Fin flexible motion characterization and bionic fish autonomous swimming numerical calculation method

Abstract

The invention discloses a fin flexible motion characterization and bionic fish autonomous swimming numerical calculation method, and belongs to the field of bionic hydrodynamics. The method aims to solve the problem that information such as motion characteristics and motion postures of fishes cannot be obtained in numerical calculation of the swimming performance of the bionic fishes by adopting a constraint state. Flexible motion of the fins is represented by fluctuating motion driven by the fin ray, motion of the fin ray is reciprocating swing motion around the fin root, variables for controlling swing motion of the fin ray are coordinates and time of the fin root in a fin coordinate system, and flexible fluctuating motion of the fins is achieved by controlling a swing angle function of the fin ray. A fin ray swing angle function is described by Fourier series; according to the method, geometric model modeling is further carried out on the bionic fish, the CFD technology is adopted for processing, then numerical solution is carried out on a CFD computational domain based on the flexible motion of the fins, and therefore autonomous swimming numerical calculation of the bionic fish is achieved.

Description

Technical Field

[0001] The invention belongs to the field of bionic hydrodynamics, and in particular relates to a method for characterizing and calculating the autonomous swimming of a bionic fish. Background Art

[0002] Fish in nature have excellent swimming ability in water. The fins on their bodies integrate propulsion and control. According to the type of fins involved in the propulsion of fish when swimming, the swimming mode of fish can be divided into body-tail fin swimming mode and middle fin-opposite fin swimming mode. Among them, the middle fin-opposite fin swimming mode has strong maneuverability and high stability swimming performance at low swimming speed. These swimming abilities are urgently needed by underwater vehicles, and are also difficult to achieve based on propeller propulsion and rudder wing control. Therefore, the development of bionic underwater vehicles by imitating the middle fin-opposite fin swimming mode of fish has important application prospects in underwater resource detection, target search and other tasks. The study of fish swimming performance and mechanism is the key to whether bionic underwater vehicles can have excellent swimming performance of fish. However, since the movement of fish fins is highly flexible and nonlinear, and the swimming of fish under the propulsion of fins involves strong fluid-solid coupling between fish body, fins and fluid, this brings great challenges to the numerical simulation of fish swimming performance.

[0003] The invention patent "A numerical calculation method for propulsion performance of a bionic undulating fin" with application number 202010001808.7 discloses a numerical calculation method for the flexible undulating motion of a bionic fish fin. However, in this numerical calculation method, the position of the bionic fish fin in space is fixed (constrained state), that is, the bionic fish fin performs flexible undulation at a constant position in space, and the hydrodynamic performance of the bionic fish fin is calculated by giving the fluid a constant movement speed. The numerical calculation method established by the invention patent with application number 202010001808.7 is completely different from the real swimming of fish. Fish in nature change their original static state or motion state under the propulsion of the fins, that is, the movement speed and movement posture of the fins are changing in real time, and it is a strong coupling effect of the fin dynamics, fish body dynamics, and fluid dynamics. Therefore, the numerical calculation of the swimming performance of the bionic fish using the constrained state cannot obtain the movement characteristics, movement posture and real flow field information of the fish, thereby causing a distortion of the swimming performance of the fish. Summary of the invention

[0004] The present invention aims to solve the problem that the information of the movement characteristics, movement posture and the like of the fish cannot be obtained when numerically calculating the swimming performance of the bionic fish using the constraint state.

[0005] A method for characterizing the flexible motion of a fish fin uses the wave motion driven by fin rays to characterize the flexible motion of the fish fin. The wave motion driven by the fin rays is as follows: The movement of the fin ray is a reciprocating swinging motion around the fin root. The variable controlling the swinging motion of fin ray i is the x coordinate of the fin root in the fish fin coordinate system xyz. i coordinates and time t; by controlling the swing angle function θ(x i , t) realizes the flexible wave motion of the fins, and the fin swing angle function θ(x i , t) is described by a Fourier series.

[0006] The fin swing angle function θ(x i , t) are as follows: Among them, ξ(x) is the fin swing angle amplitude function, f is the frequency, k=2π / λ is the wave number, and λ is the wavelength.

[0007] The fin ray swing angle amplitude function includes the following fin ray swing angle amplitude function forms: Among them, γ0 is the maximum fin swing angle amplitude, b is a non-zero constant; , , , , They are respectively one kind of fin swing angle amplitude function; is the length of the fish fin.

