A simulation method for coupling fish swimming and water flow in a culture net cage

Abstract

This invention belongs to the field of fluid simulation technology and relates to a simulation method for the coupling of fish swimming and water flow in aquaculture cages. It couples the motion model of an individual fish with a net model, calculates the force on an individual fish to obtain the force on the entire fish swarm in the cage, and calculates the porous medium coefficient of the porous medium model of the fish swarm. Assumptions are made as follows: a) the fish in the cage are of the same size and have no mutual influence; b) when the fish swarm moves against the current, they are all arranged facing the current and are uniformly distributed in the cage; c) when the fish swarm swims in a circular pattern, they are equally spaced radially and uniformly distributed vertically. Based on these assumptions, a hypothetical volumetric force source term is added to the area where the fish swarm is located to approximate the flow obstruction effect of the fish swarm; force calculations are then performed to obtain the force in the porous medium region. This invention reduces the simulation complexity of the movement of a large number of fish in aquaculture cages while ensuring the accuracy of the calculation model, achieving accurate simulation of the flow field inside and around the aquaculture cage under the influence of fish swimming.

Description

Technical Field

[0001] This invention belongs to the field of fluid simulation technology, specifically relating to a simulation method for the coupling of fish swimming and water flow in aquaculture cages. Background Technology

[0002] The expansion of marine aquaculture into deep-sea and offshore areas has become an inevitable trend for the green and efficient development of my country's marine fisheries. To date, my country has built over 50 large-scale deep-sea aquaculture cages. These cages typically have an effective aquaculture volume of tens of thousands of cubic meters, a designed annual fish production of several thousand tons, and can simultaneously raise hundreds of thousands of marine fish at high densities. The flow field inside and outside the deep-sea aquaculture cage directly affects the load on the cage and its structural safety, as well as the transport efficiency of feed particles, dissolved oxygen, and fish excrement. Since the cage is a permeable structure, its internal and external flow field characteristics are quite complex; especially under the influence of high-density fish populations within the cage, accurate analysis of the flow field characteristics inside and outside the cage is a recognized technical challenge in the industry.

[0003] Existing technologies include simulation methods for the flow field inside and around aquaculture cages. For example, Chinese patent CN105868466A discloses a refined three-dimensional numerical simulation method for fluid-structure interaction of flexible netting structures, and CN103235878A discloses a simulation method for the influence of flexible netting on wave propagation. However, the simulation of the flow field inside and around the aquaculture cage under the influence of fish swimming is not considered. Existing technologies include simulation techniques for the interaction between the swimming of a single or limited number of fish and the surrounding fluid. For example, Chinese patent CN103412991A discloses a simulation method for the influence of a netting cage on water flow, and CN118052166A discloses a simulation method for the influence of fish movement on the flow field distribution in a recirculating aquaculture pond. Although these methods involve the influence of fish, due to the large number and high density of fish in aquaculture cages, no efficient analysis method for the coupling effect of high-density fish and water flow has been reported.

[0004] The aforementioned existing technologies cannot accurately calculate the flow field inside and outside the net cage under the influence of fish swimming, and suffer from problems such as low computational efficiency and low computational accuracy. The methods are immature, and the shortcomings of some key parameters rely on experience. Although some inventions have proposed using porous media models to simulate the influence of fish movement on the flow field distribution in recirculating aquaculture ponds, their discussion of the porous media coefficient is insufficient and not applicable to simulating the influence of fish movement on the flow field inside and outside the aquaculture net cage. Summary of the Invention

[0005] The purpose of this invention is to solve the above-mentioned problems in the existing technology, establish a scientific and complete calculation method for the coupling of fish schools and flow fields, realize efficient analysis of the coupling effect between high-density fish schools and water flow in net cages, and propose a simulation method for the coupling of fish swimming and water flow in aquaculture net cages, so as to realize accurate analysis of the flow field inside and outside the net cages. This has important guiding role in the safety analysis of net cage structure, optimization of aquaculture capacity, and formulation of feeding strategies.

[0006] The technical solution of this invention is:

[0007] A simulation method for the coupling of fish swimming and water flow in aquaculture cages includes the following steps:

[0008] (1) Couple the motion model of a single fish with the net model, and obtain the force on the single fish through numerical calculation;

[0009] (2) Based on the force on a single fish, the force on the entire fish group in the net cage is obtained, and then the porous medium coefficient of the porous medium model of the fish group is calculated.

[0010] The following simplification is made for the large number of farmed fish in net cages:

[0011] a. Assume that the fish in the net cage are of the same size and do not affect each other;

[0012] b. When the fish swim against the current, assume that they are all arranged against the current and evenly distributed in the net cage;

[0013] c. When a school of fish swims in a circular pattern, it is assumed that they are equally spaced radially and uniformly distributed vertically.

