Simulation method for fish school swimming and water flow coupling in aquaculture net cage

Abstract

The invention belongs to the technical field of fluid simulation, and relates to a simulation method for fish school swimming and water flow coupling in a culture net cage, which comprises the following steps: coupling a monomer fish motion model with a netting model, calculating monomer fish stress, obtaining fish school stress of the whole net cage, and calculating a porous medium coefficient of a fish school porous medium model; assuming: a, fish bodies in the net cage have the same specification and do not influence each other; b, when the fish schools move in an incident flow mode, all the fish schools are arranged and evenly distributed in the net cage in an incident flow mode; c, when the fish schools swim in the circumferential mode, the radial intervals are equal, and the fish schools are evenly distributed in the vertical direction. Based on the hypothesis, an imaginary volume force source item is added in the area where the fish school is located to approximate the choked flow effect of the fish school; and carrying out stress calculation to obtain the stress of the porous medium area. According to the method, the accuracy of the calculation model is ensured, meanwhile, the simulation complexity of movement of a large number of fish schools in the aquaculture net cage is reduced, and accurate simulation of flow fields in and around the aquaculture net cage under the influence of fish school swimming is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of fluid simulation, and in particular relates to a simulation method for coupling the movement of fish schools and water flow in a breeding cage. Background Art

[0002] The move of marine aquaculture to deep sea and offshore has become an inevitable trend for the green and efficient development of my country's marine fishery. Up to now, my country has built more than 50 large-scale deep-sea aquaculture cages. The effective aquaculture water of deep-sea aquaculture cages can generally reach tens of thousands of cubic meters, and the designed annual fish production can reach thousands of tons. Hundreds of thousands of marine fish can be cultured at the same time, and the density of farmed fish is relatively large. The flow field inside and outside the deep-sea aquaculture cage is directly related to the load and structural safety of the cage, and will also affect the transportation efficiency of feed particles, dissolved oxygen, and fish excrement inside and outside the cage. The cage is a permeable structure, and its internal and external flow field characteristics are relatively complex; especially under the influence of high-density fish in the cage, it is a technical problem recognized by the industry to accurately analyze the flow field characteristics inside and outside the cage.

[0003] There are simulation methods for the flow field inside and around the aquaculture cage in the prior art, such as Chinese patent CN105868466A discloses a refined fluid-solid coupling three-dimensional numerical simulation method for a flexible net structure, and CN103235878A discloses a simulation method for the influence of flexible nets 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. The simulation technology for the interaction between a single or a limited number of fish swimming and the surrounding fluid in the prior art, such as a simulation method for the influence of a cage on water flow disclosed in Chinese patent CN103412991A and a simulation method for the influence of fish movement on flow field distribution in a circulating water aquaculture pond disclosed in CN118052166A, although it involves the influence of fish, due to the large number and density of fish in the aquaculture cage, there is no report on an efficient analysis method that can realize the coupling effect of high-density fish and water flow.

[0004] The above-mentioned prior art cannot accurately calculate the flow field inside and outside the cage under the influence of fish movement, and has problems such as low calculation efficiency and low calculation accuracy. The method is immature, and some key parameters rely on experience. Although the invention has proposed to use a porous medium model to simulate the influence of fish movement on the flow field distribution in a circulating water aquaculture pond, its discussion on the porous medium coefficient is insufficient and is not suitable for simulating the influence of fish movement on the flow field inside and outside the aquaculture cage. Summary of the invention

[0005] The purpose of the present invention is to solve the above-mentioned problems existing in the prior art, establish a scientific and complete calculation method for the coupling of fish schools and flow fields, realize efficient analysis of the coupling effect of high-density fish schools and water flows in cages, and propose a simulation method for the coupling of fish school swimming and water flows in aquaculture cages, so as to realize accurate analysis of the flow fields inside and outside the cages, which has an important guiding role in the safety analysis of cage structures, optimization of aquaculture capacity, formulation of feeding strategies, etc.

