Three-dimensional meshless numerical simulation method for water power characteristics of netting

Abstract

The application discloses a three-dimensional meshless numerical simulation method for water dynamic characteristics of a net. The method comprises the following steps: obtaining a net to be numerically simulated; constructing a fluid motion control equation according to a continuity equation and a momentum equation, and performing discrete processing on the fluid motion control equation based on a smoothed particle hydrodynamics method, and combining a wave making function to construct a meshless numerical water tank; performing Lagrange type particle discrete processing on the net according to the shape of the net, and combining a screen model to construct a Lagrange type net particle model; reading the Lagrange type net particle model into the meshless numerical water tank, and performing meshless coupling calculation on the net and the fluid in each time step to obtain fluid resistance received by the net. The application realizes numerical simulation of water dynamic characteristics of the net under complex marine environment by adopting the smoothed particle hydrodynamics method to disperse the fluid control equation, and can be widely applied to the field of marine engineering technology.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, and in particular to a three-dimensional meshless numerical simulation method for the hydrodynamic characteristics of netting. Background Technology

[0002] Marine ranching is an important path for the transformation and upgrading of the traditional fishery industry, and deep-sea aquaculture equipment is the core equipment for developing marine ranching. Deep-sea aquaculture faces complex wave and current environments, with extreme waves occurring frequently. As a crucial component of aquaculture cages, netting not only maintains the aquaculture space and prevents escape of farmed organisms, but also bears a significant portion of the hydrodynamic load. Establishing accurate and efficient hydrodynamic calculation methods for netting is essential for improving the safety of the entire deep-sea aquaculture equipment. While empirical formulas in related technologies simplify the complexity of practical problems to some extent, these simplifications can cause predicted results to deviate from reality. Furthermore, traditional grid-based methods suffer from numerical dissipation and have low accuracy in simulating strong nonlinear waves, making it difficult to solve the hydrodynamic characteristics of netting in complex wave fields at high sea states. In summary, the technical problems in related technologies urgently need to be solved. Summary of the Invention

[0003] In view of this, embodiments of the present invention provide a three-dimensional meshless numerical simulation method for the hydrodynamic characteristics of netting, so as to improve the accuracy of numerical simulation of the hydrodynamic characteristics of netting.

[0004] On the one hand, the present invention provides a three-dimensional meshless numerical simulation method for the hydrodynamic characteristics of netting, comprising:

[0005] Obtain the mesh fabric to be numerically simulated;

[0006] The fluid motion control equations are constructed based on the continuity equation and the momentum equation, and the fluid motion control equations are discretized based on the smooth particle fluid dynamics method. The meshless numerical water tank is then constructed by combining the wave generation function.

[0007] Based on the shape of the mesh, the mesh is subjected to Lagrange-type particle discretization processing, and a Lagrange-type mesh particle model is established by combining it with the screen model.

[0008] The Lagrange-type mesh particle model is read into the meshless numerical water tank, and meshless coupling calculations are performed on the mesh and fluid at each time step to obtain the influence of the mesh on the fluid and the fluid resistance it experiences.

[0009] Optionally, the step of constructing fluid motion control equations based on the continuity equation and momentum equation, discretizing the fluid motion control equations based on the smooth particle hydrodynamics method, and constructing a meshless numerical water tank by combining a wave generation function includes:

[0010] The netting is processed by constructing a numerical water tank model based on the right-hand Cartesian coordinate system to obtain the numerical water tank model.

[0011] The fluid motion analysis of the numerical water tank model is performed based on the continuity equation and the momentum equation to obtain the fluid motion control equation.

[0012] The fluid motion control equations are discretized and solved using the particle approximation method based on the smoothed particle fluid dynamics method, resulting in the discretized fluid motion control equations.

[0013] The numerical water tank model is simulated by combining the discretized fluid motion control equations and wave generation functions to obtain a meshless numerical water tank.

[0014] Optionally, the step of combining the discretized fluid motion control equations and wave generation function to simulate the numerical water tank model to obtain a meshless numerical water tank includes:

[0015] The free surface boundary conditions of the numerical pool model are expanded using the perturbation method to obtain the equations of motion for the push plate.

[0016] The second-order harmonic elimination process is applied to the equation of motion of the pusher plate to obtain the wave generation function;

[0017] Wave simulation is performed on the numerical water tank model using the wave generation function, and fluid motion simulation is performed on the numerical water tank model using the discretized fluid motion control equations to obtain a meshless numerical water tank.

[0018] Optionally, the step of performing fluid motion analysis on the numerical water tank model based on the continuity equation and momentum equation to obtain the fluid motion control equation includes:

[0019] By setting a wave-damping boundary for the numerical water tank model and adding a source term to the momentum equation to perform wave-damping processing, the wave-damped momentum equation is obtained.

[0020] The fluid motion analysis of the numerical water tank model is performed based on the continuity equation and the momentum equation after wave suppression to obtain the fluid motion control equation.

[0021] Optionally, the step of performing Lagrange-type particle discretization on the mesh according to its shape and establishing a Lagrange-type mesh particle model in conjunction with a screen model includes:

[0022] Based on the shape of the mesh, the mesh is subjected to Lagrange-type particle discretization to obtain the mesh particle space;

[0023] Based on the hydrodynamic formula of the screen model, the influence relationship between net particles and fluid particles is established in the net particle space, resulting in a Lagrange-type net particle model.

