A device and method for predicting the coupling hydrodynamic forces of a ship with ice and the motion of the ship

Abstract

The present application belongs to the field of ship hydrodynamics and motion prediction, and in particular to a device and method for predicting the hydrodynamics and motion of a ship coupled with ice, which first derives a Green function that satisfies the boundary conditions of the ice layer and the free surface, as well as all other conditions except the surface condition of the ship, and through the Green function, the differential equation of the velocity potential is converted into a boundary integral equation on the surface of the ship only, which introduces an extended surface at the waterline of the ship body to eliminate the influence of irregular wave frequencies; an asymptotic solution formula of the Green function is analytically derived, thereby establishing an approximate and effective solution program for the coupled interaction of the ship / wave / ice layer, and numerically calculating the results of the added mass, damping coefficient and wave exciting force of the ship body; through the method, the interaction mechanism of the water wave / ship / ice layer under different parameter characteristics can be deeply understood, and theoretical support is provided for the hydrodynamic problems, motion prediction and rational design of polar ships.

Description

Technical Field

[0001] This invention belongs to the field of ship hydrodynamics and motion prediction technology. Specifically, it is a device and method for predicting the hydrodynamics and motion of floating ice coupled with ships. Background Technology

[0002] The depletion of continental oil and natural gas resources has shifted attention to the Arctic and Antarctic regions. my country's existing resources are no longer sufficient to meet its development needs, while the polar regions contain abundant resources. Therefore, the exploration and development of the Arctic region's shared global resources are closely related to my country's economic construction, environmental changes, and future sustainable development. New transportation routes in the Arctic region also urgently need to be developed. Consequently, the study of the three-dimensional hydrodynamic problem of the coupling effect between floating ice and ships in wave fields has prompted our consideration.

[0003] Numerous domestic and international scholars have conducted research on the interaction between water waves and sea ice, primarily falling into two categories: one focusing on the changes and adjustments made by water waves propagating beneath sea ice, emphasizing water wave and flow field analysis; and the other on the changes in sea ice under the influence of waves, focusing on sea ice dynamics. Furthermore, the interaction between polar ships and sea ice mainly concentrates on ice resistance and maneuverability during ship-ice contact and icebreaking. However, research on the coupling hydrodynamics between floating ice and ships in wave fields, ship motion mechanisms, and water wave scattering characteristics is relatively scarce. Many hydrodynamic phenomena and mechanisms remain unrevealed. This fundamental research is a crucial and urgently needed area for the hydrodynamics of ships in ice-covered regions; therefore, in-depth discussion of ship hydrodynamics and water wave scattering characteristics under typical polar environments is necessary.

[0004] Currently, the commonly used Rankine source method and free-surface Green's function method are relatively traditional three-dimensional ship motion prediction methods, but their application scenarios are relatively limited. For example, the invention patent application number 201811236520.7, entitled "Ship Motion Prediction Method Based on Taylor Expansion Boundary Element Method," is not applicable to the analysis of ship hydrodynamic characteristics in ice-covered areas and cannot achieve ship motion prediction in ice-covered areas. Therefore, it is necessary to propose a method and device for coupling hydrodynamics and ship motion prediction between floating ice and ships in wave fields to ensure the safety of ships navigating in polar regions. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention discloses a device and method for predicting the coupled hydrodynamics of floating ice and ships, as well as ship motion. The fluid flow in this invention is based on linearized potential flow theory and an elastic thin-plate model of the floating ice layer, solving the hydrodynamic problem of the interaction between water waves and ships floating near a semi-infinite ice layer. The method first derives a Green's function that satisfies the boundary conditions of the ice layer and the free surface, as well as all other boundary conditions except for the ship's surface. Using the Green's function, the differential equation of the velocity potential in the flow domain is transformed into a boundary integral equation only on the ship's surface. This integral equation introduces an extended surface at the waterline of the hull to eliminate the influence of irregular wave frequencies. An asymptotic formula for the Green's function is analytically derived, thereby establishing an approximately effective solution procedure for the coupled interaction of the ship / wave / ice layer. This procedure can numerically solve for the ship's additional mass, damping coefficient, and wave excitation force.