[0014] Based on the above assumptions, the force exerted on the fish school is directly proportional to the number of fish in the school. x , y , z The forces in the three directions satisfy F fish-school = n × F fish ;

[0015] Based on the above assumptions, a hypothetical volumetric force source term is added to the area where the fish are located to approximate the flow obstruction effect of the fish, and this is achieved using a porous medium model. The formula is expressed as follows:

[0016] (9)

[0017] In the formula, F fish-school Calculate the forces acting on the fish body for the solid model. F porous The force on the fish body is represented by the source term model. ρ For fluid density,u For fluid velocity, λ For the thickness of the porous medium, A For the area of ​​the porous medium region, in the source term model λA It can be determined by the aquaculture water where the fish are located. V wf express; C ij Further expressed as:

[0018] (10)

[0019] (3) Establish a porous medium model that couples the net cage with the moving fish group, and use the porous medium model to perform force calculations;

[0020] When using a porous media model for force calculations, the model simplifies the obstruction of water flow by the solid structure to a uniformly distributed resistance in the fluid, thus failing to accurately represent the porous solid structure and making direct force analysis impossible. To address this issue, based on Newton's second law, the control volume analysis method is used to discretize the equations, and the acceleration of the porous media region is integrated to obtain the forces acting on the porous media region, expressed as follows:

[0021] (11)

[0022] In the formula, m The mass of the unit control body, F The resultant force of external forces;

[0023] When the incoming flow velocity remains constant, the momentum equation in the x-direction can be expressed as:

[0024] (12)

[0025] In the formula, F d As resistance, CS To integrate along the surface of the control volume. A The flow-facing area of ​​the porous medium region;

[0026] The above formula also applies in the y and z directions;

[0027] According to Morrison's formula, the drag coefficient C d It can be represented as:

[0028] (13).

[0029] Furthermore, in step (1), a single fish motion model is established, and the fish body swaying is a trevally motion pattern, the wave equation of which is:

[0030] (1)

[0031] (2)

[0032] In the formula, y The position of the fish's body at various points along its midline is represented by time. t and location x The parameters (the fish head coordinates are (0,0)). The parametric equation for the swing amplitude is... k This is a wavelength-dependent quantity. f For frequency-dependent quantities, a Indicates amplitude, For the initial phase, parameters l Indicates the starting position of the fish's body sway. L This indicates the length of the fish's body.

[0033] Furthermore, in step (1), a mesh model is established based on the porous medium model, and its formula is expressed as follows:

[0034] (3)

[0035] (4)

[0036] In the formula, S i yes i Towards( x , y , z Momentum source term, u j For the incoming flow velocity, μ The dynamic viscosity of the fluid. D ij and C ij This is the coefficient matrix of the porous media model. D n Indicates the normal viscous drag coefficient. D t This represents the tangential viscous drag coefficient. C n Indicates the normal inertial drag coefficient. C t This represents the tangential inertial drag coefficient;

[0037] When water flows through a porous medium region, the force acting on that porous medium region F Calculated by the following formula:

[0038] (5)

[0039] Substituting equation (3) into equation (5) yields the water flow resistance experienced by the porous media structure. F d and lift F l The expression:

[0040] (6)

[0041] (7)

[0042] In the formula, λ For the thickness of the porous medium, A The area of ​​the porous medium region;

[0043] When the planar mesh is located at any position in space, the porous medium coefficient corresponding to the mesh model should be converted by the following formula:

[0044] (8)

[0045] In the formula, β It is the normal vector of the planar mesh. n The angle with the z-axis, α and β The sine and cosine values ​​are represented by two corresponding vectors.

[0046] Furthermore, step (1) couples the individual fish motion model with the net model:

[0047] The numerical water tank uses velocity inlet boundary conditions at the inlet and pressure outlet conditions at the right outlet. The sides of the tank are set as symmetrical boundaries, the bottom is set as a no-slip wall, the top is set as a zero-shear wall, and the fish body surface is set as a non-slip boundary. The computational mesh uses an overlapping mesh method, where the background mesh includes the tank and a simplified mesh of the porous medium, and is divided into structured hexahedral meshes. The foreground mesh is the dense region where the fish body is located, and is divided into unstructured tetrahedral meshes.

[0048] Furthermore, to ensure computational accuracy, a boundary layer mesh is used to refine the three-dimensional mesh around the fish.

[0049] Furthermore, in step (1), the fluid control equations are solved using the finite volume method, and SST is employed. k - ω A turbulence model is used to solve the governing equations for calculating the flow field around the mesh.