[0006] The technical solution of the present invention is:

[0007] A simulation method for coupling the movement of fish schools and water flow in a breeding cage comprises the following steps:

[0008] (1) The single fish motion model is coupled with the net model, and the force on the single fish is obtained through numerical calculation;

[0009] (2) The stress on the entire fish school in the cage is obtained based on the stress on a single fish, and then the porous medium coefficient of the porous medium model of the fish school is calculated;

[0010] The following simplifications are made for the large numbers of farmed fish in cages:

[0011] a. Assume that the fish in the cages are of the same size and have no influence on each other;

[0012] b. When the fish school swims against the current, it is assumed that they are all arranged against the current in the cage and are evenly distributed;

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

[0014] Based on the above assumptions, the force on the fish school is proportional to the number of fish, and the force on the fish school in the x, y, and z directions satisfies F fish-school =n×F fish ;

[0015] Based on the above assumptions, a hypothetical volume force source term is added in the area where the fish school is located to approximate the flow resistance effect of the fish school, and the porous medium model is used to achieve this. The formula is expressed as follows:

[0016]

[0017] In the formula, F fish-school Calculate the force on the fish body for the solid model, F porous is the force on the fish body represented by the source term model, ρ is the fluid density, u is the fluid velocity, λ is the thickness of the porous medium, and A is the area of ​​the porous medium. In the source term model, λA can be obtained from the aquaculture water body V where the fish school is located. wf Indicates; C ij Further expressed as:

[0018]

[0019] (3) Establish a porous medium model for coupling the cage and the moving fish school, and use the porous medium model to calculate the force;

[0020] When using the porous medium model for force calculation, it is considered that the porous medium model simplifies the obstruction of the solid structure to the water flow into a uniformly distributed resistance on the fluid, resulting in the failure to specifically reflect the porous solid structure and the inability to directly perform force analysis. To solve this problem, according to Newton's second law, the control volume analysis method is used to discretize the equation, and the acceleration of the porous medium area is integrated to obtain the force of the porous medium area. The formula is expressed as follows:

[0021]

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

[0023] When the incoming flow velocity remains constant, the component of the momentum equation in the x direction is expressed as:

[0024]

[0025] In the formula, F d is the resistance, CS is the integration along the surface of the control volume, and A is the flow area of ​​the porous medium region;

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

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

[0028]

[0029] Furthermore, in the step (1), a single fish motion model is established, and the swing of the fish body is a croaker motion mode, and its wave equation is:

[0030]

[0031] Where y is the swing position of each point on the fish body midline, α(x) is the parameter of time t and position x (the fish head coordinate is (0,0)), α(x) is the parametric equation of the swing amplitude, k is the wavelength-related quantity, f is the frequency-related quantity, and a represents the amplitude. is the initial phase, parameter l represents the starting position of the fish body swing, and L represents the length of the fish body.

[0032] Furthermore, in the step (1), a net model is established based on the porous medium model, and its formula is expressed as follows:

[0033]

[0034] In the formula, S i is the momentum source term in the i direction (x, y, z), u j is the incoming flow velocity, μ is the dynamic viscosity of the fluid, D ij and C ij is the coefficient matrix of the porous media model, D n Denotes the normal viscous drag coefficient, D t represents the tangential viscous drag coefficient, C n represents the normal inertial drag coefficient, C t represents the tangential inertial drag coefficient;

[0035] When water flows through a porous medium area, the force F acting on the porous medium area is calculated by the following formula:

[0036] F=S i λA (5)

[0037] Substituting equation (3) into equation (5), we can obtain the water flow resistance F of the porous media structure: d and lift F l The expression is:

[0038]

[0039] In the formula, λ is the thickness of the porous medium, and A is the area of ​​the porous medium;

[0040] When the plane mesh is located at any position in space, the porous medium coefficient corresponding to the mesh model should be converted by the following formula:

[0041]

[0042] Where β is the angle between the normal vector n of the plane mesh and the z-axis, and the sine and cosine values ​​of α and β are expressed by two corresponding vectors respectively.

[0043] Furthermore, the step (1) couples the single fish motion model with the net model:

[0044] The velocity inlet boundary condition is adopted at the inlet of the numerical water tank, and the pressure outlet condition is adopted at the right outlet. The two sides of the water tank are set as symmetrical boundaries, the bottom is set as a no-slip wall, the top is set as a zero shear force wall, and the surface of the fish body is set as a non-slip boundary. The computational grid adopts the overlapping grid method, in which the background grid includes the water tank and the simplified mesh of the porous medium, which is divided by a structured hexahedral grid; the foreground grid is the encrypted area where the fish body is located, which is divided by an unstructured tetrahedral grid.

[0045] Furthermore, in order to ensure the calculation accuracy, the boundary layer grid is used to encrypt the three-dimensional grid around the fish body.

