Numerical simulation of manta ray swarm flocking

Abstract

The application discloses a kind of manta ray submarine cluster propulsion modeling and numerical calculation method, belong to underwater bionic robot technical field.The method includes: establishing initial cluster model;By applying coordinate transformation to surface grid node, the parameterization flexible adjustment of different cluster formation is realized;For each individual, configure active flapping motion equation, and by setting motion frequency, phase, wave number and other coupling parameters, the motion coupling relationship between individuals is established;Based on the immersed boundary method, the parameterized cluster model is coupled to the flow field solver, high-fidelity numerical calculation is carried out, and the hydrodynamic performance and full flow field information of the cluster and individual are obtained;Analysis of performance data and flow field structure reveals the cluster propulsion gain mechanism.The present application first systematically solves the problem of bionic multi-body cluster modeling and efficient calculation with active deformation, fills the technical gap in this field, and provides a key theoretical basis and design tool for the configuration design and cooperative control of bionic underwater vehicle cluster.

Description

Technical Field

[0001] This invention belongs to the field of underwater biomimetic robots, specifically relating to a method for modeling and numerical calculation of manta ray-inspired submersible swarm propulsion. Background Technology

[0002] Underwater environmental monitoring, scientific research, and resource exploration are increasingly becoming more intelligent and collaborative. Biomimetic submersibles, with their efficient propulsion and excellent biocompatibility, have become ideal platforms for performing these tasks. Among various methods for obtaining the propulsion performance of biomimetic submersibles, numerical simulation has a significant advantage over theoretical estimation and experimental measurement, as it is not limited by site and equipment conditions. The method of improving overall system performance through swarm collaboration has been widely applied in fish group swimming and multi-submersible collaborative operations. Therefore, extending the research object of numerical simulation from individuals to swarms helps to reveal the propulsion gain mechanism in biological swarm swimming and provides theoretical guidance for the formation configuration and motion coordination control of biomimetic submersibles.

[0003] Currently, research and practice on underwater vehicle swarms are mainly carried out along two relatively independent technical paths: 1. Swarm Motion Cooperative Control. This approach focuses on communication networking, task allocation, trajectory planning, and formation keeping control among multiple vehicles. Its core objective is to enable the swarm to form and stably maintain a specific geometric formation along a desired path by designing distributed or centralized controllers based on a pre-defined kinematic and dynamic model. However, this type of method typically treats individuals as rigid bodies or uses simplified dynamic models, failing to consider the complex hydrodynamic interactions induced by the active motion of individuals in real flow fields.

[0004] 2. Single / Simplified Multibody Hydrodynamic Numerical Simulation. This approach focuses on using CFD methods to reveal propulsion mechanisms and performance. Numerical simulation techniques for single biomimetic propulsion devices are relatively mature. However, for multibody systems, existing research has significant limitations: First, the research objects are mostly rigid multibody systems with fixed geometry (such as tandem cylinders or fixed airfoils), focusing on vortex-induced vibrations and flow-induced disturbances under static or simple harmonic motion, which falls under passive flow response problems (e.g., the tandem double-cylinder patent cited in the background). Second, even for fish-like swarms, existing numerical studies either use significantly simplified two-dimensional models or, although involving three-dimensional realistic fish shapes (e.g., comparative documents and academic papers), are mostly limited to the study of phenomena and performance demonstrations under specific formations and spacings. These works are "scientific research findings" for specific cases and have failed to refine and form a universal, flexibly configurable, and efficient numerical calculation method for swarm modeling of actively deformable multibody systems.

[0005] Therefore, developing a modeling and numerical method that can seamlessly integrate individual active deformation and multi-body coupling relationships, and can efficiently and flexibly calculate the hydrodynamic performance of swarm propulsion, has become a key bridge connecting "swarm hydrodynamic mechanism research" and "swarm intelligent control design". It has urgent theoretical significance and engineering value for realizing the rational design and performance leap of biomimetic submersible swarms. Summary of the Invention

[0006] The technical problem to be solved: To overcome the shortcomings of existing technologies, this invention provides a method for modeling and numerically calculating the propulsion of manta ray-inspired submersible swarms. This method establishes kinematic equations describing the active deformation of individual bodies and combines motion coupling and coordinate transformation mechanisms to achieve flexible control over the motion relationships and formation configurations among individuals within the swarm, thereby completing a high-fidelity model of the manta ray-inspired submersible swarm propulsion process. Based on this model, numerical calculations are further used to obtain the hydrodynamic performance and flow field structure of the swarm system and its individual bodies under the coupling effects of different motion and formation parameters. This invention solves the problem that existing technologies cannot realize the complex motion and formation coupling relationships between actively deformable multi-body swarms, filling the gap in manta ray-inspired submersible swarm propulsion modeling and numerical calculation.