[0050] In the calculations, the governing equations of the numerical model are discretized using the finite volume method; during the calculations, the continuity equation, velocity components, and turbulent kinetic energy are considered. k Sum of dissipation ω The residual convergence criterion is set to 10. -3The iteration process ends when the calculation converges to this criterion.

[0051] The beneficial effects of this invention are:

[0052] (1) Based on existing technologies, there are simulation methods for the flow field inside and around the aquaculture cage, but none of them can accurately simulate the flow field inside and around the aquaculture cage under the influence of fish swimming. This invention uses the dynamic mesh method and realizes the coupling effect of fish movement and the flow field of the cage mesh and its surroundings through UDF macro files.

[0053] (2) Based on the existing technology, there is a simulation technology for the interaction between the swimming of a single or limited number of fish and the surrounding fluid. However, the fish population in the aquaculture cage is large and dense, which makes it impossible to achieve efficient analysis of the coupling effect between high-density fish population and water flow. This invention uses a porous medium model to simplify and simulate the fish population and netting. While retaining the key characteristics of the fish population, it greatly improves the calculation efficiency and realizes the interaction between the fish population and the hydrodynamic characteristics of the netting cage under different motion states, vertical distribution forms and stocking densities.

[0054] (3) Based on the existing technology, there is a simulation technology that uses porous media models to simulate the influence of fish movement on the flow field distribution in a recirculating aquaculture pond. However, the discussion on the porous media coefficient is insufficient and it is not suitable for simulating the influence of fish movement on the flow field inside and outside the aquaculture cage. This invention establishes a mathematical model of the coupling effect between fish movement and the flow field of the aquaculture cage. Based on the computational fluid dynamics (CFD) method, it realizes the accurate simulation of the coupling effect between fish movement and the flow field of the cage mesh and the surrounding area, obtains the force on a single fish, and calculates the porous media coefficient of the fish group (i.e., the porous media model). While ensuring the accuracy of the calculation model, it reduces the simulation complexity of the movement of a large number of fish in the aquaculture cage, and realizes the accurate simulation of the flow field inside and around the aquaculture cage under the influence of fish swimming. Attached Figure Description

[0055] Figure 1 A schematic diagram of the fish movement and net coupling model setup ( L = 0.55 m);

[0056] Figure 2 A schematic diagram illustrating mesh generation and boundary condition settings;

[0057] Figure 3 A simplified schematic diagram of a porous medium model;

[0058] Figure 4 A schematic diagram showing the force calculations on the fish's body in various directions;

[0059] Figure 5 These are two forms of movement for schools of fish;

[0060] Figure 6 Mesh generation and boundary conditions for the numerical model;

[0061] Figure 7 This is a comparison diagram of the forces and flow velocities at measuring points in numerical simulations and model experiments when fish are present. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] To further understand the present invention, it will be further described in conjunction with the accompanying drawings and embodiments.

[0064] This invention develops a simulation method for the coupling of fish swimming and water flow in aquaculture cages. Due to the exceptionally complex mesh structure of the cages and the complexity of the fish model, with tens of thousands of fish within the cages, direct modeling and solving would result in an excessive number of computational grids and consume enormous computational resources. To reduce time costs, the effect of the fish on the flow field is simplified to a volumetric force source term, similar to the method used to simplify the mesh. Therefore, a porous medium model is used to construct models of both the fish and the cages for calculation. The steps are as follows:

[0065] (1) Establish a single fish movement model. The fish body swaying is a movement pattern of the carp family, which is close to the movement pattern of most farmed fish. Its wave equation is:

[0066] (1)

[0067] (2)

[0068] In the formula, y The position of the fish's body at various points along its midline is represented by time. t and location x The parameters (the fish head coordinates are (0,0)). The parametric equation for the swing amplitude is... k This is a wavelength-dependent quantity. f For frequency-dependent quantities, a Indicates amplitude, For the initial phase, parameters l Indicates the starting position of the fish's body sway. L This indicates the length of the fish's body.

[0069] A mesh model is established based on a porous medium model. The principle of the porous medium model is to add a volumetric force source term to the momentum equation to equivalently replace the flow obstruction effect of the actual structure. The porous medium model consists of two parts: a viscous loss term and an inertial loss term, expressed by the following formulas:

[0070] (3)

[0071] (4)

[0072] In the formula, S i yes i Towards( x , y , z Momentum source term, u j For the incoming flow velocity, μ The dynamic viscosity of the fluid. D ij and C ij This is the coefficient matrix of the porous media model. D n Indicates the normal viscous drag coefficient. D t This represents the tangential viscous drag coefficient. C n Indicates the normal inertial drag coefficient. C t This represents the tangential inertial drag coefficient. In porous media elements, momentum loss contributes to the pressure gradient, and the pressure drop is proportional to the fluid velocity (or velocity matrix).