[0006] The specific technical solution is as follows:

[0007] A device for predicting the coupling hydrodynamics and motion of floating ice and ships 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 ice field flow field 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 polar ships using the boundary element method, and solves the equations of motion for ships in the ice field in each grid cell. The prediction mechanism unit uses the Fortran language to develop relevant numerical calculation programs on the Windows platform of a computer device to predict the coupling hydrodynamics and motion of floating ice and ships in the wave field. The numerical results can be stored in a data storage device.

[0008] This invention also discloses a method for predicting the coupling hydrodynamics of floating ice and ships and ship motion. This prediction method is based on a device for predicting the coupling hydrodynamics of floating ice and ships and ship motion, and specifically includes the following steps:

[0009] Step (1) adopts the watershed matching solution method, and gives the velocity potential Laplace control equation that satisfies the entire watershed based on the linear potential flow theory, as well as various boundary conditions (including the boundary conditions at the edge of sea ice).

[0010] Step (2) uses the Green's function generated by the pulsating source, and uses Green's formula and Green's function to solve key problems such as the non-orthogonality of the eigenfunctions of the sea ice-covered watershed and the boundary conditions of the intersection of the free liquid surface and the sea ice, in order to solve the velocity potential;

[0011] Step (3) transforms the differential equation of the disturbance velocity potential into a boundary integral equation only on the ship surface, and eliminates the influence of irregular wave frequency by modifying the integral equation solved based on the boundary element method.

[0012] Step (4) can then calculate the hydrodynamic coefficients, including the damping coefficient, the added mass, and the wave excitation force;

[0013] Step (5) After solving the ship's hydrodynamic problem, the six-degree-of-freedom equations of motion for the ship can be given;

[0014] Step (6) Based on the Fortran language, a direct numerical calculation program for the problem of coupling hydrodynamics between floating ice and ships and prediction of ship motion in a three-dimensional wave field is developed, and numerical convergence and validity verification are performed. On this basis, the changes in hydrodynamic and motion characteristics of polar ships under different ice thicknesses, wave directions, and wave frequencies can be studied.

[0015] In step (1) above, 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 of wave motion and ship motion is small compared to the wavelength and ship size, for time sinusoidal motion with frequency ω, the total velocity potential is... It can be written as:

[0016]

[0017] Where η0 is the amplitude of the incident wave, and φ0 = φ I +φ D It is the scattering potential, where φ I and φ D These are the incident potential and the diffraction potential, respectively, φ j It is the radiation potential generated by the j-th mode of ship motion in six degrees of freedom, with a complex amplitude of η. j .

[0018] The prediction method in this invention is a solution to a boundary value problem, and the mass conservation requirement dictates that the velocity potential satisfies the Laplace equation throughout the fluid: in, It is a Laplace operator on a horizontal plane, and all boundary conditions in this flow field are as follows:

[0019] At the free surface, combining the linearized dynamic and kinematic free surface boundary conditions, we can obtain:

[0020]

[0021] Where g is the acceleration due to gravity, in the fluid region covered by ice, assuming there is no gap between the ice sheet and the water surface, this provides the following kinematic conditions:

[0022]

[0023] Where W is the deflection of the ice layer, w j It can be further written as:

[0024]

[0025] Combining the kinematic and dynamic boundary conditions of the interface between the ice sheet and the water surface, we can obtain:

[0026]

[0027] Where L=Eh 3 / [12(1-ν 2 [)] is the effective bending stiffness of the ice layer, m i =ρ i h is the corresponding mass per unit area. At the edge of the ice layer, applying zero bending moment and shear force conditions, it can be written as:

[0028]

[0029] Where j = 0,...,6; and where operators B and S are defined as follows:

[0030]

[0031]

[0032] The impenetrable boundary condition is satisfied on the wetted surface of the hull:

[0033]

[0034] The impenetrable boundary condition is also satisfied on the seabed:

[0035]

[0036] At infinity, radiation conditions require that radiated and scattered waves propagate outward as free surface waves and as curved gravity waves (in ice-covered areas).