[0046] Furthermore, in the step (1), the finite volume method is used to solve the fluid control equation, and the SST k-ω turbulence model is used to solve the control equation of the flow field around the net;

[0047] In the calculation, the control equations of the numerical model are discretized using the finite volume method. During the calculation, the residual convergence criteria of the continuity equation, velocity component, turbulent kinetic energy k and specific dissipation rate ω are set to 10 -3 , when the calculation converges to this standard, the iteration process ends.

[0048] Beneficial effects of the present invention:

[0049] (1) Based on the existing methods for simulating the flow field inside and around the aquaculture cage in the prior art, but none of them can achieve the problem of accurate simulation of the flow field inside and around the aquaculture cage under the influence of the movement of fish schools, the present invention uses a dynamic grid method and realizes the coupling effect between fish movement and the cage mesh and the surrounding flow field through a UDF macro file.

[0050] (2) Based on the existing technology, there is simulation technology for the interaction between the movement of a single or a limited number of fish and the surrounding fluid, but the number of fish in the aquaculture cage is large and the density is high, which cannot realize the efficient analysis of the coupling effect between high-density fish and water flow. The present invention uses a porous medium model to simplify and simulate fish and nets. While retaining the key characteristics of fish, it greatly improves the calculation efficiency and realizes the interaction between fish and the hydrodynamic characteristics of the cage under different motion states, vertical distribution forms, and stocking densities.

[0051] (3) Based on the existing technology that uses porous media models to simulate the influence of fish movement on flow field distribution in circulating water aquaculture ponds, but the discussion on porous media coefficients is insufficient and not suitable for simulating the influence of fish movement on the flow field inside and outside the aquaculture cages, the present invention establishes a mathematical model of the coupling effect between fish movement and the flow field of the aquaculture cages, and realizes accurate simulation of the coupling effect between fish movement and the cage mesh and the surrounding flow field based on the computational fluid dynamics (CFD) method, obtains the force of a single fish, and calculates the porous media coefficient of the fish school (i.e., the porous media model), thereby reducing the simulation complexity of the movement of a large number of fish in the aquaculture cages while ensuring the accuracy of the calculation model, and realizing accurate simulation of the flow field inside and around the aquaculture cages under the influence of the fish movement. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Schematic diagram of the fish movement and mesh coupling model layout (L = 0.55m);

[0053] Figure 2 Schematic diagram for meshing and boundary condition settings;

[0054] Figure 3 This is a simplified schematic diagram of the porous media model;

[0055] Figure 4 This is a schematic diagram of the calculation of forces on the fish body in all directions;

[0056] Figure 5 There are two forms of movement for schools of fish;

[0057] Figure 6 Meshing and boundary conditions for numerical models;

[0058] Figure 7 Comparison of stress and flow velocity at measuring points between numerical simulation and model test when fish are present. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] In order to further understand the present invention, the present invention will be further described in conjunction with the accompanying drawings and embodiments.

[0061] The present invention develops a simulation method for coupling the movement of fish schools and water flow in aquaculture cages. Due to the extremely complicated netting part of the cage structure, the complexity of the fish school model and the tens of thousands of fish in the cage, direct modeling and solving will result in too many computational grids and consume huge computing resources. In order to reduce time costs, the effect of fish schools on the flow field is equivalently simplified to the effect of volume force source terms by referring to the method of simplifying the netting. Therefore, using the porous medium model, the models of fish schools and cages are constructed respectively for calculation, and the steps are as follows:

[0062] (1) A single fish motion model was established. The fish body swing was in the motion mode of the croaker family, which is close to the motion form of most farmed fish. Its wave equation is:

[0063]

[0064] Where y is the swing position of each point on the fish body midline, α(x) is the parameter of time t and position x (the fish head coordinate is (0,0)), α(x) is the parametric equation of the swing amplitude, k is the wavelength-related quantity, f is the frequency-related quantity, and a represents the amplitude. is the initial phase, parameter l represents the starting position of the fish body swing, and L represents the length of the fish body.

[0065] The net model is established based on the porous medium model. The principle of the porous medium model is to add a volume force source term in the momentum equation to replace the flow resistance effect of the actual structure. The porous medium model consists of two parts, one is the viscous loss term and the other is the inertial loss term. The formula is expressed as follows:

[0066]

[0067] In the formula, S i is the momentum source term in the i direction (x, y, z), u j is the incoming flow velocity, μ is the dynamic viscosity of the fluid, D ij and C ij is the coefficient matrix of the porous media model, D n Denotes the normal viscous drag coefficient, D t represents the tangential viscous drag coefficient, C n represents the normal inertial drag coefficient, C t Indicates the tangential inertial drag coefficient. In porous media units, momentum loss contributes to the pressure gradient, and the pressure drop is proportional to the fluid velocity (or velocity matrix).