[0073] When water flows through a porous medium region, the force acting on that porous medium region F Calculated by the following formula:

[0074] (5)

[0075] Substituting formula (3) into (5) yields the water flow resistance experienced by the porous media structure. F d and lift F l The expression for is given. The direction of resistance is parallel to the direction of water flow, and the direction of lift is perpendicular to the direction of water flow.

[0076] (6)

[0077] (7)

[0078] In the formula, λ For the thickness of the porous medium, AThe area of ​​the porous medium region.

[0079] When the planar mesh is located at any position in space, the porous medium coefficient corresponding to the mesh model should be converted by the following formula:

[0080] (8)

[0081] In the formula, β It is the normal vector of the planar mesh. n The angle with the z-axis, α and β The sine and cosine values ​​can be expressed by two corresponding vectors.

[0082] The individual fish motion model is coupled with the netting model. A velocity inlet boundary condition is used at the inlet of the numerical tank, and a pressure outlet condition is used at the right outlet. The remaining boundaries are set as no-slip walls (bottom wall), zero-shear walls (top free water surface), and symmetric boundaries (both sides of the tank), respectively. The fish surface is set as a non-slip boundary. An overlapping mesh method is used for computation. The background mesh includes the tank and a simplified mesh of the porous medium, using a structured hexahedral mesh. The foreground mesh represents the refined region where the fish is located, using an unstructured tetrahedral mesh. To ensure computational accuracy, a boundary layer mesh is used to refine the 3D mesh around the fish.

[0083] The fluid control equations are solved using the finite volume method, and SST is employed. k - ω Turbulence models are used to solve the governing equations for calculating the flow field around the mesh, including: the fluid continuity equation, the Reynolds-averaged Navier-Stokes equation, the turbulent kinetic energy equation, and the turbulent dissipation rate equation.

[0084] The continuity equation for fluids is:

[0085]

[0086] The Reynolds-averaged Navier-Stokes equations are:

[0087]

[0088]

[0089]

[0090] In the formula, t It is time. u , v and w These represent the velocity components along the X, Y, and Z axes, respectively. ρ For fluid density; p For pressure;v k is the viscosity coefficient of the fluid.

[0091] Turbulent kinetic energy solved by the SST k-ω turbulence model k Sum of dissipation ω They are respectively:

[0092]

[0093] In the formula: It is a limiter used to prevent turbulence from forming in the viscous sublayer region; F 1 is a mixture function, defined as follows:

[0094]

[0095] In the formula, , y It's the distance from the wall. Near the wall... F 1=1, while in the far field F 1 will approach 0.

[0096] Eddy viscosity coefficient in the model μ t Defined as:

[0097]

[0098] In the formula, S For a constant measure of strain rate, F 2 is the second mixing function, defined as:

[0099]

[0100] In SST k - ω In the turbulence model, the other constants take the following values: α 1 = 5 / 9 α 2 = 0.44 β 1 = 3 / 40 β 2 = 0.0828, β * =9 / 100, σ k1 =0.85, σ k2 =1, σ ω1 =0.5, σ ω2 =0.856.

[0101] For a given inlet velocity and flow field characteristics, turbulent kinetic energy k Sum of dissipation ωThe initial value can be calculated using the following formula:

[0102]

[0103] In the formula, R eD The Reynolds number is obtained by using the hydraulic diameter of the tank as the characteristic length. I For turbulence intensity, u The inlet average flow velocity, l For turbulent length scale, C μ =-0.09, which is an empirical constant in the turbulence model.

[0104] In addition, the water tank outlet is set as a pressure outlet, and the remaining boundaries are respectively set as a non-slip wall (bottom wall), a zero-shear wall (top free water surface), and a symmetrical boundary (both sides of the water tank).

[0105] In the calculations, the governing equations of the numerical model were discretized using the finite volume method, and the computational network was partitioned using a hybrid structured and unstructured network approach. An unsteady implicit algorithm was used to solve the equations, and second-order upwind schemes were employed for pressure interpolation and momentum equation discretization. The SIMPLEC algorithm, known for its stability, was selected for pressure-velocity coupling. To observe convergence during the calculations, the continuity equation, velocity components, and turbulent kinetic energy were... k Sum of dissipation ω The residual convergence criterion is set to 10. -3 The iteration process ends when the calculation converges to this criterion.

