Method for identifying aeroelastic instability mechanism of damaged blade of gas compressor rotor

Abstract

The invention relates to the technical field of aeroelastic mechanics of aero-engines, in particular to a method for identifying an aeroelastic instability mechanism of a damaged blade of a gas compressor rotor based on a spectral characteristic orthogonal mode decomposition technology. According to the method, through damaged blade parameterization modeling and aeroelasticity response solution modeling, an instability mechanism identification technology is developed based on a spectrum characteristic orthogonal mode decomposition technology, and mechanism identification of aeroelasticity instability of the damaged rotor blade of the gas compressor is achieved. Compared with a traditional method, the method has the advantages that the energy redistribution process of the damaged blade in the frequency domain dimension can be captured, and the characteristics of convergent vibration, limit cycle oscillation and divergent vibration under each typical aeroelastic working condition can be effectively identified. By analyzing flow field dominant structure characteristics and frequency characteristics, physical essence identification of the instability mechanism is realized, and the technical scheme of the aeroelastic instability mechanism of the damaged blade is further perfected.

Description

Technical Field

[0001] This invention relates to the field of aeroelasticity technology for aero-engines, specifically to a method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades based on orthogonal mode decomposition of spectral features. Background Technology

[0002] As the core power system of modern national defense equipment and civil aviation, the performance of aero engines directly determines the combat effectiveness and safety reliability of aircraft. With the significant improvement of the technical performance parameters of the new generation of high-performance aero engines, the problem of blade aeroelastic instability has become increasingly prominent. This will directly cause high-frequency vibration of the blades, induce blade structural fatigue, and even cause sudden blade fracture, leading to catastrophic accidents.

[0003] The flow around compressor rotor blades exhibits a complex flow structure. Localized damage to the blades directly impacts their inherent properties, potentially reducing the aeroelastic stability margin. However, a complete physical model for the entire aeroelastic instability mechanism—where structural damage induces flow field distortion and ultimately leads to instability—has not yet been established. Furthermore, while mainstream flow field modal identification techniques can achieve dimensionality reduction and decoupling of complex models and effectively extract dynamic features, their core limitation lies in their insufficient ability to accurately characterize key frequency features. This makes it difficult to accurately identify different aeroelastic response states, especially the key transition frequency domain features during instability. Summary of the Invention

[0004] The purpose of this invention is to avoid the problem of insufficient frequency domain resolution in the study of the aeroelastic instability mechanism of compressor rotor blades damaged by existing technologies, and to provide a method for identifying the aeroelastic instability mechanism of compressor rotor blades damaged by existing technologies.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is a method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades, comprising the following steps: Step 1: Parametric modeling of damaged blades. Parametric modeling of damaged blades refers to using the shape of an undamaged healthy blade as a benchmark, employing non-uniform rational B-spline surface reconstruction technology to achieve geometric representation of the blade's point cloud data, followed by the use of Young's modulus gradient decay model to quantitatively describe the stiffness reduction law and achieve mechanical representation, and finally constructing a model including the damage initiation location. Scope of damage and stiffness attenuation coefficient The three-dimensional damage feature space is used to obtain a parameterized model of the damaged blade. Step 2: Solving and modeling the aeroelastic response of the damaged blade; Based on the parameterized model of the damaged blade constructed in Step 1, further aeroelastic response modeling is carried out. Specifically, this includes: First, for the structural module, a structural dynamics model of the damaged blade is established based on the finite element method; for the flow field module, a three-dimensional unsteady flow field model of a single flow channel of the blade is established based on computational fluid dynamics. Second, the structural module and the flow field module are coupled and modeled using fluid-structure interaction technology to form a solution model for the aeroelastic response of the damaged blade. On this basis, the aeroelastic response of the damaged blade is solved under near-stall conditions of the compressor to obtain the aeroelastic response of the damaged blade, including the transient displacement response of the structural module and the unsteady pressure distribution of the flow field module. Step 3: Orthogonal mode decomposition of spectral features; For the unsteady pressure distribution of the flow field described in step two, the spectral orthogonal mode decomposition technique is adopted. First, the snapshot matrix is ​​divided using the Welch periodogram method. To avoid spectral leakage, each block matrix is ​​windowed and overlapped with adjacent blocks. Discrete Fourier transform is performed on each block to convert it from the time domain to the frequency domain. Then, the snapshot vectors of the same frequency in each block are extracted into a new block and recombined into a new frequency-correlation matrix. The spectral orthogonal decomposition modes at each frequency are obtained by solving the eigenvectors. Finally, these modes are sorted according to the magnitude of their corresponding eigenvalues, where the eigenvalues ​​represent the energy magnitude of each mode, to obtain the spectral orthogonal modes and the corresponding spectrum. Step 4: Identification of aeroelastic instability mechanism. Based on the orthogonal modes of spectral features obtained in step three and their corresponding spectra, the aeroelastic instability mechanism is identified according to the different aeroelastic responses obtained in step two, including convergent vibration, limit cycle vibration, and divergent vibration. First, the frequency-energy transfer characteristics during the aeroelastic instability process are obtained by comparing the orthogonal mode spectra. Second, the flow field shock wave, tip leakage vortex, and inter-blade channel vortex structure are examined by comparing the orthogonal mode cloud maps. Finally, the aeroelastic instability mechanism of the damaged blade is obtained.

