A numerical calculation method for bionic flexible large deformation propulsion

Abstract

The application discloses a numerical calculation method for bionic flexible large deformation propulsion, and belongs to the technical field of underwater bionic robots. The method is aimed at the problem that the calculation efficiency and the calculation accuracy are difficult to be considered in the numerical simulation of the bionic flexible large deformation propulsion, and realizes the following core steps: based on the immersed boundary method, the flexible boundary effect is embedded in the Navier-Stokes equation of the fixed Euler grid in the form of a force source term, so that the grid distortion is fundamentally avoided; an efficient Euler point search improvement strategy is proposed, the local search range is determined according to the motion dynamics, the global search is replaced, and the calculation time is significantly reduced; a flow field grid generation method containing a self-definable uniform encryption area is adopted, so that the overall grid quantity is optimized while the calculation accuracy of the boundary area is ensured. The application realizes efficient and high-precision numerical simulation of the bionic flexible large deformation propulsion process, and provides a reliable tool for the design optimization and swimming mechanism research of the bionic submersible.

Description

Technical Field

[0001] This invention belongs to the field of underwater biomimetic robot technology, specifically relating to a numerical calculation method for biomimetic flexible large deformation propulsion. Background Technology

[0002] With the continuous advancement of my country's deep-sea strategy, the demand for underwater environmental monitoring, scientific research, and resource development is increasing. Biomimetic submersibles, with their advantages of high-efficiency propulsion and high biocompatibility, have shown promising application prospects in these marine missions. In the design and optimization of biomimetic submersibles, numerical simulation, compared to theoretical estimation and experimental measurement, has significant advantages such as accurately reproducing complex biological movements, being unrestricted by location, and not violating bioethics, making it a core method for obtaining their hydrodynamic performance.

[0003] To mimic the swimming motion of marine organisms, biomimetic submersibles typically use pectoral / tail fin flapping for underwater propulsion, during which the fins undergo large-scale flexible deformation. This poses a significant challenge to numerical simulation methods based on computational fluid dynamics, with the core challenge being how to accurately capture the complex interaction between the moving boundary and the flow field within a stable and efficient numerical framework.

[0004] Currently, the main technical approaches in the industry all have significant limitations: 1. Traditional Approach Based on Dynamic Mesh Deformation and Reconstruction: This method employs a body-fitted mesh that conforms to the moving boundary, adapting to the boundary motion through mesh deformation or local reconstruction. However, facing the continuous, large-scale, three-dimensional flexible deformation unique to biomimetic propulsion, this method is prone to severe mesh distortion and negative volume, leading to computational instability or even divergence. Although introducing mesh quality monitoring and reconstruction mechanisms can partially alleviate these issues, each step of monitoring and reconstruction incurs significant additional computational overhead, making the simulation process cumbersome, time-consuming, and computationally inefficient—an inherent and insurmountable drawback.

[0005] 2. Improvement Path Based on Overlapping Meshes and Advanced Interpolation Techniques: To improve mesh quality, techniques such as overlapping mesh coupled radial basis function (RBF) interpolation have emerged. This method divides the computational domain into foreground and background meshes and achieves data transfer through interpolation. While maintaining mesh quality to some extent, it introduces a series of complex operations such as mesh overlap region identification, interpolation weight calculation, and data exchange, resulting in high algorithm complexity and considerable computational cost from the interpolation process itself. For complex motions of 3D flexible bodies, its overall computational efficiency remains unsatisfactory.

[0006] Therefore, developing a numerical calculation method that can both inherit the inherent stability of the immersion boundary method and revolutionarily improve the efficiency of its core computational components has become a technical challenge that urgently needs to be overcome in this field. Summary of the Invention

[0007] The technical problem to be solved: To overcome the shortcomings of existing technologies, this invention provides a numerical calculation method for biomimetic flexible large deformation propulsion. This method combines boundary setting methods, flow field mesh generation methods, improved Eulerian point search methods, and numerical solution methods to achieve efficient and high-precision numerical solutions for hydrodynamic parameters and flow field structures during biomimetic flexible large deformation propulsion. It solves the problems of traditional CFD methods in simulating biomimetic flexible body large deformation propulsion, which are prone to severe mesh distortion and computational divergence due to the use of body-fitted meshes, and the large number of meshes required and low computational efficiency of existing submerged boundary methods.