[0024] Optionally, the step of performing meshless coupling calculations on the mesh and fluid at each time step includes:

[0025] The angle of attack between the plane of the Lagrange-type mesh particle model and the incoming flow direction in the meshless numerical water tank is calculated to obtain the mesh angle of attack;

[0026] The lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model are calculated based on the mesh angle of attack.

[0027] Obtain fluid particles within the influence range of the mesh in the fluid, and perform kernel function interpolation on the mesh particles based on the velocity of the fluid particles to obtain the flow velocity at the location of the mesh particles;

[0028] The fluid resistance of the mesh particles is calculated based on the flow velocity at the location of the mesh particles and the drag coefficient.

[0029] The fluid resistance experienced by the mesh is obtained by summing the fluid resistance experienced by all mesh particles on the mesh.

[0030] Optionally, the calculation of the angle of attack between the plane of the Lagrange-type mesh particle model and the incoming flow direction in the meshless numerical water tank to obtain the mesh angle of attack includes:

[0031] Select a net particle from the Lagrange-type net particle model, perform position vector calculation on the net particle, and obtain the normal vector of the net particle.

[0032] The direction of the normal vector is calculated based on the sign function to obtain the normal vector pointing in the direction of fluid flow;

[0033] The angle of attack of the mesh is obtained by calculating the inverse cosine trigonometric function of the normal vector pointing in the direction of fluid flow.

[0034] Optionally, the step of calculating the lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model based on the mesh angle of attack includes:

[0035] Obtain the mesh density of the mesh;

[0036] The lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model are calculated based on the mesh density and mesh angle of attack.

[0037] Optionally, the step of obtaining fluid particles within the influence range of the mesh in the fluid, and performing kernel function interpolation on the mesh particles based on the velocity of the fluid particles to obtain the flow velocity at the location of the mesh particles includes:

[0038] The position vector between the mesh particles and the fluid particles is calculated based on the fluid particle type. The fluid particles in the fluid that are within the influence range of the mesh are obtained based on the position vector to obtain the first fluid particle.

[0039] The fluid motion control equations are solved using the smooth particle fluid dynamics method, and the first fluid particle is updated to obtain the second fluid particle.

[0040] The flow velocity at the location of the mesh particles is obtained by calculating the mesh particles near the second fluid particle using the kernel function interpolation formula.

[0041] Optionally, the step of calculating the fluid resistance of the mesh particles based on the flow velocity at the location of the mesh particles and the drag coefficient includes:

[0042] Obtain the fluid density and the volume of the mesh particles;

[0043] The fluid resistance of the mesh particles is calculated by using the fluid density, the volume of the mesh particles, and the flow velocity at the location of the mesh particles according to the fluid resistance formula.

[0044] On the other hand, embodiments of the present invention also provide a three-dimensional numerical simulation system for the hydrodynamic characteristics of netting, comprising:

[0045] The first module is used to obtain the mesh to be numerically simulated;

[0046] The second module is used to construct the fluid motion control equation based on the continuity equation and the momentum equation, and to discretize the fluid motion control equation based on the smooth particle fluid dynamics method, and to construct a meshless numerical water tank by combining the wave generation function.

[0047] The third module is used to perform Lagrange-type particle discretization processing on the mesh according to its shape, and to establish a Lagrange-type mesh particle model in combination with the screen model.

[0048] The fourth module is used to read the Lagrange-type mesh particle model into the meshless numerical water tank, and to perform meshless coupling calculations on the mesh and the fluid at each time step to obtain the influence of the mesh on the fluid and the fluid resistance it experiences.

[0049] On the other hand, embodiments of the present invention also disclose an electronic device, including a processor and a memory;

[0050] The memory is used to store programs;

[0051] The processor executes the program to implement the method described above.

[0052] On the other hand, embodiments of the present invention also disclose a computer-readable storage medium storing a program that is executed by a processor to implement the methods described above.

[0053] On the other hand, embodiments of the present invention also disclose a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned method.

[0054] Compared with existing technologies, the present invention, employing the above technical solutions, has the following technical advantages: The present invention uses a smooth particle hydrodynamics method to discretize the fluid motion control equations to construct a meshless numerical water tank. This allows for the discretization of the fluid control equations using the smooth particle hydrodynamics method, enabling numerical simulation of the hydrodynamic characteristics of netting in complex marine environments. Furthermore, the present invention performs Lagrange-type particle discretization on the netting based on its shape and combines this with a screen model to establish a Lagrange-type netting particle model. This allows for the calculation of the resistance to the fluid from each particle on the netting, obtaining the influence of the netting on the fluid, thereby reducing the numerical dissipation faced in simulating the hydrodynamic problems of netting in complex wave and current environments. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart of a three-dimensional meshless numerical simulation method for the hydrodynamic characteristics of a net, provided in an embodiment of this application;

[0057] Figure 2 This is a schematic diagram of the structure of a numerical water tank provided in an embodiment of this application;

[0058] Figure 3 This is a flowchart of a coupled algorithm for solving the hydrodynamic characteristics of a net, provided in an embodiment of this application.

