1. A method for determining asymmetric slamming loads of a ship bow under a slope wave is characterized by comprising the following steps:

step 1: simplifying the calculation model into a rigid body;

establishing motion equation at gravity center of ship body

Wherein M is a generalized quality matrix; f (t) is the fluid load around the hull; η (t) is the motion of the rigid body center of gravity.

Step 2: simplifying the solution of the wave load of the calculation model;

when the external load force F (t) of the ship body is solved, the external load force is divided into hydrostatic force F^S(t) incident wave force F_I(t) diffraction force F_D(t) and radiation force F_R(t)

{F(t)}＝{F^S(t)}+{F_I(t)}+{F_D(t)}+{F_R(t)}

Has a hydrostatic force of

{F^S(t)}＝-[C]{η}e^iωt

Wherein C is a hydrostatic coefficient; and omega is the wave circle frequency.

Incident wave force F_I(t) and diffraction force F_D(t) together form a wave interference force F_ID(t), which is related to the form of the incident wave, is described

In the formula, xi_aIn order to be of an amplitude,andthe incident and diffracted potentials are given in units of amplitude.

By integrating the radiation pressure of the wet surface, the radiation force is obtained, i.e.

And step 3: establishing a six-degree-of-freedom motion equation at the gravity center of the calculation model under the waves;

various fluid load components acting on the ship body are substituted into the ship motion equation to obtain a quasi-static equation system

([C]-ω²([M]+[A])+iω[B]){η}＝{f}

And 4, step 4: establishing a relative motion forecasting model of a three-dimensional space of a computational model ship wave;

for an arbitrary point (x, y, z) of the vessel, the horizontal and vertical relative displacement motion forecast may be expressed as

In the formula (x)_b，y_b，z_b) The coordinates of the gravity center of the ship body are obtained; h_y、H_zRelative displacement of the vessel and the waves; beta is the angle of the wave direction; k is the wave number.

And 5: establishing a two-dimensional profile multi-degree-of-freedom asymmetric water-entering slamming model;

the ship body is sliced, the three-dimensional slamming problem is converted into two-dimensional slamming, and the calculated amount is simplified. The two-dimensional profile enters the water at lateral velocity, vertical velocity and roll velocity. The entire fluid domain boundary has an upper portion S_TBottom S_BRemote S_CDough kneading S_S. The upper part of the free surface is air, and the lower part of the free surface is water. Upper side S of the basin_TSet as pressure outlet boundary, bottom S_BAnd both sides S_CFor no slip boundary, the object surface S_SIs a slip-free rigid boundary.

Step 6: and (3) simulating an asymmetric water-entering slamming process by using a VOF (Voltage induced Fahrenheit) method, and forecasting slamming loads.

Assuming the fluid is incompressible and ignoring the viscous and gravitational effects of the fluid, a continuity equation and a momentum equation of the water-in slamming are established as

Where p is the pressure, u is the velocity vector, and ρ is the density of the fluid.

Solving the above equation by using VOF method, assuming water as basic phase, introducing phase equation

Where α is the volume fraction of the base phase, the density of the fluid can be further expressed as

ρ＝αρ₁+(1-α)ρ₂。

2. The method for determining asymmetric slamming load of ship bow under seas according to claim, wherein in step 2, a velocity potential function phi is introduced_jAnd solving by using a three-dimensional potential flow theory. Assume that the fundamental governing equations and boundary conditions around the hull are recorded

[D]：

[B]：

[F]：

[S]：

[R]：

Introducing Green function G (P, Q) to establish boundary integral equation and solve velocity potential phi_jThe unknown source intensity sigma (q) distributed on the surface of the object satisfies

Wherein P is any point in the fluid domain; s is average wet surface; q is a point at S. Substituting into the boundary condition of the object plane to obtain an integral equation of the source intensity of

Solving the linear equation set by using a surface element method to obtain the speed potential phi required by solving the wave load_j。

3. The method for determining the asymmetric slamming load of the bow of the ship under the action of the oblique waves as claimed in claim 4, wherein in the step 4, the relative movement of the ship under the action of the oblique waves comprises three forms of vertical movement, transverse movement and rolling, and the specific solution is as follows:

(1): vertical relative motion solution

The vertical relative displacement thus obtained is derived in the z direction to obtain the vertical relative movement, i.e.