[0008] The technical solution of this invention is: a numerical calculation method for biomimetic flexible large deformation propulsion, comprising the following steps: Step 1: Establish a simulation computational physics model of the biomimetic flexible body to be calculated, and divide its surface mesh to generate Lagrange node data; Step 2: Initialize simulation settings, including setting the inlet velocity, number of CFLs, time step, total number of iterations, and boundary conditions; Step 3: Construct and divide the flow field mesh of the CFD simulation calculation domain, generate a three-dimensional Eulerian mesh containing uniformly encrypted and unencrypted regions, and store the coordinate parameters of all Eulerian mesh nodes; import the Lagrange node data generated in Step 1, and ensure that the biomimetic flexible body is always located within the uniformly encrypted region throughout the entire motion process; Step 4: Set the equation of motion, calculate the position of each Lagrange node at the current time step according to the set equation of motion, and calculate the velocity of each Lagrange node by the difference with the position at the previous time step; Step 5: Using the improved Euler point search method, based on the motion displacement of the Lagrange nodes, dynamically determine and search for the neighboring Euler nodes corresponding to each Lagrange node at the current time step, establish the mapping relationship between Lagrange nodes and Euler nodes, and construct a linear equation system describing the fluid-structure interaction based on the submerged boundary method. Step 6: Iteratively solve the linear equation system constructed in Step 5 using numerical solution methods to obtain the corrected velocity field on the Eulerian grid, and allocate the corrected velocity field information to the corresponding Lagrange nodes according to the mapping relationship established in Step 5. Step 7: Based on the force information at the Lagrange nodes, calculate the hydrodynamic force, torque, input power, and propulsion efficiency of the biomimetic flexible body in three directions; Step 8: Determine whether the preset total number of iterations has been reached. If not, advance the time step and return to Step 4 to continue execution; if the preset total number of iterations has been reached, end the calculation. A further technical solution of the present invention is: in step 2, the boundary conditions are achieved by setting two layers of ghost grids outside the two-layer flow field boundary, and the coordinate parameters of the ghost grids have been generated and stored in the flow field grid division process in step 3. A further technical solution of the present invention is: in step 3, the division of the flow field mesh specifically includes the following sub-steps: Step 3.1: Set the total length of the computational domain in the x, y, and z directions, and the center coordinates and length of the uniformly encrypted region in the three directions; Step 3.2: Set the number of grid nodes in the uniformly encrypted zone in three directions; Step 3.3: Calculate the coordinates of each Euler node in the uniformly encrypted zone; use a smoothing function to calculate the coordinates of each Euler node in the unencrypted zone to ensure a continuous mesh transition from the encrypted zone to the unencrypted zone; Step 3.4: Generate the two ghost mesh layers outside the outermost mesh of the computational domain; Step 3.5: Calculate the center point coordinates and interpolation coefficients of all grid cells in three directions, and output the complete grid information.

[0009] A further technical solution of the present invention is: the equation of motion in step 4 is a displacement function describing the wave-like propulsion of the biomimetic flexible body, and its form is:

[0010] in, x This refers to the axial position. y For time step t displacement, f For fluctuation frequency, λ λ is the wavelength.

[0011] A further technical solution of the present invention is: in step 5, the improved Euler point search method is specifically as follows: In the first time step, traverse all Euler grid nodes in the uniformly encrypted region, search for and store the neighboring Euler nodes for each Lagrange node; At each subsequent time step t , t ≥2, firstly, calculate the displacement of each Lagrange node from time step n-1 to time step n based on the equation of motion. d lag Then, using the Eulerian node position corresponding to the Lagrange node stored at the previous time step as the center, extend along each of the six coordinate axes in three-dimensional space by one node corresponding to the Eulerian node. d lag The search distance is proportional to the search distance, forming a dynamic local search region; finally, the search for neighboring Euler nodes at the current time step is performed only within this local search region.

[0012] A further technical solution of the present invention is: the search distance is 2. d lag That is, the local search region is centered on the historical Euler node position and has a side length of 4. d lag The cubic region.

[0013] A further technical solution of the present invention is: in step 6, the numerical solution method adopts the prediction-correction method, specifically including: Prediction step: Solve the Navier-Stokes equations without submerged boundary force source terms to obtain the predicted velocity field at time step t+1; 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:

[0014] 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.

[0015] Final velocity field: The predicted velocity field is combined with the corrected velocity field to obtain the time step. t+ The final velocity field of 1. A further technical solution of the present invention is as follows: the process of solving the problem using the prediction-correction method is as follows: The prediction step solves 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:

[0016] in, For time step t density, For time step t velocity field, For the Laplace operator.

[0017] The correction speed is obtained by calculating the correction step using the following formula. :

[0018] Based on the predicted speed and correction speed get t+ The velocity field at time step 1 is : .