[0059] Figure 4 This is a schematic diagram of the force on a mesh fabric at a certain angle of attack in a uniform flow, provided in an embodiment of this application.

[0060] Figure 5 This is a schematic diagram of the calculation of the angle of attack of the mesh and the incoming flow provided in an embodiment of this application;

[0061] Figure 6 This is a schematic diagram illustrating the effect of discrete mesh particles on fluid particles, provided in an embodiment of this application.

[0062] Figure 7 This is a schematic diagram of flow velocity interpolation calculation at the mesh particles provided in an embodiment of this application;

[0063] Figure 8 This is a schematic diagram of a discrete model of a mesh garment provided in an embodiment of this application;

[0064] Figure 9 This is a comparison image of meshless numerical simulation results and experimental images of free liquid surface deformation of a distorted wave, provided in an embodiment of this application.

[0065] Figure 10 This is a comparison chart of calculated and experimental values ​​of the drag coefficient of a mesh fabric at different angles of attack in a uniform flow, provided by an embodiment of this application.

[0066] Figure 11 This is a comparison chart of calculated and experimental values ​​of the lift coefficient of a mesh fabric at different angles of attack in a uniform flow, provided by an embodiment of this application.

[0067] Figure 12 This is a schematic diagram of netting calculation in waves provided in an embodiment of this application;

[0068] Figure 13 This is a comparison chart of calculated and experimental values ​​of the force on a mesh garment in waves, provided in an embodiment of this application. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0070] In related technologies, the hydrodynamic loads on netting are mainly studied through model experiments, empirical formulas, and numerical simulations. In the application of empirical formulas, simplifications are often made to reduce the complexity of practical problems, which can cause the predicted results to deviate from reality to some extent. Traditional gridded methods suffer from numerical dissipation and have low accuracy in simulating strongly nonlinear waves, making it difficult to solve the hydrodynamic characteristics of netting in complex wave fields at high sea states.

[0071] In view of this, this application provides a three-dimensional meshless numerical simulation method for the hydrodynamic characteristics of netting. The numerical simulation method in this application can be applied to a terminal, a server, or software running on either a terminal or a server. The terminal can be a tablet computer, a laptop computer, a desktop computer, etc., but is not limited to these. The server can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms.

[0072] Reference Figure 1 This invention provides a three-dimensional meshless numerical simulation method for the hydrodynamic properties of netting, comprising:

[0073] S101. Obtain the mesh fabric to be numerically simulated;

[0074] S102. Construct fluid motion control equations based on the continuity equation and momentum equation, and discretize the fluid motion control equations based on the smooth particle fluid dynamics method, and construct a meshless numerical water tank by combining the wave generation function.

[0075] S103. Based on the shape of the mesh, perform Lagrange-type particle discretization on the mesh and combine it with the screen model to establish a Lagrange-type mesh particle model.

[0076] S104. The Lagrange-type mesh particle model is read into the meshless numerical water tank. At each time step, the mesh and fluid are coupled in a meshless manner to obtain the influence of the mesh on the fluid and the fluid resistance it experiences.

[0077] In this embodiment of the invention, a netting for three-dimensional numerical simulation is obtained. The continuity and momentum equations are selected as the fluid motion control equations. Based on the smooth particle fluid dynamics method, the control equations are discretized, and a meshless numerical water tank is established. Wave simulation is then performed on the meshless numerical water tank using a wave-generating function. The netting is then discretized into Lagrange-type particles, and combined with a screen model to form a novel Lagrange framework model for solving the hydrodynamic coefficients of the netting. This model calculates the resistance to the fluid from each particle on the netting, thus obtaining the influence of the netting on the fluid. Finally, the Lagrange-type netting particle model is read into the meshless numerical water tank, and meshless coupling calculations are performed on the netting and the fluid at each time step to obtain the fluid resistance experienced by the netting. This embodiment of the invention uses the smooth particle fluid dynamics method to discretize the fluid control equations, enabling numerical simulation of the hydrodynamic characteristics of netting in complex marine environments. It can address the problems of large numerical dissipation and interface capture faced by traditional meshed methods in simulating the hydrodynamic problems of netting in complex wave and current environments, particularly in high sea states with strong nonlinearity, strong convection, and large tumbling and breaking waves.

[0078] As a further optional implementation, the step of constructing fluid motion control equations based on the continuity equation and momentum equation, discretizing the fluid motion control equations based on the smoothed particle hydrodynamics method, and constructing a meshless numerical water tank by combining a wave generation function includes:

[0079] The netting is processed by constructing a numerical water tank model based on the right-hand Cartesian coordinate system to obtain the numerical water tank model.

[0080] The fluid motion analysis of the numerical water tank model is performed based on the continuity equation and the momentum equation to obtain the fluid motion control equation.

[0081] The fluid motion control equations are discretized and solved using the particle approximation method based on the smoothed particle fluid dynamics method, resulting in the discretized fluid motion control equations.

[0082] The numerical water tank model is simulated by combining the discretized fluid motion control equations and wave generation functions to obtain a meshless numerical water tank.

