A method for visualizing the movement of fish schools in aquaculture ponds based on CFD simulation

Abstract

The present invention provides a method for visualizing numerical simulation of fish school movement in a breeding pond based on CFD simulation, comprising the following steps: Step 1: Establishing a square breeding pond with arc corners and a three-dimensional fish body bionic model; Step 2: Copying the three-dimensional fish body bionic model to generate a fish school; Step 3: Importing the geometric model obtained in Step 2 into Ansys for meshing; Step 4: Using Fluent and a multi-reference system model, numerically simulating the mesh file obtained in Step 3, simulating the flow state in the breeding pond when the fish school starts to move and reaches a stable flow field in the breeding pond when the breeding pond is running and the fish school moves according to a circular fixed trajectory in the breeding pond. The technical solution of the present invention can monitor the hydrodynamic conditions in the pond in real time, and can also assist in the design of the breeding pond and parameter setting.

Description

Technical Field

[0001] The present invention relates to the field of aquaculture engineering, and in particular to a method for visualizing numerical simulation of fish movement in a culture pond based on CFD simulation. Background Art

[0002] Many numerical simulation studies on flow field characteristics in aquaculture ponds at home and abroad use numerical simulation methods to construct aquaculture pond models with various parameters, simulate the flow field conditions in aquaculture ponds in recirculating water aquaculture systems under different parameters, and then verify and complement each other with model experiments, which jointly promotes the research and application of the hydrodynamic characteristics of aquaculture pond systems and provides theoretical support for optimizing the structure of aquaculture ponds and improving the self-purification capacity of aquaculture ponds.

[0003] Existing studies have shown that the presence of fish also affects the flow field characteristics of the aquaculture pond. The swimming behavior of fish produces turbulence and enhanced water mixing, which can cause changes in the system's velocity distribution and increase water circulation resistance. Studies have found that when fish are stocked in the aquaculture pond system, the average flow velocity of the system flow field decreases, turbulence increases, water circulation resistance increases, and the flow velocity distribution changes. Summary of the invention

[0004] In order to solve the problem of not considering the influence of fish movement in the process of constructing the circulating water flow field, the present invention provides a numerical simulation method for visualizing the movement of fish in a breeding pond based on CFD simulation.

[0005] The technical means adopted by the present invention are as follows:

[0006] A method for visualizing the movement of fish schools in a breeding pond based on CFD simulation includes the following steps:

[0007] Step 1: According to the pre-set parameters of the breeding pond, including the pond type, the location of the water inlet structure and the water depth, a square breeding pond with arc corners was established in Ansys Geometry, and a three-dimensional fish bionic model was established using Solidworks;

[0008] Step 2: Import the three-dimensional fish bionic model into the breeding pond through the software interface of Solidworks and Ansys, and copy the three-dimensional fish bionic model to generate a school of fish, and set the calculation domain in the Geometry of Ansys as the fluid domain; divide the area in the breeding pond into two subdomains according to whether it includes the school of fish, the area including the school of fish is the moving grid area, and the rest of the area is the static grid area, and use the Subtract in the Boolean operation to subtract the overlapped part of the school of fish and the water in the breeding pond;

[0009] Step 3: Import the geometric model obtained in step 2 into the Meshing section of Ansys for meshing, mesh the aquaculture pond using tetrahedral meshes, and adjust the size and number of meshes by adjusting the unit size parameters and associated value parameters in the Meshing section;

[0010] Step 4: Fluent is used to perform numerical simulation on the grid file obtained in step 3 using a multiple reference system model, simulating the flow state in the breeding pond when the fish school starts to move and reaches a stable flow field in the breeding pond when the breeding pond is running and the fish school moves along a circular fixed trajectory in the breeding pond. The numerical simulation process specifically includes the following steps:

[0011] Step 4-1: Import the grid file into Fluent and set basic parameters, including fluid material, RNG k-ε model, sub-relaxation factor of turbulent kinetic energy and turbulent dissipation rate;

[0012] Step 4-2: In Fluent, using Frame Motion, a three-dimensional rectangular coordinate system is established with the center of the bottom of the breeding pond as the origin, and the Y axis is used as the rotation axis, so that the fish school moves in a circular fixed trajectory around the rotation axis;

