Three-dimensional swirling flow field dynamic characteristic analysis method based on CFD-DMD cooperation

Abstract

The invention discloses a three-dimensional swirling flow field dynamic characteristic analysis method based on CFD-DMD collaboration, and the method achieves the efficient and precise analysis of the dynamic characteristics of a three-dimensional swirling flow field through constructing a complete technical link of accurate collection of CFD flow field data, DMD modal decomposition and screening, and multi-software collaboration post-processing. The dynamic characteristic analysis method for the three-dimensional swirling flow field comprises the following steps: step 1, acquiring CFD flow field data to obtain a dynamic flow field snapshot; step 2, DMD modal decomposition and dominant modal screening are carried out, and dynamic characteristic parameters are extracted; and step 3, performing multi-software collaborative post-processing, and visualizing the dynamic characteristics.

Description

Technical Field

[0001] This invention belongs to the field of fluid mechanics technology, specifically relating to a method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy. Background Technology

[0002] Three-dimensional swirling flow fields are common flow patterns in industrial equipment (such as cyclone separators and swirling burners). Their core characteristic is the formation of strong swirling turbulence by fluid rotation around a central axis, accompanied by the unsteady motion of large-scale coherent structures (such as swirling vortex cores). The dynamic characteristics of these structures directly affect key performance aspects of the equipment, such as separation efficiency and energy loss. Currently, Computational Fluid Dynamics (CFD) is the mainstream technology for acquiring three-dimensional swirling flow field data. By solving the Navier-Stokes equations, high spatiotemporal resolution data of parameters such as velocity (tangential, axial, and radial), vorticity, and pressure in the flow field can be output. In industry, CFD software such as Fluent is commonly used to implement this process. Specific operations include: constructing a geometric model, mesh generation, setting boundary conditions, selecting a turbulence model, calculation and solution, and data acquisition, providing a foundation for subsequent flow field analysis.

[0003] To extract large-scale coherent structures from complex flow fields, flow field mode decomposition (PDD) has become an important analytical tool, with typical methods including intrinsic orthogonal decomposition (POD) and dynamic mode decomposition (DMD). POD extracts dominant modes by performing singular value decomposition on the snapshot matrix, using energy percentage as an indicator. However, it only reflects the static energy distribution of the flow field and cannot provide dynamic parameters such as mode frequency and growth / decay rate. DMD relies solely on energy indicators to select modes, failing to consider the correlation between actual dynamic phenomena in the swirling flow field (such as the dominant frequency of the vortex core) and mode decay rate. This easily leads to misclassification of weak modes corresponding to numerical noise and rapidly decaying pseudo-modes as core dynamic modes, resulting in an inability to accurately identify dynamic modes that reflect the essence of the swirling flow field.

[0004] Existing three-dimensional swirling flow dynamic characteristic analysis techniques still have the following shortcomings: (1) The problem that existing CFD simulations cannot accurately capture the dynamic evolution characteristics of three-dimensional swirling flow fields. In existing technologies, although CFD simulation can output high spatiotemporal resolution data of three-dimensional swirling flow fields (such as velocity and vorticity), it can only realize the numerical representation of the flow field and cannot separate the key information reflecting the dynamic characteristics from the complex strong swirling turbulent flow field. It is difficult to identify large-scale coherent structures (such as swirling vortex cores) and cannot quantify the evolution of modes over time (such as frequency and decay rate). Even if the dominant frequency of the swirling vortex core is determined by Fast Fourier Transform (FFT), it is still impossible to correlate the spatiotemporal changes of the three-dimensional flow field corresponding to that frequency (such as the evolution of vortex structure morphology and energy transfer process), which makes it impossible to reveal the dynamic flow mechanism of the swirling flow field in depth.