[0083] In the embodiments of the invention, reference is made to... Figure 2This paper presents a schematic diagram of a meshless numerical water tank model. Benefiting from the characteristics of the weakly compressible smooth particle fluid dynamics method, the free surface boundary conditions in the constructed meshless numerical water tank are automatically satisfied without further processing. A right-handed Cartesian coordinate system is used, with the origin located at the leftmost end of the numerical water tank. In the meshed model, the positive direction of the x-axis is defined as the flow direction, the y-axis is perpendicular to the flow direction, and the z-axis is vertically upward. The left end of the numerical water tank is defined as the wave inlet boundary or inflow boundary, and the right end is defined as the wave dissipation boundary or outflow boundary. The other sidewalls and bottom of the tank are defined as solid wall boundaries. During numerical calculation, the shear stress on the solid wall boundaries is set to 0, thus constructing the numerical water tank model. Then, based on the conservation of mass and momentum, the basic governing equations of the fluid, namely the continuity equation and the momentum equation, are derived. Fluid motion analysis is performed on the numerical water tank model according to the continuity and momentum equations to obtain the fluid motion governing equations. The expression of the continuity equation is shown below:

[0084]

[0085] In the formula, t represents time, and ρ represents fluid density. For Hamiltonian operators, Represents the fluid velocity vector;

[0086] The momentum equation is expressed as follows:

[0087]

[0088] In the formula, T represents the total stress tensor. It can be expanded as follows:

[0089]

[0090] In the formula, p represents the isotropic pressure of the fluid element, and λ and μ are the bulk viscosity coefficient and dynamic viscosity coefficient, respectively. For low-speed flow in marine engineering, fluid compressibility can be ignored, that is... The final momentum equation is written as follows:

[0091]

[0092] In the formula, This refers to the wave-damping term, used to eliminate wave energy entering the wave-damping area to prevent wave reflection at the boundary. This term only works in the wave-damping area; it does not affect other areas. This indicates that the mesh has an effect on the fluid, which only affects the fluid around the mesh and not the fluid further away from it. This item is a key item in the hydrodynamic calculation of the netting.

[0093] As a meshless method based on the Lagrange perspective, the smoothed particle hydrodynamics method also requires establishing the relationships between pressure and density, as well as displacement and velocity, to close the equation set. The added equations are:

[0094]

[0095]

[0096] In the formula, c0 represents the artificial speed of sound, and ρ0 represents the initial density of the fluid. This represents the position vector of a fluid particle.

[0097] Smoothed particle hydrodynamics is based on the kernel approximation, using the particle approximation to discretize and solve the governing equations. In the kernel approximation theory, any continuous function... Its derivative can be obtained from the function values ​​within the compactly supported region Ω. The expression obtained through kernel approximation interpolation is as follows:

[0098]

[0099] In the formula, Known as The kernel approximation, Indicates relative position The gradient. Let h be the kernel function, where h is called the smooth length, and the kernel function is zero outside the smooth length. The obtained continuity and momentum equations are discretized, and the flow field is discretized into uniformly distributed Lagrangian-type particles, with physical information such as density, pressure, and velocity bound to the particles. The discretized governing equations are shown below, and the expression for the discretized continuity equation is shown below:

[0100]

[0101] In the formula, the subscript j represents the neighboring particle of particle i, W ij This represents the simplified form of the kernel function. The last term on the right-hand side of the continuity equation is a density dissipation term, used to prevent high-frequency density fluctuations. The calculation employs the particle approximation method modified by matrix regularization, and the equation is:

[0102]

[0103] The expression for the discretized momentum equation is shown below:

[0104]

[0105] In the equation, the second term on the right-hand side of the momentum equation is an artificial viscosity term, used to ensure the stability of the numerical simulation. In the field of marine engineering, inertial forces dominate wave and flow simulations, and the influence of physical viscosity can be ignored. Finally, the numerical pool model is simulated using the discretized fluid motion control equations and wave generation functions to obtain a meshless numerical pool.

[0106] As a further optional implementation, the simulation of the numerical water tank model by combining the discretized fluid motion control equations and wave generation function to obtain a meshless numerical water tank includes:

[0107] The free surface boundary conditions of the numerical pool model are expanded using the perturbation method to obtain the equations of motion for the push plate.

[0108] The second-order harmonic elimination process is applied to the equation of motion of the pusher plate to obtain the wave generation function;

[0109] Wave simulation is performed on the numerical water tank model using the wave generation function, and fluid motion simulation is performed on the numerical water tank model using the discretized fluid motion control equations to obtain a meshless numerical water tank.

[0110] In this embodiment of the invention, waves are generated in a meshless numerical water tank using a physics-based wave generation method. The equations of motion for the pusher plate are obtained by expanding the boundary conditions of the free surface using a perturbation method. The basic wave generation equations are in sinusoidal form and are as follows:

[0111]

[0112] In the formula, t is the time parameter, k0 is the wave number of the target wave, and ω is the dispersion relation of finite water depth. 2 =gk0tanhk0h deep Decision, h deep ω is the water depth of the numerical pool, ω is the angular frequency of the target wave, a is the wave amplitude of the target wave, and ξ0 is the amplitude of the wavemaker plate when it moves sinusoidally, which can be determined by the wave amplitude a, wave number k0, and water depth h of the target wave. deep The information was calculated from this data.