[0013] Step 4-3: Setting other parameters of the solver, including: setting the dynamic parameters of water, including water inlet speed, water flow resistance and water flow pressure, defining boundary conditions, and when using the multiple reference system model to perform numerical simulation calculations of the model, setting the rotation speed of the moving grid area according to the movement speed and turning angle of the fish school, and setting the external static grid area to a static state, setting the side wall and bottom surface of the breeding pond to static boundary conditions, and setting the fish school to a dynamic wall boundary condition; setting the contact area between the three-dimensional fish bodies in the fish school as the internal interface; setting the residual of the model monitor and keeping it at 10 -4 , initialize the values ​​of all zones in Fluent, set the number of iteration steps, automatically save the number of steps, observe whether the residual curve converges to the set residual value in each step of the transient calculation, until the model converges, and the obtained model can be used to simulate the flow state in the breeding pond when the fish school starts to move and reaches the flow field stability in the breeding pond when the breeding pond is running and the fish school moves along a circular fixed trajectory in the breeding pond.

[0014] Furthermore, step 5 is included: after the simulation is completed, CFD-POST is entered to post-process the numerical simulation results calculated in Fluent to show the influence of the movement of the fish school along the circular fixed trajectory on the hydrodynamic force and flow field in the breeding pond:

[0015] (1) by obtaining a vorticity diagram generated after the flow field in the culture pond is stabilized, the influence of the movement of the school of fish on the hydrodynamics in the culture pond is expressed;

[0016] (2) by obtaining a streamline diagram generated after the flow field in the aquaculture pond reaches stability, the influence of the fish school on the movement trajectory of water particles in the aquaculture pond is expressed;

[0017] (3) A velocity cloud diagram of the aquaculture pond cross section is generated by intercepting the numerical simulation process to show the influence of the fixed trajectory movement of the fish school on the flow field in the aquaculture pond.

[0018] Furthermore, in step 3, the association value is set to 0, the unit size is set to 7.8 mm, and the number of grids obtained by meshing is 3642502, the number of nodes is 635880, and the maximum grid size is 8 mm.

[0019] Furthermore, in step 4, the circular fixed trajectory is determined by the position of the three-dimensional fish body in the breeding pond, including the distance between the position of the three-dimensional fish body and the central axis of the breeding pond and the distance between the three-dimensional fish body and the bottom of the breeding pond.

[0020] Furthermore, in step 4, it is characterized in that when the average hydrodynamic velocity in the breeding pond is almost unchanged, the flow field in the breeding pond is stable.

[0021] Furthermore, step 4-1 also includes, when using Fluent for numerical simulation, using a steady-state method for solution, the initial conditions are: the inlet velocity v=1m / s, the outlet is set to the outlet pressure outlet; the fluid material is set to liquid water; the continuous phase and the discrete phase both use the pressure implicit solution method, and the Coupled method is used to couple the pressure and velocity, the pressure and momentum are solved based on the second-order upwind discrete format, the turbulent kinetic energy and turbulent dissipation rate are solved based on the second-order upwind discrete format, the sub-relaxation factor of the pressure is set to 0.3, the sub-relaxation factor of the momentum is set to 0.7, and the sub-relaxation factor of the turbulent kinetic energy and turbulent dissipation rate is set to 0.8.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] 1. The method for visualizing the movement of fish schools in aquaculture ponds based on CFD simulation provided by the present invention simulates the influence of the movement of fish schools along a circular fixed trajectory in aquaculture ponds on the hydrodynamic conditions of aquaculture ponds, which is closer to the hydrodynamic environment of the actual operation of aquaculture systems.

[0024] 2. The method for visualizing the movement of fish schools in aquaculture ponds based on CFD simulation provided by the present invention is suitable for simulating the swimming behavior of fish schools in aquaculture ponds. The method for simulating the swimming of fish schools in aquaculture ponds adopts a multiple reference frame model (MRF). Compared with the dynamic grid technology, the method has the advantage of less computational complexity and has significant advantages in simulating fish schools. The MRF model is more suitable for simulating the movement of fish schools in aquaculture ponds.

