Bionic submersible vehicle heterogeneous cluster push modeling and numerical calculation method

Abstract

The present application relates to a kind of bionic submersible heterogeneous cluster propulsion modeling and numerical calculation method, belong to underwater bionic robot technical field;The method comprises: for the individual of different size and / or different propulsion mode in cluster respectively establishing physical model and surface grid;Through coordinate transformation, cluster formation is flexibly configured;For the individual of different propulsion mode, respectively set and couple its active deformation equation of motion;Motion interference detection is carried out;Based on the immersed boundary method, fluid-solid coupling effect is iteratively solved, and the hydrodynamic parameters and flow field information of cluster and individual are calculated.The present application solves the problem that existing method cannot carry out high-fidelity modeling and simulation to heterogeneous cluster with differences in size and propulsion mode, can effectively reveal the propulsion gain mechanism of heterogeneous cluster, and provides quantitative basis for the optimization design and cooperative control of bionic submersible heterogeneous formation.

Description

Technical Field

[0001] This invention belongs to the field of underwater biomimetic robot technology, specifically relating to a method for modeling and numerical calculation of heterogeneous swarm propulsion of biomimetic submersibles. Background Technology

[0002] With the continuous advancement of my country's deep-sea strategy, tasks such as marine resource exploration are increasingly evolving towards intelligence and collaboration. Biomimetic submersibles, with their efficient propulsion and excellent biocompatibility, have become ideal platforms for performing these tasks. Methods to improve overall system performance through swarm collaboration have been validated in fish groups and multi-submersible collaboration; among these, heterogeneous swarms composed of individuals of different sizes and propulsion modes are more conducive to achieving functional complementarity, thereby adapting to complex and ever-changing operational requirements. Therefore, conducting research on heterogeneous swarm propulsion modeling and numerical methods not only helps to deepen the understanding of the propulsion gain mechanism of biological heterogeneous swarms but also provides important support for the collaborative design and control of heterogeneous biomimetic submersible formations.

[0003] Currently, significant progress has been made in the research of hydrodynamic performance of biomimetic thrusters and swarms. For example, numerical calculation methods or experimental parameter acquisition schemes for the hydrodynamic performance of a single type of biomimetic thruster (such as wave fins) have been developed, the core of which lies in the accurate evaluation of the performance of isomorphic individuals. Furthermore, computational fluid dynamics (CFD) methods have been used to explore the swarm swimming mechanism of the same species (such as manta rays) in fixed formations such as tandem, triangular, or staggered formations, revealing the fluid dynamic laws by which isomorphic individuals achieve energy savings or thrust enhancement through wake vortex interactions.

[0004] However, when addressing the propulsion modeling and simulation requirements of heterogeneous biomimetic submersible swarms, existing research suffers from a disconnect between "upper-level system control" and "lower-level hydrodynamics," and is limited to the analysis of "homogeneous systems." It lacks a unified methodological framework that can couple and quantify the performance of swarms composed of individuals with different sizes and propulsion modes, starting from their physical essence.

[0005] Therefore, in the field of biomimetic underwater vehicle engineering, there is an urgent need to break through the existing paradigm of isomorphic swarm research and develop a method capable of high-fidelity propulsion process modeling and efficient numerical calculation for biomimetic submersible swarms with heterogeneous dimensions and patterns. This method aims to fill the technological gap from "heterogeneous individual description" to "simulation of swarm coupling effects," providing indispensable theoretical tools and quantitative basis for revealing the cooperative propulsion gain mechanism of heterogeneous swarms and guiding the optimal design and cooperative motion control of hybrid biomimetic submersible formations. 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 a heterogeneous swarm of biomimetic submersibles. This method establishes motion equations for individuals with different configurations within the heterogeneous swarm, thereby controlling the motion coupling relationships between individuals. Furthermore, it utilizes coordinate transformation to flexibly adjust formation parameters, thus achieving high-fidelity modeling of the heterogeneous swarm propulsion process. Based on this model, numerical calculations can obtain the hydrodynamic performance and complex flow field structure of the swarm system and its constituent individuals under the coupling effects of various motion and formation parameters. This solves the problems of existing technologies in simulating heterogeneous swarms of biomimetic submersibles, which struggle to effectively control the active deformation motion of individuals and accurately characterize the complex motion and formation coupling relationships between individuals of different sizes and propulsion modes.