[0068] When water flows through a porous medium area, the force F acting on the porous medium area is calculated by the following formula:

[0069] F=S i λA (5)

[0070] Substituting formula (3) into (5) we can get the water flow resistance F of the porous media structure: d and lift F l The direction of the drag is parallel to the water flow, and the direction of the lift is perpendicular to the water flow.

[0071]

[0072] Where λ is the thickness of the porous medium and A is the area of ​​the porous medium.

[0073] When the plane mesh is located at any position in space, the porous medium coefficient corresponding to the mesh model should be converted by the following formula:

[0074]

[0075] Where β is the angle between the normal vector n of the plane mesh and the z-axis, and the sine and cosine values ​​of α and β can be expressed by two corresponding vectors respectively.

[0076] The single fish motion model is coupled with the net model. The velocity inlet boundary condition is used at the inlet of the numerical flume, and the pressure outlet condition is used at the right outlet. The remaining boundaries are set as no-slip walls (bottom walls), zero shear walls (top free water surface), symmetric boundaries (both sides of the flume), and the surface of the fish body is set as a non-slip boundary. The computational grid adopts the overlapping grid method, in which the background grid includes the flume and the simplified mesh of the porous medium, and is divided by a structured hexahedral grid; the foreground grid is the encrypted area where the fish body is located, and is divided by an unstructured tetrahedral grid. To ensure the calculation accuracy, the boundary layer grid is used to encrypt the three-dimensional grid around the fish body.

[0077] The finite volume method is used to solve the fluid control equations, and the SST k-ω turbulence model is used to solve the control equations of the flow field around the net, including: the fluid continuity equation, the Reynolds-averaged Navier-Stokes equations, the turbulent kinetic energy equation and the turbulent dissipation rate equation.

[0078] The continuity equation for a fluid is:

[0079]

[0080] The Reynolds-averaged Navier-Stokes equations are:

[0081]

[0082]

[0083] Where t is time, u, v and w represent the velocity components of the X, Y and Z axes respectively; ρ is the fluid density; p is the pressure; v k is the viscosity coefficient of the fluid motion.

[0084] The turbulent kinetic energy k and specific dissipation rate ω solved by the SST k-ω turbulence model are:

[0085]

[0086] Where: It is a restrictor used to avoid the formation of turbulence in the viscous bottom region; F 1 is a mixing function, defined as follows:

[0087]

[0088] In the formula, y is the distance from the wall. 1 =1, and in the far field F 1 will approach 0.

[0089] The eddy viscosity coefficient μ in the model t Defined as:

[0090]

[0091] Where S is the invariant measure of strain rate, F 2 is the second mixing function, defined as:

[0092]

[0093] In the SST k-ω turbulence model, other constants are: 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.

[0094] For a given inlet velocity and flow field characteristics, the initial values ​​of the turbulent kinetic energy k and the specific dissipation rate ω can be calculated according to the following formulas:

[0095]

[0096] In the formula, R eD is the Reynolds number obtained by taking the hydraulic diameter of the flume as the characteristic length, I is the turbulence intensity, u is the average inlet velocity, l is the turbulence length scale, and C μ =-0.09, which is an empirical constant in the turbulence model.

[0097] In addition, the outlet of the water tank is set as a pressure outlet, and the remaining boundaries are set as no-slip wall (bottom wall), zero shear wall (top free water surface), and symmetric boundaries (both sides of the water tank).

[0098] In the calculation, the control equations of the numerical model are discretized using the finite volume method, and the computational network is partitioned using a mixture of structured networks and unstructured networks. The unsteady implicit algorithm is used to solve the equations, and the second-order upwind scheme is used for pressure interpolation and momentum equation discretization. The SIMPLEC algorithm with good stability is selected for pressure-velocity coupling. In order to observe the convergence during the calculation process, the residual convergence criteria of the continuity equation, velocity component, turbulent kinetic energy k, and specific dissipation rate ω are set to 10 -3 , when the calculation converges to this standard, the iteration process ends.