[0019] A further technical solution of the present invention is as follows: In step 7, when calculating hydrodynamic forces and torques, the forces on the Lagrange nodes are first vector-summed to obtain the total fluid force and torque on the submerged boundary. Then, according to Newton's third law, the signs are reversed to obtain the thrust, lift, lateral force, roll moment, pitch moment, and yaw moment on the biomimetic flexible body.

[0020] A numerical calculation system for biomimetic flexible large deformation propulsion includes: The model preprocessing module is configured to build a simulation computational physics model of the biomimetic flexible body to be calculated, divide its surface mesh, and generate and output Lagrange node data. The initial setup module is configured to set the simulation's inlet velocity, number of CFLs, total number of time steps, and boundary condition parameters; The flow field mesh construction module is configured to construct a three-dimensional flow field Eulerian mesh based on computational domain parameters. The Eulerian mesh includes a uniformly encrypted region surrounding the biomimetic flexible body and an outer unencrypted region, and outputs the coordinates of all Eulerian mesh nodes. The module is also configured to receive the Lagrange node data and ensure that the motion trajectory of the biomimetic flexible body always lies within the uniformly encrypted region. The motion calculation module is configured to calculate the position and velocity of each Lagrange node at each time step according to the preset biomimetic flexible body motion equation. The interaction relationship construction module is configured to execute the improved Euler point search algorithm. Based on the motion displacement of the Lagrange node, it dynamically determines and searches for the neighboring Euler node corresponding to each Lagrange node at the current time step, thereby establishing the mapping relationship between the Lagrange node and the Euler node, and constructs a linear equation system describing the fluid-structure interaction based on the principle of the submerged boundary method. The flow field solution module is configured to iteratively solve the linear equations using a numerical solver to obtain the corrected velocity field on the Eulerian grid, and to transfer the velocity field information to the Lagrange nodes using the mapping relationship. The performance analysis module is configured to calculate the hydrodynamic, torque, power, and propulsion efficiency parameters of the biomimetic flexible body based on the force information on the Lagrange nodes. The iterative control module is configured to control the progression of simulation time steps and terminate the calculation process when the preset total number of time steps is reached.

[0021] Beneficial effects The beneficial effects of this invention are as follows: This invention proposes a numerical calculation method for biomimetic flexible large deformation propulsion, achieving efficient and accurate calculation of the flexible large deformation propulsion process of a biomimetic submersible, effectively reducing simulation calculation costs. Specifically, the flow field mesh generation method, by setting uniformly refined regions according to the object size, significantly reduces the overall mesh count while ensuring calculation accuracy, thereby shortening the simulation time. Furthermore, this method further accelerates and accurately completes the Euler point search step through an improved search strategy, significantly improving computational efficiency while ensuring the accuracy of the calculation results. Specific effects are analyzed as follows: 1. The original "dynamic local search based on physical displacement" algorithm in this invention rapidly narrows the search range from the entire domain to a minimal neighborhood determined by the motion law. As shown in the specific implementation, this improved strategy reduces the search time per unit time step from 21.3 seconds to 7.2 seconds, improving efficiency by up to 65%. This fundamentally overcomes the efficiency bottleneck restricting the engineering application of the submerged boundary method, making it possible to efficiently simulate complex, long-term flexible large deformation motions, significantly reducing computational resources and time costs.

[0022] 2. This invention inherits the core advantage of the submerged boundary method using a fixed background Eulerian mesh, completely avoiding the fatal problems of mesh distortion and negative volume caused by large deformation of flexible bodies in traditional dynamic mesh methods, thus ensuring computational stability from the source. Simultaneously, by setting a uniformly refined region surrounding the moving body, sufficient spatial resolution is provided in key flow field regions, ensuring accurate capture of fluid-structure interaction forces and eddy dynamics details. Verification results (e.g.) Figure 4 , 5 (and comparison table), the calculation results of this invention have an error of less than 2% compared with existing technologies and experimental data, and the vortex structure evolution is highly consistent, proving its high precision characteristics under high stability.

[0023] 3. The numerical calculation method of this invention integrates boundary setting, flow field mesh generation, Euler point search improvement and numerical solution, which can effectively obtain key flow field information such as hydrodynamic parameters, pressure field distribution and vortex structure evolution in the biomimetic flexible large deformation propulsion process. It provides a reliable basis for revealing the mechanism of biological swimming and optimizing the design of biomimetic submersibles, and has positive significance for promoting the independent and controllable development of industrial software in my country.