[0007] The technical solution of this invention is: a method for modeling and numerically calculating the swarm propulsion of manta ray-inspired submersibles, characterized by comprising the following steps: Step 1: Physical model initialization; establish a physical model of a single manta ray-inspired submersible and generate its surface mesh; combine the surface mesh data of the individual units according to the cluster size requirements to form the initial physical model of the cluster; Step 2: Cluster formation parameterization adjustment; apply a preset coordinate transformation to the surface mesh node coordinates corresponding to different individuals in the initial physical model of the cluster, so as to adjust the cluster into a formation with the target geometric configuration without regenerating the surface mesh; Step 3: Cluster motion coupling modeling; Configure kinematic equations describing the active flapping motion of each individual in the cluster, and establish the motion coupling relationship between different individuals in the time domain or space by setting coupling parameters in the kinematic equations; Step 4: Numerical solution of flow field-structure coupling; Based on the submerged boundary method, the fluid control equations are constructed, and the cluster geometry obtained in Step 2 is coupled with the cluster motion model established in Step 3. Through numerical iteration, the transient and average hydrodynamic parameters and flow field information of the cluster system during the propulsion process are obtained. Step 5: Results Output and Performance Analysis; Output the thrust, lift, torque and efficiency parameters calculated in Step 4, and analyze the cluster propulsion performance in conjunction with the flow field structure information. A further technical solution of the present invention is: in step 2, the target geometric configuration includes, but is not limited to, one of the following: serial arrangement, parallel arrangement, vertical arrangement, staggered arrangement of body length and span direction, staggered arrangement of body length and vertical direction, and three-dimensional staggered arrangement in space; wherein, the coordinate transformation is a translation transformation performed according to the preset body length direction spacing, span direction spacing and vertical direction spacing. A further technical solution of the present invention is: in step 3, the motion coupling relationship includes temporal coupling and spatial coupling; The temporal coupling is achieved by setting different motion frequencies or phase differences for the kinematic equations of different individuals; The spatial coupling is achieved by setting different wavenumbers or amplitudes for the kinematic equations of different individuals.

[0008] A further technical solution of the present invention is: the kinematic equation is used to describe the coupled motion of the spanwise and chordwise deformation of the pectoral fin, and its expression is: Regarding the left wing:

[0009] Regarding the right wing:

[0010] in, A For amplitude, t For time; ( x 0, y 0, z 0) represents the initial position coordinates of the manta ray model; x , y , z )for t Position coordinates at that moment; W n It is a dimensionless wavenumber; f The frequency of the pectoral fin flapping; For chordal wave control parameters; This represents the maximum bending angle. u , d To adjust the parameters of the vertical offset of the motion, To adjust the parameters of motion phase for different individuals; ML The body length is designed to resemble that of a manta ray submersible model. MW The model is a manta ray-inspired submersible with a half-length span.

[0011] A further technical solution of the present invention is: after step 3 and before step 4, it further includes: Step 3a: Motion interference detection; Based on the cluster surface grid node coordinates adjusted in step 2, detect whether the spatial positions of different individuals in the cluster will overlap during the motion under the coupled motion established in step 3; if interference is detected, the process is interrupted and an alarm is triggered; if no interference is detected, continue to step 4. A further technical solution of the present invention is: the motion interference detection in step 3a adopts the ray projection method, specifically including: for a surface mesh node of a body, emitting rays in at least three non-collinear directions in space, calculating the number of intersections between each ray and the surface mesh of another body; if the number of intersections of any ray is odd, it is determined that positional overlap has occurred.

[0012] A further technical solution of the present invention is: the specific process of motion interference detection includes: S1. Based on the Lagrange point grid coordinates and connection relationships obtained in step 1, construct the model surface triangle set T, and calculate the outer axis-aligned bounding box of the model; S2. Determine whether the point P to be detected is located within the bounding box: if not, it is determined that no interference occurs; if yes, proceed to the next step. S3. Starting from the point P to be detected, construct at least three non-collinear unit ray direction vectors. d k ; S4. For each ray, establish the ray equation and the centroid coordinate equation of the triangular mesh, and solve the linear equation system to obtain the parameter set. k , i , j ] T ; S5. Determine whether the parameter group simultaneously satisfies the following conditions:

[0013] in, k The distance parameter on the ray; i and j These are the components of the centroid coordinates; h It is a unit direction vector; , This is an auxiliary vector.

[0014] If the conditions are met, it is recorded as a valid intersection. S6. Count the total number of valid intersections between all rays and the triangle set T: if the number of intersections is odd, then the point P is located inside the object and interference occurs; if the number of intersections is even, then the point P is located outside the object and no interference occurs. S7. When interference is detected, output an image and mark the overlapping positions to assist in adjusting the cluster arrangement.

[0015] A further technical solution of the present invention is: step 4 specifically includes: Step 4.1: Construct a background Euler mesh containing a uniformly encrypted region, and ensure that the cluster remains within the uniformly encrypted region throughout the movement; Step 4.2: At each time step, determine the cluster position and velocity based on the current motion state, and construct a Navier-Stokes equation discrete system containing boundary force source terms using the submerged boundary method; Step 4.3: The discrete system is iteratively solved using the prediction-correction method to obtain the flow field velocity and pressure distribution at the next time step; Step 4.4: Calculate the forces acting on the Lagrange nodes of the cluster based on the flow field solution, and integrate to obtain the hydrodynamic forces and moments of each individual node and the cluster as a whole; Step 4.5: Determine whether the set total time step has been reached. If not, return to step 4.2 to calculate the next time step.