[0025] 3. The method for visualizing the movement of fish schools in aquaculture ponds based on CFD simulation provided by the present invention provides a method for real-time monitoring of the hydrodynamic conditions in aquaculture ponds in simulated factory-scale recirculating aquaculture systems. It can also assist in the design of aquaculture ponds and parameter setting, and has the advantages of low cost, high efficiency, convenience, and environmental protection.

[0026] Based on the above reasons, the present invention can be widely promoted in the field of circulating water aquaculture engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0028] Figure 1 (a) and (b) are schematic diagrams of the aquaculture pond model established by the present invention when there is no fish body / there is one fish body in the aquaculture pond model established by the present invention.

[0029] Figure 2 This is a flow field cloud diagram of the cross section of the breeding pond where a fish is released every 500 iterations during the 0-4000 iterations.

[0030] Figure 3 Schematic diagram of a model of a culture pond including a school of fish established for the present invention.

[0031] Figure 4 (a) and (b) are the cross-sectional flow velocity cloud diagrams when the flow field reaches a stable state when there are / are fish schools in the aquaculture pond model, respectively.

[0032] Figure 5 (a) and (b) are the streamline diagrams in the aquaculture pond when the flow field is running to a stable state with and without fish in the aquaculture pond model, respectively.

[0033] Figure 6 (a) and (b) are the vortex diagrams of the aquaculture pond when the flow field is running to a stable state with and without fish in the aquaculture pond model, respectively. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings 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. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. 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.

[0035] Example 1

[0036] The flow field conditions in an empty culture pond and a culture pond under the action of a school of fish were obtained when the flow state was stable.

[0037] A method for visualizing the movement of fish schools in a breeding pond based on CFD simulation includes the following steps:

[0038] Step 1: According to the pre-set parameters of the breeding pond, including the pond type, the location of the water inlet structure and the water depth, a square breeding pond with arc corners was established in Ansys Geometry, and a three-dimensional fish bionic model was established using Solidworks;

[0039] Step 2: Import the three-dimensional fish bionic model into the breeding pond through the software interface of Solidworks and Ansys, and copy the three-dimensional fish bionic model to generate a school of fish, and set the calculation domain in the Geometry of Ansys as the fluid domain; divide the area in the breeding pond into two subdomains according to whether it includes the school of fish, the area including the school of fish is the moving grid area, and the rest of the area is the static grid area, and use the Subtract in the Boolean operation to subtract the overlapped part of the school of fish and the water in the breeding pond;

[0040] Preferably, this embodiment selects an eight-meter square arc-cornered breeding pond as a modeling object, and scales the breeding pond in proportion according to a scaling ratio of 8:1, and obtains a square breeding pond with an arc corner having a side length of 1 meter and an arc radius of 0.25 meters; the fish body is simplified to an ellipsoidal sphere, and 51 fish are replicated in the breeding pond, and the proportionally reduced fish models are evenly distributed in the upper, middle and lower layers of the breeding pond;

[0041] Step 3: Import the geometric model obtained in step 2 into the Meshing section of Ansys for meshing, and use tetrahedral meshing to mesh the aquaculture pond. The tetrahedral meshing method has better adaptability to complex geometries, and the size and number of the meshes are adjusted by adjusting the element size parameter (element size) and the relevance parameter (relevance) in the Meshing section;

[0042] Step 4: Fluent is used to perform numerical simulation on the grid file obtained in step 3 using a multiple reference system model, simulating the flow state in the breeding pond when the fish school starts to move and reaches a stable flow field in the breeding pond when the breeding pond is running and the fish school moves along a circular fixed trajectory in the breeding pond. The numerical simulation process specifically includes the following steps:

[0043] Step 4-1: Import the grid file into Fluent and set basic parameters, including fluid material, RNG k-ε model, sub-relaxation factor of turbulent kinetic energy and turbulent dissipation rate;