[0113] Since the above linear wave-generating equation is not suitable for strongly nonlinear waves, and second-order harmonics are generated during the wave-generating process, the second-order harmonic elimination process is performed on the pusher motion equation to obtain the wave-generating function.

[0114] An additional second-order motion is superimposed on the pusher motion equation to eliminate the second-order harmonics generated during wave generation and to improve the wave generation equation's ability to simulate strong nonlinearities. The improved wave generation equation is as follows:

[0115]

[0116] In the formula, the second term on the right-hand side of the equation represents the additional second-order motion.

[0117] Finally, wave simulation is performed on the numerical pool model using a wave generation function, and fluid motion simulation is performed on the numerical pool model using the discretized fluid motion control equations to obtain a meshless numerical pool.

[0118] As a further optional implementation, the step of performing fluid motion analysis on the numerical water tank model based on the continuity equation and momentum equation to obtain the fluid motion control equation includes:

[0119] By setting a wave-damping boundary for the numerical water tank model and adding a source term to the momentum equation to perform wave-damping processing, the wave-damped momentum equation is obtained.

[0120] The fluid motion analysis of the numerical water tank model is performed based on the continuity equation and the momentum equation after wave suppression to obtain the fluid motion control equation.

[0121] In this embodiment of the invention, to prevent wave reflection from affecting the numerical simulation results, a source term is added to the momentum equation to mitigate wave reflection, similar to the mesh method. The formula for the source term is:

[0122]

[0123] In the formula, q damper This is the numerical damping sponge layer coefficient, typically taken as 4. Represents the spatial coordinates of a Lagrange particle. L represents the coordinates of the starting point where numerical wave attenuation begins. damper This indicates the length of the wave-damping area. In this embodiment, the length of the wave-damping area is set to be 1 times the wavelength of the target wave. Wave-damping is only performed within the defined wave-damping area; other areas are excluded.

[0124] As a further optional implementation, the step of performing Lagrange-type particle discretization on the mesh according to its shape and establishing a Lagrange-type mesh particle model in conjunction with a screen model includes:

[0125] Based on the shape of the mesh, the mesh is subjected to Lagrange-type particle discretization to obtain the mesh particle space;

[0126] Based on the hydrodynamic formula of the screen model, the influence relationship between net particles and fluid particles is established in the net particle space, resulting in a Lagrange-type net particle model.

[0127] In this embodiment of the invention, based on the shape of the netting, the netting is discretized into Lagrange-type particles, and combined with a screen model to form a novel Lagrange framework model for solving the hydrodynamic coefficients of the netting. Each Lagrange-type netting particle occupies a cube space centered on its position with a side length equal to the particle's distance from the particle. The hydrodynamic forces acting on this cube space are solved using the screen model at the particle's position. The Lagrange-type netting particle model starts from each particle on the netting and introduces the screen model's hydrodynamic formula to establish the relationship between the influence of netting particles and fluid particles. The screen model is a hydrodynamic calculation model for the netting, discretizing the entire netting model into interconnected screen cells. Each cell covers a portion of the netting's ropes and mesh nodes, and the hydrodynamic forces on the cell are calculated according to the following formula:

[0128]

[0129]

[0130] In the formula, ρ represents the fluid density, A represents the projected area of ​​the cell in the direction of fluid flow, and U... rel C represents the relative velocity between the fluid and the cell. D C L These represent the drag coefficient and lift coefficient of the cell, respectively.

[0131] As a further optional implementation, the step of performing meshless coupling calculations on the mesh and fluid at each time step includes:

[0132] The angle of attack between the plane of the Lagrange-type mesh particle model and the incoming flow direction in the meshless numerical water tank is calculated to obtain the mesh angle of attack;

[0133] The lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model are calculated based on the mesh angle of attack.

[0134] Obtain fluid particles within the influence range of the mesh in the fluid, and perform kernel function interpolation on the mesh particles based on the velocity of the fluid particles to obtain the flow velocity at the location of the mesh particles;

[0135] The fluid resistance of the mesh particles is calculated based on the flow velocity at the location of the mesh particles and the drag coefficient.

[0136] The fluid resistance experienced by the mesh is obtained by summing the fluid resistance experienced by all mesh particles on the mesh.

[0137] Reference Figure 3In this embodiment of the invention, a Lagrange-type mesh particle model is read into the established meshless numerical water tank. At each time step, the coupled calculation of the mesh and the fluid is implemented. The specific implementation process is as follows: First, the angle of attack between each mesh particle and the incoming flow is calculated in real time. Then, the lift coefficient and drag coefficient at each mesh particle are calculated. Since physical information such as position, velocity, and density are bound to the particles in the meshless numerical method, the positions of fluid particle i and mesh particle j in the simulation area are calculated by distinguishing particle types, and it is determined whether they are less than the set mesh influence range. If they are less, it indicates that the fluid particle is within the influence range of the mesh model, and the influence term of the mesh on the fluid particle is calculated; otherwise, the term is zero. Then, the continuity equation and momentum equation are solved based on the smoothed particle fluid dynamics method to update the spatial position, velocity, and pressure information of fluid particle i. Finally, the flow velocity at the location of the mesh particle is obtained according to the kernel function interpolation formula, and the fluid resistance at that location is calculated. The fluid resistance experienced by the particles on the entire mesh is summed, and the total fluid resistance experienced by the entire mesh is output. By continuously repeating this process, numerical simulations of fluid resistance and surrounding flow field information of mesh with different geometries and angles of attack under complex environments can be achieved.