[0005] (2) The independent operation of multiple stages leads to low efficiency and poor compatibility in the dynamic analysis of three-dimensional swirling flow fields. Current dynamic modal analysis of three-dimensional swirling flow fields requires data from multiple sources and involves several independent steps, including mesh generation (performed in ICEM software), CFD calculation (performed in Fluent software), DMD analysis (performed in Matlab software), and flow field post-processing (performed in Tecplot software). In this process, on the one hand, the unstructured mesh flow field data (ASCII files) output by Fluent software does not contain node connectivity relationships. Directly importing this data into the DMD analysis stage can easily lead to misalignment between the flow field information and the mesh node mapping, resulting in deviations in the dynamic modal calculations. On the other hand, Tecplot is extremely inefficient at reading ASCII format dynamic modal data, failing to efficiently present the dynamic evolution results. The overall analysis cycle is long and the operation is cumbersome, making it difficult to meet the need for efficient analysis of the dynamic characteristics of three-dimensional swirling flow fields.

[0006] (3) The lack of scientific standards for screening dynamic modes of three-dimensional swirling flow fields and the ambiguity in identifying core dynamic features. In existing technologies, there is a lack of clear criteria for screening dynamic modes of three-dimensional swirling flow fields. The correlation between the dynamic characteristics of modes (such as decay rate and frequency) and actual flow phenomena (such as the dominant frequency of the vortex core) is not combined, which makes it impossible to accurately identify the core dynamic modes with physical significance. It is easy to misjudge the pseudo-modes with fast decay and the weak modes corresponding to numerical noise as key dynamic modes. It is also impossible to clarify the contribution of different dynamic modes to the overall dynamic characteristics of the swirling flow field, which restricts the pertinence of the optimization design of swirling flow fields based on dynamic characteristics. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention aims to provide a method for analyzing the dynamic characteristics of three-dimensional swirling flow fields based on CFD-DMD collaboration. By constructing a complete technical chain of "accurate acquisition of CFD flow field data - DMD mode decomposition and screening - multi-software collaborative post-processing", it achieves efficient and accurate analysis of the dynamic characteristics of three-dimensional swirling flow fields.

[0008] To achieve the above objectives, the present invention may adopt the following specific technical solutions: The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy includes the following steps: Step 1: Acquire CFD flow field data and obtain a dynamic flow field snapshot; Step 2: DMD mode decomposition and dominant mode selection, extracting dynamic characteristic parameters; Step 3: Multi-software collaborative post-processing to visualize dynamic characteristics.

[0009] Furthermore, the specific operation of step 1 is as follows: Step 1-1, Geometric Modeling and Mesh Generation: For the target 3D swirling flow field, a geometric model is constructed using ICEM software, and an unstructured hexahedral mesh is generated. The mesh is then refined in the core region of the swirling flow to ensure that the total number of meshes meets the high-resolution requirements. At the same time, the coordinates of the mesh nodes and the node connection relationships of the unstructured mesh are recorded to provide a basis for subsequent data mapping. Step 1-2, CFD simulation parameter settings: Numerical simulation is performed using Fluent software. The large eddy simulation turbulence model is selected, and the core parameters are set, including fluid properties, boundary conditions, time parameters, and data output format definitions.

[0010] Furthermore, the specific operation of step 2 is as follows: Step 2-1: Write a data preprocessing script; Step 2-2: Write the DMD calculation script and execute the mode decomposition. Steps 2-3: Establish a three-dimensional screening criterion of "energy-attenuation rate-frequency" to conduct multi-dimensional screening of dominant modes.

[0011] Further, in step 2-1, the ICEM mesh node information file is read and stored as a "node information.mat" file; the ASCII format snapshot files output by Fluent are read in batches, and the geometric information and flow field data are automatically separated and stored as "geometric information.mat" and "flow field snapshot.mat" files respectively; the original flow field data is normalized and the spatial dimension is compressed from three dimensions to one dimension, and then the snapshot matrices X and Y required for DMD analysis are constructed: matrix X consists of the 1st to n-1st snapshots, and matrix Y consists of the 2nd to nth snapshots, with the column direction of the matrix representing spatial nodes and the row direction representing time steps.