[0106] (2) Establish a porous medium model coupling the net cage and the moving fish swarm. Based on the principle of the porous medium model, an imaginary volumetric force source term can be added to the area where the fish swarm is located to approximate the flow obstruction effect of the fish swarm, and this can be achieved with the help of the porous medium model. Since the gaps between the fish bodies are large, the influence of viscosity is small and can be ignored. Therefore, its formula is expressed as follows:

[0107] (9)

[0108] In the formula, F fish-school Calculate the forces acting on the fish body for the solid model. F porous The force on the fish body is represented by the source term model. ρ For fluid density, u For fluid velocity, λ For the thickness of the porous medium, A For the area of ​​the porous medium region, in the source term model λA It can be determined by the aquaculture water where the fish are located. V wf express.C ij This can be further expressed as:

[0109] (10)

[0110] Assuming that the fish do not affect each other, and the force exerted on the fish school is directly proportional to the number of fish, it can be assumed that the fish school is in a state of equilibrium. x , y , z The forces in the three directions satisfy F fish-school = n × F fish .

[0111] (3) Force calculations were performed using a porous media model. Based on Newton's second law, the equations were discretized using the control volume analysis method. Simultaneously, the acceleration of the porous media region was integrated using the integration function of Ansys Fluent post-processing to obtain the force in the porous media region. The specific formula is expressed as follows:

[0112] (11)

[0113] In the formula, m The mass of the unit control body, F It is the resultant force of external forces.

[0114] When the incoming flow velocity remains constant, neglecting the shear stress of the fluid, the momentum equation in the x-direction can be expressed as:

[0115] (12)

[0116] In the formula, F d As resistance, CS To integrate along the surface of the control volume. p For pressure, A For the porous medium region area, the above formula also applies in the y and z directions. Furthermore, according to Morrison's formula, the drag coefficient... C d It can be represented as:

[0117] (13) Example

[0118] Numerical simulations of the effect of individual fish on localized netting were conducted to analyze and obtain hydrodynamic coefficients, which were then used to calculate the porous media coefficients of a fish swarm porous media model. The process included the following steps:

[0119] Step 1: The mesh portion was simulated using a porous dielectric plate with a certain thickness. The plate was 1 m long and 1 m wide, and 50 mm thick. Generally, the porous dielectric coefficient can be obtained by fitting the force measured in a physical model experiment. In this embodiment, the porous dielectric coefficient was taken as the normal inertial drag coefficient. C n = 4.985 m -1 and tangential inertial drag coefficient C t =1.660 m -1 .

[0120] Based on the Atlantic salmon, a biomimetic three-dimensional fish model was created using Solidworks. The fish model is approximately 0.55 m long and weighs 1.5667 kg. The fish's body movement was modeled using the trevally motion equations.

[0121] Step 2: Couple the biomimetic fish 3D model with the mesh model through the Solidworks and Ansys software interface, such as... Figure 1 As shown, a velocity inlet boundary condition was used at the inlet, and a uniform water flow of 0.5 m / s along the X direction was set. A pressure outlet condition was used at the right outlet of the tank.

[0122] To more accurately simulate the actual hydrodynamic environment, symmetrical boundary conditions were adopted for the four sides of the numerical tank. In addition, the surface of the fish body was set as a non-slip boundary, and the fish body oscillated in a wave-like manner (see formulas (1) and (2) for the corresponding wave equations). The movement of the fish body was realized by using the DEFINE_GRID_MOTION macro in the Fluent UDF dynamic mesh function.

[0123] Step 3: The computational mesh employs an overlapping mesh method. The background mesh includes the water tank and simplified mesh panels of the porous medium, using a structured hexahedral mesh. The foreground mesh represents the refined region where the fish is located, using an unstructured tetrahedral mesh. To ensure computational accuracy, a boundary layer mesh is used to refine the 3D mesh surrounding the fish. Figure 2 As shown.

[0124] Step 4: Using the continuity equation and the Reynolds-averaged Navier-Stokes equations as the governing equations of the mathematical model to describe fluid motion, SST is employed. k - ωThe turbulence model and governing equations form a closed system of equations, facilitating solution. Furthermore, the tank outlet is designated as a pressure outlet, and the remaining boundaries are defined as no-slip walls (bottom walls), zero-shear walls (top free water surface), and symmetric boundaries (both sides of the tank), respectively. In the calculations, the governing equations of the numerical model are discretized using the finite volume method, and the computational mesh is a hybrid of structured and unstructured meshes. An unsteady implicit algorithm is employed to solve the equations; second-order upwind schemes are used for pressure interpolation and momentum equation discretization, which contributes to rapid convergence and improved solution accuracy. The SIMPLEC algorithm is selected for pressure-velocity coupling.