[0016] A further technical solution of the present invention is as follows: the process of solving the prediction-correction method is as follows: Prediction step: Solve the Navier-Stokes equations without submerged boundary force source terms, thus obtaining... t+ Density of 1 time step and prediction speed The expression is as follows:

[0017] in,, For time step t density, For time step t velocity field, For the Laplace operator.

[0018] Correction step: Combining the constructed linear equations including the contribution of the submerged boundary force source, the predicted velocity field is corrected to obtain the corrected velocity field at time step t+1; the expression of the linear equations is:

[0019] In the formula, For the density of the fluid, u For speed, p For pressure, The coefficient of dynamic viscosity, f The additional force term representing the boundary effect, I Unit tensor; The correction speed is obtained by calculating the correction step using the following formula. :

[0020] Final velocity field: The predicted velocity field is combined with the corrected velocity field to obtain the final velocity field at time step t+1. : .

[0021] A further technical solution of the present invention is: in step 5, the performance analysis specifically includes: Compare the average thrust coefficient and propulsion efficiency of the cluster as a whole and its individual members under different formation parameters; Extract and visualize the three-dimensional vortex structure in the flow field, and analyze the interaction modes between different individual wake vortices; By linking changes in hydrodynamic performance with the evolution of vortex structure in the flow field, the hydrodynamic mechanism of cluster propulsion gain or loss is revealed.

[0022] Beneficial effects The beneficial effects of this invention are as follows: This invention provides a modeling and numerical calculation method for the swarm propulsion of manta ray-inspired submersibles. This swarm propulsion modeling method constructs the motion equations of the manta ray-inspired submersibles, controls the motion coupling relationship between individual swarm members, and controls the formation coupling relationship between different members through coordinate transformation, thereby achieving modeling of the manta ray-inspired submersible swarm propulsion process. Combined with this modeling method, the numerical calculation method achieves efficient and accurate calculation of the hydrodynamic parameters and flow field information of the swarm propulsion through the submerged boundary method. The modeling method of this invention is widely applicable to various swarm operating conditions, and the numerical calculation method can complete calculations quickly and accurately, providing guidance for revealing the gain mechanism of biological swarm propulsion and the formation setting and motion parameter control of biomimetic underwater vehicles. Specific effects are analyzed as follows: 1. This invention, by constructing a unified parametric model integrating individual active deformation, multibody motion coupling, and formation geometric constraints, and combining it with a fluid-structure interaction solver based on the submerged boundary method, achieves for the first time a systematic, programmable, and high-fidelity numerical simulation of the propulsion process of a biomimetic submersible swarm requiring large-scale active deformation. This fills the technical gap between "refined flow field calculation" and "multibody cooperative relationship description" in existing technologies, providing an indispensable foundational tool for in-depth research on the mechanism of swarm propulsion.

[0023] 2. The modeling framework proposed in this invention possesses excellent parametric characteristics. Through coordinate transformation, cluster formations (such as series, parallel, staggered, and 3D arrangements) can be flexibly and quickly adjusted without requiring re-meshing for each new formation, greatly improving design iteration efficiency. Simultaneously, by introducing coupling parameters (such as phase difference, frequency, and wavenumber) into the individual kinematic equations, the complex temporal and spatial motion relationships between individuals can be accurately described and flexibly controlled. This method can easily adapt to cluster operating conditions with different numbers of individuals, different formation configurations, and different motion modes.

[0024] 3. The submerged boundary method used in this invention effectively avoids the mesh distortion problem when traditional dynamic meshes deal with multiple large deformable bodies, ensuring the stability and robustness of the calculation. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the overall calculation process of the cluster advancement modeling and numerical calculation method in this embodiment of the invention.

[0026] Figure 2 This is a schematic diagram of a manta ray-inspired submersible cluster and grid in an embodiment of the present invention.

[0027] Figure 3 This is a diagram showing the interference detection results of the numerical calculation method in this embodiment of the invention.

[0028] Figure 4 A schematic diagram of the experimental setup used to verify the numerical calculation method of this invention.

[0029] Figure 5 This is a comparison chart of simulation results and experimental results using the numerical calculation method of this invention.

[0030] Figure 6 This is a schematic diagram of the cluster vortex structure of the manta ray-inspired submersible obtained using the numerical calculation method of this invention. Detailed Implementation

[0031] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0032] The key to numerical calculations of manta ray-inspired submersible swarm propulsion lies in accurately describing the coupling relationship between the motion parameters and formation parameters of individual components. The overall hydrodynamic performance of the swarm system is not a simple linear summation of the individual performances; the vortex field generated by the motion of each component significantly alters the incoming flow conditions and surface pressure distribution of its neighbors. Existing simulation techniques for multibody systems mainly focus on rigid bodies with fixed geometry and no active deformation (such as tandem cylinders), with research emphasizing vortex shedding and fluid disturbance forces in the fixed wake under static or simple harmonic motion conditions—essentially passive flow response problems. However, for swarm systems requiring active deformation and with strong coupling between the motion and formation parameters of individual components, corresponding modeling and numerical calculation techniques are still lacking.