[0037] A further improvement of this invention is that, in step (2), the Green's function G(p,q) can transform the solution of the velocity potential at any point in the flow field to all boundary surfaces of the flow domain, establishing corresponding boundary integral equations for solution, where p(x,y,z) is the field point and q(ξ,η,ζ) is the source point. Once G(p,q) is obtained, the unknown velocity potential in the flow field can be found through the boundary integral equations. G should satisfy the following governing equations throughout the fluid:

[0038]

[0039] In the z-direction, the vertical mode Z of the free liquid surface m (z)(m=0,1,...,∞) and the vertical mode Q of the ice-covered region m (z)(m=-2,-1,...,∞) is represented as:

[0040]

[0041] Where, k m It is a root of the free surface dispersion equation (k0 is a pure real root; k m It is an infinite number of purely negative imaginary roots, m = 1, ..., ∞); κ m It is the root of the ice sheet dispersion equation (κ) -2 and κ -1 These are two complex roots with negative imaginary parts and symmetric about the imaginary axis; κ0 is a pure real root, κ m There are an infinite number of purely negative imaginary roots, m = 1, ..., ∞, and the dispersion equation is as follows:

[0042] gktanh(kH)-ω 2 =0 and(Lk) 4 +ρ w gm i ω 2 )ktanh(kH)-ρ w ω 2 =0 (13)

[0043] Then, equation (11) in the y-direction becomes a series of standard second-order ordinary differential equations, which can be easily solved and can be written as:

[0044]

[0045] in, and To satisfy the far-field condition, choose when β m and γ m When it is a complex number, Im(β) m )≤0 and Im(γ) m )≤0, when they β m and γ m When β is a pure real number, m >0 and γ m >0; unknown coefficient a m and b m The equation F above can be solved by combining velocity and pressure continuity at the wave-sea ice interface with sea ice edge conditions, and can be written as:

[0046]

[0047] Where the integral path from 0 to +∞ should pass through the point k = k0, r1 is the distance between p and q, r2 is the distance between p and its mirror image point q with respect to the flat seabed; J0(kR) is the zeroth-order Bessel function of the first kind, and R is the horizontal distance between p and q. Combining all boundary conditions, the solution matrix equation is further obtained as follows:

[0048]

[0049] Furthermore, on the wetted surface of the hull, using the Green's function G, the disturbance velocity potential can be transformed into a boundary integral equation on the average wetted surface of the ship, i.e.

[0050]

[0051] Where ι is the solid coefficient of p, however, at certain frequencies the solution to the above equation may not exist or may not be unique. To remove the influence of irregular frequencies, the above equation is further modified as follows:

[0052]

[0053]

[0054] Among them, S E It is the interior of a ship or its extended surface on the water surface.

[0055] Furthermore, regarding the aforementioned ship hydrodynamic problem, finding the velocity potential φ... j Then, the pressure at any point in the fluid can be calculated using the linearized Bernoulli equation. The hydrodynamic forces on the ship can then be obtained by integrating and averaging the dynamic pressure on the wetted ship surface. Based on the decomposition of the velocity potential in the equation, we can divide the total hydrodynamic force into two parts: the wave excitation force f. E,j :

[0056]

[0057] The radiation force generated by the forced vibration motion of a ship can be written as the additional mass μ. jk and damping coefficient λ jk ,Right now

[0058]

[0059] Furthermore, regarding the ship motion prediction problem, after solving the ship hydrodynamic problem, the three-dimensional complex amplitude η of the ship motion... j The following can be obtained from the six-degree-of-freedom equations of motion of the floating body:

[0060]

[0061] Among them, M jk For the ship mass matrix, B jk Let C be the damping matrix of the ship. jk This is the restoring force matrix.