[0044] Step 4-2: In Fluent, use Frame Motion to establish a three-dimensional rectangular coordinate system with the center of the bottom of the breeding pond as the origin, and use the Y axis as the rotation axis to make the fish school move in a circular fixed trajectory around the rotation axis; specifically, in the Frame Motion option, lock the rotation axis through the coordinates of the two points (0,0,0) and (0,1,0), and set the fish school to "moving wall";

[0045] Step 4-3: Setting other parameters of the solver, including: setting the dynamic parameters of water, including water inlet speed, water flow resistance and water flow pressure, defining boundary conditions, and when using the multiple reference system model to perform numerical simulation calculations of the model, setting the rotation speed of the moving grid area according to the movement speed and turning angle of the fish school, and the external static grid area is in a static state, setting the side wall and bottom surface of the breeding pond as static boundary conditions, and setting the fish school as a moving wall boundary condition (moving wall); setting the contact area between the three-dimensional fish bodies in the fish school as the internal interface (interior); setting the residual of the model monitor (monitor) and keeping it at 10 -4 , initialize the values ​​of all zones in Fluent, set the number of iteration steps, automatically save the number of steps, and observe whether the residual curve converges to the set residual value in each step of transient calculation until the model converges, such as Figure 2 As shown, the operation process of the numerical simulation model established by the present invention and the change of the flow field in the breeding pond gradually tending to be stable are shown. The final model can be used to simulate the flow state in the breeding pond when the fish school starts to move and reaches the flow state when the flow field in the breeding pond is stable, when the breeding pond is running and the fish school moves along a circular fixed trajectory in the breeding pond.

[0046] Furthermore, step 5 is included: after the simulation is completed, CFD-POST is entered to post-process the numerical simulation results calculated in Fluent to show the influence of the movement of the fish school along the circular fixed trajectory on the hydrodynamic force and flow field in the breeding pond:

[0047] (1) The influence of the movement of the school of fish on the hydrodynamics in the aquaculture pond is shown by obtaining a vorticity diagram generated after the flow field in the aquaculture pond is stabilized:

[0048] like Figure 6 As shown in the figure, according to the vorticity diagram, it can be seen that there are not many vortex structures in the fishless breeding pond, and the vortex structures are significantly increased in the breeding pond with fish. The presence of fish increases the vortex structure of the breeding pond and produces a small vortex area. The existence of the small vortex area causes a large energy loss.

[0049] (2) The influence of the fish school on the movement trajectory of the water particles in the aquaculture pond is shown by obtaining the streamline diagram generated after the flow field in the aquaculture pond reaches stability:

[0050] like Figure 5 As shown in the figure, the streamline diagram is obtained by taking 100 particles at the water inlet to obtain their motion trajectories. By comparison, it can be seen that compared with the fish culture pond, the movement distance of random particles in the fish culture pond is significantly shortened. Since the number of large cycles of the two working conditions is the same, the particle movement distance is shortened, so the movement of each water particle in the culture pond slows down;

[0051] (3) The velocity cloud diagram of the cross-section of the aquaculture pond is generated by intercepting the numerical simulation process to show the influence of the fixed trajectory movement of the fish school on the flow field in the aquaculture pond:

[0052] like Figure 4 As shown in the figure, by comparison, the cloud map in the fish breeding pond has changed under the influence of fish. The fish's countercurrent swimming has an impact on the flow field distribution of the breeding pond. A low flow velocity area appears in the center of the breeding pond, the flow velocity of the breeding pond decreases, and the flow velocity near the drain in the center of the pond also decreases significantly.

[0053] The numerical simulation method provided by the present invention can simulate the flow conditions in the breeding pond after the recirculating aquaculture system reaches stability in normal operation, and then various hydraulic indicators can be obtained by simulating different breeding ponds, so as to determine how to arrange the equipment in the breeding pond (water inlet structure, drainage structure, pool type, etc.) to better provide a water environment suitable for the growth of fish.

[0054] Furthermore, in step 3, the association value is set to 0, the unit size is set to 7.8 mm, and the number of grids obtained by meshing is 3642502, the number of nodes is 635880, and the maximum grid size is 8 mm.