[0033] The existing technology, "A Method for Establishing a Mathematical Model of Unsteady Aerodynamics for the Wake Galloping of Tandem Double Cylindrical Bodies," Chinese Patent CN113204821B, provides a modeling and solution scheme for geometrically fixed, rigid multibody systems. This scheme, based on the assumptions of shape invariance and rigidity, is incompatible with the active deformation requirements involved in current manta ray swarm propulsion systems. Furthermore, the flow coupling mechanism it focuses on is fundamentally different from the complex motion coupling between multiple flexible bodies. Therefore, the existing method is difficult to apply to the propulsion problem of manta ray swarm propulsion systems that require active deformation and involve motion and formation coupling between individuals. This results in an inability to deeply analyze the hydrodynamic gain mechanism of swarm propulsion, and makes it difficult to determine the optimal swarm configuration and coordination strategy.

[0034] Therefore, the core contradiction of the existing technology is that, on the one hand, the cluster collaborative control technology lacks a high-fidelity hydrodynamic interaction model as the input and verification basis for its algorithm design; on the other hand, the existing hydrodynamic numerical simulation methods are difficult to directly support the flexible and efficient performance analysis and optimization design of biomimetic submersible clusters that need to actively deform and have strong motion and formation coupling between individuals.

[0035] To address the above problems, this invention proposes a method for modeling and numerically calculating the propulsion of a manta ray-inspired submersible swarm, comprising the following steps: Step 1: Physical model initialization; establish a physical model of a single manta ray-inspired submersible and generate its surface mesh; combine the surface mesh data of the individual units according to the cluster size requirements to form the initial physical model of the cluster; Step 2: Cluster formation parameterization adjustment; apply a preset coordinate transformation to the surface mesh node coordinates corresponding to different individuals in the initial physical model of the cluster, so as to adjust the cluster into a formation with the target geometric configuration without regenerating the surface mesh; Step 3: Cluster motion coupling modeling; Configure kinematic equations describing the active flapping motion of each individual in the cluster, and establish the motion coupling relationship between different individuals in the time domain or space by setting coupling parameters in the kinematic equations; Step 4: Numerical solution of flow field-structure coupling; Based on the submerged boundary method, the fluid control equations are constructed, and the cluster geometry obtained in Step 2 is coupled with the cluster motion model established in Step 3. Through numerical iteration, the transient and average hydrodynamic parameters and flow field information of the cluster system during the propulsion process are obtained. Step 5: Results Output and Performance Analysis; Output the thrust, lift, torque and efficiency parameters calculated in Step 4, and analyze the cluster propulsion performance in conjunction with the flow field structure information.

[0036] The above technical solution will be further analyzed below with reference to the accompanying drawings: In one embodiment, refer to Figure 1As shown, a method for modeling and numerically calculating the propulsion of a manta ray-inspired submersible swarm consists of the following core steps: First, a basic physical model is established through geometric modeling and mesh generation. Second, coupled models controlling the swarm's spatial configuration and temporal motion are established through coordinate transformation and kinematic equations. Finally, this parameterized swarm model is coupled to a flow field solver based on the submerged boundary method (IBM) for high-fidelity numerical calculations to obtain hydrodynamic performance and flow field information. Flow field analysis reveals the physical mechanisms underlying performance differences. The entire process forms a complete closed loop from "parameter input" to "mechanism output." The specific steps are as follows: Step 1: Refer to Figure 2 As shown, a simulation computational physical model is established and a triangular surface mesh is generated. Taking the manta ray model as an example, a numerical computational model of the manta ray is established using reverse engineering technology. By measuring the dimensions of the actual object, three-dimensional point data of the object is obtained. Then, three-dimensional curves are constructed using the point data, and further three-dimensional surfaces are constructed, thereby reconstructing the CAD model of the actual object. In this embodiment, the body length of the manta ray model is used as... ML Indicates that half-body width is used MW Indicates body thickness TL It means that M L =1.85m, MW =1.45m, TL =0.35m. The individual manta ray model was imported into ICEM software for triangular surface mesh generation, and Lagrange point data was output. Then, according to the requirement of the number of isomorphic clusters, the individual Lagrange point data were combined to form the initial physical model file of the cluster, which was then input into the numerical calculation method.

[0037] Step 2: Initialize simulation settings. Set the input speed according to... CFL =0.5 sets the duration of a single time step; sets the total number of iterations to be greater than 5 flapping cycles to ensure that the mechanical performance has stabilized; sets the boundary conditions for the inlet, outlet, and four far-field walls.

[0038] Step 3: Generate the flow field mesh and determine the flow field region. The fluid domain mesh is generated uniformly using a mesh generation method, storing parameters such as the coordinates of the numerical computation domain mesh nodes. Import the object's triangular mesh nodes, i.e., Lagrange node data, ensuring that the object remains within a uniformly dense mesh region initially and throughout the entire motion process. In this embodiment, the surrounding flow field range is determined based on the model size, with a total flow field size of 18.5. ML ×16.2 ML ×16.2 ML The size of the uniformly encrypted zone is 3.9. ML ×3.9 ML ×1.6 ML The mesh size of the uniformly encrypted zone is 0.0135. ML .