[0062] Furthermore, the numerical results are dimensionalized based on a combination of three fundamental parameters, namely water density ρ. w, gravitational acceleration g and half the ship's beam; in addition, the infinite series in equation (14) is truncated to a finite number of M G For boundary integral equations (18) and (19), the ship's average wetted surface S B Discretize into N B The unit, and the extended inner surface S introduced to remove irregular frequencies. E Discretize into N E Element. Assuming a constant velocity potential in each grid element, the fixed angle coefficient in equation (18) is always 2π in each element, by appropriately setting M... G N B and N E This allows us to obtain numerical results with a predetermined level of precision.

[0063] The beneficial effects of this invention are as follows: Based on Green's function, this invention considers the hydrodynamic problem under the coupled effects of ship, waves, and ice floes. It achieves high numerical accuracy in hydrodynamic prediction across the entire wave number range, and over a large wavelength range near the ship in the ice edge region. Furthermore, the use of this prediction method significantly improves computational efficiency. Attached Figure Description

[0064] Figure 1 This is a structural block diagram of the device for predicting the coupling of ice floes and ship hydrodynamics and ship motion according to the present invention.

[0065] Figure 2 This is a flowchart illustrating the method for predicting the coupling hydrodynamics of floating ice and ships and the ship motion of the present invention. Detailed Implementation

[0066] To enhance understanding of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are only used to explain the present invention and do not constitute a limitation on the scope of protection of the present invention.

[0067] Example: Figure 1 As shown, a device for predicting the coupling hydrodynamics of floating ice and ships and the motion of ships includes a first mechanism unit 1, a second mechanism unit 2, and a prediction mechanism unit 3. The first mechanism unit 1 is used to construct a boundary value problem solution model for the ice flow field based on linearized potential flow theory, and to establish a numerical solution algorithm based on Green's function. The second mechanism unit 2 constructs a boundary element computation grid for polar ships based on the boundary element method, and solves the problem in each grid cell to construct the hydrodynamic and motion equations of ships in the ice area. The prediction mechanism unit 3 uses the Fortran language to develop relevant numerical calculation programs on the Windows platform of a computer device to predict the coupling hydrodynamics of floating ice and ships and the motion of ships in the wave field. The numerical results can be stored in a data storage device.

[0068] The specific workflow of this embodiment is as follows: Figure 2 As shown:

[0069] A method for predicting the coupled hydrodynamics of floating ice and ships in a wave field is proposed. First, a Green's function is derived, which satisfies the boundary conditions of the ice layer and the free surface, as well as all other boundary conditions except for the ship surface condition. Through the Green's function, the differential equation of the velocity potential in the water domain is transformed into a boundary integral equation only on the ship surface. This integral equation introduces an extension surface at the waterline of the hull to eliminate the influence of irregular wave frequencies. The asymptotic formula of the Green's function is analytically derived, thereby establishing an approximately effective solution program for the coupled interaction of ship / wave / ice layer. The program can numerically solve for the ship's additional mass, damping coefficient, and wave excitation force.

[0070] In the above method, 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 of wave motion and ship motion is small compared to the wavelength and ship size, for time sinusoidal motion with frequency ω, the total velocity potential... It can be written as:

[0071]

[0072] Where η0 is the amplitude of the incident wave, and φ0 = φ I +φ D It is the scattering potential, where φ I and φ D These are the incident potential and the diffraction potential, respectively, φ j It is the radiation potential generated by the j-th mode of ship motion in six degrees of freedom, with a complex amplitude of η. j .

[0073] The above method solves a boundary value problem, where mass conservation requires the velocity potential to satisfy Laplace's equation throughout the fluid: in, It is a Laplace operator on a horizontal plane, and all boundary conditions in this flow field are as follows:

[0074] At the free liquid surface, combining the linearized dynamics and kinematic free surface boundary conditions, we can obtain:

[0075]

[0076] Where g is the acceleration due to gravity, in the fluid region covered by ice, assuming there is no gap between the ice sheet and the water surface, this provides the following kinematic conditions:

[0077]

[0078] Where W is the deflection of the ice layer, w jIt can be further written as:

[0079]

[0080] Combining the kinematic and dynamic boundary conditions of the interface between the ice sheet and the water surface, we can obtain:

[0081]