[0012] Furthermore, in step 2-2, the process of performing mode decomposition is as follows: Singular Value Decomposition: Perform SVD decomposition on the snapshot matrix X. The first r principal singular values ​​are retained, and the small singular values ​​are truncated to reduce numerical noise. The value of r is such that the proportion of the first r singular values ​​is ≥99.9%. Among them, U is the left singular matrix, which is an m×m unitary matrix representing the spatial mode; Σ is the singular value matrix, which is a positive semi-definite m×n diagonal matrix representing the mode strength. The conjugate transpose of the right singular matrix is ​​an n×n unitary matrix representing time correlation; Approximate calculation of the evolution matrix: Based on the truncated U, Σ, V matrices, according to the formula Calculate the approximate value of the linear evolution matrix; à is the matrix after the similarity transformation of matrix A. Let U be the conjugate transpose of U, Y be the snapshot matrix consisting of the 2nd to nth snapshots, and V be the truncated right singular matrix. This is the pseudo-inverse of Σ after truncation; Eigenvalue and Mode Extraction: Eigenvalue decomposition is performed on à to obtain eigenvalues ​​λ and eigenvectors v, according to the formula... Calculate the DMD modes, where φ is the DMD mode, v is the eigenvector, and λ is the eigenvalue; Dynamic parameter calculation: The modal attenuation rate is calculated using the formula ψ=Re {lgλ} / Δt, where Re {lgλ} is the real part of the logarithm of the eigenvalues ​​and Δt is the snapshot interval; the modal frequency is calculated using the formula ω=Im {lgλ} / Δt, where Im {lgλ} is the imaginary part of the logarithm of the eigenvalues; and the modal energy is calculated using the sum of squares of the amplitudes of each node at each time point.

[0013] Furthermore, in steps 2-3, the three-dimensional screening criteria of "energy-attenuation rate-frequency" are as follows: Energy screening: retain the top 30% of modes by modal energy; Attenuation rate screening: retain modes with an absolute attenuation rate ≤ 5; Frequency screening: Based on the known dynamic characteristics of the three-dimensional swirling flow field, modes whose frequencies deviate from the target frequency or integer multiples of the target frequency by ≤5% are retained, and finally the dominant modes are screened out.

[0014] Furthermore, the specific operation of step 3 is as follows: Step 3-1: Write a modal data output script, read the dominant modal data obtained from DMD calculation, restore the one-dimensional data to three-dimensional data, combine the node coordinates and connection relationships in "node information.mat", and add a file header according to the Tecplot file format requirements to generate dat files of each mode evolution over time. Step 3-2: Write a batch script to call Tecplot's built-in preplot program through batch commands to convert .dat files into binary .plt files in batches. Step 3-3: Visualization and analysis of dynamic characteristics. Import the plt file of all time points of a single mode into Tecplot, and use velocity field visualization, vortex structure visualization and flow field reconstruction to verify and present the dynamic characteristics.

[0015] Specifically, velocity field visualization displays the tangential, axial, and radial velocity distributions of the dominant modes through cross-sections; vortex structure visualization identifies vortex structures using the Q criterion and visualizes the evolution of modes over time; flow field reconstruction verifies the generation of a reconstructed flow field from the first k dominant modes, and compares it with the original CFD flow field to verify the dominant modes' ability to cover dynamic characteristics.

[0016] Compared with the prior art, the present invention has the following advantages: (1) Establish a multi-dimensional dominant mode screening criterion to avoid misjudging pseudo-modes. Existing technologies only use "modal energy" as a single screening index, which easily leads to the misjudgment of weak modes corresponding to numerical noise and rapidly decaying pseudo-modes as core modes. This invention innovatively proposes a three-dimensional screening logic of "energy-decay rate-frequency": first, retain the top 30% of modes in terms of energy, then screen stable modes with an absolute value of decay rate ≤ 5, and finally match the known dynamic characteristics of the swirling flow field, which can accurately identify dominant modes with physical significance.