[0039] Step 4: Formation Adjustment. Since each individual is processed independently during triangular mesh generation, its Lagrange point coordinates are not in the expected formation position. By applying coordinate transformations to the Lagrange point coordinates of different individuals in the cluster, the formation of different clusters can be adjusted without regenerating the Lagrange point coordinates. In the input physical model file, the coordinates of different individuals in the cluster are at the same location, and the distance between them along the length direction is assumed to be... D X The span in the longitudinal direction is D Y The vertical spacing is D Z During formation adjustments, different manta ray models are distinguished by the order of Lagrange points. The position of one manta ray model is fixed, and a local coordinate system is established based on this position. The remaining models are then used as the basis for further adjustments. D X , D Y , D Z The size of the model is determined by translating it in three-dimensional space to achieve any desired formation. It's important to note that during translation, different manta ray models must not overlap to ensure computational validity. (This is in conjunction with...) Figure 2 In this embodiment, two bodies are arranged in an alternating pattern, with a spacing between individuals of [missing information]. D X =1.1, 1.2, 1.3ML, D Y =1.03, 2ML, D Z =0TL.

[0040] Step 5: Establish motion equations to control the flapping motion of the manta ray model. The manta ray model maintains a constant pectoral fin length during motion and achieves coupling of spanwise and chordal deformation. Motion coupling mainly includes two types: temporal coupling and spatial coupling. Temporal coupling mainly refers to the relative temporal relationship of periodic movements between individuals, while spatial coupling mainly refers to the coupling effect caused by differences in spatial parameters of individual movements.

[0041] Temporal coupling mainly includes frequency coupling and phase coupling. Frequency coupling can be achieved by setting different values ​​for f in the equations of motion for different individuals.

[0042] The equations of motion for different individuals within a cluster are not entirely identical; this embodiment will describe the equations of motion for the cluster. Definition For the phase difference between different individuals in a homogeneous cluster, Set phase difference The resulting equations of motion are as follows: The equation of motion for the left wing is:

[0043] The equation of motion for the right wing is:

[0044] In the formula, A For amplitude, t For time; ( x 0, y 0, z 0) represents the initial position coordinates of the manta ray model; x , y , z (Time step) t Position coordinates; W n It is a dimensionless wavenumber; f The frequency of the pectoral fin flapping; For chordal wave control parameters; This represents the maximum bending angle. u , d To adjust the parameters of the vertical offset of the motion, To adjust the parameters of the motion phase of different individuals, wavenumber coupling is used by adjusting the wavenumber in the motion equations of different individuals. W n Implementation. (Combined with appendix) Figure 2 In this embodiment, the phase difference between the front and rear manta rays is set. For 0 degrees and 180 degrees, wavenumber W n =0.4, bias parameter u= 0, d= 1.

[0045] Spatial coupling mainly includes wavenumber coupling and amplitude coupling. Wavenumber coupling is achieved by adjusting the wavenumber Wn in the equations of motion for different individuals. Amplitude coupling can be achieved by setting different values ​​for A in the equations of motion for different individuals, or by setting two bias parameters u and d to shift the axis of symmetry of motion vertically along the z-direction.

[0046] Reference Figure 3 As shown, the specific process of interferometric detection is as follows: Based on the Lagrange point grid coordinates and relationships obtained in step 1, construct the model surface set. T Obtain the bounding box of the cube to initially determine the points to be detected. P Whether it is within the bounding box. If it is within the bounding box, continue execution; otherwise, no interference occurs.

[0047] If it is inside the bounding box, then the point to be detected will be... P Starting from a point, construct at least three non-collinear unit ray direction vectors. dk .

[0048] (1) Ray equation: Defined from the target point P The equation of the emitted ray is:

[0049] in, P As the starting point of the ray, h Let k be the unit direction vector, and k be the distance parameter on the ray.

[0050] (2) Centroid coordinate equation: The triangular mesh is formed by the vertices V 0、 V 1. V 2. Definition. Any point inside a triangle can be represented as:

[0051] Where i and j are the barycentric coordinate components, and satisfy... .

[0052] (3) Solving the linear equation system: Let the ray intersect the triangle, that is... A system of linear equations can be obtained through vector transformation:

[0053] The auxiliary vector is defined as follows:

[0054] (4) Judgment criterion: For each set of solutions [ k,i,j ] T For an intersection to be considered valid, the following set of inequalities must be satisfied simultaneously:

[0055] in, A very small positive threshold is set to prevent numerical precision errors. If the number of intersections is odd, then the point... P Inside an object, if the number of intersections is even, then that point... P Outside the object. If a point appears. P In cases where objects are inside each other, the output image shows the overlapping areas to help adjust the cluster arrangement.

[0056] Step 6: Obtain the object's position based on the equations of motion and the current time step, and obtain the object's velocity by differencing its position from the previous time step; complete the search for the corresponding Eulerian node for each Lagrange node and save the data. Construct a system of linear equations; iteratively solve the system of linear equations using numerical methods, and distribute the calculation results from the Eulerian nodes to the Lagrange nodes; calculate and save the flux of all grids within the fluid domain.

[0057] In the initial search for Euler points, a carpet search strategy is adopted to store the obtained Euler points. In subsequent time steps, the search range is changed to extend by two grid scales in each of the six directions of the Euler point position stored in the previous time step.