[0099] (2) Establish a porous medium model that couples the cage with the moving fish school. Based on the principle of the porous medium model, a hypothetical volume force source term can be added to the area where the fish school is located to approximate the flow resistance effect of the fish school, and this can be achieved with the help of the porous medium model. Due to the large gaps between the fish bodies, the influence of the viscosity is small and can be ignored, so the formula is expressed as follows:

[0100]

[0101] In the formula, F fish-school Calculate the force on the fish body for the solid model, F porous is the force on the fish body represented by the source term model, ρ is the fluid density, u is the fluid velocity, λ is the thickness of the porous medium, and A is the area of ​​the porous medium. In the source term model, λA can be obtained from the aquaculture water body V where the fish school is located. wf Indicates. ij It can be further expressed as:

[0102]

[0103] Assuming that the fish bodies have no influence on each other, the force on the fish school is proportional to the number of fish. It can be considered that the force on the fish school in the x, y, and z directions satisfies F fish-school =n×F fish .

[0104] (3) The porous media model is used to calculate the force. According to Newton's second law, the control volume analysis method is used to discretize the equation. At the same time, with the help of the integration function of Ansys Fluent post-processing, the acceleration of the porous media area is integrated to obtain the force of the porous media area. The specific formula is expressed as follows:

[0105]

[0106] Where m is the mass of the unit control body and F is the resultant external force.

[0107] When the incoming flow velocity remains constant and the shear stress of the fluid is ignored, the component of the momentum equation in the x direction can be expressed as:

[0108] F d =∫ CS pdA-∫ CS upu i dA (12)

[0109] In the formula, F d is the resistance, CS is the integral along the surface of the control body, p is the pressure, A is the area of ​​the porous medium, and the above formula is also applicable in the y and z directions. In addition, according to Morrison's formula, the resistance coefficient Cd It can be expressed as:

[0110]

[0111] Example 1

[0112] The numerical simulation of the effect of a single fish on a local net is carried out to analyze and obtain the hydrodynamic coefficient, and then the porous medium coefficient of the fish school porous medium model is calculated. The following steps are included:

[0113] Step 1: The mesh part is simulated by a porous medium plate with a certain thickness. The length and width of the plate are 1m and the thickness is 50mm. Generally speaking, the value of the porous medium coefficient can be obtained by fitting the force measured by the physical model test. In this embodiment, the values ​​of the porous medium coefficient are the normal inertial resistance coefficient C n =4.985m -1 and the tangential inertial drag coefficient C t =1.660m -1 .

[0114] Based on the Atlantic salmon, a bionic fish 3D model was built using Solidworks. The fish model is about 0.55m long and weighs 1.5667kg. The swing of the fish body is based on the motion equation of the croaker family.

[0115] Step 2: Use the Solidworks and Ansys software interfaces to couple the bionic fish 3D model with the net model. Figure 1 As shown in the figure, the velocity inlet boundary condition is used at the inlet, and the water flow is set to have a uniform velocity of 0.5 m / s along the X direction. The pressure outlet condition is used at the right outlet of the water tank.

[0116] In order to more accurately simulate the actual hydrodynamic environment, symmetric boundary conditions are used on the four sides of the numerical tank. In addition, the surface of the fish body is set as a non-slip boundary, and the fish body swings in a wave-like manner (the corresponding wave equations are shown in formulas (1) and (2)). The DEFINE_GRID_MOTION macro in the Fluent UDF dynamic grid function is used to realize the movement of the fish body.

[0117] Step 3: The calculation grid uses the overlapping grid method, where the background grid includes the water tank and the simplified mesh of the porous medium, and is divided by a structured hexahedral grid. The foreground grid is the encrypted area where the fish body is located, and is divided by an unstructured tetrahedral grid. To ensure the calculation accuracy, the boundary layer grid is used to encrypt the three-dimensional grid around the fish body. Figure 2 shown.

[0118] Step 4: The continuity equation and the Reynolds-averaged Navier-Stokes equation are used as the control equations of the mathematical model to describe the fluid motion. The SST k-ω turbulence model and the control equations are used to form a closed set of equations for easy solution. In addition, the outlet of the water tank is set as a pressure outlet, and the remaining boundaries are set as no-slip walls (bottom walls), zero shear walls (top free water surfaces), and symmetric boundaries (both sides of the water tank). In the calculation, the control equations of the numerical model are discretized using the finite volume method, and the computational grid is divided using a mixture of structured grids and unstructured grids. The unsteady implicit algorithm is used to solve the equations, and the second-order upwind scheme is used for pressure interpolation and momentum equation discretization, which is conducive to the rapid convergence of the solution and improves the accuracy of the solution. The SIMPLEC algorithm is selected for pressure-velocity coupling.