[0006] Furthermore, the damage parameter in step one is defined as a dimensionless parameter, namely the stiffness attenuation coefficient. Defined as Young's modulus after material degradation The ratio to the original D; the location of the damage initiation. Indicates the height along the leaf Damage initiation height Normalized position ; extent of damage Used to quantify the relative extent of the damaged area along the leaf height. .

[0007] Furthermore, the solution of the structural modules in step two is based on the structural dynamics equations: , in, These are the structural mass matrix, damping matrix, and stiffness matrix, respectively. For the resultant external force of the structure, This represents its acceleration, velocity, and displacement. The finite element method is used for spatial discretization, the energy-momentum conservation method is used for time progression, and finally, the displacement response of the structure is solved based on Newton's method. The flow field module is based on the three-dimensional Reynolds-averaged three-dimensional Navier-Stokes equations in a rotating coordinate system: , Among them, Indicates having boundaries The fixed control body, solution vector Regarding circulation volume Viscous flux and source item They can be written in component form as shown in the following formulas: , , in Represents density, Here, E represents pressure, K represents the relative total energy per unit mass, and T represents temperature. , and These represent the displacement, velocity, and speed relative to the rotating reference frame in three directions, respectively. It has a dynamic viscosity coefficient The viscous stress tensor is approximated as that of an ideal gas using Sutherland's law. For numerical solutions, a second-order accurate backward Euler scheme is used for time integration, and a second-order accurate upwind scheme is applied for spatial discretization. Double-precision floating-point numbers are used for all calculations, and the SST turbulence model is employed. Turbulence model; In the coupled modeling described above, the pressure load of the flow field module on the coupling interface is transferred to the structural module in the solution of each time step. The structural module obtains a new displacement response, which is then transferred to the flow field model to realize the aeroelastic response solution modeling of the damaged blade.

[0008] Furthermore, the specific process of the spectral feature orthogonal mode decomposition technique described in step three includes: first, sampling at equal time intervals to obtain unsteady flow field pressure distribution data, i.e., snapshot data. , Representing the coordinates and time of the snapshot point in three directions, the time-domain snapshot data is assembled based on the Welch periodogram as follows: , Among them, superscript Indicates the first A snapshot of a data block. The number of overlapping data blocks in the division. If each data block contains a number of snapshots, then the individual snapshots within a data block are: , in, This indicates the number of snapshots that overlap between adjacent data blocks, typically selected as... ; Each data block is windowed using a symmetric function, employing a Hamming window: , The weighted snapshot data is transformed to the frequency domain using a discrete Fourier transform to obtain the first... The Fourier transform data of each data block is as follows: , According to frequency The algorithm rearranges the snapshot data in the above formula to form a frequency-based algorithm. The following snapshot matrix: , Cross-spectral density matrix at ... Build as: , right Perform eigenvalue decomposition: , in, These are the eigenvector matrix and eigenvalue matrix of the eigenvalue decomposition, respectively. Finally, construct the orthogonal modes of spectral features. , is represented as: , Spectral characteristic orthogonal modes at each frequency The orthogonality is maintained in both the spatiotemporal inner product and the spatial inner product. The eigenvalues ​​quantify the energy of each mode and reflect the contribution ratio of each mode in the flow field.