[0058] This section explains the specific iterative process of the computational method. The effect of the boundary on the flow field is represented by a force source. f The form is reflected in the Navier-Stokes equations:

[0059] In the formula, For the density of the fluid, u For speed, p For pressure, The coefficient of dynamic viscosity, f The additional force term representing the boundary effect, I It is a unit tensor.

[0060] Based on the conventional Navier-Stokes equations:

[0061]

[0062] The prediction-correction method is used to solve the problem. The prediction step solves the conventional Navier-Stokes equations to obtain the solution. t+ Density of 1 time step and prediction speed :

[0063] The correction speed is obtained by calculating the correction step using the following formula. ,

[0064] Based on the predicted speed and correction speed get t+ The velocity field at time step 1 is :

[0065] The data interaction between Lagrange nodes and Euler nodes is as follows:

[0066]

[0067] Step 7: Calculate the hydrodynamic forces and torques of the object based on the forces at the Lagrange nodes, decompose the forces and torques in three directions to obtain the thrust, lift, and lateral forces, and calculate the input power and efficiency of the object. In this embodiment, the force applied to the object can be... x , y , z The thrust is obtained by decomposing the material in three directions. T Lift L Dimensionless thrust coefficient C T and lift coefficient C L as follows:

[0068]

[0069] in, For density, U The inlet velocity is given. Power, power factor, and efficiency are as follows:

[0070]

[0071]

[0072] in, Power For input power, For Lagrange forces, U body For the model in each boundary unit ds Deformation rate at that point, C P For power coefficient, For efficiency, C D This is to reduce scouring resistance.

[0073] Step 8: Use the local vortex structure analysis method to refine the obtained flow field data and determine the root cause of the differences in hydrodynamic performance caused by the changes in different cluster formation parameters and motion coupling parameters.

[0074] In one embodiment, the flow field mesh generation method includes the following steps: Step 1: Set the computational domain length in the x, y, and z directions. Set the coordinates of the center point of the uniformly encrypted region in the x, y, and z directions and the length of the uniformly encrypted region. The computational domain length and the length of the uniformly encrypted region can be adjusted according to the CFD calculation requirements. Step 2: Set the number of grid cells in the uniformly dense region in the x, y, and z directions, and set the grid number located at the center point of the uniformly dense region in the x, y, and z directions. The number of grid cells in the uniformly dense region can be adjusted according to the size of the object features. Step 3: Obtain the coordinates of each Euler node in the x, y, and z directions in the uniformly encrypted region; to ensure the continuity of the mesh transition between the uniformly encrypted region and the unencrypted region, set the coordinates of each Euler node in the x, y, and z directions in the unencrypted region using a function; Step 4: Add two more ghost meshes outside the outer mesh, with the length of each mesh determined by the size of its adjacent internal meshes; Step 5: Calculate the center point coordinates of each grid in the x, y, and z directions, the interpolation relationship with the two grids before and after it, and output the generated grid.

[0075] In one embodiment, adjustable parameters in the cluster include the number of clusters, cluster formation, and cluster motion parameters. Specifically, adjusting the number of clusters and formation includes the following: When using a variable single-spacing arrangement, there are: tandem arrangement (spacing only in the length direction); parallel arrangement (spacing only in the span direction); and perpendicular arrangement (spacing only in the vertical direction). When using a variable double-spacing staggered arrangement, there are: length-span staggered arrangement; length-vertical staggered arrangement; and length-vertical staggered arrangement. A three-dimensional spatial arrangement is also possible, with length-span-vertical staggered arrangement. In each arrangement, the cluster size is typically two or three bodies.

[0076] For multi-body clusters of three or more bodies, the formations include: a four-body diamond arrangement, with one manta ray-like submersible in front, two manta ray-like submersibles in the middle, and one manta ray-like submersible following the center line behind; and a six-body diamond arrangement, with one manta ray-like submersible in front, two manta ray-like submersibles in the middle, and three manta ray-like submersibles following behind.

[0077] In one embodiment, a parallel computing method is used in the iterative computation of the homogeneous cluster, and the following scheme is adopted: The programming language used for this numerical calculation method employs Open MP (OMP) parallelism, which allows threads to share the same set of memory variables and is relatively easy to operate. This addresses the problem of significantly increased computation time due to the increased number of object and flow field mesh points. Parallel computation improves computational efficiency by over 50%, while maintaining complete consistency with serial computation results.

[0078] Experiments and verification: To verify the accuracy of the numerical calculation results of this invention, experiments were conducted on manta ray monomorphs and dimorphs using PIV (pill-in-pill). A schematic diagram of the experimental platform is shown below. Figure 4 As shown, the experimental results are compared with the simulation results as follows. Figure 5 As shown in the figure. Numerical simulations reveal that region Z1 consists of the attached fin tip vortex and the initial detached fin tip vortex. 2-4 The region represents the propagation process along the flow direction after the fin tip vortex detaches, and the overall pattern is sinusoidal. As can be seen from the prototype experiment, the initial detached fin tip vortex was captured in region Z1, and Z... 2-4 The propagation path of the regional fin tip vortex matches the numerical simulation. The numerical simulation shows that after the manta ray fin tip vortex detaches, it propagates along the flow direction through Z... 1,2 In the Z2 region, the vortex structure eventually dissipated and did not continue to propagate along the flow direction. The intensity of the manta ray fin tip vortex and the vortex in the Z3 region both increased, which is consistent with the flow field images obtained from the prototype experiment. This indicates that the calculation method presented here has high reliability in simulating MPF fish swimming and fish schooling.