[0082] Where L=Eh 3 / [12(1-ν 2 [)] is the effective bending stiffness of the ice layer, m i =ρ i h is the corresponding mass per unit area. At the edge of the ice layer, applying zero bending moment and shear force conditions, it can be written as:

[0083]

[0084] Where j = 0,...,6; and where operators B and S are defined as follows:

[0085]

[0086]

[0087] The impenetrable boundary condition is satisfied on the wetted surface of the hull:

[0088]

[0089] The impenetrable boundary condition is also satisfied on the seabed:

[0090]

[0091] At infinity, radiation conditions require that radiated and diffracted waves propagate outward as free surface waves and as curved gravity waves (in ice-covered areas).

[0092] In the above method, the Green's function G(p,q) can transform the solution of the velocity potential at any point in the flow field to all boundary surfaces of the flow domain, establishing corresponding boundary integral equations for solution, where p(x,y,z) is the field point and q(ξ,η,ζ) is the source point. Once G(p,q) is obtained, the unknown velocity potential in the flow field can be found through the boundary integral equations. G should satisfy the following governing equations throughout the fluid, or:

[0093]

[0094] In the z-direction, the vertical mode Z of the free liquid surface m (z)(m=0,1,...,∞) and the vertical mode Q of the ice-covered region m(z)(m=-2,-1,...,∞) is represented as:

[0095]

[0096] Where, k m It is a root of the free surface dispersion equation (k0 is a pure real root; k m It is an infinite number of purely negative imaginary roots, m = 1, ..., ∞); κ m It is the root of the ice sheet dispersion equation (κ) -2 and κ -1 These are two complex roots with negative imaginary parts and symmetric about the imaginary axis; κ0 is a pure real root, κ m There are an infinite number of purely negative imaginary roots, m = 1, ..., ∞, and the dispersion equation is as follows:

[0097] gktanh(kH)-ω 2 =0 and(Lk) 4 +ρ w gm i ω 2 )ktanh(kH)-ρ w ω 2 =0 (35)

[0098] Then, equation (11) in the y-direction becomes a series of standard second-order ordinary differential equations, which can be easily solved and can be written as:

[0099]

[0100] in, and To satisfy the far-field condition, we choose when β m and γ m When it is a complex number, Im(β) m )≤0 and Im(γ) m )≤0, when they β m and γ m When β is a pure real number, m >0 and γ m >0; unknown coefficient a m and b m The equation F above can be solved by combining velocity and pressure continuity at the wave-sea ice interface with sea ice edge conditions, and can be written as:

[0101]

[0102] Where the integral path from 0 to +∞ should pass through the point k = k0, r1 is the distance between p and q, r2 is the distance between p and its mirror image point q with respect to the flat seabed; J0(kR) is the zeroth-order Bessel function of the first kind, and R is the horizontal distance between p and q. Combining all boundary conditions, the solution matrix equation is further obtained as follows:

[0103]

[0104] In the above embodiments, on the wetted surface of the hull, using the Green's function G, we can transform the disturbance velocity potential into a boundary integral equation on the average wetted surface of the ship, i.e.

[0105]

[0106] Where ι is the solid coefficient of p, however, at certain frequencies the solution to the above equation may not exist or may not be unique. To remove the influence of irregular frequencies, the above equation is further modified as follows:

[0107]

[0108] Among them, S E It is the interior of a ship or its extended surface on the water surface.

[0109] In the above embodiments, the ship hydrodynamic problem involves finding the velocity potential φ. j Then, the pressure at any point in the fluid can be calculated using the linearized Bernoulli equation. The hydrodynamic forces on the ship can then be obtained by integrating and averaging the dynamic pressure on the wetted ship surface. Based on the decomposition of the velocity potential in the equation, we can divide the total hydrodynamic force into two parts: the wave excitation force f. E,j :

[0110]

[0111] The radiation force generated by the forced vibration motion of a ship can be written as the additional mass μ. jk and damping coefficient λ jk ,Right now

[0112]

[0113] In the above embodiments, the ship motion prediction problem, after solving the ship hydrodynamic problem, yields the three-dimensional complex amplitude η of the ship motion. j The following can be obtained from the six-degree-of-freedom equations of motion of the floating body:

[0114]

[0115] Among them, M jk For the ship mass matrix, B jk Let C be the damping matrix of the ship.jk This is the restoring force matrix.