[0008] A numerical calculation method for autonomous swimming of a bionic fish comprises the following steps: Step 1: Establish a geometric model of a bionic fish with any middle fin-opposite fin swimming mode: Step 2, establish a CFD calculation domain including the bionic fish geometric model, mesh the calculation domain, generate a numerical calculation volume mesh, record the geometric domain of the bionic fish geometric model in the calculation domain as the internal calculation domain, and apply a dynamic mesh method to the numerical calculation volume mesh of the internal calculation domain; Step 3, setting different grid scales of the bionic fish surface and the computational domain, obtaining at least three sets of numerical calculation volume grids with increasing numbers, and performing grid convergence verification to select the numerical calculation volume grid; Step 4: Based on the above-mentioned method for characterizing the flexible motion of fish fins, establish the swing angle function θ(x i ,t), set the time term in the fin swing angle function to zero, set other parameter values ​​in the fin swing angle function, and initialize the flexible motion of the fin after the flow field is initialized; Step 5, set the time step Δt, set the total solution time t1, and the iteration time step number n1 to t1 / Δt; Step 6, at the nth time step, the current solution time t = n×Δt is input into the fish fin flexible motion characterization method, the coordinates of the fish fin surface mesh nodes at the current solution time are updated, and the numerical calculation volume mesh is deformed and reconstructed based on the moving mesh method; Step 7, numerically solve the CFD calculation domain to obtain the flow field information around the bionic fish, calculate the hydrodynamic force and torque on the bionic fish, and calculate the power consumption of the fish body and fins; determine the directions of the components of the pressure and viscous force on the x-axis of the grid units on the surface of the fish body and fins, integrate the components of the pressure and viscous force on the x-axis in the same direction as the swimming direction to obtain pure thrust, and integrate the components of the pressure and viscous force on the x-axis in the opposite direction to the swimming direction to obtain pure resistance; Step 8: At the nth time step, the linear velocity and angular velocity of the bionic fish are solved based on the calculated hydrodynamic force and torque on the bionic fish, and the displacement and posture change of the bionic fish are obtained based on the linear velocity and angular velocity; Step 9: updating the displacement and posture of the bionic fish in the geodetic coordinate system according to the displacement and posture changes of the bionic fish, and updating the displacement of the numerical calculation domain and the numerical calculation volume grid in the geodetic coordinate system according to the displacement of the bionic fish; The position of the bionic fish in the geodetic coordinate system is updated based on the calculated displacement and posture changes of the bionic fish, so that the bionic fish can swim autonomously under the propulsion of the fins. Step 10: Determine whether n is less than n1; if so, the time step is incremented by 1, and return to step 5 to solve the n+1th time step; if not, the solution ends.

[0009] Furthermore, the method for calculating the autonomous swimming numerical value of a bionic fish further comprises the following steps: Step 11, calculate the swimming characteristic time curve of the bionic fish under the set parameter values ​​of the fin flexible motion, including the time curves of linear velocity, angular velocity, linear acceleration, angular acceleration, displacement, and attitude angle; the hydrodynamic characteristic time curve of the bionic fish, including the time curves of force, torque, and power consumption.

[0010] Furthermore, the process of calculating the hydrodynamic force and torque on the bionic fish in step 7 includes: The standard wall function method is used to discretize the governing equations of the fluid using the finite volume method and a pressure-based transient solver. The SIMPLEC algorithm is applied to the pressure-velocity coupling, using a first-order implicit format in time and a second-order upwind format in space. The pressure and viscous force on the mesh units of the body and fins of the bionic fish are integrated to obtain the hydrodynamic force and torque on the bionic fish: M z = ∫ S { r × [ ( − pn 1 + τ n 1 ) n 1 + ( − pn 2 + τ n 2 ) n 2 ] } dS in, , represents the hydrodynamic forces in the x and y directions; represents the moment in the z direction; p is the pressure vector of the mesh unit dS on the surface of the fish body and fins, n1 is the unit vector in the x-axis direction, n2 is the unit vector in the y-axis direction, τ is the viscous stress of the mesh unit dS on the surface of the fish body and fins, and r is the position vector relative to the center of mass.

[0011] Furthermore, in the process of calculating the power consumption of the fish body and the fins in step 7, the power consumption of the fins The pressure p and viscosity force on the grid unit on the surface of the fish fin and the movement speed u of the grid unit f Integrating the vector product of gives: Among them, f=1, 2, 3 represent the three coordinate axes x, y, and z respectively.

[0012] Furthermore, the pure thrust and pure resistance obtained in step 7 are as follows: in, and are the pure thrust and pure resistance exerted on the fish body and fins.