[0017] (2) Solve the problem of data compatibility among multiple software programs and shorten the analysis cycle through batch processing. Existing technologies for DMD analysis of flow fields are time-consuming, with the core bottleneck being the large volume of flow field snapshot data and the inconsistent data formats among different software programs. This invention improves efficiency through four key optimizations: ① Data preprocessing scripts read snapshot files in batches, separating geometric information from flow field data; ② DMD calculation scripts compress three-dimensional space into one dimension, automatically perform singular value decomposition and eigenvalue calculation, and retain key modal information; ③ Modal output scripts restore one-dimensional data to three dimensions, combine node coordinates, node connection relationships, and Tecplot file format to generate .dat files showing the evolution of modes over time; ④ Batch processing scripts automatically convert ASCII format .dat files into binary .plt files, reducing storage by 60% and improving reading efficiency by 90%.

[0018] (3) It is not bound to a specific device and only requires fine-tuning of parameters to adapt. Existing technologies often develop analysis processes for a single device, and data processing scripts need to be rewritten after changing the device; the core technology link of this invention has universality: for other three-dimensional swirling fields such as swirling separators and swirling burners, dynamic characteristic analysis can be achieved by only adjusting the boundary conditions of CFD simulation, the mesh refinement area, and the frequency threshold of DMD screening, without the need to reconstruct the technical framework. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0021] like Figure 1 As shown, a method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy includes the following steps: (a) Step 1: CFD flow field data acquisition to obtain a highly adaptable dynamic flow field snapshot.

[0022] (1) Geometric modeling and mesh generation For the target three-dimensional swirling field (such as a cyclone separator or a swirling burner), a geometric model is constructed using ICEM software (taking a cyclone separator as an example, the model includes the separation space, overflow pipe, and ash hopper). An unstructured hexahedral mesh is divided, and the mesh is refined in the core swirling region (such as the bottom of the overflow pipe and near the dust discharge port) to ensure that the total number of meshes meets the high-resolution requirements (e.g., the number of meshes in a cyclone separator is ≥1.6 million). At the same time, the coordinates of the mesh nodes and the node connection relationships of the unstructured mesh are recorded (8 nodes constitute 1 hexahedral mesh, and a node connection index is established according to the mesh number) to provide a basis for subsequent data mapping.

[0023] (2) CFD simulation parameter settings Numerical simulation was performed using Fluent software, selecting the Large Eddy Simulation (LES) turbulence model (suitable for strongly swirling unsteady flows), and setting the core parameters as follows: Fluid properties: Set density (e.g., air 1.225 kg / m³) and viscosity (e.g., air 17.9 × 10⁻⁶) according to actual working conditions. -6 Pa・s).

[0024] Boundary conditions: The inlet is set as a velocity boundary (e.g., the inlet velocity of a cyclone separator is 12-28 m / s), and the outlet is set as a pressure outlet.

[0025] Time parameters: Time step less than 5 × 10 -4 s (to ensure the capture of high-frequency dynamic features), first calculate a certain time (to ensure that the flow time is greater than the convection feature time) to allow the flow field to reach a stable fluctuation state, and then continue to calculate the time required for sampling (which needs to be determined according to the sampling frequency and the number of samples) to collect a three-dimensional flow field snapshot.

[0026] Data output format definition: Configure Fluent to automatically output ASCII format files during the calculation process. Each file contains the three-dimensional velocity, vorticity and other flow field parameters of all grid nodes at the current time. Ensure that the file names are numbered in chronological order (e.g., "data_001.dat" to "data_256.dat") to facilitate subsequent batch reading.

[0027] (ii) Step 2: DMD mode decomposition and dominant mode screening to accurately extract dynamic characteristic parameters.

[0028] (1) Data preprocessing (Matlab script development) Write a data preprocessing script (data.m) to implement the following functions: ① Read the ICEM mesh node information file and save it as a "node information.mat" file.

[0029] ② Batch read ASCII format snapshot files output by Fluent, automatically separate geometric information (node ​​coordinates, node connection relationships) and flow field data (three-dimensional velocity), and store them as "geometry information.mat" and "flow field snapshot.mat" files respectively.