(2): solving for lateral relative motion

The transverse relative displacement thus determined is derived in the y direction to obtain the transverse relative movement, i.e.

(3): roll relative motion solution

The roll motion is taken as the sole quantity of the underwater motion, the displacement changes caused by it are taken into account individually, and under the rigid body model, the rotation of the structure is kept consistent with the motion form at the center of gravity of the structure in three-dimensional space, i.e. the rotation is carried out in the form of a motion

w＝η₄。

4. The method for determining asymmetric slamming loads of ship bow under seas according to claim, wherein in step 6, the momentum equation is solved discretely based on a finite volume method, the time term adopts Euler hidden format, and each term in the momentum equation is discretized into

In the formula, the superscripts n and r denote the current time step (value known) and the predicted time step (value unknown), respectively, the subscript f denotes the value of the grid surface, V_pVolume of the grid, Δ t is the time step, F_fAs a flux, S denotes a plane vector of the grid cell. Velocity of the surface of the gridCan be obtained according to the speed of the centers of adjacent body units, and can be obtained by adopting a center difference method, namely Is the normal gradient of the surface velocity, noted

Where subscripts P and N denote the speed of the current grid and the adjacent grid, respectively, | S_f| is the modulus of the surface vector, | d | is the distance between the grids. In phase equationThe time item is dispersed in a hidden format, and the volume fraction is dispersed in a standard finite difference mode, i.e.

In the formula, superscripts n and n +1 respectively represent a previous time step and a subsequent time step,is the surface flux.

Technical Field

Slamming of the bow of the hull often occurs due to the interaction of the waves and the vessel. Such slamming can cause the hull to vibrate, slow down and in severe cases even directly damage the hull structure. Hull slamming intensity is an important issue in ship structure design, however due to the high randomness of the marine environment and the strong non-linearity of the free surface during slamming, slamming load prediction is a very challenging problem.

To simplify the hull slamming problem, slice theory is often introduced, converting it into a simple two-dimensional water-in problem. The prediction of rigid body water-ingress slamming is currently largely divided into two categories, potential flow theory and computational fluid dynamics. Methods based on the potential flow theory present numerical difficulties in dealing with complex free surfaces and are difficult to consider for more complex flow phenomena such as flow separation, air circulation, etc. Although these complex fluid forms can be handled by computational fluid dynamics-based methods, there are still some problems to be further improved in the reconstruction of the free surface, the accuracy of the computation, and the convergence.

Hull slamming requires consideration of wave interactions, a problem that is more complex than the water entry problem. Therefore, prediction is generally performed by combining a two-dimensional model with a wave-resistance theory, and in recent years, a prediction method considering a three-dimensional effect is available, but the prediction method is limited to an excessively large calculation amount and is not yet popular. Although the underwater impact theory and the wave resistance theory are greatly developed, in the forecast of the actual ship body slamming load, the slamming condition of the symmetrical ship body facing waves is focused, and only the influence of vertical speed is considered. However, hull slamming under seas is more common due to course and complex marine environment, where lateral speed and lateral rolling motion of the hull can have a significant impact on the load.

In view of the fact that ship body slamming under oblique waves and the fact that asymmetric motions of waves and ships have great influence on the prediction accuracy of slamming loads, the research provides a method for determining asymmetric slamming loads of ship bow under oblique waves. Firstly, the wave mass point effect and asymmetric ship body motion are calculated based on the wave resistance theory, the motion time history of ship body slamming speed is obtained, and then the forecast of slamming load is carried out by taking a complex flow form (flow separation and air effect) into account through a computational fluid dynamics method. Compared with the method that only the influence of the vertical relative speed is considered in most researches, the method takes the influence of the transverse speed and the rolling motion into account when the ship body slamming load is forecasted, and the method can reflect the real slamming load in the case of oblique waves. The invention enriches the form of slamming load forecast, and the comprehensive consideration of multiple motion factors provides guarantee for the effectiveness of load forecast.