[0013] Beneficial effects: The present invention establishes a method for characterizing the flexible motion of fish fins in the middle fin-pair fin swimming mode of fish, which can simulate the flexible wave motion of fish fins in linear or nonlinear traveling waves, and further establishes a numerical simulation method for the autonomous swimming of bionic fish under the coupling of fish fin dynamics-fish body dynamics-fluid dynamics. This method can perform accurate and high-quality numerical calculations on the real swimming behavior of fish in nature, and obtain the motion characteristics and motion posture of bionic fish during swimming, and can further obtain detailed motion characteristics and hydrodynamic characteristics, specifically linear velocity, angular velocity, displacement, posture angle, force, torque, power consumption, etc., and can also assist in obtaining the surface pressure distribution and flow field information of the fish body. Compared with the existing numerical simulation method of fish swimming characteristics based on constraint models, the method proposed in the present invention can truly obtain the swimming characteristics and mechanism of fish, and provide support for the development of high-performance bionic robot fish. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of the numerical calculation method of the present invention; Figure 2The bionic fish geometric model of the present invention; Figure 3 is the CFD calculation domain of the present invention; Figure 4 A numerical calculation volume grid of the present invention; Figure 5 A schematic diagram of the flexible motion of the fin established by the present invention; Figure 6 Five kinds of fish fin flexible motion waveforms established for the present invention; Figure 7 The time history curve of the bionic fish line speed and angular speed calculated by the present invention; Figure 8 The time history curve of the displacement and posture angle of the bionic fish calculated by the present invention; Fig. 9 The hydrodynamic force and torque time history curve of the bionic fish calculated by the present invention; Fig.10 The power consumption time history curve of the fin calculated by the present invention; Fig.11 The surface pressure distribution diagram of the bionic fish calculated by the present invention; Fig.12 The three-dimensional vortex structure diagram of the flow field calculated by the present invention; Fig.13 This is a schematic diagram of the CFD calculation domain mesh node spring system; Fig.14 Schematic diagram of local reconstruction of the CFD calculation domain mesh. DETAILED DESCRIPTION

[0015] In order to solve the problems existing in the background technology, the present invention constructs a method for characterizing the flexible motion of fish fins in the middle fin-pair fin swimming mode of fish, which can accurately simulate the flexible motion of fish fins in different motion modes; at the same time, a numerical solution method for the coupling of fish fin dynamics-fish body dynamics-fluid dynamics is proposed, which can accurately numerically solve the autonomous swimming process of bionic fish under the propulsion of flexible fin fluctuations.

[0016] Specific implementation method 1: Combination Figure 1 To explain this embodiment, This embodiment is a numerical calculation method for autonomous swimming of a bionic fish including a method for characterizing the flexible motion of a fish fin, including: Step 1: Establish a geometric model of a bionic fish with any middle fin-opposite fin swimming mode: The bionic fish geometric model can be based on scanning the surface of a live fish with a 3D laser scanner to obtain a point cloud of the body and fins of the live fish in space, and processing the point cloud with the reverse engineering software Geomagic Studio to generate a 3D model of the fish body and fins, which is then imported into the computer-aided design software for further smoothing, such as Figure 2 The geometric model of the freshwater stingray obtained by laser scanning and processing as shown in (a) in the figure; for some types of fish, the fins are thin, and the point cloud obtained by scanning will have a large error. For this type of fin, the outline of the fin can be used to directly model the fin; in addition, due to the complex body shape characteristics of fish in nature, the body geometry characteristics of some fish are not convenient for the engineering design of bionic underwater vehicles, so computer-aided design software can also be used to directly model the fish body and fins to establish a simplified bionic fish geometry model for engineering applications, such as Figure 2 The geometric model of the bionic ray shown in (b); Step 2, establish the CFD calculation domain and boundary conditions including the bionic fish geometric model, mesh the calculation domain, generate numerical calculation volume mesh, and apply the dynamic mesh method to the numerical calculation volume mesh of the internal calculation domain; Import the bionic fish geometric model processed by computer-aided design software into meshing software, such as gambit, icem, fluent meshing, pointwise, etc., and then establish a large geometric entity. This geometric entity can be a cuboid, cylinder, sphere, etc., and its form is not limited. Its scale must be large enough to meet the requirements of numerical calculation of the bionic fish swimming performance, which is recorded as a large domain; we take a cuboid as an example; then, establish a CFD calculation domain, and this implementation method provides two methods: the first method is to use Boolean operations, use the large domain to perform subtraction operations on the bionic fish geometric model, generate new geometric entities, and then divide the new geometric entities into blocks, and use the geometric domain directly containing the bionic fish geometric model as the internal calculation domain, and the remaining geometric entities are the external calculation domain; the second method is to establish a smaller-scale geometric entity containing the bionic fish geometric model, recorded as a small domain, and use the small domain to perform subtraction operations on the bionic fish set model to form a new geometric entity, which is the internal calculation domain, and the large domain is the external calculation domain; such as Figure 3 As shown, (a) shows the external computing domain, and (b) shows the internal computing domain; The CFD calculation domain established by the first method has an interface between the internal calculation domain and the external calculation domain. During numerical calculation, the flow field information of the internal calculation domain and the external calculation domain is transmitted through the interface. During meshing, the internal calculation domain is meshed with tetrahedral meshes, and the interface between the internal calculation domain and the external calculation domain is meshed with quadrilateral meshes. The quadrilateral mesh on the interface between the internal calculation domain and the external calculation domain is used as a condition to quickly stretch outward to the boundary of the external calculation domain to generate a hexahedral mesh. For other areas of the external calculation domain, hexahedral meshes are generated based on the adjacent volume meshes. The CFD calculation domain established by the second method has no interface between the internal calculation domain and the external calculation domain. During numerical calculation, the internal calculation domain and the external calculation domain are set as overlapping grids. The hole digging algorithm is used to delete the volume grids overlapping the internal calculation domain and the external calculation domain. Only the volume grids overlapping the internal calculation domain boundary are retained to exchange information between the internal and external calculation domains. The flow field information of the internal and external calculation domains is transmitted through volume grid interpolation. When meshing, the internal calculation domain is meshed with tetrahedral grids, and the external calculation domain is directly meshed with hexahedral grids. The computational domain mesh is Figure 4 As shown; The boundary conditions of the external computational domain are set as follows: the velocity and pressure are set to zero gradient on the boundary downstream of the bionic fish, and the velocity is set to zero and the pressure is set to zero gradient on the remaining boundaries; During the numerical calculation of the bionic fish's autonomous swimming, the flexible movement of the fish's fins will cause the mesh topology of the internal computational domain to change. It is necessary to apply the dynamic mesh method to deform and reconstruct the volume mesh of the internal computational domain, deform the volume mesh based on the spring smoothing method, and re-divide the volume mesh using the local mesh reconstruction method. Combination Fig.13 The mesh deformation method based on spring smoothing regards the connection between mesh nodes as springs, and the mesh in the entire computational domain as a spring system that has reached equilibrium. When the boundary is displaced, the spring system will generate internal forces, and the new positions of each mesh node are determined according to the balance of forces between the nodes of the spring system. According to Hooke's law, the spring tension between mesh nodes i and j is: Among them, K ij is the spring stiffness coefficient between grid nodes i and j, Δx j and Δx i are the displacements of mesh nodes i and j respectively.