[0030] ③ Normalize the original flow field data and compress the spatial dimension from three dimensions to one dimension. Then construct the snapshot matrices X and Y required for DMD analysis: matrix X consists of the first to n-1 snapshots, and matrix Y consists of the second to n snapshots. The column direction of the matrix is ​​the spatial nodes (m nodes), and the row direction is the time step (n time steps).

[0031] (2) DMD calculation (Matlab script development) Write a DMD calculation script (DMD.m) and perform mode decomposition according to the following steps: ① Singular Value Decomposition (SVD): Perform SVD decomposition on the snapshot matrix X ( ), retaining the first r principal singular values ​​(truncating small singular values ​​to reduce numerical noise, with r taking the value that the first r singular values ​​account for ≥99.9%); where U is the left singular matrix, an m×m unitary matrix representing the spatial pattern; Σ is the singular value matrix, a positive semi-definite m×n diagonal matrix representing the pattern strength; is the conjugate transpose of the right singular matrix, and is an n×n unitary matrix representing the time correlation.

[0032] ② Approximate calculation of the evolution matrix: Based on the truncated U, Σ, and V matrices, according to the formula Calculate the approximate value of the linear evolution matrix; where à is the matrix after similarity transformation of matrix A. Let U be the conjugate transpose of U, Y be the snapshot matrix consisting of the 2nd to nth snapshots, and V be the truncated right singular matrix. This is the pseudo-inverse of Σ after truncation.

[0033] ③ Eigenvalue and Mode Extraction: Perform eigenvalue decomposition on à to obtain eigenvalues ​​λ and eigenvectors v, and then extract them according to the formula... Calculate the DMD modes; where φ is the DMD mode, v is the eigenvector, and λ is the eigenvalue.

[0034] ④ Dynamic parameter calculation: The modal attenuation rate is calculated according to the formula ψ=Re {lgλ} / Δt, where Re {lgλ} is the real part of the logarithm of the eigenvalues ​​and Δt is the snapshot interval; the modal frequency is calculated according to the formula ω=Im {lgλ} / Δt, where Im {lgλ} is the imaginary part of the logarithm of the eigenvalues; the modal energy is calculated according to the sum of squares of the amplitudes of each node at each time.

[0035] (3) Multi-dimensional screening of dominant modes Breaking through the existing single energy screening standard, a three-dimensional screening criterion of "energy-attenuation rate-frequency" is established: Energy screening: retain the top 30% of modes by modal energy; Attenuation rate screening: retain modes with an absolute attenuation rate ≤ 5 (to ensure mode stability and exclude pseudo modes with rapid attenuation). Frequency screening: Based on the known dynamic characteristics of the three-dimensional swirling flow field (such as the dimensionless frequency of the vortex core of the cyclone separator being 0.684), modes whose frequency deviates from the target frequency or an integer multiple (2nd harmonic, 3rd harmonic) of the target frequency by ≤5% are retained, and finally the dominant mode is screened out.

[0036] (III) Step 3: Multi-software collaborative post-processing for efficient visualization of dynamic characteristics.

[0037] (1) Write the modal data output script (tecplot.m) Read the dominant mode data obtained from DMD calculation, restore the one-dimensional data to three-dimensional data, combine the node coordinates and connection relationships in "node information.mat", and add a file header (including grid type, variable definition, number of nodes) according to Tecplot file format requirements to generate dat files (such as "mode1_001.dat") that show the evolution of each mode over time.

[0038] (2) Write a batch script (preplot.bat) Since .dat files are still ASCII files, Tecplot's reading efficiency is not high. Therefore, by using batch commands to call Tecplot's built-in preplot program, the .dat files can be converted into binary .plt files in batches. After conversion, the file storage space is reduced by 60%, and the software's reading efficiency is improved by more than 90%.