[0116] In the above method, the numerical results are dimensionalized based on a combination of three basic parameters, namely water density ρ. w , gravitational acceleration g and half the ship's beam; in addition, the infinite series in equation (14) is truncated to a finite number of M G For boundary integral equations (18) and (19), the ship's average wetted surface S B Discretize into N B The unit, and the extended inner surface S introduced to remove irregular frequencies. E Discretize into N E Element. Assuming a constant velocity potential in each grid element, the fixed angle coefficient in equation (18) is always 2π in each element, by appropriately setting M... G N B and N E This allows us to obtain numerical results with a predetermined level of precision.

[0117] The above method can be summarized into the following steps:

[0118] (1) The watershed matching solution method is adopted. Based on the linear potential flow theory, the Laplace control equation of velocity potential for the entire watershed is given, as well as various boundary conditions (including the boundary conditions at the edge of sea ice).

[0119] (2) The Green function generated by the pulsating source is used to solve key problems such as the non-orthogonality of the eigenfunctions of the sea ice-covered watershed and the boundary conditions of the intersection of the free liquid surface and the sea ice by using the Green formula and the Green function to solve the velocity potential.

[0120] (3) The differential equation of the disturbance velocity potential is transformed into a boundary integral equation only on the ship surface, and the influence of irregular wave frequency is eliminated by modifying the integral equation solved based on the boundary element method.

[0121] (4) Then the hydrodynamic coefficients, including damping coefficients, added mass, and wave excitation force, can be calculated.

[0122] (5) After solving the ship hydrodynamic problem, the six-degree-of-freedom motion equations of the ship can be given;

[0123] (6) Based on the Fortran language, a direct numerical calculation program for the problem of coupling hydrodynamics between floating ice and ships and prediction of ship motion in a three-dimensional wave field was developed, and numerical convergence and validity verification were performed. On this basis, the changes in hydrodynamic and motion characteristics of polar ships under different ice thicknesses, wave directions, and wave frequencies can be studied.

[0124] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the coupled hydrodynamics and motion of floating ice and ships, using a device for predicting the coupled hydrodynamics and motion of floating ice and ships, the device comprising 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 ice field flow field 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 polar ships based on the boundary element method, and solves in each grid cell to construct the hydrodynamic and motion equations of ships in the ice field; the prediction mechanism unit uses Fortran language to develop relevant numerical calculation programs on a Windows platform of a computer device to predict the coupled hydrodynamics and motion of floating ice and ships in the wave field, and the numerical results can be stored in a data storage device; Specifically, the following steps are included: Step (1) adopts the watershed matching solution method, and gives the velocity potential Laplace control equation that satisfies the entire watershed, as well as various boundary conditions, based on the linear potential flow theory. Step (2) uses the Green's function generated by the pulsating source, and uses Green's formula and Green's function to solve the key problems of the sea ice-covered watershed, in order to solve the velocity potential; Step (3) transforms the differential equation of the disturbance velocity potential into a boundary integral equation only on the ship surface, and eliminates the influence of irregular wave frequency by modifying the integral equation solved based on the boundary element method. Step (4) calculates the hydrodynamic coefficients, including the damping coefficient, the added mass, and the wave excitation force; Step (5) gives the six-degree-of-freedom equations of motion for the ship; Step (6) Based on the Fortran language, develop a direct numerical calculation program for the problem of coupling hydrodynamics between floating ice and ships and prediction of ship motion in a three-dimensional wave field, and perform numerical convergence and validity verification. In step (1), 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 wave motion and ship motion are smaller than the ship size, for time sinusoidal motion with frequency ω, the total velocity potential... Written as: Where η0 is the amplitude of the incident wave, and φ0 = φ I +φ D It is the scattering potential, where φ I and φ D These are the incident potential and the diffraction potential, respectively, φ j It is the radiation potential generated by the j-th mode of ship motion in six degrees of freedom, with a complex amplitude of η. j ; The conservation of mass requires that the velocity potential satisfy Laplace's equation throughout the fluid: （2） in, It is a Laplace operator on a horizontal plane, and all boundary conditions in this flow field are as follows: At a free liquid surface, combining the dynamic and kinematic boundary conditions of the free surface, we can obtain: （3） in, Assuming no gap between the ice sheet and the water surface in a fluid region covered by ice, and considering gravitational acceleration, the following kinematic conditions are provided: （4） in, It is the deflection of the ice layer. It can be further written as: （5） Combining the kinematic and dynamic boundary conditions of the interface between the ice sheet and the water surface, we can obtain: （6） in, It is the effective bending stiffness of the ice layer. Given the corresponding mass per unit area, at the edge of the ice layer, applying zero bending moment and shear force conditions, we can obtain: （7） in, ; operator and They are defined as follows: （8） （9） The impenetrable boundary condition is satisfied on the wetted surface of the hull: （10） The impenetrable boundary condition is also satisfied on the seabed: （11） At infinity, radiation conditions require that radiated and diffracted waves propagate outward as free surface waves and as curved gravitational waves.