[0055] Furthermore, in step 4, the circular fixed trajectory is determined by the position of the three-dimensional fish body in the breeding pond, including the distance between the position of the three-dimensional fish body and the central axis of the breeding pond and the distance between the three-dimensional fish body and the bottom of the breeding pond.

[0056] Furthermore, in step 4, it is characterized in that when the average hydrodynamic velocity in the breeding pond is almost unchanged, the flow field in the breeding pond reaches a stable state; it is also possible to determine whether the flow field in the breeding pond reaches a stable state by monitoring other parameters of the flow field in the breeding pond.

[0057] Furthermore, step 4-1 also includes, when using Fluent for numerical simulation, using a steady-state method for solution, the initial conditions are: the inlet velocity v=1m / s, the outlet is set to the outlet pressure outlet; the fluid material is set to liquid water; the continuous phase and the discrete phase both use the pressure implicit solution method, and the Coupled method is used to couple the pressure and velocity, the pressure and momentum are solved based on the second-order upwind discrete format, the turbulent kinetic energy and turbulent dissipation rate are solved based on the second-order upwind discrete format, the sub-relaxation factor of the pressure is set to 0.3, the sub-relaxation factor of the momentum is set to 0.7, and the sub-relaxation factor of the turbulent kinetic energy and turbulent dissipation rate is set to 0.8.

[0058] Furthermore, in step 4-1, after importing the mesh file into Fluent, you first need to check the mesh file through the cheat function. Only after there is no problem can you proceed to the next step of model solving. The quality of mesh division is very important for model solving. After the inspection is completed, the mesh is smoothed (smooth / swap) to further rearrange the number of nodes and correct the connectivity of the mesh units.

[0059] Furthermore, step 3 also includes: performing grid encryption processing on the fish bodies and the water inlets and outlets in the breeding pond, not performing grid encryption processing on other fluid areas, and naming each fish body and the water inlets and outlets.

[0060] Further, in this embodiment, in step 1, the breeding pond is obtained by scaling the actual circulating water breeding pond and the square arc-corner breeding pond at a ratio of 8:1; the fish body of the three-dimensional fish bionic model is 26 cm long, the maximum width b=2.6 cm, and the maximum height h=2.6 cm; the breeding pond is 1 meter long, 1 meter wide, the arc radius R is 0.25 m, and the depth is 0.2 m; a water inlet pipe of the breeding pond is relatively arranged and vertically arranged on the inner wall of the breeding pond, and 18 water inlet holes are evenly opened in the vertical direction of the water inlet pipe, and the distance C from the center of the water inlet hole to the pool wall is 0.02 m; in step 4, the movement trajectory of the fish body is a horizontal arc trajectory with a radius of 0.25 m and a constant movement speed of 0.2 rad / s.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for visualizing the movement of fish schools in aquaculture ponds based on CFD simulation, characterized in that: The following steps are involved: Step 1: According to the pre-set parameters of the breeding pond, including the pond type, the location of the water inlet structure and the water depth, a square breeding pond with arc corners was established in Ansys Geometry, and a three-dimensional fish bionic model was established using Solidworks; Step 2: Import the three-dimensional fish bionic model into the breeding pond through the software interface of Solidworks and Ansys, and copy the three-dimensional fish bionic model to generate a school of fish, and set the calculation domain in the Geometry of Ansys as the fluid domain; divide the area in the breeding pond into two subdomains according to whether it includes the school of fish, the area including the school of fish is the moving grid area, and the rest of the area is the static grid area, and use the Subtract in the Boolean operation to subtract the overlapped part of the school of fish and the water in the breeding pond; Step 3: Import the geometric model obtained in step 2 into the Meshing section of Ansys for meshing, mesh the aquaculture pond using tetrahedral meshes, and adjust the size and number of meshes by adjusting the unit size parameters and associated value parameters in the Meshing section; Step 4: Fluent is used to perform numerical simulation on the grid file obtained in step 3 using a multiple reference system model, simulating the flow state in the breeding pond when the fish school starts to move and reaches a stable flow field in the breeding pond when the breeding pond is running and the fish school moves along a circular fixed trajectory in the breeding pond. The numerical simulation process specifically includes the following steps: Step 4-1: After importing the grid file into Fluent, set the basic parameters, including fluid material, RNG k-ε model, sub-relaxation factor of turbulent kinetic energy and turbulent dissipation rate; Step 4-2: In Fluent, using Frame Motion, a three-dimensional rectangular coordinate system is established with the center of the bottom of the breeding pond as the origin, and the Y axis is used as the rotation axis, so that the fish school moves in a circular fixed trajectory around the rotation axis; Step 4-3: Setting other parameters of the solver, including: setting the dynamic parameters of water, including water inlet speed, water flow resistance and water flow pressure, defining boundary conditions, and when using the multiple reference system model to perform numerical simulation calculations of the model, setting the rotation speed of the moving grid area according to the movement speed and turning angle of the fish school, and setting the external static grid area to a static state, setting the side wall and bottom surface of the breeding pond to static boundary conditions, and setting the fish school to a dynamic wall boundary condition; setting the contact area between the three-dimensional fish bodies in the fish school as the internal interface; setting the residual of the model monitor and keeping it at 10 -4 , initialize the values ​​of all zones in Fluent, set the number of iteration steps, automatically save the number of steps, observe whether the residual curve converges to the set residual value in each step of the transient calculation, until the model converges, and the obtained model can be used to simulate the flow state in the breeding pond when the fish school starts to move and reaches the flow field stability in the breeding pond when the breeding pond is running and the fish school moves along a circular fixed trajectory in the breeding pond.