[0007] The technical solution of this invention is: a method for modeling and numerically calculating heterogeneous swarm propulsion of biomimetic submersibles, comprising the following steps: Step 1. Modeling and Meshing: Establish an independent simulation physical model for each individual in the heterogeneous cluster, and perform surface meshing on the physical model of each individual to obtain the Lagrange point data of each individual; the heterogeneous cluster refers to a cluster composed of at least two biomimetic submersible individuals that differ in geometric size and / or propulsion mode; Step 2. Initialization and computational domain construction: Set the initial and boundary conditions for the simulation, construct the computational fluid dynamics (CFD) simulation computational domain and perform mesh generation, and import the Lagrange point data into the computational domain; Step 3. Cluster configuration: Adjust the spatial relationships of different individuals in the heterogeneous cluster to configure a predetermined cluster formation; Step 4. Heterogeneous motion coupling: Set active deformation motion equations corresponding to their propulsion modes for different individuals in the heterogeneous cluster, and establish motion coupling relationships between individuals based on the motion equations; Step 5. Interference detection: Based on the configuration in Steps 3 and 4, detect whether spatial interference occurs between different individuals in the heterogeneous cluster during their movement; Step 6. Fluid-structure interaction solution: If there is no interference, then based on the submerged boundary method, combined with the above motion equations, Lagrange point data and flow field grid data, the interaction between the flow field and each body in the heterogeneous cluster at each time step is iteratively solved to obtain the flow field information; Step 7. Calculation of hydrodynamic parameters: Based on the solution results of Step 6, calculate the hydrodynamic parameters of the heterogeneous cluster system and each individual body; Step 8. Iteration and Output: Repeat steps 3 to 7 until the preset solution time step is reached, and output the final hydrodynamic performance data and flow field information.

[0008] A further technical solution of the present invention is that the heterogeneous cluster includes at least one of the following types: Type A: Size heterogeneous clusters where individuals have similar geometric shapes but different sizes in proportion; Type B: Heterogeneous clusters of individuals employing at least two different propulsion patterns: the body / tail fin BCF propulsion pattern and the central fin / opposite fin MPF ​​propulsion pattern; among which, When the heterogeneous cluster is a propulsion mode heterogeneous cluster and includes MPF propulsion mode individuals, the motion equation of the MPF propulsion mode individuals describes the coupled motion of their pectoral fin spanwise deformation and chordal traveling wave propagation. When the heterogeneous cluster is a propulsion mode heterogeneous cluster and contains BCF propulsion mode individuals, the motion equation of the BCF propulsion mode individuals describes the traveling wave propagation motion along their body axis.

[0009] A further technical solution of the present invention is: In step 4, the motion equations for heterogeneous clusters of different sizes of type A are: The equation of motion for the left wing is:

[0010] The equation of motion for the right wing is:

[0011] 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 n Let n be the length of the manta ray-inspired submersible model. MW n Let n be the semi-span of the nth manta ray-inspired submersible model, where n represents the nth individual in the heterogeneous cluster of type A.

[0012] A further technical solution of the present invention is: In step 4, the motion equations for heterogeneous clusters of propulsion modes with different combinations of type B modes are: In type B, the equation of motion for a BCF individual is:

[0013] Where x is the axial position; y is the displacement at time step t; the quadratic term is the maximum amplitude equation; and f is the oscillation frequency. Wavelength; In type B, the equation of motion for an MPF ​​individual is: The equation of motion for the left wing is:

[0014] The equation of motion for the right wing is:

[0015] 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 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 m Let m be the length of the manta ray-inspired submersible model. MW m Let m be the half span of the m-th manta ray-inspired submersible model, where m represents the m-th manta ray-inspired vehicle individual in the heterogeneous cluster of type B.

[0016] A further technical solution of the present invention is: in step 3, the spatial positional relationship is adjusted by applying a uniform coordinate transformation to the Lagrange point data. The coordinate transformation includes translation, rotation and their combinations, to configure different spatial formations including serial, parallel, perpendicular or three-dimensional interlacing.

[0017] A further technical solution of the present invention is: in step 5, the interference detection adopts the ray projection method, specifically including: for a surface grid 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 grid of another body; if the number of intersections of any ray is odd, it is determined that positional overlap has occurred.