[0017] The spring force at mesh node i is: Among them, n iis the number of grid nodes adjacent to grid node i.

[0018] K ij is defined as: Among them, K fa is the spring stiffness coefficient constant; , are the position vectors of grid nodes i and j respectively.

[0019] After the flow field is initialized, the initial force of the mesh nodes in the computational domain can be determined by the initial coordinate values. When the mesh nodes on the surface of the bionic fish are displaced, in order to ensure that the spring force of the mesh nodes remains unchanged, the new coordinates of the mesh nodes in the internal computational domain are obtained by solving the following linear equations: [ − ∑ j = 1 n i K 1 j − ∑ j = 1 n i K 2 j a ik i ≠ k a ik i ≠ k ⋱ − ∑ j = 1 n i K Nj ] [ Δ x 1 Δ x 2 ⋮ Δ x N ] = [ F 1 F 2 ⋮ F N ] in, are the elements diagonally above and below each other, ; That is, the above ; Since the linear equations are diagonally dominant, both Jacobi and Seidel iteration formats converge. The component form Jacobi iteration format is: in, Denotes the Δx corresponding to the iteration step q j ; The convergence criterion of the above formula is controlled by the convergence tolerance ε and the number of iteration steps q. The iteration stops when any condition is met.

[0020] ε is: Where rms represents the root mean square displacement of the nodes in the internal computational domain at the qth iteration.

[0021] When the bionic fish swims, the mesh nodes on the surface of the fin will move, so Jacobi scanning is used to solve the equation on the nodes of the internal computational domain. When the convergence criterion is met, the position of all nodes in the internal computational domain at time step n+1 is obtained from the position of all nodes at time step n: in, Displacement of node i in the internal computational domain calculated to meet the convergence tolerance ε or the number of iterations q.

[0022] The mesh deformation method based on spring smoothing does not change the mesh topology of the internal computational domain. When the fins perform flexible deformation movements, relying solely on mesh deformation will increase the mesh scale, leading to excessive increase in skewness, a sharp drop in mesh quality, and even the generation of negative volume meshes, which will seriously affect the calculation accuracy and even cause calculation failure.