[0125] To observe convergence during the calculation, the continuity equation, velocity components, and turbulent kinetic energy are... k Sum of dissipation ω The residual convergence criterion is set to 10. -3 The iteration process ends when the calculation converges to this criterion.

[0126] Step 5: After the simulation is completed, the calculated numerical simulation results are post-processed to represent the influence of the three-dimensional fish tail-wagging motion on the hydrodynamics of the net. The propulsive force experienced by the fish body during the tail-wagging acceleration phase is extracted. F d and lateral force F l It can be observed that both the thrust and lateral forces exhibit typical periodic changes, with the thrust... F d The frequency of change is the lateral force F l The thrust and lateral force are twice that of the yaw rate, and both reach their maximum values ​​when the yaw rate reaches its maximum position, resulting in instantaneous maximum thrust and lateral force of 0.485 N and 2.15 N, respectively.

[0127] 2. Numerical simulation of hydrodynamics of a single net cage under fish swarm movement

[0128] Step 6: Establish a porous medium model coupling the net cage and the moving fish school.

[0129] The complexity of the fish swarm model and the sheer number of fish (tens of thousands) within the net cages make numerical simulations extremely costly. To reduce time costs, the effect of the fish swarm on the flow field is simplified to a volumetric force source term, similar to the method used to simplify netting. Figure 3 As shown.

[0130] The fish farmed in net cages are numerous, possess complex swimming abilities and unique living habits, and are influenced by farming activities and the environment. It is impractical to consider the real-time distribution characteristics and swimming status of farmed fish and use numerical simulations to accurately study their impact on the flow field around the net cages. However, in the high-density farming environment of marine ranches, the influence of farmed fish on the flow field cannot be ignored. Statistically, the farmed fish population can be considered uniformly distributed in a specific time and space. To simulate the swimming behavior of the fish population using numerical methods, the following simplifications are made:

[0131] (1) Assume that the fish in the net cage are of the same size and have no influence on each other.

[0132] (2) When the fish swim against the current, assume that they are all arranged against the current in the net cage and are evenly distributed.

[0133] (3) When the fish swim in a circular pattern, it is assumed that they are equally spaced in the radial direction and evenly distributed in the vertical direction.

[0134] Based on the above assumptions, the flow obstruction effect of the fish school is considered to be uniformly distributed. Therefore, an imaginary volumetric force source term can be added to the region where the fish school is located to approximate the flow obstruction effect of the fish school, and this can be achieved using a porous medium model.

[0135] Based on the above assumptions, since the fish do not affect each other, the force exerted on the fish school is directly proportional to the number of fish. Therefore, it can be assumed that the fish school... x , y , z The forces in the three directions satisfy F fish-school = n × F fish Therefore, it is only necessary to calculate the forces acting on a single fish using a numerical model. F fish ( F x , F y , F z ),like Figure 4 As shown, the porous medium coefficient of the fish swarm under three-dimensional working conditions can be derived.

[0136] In marine cage culture, carnivorous fish are the main species, and their stocking density is usually maintained between 10 and 15 kg per cubic meter. Assuming the fish density is the same as the water density, the fish volume fraction will be between 1% and 1.5%. Taking Atlantic salmon as an example, the average weight of a single fish is about 1.556 kg and the body length is 0.55 m. If we calculate based on stocking 14,663 fish, the stocking density will be close to 11.348 kg per cubic meter, and the fish will occupy 1.135% of the cage volume. As shown in Table 1, the porous medium coefficient per 10,000 salmon is derived from the force combination formula (10) calculated numerically. If the stocking density is other, it can be calculated based on the number of fish.

[0137] Table 1. Calculation Table of Porous Media Model Coefficients for Fish Schools

[0138]

[0139] Step 7: Numerical calculation of hydrodynamic model of net cage under fish movement. The numerical tank is 240 m long, 80 m wide, and 20 m deep. The diameter of the aquaculture net cage is 16 m, the height is 10 m, the mesh size is 29 mm, the net wire diameter is 2.8 mm, and the net material is PA. A cylindrical porous medium region with a certain thickness is used to approximate the net. At the same time, in order to simplify the analysis, the fish are also regarded as a porous medium region, and the force on the fish body is solved by numerical method. Then, the correlation coefficient of the porous medium model is determined by formula (10).

[0140] During aquaculture, fish in net cages typically exhibit two states of movement (see...). Figure 5 When the incoming current is slow, the fish will arrange themselves in a circular pattern around the net cage, a phenomenon known as circular swimming. When the incoming current is fast, the fish will arrange themselves against the current, a phenomenon known as current-facing movement. In calculations, current-facing movement is defined using a Cartesian coordinate system, while circular swimming is defined using multiple reference frames.