[0138] As a further optional implementation, the calculation of the angle of attack between the plane of the Lagrange-type mesh particle model and the incoming flow direction in the meshless numerical water tank to obtain the mesh angle of attack includes:

[0139] Select a net particle from the Lagrange-type net particle model, perform position vector calculation on the net particle, and obtain the normal vector of the net particle.

[0140] The direction of the normal vector is calculated based on the sign function to obtain the normal vector pointing in the direction of fluid flow;

[0141] The angle of attack of the mesh is obtained by calculating the inverse cosine trigonometric function of the normal vector pointing in the direction of fluid flow.

[0142] In this embodiment of the invention, the hydrodynamic coefficient of the mesh can be obtained through model experiments. Figure 4 A force diagram of the mesh is given. Based on the lift and drag coefficients of the mesh, its lift coefficient and drag coefficient can be calculated using the following formulas:

[0143]

[0144]

[0145] Even without model experiments, it can be obtained through empirical formulas. First, the angle of attack between the mesh plane and the incoming flow direction needs to be determined. The angle of attack is defined as the angle formed by the normal of the mesh and the incoming flow, ranging from 0 to... Between. The angle of attack at each discretized mesh particle can be calculated, referring to... Figure 5 This diagram illustrates the solution for the angle of attack of a mesh particle. By selecting the two closest mesh particles around the first mesh particle, their relative position vectors are calculated. Therefore, the normal vector at that particle can be obtained, using the following formula:

[0146]

[0147] The direction of the normal vector obtained at this point is uncertain. We then use the sign function to obtain the normal vector pointing in the direction of fluid flow, i.e.:

[0148]

[0149] Finally, by solving the inverse cosine trigonometric function, we obtain the angle of attack between the mesh-coated particle and the incoming flow, i.e.:

[0150]

[0151] As a further optional implementation, the step of calculating the lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model based on the mesh angle of attack includes:

[0152] Obtain the mesh density of the mesh;

[0153] The lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model are calculated based on the mesh density and mesh angle of attack.

[0154] In this embodiment of the invention, for a mesh forming a certain angle of attack θ with the incoming flow direction, the lift and drag coefficients of the mesh are calculated using the following formulas, where the lift and drag coefficients are respectively:

[0155]

[0156]

[0157] In the formula, S n The density of the mesh is a physical property of the mesh.

[0158] As a further optional implementation, the step of obtaining fluid particles in the fluid that are within the influence range of the mesh, and performing kernel function interpolation on the mesh particles based on the velocity of the fluid particles to obtain the flow velocity at the location of the mesh particles includes:

[0159] The position vector between the mesh particles and the fluid particles is calculated based on the fluid particle type. The fluid particles in the fluid that are within the influence range of the mesh are obtained based on the position vector to obtain the first fluid particle.

[0160] The fluid motion control equations are solved using the smooth particle fluid dynamics method, and the first fluid particle is updated to obtain the second fluid particle.

[0161] The flow velocity at the location of the mesh particles is obtained by calculating the mesh particles near the second fluid particle using the kernel function interpolation formula.

[0162] In this embodiment of the invention, reference is made to Figure 6 This is a schematic diagram illustrating the influence of surrounding mesh particles on fluid particles. In the numerical simulation, the area affected by the mesh particles is taken as one time the smooth length of the particles. Within this range, the mesh has an effect on the fluid, or in other words, the fluid is affected by the mesh. Outside this range...

[0163] The effect of the mesh on fluid particle i is represented as:

[0164]

[0165] In the formula, Δx represents the discrete distance between mesh particles, and W ij This represents the value of the kernel function. The velocity of mesh particle j relative to fluid particle i is represented by the following formula: C D,j C represents the drag coefficient at point j of the mesh particle. L,j This represents the lift coefficient at point j of the mesh particle, which is related to the angle of attack of the mesh relative to the flow direction.

[0166] Reference Figure 7 The flow velocity at point j of the mesh particle It can be obtained by interpolating the velocities of surrounding fluid particles, and the calculation formula is:

[0167]

[0168] As a further optional implementation, the step of calculating the fluid resistance of the mesh particles based on the flow velocity at the location of the mesh particles and the drag coefficient includes:

[0169] Obtain the fluid density and the volume of the mesh particles;

[0170] The fluid resistance of the mesh particles is calculated by using the fluid density, the volume of the mesh particles, and the flow velocity at the location of the mesh particles according to the fluid resistance formula.

[0171] In this embodiment of the invention, the fluid resistance formula for the mesh is as follows:

[0172]

[0173] In the formula, ρ represents the fluid density, and U rel,j V represents the flow velocity at the mesh particles. j It represents the volume of discrete mesh particles. The total fluid resistance experienced by the mesh can be obtained by superimposing the resistance experienced by individual mesh particles.