[0079] The hydrodynamic parameters of the four-body diamond isomorphic cluster obtained using the cluster modeling and numerical calculation methods given in this invention are as follows.

[0080] A four-body diamond isomorphic cluster vortex structure, such as Figure 6 As shown. The magnitude of the manta ray's thrust and ω y , ω z Directly related, although ω x While it doesn't directly contribute to thrust, it affects wake diffusion, thus influencing thrust. The three-dimensional vortex structure of manta rays during their swimming state is classified into three types: LEV (leading-edge vortex), TEV (tail-edge vortex), and TV (tip-edge vortex). LEV and TEV are mainly composed of... ω y Composition, TV mainly consists of ω z In terms of composition, the thrust-to-thrust (TV) effect has a positive impact, while the thrust-to-thrust (LEV) and thrust-to-thrust (TEV) effects have a negative impact. In the diamond formation, under the three phase flapping conditions, the thrust coefficient of MANTA4 is not ideal due to the complex wakes generated by the first three manta rays, and is lower than that of a single manta ray. Due to the addition of MANTA4, the overall average thrust of this four-body diamond formation also decreases. In the sparse formation with out-of-phase flapping, MANTA4's thrust coefficient increases, and its thrust performance is the best within the entire swarm. Therefore, the overall average thrust also increases in these two conditions. Because the jet effect of the leading manta ray weakens MANTA4's thrust, and due to the interference of the upstream manta ray's wake, more small vortices are generated around MANTA4's body and in its wake, thus reducing propulsion efficiency. Figure 6In the middle (b) of the four manta rays, due to the increased spacing, the wake of MANTA1 interacts with MANTA2 and MANTA3 respectively. It can be seen that the tail vortices on both sides of MANTA1 tilt towards both ends as they develop backward. Before its tail vortex develops to the position of MANTA4, the vortex energy has been exhausted. Therefore, the influence of MANTA1 on MANTA4 is very weak.

[0081] In summary, this invention presents a modeling and numerical calculation method for manta ray-inspired submersible swarm propulsion. By modeling the coupling of motion parameters and formation parameters among multiple bodies in the manta ray-inspired submersible swarm propulsion, and combining this with numerical calculation methods, the hydrodynamic parameters of the swarm system and each individual body are calculated. This yields flow field information under swarm conditions where motion and formation parameters are coupled, providing guidance for revealing the gain mechanism of biological swarm propulsion and for the formation setting and motion parameter control of biomimetic underwater vehicles.

[0082] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for modeling and numerically calculating the propulsion of a manta ray-inspired submersible swarm, characterized in that, Includes the following steps: Step 1: Physical model initialization; establish a physical model of a single manta ray-inspired submersible and generate its surface mesh; combine the surface mesh data of the individual units according to the cluster size requirements to form the initial physical model of the cluster; Step 2: Cluster formation parameterization adjustment; apply a preset coordinate transformation to the surface mesh node coordinates corresponding to different individuals in the initial physical model of the cluster, so as to adjust the cluster into a formation with the target geometric configuration without regenerating the surface mesh; Step 3: Modeling the motion coupling of the cluster; Each individual in the cluster is configured with a kinematic equation describing its active flapping motion, and a kinematic coupling relationship between different individuals in the time domain or space is established by setting coupling parameters in the kinematic equation. Step 4: Numerical solution of flow field-structure coupling; Based on the submerged boundary method, the fluid control equations are constructed, and the cluster geometry obtained in Step 2 is coupled with the cluster motion model established in Step 3. Through numerical iteration, the transient and average hydrodynamic parameters and flow field information of the cluster system during the propulsion process are obtained. Step 5: Results Output and Performance Analysis; Output the thrust, lift, torque and efficiency parameters calculated in Step 4, and analyze the cluster propulsion performance in conjunction with the flow field structure information.

2. The method for modeling and numerical calculation of manta ray-inspired submersible swarm propulsion according to claim 1, characterized in that: In step 2, the target geometric configuration includes, but is not limited to, one of the following: serial arrangement, parallel arrangement, vertical arrangement, staggered arrangement of body length and span, staggered arrangement of body length and vertical direction, and staggered arrangement of three-dimensional space; wherein, the coordinate transformation is a translation transformation performed according to the preset body length direction spacing, span direction spacing and vertical direction spacing.

3. The method for modeling and numerical calculation of manta ray-inspired submersible swarm propulsion according to claim 1, characterized in that: In step 3, the motion coupling relationship includes temporal coupling and spatial coupling; The temporal coupling is achieved by setting different motion frequencies or phase differences for the kinematic equations of different individuals; The spatial coupling is achieved by setting different wavenumbers or amplitudes for the kinematic equations of different individuals.