[0018] A further technical solution of the present invention is: the specific process of the interference detection includes: Step 5.1. Based on the Lagrange point mesh coordinates and connection relationships obtained in Step 1, construct the triangle set T on the model surface and calculate the outer axis-aligned bounding box of the model; Step 5.2. 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. Step 5.3. Starting from the point P to be detected, construct at least three non-collinear unit ray direction vectors. d k ; Step 5.4. For each ray, establish the ray equation and the barycenter coordinate equation of the triangular mesh, and solve the linear equation system to obtain the parameter set. k , i , j ] T ; Step 5.5. Determine whether the parameter set simultaneously satisfies the following conditions:

[0019] Where k is the distance parameter on the ray; i and j are the centroid coordinate components; and h is the unit direction vector. , This is an auxiliary vector.

[0020] If the conditions are met, it is recorded as a valid intersection. Step 5.6. Count the total number of valid intersections between all rays and the triangular mesh set T: if the number of intersections is odd, then the point P is determined to be inside the object and interference has occurred; if the number of intersections is even, then the point P is determined to be outside the object and no interference has occurred. Step 5.7. When interference is detected, output an image and mark the overlapping positions to assist in adjusting the cluster arrangement.

[0021] A further technical solution of the present invention is: step 6 specifically includes: Step 6.1: Construct a background Euler mesh containing a uniformly encrypted region, and ensure that the heterogeneous cluster remains within the uniformly encrypted region throughout the movement; Step 6.2: 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 6.3: Use the prediction-correction method to iteratively solve the discrete system to obtain the flow field velocity and pressure distribution at the next time step; Step 6.4: 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 6.5: Determine whether the set total time step has been reached. If not, return to step 6.2 to calculate the next time step.

[0022] 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:

[0023] in, for t Density of time steps for t The velocity field at the time step For the Laplace operator.

[0024] 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:

[0025] 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. :

[0026] 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. : .

[0027] A further technical solution of the present invention is: the hydrodynamic parameters calculated in step 7 include thrust coefficient, lift coefficient, input power and propulsion efficiency; the flow field information output in step 8 includes vorticity field and pressure field data, which are used to analyze the wake vortex interaction mechanism of the heterogeneous cluster.

[0028] Beneficial effects The beneficial effects of this invention are as follows: This invention provides a modeling and numerical calculation method for heterogeneous swarm propulsion of biomimetic submersibles. This heterogeneous swarm propulsion modeling method constructs motion equations for biomimetic submersible models of different sizes and propulsion modes, achieving a realistic and accurate description of the swimming process of individual individuals in the heterogeneous swarm, and realizing the coupling relationship between formation parameters and motion parameters of different individuals. Combining this modeling method with numerical calculation methods, the hydrodynamic parameters and flow field information of the heterogeneous swarm propulsion are calculated using 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 proposes for the first time a complete and unified modeling and computational framework specifically designed to solve the propulsion simulation challenges of biomimetic submersible swarms composed of individuals of different sizes and propulsion modes (MPF / BCF). By establishing and coupling unique motion equations for each heterogeneous individual and introducing coordinate transformations to flexibly adjust formation, this invention successfully achieves a high-fidelity mathematical description of the dual complex characteristics of "individual heterogeneity" and "swarm coupling." This effectively fills the gap in existing technologies that can only handle isomorphic systems or rigid multibody systems, advancing biomimetic swarm simulation research from "isomorphic analysis" to a new stage of "heterogeneous design and optimization."

[0029] 2. By combining the aforementioned heterogeneous modeling method with high-precision submerged boundary method (IBM) numerical calculations, this invention can accurately solve the unsteady flow field of heterogeneous clusters during motion. This method can not only output macroscopic hydrodynamic parameters such as thrust, power, and propulsion efficiency for the entire cluster system and each individual component, but also reveal the microscopic evolution of vortex structures and energy transfer paths (as shown in the attached figure, where the tuna tail vortex is absorbed and amplified by the manta ray). This allows researchers to quantitatively analyze the impact of multi-parameter coupling, such as size differences, motion phase differences, and formation spacing, on cluster performance, fundamentally elucidating the hydrodynamic mechanisms underlying the synergistic gains or losses generated by heterogeneous clusters.