Disclosure of Invention

The invention aims to provide a method for determining asymmetric slamming loads of a ship bow under the action of oblique waves, overcomes the defect that asymmetric motion forms cannot be fully considered in the conventional ship slamming load forecasting, and provides a high-precision method for determining the ship slamming loads under a complex marine environment.

In order to realize the purpose of the invention, the invention adopts the following technical scheme:

(1) neglecting the influence of wave load on the deformation of the hull structure during navigation, simplifying the hull into a rigid model, and obtaining a motion model at the center of gravity of the hull according to Newton's second law in a general form

Wherein M is a generalized quality matrix; f (t) is the fluid load around the hull; η (t) is the motion of the rigid body center of gravity.

(2) And simplifying the solution of the wave load of the calculation model. Assuming that the fluid domain satisfies the Laplace equation, the fluid domain includes four boundaries: bottom boundary S_BFree surface boundary S_FArticle surfaceBoundary S_SAnd truncating the boundary S_R. Using the three-dimensional potential flow theory, the mathematical expressions of the basic governing equations and boundary conditions in the rigid body model are as follows:

[D]:

[B]:

[F]:

[S]:

[R]:

to obtain a velocity potential phi_jIntroducing a Green's function G (P, Q) to establish a boundary integral equation, and satisfying the unknown source intensity distributed on the surface of the object

Wherein P is any point in the fluid domain; s is average wet surface; q is a point located on S. Substituting into the boundary condition of the object plane to obtain an integral equation of the source intensity of

The surface element method is adopted to solve the equation, and the basic idea is to disperse the wet surface by utilizing a triangular/quadrilateral surface element and then convert the equation into a linear equation set with unknown source intensity.

The fluid load F (t) acting on the hull structure can be dividedThe method comprises the following two types: hydrostatic load F^S(t) and hydrodynamic load F^D(t) of (d). The hydrodynamic load can be further decomposed into an incident wave force F_I(t) diffraction force F_D(t) and radiation force F_R(t) of (d). Thus, the total fluid load can be broken down into

{F(t)}＝{F^S(t)}+{F_I(t)}+{F_D(t)}+{F_R(t)}

For hydrostatic load F^S(t), assuming that the vessel motion is linear, simplification is to

{F^S(t)}＝-[C]{η}e^iωt

Where C is the hydrostatic coefficient, which can be obtained by integrating the hydrostatic pressure along the average wet surface of the hull. Incident wave force F_I(t) and diffraction force F_D(t) jointly constitute a wave interference force F_ID(t), which is related to the form of the incident wave, is described

In the formula, ζ_aIn order to be of an amplitude,andthe incident and diffracted potentials are given in units of amplitude. By integrating the radiation pressure of the wet surface, the radiation force is obtained, i.e.

In the equation of motion of a vessel, the radiation force is usually expressed in the form of a three-dimensional hydrodynamic coefficient, denoted as

In the formula, A is an additional mass and B is a damping coefficient.

(3) And establishing a six-degree-of-freedom motion equation at the gravity center of the hull under the waves. Various fluid load components acting on the ship body are substituted into the ship motion equation (1), a time term is eliminated, and a quasi-static equation system is obtained as

([C]-ω²([M]+[A])+iω[B]){η}＝{f}

And solving the motion equation set by adopting a Gaussian elimination method to obtain a real part and an imaginary part of the six-degree-of-freedom motion. The amplitude and phase of the vessel motion may be expressed as

(4) And establishing a relative motion forecasting model of the three-dimensional space of the calculation model. The motion form of the bow is different from the gravity center, when the ship body is assumed to be a rigid body, the motion form of the three-dimensional space of the ship body can be obtained according to the rigid body motion theory, and the motion of the three-dimensional space is usually solved in a relative motion form by considering the influence of waves. Assuming that the hull encounters a unit harmonic, for any point (x, y, z) of the hull, the horizontal and vertical relative displacements can be expressed as

In the formula (x)_b,y_b,z_b) The coordinates of the gravity center of the ship body are obtained; h_y、H_zRelative displacement of the vessel and the waves; beta is the angle of the wave direction; k is the wave number. Horizontal velocity y_vAnd a vertical velocity z_vIs expressed as

In the formula u_wAnd w_wVertical and horizontal wave velocities, respectively.