[0023] Local grid reconstruction is one of the effective methods to solve large boundary displacement and large deformation grids. The deformed grid is judged by scale and skewness. The whole process is as follows: (1) Traverse all the deformed grids to determine whether the skewness is greater than the threshold, or the scale is less than the minimum scale or greater than the maximum scale standard. If any condition is met, mark the grid cell C to be deleted. i ,like Fig.14 The grid cells in the shaded area, where (a) is a display diagram of the grid cells to be deleted, and (b) is a display diagram of the grid cells to be deleted and re-divided; (2) Search grid cell C i Non-boundary nodes N j ( Fig.14 (a) shows four nodes), with each node N j The surrounding layer of grid cells is centered with C i Mark them together as grid cells to be deleted; (3) Removing the grid cells to be deleted will form closed cavities, and the adjacent different nodes N j The surrounding grid cells are merged into the same closed cavity, such as Fig.14 (a) The closed cavity enclosed by the dotted line; (4) Extract the boundary of each closed cavity, re-divide the grid cells using the front advancing method, and optimize the newly divided grid by combining edge exchange and grid smoothing to meet the scale and skewness standards, such as Fig.14 As shown in (b); (5) The integral conservation remapping method is used to map the conservation of the flow field parameters in the grid before reconstruction to the reconstructed grid cells.

[0024] Step 3, setting different grid scales of the bionic fish surface and the computational domain, obtaining at least three sets of numerical calculation volume grids with increasing numbers, verifying the grid convergence, and selecting a suitable numerical calculation volume grid; In order to ensure the convergence of the grid used for numerical calculation, at least three sets of numerical calculation volume grids with different increasing numbers should be divided, and the autonomous swimming of the bionic fish should be numerically calculated to judge the convergence of the numerical calculation results. If there is a convergence trend, the numerical calculation volume grid with convergent results can be selected to carry out the calculation.

[0025] Step 4: Based on the fin flexible motion characterization method, establish the fin swing angle function θ(x i , t), set the time term in the fin swing angle function to zero, set other parameter values ​​in the fin swing angle function, and initialize the flexible motion of the fin after the flow field is initialized; The method for characterizing the flexible motion of the fish fin is as follows: The flexible movement of the fish fin is considered as the wave motion driven by the fin rays, and the movement of the fin rays is the reciprocating swinging motion around the fin root. Figure 5 The state of the fish fin without flexible motion is the black plane, the state of flexible wave motion at a certain moment is the pink surface, the dotted line is the state of a fin ray swing angle of zero, and the corresponding solid line is the swing position of the fin ray at a certain moment. The variable controlling the swing motion of fin ray i can be decomposed into the x and y of the fin root in the fin coordinate system xyz. i Coordinates and time t, the fish fin coordinate system xyz is set at the leading edge of the fish fin, the positive direction of the x-axis points from the leading edge to the trailing edge of the fish fin, the positive direction of the z-axis is vertically upward, and the y-axis satisfies the right-hand rule.

[0026] By controlling the swing angle function θ(x i , t) realizes the flexible wave motion of the fins, and the fin swing angle function θ(x i , t) is described by the Fourier series: θ ( x i , t ) = a 0 + ∑ p = 1 N [ a p cos ( p ω t ) + b p sin ( p ω t ) ] Among them, p represents the number of terms in the Fourier series, a0, a p and b p is the coefficient in the expansion, ω is the frequency, and N is the total number of terms in the Fourier series.

[0027] The Fourier series can be restated in traveling wave form as follows: in, , By collecting the kinematic characteristics of the fins of live fish during swimming, the Fourier coefficient a is obtained based on nonlinear least squares curve fitting. p and b p .

[0028] The angle of the fin swing described by Fourier series is θ(x i , t), without loss of generality, for the middle fin-opposite fin swimming mode of fish, in most of the flexible motions of the fins, the first Fourier coefficient h1 usually dominates, and the phase angle Along the x-axis, from the leading edge to the trailing edge of the fin, the variation with x is almost linear, so the first Fourier mode can be used as a good approximation of the flexible motion of the fin: Among them, ξ(x) is the fin swing angle amplitude function, f is the frequency, k=2π / λ is the wave number, and λ is the wavelength.

[0029] The fin swing angle amplitude function can be divided into five modes: (1) Constant amplitude mode, in which the swing angle amplitudes of all fin rays are equal, that is, the swing angle amplitude function is a non-zero constant; (2) A linear increase mode starting from zero. In this mode, the swing angle amplitude function of the fin is also equal to zero when x is equal to zero, and increases linearly with the increase of x; (3) A linear increase mode starting from a non-zero value. In this mode, the fin angle amplitude function is a non-zero constant when x is equal to zero, and increases linearly with the increase of x; (4) A nonlinear increase mode starting from zero. In this mode, the swing angle amplitude function of the fin is also equal to zero when x is equal to zero, and increases nonlinearly with the increase of x; (5) A nonlinear increase mode starting from a non-zero value. In this mode, the swing angle amplitude function of the fin is a non-zero constant when x is equal to zero, and increases nonlinearly as x increases; Without loss of generality, five modes of fin swing angle amplitude functions can be established, corresponding to wave types 1 to 5 respectively: Among them, γ0 is the maximum fin swing angle amplitude, b is a non-zero constant; is the length of the fish fin (in the direction of the fish body length).