[0030] 3. This invention significantly improves the practicality and efficiency of the method by integrating key technologies such as coordinate transformation and formation adjustment, efficient interferometric detection algorithm (ray projection method), and parallel computing (OpenMP). Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the overall computational process of the heterogeneous cluster advancement modeling and numerical simulation method of the present invention.

[0032] Figure 2 This is a schematic diagram of the tuna model and manta ray model used in this invention.

[0033] Figure 3 This is a schematic diagram of the manta ray-tuna heterogeneous cluster of the present invention.

[0034] Figure 4 This is a diagram showing the interference detection results of the numerical calculation method of the present invention.

[0035] Figure 5 This is a schematic diagram of the hydrodynamic coefficients of the vertical heterogeneous cluster obtained using the numerical calculation method of this invention.

[0036] Figure 6 This is a schematic diagram of a vertical heterogeneous clustered vortex structure obtained using the numerical calculation method of this invention.

[0037] Figure 7 This is a schematic diagram of the hydrodynamic coefficients of the staggered heterogeneous cluster obtained using the numerical calculation method of this invention.

[0038] Figure 8 This is a schematic diagram of the staggered heterogeneous clustered vortex structure obtained using the numerical calculation method of this invention. Detailed Implementation

[0039] 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.

[0040] The key to numerical calculations of heterogeneous swarm propulsion for biomimetic submersibles lies in accurately describing the coupling relationships of motion and formation parameters among individuals of different sizes and propulsion modes. Here, "heterogeneous" mainly includes two scenarios: first, submersibles with similar geometric configurations but different sizes (e.g., manta ray-inspired submersibles of different sizes); and second, submersibles with different geometric configurations and motion modes (e.g., a mixed formation of manta ray-inspired and tuna-inspired submersibles). In heterogeneous swarm systems, the hydrodynamic performance of each submersible is significantly influenced by the size, configuration, and motion of other individuals within the formation, making their interaction mechanisms far more complex than those of homogeneous swarms. Existing simulation studies for multibody systems mainly focus on rigid multibody systems with fixed geometry and no active deformation (e.g., tandem cylinders), emphasizing the analysis of vortex shedding and fluid disturbance forces in the wake under static or simple harmonic motion conditions—essentially passive flow response problems. However, for heterogeneous swarms composed of individuals of different sizes and propulsion modes, with strong coupling between their motion and formation, corresponding modeling and numerical calculation methods remain lacking.

[0041] The existing technology, "A Method for Establishing a Mathematical Model of Unsteady Aerodynamics for the Wake Gallop of Tandem Double Cylindrical Bodies," Chinese patent CN113204821B, provides a modeling and solution scheme for rigid multibody systems with fixed geometric shapes. However, this scheme, based on the assumptions of invariant shape and rigid body motion, is fundamentally incompatible with the core requirement of active, flexible deformation of individuals in heterogeneous clusters. Furthermore, the coupling mechanisms it studies, such as wake interference, are fundamentally different from the complex dynamic couplings arising from differences in size, configuration, and motion modes among multiple flexible bodies in heterogeneous clusters. Therefore, the existing method is difficult to apply to the propulsion simulation of heterogeneous biomimetic flexible clusters with similar shapes but different sizes, or with different shapes and motion modes. This results in the inability to effectively analyze the hydrodynamic interaction mechanism under heterogeneous clusters, making it difficult to quantify performance gains and determine the optimal heterogeneous combination and cooperative strategy.

