

[0120] In the above method, the numerical results are dimensionless based on a combination of three basic parameters, namely the length L of the floating body. s The gravitational acceleration g and fluid density ρ0 were used as the basis for the calculation. Furthermore, the convergence of the mesh was verified by using a rectangular barge docked in the port, and the sway coefficient was consistent with previous studies.

[0121] (6) Based on the Fortran language, a direct numerical calculation program was developed for the problem of predicting the coupled hydrodynamics of waves and ships within a harbor and the prediction of ship motion. Numerical convergence and validity verification were then performed. Based on this, the influence of incident wave direction, ship position, and harbor topography on the hydrodynamic and motion characteristics of ships within the port can be studied.

[0122] Example 2

[0123] like Figure 2 As shown in this embodiment, a ship motion prediction system with coupled hydrodynamics in a free-face harbor includes a first mechanism unit, a second mechanism unit, and a prediction mechanism unit. The first mechanism unit is used to construct a boundary value problem solution model for the flow field inside and outside the free-face harbor based on linearized potential flow theory, and to establish a numerical solution algorithm based on Green's function. The second mechanism unit constructs a boundary element computational grid for the ship using the boundary element method, and solves the equations of motion for the ship in the harbor by solving each grid cell. The prediction mechanism unit uses the Fortran language to develop relevant numerical calculation programs on the Windows platform of the computer device to predict the coupled hydrodynamics and ship motion of waves in the free-face harbor, and the numerical results can be stored on the data storage device.

Claims

1. A method for predicting ship motion in a free-face harbor coupled with hydrodynamics, characterized in that, Includes the following steps: (1) The watershed of the free-faced port is decomposed into an internal sub-domain and an external sub-domain. Based on the linear potential flow theory, the velocity potential Laplace control equation and boundary conditions that satisfy the entire watershed of the free-faced port are given. Matching conditions are applied on the boundary surfaces of the internal and external sub-domains of the free-faced port to ensure the continuity of velocity and pressure. (2) Using Green's formula and Green's function, the boundary integral equations of the inner subdomain and the outer subdomain of the free surface port are constructed respectively; (3) Discretize the boundaries of the inner subdomain and the outer subdomain of the free surface port into elements, and solve the velocity potential on all elements at the same time. Obtain the pressure through the linearized Bernoulli equation based on the obtained velocity potential. (4) Based on the obtained pressure, the hydrodynamic forces acting on the hull are calculated by integrating the pressure on the wet surface of the hull; (5) Obtain the six-degree-of-freedom equations of motion of the ship based on the hydrodynamic forces acting on the hull, and predict the ship's motion based on the obtained equations of motion; The velocity potential of the entire basin in the free-faced harbor is: in, For real part; The imaginary unit; The original frequency; Let the coordinate system be a coordinate system with the origin at a point on the interface between the inner subdomain and the outer subdomain of the free port. For a specific moment; This is a coordinate system with the center of the ship as the origin; It is the scattering potential; Radiation potential; Corresponding to the hull Translational motion in three directions; Corresponding to the hull circumference Rotational motion in three directions; For the first time in ship motion Complex amplitude under modal conditions; The velocity potential satisfies Laplace's equations throughout the entire free-face port basin: The impenetrable condition of the port walls within the free-faced port subdomain. for: in, Represents the outward unit normal vector of the surface; Boundary conditions on the hull surface Represented as: in Let be the unit normal vector of the hull surface. ; In the subdomain outside the free surface harbor, the boundary conditions of the free surface are satisfied. Boundary conditions for coastal walls For along An axis extending to infinity is represented as: At this point, the velocity potential also satisfies the radiation condition at infinity. , is represented as: in, , These are the pure real roots of the following dispersion equation: in, For water depth; At the interface between the inner subdomain and the outer subdomain of the free port On At this point, the continuity condition for ensuring the continuity of velocity and pressure is: , , in, The radiation potential of the subdomain within the free-faced port; The radiation potential of the free-faced port's external subdomain.

2. The ship motion prediction method according to claim 1, characterized in that, The boundary conditions in step (1) include: Boundary conditions of free surfaces for: in, , It is gravitational acceleration; Boundary conditions at the bottom of the fluid for: 。 3. The ship motion prediction method according to claim 2, characterized in that, Within the free-face subdomain, the Laplace equation in the watershed is transformed into a boundary integral equation using the Green's function, i.e.: in, It is the midfield point of the sub-domain within the Free Port. The solid angle at the source point Integral It is a Green's function in the subdomain inside the free surface port.

4. The ship motion prediction method according to claim 3, characterized in that, In the outer subdomain of the free-face harbor, the boundary integral equation obtained from the Green's function is: in, It is the midfield point of the outer subdomain of the free port. The fixed angle coefficient, field point Located at the interface superior.

5. The ship motion prediction method according to claim 4, characterized in that, The boundary integral equation of the subdomain inside the free-face harbor, after being discretized into elements, is as follows: in, It is the total number of units. It is a unit Surface; The boundary integral equation of the outer subdomain of the free-face harbor, after being discretized into elements, is as follows: in, It represents the total number of units.

6. The ship motion prediction method according to claim 5, characterized in that, The hydrodynamic forces acting on the hull in step (4) include wave excitation force and radiation force; wave excitation force The calculation formula is: in, Indicates fluid density; Radiative force is written as additional mass and damping coefficient The formula is: , 。 7. The ship motion prediction method according to claim 6, characterized in that, Three-dimensional complex amplitude of ship motion The following can be obtained using the six-degree-of-freedom equations of motion for a floating body: in, Indicates the first One degree of freedom, For quality coefficient, The static water restoring force coefficient.

8. A forecasting system applying the ship motion forecasting method according to any one of claims 1 to 7, characterized in that, The system comprises a first mechanism unit, a second mechanism unit, and a forecast mechanism unit. The first mechanism unit decomposes the free-faced harbor's watershed into an internal free-faced harbor sub-domain and an external free-faced harbor sub-domain. Based on linear potential flow theory, it provides the Laplace governing equations and boundary conditions for the velocity potential of the entire free-faced harbor watershed. Matching conditions are applied to the boundary surfaces of the internal and external free-faced harbor sub-domains to ensure the continuity of velocity and pressure. Furthermore, using Green's formula and Green's function, boundary integral equations for the internal and external free-faced harbor sub-domains are constructed, respectively. The second mechanism unit discretizes the boundaries of the internal and external free-faced harbor sub-domains into elements and solves for the velocity potential on all elements. Based on the obtained velocity potential, the pressure is obtained through a linearized Bernoulli equation. Based on the obtained pressure, the hydrodynamic forces acting on the hull are calculated by integrating the pressure on the wetted surface of the hull. Based on the hydrodynamic forces acting on the hull, the six-degree-of-freedom motion equations of the ship are obtained. The forecasting unit is used to forecast the motion of a ship based on the obtained equations of motion.

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