[0030] The fin ray swing angle amplitude function constructed by the present invention can obtain three modes of fin ray swing angle amplitude: linear increase, nonlinear increase, and zero slope, as well as the wave characteristics of fish fins under different initial swing angle amplitude conditions. By changing γ0, a parametric study is carried out on the autonomous swimming characteristics and mechanism of bionic fish.

[0031] Figure 6 The fin morphological changes of the bionic fish under five wave patterns are given, among which (a)-(e) correspond to the fin morphological changes of wave patterns 1 to 5 reflected by the fin ray swing angle amplitude function. The fin flexible motion characterization method and the fin ray swing angle amplitude function established in the present invention can accurately simulate the characteristics of the fish's intermediate fin-pair fin swimming mode and accurately construct the wave pattern characteristics of the fish fin.

[0032] Step 5, set the time step Δt, set the total solution time t1, and the iteration time step number n1 to t1 / Δt; The total solution time t1 should ensure that the autonomous swimming of the bionic fish reaches a stable cruising state at the end of the solution, that is, the periodic average value of the forward speed of the bionic fish in two adjacent swimming cycles differs by less than 0.1%; at least three different time steps Δt are set to perform numerical calculations on the autonomous swimming of the bionic fish and judge the convergence of the numerical calculation results. If the results are converged, the convergent time step Δt can be selected to carry out the calculation; after calculation verification, Δt can be taken as one two hundredth of the pectoral fin movement period (1 / 200f) to obtain a converged result. If the computing resources are relatively abundant, it can be taken as 1 / 400f, or even smaller; in one iterative time step, the number of iterations is not less than 20 or 40 times; Step 6, at the nth time step, the current solution time t = n×Δt is input into the fish fin flexible motion characterization method, the coordinates of the fish fin surface mesh nodes at the current solution time are updated, and the numerical calculation volume mesh is deformed and reconstructed based on the moving mesh method; The same method as step 4, the fin swing angle function θ(x i , t) begins to progress, the fins move flexibly under the control of the fin rays, and the volume mesh of the internal computational domain is deformed and reconstructed based on the moving mesh method in step 2; Step 7, numerically solve the CFD calculation domain to obtain the flow field information around the bionic fish, calculate the hydrodynamic force and torque on the bionic fish, and calculate the power consumption of the fish body and fins; determine the directions of the components of the pressure and viscous force on the x-axis of the grid units on the surface of the fish body and fins, integrate the components of the pressure and viscous force on the x-axis in the same direction as the swimming direction to obtain pure thrust, and integrate the components of the pressure and viscous force on the x-axis in the opposite direction to the swimming direction to obtain pure resistance; When numerically solving the CFD computational domain, the governing equations for the fluid are the three-dimensional viscous incompressible continuity and Reynolds-averaged Navier-Stokes equations: Among them, u i and u j is the time-averaged velocity term, x i and x j are the Cartesian coordinate components, ρ is the fluid density, p is the time-averaged pressure, μ is the dynamic viscosity coefficient, is the Reynolds stress term, S i is the source term; The turbulence model adopts the SST k-ω two-equation model. The SST k-ω turbulence model effectively combines the robustness and accuracy of the k-ω turbulence model in the near-wall region with the free stream independence of the k-ε turbulence model in the far field. The SST k-ω two-equation model is as follows: Among them, Γ k and Γ ω are the effective diffusion terms of k and ω respectively; G k and G ω are the generated terms of k and ω respectively; Y k and Y ω are the dissipation sources of k and ω respectively; S k and S ω are custom sources of k and ω respectively.

[0033] The standard wall function method is used to discretize the governing equations of the fluid using the finite volume method and a pressure-based transient solver. The SIMPLEC algorithm is applied to the pressure-velocity coupling, using a first-order implicit format in time and a second-order upwind format in space. The pressure and viscous force on the mesh units of the body and fins of the bionic fish are integrated to obtain the hydrodynamic force and torque on the bionic fish: M z = ∫ S { r × [ ( − pn 1 + τ n 1 ) n 1 + ( − pn 2 + τ n 2 ) n 2 ] } dS in, , represents the hydrodynamic forces in the x and y directions; represents the moment in the z direction; p is the pressure vector of the mesh unit dS on the surface of the fish body and fins, n1 is the unit vector in the x-axis direction, n2 is the unit vector in the y-axis direction, τ is the viscous stress of the mesh unit dS on the surface of the fish body and fins, and r is the position vector relative to the center of mass; The calculated hydrodynamic forces (longitudinal and lateral forces) and moments of the bionic fish are as follows: Fig. 9 As shown; Power consumption of fins The pressure p and viscosity force on the grid unit on the surface of the fish fin and the movement speed u of the grid unit f Integrating the vector product of gives: Among them, f=1, 2, 3 represent the three coordinate axes x, y, and z respectively.