[0042] To address the problems existing in current technologies, this invention proposes a method for modeling and numerically calculating the heterogeneous swarm propulsion of biomimetic submersibles, characterized by the following steps: Step 1. Modeling and Meshing: Establish an independent simulation physical model for each individual in the heterogeneous cluster, and perform surface meshing on the physical model of each individual to obtain the Lagrange point data of each individual; the heterogeneous cluster refers to a cluster composed of at least two biomimetic submersible individuals that differ in geometric size and / or propulsion mode; Step 2. Initialization and computational domain construction: Set the initial and boundary conditions for the simulation, construct the computational fluid dynamics (CFD) simulation computational domain and perform mesh generation, and import the Lagrange point data into the computational domain; Step 3. Cluster configuration: Adjust the spatial relationships of different individuals in the heterogeneous cluster to configure a predetermined cluster formation; Step 4. Heterogeneous motion coupling: Set active deformation motion equations corresponding to their propulsion modes for different individuals in the heterogeneous cluster, and establish motion coupling relationships between individuals based on the motion equations; Step 5. Interference detection: Based on the configuration in Steps 3 and 4, detect whether spatial interference occurs between different individuals in the heterogeneous cluster during their movement; Step 6. Fluid-structure interaction solution: If there is no interference, then based on the submerged boundary method, combined with the above motion equations, Lagrange point data and flow field grid data, the interaction between the flow field and each body in the heterogeneous cluster at each time step is iteratively solved to obtain the flow field information; Step 7. Calculation of hydrodynamic parameters: Based on the solution results of Step 6, calculate the hydrodynamic parameters of the heterogeneous cluster system and each individual body; Step 8. Iteration and Output: Repeat steps 3 to 7 until the preset solution time step is reached, and output the final hydrodynamic performance data and flow field information.

[0043] Specifically, the heterogeneous clusters include at least one of the following types: Type A: Size heterogeneous clusters where individuals have similar geometric shapes but different sizes in proportion; Type B: Heterogeneous clusters of propulsion patterns in which individuals employ at least two different combinations of the body / tail fin BCF propulsion pattern and the central fin / opposite fin MPF ​​propulsion pattern.

[0044] The above technical solution will be further explained below with reference to the accompanying drawings: In one embodiment, this invention provides a method for modeling and numerically calculating the heterogeneous swarm propulsion of a biomimetic submersible, aiming to achieve high-fidelity simulation of the propulsion process of a swarm composed of individuals with different propulsion modes of type B. The overall calculation process is as follows: Figure 1 As shown. The following example, a heterogeneous cluster consisting of one manta ray-inspired submersible (MPF mode) and one tuna-inspired submersible (BCF mode), will be used to illustrate the implementation of the method of the present invention in detail. Those skilled in the art will understand that the number of clusters, their specific types (such as heterogeneous clusters of the same size), and their formation can be adjusted according to actual needs, all of which are within the scope of protection of the present invention.

[0045] Step 1: Refer to Figure 2 As shown, a simulation physical model is established and a triangular surface mesh is generated. This embodiment uses... Figure 2 (a) Manta Ray Model and Figure 2 (b) The tuna model serves as the physical model for a heterogeneous cluster. The manta ray model is built using reverse engineering techniques. 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 built to reconstruct the CAD model of the actual object. The tuna model is controlled by shape equations. It consists of a smooth body and a high aspect ratio tail fin, ignoring all small fins. The contour curve equations of the body and tail fin on the cross-section at the central axis are as follows:

[0046] Equation of the caudal fin anterior / posterior margin contour curve:

[0047] In this embodiment, the body length of the manta ray model is represented by M. L It indicates that the half-length extension is used MW It means that among them ML =1.85m, MW =1.45m, body length of the tuna model TL = ML=1.85m.

[0048] The individual manta ray model and the individual tuna model were imported into ICEM software to generate triangular surface meshes and output Lagrange point data. Then, according to the requirements of the number of heterogeneous clusters, the Lagrange point data of the two models were combined to form the initial physical model of the heterogeneous cluster, which was then input into the numerical calculation method.

[0049] Step 2: Initialize simulation settings. Set the inlet velocity and the duration of a single time step based on CFL=0.5; set the total number of iterations to be greater than 5 flapping cycles to ensure that the mechanical properties have stabilized; set the boundary conditions for the inlet, outlet, and four far-field walls.

[0050] Step 3: Generate the flow field mesh, determine the flow field region, and simulate the flow field environment around the physical model. The fluid domain mesh is generated uniformly using a mesh generation method. In this embodiment, the surrounding flow field range is determined based on the model size, and the total flow field size is 16. ML ×16 ML ×16 ML The uniformly encrypted region size is 2.72. ML ×1.95 ML ×1.62 ML The mesh size of the uniformly encrypted zone is 0.01. ML .

[0051] Import the heterogeneous cluster Lagrange point data generated in step 1 and the flow field mesh data generated in step 3 into the CFD solver. During initialization, ensure that the Lagrange points of all individuals are located within the uniformly refined region of the flow field mesh.