[0024] In summary, this invention successfully resolves the long-standing contradiction of "difficulty in balancing accuracy, stability, and efficiency" in the numerical simulation of biomimetic flexible large deformation propulsion. Through a series of innovative designs, it achieves a leap in computational efficiency and a solid guarantee of simulation reliability, which has significant theoretical implications and broad engineering application value. Attached Figure Description

[0025] Figure 1This is a schematic diagram of the numerical calculation method in an embodiment of the present invention.

[0026] Figure 2 This is a schematic diagram of the tuna model used in an embodiment of the present invention.

[0027] Figure 3 This is a flowchart illustrating the process of solving hydrodynamic parameters in an embodiment of the present invention.

[0028] Figure 4 This is a comparative diagram of the tuna flow force coefficients obtained using 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 diagram of the vortex structure of the tuna swimming flow field 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] In nature, fish primarily propel themselves by flapping their pectoral / tail fins. Biomimetic submersibles are designed to mimic the shape and kinematics of fish, and their fins often undergo significant deformation during movement. In CFD calculations, using conventional body-fitted meshes can lead to severe mesh distortion due to these complex deformations. Reconstructing the mesh at each step would drastically reduce computational efficiency. The submerged boundary method effectively solves this problem by transforming the effects of large deformations of a flexible body on the flow field into dynamic force terms on a fixed Eulerian mesh.

[0033] The existing technology, "A Numerical Simulation Calculation Method for Pectoral Fin Propulsion of a Manta Ray-Inspired Underwater Vehicle," Chinese patent CN118194444 A, provides a numerical calculation method for a biomimetic underwater vehicle. This method uses mesh deformation and reconstruction techniques to ensure the stability of the numerical simulation. However, it requires monitoring the mesh quality at each step, and if a low-quality mesh appears, the mesh needs to be reconstructed. This process is cumbersome and computationally inefficient. Currently, the simulation of the hydrodynamic performance of biomimetic submersibles with flexible and large deformations typically uses mesh deformation and reconstruction methods to ensure computational convergence. This process is complex and time-consuming.

[0034] An emerging approach based on the submerged boundary method is being developed in existing technologies. This method processes the flow field using a fixed background Eulerian mesh, embedding the influence of the moving boundary into the governing equations as force source terms. This fundamentally avoids mesh distortion caused by boundary motion, making it theoretically well-suited for simulating flexible large deformations. Related academic research (such as "Formation effects on the group propulsion performance of manta rays") has confirmed its stability and potential in biomimetic motion simulations. However, the traditional submerged boundary method faces a key performance bottleneck in practical implementation: at each time step, it requires dense neighbor search and interpolation operations (i.e., "Eulerian point search") for a large number of Lagrange points on the boundary within their surrounding Eulerian mesh. To maintain versatility, this search is typically performed over a large area or even globally, resulting in extremely high computational costs. This severely offsets its advantage of mesh stability, making it difficult to meet the overall computational efficiency requirements of practical engineering applications.

[0035] In summary, existing technologies face a dilemma when dealing with numerical simulations of biomimetic flexible large deformation propulsion: either adopting a mesh deformation / reconstruction path, which faces the dual pressure of stability and efficiency; or adopting the submerged boundary method path, which achieves stability but is hampered by the huge computational overhead brought about by Eulerian-Lagrange point interactions.