[0009] The beneficial effects of this invention are as follows: This invention provides a method for identifying the aeroelastic instability mechanism of damaged compressor rotor blades. Through parametric modeling of the damaged blade and aeroelastic response modeling, an instability mechanism identification technique is developed based on orthogonal mode decomposition (OMD) technology, enabling the identification of the aeroelastic instability mechanism of damaged compressor rotor blades. Compared to traditional methods, this technique can capture the energy redistribution process of the damaged blade in the frequency domain, effectively identifying the characteristics of convergent vibration, limiting cycle oscillation, and divergent vibration under various typical aeroelastic operating conditions. By analyzing the dominant structural and frequency characteristics of the flow field, the physical essence of the instability mechanism is identified, further improving the technical system of aeroelastic instability mechanism of damaged blades. Attached Figure Description

[0010] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of the single-channel computational grid configuration of NASA Rotor 37, an embodiment of the present invention. Figure 3 This is a schematic diagram of the aeroelastic response of NASA Rotor 37 under different pressure ratios in a damaged state, as an embodiment of the present invention. Figure 4 This is a schematic diagram of the SPOD energy-frequency distribution and energy extraction under the convergence, limit cycle, and divergence conditions of the damage state of NASA Rotor 37, as described in the embodiment of the present invention. Figure 5 This is a schematic diagram of the chordal distribution of SPOD modes under flutter conditions in a damaged state of NASA Rotor 37, as an embodiment of the present invention. Figure 6 This is a schematic diagram of the first-order mode at the frequency under the convergence, limit cycle, and divergence conditions of the damage state of NASA Rotor 37, as an embodiment of the present invention. Detailed Implementation

[0011] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0012] To achieve the above objectives, the present invention provides the following specific embodiments: Figure 1 As shown, a method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades includes the following steps: Step 1: Parametric modeling of damaged blades. Parametric modeling of damaged blades refers to using the shape of an undamaged healthy blade as a benchmark, employing non-uniform rational B-spline surface reconstruction technology to achieve geometric representation of the blade's point cloud data, followed by the use of Young's modulus gradient decay model to quantitatively describe the stiffness reduction law and achieve mechanical representation, and finally constructing a model including the damage initiation location. Scope of damage and stiffness attenuation coefficient The three-dimensional damage feature space is used to obtain a parameterized model of the damaged blade. Step 2: Solving and modeling the aeroelastic response of the damaged blade; Based on the parameterized model of the damaged blade constructed in Step 1, further aeroelastic response modeling is performed. Specifically, this includes: First, for the structural module, a structural dynamics model of the damaged blade is established based on the finite element method; for the flow field module, a three-dimensional unsteady flow field model of a single flow channel of the blade is established based on computational fluid dynamics. Second, the structural module and the flow field module are coupled and modeled using fluid-structure interaction technology to form a solution model for the aeroelastic response of the damaged blade. Based on this, the aeroelastic response of the damaged blade is solved under near-stall conditions of the compressor, yielding the aeroelastic response of the damaged blade, including the transient displacement response of the structural module and the unsteady pressure distribution of the flow field module. Step 3: Orthogonal mode decomposition of spectral features; For the unsteady pressure distribution of the flow field described in step two, the spectral orthogonal mode decomposition technique is adopted. First, the snapshot matrix is ​​divided using the Welch periodogram method. To avoid spectral leakage, each block matrix is ​​windowed and overlapped with adjacent blocks. Discrete Fourier transform is performed on each block to convert it from the time domain to the frequency domain. Then, the snapshot vectors of the same frequency in each block are extracted into a new block and recombined into a new frequency-correlation matrix. The spectral orthogonal decomposition modes at each frequency are obtained by solving the eigenvectors. Finally, these modes are sorted according to the magnitude of their corresponding eigenvalues, where the eigenvalues ​​represent the energy magnitude of each mode, to obtain the spectral orthogonal modes and the corresponding spectrum. Step 4: Identification of aeroelastic instability mechanism. Based on the orthogonal modes of spectral features obtained in step three and their corresponding spectra, the aeroelastic instability mechanism is identified according to the different aeroelastic responses obtained in step two, including convergent vibration, limit cycle vibration, and divergent vibration. First, the frequency-energy transfer characteristics during the aeroelastic instability process are obtained by comparing the orthogonal mode spectra. Second, the flow field shock wave, tip leakage vortex, and inter-blade channel vortex structure are examined by comparing the orthogonal mode cloud maps. Finally, the aeroelastic instability mechanism of the damaged blade is obtained.