It is noted that the roll motion is taken as a separate quantity of the underwater motion, the displacement changes caused by it are taken into account separately, and that under the rigid body model the rotation of the structure is kept in agreement in three-dimensional space with the motion pattern at the centre of gravity of the structure, i.e. the roll motion is kept in agreement

w＝η₄

(5) And establishing an asymmetric water-entering slamming model. And slicing the ship body, converting the three-dimensional slamming problem into two-dimensional slamming and simplifying the calculated amount. Hull section at transverse velocity y_vVertical velocity z_vAnd roll velocity w into the water, with an upper portion S across the fluid domain boundary_TBottom S_BRemote S_CDough kneading S_S. The upper part of the free surface is air, and the lower part of the free surface is water. Upper side S of the basin_TSet as pressure outlet boundary, bottom S_BAnd both sides S_CFor no slip boundary, the object surface S_SIs a slip-free rigid boundary.

(6) And solving the water-entering slamming problem by applying a VOF method and forecasting the slamming load. And establishing a two-phase flow model of the water inlet impact problem based on an N-S equation. Assuming the fluid is incompressible and neglecting the viscous and gravitational effects of the fluid, the continuity equation and momentum equation are simplified to

Where p is the pressure, u is the velocity vector, and ρ is the density of the fluid. Solving the above equation by using VOF method, assuming water as basic phase, introducing phase equation

Wherein α is the volume fraction of the base phase. The density of the fluid can be further expressed as

ρ＝αρ₁+(1-α)ρ₂

In the formula, ρ₁And ρ₂The densities of water and air, respectively, are typically taken to be 1.0X 10³kg/m³And 1.25kg/m³. The equations form a continuity equation, a momentum equation and a phase equation for solving a two-phase flow model by applying the VOF method. And (4) determining the relative motion relation of the ship waves given in the step (4) when the water enters.

Advantageous effects

The current ship body slamming load forecast mainly focuses on wave-facing symmetrical slamming, only the influence of vertical speed is considered, and the ship body slamming under oblique waves is influenced by ship body rolling and rolling motion, so that obvious asymmetrical slamming can occur. The method further extends the prediction of slamming loads to the wave situation, taking into account a variety of motion patterns, which more realistically reflect the slamming loads encountered in complex marine environments. The method is established based on a two-step walking mode of mixing ship body movement and water-entering slamming, the processing mode can avoid the coupling solution between the ship body movement and the water-entering slamming, the calculation efficiency is effectively improved, meanwhile, the influence of each parameter on the calculation mode can be visually analyzed, and further the general rule of the oblique wave asymmetric slamming load can be mastered on the basic principle.

Drawings

FIG. 1 is a schematic flow diagram of a method for determing an asymmetric slamming load of a bow in a seas;

FIG. 2 is a schematic view of the fluid domains and boundaries of a hull in which the hull is located, illustrating an asymmetric water slamming of the hull;

FIG. 3 is the relative motion history of the ship waves (entry phase);

FIG. 4 is a schematic diagram of an asymmetric water-ingress slamming model of a hull;

FIG. 5 is a pressure history of forecasts under rough sea;

fig. 6 is a two-sided pressure distribution forecasted under a strake.

Detailed Description

In order to make the technical purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention are further described below with reference to the accompanying drawings and specific embodiments.

The invention provides a method for determining asymmetric slamming load of a bow under oblique waves, which comprises the following steps as shown in figure 1:

and 1) assuming the ship body as a rigid model, and neglecting the influence of wave load on the deformation of the ship body structure during navigation. The model of the motion at the weight center of the ship conforms to Newton's second law, i.e.

Wherein M is a generalized quality matrix; f (t) is the fluid load around the hull; η (t) is the motion of the rigid body center of gravity.