[0039] (3) Dynamic characteristic visualization analysis (Tecplot operation) Import the plt file for all time points of a single mode into Tecplot and present the dynamic characteristics in the following way: ① Velocity field visualization: Displays the tangential, axial, and radial velocity distributions of the dominant mode through cross-sections; ② Vortex structure visualization: Identify vortex structures using the Q criterion and visualize the evolution of modes over time; ③ Flow field reconstruction verification: The reconstructed flow field is generated by superimposing the first k dominant modes and compared with the original CFD flow field to verify the coverage of dynamic characteristics by the dominant modes. Example

[0040] The dynamic modal analysis of the cyclone separator includes the following: (1) CFD calculation scheme DMD analysis was performed on the numerical simulation results of the gas-phase flow field inside the cyclone separator. A Lapple-type single-inlet cyclone separator (swirl number Sw = 3.14) was numerically simulated. LES was used to simulate the gas-phase flow, with an inlet velocity of 20 m / s and a time step of [missing information]. The time step is 4000 steps, which means the flow time is 2.0 s, ensuring that the flow within the cyclone separator reaches a stable fluctuation state. Then, the flow time is calculated for another 0.512 s, and data is collected simultaneously. That is, an ASCII file containing the coordinates of all nodes and the velocities in the x, y, and z directions is output every 0.002 s, for a total of 256 flow field snapshots.

[0041] (2) Modal decomposition scheme ① During Fluent calculations, an ASCII file containing grid node coordinates and flow field information is output at regular time steps.

[0042] ② In Matlab, the data.m script is used to read in the calculation results of Fluent and store the geometric information and flow field snapshot matrix separately; the DMD.m script is used to perform DMD calculation on the snapshot matrix and output the mode matrices of each order; the tecplot.m script is used to extract the modal information, and at the same time combine the geometric information and node information, and by adding a file header, output the evolution process of each mode over time into a dat file format that Tecplot can read.

[0043] ③ Since the .dat file is still an ASCII file, Tecplot's reading efficiency is not high. Therefore, a batch processing command is used to convert it into a binary .plt file by calling the software's built-in preplot program. Testing showed that the converted .plt file occupies 40% of the original storage space, and the reading efficiency is improved by more than 90%.

[0044] In the above process, since Fluent is a solver based on unstructured meshes, the connectivity between nodes, in addition to the coordinates of the mesh nodes, is crucial for the correct mapping of the flow field information output by the DMD to the corresponding mesh nodes. An unstructured hexahedral mesh is defined by 8 mesh nodes, which are connected sequentially according to their mesh numbers. However, the ASCII file output by Fluent does not contain the node connectivity. Therefore, the node connectivity is exported through ICEM and provided to the tecplot.m script, thereby ensuring the accurate mapping of the flow field information.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy, characterized in that, Includes the following steps: Step 1: Acquire CFD flow field data and obtain a dynamic flow field snapshot; Step 2: DMD mode decomposition and dominant mode selection, extracting dynamic characteristic parameters; Step 3: Multi-software collaborative post-processing to visualize dynamic characteristics.

2. The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy as described in claim 1, characterized in that, The specific steps of step 1 are as follows: Step 1-1, Geometric Modeling and Mesh Generation: For the target 3D swirling flow field, a geometric model is constructed using ICEM software, and an unstructured hexahedral mesh is generated. The mesh is then refined in the core region of the swirling flow to ensure that the total number of meshes meets the high-resolution requirements. At the same time, the coordinates of the mesh nodes and the node connection relationships of the unstructured mesh are recorded to provide a basis for subsequent data mapping. Step 1-2, CFD simulation parameter settings: Numerical simulation is performed using Fluent software. The large eddy simulation turbulence model is selected, and the core parameters are set, including fluid properties, boundary conditions, time parameters, and data output format definitions.

3. The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy as described in claim 1, characterized in that, The specific steps for step 2 are as follows: Step 2-1: Write a data preprocessing script; Step 2-2: Write the DMD calculation script and execute the mode decomposition. Steps 2-3: Establish a three-dimensional screening criterion of "energy-attenuation rate-frequency" to conduct multi-dimensional screening of dominant modes.