[0174] The simulation experiments conducted in this embodiment of the invention are as follows: Based on the hydrodynamic environment, two types of tests were set up: wave environment and uniform flow environment. In the uniform flow environment test, the netting was a flat sheet netting, 1 meter long and 1 meter wide, with a netting density S. n =0.184. The netting was fixedly placed in the test pool. The dimensions of the test pool were 4.5 meters in length, 3.66 meters in width, and 2.44 meters in depth. The netting was completely submerged and fixed in the water, with its plane 1.5 meters from the left end of the pool, its geometric center 1.83 meters from the side wall, and 1.22 meters from the water surface. The flow velocity was set at 0.5 meters per second, and the netting plane was at 0°, 30°, and 75° to the incoming flow. In the wave test environment, the netting was a flat plate, 1 meter long and 0.5 meters wide, with a density S... n =0.288, the test pool is 25 meters long, 0.5 meters wide, and 1.0 meter deep, with a water depth of 0.62 meters. A wave generator is located at the left end of the test pool, and a net is vertically fixed at a distance of 8.3 meters from the wave generator.

[0175] Numerical models were established based on experimental parameters. Depending on the marine environment, models were divided into uniform flow environments and wave environments. In the uniform flow environment, the left end of the meshless numerical pool was defined as the inflow boundary with a flow velocity of 0.5 m / s; the right end was defined as the outflow boundary. Figure 8 As shown, the mesh is discretized into Lagrange-type particles with a particle spacing of 0.05 meters. The angle of attack of the mesh is calculated, and then the lift coefficient and drag coefficient of each mesh particle are calculated. Finally, the fluid motion is controlled by combining the continuity equation and the momentum equation. Based on the smooth particle fluid dynamics method, the control equation is discretized, and the numerical simulation of the hydrodynamic characteristics of the mesh in a uniform flow can be realized.

[0176] Before conducting meshless numerical simulations of hydrodynamics in a wave environment, it is necessary to verify the wave-generating capability of the meshless numerical simulation tank. Distorted waves, as common strongly nonlinear waves, exhibit large deformations of the free surface and tumbling / breaking phenomena. First, a simulation of disordered waves is conducted in a meshless numerical simulation tank, and the simulation results are compared with experimental values, referencing... Figure 9 , Figure 9As can be seen, the deformation of the deformed free surface of the wave obtained by the meshless numerical water tank simulation is in good agreement with the experimental results, and the wave rolling phenomenon is consistent, proving that the numerical water tank based on the smooth particle hydrodynamics method is accurate and feasible in handling problems such as large deformation of the free surface and wave rolling and breaking.

[0177] Next, a numerical simulation of the hydrodynamics of the netted environment was conducted. The left end of the meshless numerical pool was set as the wave-generating boundary, and waves were generated using a pusher plate method, based on the given target wave number k0 and water depth h. deep By substituting the circular frequency ω into the wave-generating function, wave generation can be achieved; the right end of the meshless numerical water tank is set as the wave-dissipating boundary, and the waves entering the wave-dissipating region are dissipated using a momentum source; such as Figure 8 As shown, the netting is discretized into Lagrange-type particles with a particle spacing of 0.05 meters. The angle of attack of the netting is calculated, and then the lift coefficient and drag coefficient of each netting particle are calculated. Finally, the fluid motion is controlled by combining the continuity equation and the momentum equation. Based on the smooth particle fluid dynamics method, the control equation is discretized, and the numerical simulation of the hydrodynamic characteristics of netting in complex waves can be realized.

[0178] A velocity distribution around a net with different angles of attack is set in a uniform flow. There is a velocity attenuation zone in front of the net, and a larger attenuation zone behind the net, which is wider than the projected width of the net in the direction of water flow. (Refer to...) Figure 10 and Figure 11 The numerical simulation results were compared with the experimental values ​​of the model for the resistance on the mesh at different angles of attack. The numerical simulation results were in good agreement with the experimental values, with the maximum relative error not exceeding 15%, indicating that the numerical simulation results were consistent with reality.

[0179] The velocity distribution on the vertical mesh and at the wave surface in the wave can be referenced. Figure 12 The comparison between the calculated results of the vertical netting in the waves and the model test values ​​can be found by referring to... Figure 13 Since waves are the reciprocating motion of water particles, the resistance experienced by the netting also exhibits a similar changing pattern. The results show that the numerical calculations agree well with the experimental values ​​for both the peak and trough values ​​of the resistance, with a maximum relative error of no more than 10%, indicating that the numerical simulation results are consistent with reality.