And 2) simplifying the solution of the wave load of the calculation model. As shown in fig. 2, the hull peripheral watershed D includes four boundaries: bottom boundary S_BFree surface boundary S_FBoundary of object plane S_SAnd truncating the boundary S_R. Assuming that a flow field is not rotating, is not viscous and is not compressible, a fluid domain meets a Laplace equation, a velocity potential is introduced, and a basic control equation and boundary conditions are expressed as

To obtain a velocity potential phi_jIntroducing a Green's function G (P, Q) to establish a boundary integral equation, and satisfying the unknown source intensity distributed on the surface of the object

Wherein P is any point in the fluid domain; s is average wet surface; q is a point at S. Substituting into the boundary condition of the object plane to obtain an integral equation of the source intensity of

The surface element method is adopted to solve the equation, and the basic idea is to disperse the wet surface by utilizing a triangular/quadrilateral surface element and then convert the equation into a linear equation set with unknown source intensity.

The fluid loads f (t) acting on the hull structure can be divided into two categories: hydrostatic load F^S(t) and hydrodynamic load F^D(t) of (d). The hydrodynamic load can be further decomposed into an incident wave force F_I(t) diffraction force F_D(t) and radiation force F_R(t) of (d). Thus, the total fluid load can be broken down into

{F(t)}＝{F^S(t)}+{F_I(t)}+{F_D(t)}+{F_R(t)} (5)

For hydrostatic load F^S(t), assuming that the vessel motion is linear, simplification is to

{F^S(t)}＝-[C]{η}e^iωt(6) Where C is the hydrostatic coefficient, which can be obtained by integrating the hydrostatic pressure along the average wet surface of the hull. Incident wave force F_I(t) and diffraction force F_D(t) jointly constitute a wave interference force F_ID(t), which is related to the form of the incident wave, is described

In the formula, ζ_aIn order to be of an amplitude,andthe incident and diffracted potentials are given in units of amplitude. By integrating the radiation pressure of the wet surface, the radiation force is obtained, i.e.

In the equation of motion of a vessel, the radiation force is usually expressed in the form of a three-dimensional hydrodynamic coefficient, denoted as

In the formula, A is an additional mass and B is a damping coefficient.

And 3) establishing a six-degree-of-freedom motion equation at the gravity center of the hull under the waves. Various fluid load components (equations ((6), (7) and (8)) acting on the ship body are substituted into the ship motion equation (1), a time term is eliminated, and a quasi-static equation system is obtained as

([C]-ω²([M]+[A])+iω[B]){η}＝{f} (10)

The motion equation is a linear equation set, and can be solved by adopting a Gaussian elimination method, so that a real part and an imaginary part of the six-degree-of-freedom motion are obtained, and the amplitude and the phase of the ship motion can be expressed as

And 4) establishing a relative motion forecasting model of the ship wave three-dimensional space. The motion form of the bow is different from the gravity center, when the ship body is assumed to be a rigid body, the motion form of the three-dimensional space of the ship body can be obtained according to the rigid body motion theory, and the motion of the three-dimensional space is usually solved in a relative motion form by considering the influence of waves. Assuming that the hull encounters a unit harmonic, for any point (x, y, z) of the hull, the horizontal and vertical relative displacements can be expressed as

In the formula (x)_b,y_b,z_b) The coordinates of the gravity center of the ship body are obtained; h_y、H_zRelative displacement of the vessel and the waves; beta is the angle of the wave direction; k is the wave number. Relative horizontal velocity y of ship waves_vAnd a vertical velocity z_vIs expressed as

In the formula u_wAnd w_wVertical and horizontal wave velocities, respectively.

It is noted that the roll motion is taken as a separate quantity of the underwater motion, the displacement changes caused by it are taken into account separately, and that under the rigid body model the rotation of the structure is kept in agreement in three-dimensional space with the motion pattern at the centre of gravity of the structure, i.e. the roll motion is kept in agreement

w＝η₄ (16)

By adopting the steps 1-4, the time history of the transverse motion, the vertical motion and the transverse shaking motion of the specific section of the ship body can be obtained, as shown in fig. 3.