[0052] Step 4: Formation Adjustment. In the input physics model file, the coordinates of different individuals in the cluster are at the same position, and the spacing along the length direction is set to... D X The span in the longitudinal direction is D Y The vertical spacing is D Z During formation adjustments, different physical models are distinguished by the order of Lagrange points. The position of one physical model is fixed, and a local coordinate system is established based on this position, according to the remaining models. D X , D Y , D Z Size, translate the model in 3D space to achieve any desired formation; combined with attachments Figure 2 Set up a two-body series arrangement with an individual spacing of [missing information]. D x =1.1 ML -1.8 ML, D Y =0, D Z =0.

[0053] Step 5: Define the equations of motion and set up coupling for heterogeneous individuals.

[0054] This step is the core of the "heterogeneous" and "coupled" modeling. It involves defining and setting the active deformation motion equations for individuals with two different propulsion modes within the cluster.

[0055] 1. Establish motion equations to control the flapping motion of the manta ray model.

[0056] Existing research indicates that manta ray locomotion can be viewed as a coupling of spanwise and chordwise deformation. Based on the actual locomotion patterns of biological organisms with constant body length, the equations of motion for considering the coupling of spanwise and chordwise deformation without considering asymmetric locomotion are as follows: The equation of motion for the left wing is: The equation of motion for the right wing is: 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. In heterogeneous clusters, since the motion equations of different individuals are not exactly the same, in this embodiment, the motion frequency of the manta ray model is set. f =1Hz, wavenumber W n =0.4, amplitude 0.35 ML , m=1.

[0057] 2. Establish motion equations to control the flapping motion of the tuna model.

[0058] Tuna geometric shape along x The axis exhibits symmetry and is perpendicular to x The cross-section of the axis is elliptical, and the ratio of its major to minor axis is 1.5:1. (Tuna model length) TLBoth are 1.85m. The movement of a tuna can be viewed as a wave propagating backward along its body with different amplitudes, and the equation of motion is as follows:

[0059] In the formula, x In axial position; y For time step t The displacement; f It is the fluctuation frequency; in this invention, 4Hz is selected, corresponding to... St It is 1.44; The wavelength is 1.25 times the body length in this invention.

[0060] Reference Figure 3 As shown, this embodiment distinguishes different individuals in a heterogeneous cluster using Lagrange points and sets the spacing between individuals. D x =0.1 ML -0.8 ML The tuna flapping frequency was set to 1 Hz, and the amplitude to 0.1. TL .

[0061] Step 5: Refer to Figure 4 The diagram illustrates the specific process for motion interference detection.

[0062] Based on the Lagrange point mesh 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.

[0063] 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. d k .

[0064] (1) Ray equation: Defined from the target point P The equation of the emitted ray is:

[0065] in, P As the starting point of the ray, h It is a unit direction vector. k This represents the distance parameter along the ray.

[0066] (2) Centroid coordinate equation: The triangular facet is formed by the vertex V 0、 V 1. V 2. Definition. Any point within a surface can be represented as:

[0067] in, i and j Let be the barycentric coordinate components, and satisfy . .

[0068] (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:

[0069] The auxiliary vector is defined as:

[0070] (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:

[0071] 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.

[0072] 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.

[0073] Step 7: Explain the specific iterative process of the calculation method. The effect of the boundary on the flow field is expressed through a force source. f The form is reflected in the Navier-Stokes equations:

[0074] 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.

[0075] Based on the conventional Navier-Stokes equations:

[0076]

[0077] 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 :

[0078] The correction speed is obtained by calculating the correction step using the following formula. ,

[0079] Based on the predicted speed and correction speed get t+ The velocity field at time step 1 is :

[0080] The data interaction between Lagrange nodes and Euler nodes is as follows:

[0081]

[0082] Step 8: 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:

[0083]

[0084] in, For density, U For the inlet speed, BL The characteristic length of the object. Power, power coefficient, and efficiency are as follows:

[0085]

[0086]

[0087] in, PowerFor 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.

[0088] Step 9: 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.