2. The method for predicting the coupling hydrodynamics of floating ice and ships and ship motion according to claim 1, characterized in that, In step (2), the Green's function The solution for the velocity potential at any point within the flow field is transformed into a solution for all boundary surfaces of the flow domain, and corresponding boundary integral equations are established for solving. As the venue, As the source point, once obtained The unknown velocity potential in the flow field can be found through the boundary integral equation. The following governing equations should be satisfied throughout the fluid: （12） Vertical mode of the free liquid surface in the z-direction Vertical modes of ice-covered areas It is represented as: （13） in, It is a root of the free surface dispersion equation. It is a pure, solid root. It is an infinite number of purely negative imaginary roots. ; It is a root of the ice sheet dispersion equation. and These are two complex roots with negative imaginary parts and symmetric about the imaginary axis. It is a pure, solid root. It is an infinite number of purely negative imaginary roots. ; The dispersion equation is as follows: （14） Then, equation (12) in the y-direction becomes a series of standard second-order ordinary differential equations, which can be written as: （15） in, , In order to meet the far-field conditions, we choose when and When it is a complex number When they and When it is a pure real number, and Unknown coefficients and The above equation can be solved by combining velocity and pressure continuity at the wave-sea ice interface with sea ice edge conditions. It can be written as: （16） From 0 to The integration path should be through point, yes and The distance between them yes And regarding the mirror point of a flat seabed The distance between them; It is a zeroth-order Bessel function of the first kind. yes and The horizontal distance between them, combined with all boundary conditions, further yields the following solution matrix equation: （17）。 3. The method for predicting the coupling hydrodynamics of floating ice and ships and ship motion according to claim 2, characterized in that, On the wet surface of the hull, using the Green's function The disturbance velocity potential is transformed into a boundary integral equation on the average wetted surface of the ship, i.e. （18） in, Is To remove the influence of irregular frequencies, the fixed angle coefficient of the above formula is further modified as follows: （19） （20） Among them, S E It is the interior of a ship or its extended surface on the water surface.

4. The method for predicting the coupling hydrodynamics of floating ice and ships and ship motion according to claim 3, characterized in that, The total hydrodynamic force is divided into two parts: wave excitation force f. E,j : （21） The radiation force generated by the forced vibration motion of a ship can be written as the added mass. and damping coefficient ,Right now （22）。 5. The method for predicting the coupling hydrodynamics of floating ice and ships and ship motion according to claim 4, characterized in that, After solving the ship hydrodynamic problem, the three-dimensional complex amplitude of the ship's motion is obtained. The following can be obtained from the six-degree-of-freedom equations of motion of the floating body: （23） Among them, M jk For the ship mass matrix, B jk Let C be the damping matrix of the ship. jk This is the restoring force matrix.

Images