[0180] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0181] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0182] The above is a detailed description of the preferred embodiments of the present invention, but the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A three-dimensional meshless numerical simulation method for the hydrodynamic characteristics of a net, characterized in that, The method includes: Obtain the mesh fabric to be numerically simulated; The fluid motion control equations are constructed based on the continuity equation and the momentum equation, and the fluid motion control equations are discretized based on the smooth particle fluid dynamics method. The meshless numerical water tank is then constructed by combining the wave generation function. Based on the shape of the mesh, the mesh is subjected to Lagrange-type particle discretization processing, and a Lagrange-type mesh particle model is established by combining it with the screen model. The Lagrange-type mesh particle model is read into the meshless numerical water tank, and meshless coupling calculations are performed on the mesh and fluid at each time step to obtain the influence of the mesh on the fluid and the fluid resistance it experiences. The process involves constructing fluid motion control equations based on the continuity and momentum equations, discretizing these equations using smooth particle hydrodynamics, and then constructing a meshless numerical water tank using a wave generation function. The netting is processed by constructing a numerical water tank model based on the right-hand Cartesian coordinate system to obtain the numerical water tank model. The fluid motion analysis of the numerical water tank model is performed based on the continuity equation and the momentum equation to obtain the fluid motion control equation. The fluid motion control equations are discretized and solved using the smoothed particle fluid dynamics method through kernel function approximation and particle approximation to obtain the discretized fluid motion control equations. The numerical water tank model is simulated by combining the discretized fluid motion control equations and wave generation function to obtain a meshless numerical water tank. The step of performing Lagrange-type particle discretization on the mesh according to its shape, and establishing a Lagrange-type mesh particle model by combining it with a screen model, includes: Based on the shape of the mesh, the mesh is subjected to Lagrange-type particle discretization to obtain the mesh particle space; Based on the hydrodynamic formula of the screen model, the influence relationship between net particles and fluid particles is established in the net particle space to obtain a Lagrange-type net particle model. The step of performing meshless coupling calculations on the mesh and fluid at each time step includes: The angle of attack between the plane of the Lagrange-type mesh particle model and the incoming flow direction in the meshless numerical water tank is calculated to obtain the mesh angle of attack; The lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model are calculated based on the mesh angle of attack. The fluid particles within the influence range of the mesh in the fluid are obtained, and the mesh particles are interpolated using a kernel function based on the velocity of the fluid particles to obtain the flow velocity at the location of the mesh particles; The fluid resistance of the mesh particles is calculated based on the flow velocity at the location of the mesh particles and the drag coefficient. The fluid resistance experienced by the mesh is obtained by summing the fluid resistance experienced by all mesh particles on the mesh.

2. The method according to claim 1, characterized in that, The numerical water tank model is simulated by combining the discretized fluid motion control equations and wave generation functions to obtain a meshless numerical water tank, including: The free surface boundary conditions of the numerical pool model are expanded using the perturbation method to obtain the equations of motion for the push plate. The second-order harmonic elimination process is applied to the motion equation of the pusher plate to obtain the wave generation function; Wave simulation is performed on the numerical water tank model using the wave generation function, and fluid motion simulation is performed on the numerical water tank model using the discretized fluid motion control equations to obtain a meshless numerical water tank.

3. The method according to claim 1, characterized in that, The process of performing fluid motion analysis on the numerical water tank model based on the continuity equation and momentum equation yields the fluid motion control equations, including: By setting a wave-damping boundary for the numerical water tank model and adding a source term to the momentum equation to perform wave-damping processing, the wave-damped momentum equation is obtained. The fluid motion analysis of the numerical water tank model is performed based on the continuity equation and the momentum equation after wave suppression to obtain the fluid motion control equation.

4. The method according to claim 1, characterized in that, The calculation of the angle of attack between the plane of the Lagrange-type mesh particle model and the incoming flow direction in the meshless numerical water tank yields the mesh angle of attack, including: Select net particles from the Lagrange-type net particle model, perform position vector calculation on the net particles, and obtain the normal vector of the net particles; The direction of the normal vector is calculated based on the sign function to obtain the normal vector pointing in the direction of fluid flow; The angle of attack of the mesh is obtained by calculating the inverse cosine trigonometric function of the normal vector pointing in the direction of fluid flow.

5. The method according to claim 1, characterized in that, The calculation of the lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model based on the mesh angle of attack includes: Obtain the mesh density of the mesh; The lift coefficient and drag coefficient of each mesh particle in the Lagrange-type mesh particle model are calculated based on the mesh density and mesh angle of attack.

6. The method according to claim 1, characterized in that, The step of obtaining fluid particles within the influence range of the mesh in the fluid, and performing kernel function interpolation on the mesh particles based on the velocity of the fluid particles to obtain the flow velocity at the location of the mesh particles, includes: The position vector between the mesh particles and the fluid particles is calculated based on the fluid particle type. The fluid particles in the fluid that are within the influence range of the mesh are obtained based on the position vector to obtain the first fluid particle. The fluid motion control equations are solved using the smooth particle fluid dynamics method, and the first fluid particle is updated to obtain the second fluid particle. The flow velocity at the location of the mesh particles is obtained by calculating the mesh particles near the second fluid particle using the kernel function interpolation formula.

7. The method according to claim 1, characterized in that, The calculation of the fluid resistance of the mesh particles based on the flow velocity at the location of the mesh particles and the drag coefficient includes: Obtain the fluid density and the volume of the mesh particles; The fluid resistance of the mesh particles is calculated by using the fluid density, the volume of the mesh particles, and the flow velocity at the location of the mesh particles according to the fluid resistance formula.

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