[0034] The power consumption of the fish body and fins is calculated as Fig.10 As shown; Pure thrust on the fish body and fins and pure resistance : Pure thrust With pure resistance The sum corresponds to .

[0035] Step 8: At the nth time step, the linear velocity and angular velocity of the bionic fish are solved based on the calculated hydrodynamic force and torque on the bionic fish, and the displacement and posture change of the bionic fish are obtained by using the second-order Runge-Kutta integration on the linear velocity and angular velocity; The calculation methods of the linear velocity and angular velocity of the bionic fish include the cubic second-order backward difference method and the second-order Runge-Kutta integration method; The cubic second-order backward difference method is: Among them, m is the mass of the bionic fish, U X and U Y are the two linear velocities in the XOY plane, F X and F Y They are the two hydrodynamic forces in the XOY plane. The superscripts n, n-1 and n-2 are the time steps, which are used to indicate that the parameters are the parameters in the corresponding time step. z ,I z and M z are the angular velocity, moment of inertia and hydrodynamic torque in the coordinate system of the bionic fish's center of mass, respectively; The second-order Runge-Kutta integration method is: The calculated linear velocity of the bionic fish (U X and U Y ) and angular velocity ω Z like Figure 7 As shown; After the linear velocity and angular velocity of the bionic fish are calculated by any of the above two methods, the displacement and posture change of the bionic fish are obtained by using the second-order Runge-Kutta integral; the displacement (longitudinal displacement and lateral displacement) and posture angle of the bionic fish are calculated as follows: Figure 8 As shown; Step 9: updating the displacement and posture of the bionic fish in the geodetic coordinate system according to the displacement and posture changes of the bionic fish, and updating the displacement of the numerical calculation domain and the numerical calculation volume grid in the geodetic coordinate system according to the displacement of the bionic fish; The position of the bionic fish in the earth coordinate system is updated based on the calculated displacement and posture changes of the bionic fish, so that the bionic fish can swim autonomously under the propulsion of the fins.

[0036] Step 10: Determine whether n is less than n1; if yes, the time step is incremented by 1, and return to step 5 to solve the n+1th time step; if no, the solution ends; Step 11, calculate the swimming characteristic time history curve of the bionic fish under the set parameter value of the flexible motion of the fin, including the time history curves of linear velocity, angular velocity, linear acceleration, angular acceleration, displacement, and attitude angle; the hydrodynamic characteristic time history curve of the bionic fish, including the time history curves of force, torque, and power consumption; the pressure distribution on the surface of the fish body and the tail fin can be post-processed and displayed, such as Fig.11 As shown; and the vortex structure characteristics of the flow field are post-processed and displayed, as shown Fig.12 As shown; The swimming mechanism of the bionic fish is analyzed based on the obtained information such as the swimming characteristics, hydrodynamic characteristics, surface pressure distribution, flow field vortex structure, etc. By changing the parameter values ​​of the flexible motion of the fish fins, the numerical calculation results of autonomous swimming under different parameters are obtained, and the influence of the parameter values ​​on the swimming mechanism is analyzed.

[0037] The numerical calculation method constructed by the present invention can be realized by independently writing a CFD program, or the numerical calculation method proposed by the present invention can be transplanted into an open source CFD program package (such as openfoam, NNW-PHengLEI, etc.) or a user-defined function (UDF) can be written and compiled into the main program of a commercial software with a secondary development interface (such as ansys flent, star ccm, etc.), so as to realize the numerical calculation of the autonomous swimming of fish in the intermediate fin-opposite fin swimming mode.

[0038] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for characterizing the flexible motion of a fish fin, characterized in that: The flexible motion of the fish fins is characterized by the wave motion driven by the fin rays. The wave motion driven by the fin rays is as follows: The movement of the fin ray is a reciprocating swinging motion around the fin root. The variable controlling the swinging motion of fin ray i is the x coordinate of the fin root in the fish fin coordinate system xyz. i coordinates and time t; by controlling the swing angle function θ(x i , t) realizes the flexible wave motion of the fins, and the fin swing angle function θ(x i , t) is described by Fourier series; The fin swing angle function θ(x i , t) are as follows: Among them, ξ(x) is the fin swing angle amplitude function, f is the frequency, k=2π / λ is the wave number, and λ is the wavelength; The fin ray swing angle amplitude function includes the following fin ray swing angle amplitude function forms: Among them, γ0 is the maximum fin swing angle amplitude, b is a non-zero constant; , , , , They are respectively one kind of fin swing angle amplitude function; is the length of the fish fin.