[0119] In order to observe the convergence during the calculation process, the residual convergence criteria of the continuity equation, velocity component, turbulent kinetic energy k and specific dissipation rate ω were set to 10 -3 , when the calculation converges to this standard, the iteration process ends.

[0120] Step 5: After the simulation is completed, the calculated numerical simulation results are post-processed to show the influence of the three-dimensional fish tail swinging motion on the hydrodynamics of the net. The propulsion force F exerted on the fish body during the acceleration stage of tail swinging is extracted. d and the lateral force F l It can be found that both the propulsion force and the lateral force show typical periodic changes. The propulsion force F d The frequency of change is the lateral force F l Both of them reach the maximum value when the swing amplitude reaches the maximum position, and the instantaneous maximum propulsion force and lateral force are 0.485N and 2.15N respectively.

[0121] 2. Numerical simulation of hydrodynamics of single cage under fish movement

[0122] Step 6: Establish a porous media model of the coupling between the cage and the moving fish school.

[0123] The complexity of the fish school model and the tens of thousands of fish in the cage make the numerical simulation cost extremely high. In order to reduce the time cost, the effect of the fish school on the flow field is simplified to the effect of the volume force source term by referring to the method of simplifying the net, such as Figure 3 shown.

[0124] The number of farmed fish in the cages is huge and they have complex swimming abilities and unique living habits, and are affected by farming activities and the environment. It is obviously unrealistic to consider the real-time distribution characteristics and swimming status of farmed fish and use numerical simulation methods to accurately study the impact of farmed fish on the flow field around the cages. In the high-density farming environment of the marine ranch, the impact of farmed fish on the flow field environment cannot be ignored. From a statistical point of view, it can be considered that farmed fish are evenly distributed in a specific time and space. In order to simulate the swimming behavior of fish schools by numerical methods, the fish schools are simplified as follows:

[0125] (1) Assume that the fish in the cages are of the same size and have no influence on each other.

[0126] (2) When the fish swim against the current, it is assumed that they are all arranged against the current in the cage and are evenly distributed.

[0127] (3) When fish schools swim in a circular pattern, they are assumed to be equally spaced radially and evenly distributed vertically.

[0128] Based on the above assumptions, it is believed that the flow-blocking effect of the fish school is uniformly distributed. Therefore, an imaginary volume force source term can be added in the area where the fish school is located to approximate the flow-blocking effect of the fish school, and this can be achieved with the help of a porous medium model.

[0129] According to the above assumptions, since the fish bodies have no influence on each other, the force on the fish school is directly proportional to the number of fish. It can be considered that the force on the fish school in the x, y, and z directions satisfies F fish-school =n×F fish Therefore, only the force F of a single fish body needs to be calculated by numerical model. fish (F x , F y , F z ),like Figure 4 As shown in the figure, the porous medium coefficient of the fish school under three-dimensional conditions can be derived.

[0130] In marine cage aquaculture, carnivorous fish are the main aquaculture targets, and their stocking density is usually maintained between 10 and 15 kg per cubic meter. Assuming that the density of fish is the same as that of water, the volume fraction of fish will be in the range of 1% to 1.5%. Taking Atlantic salmon as an example, the average weight of a single salmon is about 1.556 kg and the body length is 0.55 m. If calculated based on 14,663 salmon, the stocking density will be close to 11.348 kg per cubic meter, and the fish occupy 1.135% of the cage volume. As shown in Table 1, the porous medium coefficient per 10,000 salmon is derived from the numerically calculated force combined with formula (10). If the aquaculture density is other, it only needs to be converted according to the aquaculture quantity.

[0131] Table 1 Calculation table of coefficients of fish school porous media model

[0132]

[0133]

[0134] Step 7: Calculation of the numerical model of the hydrodynamics of the cage under the movement of the fish school. The numerical water tank is 240m long, 80m wide and 20m deep. The diameter of the aquaculture cage is 16m, the height is 10m, the mesh size is 29mm, the diameter of the net wire is 2.8mm, and the net material is PA. A cylindrical porous medium area with a certain thickness is used to approximate the net. At the same time, in order to simplify the analysis, the fish school is also regarded as a porous medium area, and the force on the fish body is solved by a numerical method, and then the correlation coefficient of the porous medium model is determined by formula (10).

[0135] During the culture process, fish in cages usually have two kinds of movement states (see Figure 5 ), when the incoming flow speed is low, the fish will be arranged around the circumference of the cage, which is called the circular swimming of the fish; when the incoming flow speed is high, the fish will be arranged against the water flow, which is called the upstream movement of the fish. In the calculation, the upstream movement of the fish is defined by the rectangular coordinate system, while the circular swimming is defined by multiple reference systems.