[0141] Experimental Example 1

[0142] Experimental Verification of the Fish School and Net Cage Coupling Model

[0143] To verify the numerical model proposed in this invention, a physical experimental model verification was conducted in a PIV (Polymerization in Vacuum) tank. The tank was 0.45 m wide and 0.4 m deep. The experimental net cage had a diameter of 0.3 m and a height of 0.2 m, containing a certain number of carp, each approximately 7 cm in length. Experimental flow velocities were set at 0.06 m / s, 0.12 m / s, and 0.18 m / s, and two different experimental conditions were designed: an empty net cage and a net cage containing 60 fish. During the experiment, the resistance of the net cage was recorded using a force sensor, and the flow velocity at a measuring point 60 cm behind the net was recorded using an ADV (Advanced Dynamics in Vacuum) current meter.

[0144] Based on the above experimental model, a net cage model and numerical flume were constructed at a 1:1 scale. The net cage diameter was 0.3 m, with the netting replaced by a 5 mm thick porous media region. The numerical flume inlet was a velocity inlet with velocities of 0.06 m / s, 0.12 m / s, and 0.18 m / s, respectively. The outlet was the outflow boundary, with the top boundary set as a smooth wall without shear force, and the bottom boundary and sidewalls set as non-slip walls. Figure 6 The diagram shows the meshing of the numerical model. The model uses a polyhedral mesh with prismatic layers at the boundaries. To avoid computational errors caused by meshing issues, this invention first verifies the mesh convergence of the established numerical model. By adjusting the minimum and maximum mesh sizes and the range of locally refined regions, three mesh counts were obtained: 740,000, 1,140,000, and 2,150,000. The mesh count converged at approximately 1,140,000. Subsequent meshing will be performed according to the corresponding settings.

[0145] The mesh density in the experiment was 0.216. Since experimental data on the stress of a single mesh sheet was lacking, the stress on the mesh sheet at this density was determined using empirical formulas. , The conclusion is drawn based on the resistance of the mesh ( C d ), lift ( C l The data was used to iteratively obtain the porous medium coefficients of the mesh through an iterative gradient descent algorithm. C n =100.0 m -1 , C t =38.0 m -1 The above coefficients were substituted into the established numerical model, and the results of the numerical simulation and the model test were compared. The forces and flow velocities at the measuring points of both models showed good agreement in terms of both numerical values ​​and trends, with the average error of the resistance being 14.3% and the average error of the flow velocity being 3.59%. Therefore, simplifying the mesh using a porous medium model can effectively simulate the forces acting on the mesh cage and the flow field around it.

[0146] Based on the verification of the empty net cage, the numerical simulation conditions with fish swarms were verified by combining model experiments. Among them, the porous medium coefficient in the source term model used to simplify the fish swarms is derived from formula (10), that is, the porous medium coefficient is derived by calculating the force of a real fish under flow from different directions through numerical simulation. C ijThe three-dimensional calculation model and calculation results of the fish body are shown in Table 2. The fish body model is basically consistent with the properties of the experimental carp. The measured force on the fish body is fitted with formula (10) to obtain the porous medium coefficients in three directions of the fish group. The fitting results are as follows: 0.003183 n 0.05144 n 0.3152 n ,in n Let represent the number of fish. Since the fish were observed to move against the current in the experiment, the porous medium coefficient matrix of the source term model can be expressed as:

[0147]

[0148] Table 2. Resistance of a 7.5 g fish model against the current in the x, y, and z directions during the model experiment.

[0149]

[0150] Table 2. Resistance of a 7.5 g fish model against the current in the x, y, and z directions during the model experiment.

[0151] Figure 7 The numerical simulation results and the measured force on the net cage and the flow velocity at the measuring point are compared with those obtained from the model test when the fish density is at its maximum, with the inflow rate being 0.06 m / s, 0.12 m / s, and 0.18 m / s. The figures show that the two are in good agreement in terms of both numerical values ​​and trends. Furthermore, the numerical simulation results show that the fish's orientation towards the current has almost no effect on the force on the net cage, which is basically consistent with the results measured in the experiment.