2. A numerical calculation method for the autonomous swimming of a bionic fish, characterized in that: The following steps are involved: Step 1: Establish a geometric model of a bionic fish with any middle fin-opposite fin swimming mode: Step 2, establish a CFD calculation domain including the bionic fish geometric model, mesh the calculation domain, generate a numerical calculation volume mesh, record the geometric domain of the bionic fish geometric model in the calculation domain as the internal calculation domain, and apply a dynamic mesh method to the numerical calculation volume mesh of the internal calculation domain; Step 3, setting different grid scales of the bionic fish surface and the computational domain, obtaining at least three sets of numerical calculation volume grids with increasing numbers, and performing grid convergence verification to select the numerical calculation volume grid; Step 4: Based on the method for characterizing the flexible motion of a fish fin described in claim 1, establish a fin swing angle function θ(x i , t), set the time term in the fin swing angle function to zero, set other parameter values ​​in the fin swing angle function, and initialize the flexible motion of the fin after the flow field is initialized; Step 5: Set the time step Δt, set the total solution time t1, and the number of iteration time steps n1 to t1 / Δt; Step 6, at the nth time step, the current solution time t = n×Δt is input into the fish fin flexible motion characterization method, the coordinates of the fish fin surface mesh nodes at the current solution time are updated, and the numerical calculation volume mesh is deformed and reconstructed based on the moving mesh method; Step 7, numerically solve the CFD calculation domain to obtain the flow field information around the bionic fish, calculate the hydrodynamic force and torque on the bionic fish, and calculate the power consumption of the fish body and fins; determine the directions of the components of the pressure and viscous force on the x-axis of the grid units on the surface of the fish body and fins, integrate the components of the pressure and viscous force on the x-axis in the same direction as the swimming direction to obtain pure thrust, and integrate the components of the pressure and viscous force on the x-axis in the opposite direction to the swimming direction to obtain pure resistance; Step 8: At the nth time step, the linear velocity and angular velocity of the bionic fish are solved based on the calculated hydrodynamic force and torque on the bionic fish, and the displacement and posture change of the bionic fish are obtained based on the linear velocity and angular velocity; Step 9: updating the displacement and posture of the bionic fish in the geodetic coordinate system according to the displacement and posture changes of the bionic fish, and updating the displacement of the numerical calculation domain and the numerical calculation volume grid in the geodetic coordinate system according to the displacement of the bionic fish; The position of the bionic fish in the geodetic coordinate system is updated based on the calculated displacement and posture changes of the bionic fish, so that the bionic fish can swim autonomously under the propulsion of the fins. Step 10: Determine whether n is less than n1; if so, the time step is incremented by 1, and return to step 5 to solve the n+1th time step; if not, the solution ends.

3. The method for calculating the autonomous swimming of a bionic fish according to claim 2, characterized in that: The following steps are also included: Step 11, calculate the swimming characteristic time curve of the bionic fish under the set parameter values ​​of the fin flexible motion, including the time curves of linear velocity, angular velocity, linear acceleration, angular acceleration, displacement, and attitude angle; the hydrodynamic characteristic time curve of the bionic fish, including the time curves of force, torque, and power consumption.

4. The method for calculating the autonomous swimming of a bionic fish according to claim 2 or 3, characterized in that: The process of calculating the hydrodynamic force and torque on the bionic fish in step 7 includes: The standard wall function method is used to discretize the governing equations of the fluid using the finite volume method and a pressure-based transient solver. The SIMPLEC algorithm is applied to the pressure-velocity coupling, using a first-order implicit format in time and a second-order upwind format in space. The pressure and viscous force on the mesh units of the body and fins of the bionic fish are integrated to obtain the hydrodynamic force and torque on the bionic fish: in, , represents the hydrodynamic forces in the x and y directions; represents the moment in the z direction; p is the pressure vector of the mesh unit dS on the surface of the fish body and fins, n1 is the unit vector in the x-axis direction, n2 is the unit vector in the y-axis direction, τ is the viscous stress of the mesh unit dS on the surface of the fish body and fins, and r is the position vector relative to the center of mass.

5. The method for calculating the autonomous swimming of a bionic fish according to claim 4, characterized in that: In the process of calculating the power consumption of the fish body and the fins in step 7, the power consumption of the fins The pressure p and viscosity force on the grid unit on the surface of the fish fin and the movement speed u of the grid unit f Integrating the vector product of gives: Among them, f=1, 2, 3 represent the three coordinate axes x, y, and z respectively.

6. The method for calculating the autonomous swimming of a bionic fish according to claim 5, characterized in that: The pure thrust and pure drag obtained in step 7 are as follows: in, and are the pure thrust and pure resistance exerted on the fish body and fins.

Images