4. The method for modeling and numerical calculation of manta ray-inspired submersible swarm propulsion according to claim 1, characterized in that: The kinematic equations are used to describe the coupled motion of the spanwise and chordwise deformation of the pectoral fin, and their expression is as follows: Regarding the left wing: Regarding the right wing: in, A For amplitude, t For time; ( x 0, y 0, z 0) represents the initial position coordinates of the manta ray model; x , y , z (Time step) t Position coordinates; W n It is a dimensionless wavenumber; f The frequency of the pectoral fin flapping; For chordal wave control parameters; This represents the maximum bending angle. u , d To adjust the parameters of the vertical offset of the motion, To adjust the parameters of motion phase for different individuals; ML The body length is designed to resemble that of a manta ray submersible model. MW The model is a manta ray-inspired submersible with a half-length span.

5. The method for modeling and numerically calculating the swarm propulsion of manta ray-inspired submersibles according to claim 1, characterized in that: After step 3 and before step 4, it also includes: Step 3a: Motion interference detection; Based on the cluster surface grid node coordinates adjusted in step 2, detect whether the spatial positions of different individuals in the cluster will overlap during the motion under the coupled motion established in step 3; if interference is detected, the process is interrupted and an alarm is triggered; if no interference is detected, continue to step 4.

6. The method for modeling and numerically calculating the swarm propulsion of a manta ray-inspired submersible according to claim 5, characterized in that: The motion interference detection in step 3a uses the ray projection method, which specifically includes: for a surface mesh node of a body, emitting rays in at least three non-collinear directions in space, and calculating the number of intersections between each ray and the surface mesh of another body; if the number of intersections of any ray is odd, it is determined that positional overlap has occurred.

7. The method for modeling and numerical calculation of manta ray-inspired submersible swarm propulsion according to claim 5, characterized in that: The specific process for motion interference detection includes: S1. Based on the Lagrange point grid coordinates and connection relationships obtained in step 1, construct the model surface triangle set T, and calculate the outer axis-aligned bounding box of the model; S2. Determine whether the point P to be detected is located within the bounding box: if not, it is determined that no interference occurs; if yes, proceed to the next step. S3. Starting from the point P to be detected, construct at least three non-collinear unit ray direction vectors. d k ; S4. For each ray, establish the ray equation and the centroid coordinate equation of the triangular mesh, and solve the linear equation system to obtain the parameter set. k , i , j ] T ; S5. Determine whether the parameter group simultaneously satisfies the following conditions: Where k is the distance parameter on the ray; i and j are the centroid coordinate components; and h is the unit direction vector. , For auxiliary vectors; If the conditions are met, it is recorded as a valid intersection. S6. Count the total number of valid intersections between all rays and the triangle set T: if the number of intersections is odd, then the point P is located inside the object and interference occurs; if the number of intersections is even, then the point P is located outside the object and no interference occurs. S7. When interference is detected, output an image and mark the overlapping positions to assist in adjusting the cluster arrangement.

8. The method for modeling and numerical calculation of manta ray-inspired submersible swarm propulsion according to claim 1, characterized in that: Step 4 specifically includes: Step 4.1: Construct a background Euler mesh containing a uniformly encrypted region, and ensure that the cluster remains within the uniformly encrypted region throughout the movement; Step 4.2: At each time step, determine the cluster position and velocity based on the current motion state, and construct a Navier-Stokes equation discrete system containing boundary force source terms using the submerged boundary method; Step 4.3: The discrete system is iteratively solved using the prediction-correction method to obtain the flow field velocity and pressure distribution at the next time step; Step 4.4: Calculate the forces acting on the Lagrange nodes of the cluster based on the flow field solution, and integrate to obtain the hydrodynamic forces and moments of each individual node and the cluster as a whole; Step 4.5: Determine whether the set total time step has been reached. If not, return to step 4.2 to calculate the next time step.

9. The method for modeling and numerically calculating the swarm propulsion of a manta ray-inspired submersible according to claim 8, characterized in that: The process of solving the prediction-correction method is as follows: Prediction step: Solve the Navier-Stokes equations without submerged boundary force source terms, thus obtaining... t+ Density of 1 time step and prediction speed The expression is as follows: in, For time steps t density, For time steps t velocity field, For the Laplace operator; Correction step: Combining the constructed linear equations including the contribution of the submerged boundary force source, the predicted velocity field is corrected to obtain the corrected velocity field at time step t+1; the expression of the linear equations is: In the formula, For the density of the fluid, u For speed, p For pressure, The coefficient of dynamic viscosity, f The additional force term representing the boundary effect, I Unit tensor; The correction speed is obtained by calculating the correction step using the following formula. : Final velocity field: The predicted velocity field is combined with the corrected velocity field to obtain the final velocity field at time step t+1. : 。 10. The method for modeling and numerically calculating the swarm propulsion of manta ray-inspired submersibles according to claim 1, characterized in that: In step 5, the performance analysis specifically includes: Compare the average thrust coefficient and propulsion efficiency of the cluster as a whole and its individual members under different formation parameters; Extract and visualize the three-dimensional vortex structure in the flow field, and analyze the interaction modes between different individual wake vortices; By linking changes in hydrodynamic performance with the evolution of vortex structure in the flow field, the hydrodynamic mechanism of cluster propulsion gain or loss is revealed.

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