[0013] Furthermore, the damage parameter in step one is defined as a dimensionless parameter, namely the stiffness attenuation coefficient. Defined as Young's modulus after material degradation The ratio to the original D; the location of the damage initiation. Indicates the height along the leaf Damage initiation height Normalized position ; extent of damage Used to quantify the relative extent of the damaged area along the leaf height. .

[0014] Furthermore, the solution of the structural modules in step two is based on the structural dynamics equations: , in, These are the structural mass matrix, damping matrix, and stiffness matrix, respectively. For the resultant external force of the structure, This represents its acceleration, velocity, and displacement. The finite element method is used for spatial discretization, the energy-momentum conservation method is used for time progression, and finally, the displacement response of the structure is solved based on Newton's method. The flow field module is based on the three-dimensional Reynolds-averaged three-dimensional Navier-Stokes equations in a rotating coordinate system: , Among them, Indicates having boundaries The fixed control body, solution vector Regarding circulation volume Viscous flux and source item They can be written in component form as shown in the following formulas: , , in Represents density, Here, E represents pressure, K represents the relative total energy per unit mass, and T represents temperature. , and These represent the displacement, velocity, and speed relative to the rotating reference frame in three directions, respectively. It has a dynamic viscosity coefficient The viscous stress tensor is approximated as that of an ideal gas using Sutherland's law. For numerical solutions, a second-order accurate backward Euler scheme is used for time integration, and a second-order accurate upwind scheme is applied for spatial discretization. Double-precision floating-point numbers are used for all calculations, and the SST turbulence model is employed. Turbulence model; In the coupled modeling described above, the pressure load of the flow field module on the coupling interface is transferred to the structural module in the solution of each time step. The structural module obtains a new displacement response, which is then transferred to the flow field model to realize the aeroelastic response solution modeling of the damaged blade.

[0015] Furthermore, the specific process of the spectral feature orthogonal mode decomposition technique described in step three includes: first, sampling at equal time intervals to obtain unsteady flow field pressure distribution data, i.e., snapshot data. , Representing the coordinates and time of the snapshot point in three directions, the time-domain snapshot data is assembled based on the Welch periodogram as follows: , Among them, superscript Indicates the first A snapshot of a data block. The number of overlapping data blocks in the division. If each data block contains a number of snapshots, then the individual snapshots within a data block are: , in, This indicates the number of snapshots that overlap between adjacent data blocks, typically selected as... ; Each data block is windowed using a symmetric function, employing a Hamming window: , The weighted snapshot data is transformed to the frequency domain using a discrete Fourier transform to obtain the first... The Fourier transform data of each data block is as follows: , According to frequency The algorithm rearranges the snapshot data in the above formula to form a frequency-based algorithm. The following snapshot matrix: , Cross-spectral density matrix at ... Build as: , right Perform eigenvalue decomposition: , in, These are the eigenvector matrix and eigenvalue matrix of the eigenvalue decomposition, respectively. Finally, construct the orthogonal modes of spectral features. , is represented as: , Spectral characteristic orthogonal modes at each frequency The orthogonality is maintained in both the spatiotemporal inner product and the spatial inner product. The eigenvalues ​​quantify the energy of each mode and reflect the contribution ratio of each mode in the flow field.

[0016] The following is an implementation verification of the aeroelastic instability mechanism identification method for compressor rotor damaged blades of the present invention in the flutter mechanism identification of compressor rotor blades under NASA Rotor37 damage state, specifically including: NASA Rotor37 is a scaled-down prototype of a low-aspect-ratio inlet stage designed for an eight-stage compressor. This rotor has a comprehensive experimental database, and its hub-to-tip supersonic flow characteristics are typical of military inlet rotors. Key design parameters are as follows: choke flow rate 20.93 kg / s, design point (96.5% choke flow rate: 20.19 kg / s) pressure ratio 2.106; 36 blades, aspect ratio 1.19, hub-to-tip radius ratio 0.7; operating tip clearance 0.4 mm (0.45% of blade height); tip linear velocity 454 m / s (corresponding to a rotational speed of 17,188.7 rpm). The numerical model employs a single-channel periodic simplification strategy, such as... Figure 2 As shown, peak efficiency is reached at a normalized mass flow rate of 0.98, and near the stall boundary is at 0.925. The material is Maraging Steel 200. Based on stress distribution research, the chordal damage area is limited to 1 / 3 to 2 / 3 of the chord length at the leading edge. In this example, the damage parameters are set as follows: (Stiffness reduction) (Extending damage range) (Extension starting height). Figure 2 This is a schematic diagram of the solid model of NASA Rotor 37 and the single-channel computational grid configuration of the fluid domain. Figure 3 This is a schematic diagram of the aeroelastic response of NASA Rotor 37 under different pressure ratios in a damaged state. The horizontal axis represents time, and the vertical axis represents the displacement at the leading edge of the blade tip.