[0152] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, alterations, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A simulation method for the coupling of fish swimming and water flow in aquaculture cages, characterized in that, Includes the following steps: (1) Establish a single fish motion model and a net model based on the porous medium model. The formula is expressed as follows: （3） （4） In the formula, S i yes i Towards( x , y , z Momentum source term, u j For the incoming flow velocity, μ The dynamic viscosity of the fluid. D ij and C ij This is the coefficient matrix of the porous media model. D n Indicates the normal viscous drag coefficient. D t This represents the tangential viscous drag coefficient. C n Indicates the normal inertial drag coefficient. C t This represents the tangential inertial drag coefficient; The motion model of a single fish is coupled with the netting model, and the forces acting on the single fish are obtained through numerical calculation. (2) Based on the force on a single fish, the force on the entire fish group in the net cage is obtained, and then the porous medium coefficient of the porous medium model of the fish group is calculated. The following simplification is made for the large number of farmed fish in net cages: a. Assume that the fish in the net cage are of the same size and do not affect each other; b. When the fish swim against the current, assume that they are all arranged against the current and evenly distributed in the net cage; c. When a school of fish swims in a circular pattern, it is assumed that they are equally spaced radially and uniformly distributed vertically. Based on the above assumptions, the force exerted on the fish school is directly proportional to the number of fish in the school. x , y , z The forces in the three directions satisfy F fish-school = n × F fish ; Based on the above assumptions, a hypothetical volumetric force source term is added to the area where the fish are located to approximate the flow obstruction effect of the fish, and this is achieved using a porous medium model. The formula is expressed as follows: （9） In the formula, F fish-school Calculate the forces acting on the fish body for the solid model. F porous The force on the fish body is represented by the source term model. ρ For fluid density, u For fluid velocity, λ For the thickness of the porous medium, A The area of ​​the porous media region, the aquaculture water body where the fish are located. V wf From the source term model λA express; C ij Further expressed as: （10） (3) The porous medium coefficient calculated by formula (10) C ij Substitute into formula (3) to establish a porous medium model of the coupling between the net cage and the moving fish group, and use the Reynolds-averaged Navier-Stokes equation and the porous medium model to calculate the force; The equations are discretized using the control volume analysis method, and the acceleration of the porous medium region is integrated to obtain the force in the porous medium region, as expressed in the following formula: （11） In the formula, m The mass of the unit control body, F The resultant force of external forces; When the incoming flow velocity remains constant, the momentum equation in the x-direction can be expressed as: （12） In the formula, F d As resistance, CS To integrate along the surface of the control volume. p For pressure, A The area of ​​the porous medium region; The above formula also applies in the y and z directions; According to Morrison's formula, the drag coefficient C d Represented as: （13）。 2. The simulation method according to claim 1, characterized in that, In step (1), a single fish motion model is established, and the fish body swaying is a trevally motion pattern, the wave equation of which is: （1） （2） In the formula, y The position of the fish's body at various points along its midline is represented by time. t and location x The parameters, The parametric equation for the swing amplitude is... k This is a wavelength-dependent quantity. f For frequency-dependent quantities, a Indicates amplitude, For the initial phase, parameters l Indicates the starting position of the fish's body sway. L This indicates the length of the fish's body.

3. The simulation method according to claim 1, characterized in that, In step (1), when water flows through the porous medium region, the force F acting on the porous medium region is calculated by the following formula: （5） Substituting equation (3) into equation (5) yields the water flow resistance experienced by the porous media structure. F d and lift F l The expression: （6） （7） In the formula, λ For the thickness of the porous medium, A The area of ​​the porous medium region; When the planar mesh is located at any position in space, the porous medium coefficient corresponding to the mesh model should be converted by the following formula: （8） In the formula, β It is the normal vector of the planar mesh. n The angle with the z-axis, α and β The sine and cosine values ​​are represented by two corresponding vectors.

4. The simulation method according to claim 1, characterized in that, Step (1) couples the individual fish motion model with the net model: The numerical water tank uses velocity inlet boundary conditions at the inlet and pressure outlet conditions at the right outlet. The sides of the tank are set as symmetrical boundaries, the bottom is set as a no-slip wall, the top is set as a zero-shear wall, and the fish body surface is set as a non-slip boundary. The computational mesh uses an overlapping mesh method, where the background mesh includes the tank and a simplified mesh of the porous medium, and is divided into structured hexahedral meshes. The foreground mesh is the dense region where the fish body is located, and is divided into unstructured tetrahedral meshes.

5. The simulation method according to claim 4, characterized in that, To ensure computational accuracy, a boundary layer mesh is used to refine the three-dimensional mesh around the fish.

6. The simulation method according to claim 1, characterized in that, In step (1), the fluid control equations are solved using the finite volume method, and SST is used. k - ω A turbulence model is used to solve the governing equations for calculating the flow field around the mesh. In the calculation, the governing equations of the numerical model are discretized using the finite volume method; During the calculation, the continuity equation, velocity components, and turbulent kinetic energy are considered. k Sum of dissipation ω The residual convergence criterion is set to 10. -3 The iteration process ends when the calculation converges to this criterion.

Images