[0089] Implementation effect analysis: The numerical calculation method of this invention is used to obtain St= The hydrodynamic coefficient of the vertical heterogeneous cluster at 1.44 is as follows: Figure 4 As shown, its vortex structure is as follows Figure 5 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 The composition shows that the TV (transient vortex) has a positive effect on thrust, while the LEV (leakage vortex) and TEV (transient vortex) have a negative effect. The tuna's upper surface appendages exhibit higher spanwise vortex intensity and a longer adsorption distance, resulting in higher initial energy upon vortex detachment. The tail peduncle region also has higher vortex energy and a smaller distribution spacing. In the manta ray, the spanwise vortices of the upper surface and tail disappear without vortex detachment, while the lower surface appendage vortex intensity decreases, leading to lower initial negative vortex energy at tail detachment. This energy dissipates more rapidly during propagation and exhibits an upward deflection trend. The manta ray's vertical vortex effectively prevents the tuna's own vertical vortex from spreading spanwise, making the vortex energy more concentrated and less prone to dissipation. Furthermore, its influx into the tuna wake significantly increases the number and energy of vortices. The manta ray's chordal vortex street envelops the tuna wake, hindering its lateral diffusion, but the number of vortices in the inner two rows of vortices decreases.

[0090] The numerical calculation method of this invention is used to obtain St= The hydrodynamic coefficient of the staggered heterogeneous cluster at 1.44 is as follows: Figure 6 As shown, its vortex structure is as follows Figure 7As shown. The attachment distance and detachment location of the spanwise vortices on the upper and lower surfaces of tuna are similar to those of single-species swimming. The vortex intensity is increased at the tail stalk, and the vortex street in the wake field does not show deflection, propagating along the flow direction for a longer time and over a greater distance. The vortex intensity of the attachments on the upper and lower surfaces of manta rays is increased, leading to an increase in the initial detachment vortex intensity. (Manta ray) R The vertical vortex in region 2 is absorbed by the tuna, reducing the energy of the manta ray's tail rim vortex and enhancing the energy of the tuna's tail vortex, making the vortex less prone to dissipation during propagation along the flow direction. The low-energy chordal vortex of the manta ray merges into the chordal vortex of the tuna, bringing an energy boost without disrupting the original structure of the tuna vortex.

[0091] 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 heterogeneous swarm propulsion of biomimetic submersibles, characterized in that, Includes the following steps: Step 1. Modeling and Meshing: Establish an independent simulation physical model for each individual in the heterogeneous cluster, and perform surface meshing on the physical model of each individual to obtain the Lagrange point data of each individual; the heterogeneous cluster refers to a cluster composed of at least two biomimetic submersible individuals that differ in geometric size and / or propulsion mode; Step 2. Initialization and computational domain construction: Set the initial and boundary conditions for the simulation, construct the computational fluid dynamics (CFD) simulation computational domain and perform mesh generation, and import the Lagrange point data into the computational domain; Step 3. Cluster configuration: Adjust the spatial relationships of different individuals in the heterogeneous cluster to configure a predetermined cluster formation; Step 4. Heterogeneous motion coupling: Set active deformation motion equations corresponding to their propulsion modes for different individuals in the heterogeneous cluster, and establish motion coupling relationships between individuals based on the motion equations; Step 5. Interference detection: Based on the configuration in Steps 3 and 4, detect whether spatial interference occurs between different individuals in the heterogeneous cluster during their movement; Step 6. Fluid-structure interaction solution: If there is no interference, then based on the submerged boundary method, combined with the above motion equations, Lagrange point data and flow field grid data, the interaction between the flow field and each body in the heterogeneous cluster at each time step is iteratively solved to obtain the flow field information; Step 7. Calculation of hydrodynamic parameters: Based on the solution results of Step 6, calculate the hydrodynamic parameters of the heterogeneous cluster system and each individual body; Step 8. Iteration and Output: Repeat steps 3 to 7 until the preset solution time step is reached, and output the final hydrodynamic performance data and flow field information.

2. The method for modeling and numerical calculation of heterogeneous swarm propulsion of a biomimetic submersible according to claim 1, characterized in that: The heterogeneous cluster includes at least one of the following types: Type A: Size heterogeneous clusters where individuals have similar geometric shapes but different sizes in proportion; Type B: Heterogeneous clusters of individuals employing at least two different propulsion patterns: the body / tail fin BCF propulsion pattern and the central fin / opposite fin MPF ​​propulsion pattern; among which, When the heterogeneous cluster is a propulsion mode heterogeneous cluster and includes MPF propulsion mode individuals, the motion equation of the MPF propulsion mode individuals describes the coupled motion of their pectoral fin spanwise deformation and chordal traveling wave propagation. When the heterogeneous cluster is a propulsion mode heterogeneous cluster and contains BCF propulsion mode individuals, the motion equation of the BCF propulsion mode individuals describes the traveling wave propagation motion along their body axis.