[0017] The damaged blade was at a total pressure ratio of... It exhibits convergent oscillations, limit cycle oscillations, and divergent oscillations, such as Figure 3 As shown. Strictly speaking, limit cycle oscillation is a critical flutter state and also belongs to the category of flutter. However, to distinguish between constant-amplitude oscillation and divergent oscillation, they are described as limit cycles and flutter, respectively. At the sampling time step... Under various aeroelastic typical operating conditions, 640 data points were collected, covering approximately four vibration cycles. In the spectral feature orthogonal modal decomposition method, each data block contains 128 snapshots, with 64 snapshots overlapping, identifying six dominant modes of the spectral feature orthogonal modes. Among these, the spanwise mode represents the flow field characteristics at the first layer of the blade surface grid, and the chordal mode represents the inter-blade flow characteristics at 10% of the blade tip. For example... Figure 4This diagram illustrates the orthogonal modal energy-frequency distribution and energy cutoff of NASA Rotor 37 under flutter, limit cycle, and steady-state conditions. The horizontal axis represents frequency, and the vertical axis represents eigenvalues, indicating the magnitude of energy. Figure 5 This is a schematic diagram of the orthogonal modal chordal distribution of the spectral characteristics of NASA Rotor 37 under flutter conditions in a damaged state, located at a position 10% away from the casing.

[0018] The orthogonal mode decomposition method based on spectral characteristics arranges eigenvalues ​​in descending order of energy, facilitating the identification of the dominant flow structure and capturing energy variations across the spectrum. Since these eigenvalues ​​significantly contribute to the total energy, the first three peak frequencies are selected in this example. , and The first two modes at that point serve as the dominant orthogonal spectral features. Represents frequency The first First-order modes. Furthermore, although high frequencies... The energy compared to the first two peak frequencies ( , While an order of magnitude lower, it remains significant as a complement to the dominant flow mode. It is worth noting that in... A nearby non-peak frequency also exhibits higher energy. By comparing this non-peak frequency with... The flow field structures of the two were examined, revealing similar flow structures, further demonstrating the rationale for choosing the peak frequency as the representative mode. From steady-state conditions to the limiting cycle, high frequencies ( The energy remains basically unchanged, but the low frequency ( ) and intermediate frequency ( A significant energy transfer occurs between the limiting cycle and the flutter condition, highlighting a characteristic of the limiting cycle oscillation: although low-frequency energy dominates in both steady-state and flutter conditions, the limiting cycle produces a distinct peak at the mid-frequency, indicating that the limiting cycle promotes the coupling of large-scale flow structures with higher-order perturbations. As the system evolves from the limiting cycle to the flutter condition, energy redistribution occurs. The most significant mid-frequency component in the limiting cycle stage (…) In the flutter state, it shifts to lower frequencies, while high-frequency energy ( It also shifts slightly to lower frequencies, indicating that flutter is dominated by low frequencies.

[0019] Figure 5 The flutter modes shown, based on the frequency distribution, are specifically characterized by shock wave dominance. Large-scale channel disturbances and small-scale pulsating perturbations ( For mid-frequency modes ( The distribution of structures near the leading edge is the most significant distinguishing feature. Figure 6Comparison of three working conditions The first mode at the specified frequency. Under flutter conditions, the shock wave near the leading edge remains intact in terms of spanwise intensity and coverage, unaffected by large-scale channel vortices; however, under steady-state and limiting cycle conditions, the interaction between the shock wave and large-scale vortices disrupts the propagation of the shock wave.