[0136] Test Example 1

[0137] Experimental verification of the fish school and cage coupling model

[0138] In order to verify the numerical model proposed in the present invention, a physical test model verification was carried out in a PIV flume with a width of 0.45m and a water depth of 0.4m. The diameter of the test cage is 0.3m and the height is 0.2m. There are a certain number of carp schools inside, and the length of each carp is about 7cm. The test flow rate is 0.06m / s, 0.12m / s, and 0.18m / s, and two different test conditions are designed: an empty cage and a cage containing 60 fish. During the test, the resistance of the cage is recorded by a force sensor, and the flow rate at the measuring point 60cm behind the net is recorded by an ADV flow meter.

[0139] According to the above test model, a cage model and a numerical flume were established at a scale of 1:1. The cage diameter was 0.3m, and the net was replaced by a 5mm thick porous medium area. The inlet of the numerical flume was the velocity inlet, and its velocities were 0.06m / s, 0.12m / s, and 0.18m / s, respectively. The outlet was the outflow boundary, and the top boundary was set as a smooth wall without shear force, and the bottom boundary and side walls were set as no-slip walls. Figure 6The figure shows the mesh division of the numerical model. The numerical model is divided by polyhedral mesh, and the prismatic layer mesh is divided at the boundary. In order to avoid calculation errors caused by mesh problems, the present invention first verifies the mesh convergence of the established numerical model, and obtains three types of meshes of 740,000, 1.14 million and 2.15 million by adjusting the minimum and maximum mesh sizes and the range of the local encrypted area. The number of meshes has converged when it reaches about 1.14 million, and the model will be meshed according to the corresponding settings in the future.

[0140] The density of the net in the test is 0.216. Due to the lack of test data on the stress of a single mesh, the stress of the mesh under this density is calculated using the empirical formula C d =0.04+(-0.04+0.33S+6.54S 2 -4.88S 3 )cosα',C l =(-0.05S+2.3S 2 -1.76S 3 )sin(2α'). According to the resistance of the mesh (C d ), lift (C l ) data, and the porous medium coefficients of the mesh are obtained by continuous iteration based on the iterative gradient descent algorithm, which are C n =100.0m -1 , C t =38.0m -1 The above coefficients were introduced into the established numerical model, and the numerical simulation and model test results were compared. The forces and flow velocities of the two measuring points were well matched in terms of values ​​and trends, with the average error of resistance being 14.3% and the average error of flow velocity being 3.59%. Therefore, using the porous media model to simplify the net can better simulate the forces of the net box and the flow field around it.

[0141] Based on the above verification of the empty cage, the numerical simulation conditions when fish schools exist are verified in combination with model tests. Among them, the porous medium coefficient in the source term model used to simplify the fish school is derived from formula (10), that is, the porous medium coefficient C is derived by numerically simulating the forces on a real fish under flow from different directions. ij The 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 to formula (10) to obtain the porous medium coefficients in the three directions of the fish school. The fitting results are: 0.003183n, 0.05144n, and 0.3152n, where n is the number of fish bodies. Since the fish bodies were observed to move in the form of upstream flow in the experiment, the porous medium coefficient matrix form of the source term model can be expressed as

[0142]

[0143] Table 2 Resistance of the 7.5g fish model in the x, y and z directions in the model test

[0144]

[0145] Figure 7 When the fish density is the maximum, the numerical simulation results are compared with the cage force and measuring point flow velocity measured by the model test when the incoming flow is 0.06m / s, 0.12m / s, and 0.18m / s. It can be seen from the figure that the two are in good agreement in terms of both numerical values ​​and trends, and the fish school's flow-facing state in the numerical simulation results has almost no effect on the cage force, which is basically consistent with the results measured in the experiment.