And 5) establishing an asymmetric water-entering slamming model. The ship body is sliced, the three-dimensional slamming problem is converted into two-dimensional slamming, and the calculated amount is simplified. Hull section at transverse velocity y_v(formula (14)) and a vertical velocity z_v(formula (15)) and the roll velocity w into water, as shown in FIG. 4. The entire fluid domain boundary has an upper portion S_TBottom S_BRemote S_CDough kneading S_S. The upper part of the free surface is air, and the lower part of the free surface is water. Upper side S of the basin_TSet as pressure outlet boundary, bottom S_BAnd both sides S_CFor no slip boundary, the object surface S_SIs a slip-free rigid boundary.

And 6) solving the water-entering slamming problem by applying a VOF method and forecasting the slamming load. And establishing a two-phase flow model of the water inlet impact problem based on an N-S equation. Assuming the fluid is incompressible and neglecting the viscosity and gravitational effects of the fluid, the continuity equations and momentum equations are reduced to

Where p is the pressure, u is the velocity vector, and ρ is the density of the fluid. Solving the above equation by using VOF method, assuming water as basic phase, introducing phase equation

Wherein α is the volume fraction of the base phase. The density of the fluid can be further expressed as

ρ＝αρ₁+(1-α)ρ₂ (20)

In the formula, ρ₁And ρ₂The densities of water and air, respectively, are typically taken to be 1.0X 10³kg/m³And 1.25kg/m³. Equations (17), (18), and (19) constitute a continuity equation, a momentum equation, and a phase equation for solving the two-phase flow model using the VOF method. The water entry speed is determined by the ship wave relative motion relation (equations (14) - (16)) given in the step (4). In numerical simulation, a momentum equation is subjected to discrete solution based on a finite volume method, a time item adopts an Euler hidden format, and each item of an expression (18) is discrete into

In the formula, the superscripts n and r denote the current time step (value known) and the predicted time step (value unknown), respectively, the subscript f denotes the value of the grid surface, V_pVolume of the grid, Δ t is the time step, F_fAs a flux, S denotes a plane vector of the grid cell. Velocity of the surface of the gridCan be obtained according to the speed of the centers of adjacent body units, and can be obtained by adopting a center difference method, namely Is the normal gradient of the surface velocity, noted

Where subscripts P and N denote the speed of the current grid and the adjacent grid, respectively, | S_fAnd | d | is the distance between grids. It is noted that in equation (18) the dispersion of the flow term, where the flux F_fThe speed at the current known time step is used for calculation and another predicted speed is kept as an unknown quantity. This process of knowing one of the velocities and retaining the other unknown velocity is linearization. Substituting formulae (21) to (24) for formula (18), and introducing a pressure gradient and a source term, having

Wherein

In finding the predicted speedThereafter, the pressure term and source term in equation (18) are again removed and shifted, the symbol HbyA is used instead of the predicted time step velocity, and is defined as follows

It can be seen that within a certain time step A_P，A_NAnd E_PAll remain unchanged and are unique unknownsCan be obtained by equation (29). It is noted that the continuity equation is not used at this time, which means that it is predictedThe mass conservation is not necessarily satisfied, and the correction can be performed by adopting a common PISO algorithm.

In the phase equation (20), the time term is dispersed in a hidden format, and the volume fraction is dispersed in a standard finite difference mode, namely

In the formula, superscripts n and n +1 respectively represent a previous time step and a subsequent time step,is the surface flux. In the time stepping solving process, when water or air (alpha) exists in the grid_a0 or 1), the area flux is obtained using a standard central difference mode when the grid is the air and water interface (0)<α_a<1) The free surface is described by a geometric reconstruction mode. During the time stepping, the pressure of each node is monitored, and the pressure time history result (figure 5) of each part and the pressure distribution (figure 6) of the whole section can be obtained.

Finally, it should be noted that: the above embodiments are merely illustrative and not restrictive of the technical solutions of the present invention, and any equivalent substitutions and modifications or partial substitutions made without departing from the spirit and scope of the present invention should be included in the scope of the claims of the present invention.