3. The method for modeling and numerical calculation of heterogeneous swarm propulsion of a biomimetic submersible according to claim 2, characterized in that: In step 4, the equations of motion for heterogeneous clusters of different sizes of type A are as follows: The equation of motion for the left wing is: The equation of motion for the right wing is: 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 n Let n be the length of the manta ray-inspired submersible model. MW n Let n be the semi-span of the nth manta ray-inspired submersible model, where n represents the nth individual in the heterogeneous cluster of type A.

4. The method for modeling and numerical calculation of heterogeneous swarm propulsion of a biomimetic submersible according to claim 2, characterized in that: In step 4, the motion equations for the heterogeneous clusters of propulsion modes with different combinations of type B modes are as follows: In type B, the equation of motion for a BCF individual is: Where x is the axial position; y is the displacement at time step t; the quadratic term is the maximum amplitude equation; and f is the oscillation frequency. Wavelength; In type B, the equation of motion for an MPF ​​individual is: The equation of motion for the left wing is: The equation of motion for the right wing is: 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 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 m Let m be the length of the manta ray-inspired submersible model. MW m Let m be the half span of the m-th manta ray-inspired submersible model, where m represents the m-th manta ray-inspired vehicle individual in the heterogeneous cluster of type B.

5. The method for modeling and numerical calculation of heterogeneous swarm propulsion of a biomimetic submersible according to claim 1, characterized in that: In step 3, the spatial positional relationship is adjusted by applying a uniform coordinate transformation to the Lagrange point data. The coordinate transformation includes translation, rotation and their combinations, to configure different spatial formations, including serial, parallel, perpendicular or three-dimensional interlacing.

6. The method for modeling and numerical calculation of heterogeneous swarm propulsion of a biomimetic submersible according to claim 1, characterized in that: In step 5, the interference detection 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 heterogeneous swarm propulsion of a biomimetic submersible according to claim 6, characterized in that: The specific process of the interference detection includes: Step 5.

1. Based on the Lagrange point mesh coordinates and connection relationships obtained in Step 1, construct the triangle set T on the model surface and calculate the outer axis-aligned bounding box of the model; Step 5.

2. 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. Step 5.

3. Starting from the point P to be detected, construct at least three non-collinear unit ray direction vectors. d k ; Step 5.

4. For each ray, establish the ray equation and the barycenter coordinate equation of the triangular mesh, and solve the linear equation system to obtain the parameter set [k, i , j ] T ; Step 5.

5. Determine whether the parameter set simultaneously satisfies the following conditions: 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; , For auxiliary vectors; If the conditions are met, it is recorded as a valid intersection. Step 5.

6. Count the total number of valid intersections between all rays and the triangular mesh set T: if the number of intersections is odd, then the point P is determined to be inside the object and interference has occurred; if the number of intersections is even, then the point P is determined to be outside the object and no interference has occurred. Step 5.

7. 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 heterogeneous swarm propulsion of a biomimetic submersible according to claim 1, characterized in that: Step 6 specifically includes: Step 6.1: Construct a background Euler mesh containing a uniformly encrypted region, and ensure that the heterogeneous cluster remains within the uniformly encrypted region throughout the movement; Step 6.2: 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 6.3: Use the prediction-correction method to iteratively solve the discrete system to obtain the flow field velocity and pressure distribution at the next time step; Step 6.4: 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 6.5: Determine whether the set total time step has been reached. If not, return to step 6.2 to calculate the next time step.

9. The method for modeling and numerical calculation of heterogeneous swarm propulsion of a biomimetic 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 t Density of time steps for t The velocity field at the time step 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. A method for modeling and numerically calculating heterogeneous swarm propulsion of a biomimetic submersible according to any one of claims 1-9, characterized in that: The hydrodynamic parameters calculated in step 7 include thrust coefficient, lift coefficient, input power, and propulsion efficiency; the flow field information output in step 8 includes vorticity field and pressure field data, which are used to analyze the wake vortex interaction mechanism of the heterogeneous cluster.

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