[0036] Based on the above problems, this invention proposes a numerical calculation method for biomimetic flexible large deformation propulsion, comprising the following steps: Step 1: Establish a simulation computational physics model of the biomimetic flexible body to be calculated, and divide its surface mesh to generate Lagrange node data; Step 2: Initialize simulation settings, including setting the inlet velocity, number of CFLs, time step, total number of iterations, and boundary conditions; Step 3: Construct and divide the flow field mesh of the CFD simulation calculation domain, generate a three-dimensional Eulerian mesh containing uniformly encrypted and unencrypted regions, and store the coordinate parameters of all Eulerian mesh nodes; import the Lagrange node data generated in Step 1, and ensure that the biomimetic flexible body is always located within the uniformly encrypted region throughout the entire motion process; Step 4: Calculate the position of each Lagrange node at the current time step according to the set motion equation, and calculate the motion velocity of each Lagrange node by the difference with the position at the previous time step; Step 5: Using the improved Euler point search method, based on the motion displacement of the Lagrange nodes, dynamically determine and search for the neighboring Euler nodes corresponding to each Lagrange node at the current time step, establish the mapping relationship between Lagrange nodes and Euler nodes, and construct a linear equation system describing the fluid-structure interaction based on the submerged boundary method. Step 6: Iteratively solve the linear equation system constructed in Step 5 using numerical solution methods to obtain the corrected velocity field on the Eulerian grid, and allocate the corrected velocity field information to the corresponding Lagrange nodes according to the mapping relationship established in Step 5. Step 7: Based on the force information at the Lagrange nodes, calculate the hydrodynamic force, torque, input power, and propulsion efficiency of the biomimetic flexible body in three directions; Step 8: Determine whether the preset total number of iterations has been reached. If not, advance the time step and return to Step 4 to continue execution; if the preset total number of iterations has been reached, end the calculation. This invention also proposes a numerical calculation system for biomimetic flexible large deformation propulsion, comprising: The model preprocessing module is configured to build a simulation computational physics model of the biomimetic flexible body to be calculated, divide its surface mesh, and generate and output Lagrange node data. The initial setup module is configured to set the simulation's inlet velocity, number of CFLs, total number of time steps, and boundary condition parameters; The flow field mesh construction module is configured to construct a three-dimensional flow field Eulerian mesh based on computational domain parameters. The Eulerian mesh includes a uniformly encrypted region surrounding the biomimetic flexible body and an outer unencrypted region, and outputs the coordinates of all Eulerian mesh nodes. The module is also configured to receive the Lagrange node data and ensure that the motion trajectory of the biomimetic flexible body always lies within the uniformly encrypted region. The motion calculation module is configured to calculate the position and velocity of each Lagrange node at each time step according to the preset biomimetic flexible body motion equation. The interaction relationship construction module is configured to execute the improved Euler point search algorithm. Based on the motion displacement of the Lagrange node, it dynamically determines and searches for the neighboring Euler node corresponding to each Lagrange node at the current time step, thereby establishing the mapping relationship between the Lagrange node and the Euler node, and constructs a linear equation system describing the fluid-structure interaction based on the principle of the submerged boundary method. The flow field solution module is configured to iteratively solve the linear equations using a numerical solver to obtain the corrected velocity field on the Eulerian grid, and to transfer the velocity field information to the Lagrange nodes using the mapping relationship. The performance analysis module is configured to calculate the hydrodynamic, torque, power, and propulsion efficiency parameters of the biomimetic flexible body based on the force information on the Lagrange nodes. The iterative control module is configured to control the progression of simulation time steps and terminate the calculation process when the preset total number of time steps is reached.

[0037] The above technical solution will be further analyzed below with reference to the accompanying drawings: In one embodiment, propulsion performance is calculated using a simulated tuna model as an example.

[0038] Reference Figure 1 As shown in the figure, the entire process of numerical calculation of hydrodynamic performance of a tuna-inspired flexible propulsion model in this embodiment includes the following steps: Step 1: Combining Figure 2 As shown, a simulation physical model is established using a tuna as the object, and a triangular surface mesh is generated. The tuna model 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:

[0039] Equation of the caudal fin anterior / posterior margin contour curve:

[0040] A model is constructed based on the equations. The model is then imported into ICEM to generate a triangular surface mesh and output Lagrange point data, which is used as the initial values ​​for the physical model and input into the numerical calculation method.

[0041] Step 2: Initialize simulation settings. Set the basic parameters required for the simulation: Inlet speed: Set according to the incoming flow conditions.

[0042] Short duration: Set the duration of a single time step based on CFL=0.5; Total number of iterations: set to 9000 steps to ensure that the mechanical properties have stabilized; Boundary conditions: The computational domain is defined as one inlet, one outlet, and four far-field walls. The inlet and outlet are determined based on the preset inlet velocity magnitude and direction, and the location of the walls.

[0043] Step 3: Construct the fluid computational domain required for CFD simulation and generate the background Eulerian mesh. The specific process of the flow field mesh generation method is as follows: 1. Determine the computational domain: Define the flow field region and simulate the flow environment surrounding the physical model. The fluid domain mesh is generated uniformly using a mesh generation method. In this application, the surrounding flow field range is determined based on the model size, with a total flow field size of 7.5. TL ×2 TL ×2 TL ,in, TL This is the total length of the replica tuna model; 2. Set a uniform density zone: Define a density zone of size 1.5 around the model's motion trajectory. TL ×1 TL ×1 TL The rectangular region is designated as a uniformly refined area. The mesh size in this region is refined to 0.01. TL This ensures sufficient resolution for complex flow structures and vortex shedding near the model. The location of the center point of the densification zone is determined based on the initial position of the model.