[0146] The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still modify the technical solutions described in the above embodiments, or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, modification, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A simulation method for coupling the movement of fish schools and water flow in aquaculture cages, characterized in that: The following steps are involved: (1) The single fish motion model is coupled with the net model, and the force on the single fish is obtained through numerical calculation; (2) The stress on the entire fish school in the cage is obtained based on the stress on a single fish, and then the porous medium coefficient of the porous medium model of the fish school is calculated; The following simplifications are made for the large numbers of farmed fish in cages: a. Assume that the fish in the cages are of the same size and have no influence on each other; b. When the fish school swims against the current, it is assumed that they are all arranged against the current in the cage and are evenly distributed; c. When the fish school swims in a circular pattern, it is assumed that they are equally spaced radially and evenly distributed vertically; Based on the above assumptions, the force on the fish school is proportional to the number of fish, and the force on the fish school in the x, y, and z directions satisfies F fish-school =n×F fish ; Based on the above assumptions, a hypothetical volume force source term is added in the area where the fish school is located to approximate the flow resistance effect of the fish school, and this is achieved with the help of a porous medium model. The formula is expressed as follows: In the formula, F fish-school Calculate the force on the fish body for the solid model, F porous is the force on the fish body represented by the source term model, ρ is the fluid density, u is the fluid velocity, λ is the thickness of the porous medium, and A is the area of ​​the porous medium. In the source term model, λA can be obtained from the aquaculture water body V where the fish school is located. wf Indicates; C ij Further expressed as: (3) Establish a porous medium model for coupling the cage and the moving fish school, and use the porous medium model to calculate the force; The control volume analysis method is used to discretize the equation, and the acceleration of the porous medium area is integrated to obtain the force in the porous medium area. The formula is as follows: In the formula, m is the mass of the unit control body, and F is the resultant external force; When the incoming flow velocity remains constant, the component of the momentum equation in the x direction is expressed as: F d =∫ CS pdA-∫ CS up i dA (12) In the formula, F d is the resistance, CS is the integral along the surface of the control volume, p is the pressure, and A is the area of ​​the porous medium; The above formula is also applicable in the y and z directions; According to Morrison's formula, the drag coefficient C d It is expressed as:

2. The simulation method according to claim 1, characterized in that: In the step (1), a single fish motion model is established, and the swing of the fish body is a croaker motion mode, and its wave equation is: Where y is the swing position of each point on the fish body midline, α(x) is the parameter of time t and position x (the fish head coordinate is (0,0)), α(x) is the parametric equation of the swing amplitude, k is the wavelength-related quantity, f is the frequency-related quantity, and a represents the amplitude. is the initial phase, parameter l represents the starting position of the fish body swing, and L represents the length of the fish body.

3. The simulation method according to claim 1, characterized in that: In the step (1), a net model is established based on a porous medium model, and its formula is expressed as follows: In the formula, S i is the momentum source term in the i direction (x, y, z), u j is the incoming flow velocity, μ is the dynamic viscosity of the fluid, D ij and C ij is the coefficient matrix of the porous media model, D n Denotes the normal viscous drag coefficient, D t represents the tangential viscous drag coefficient, C n represents the normal inertial drag coefficient, C t represents the tangential inertial drag coefficient; When water flows through a porous medium area, the force F acting on the porous medium area is calculated by the following formula: F=S i λA (5) Substituting equation (3) into equation (5), we can obtain the water flow resistance F of the porous media structure: d and lift F l The expression is: In the formula, λ is the thickness of the porous medium, and A is the area of ​​the porous medium; When the plane mesh is located at any position in space, the porous medium coefficient corresponding to the mesh model should be converted by the following formula: Where β is the angle between the normal vector n of the plane mesh and the z-axis, and the sine and cosine values ​​of α and β are expressed by two corresponding vectors respectively.

4. The simulation method according to claim 1, characterized in that: The step (1) couples the single fish motion model with the net model: The velocity inlet boundary condition is adopted at the inlet of the numerical water tank, and the pressure outlet condition is adopted at the right outlet. The two sides of the water tank are set as symmetrical boundaries, the bottom is set as a no-slip wall, the top is set as a zero shear force wall, and the surface of the fish body is set as a non-slip boundary. The computational grid adopts the overlapping grid method, in which the background grid includes the water tank and the simplified mesh of the porous medium, which is divided by a structured hexahedral grid; the foreground grid is the encrypted area where the fish body is located, which is divided by an unstructured tetrahedral grid.

5. The simulation method according to claim 4, characterized in that: In order to ensure the calculation accuracy, the boundary layer grid is used to encrypt the three-dimensional grid around the fish body.

6. The simulation method according to claim 1, characterized in that: In the step (1), the finite volume method is used to solve the fluid control equation, and the SST k-ω turbulence model is used to solve the control equation of the flow field around the net; In the calculation, the governing equations of the numerical model are discretized using the finite volume method; During the calculation process, the residual convergence criteria of the continuity equation, velocity component, turbulent kinetic energy k and specific dissipation rate ω were set to 10 -3 , when the calculation converges to this standard, the iteration process ends.

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