4. The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy as described in claim 3, characterized in that, In step 2-1, the ICEM mesh node information file is read and stored as a "node information.mat" file; Batch read ASCII format snapshot files output by Fluent, automatically separate geometric information and flow field data, and store them as "geometric information.mat" and "flow field snapshot.mat" files respectively; The original flow field data is normalized and the spatial dimension is compressed from three dimensions to one dimension. Then, the snapshot matrices X and Y required for DMD analysis are constructed: matrix X consists of the first to n-1 snapshots, and matrix Y consists of the second to n snapshots. The column direction of the matrix is ​​the spatial node, and the row direction is the time step.

5. The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy according to claim 4, characterized in that, In step 2-2, the process of performing mode decomposition is as follows: Singular Value Decomposition: Perform SVD decomposition on the snapshot matrix X. The first r principal singular values ​​are retained, and the small singular values ​​are truncated to reduce numerical noise. The value of r is such that the proportion of the first r singular values ​​is ≥99.9%. Among them, U is the left singular matrix, which is an m×m unitary matrix representing the spatial mode; Σ is the singular value matrix, which is a positive semi-definite m×n diagonal matrix representing the mode strength. The conjugate transpose of the right singular matrix is ​​an n×n unitary matrix representing time correlation; Approximate calculation of the evolution matrix: Based on the truncated U, Σ, V matrices, according to the formula Calculate the approximate value of the linear evolution matrix; à is the matrix after the similarity transformation of matrix A. Let U be the conjugate transpose of U, Y be the snapshot matrix consisting of the 2nd to nth snapshots, and V be the truncated right singular matrix. This is the pseudo-inverse of Σ after truncation; Eigenvalue and Mode Extraction: Eigenvalue decomposition is performed on à to obtain eigenvalues ​​λ and eigenvectors v, according to the formula... Calculate the DMD modes, where φ is the DMD mode, v is the eigenvector, and λ is the eigenvalue; Dynamic parameter calculation: The modal attenuation rate is calculated using the formula ψ=Re {lgλ} / Δt, where Re {lgλ} is the real part of the logarithm of the eigenvalues ​​and Δt is the snapshot interval; the modal frequency is calculated using the formula ω=Im {lgλ} / Δt, where Im {lgλ} is the imaginary part of the logarithm of the eigenvalues; and the modal energy is calculated using the sum of squares of the amplitudes of each node at each time point.

6. The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy as described in claim 3, characterized in that, In steps 2-3, the three-dimensional screening criteria of "energy-attenuation rate-frequency" are as follows: Energy screening: retain the top 30% of modes by modal energy; Attenuation rate screening: retain modes with an absolute attenuation rate ≤ 5; Frequency screening: Based on the known dynamic characteristics of the three-dimensional swirling flow field, modes whose frequencies deviate from the target frequency or integer multiples of the target frequency by ≤5% are retained, and finally the dominant modes are screened out.

7. The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy as described in claim 1, characterized in that, The specific steps for step 3 are as follows: Step 3-1: Write a modal data output script, read the dominant modal data obtained from DMD calculation, restore the one-dimensional data to three-dimensional data, combine the node coordinates and connection relationships in "node information.mat", and add a file header according to the Tecplot file format requirements to generate dat files of each mode evolution over time. Step 3-2: Write a batch script to call Tecplot's built-in preplot program through batch commands to convert .dat files into binary .plt files in batches. Step 3-3: Visualization and analysis of dynamic characteristics. Import the plt file of all time points of a single mode into Tecplot, and use velocity field visualization, vortex structure visualization and flow field reconstruction to verify and present the dynamic characteristics.

8. The method for analyzing the dynamic characteristics of a three-dimensional swirling flow field based on CFD-DMD synergy as described in claim 7, characterized in that, Velocity field visualization displays the tangential, axial, and radial velocity distributions of the dominant mode through cross-sections; vortex structure visualization identifies vortex structures using the Q criterion and visualizes the evolution of the mode over time; flow field reconstruction verifies the generation of a reconstructed flow field from the first k dominant modes and compares it with the original CFD flow field to verify the dominant mode's ability to cover dynamic characteristics.

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