[0044] 3. Mesh Generation: Using the flow field mesh generation method of this invention, a structured Eulerian mesh is generated programmatically for the entire computational domain. The mesh smoothly transitions from the encrypted region to the unencrypted region. Simultaneously, two layers of ghost mesh are automatically generated at the outermost layer of the computational domain for boundary condition handling. Finally, the coordinates, element volume, surface information, and other parameters of all Eulerian mesh nodes are stored.

[0045] 4. Import Lagrange nodes: Import the Lagrange node data generated in step 1 into the system and verify that all Lagrange nodes are initially located within the above-mentioned uniform encryption zone.

[0046] Step 4: Write the equations for flexible large deformation motion. From the shape curve equations, it can be seen that the origin of the tuna's coordinate system is chosen at a distance of 30% of the body length from the head. The tuna's geometric shape follows... x The axis exhibits symmetry and is perpendicular to x The cross-section of the axis is elliptical, and the ratio of its major axis to its minor axis is 1.5:1. The equation of motion for the tuna is as follows:

[0047] In the formula, x In axial position; y For time step t The displacement; the quadratic term is the equation for the maximum amplitude; f The fluctuation frequency is selected in this invention as 0.5Hz, 1Hz, 2Hz, and 4Hz, corresponding to... St The values ​​are 0.18, 0.36, 0.72, and 1.44. The wavelength is 1.25 times the body length in this invention.

[0048] Step 5: Improved computational efficiency of the Euler point search method.

[0049] The core of this step lies in efficiently establishing the interaction relationship between the moving boundary (Lagrange point) and the fixed flow field grid (Euler point).

[0050] First search: at the initial time step ( t =0), traverse all Euler grid nodes in the uniformly encrypted region, find the neighboring Euler nodes for each Lagrange node, establish the initial mapping relationship and store it.

[0051] Improved dynamic search: in subsequent time steps ( t =n, n≥2), first calculate the displacement of each Lagrange node from the previous step to the current step according to the equation of motion. dlag .

[0052] Then, instead of performing a global traversal, the process is centered on the position of the Eulerian node corresponding to the Lagrange node in the previous time step, and extends in six directions (±) in three-dimensional space. x , ± y , ± z Each extension 2 d lag The distance forms a dynamic, local cube search box that is much smaller than the global encryption zone.

[0053] The search for nearest neighbors at the current time step is performed only within the Euler nodes of this local search box. This significantly reduces the number of nodes searched.

[0054] Based on actual calculation results, for the same tuna model, the improved Euler point search method can significantly shorten the calculation time and improve the calculation efficiency.

[0055]

[0056] Step 6: Combining Figure 3 This section explains the iterative process of the numerical solution method. The effect of the boundary on the flow field is transmitted through a force source. f The form is reflected in the Navier-Stokes equations:

[0057] 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.

[0058] Based on the conventional Navier-Stokes equations, for three-dimensional problems, the Navier-Stokes equations can be discretized using the finite volume method:

[0059]

[0060]

[0061] In the formula, n , , , These represent the control volume number, control volume volume, control volume surface number, and the first control volume within the control volume, respectively. j Area of ​​each interface; , , These represent the conserved variables, flux, and velocity vector, respectively. Flux is calculated by solving the continuous Boltzmann equations.

[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] In the formula, d For grid spacing, D It has a continuous kernel distribution.

[0068] The velocity at the Lagrange point can be obtained based on the boundary conditions. And satisfy:

[0069] The correction velocity at the Lagrange point is obtained by solving the above system of linear equations. And obtain the Euler point correction speed.

[0070] According to Newton's second law and the principle of action and reaction, the forces acting on the submerged boundary can be calculated by summing the forces acting at the Lagrange point. The forces acting on the fluid at the Lagrange point are:

[0071] The net force exerted on the fluid by the immersion boundary is:

[0072] According to the principle of action and reaction, the forces acting on the immersion boundary are:

[0073] Step 7: The force applied to the object can be... x , y , z Decompose the force in three directions to obtain the thrust. T Lift L Dimensionless thrust coefficient C T Lift coefficient C L Yaw moment coefficient C QZ Pitch moment coefficient C QY Rolling moment coefficient C QX as follows:

[0074]

[0075]

[0076]

[0077]

[0078] in, For density, U For the inlet speed, TL The characteristic length of the object, Q Z , Q Y , Q X To bypass z axis, y shaft and x The shaft's yaw moment, pitch moment, and roll moment. Power, power factor, and efficiency are as follows:

[0079]

[0080]

[0081] in, P 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.