2. The method for visualizing the movement of fish schools in a breeding pond based on CFD simulation according to claim 1, characterized in that: The process also includes step 5: after the simulation is completed, CFD-POST is entered to post-process the numerical simulation results calculated in Fluent to show the influence of the movement of the fish school along a circular fixed trajectory on the hydrodynamic force and flow field in the breeding pond: (1) by obtaining a vorticity diagram generated after the flow field in the culture pond is stabilized, the influence of the movement of the school of fish on the hydrodynamics in the culture pond is expressed; (2) by obtaining a streamline diagram generated after the flow field in the aquaculture pond reaches stability, the influence of the fish school on the movement trajectory of water particles in the aquaculture pond is expressed; (3) A velocity cloud diagram of the aquaculture pond cross section is generated by intercepting the numerical simulation process to show the influence of the fixed trajectory movement of the fish school on the flow field in the aquaculture pond.

3. The method for visualizing the movement of fish schools in a culture pond based on CFD simulation according to claim 1, characterized in that: In step 3, the association value is set to 0, the element size is set to 7.8 mm, and the final number of grids obtained by meshing is 3642502, the number of nodes is 635880, and the maximum grid size is 8 mm.

4. The method for visualizing the movement of fish schools in a culture pond based on CFD simulation according to claim 1, characterized in that: In step 4, the circular fixed trajectory is determined by the position of the three-dimensional fish body in the breeding pond, including the distance between the position of the three-dimensional fish body and the central axis of the breeding pond and the distance between the three-dimensional fish body and the bottom of the breeding pond.

5. The method for visualizing the movement of fish schools in a culture pond based on CFD simulation according to claim 1, wherein in step 4, When the average hydrodynamic velocity in the breeding pond is almost unchanged, the flow field in the breeding pond is stable.

6. According to the numerical simulation method for visualizing the movement of fish schools in aquaculture ponds based on CFD simulation according to claim 1, step 4-1 also includes: when using Fluent for numerical simulation, a steady-state method is selected for solution, and the initial conditions are: the inlet velocity v=1m / s, the outlet is set as the outlet pressure outlet; the fluid material is set to liquid water; the continuous phase and the discrete phase both use the pressure implicit solution method, and the Coupled method is selected to couple the pressure and velocity, the pressure and momentum are solved based on the second-order upwind discrete format, the turbulent kinetic energy and turbulent dissipation rate are solved based on the second-order upwind discrete format, the sub-relaxation factor of the pressure is set to 0.3, the sub-relaxation factor of the momentum is set to 0.7, and the sub-relaxation factor of the turbulent kinetic energy and the turbulent dissipation rate is set to 0.8.

Images