[0082] Verification domain effect: The current force coefficient of tuna at different Strouhal numbers is as follows Figure 4 As shown, the calculation results of this invention are compared with those of tuna in the prior art under different conditions. St The downstream force coefficients are compared in the table below, and the errors are all within 2%, indicating that the numerical calculation method of the present invention can accurately calculate the propulsion force under flexible large deformation.

[0083]

[0084] To verify the accuracy of the numerical calculation results of this invention in obtaining the vortex structure, a flapping PIV experiment was conducted. The experimental results were 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 flexible large deformation propulsion.

[0085] The vortex structure diagram of the tuna swimming flow field is shown below. Figure 6 As shown, the vortex structure is identified using the Q criterion. A distinct vortex structure detaches from the tuna's surface at the rear, forming a jet region. The fluid in this jet region moves backward, meaning the tuna exerts a backward force on the surrounding fluid, which in turn exerts a forward force on the tuna, propelling it forward.

[0086] along with St As the number of vortex pairs increases, the initial single-row vortex rings in the wake field evolve into double-row vortex pairs. This is accompanied by an increase in the number of vortex pairs and a decrease in the spacing between them. During propagation along the flow direction, the vortex structure exhibits better integrity, longer dissipation time, less interference between vortex pairs, and fewer broken vortices in the flow field. St At 1.44, the vortex intensity increases and the spacing between vortex pairs continues to decrease, which brings a significant increase in thrust. However, the excessively fast tail beat frequency causes the tail fin to swing back rapidly, breaking the newly formed tail vortex and destroying the structural integrity of the vortex pair. The flow field is filled with broken vortices, and the propagation distance of the vortex pair along the flow direction is shortened, the dissipation velocity is accelerated, and the interference between vortex pairs is intensified.

[0087] In summary, the numerical calculation method proposed in this invention for biomimetic flexible large deformation propulsion, compared with conventional body-fitted mesh numerical calculation methods, utilizes a flexibly adjustable flow field mesh generation method and an efficient numerical solution method. This is further demonstrated by the application of different methods to tuna. St Downstream hydrodynamic verification enables rapid and accurate solutions to the stress conditions and flow field structure of objects under large deformations.

[0088] 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 numerical calculation method for biomimetic flexible large deformation propulsion, characterized in that, Includes the following steps: Step 1: Establish a simulation computational physics model of the biomimetic flexible body to be calculated, and divide its surface mesh to generate Lagrange node data; Step 2: Initialize simulation settings, including setting the inlet velocity, number of CFLs, time step, total number of iterations, and boundary conditions; Step 3: Construct and divide the flow field mesh of the CFD simulation calculation domain, generate a three-dimensional Eulerian mesh containing uniformly encrypted and unencrypted regions, and store the coordinate parameters of all Eulerian mesh nodes; import the Lagrange node data generated in Step 1, and ensure that the biomimetic flexible body is always located within the uniformly encrypted region throughout the entire motion process; Step 4: Set the equation of motion, calculate the position of each Lagrange node at the current time step according to the set equation of motion, and calculate the velocity of each Lagrange node by the difference with the position at the previous time step; Step 5: Using the improved Euler point search method, based on the motion displacement of the Lagrange nodes, dynamically determine and search for the neighboring Euler nodes corresponding to each Lagrange node at the current time step, establish the mapping relationship between Lagrange nodes and Euler nodes, and construct a linear equation system describing the fluid-structure interaction based on the submerged boundary method. Step 6: Iteratively solve the linear equation system constructed in Step 5 using numerical solution methods to obtain the corrected velocity field on the Eulerian grid, and allocate the corrected velocity field information to the corresponding Lagrange nodes according to the mapping relationship established in Step 5. Step 7: Based on the force information at the Lagrange nodes, calculate the hydrodynamic force, torque, input power, and propulsion efficiency of the biomimetic flexible body in three directions; Step 8: Determine whether the preset total number of iterations has been reached. If not, advance the time step and return to Step 4 to continue execution; if the preset total number of iterations has been reached, end the calculation.

2. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 1, characterized in that: In step 2, the boundary conditions are achieved by setting two layers of ghost meshes outside the flow field boundary. The coordinate parameters of the ghost meshes have been generated and stored during the flow field meshing process in step 3.

3. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 2, characterized in that: Step 3, the division of the flow field mesh, specifically includes the following sub-steps: Step 3.1: Set the total length of the computational domain in the x, y, and z directions, and the center coordinates and length of the uniformly encrypted region in the three directions; Step 3.2: Set the number of grid nodes in the uniformly encrypted zone in three directions; Step 3.3: Calculate the coordinates of each Euler node in the uniformly encrypted zone; use a smoothing function to calculate the coordinates of each Euler node in the unencrypted zone to ensure a continuous mesh transition from the encrypted zone to the unencrypted zone; Step 3.4: Generate the two ghost mesh layers outside the outermost mesh of the computational domain; Step 3.5: Calculate the center point coordinates and interpolation coefficients of all grid cells in three directions, and output the complete grid information.

4. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 1, characterized in that: In step 4, the equation of motion is a displacement function describing the wave-like propulsion of the biomimetic flexible body, and its form is: in, x This refers to the axial position. y For time step t displacement, f For fluctuation frequency, λ λ is the wavelength.

5. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 1, characterized in that: In step 5, the improved Euler point search method is specifically as follows: In the first time step, traverse all Euler grid nodes in the uniformly encrypted region, search for and store the neighboring Euler nodes for each Lagrange node; At each subsequent time step t , t ≥2, firstly, calculate the displacement of each Lagrange node from time step n-1 to time step n based on the equation of motion. d lag Then, using the Eulerian node position corresponding to the Lagrange node stored at the previous time step as the center, extend along each of the six coordinate axes in three-dimensional space by one node corresponding to the Eulerian node. d lag The search distance is proportional to the search distance, forming a dynamic local search region; finally, the search for neighboring Euler nodes at the current time step is performed only within this local search region.

6. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 5, characterized in that: The search distance is 2. d lag That is, the local search region is centered on the historical Euler node position and has a side length of 4. d lag The cubic region.

7. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 1, characterized in that: In step 6, the numerical solution method adopts the prediction-correction method, specifically including: Prediction step: Solve the Navier-Stokes equations without submerged boundary force source terms to obtain the time step. t +1 predicted velocity field; Correction step: The predicted velocity field is corrected by combining the constructed linear equations that include the contribution of the submerged boundary force source to obtain the time step. t +1 correction velocity field; the linear equations are expressed as follows: 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; Final velocity field: The predicted velocity field is combined with the corrected velocity field to obtain the time step. t The final velocity field is +1.

8. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 7, characterized in that: The process of solving the problem using the prediction-correction method is as follows: The prediction step solves 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 step t density, For time step t velocity field, For the Laplace operator. The correction speed is obtained by calculating the correction step using the following formula. : Based on the predicted speed and correction speed get t+ The velocity field at time step 1 is : 。 9. The numerical calculation method for biomimetic flexible large deformation propulsion according to claim 8, characterized in that: In step 7, when calculating hydrodynamic forces and torques, the forces at the Lagrange nodes are first vector-summed to obtain the total fluid forces and torques acting on the submerged boundary. Then, according to Newton's third law, the signs are reversed to obtain the thrust, lift, lateral force, roll moment, pitch moment, and yaw moment acting on the biomimetic flexible body.

10. A numerical calculation system for biomimetic flexible large deformation propulsion, used to execute the numerical calculation method according to any one of claims 1-9, characterized in that, include: The model preprocessing module is configured to build a simulation computational physics model of the biomimetic flexible body to be calculated, divide its surface mesh, and generate and output Lagrange node data. The initial setup module is configured to set the simulation's inlet velocity, number of CFLs, total number of time steps, and boundary condition parameters; The flow field mesh construction module is configured to construct a three-dimensional flow field Eulerian mesh based on computational domain parameters. The Eulerian mesh includes a uniformly encrypted region surrounding the biomimetic flexible body and an outer unencrypted region, and outputs the coordinates of all Eulerian mesh nodes. The module is also configured to receive the Lagrange node data and ensure that the motion trajectory of the biomimetic flexible body always lies within the uniformly encrypted region. The motion calculation module is configured to calculate the position and velocity of each Lagrange node at each time step according to the preset biomimetic flexible body motion equation. The interaction relationship construction module is configured to execute the improved Euler point search algorithm. Based on the motion displacement of the Lagrange node, it dynamically determines and searches for the neighboring Euler node corresponding to each Lagrange node at the current time step, thereby establishing the mapping relationship between the Lagrange node and the Euler node, and constructs a linear equation system describing the fluid-structure interaction based on the principle of the submerged boundary method. The flow field solution module is configured to iteratively solve the linear equations using a numerical solver to obtain the corrected velocity field on the Eulerian grid, and to transfer the velocity field information to the Lagrange nodes using the mapping relationship. The performance analysis module is configured to calculate the hydrodynamic, torque, power, and propulsion efficiency parameters of the biomimetic flexible body based on the force information on the Lagrange nodes. The iterative control module is configured to control the progression of simulation time steps and terminate the calculation process when the preset total number of time steps is reached.

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