[0020] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades, characterized in that, Includes the following steps: Step 1: Parametric modeling of damaged blades: Parametric modeling of damaged blades refers to using the shape of an undamaged healthy blade as a benchmark, employing non-uniform rational B-spline surface reconstruction technology to achieve geometric representation of the blade's point cloud data, followed by the use of Young's modulus gradient decay model to quantitatively describe the stiffness reduction law and achieve mechanical representation, and finally constructing a model including the damage initiation location. Scope of damage and stiffness attenuation coefficient The three-dimensional damage feature space is used to obtain a parameterized model of the damaged blade. Step 2: Solving and modeling the aeroelastic response of the damaged blade; Based on the parameterized model of the damaged blade constructed in Step 1, further aeroelastic response modeling is performed; specifically including: First, for the structural module, a structural dynamics model of the damaged blade is established based on the finite element method. For the flow field module, a three-dimensional unsteady flow field model of a single flow channel of the blade is established based on computational fluid dynamics. Second, the structural module and the flow field module are coupled and modeled using fluid-structure interaction technology to form a solution model for the aeroelastic response of the damaged blade. On this basis, the aeroelastic response of the damaged blade is solved under the near-stall condition of the compressor to obtain the aeroelastic response of the damaged blade, including the transient displacement response of the structural module and the unsteady pressure distribution of the flow field module. Step 3: Orthogonal mode decomposition of spectral features: For the unsteady pressure distribution of the flow field described in step two, the spectral orthogonal mode decomposition technique is adopted. First, the snapshot matrix is ​​divided using the Welch periodogram method. To avoid spectral leakage, each block matrix is ​​windowed and overlapped with adjacent blocks. Discrete Fourier transform is performed on each block to convert it from the time domain to the frequency domain. Then, the snapshot vectors of the same frequency in each block are extracted into a new block and recombined into a new frequency-correlation matrix. The spectral orthogonal decomposition modes at each frequency are obtained by solving the eigenvectors. Finally, these modes are sorted according to the magnitude of their corresponding eigenvalues, where the eigenvalues ​​represent the energy magnitude of each mode, to obtain the spectral orthogonal modes and the corresponding spectrum. Step 4: Identification of aeroelastic instability mechanism. Based on the orthogonal modes of spectral features obtained in step three and their corresponding spectra, the aeroelastic instability mechanism is identified according to the different aeroelastic responses obtained in step two, including convergent vibration, limit cycle vibration, and divergent vibration. First, the frequency-energy transfer characteristics during the aeroelastic instability process are obtained by comparing the orthogonal mode spectra. Second, the flow field shock wave, tip leakage vortex, and inter-blade channel vortex structure are examined by comparing the orthogonal mode cloud maps. Finally, the aeroelastic instability mechanism of the damaged blade is obtained.

2. The method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades as described in claim 1, characterized in that, The damage parameter in step one is defined as a dimensionless parameter, namely the stiffness attenuation coefficient. Defined as Young's modulus after material degradation The ratio to the original D; the location of the damage initiation. Indicates the height along the leaf Damage initiation height Normalized position ; extent of damage Used to quantify the relative extent of the damaged area along the leaf height. .

3. The method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades as described in claim 1, characterized in that, The solution to the structural modules described in step two is based on the structural dynamics equations: ， in, These are the structural mass matrix, damping matrix, and stiffness matrix, respectively. For the resultant external force of the structure, It represents its acceleration, velocity, and displacement; spatial discretization is performed using the finite element method, time progression is performed using the energy-momentum conservation method, and finally the displacement response of the structure is solved based on Newton's method.

4. The method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades as described in claim 1, characterized in that, The flow field module in step two is based on the three-dimensional Reynolds-averaged three-dimensional Navier-Stokes equations in a rotating coordinate system: ， Among them, Indicates having boundaries The fixed control body, solution vector Regarding circulation volume Viscous flux and source item They can be written in component form as shown in the following formulas: ， ， in Represents density, Here, E represents pressure, K represents the relative total energy per unit mass, and T represents temperature. , and These represent the displacement, velocity, and speed relative to the rotating reference frame in three directions, respectively. It has a dynamic viscosity coefficient The viscous stress tensor is approximated as that of an ideal gas using Sutherland's law. For numerical solutions, a second-order accurate backward Euler scheme is used for time integration, and a second-order accurate upwind scheme is applied for spatial discretization. Double-precision floating-point numbers are used for all calculations, and the SST turbulence model is employed. Turbulence model.

5. The method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades as described in claim 1, characterized in that, In step two, the coupled modeling process transfers the pressure load on the coupling interface of the flow field module to the structural module in each time step. The structural module then obtains a new displacement response, which is then transferred to the flow field model to achieve the aeroelastic response modeling of the damaged blade.

6. A method for identifying the aeroelastic instability mechanism of compressor rotor damaged blades as described in any one of claims 1-5, characterized in that, The specific process of the spectral feature orthogonal mode decomposition technique described in step three includes: First, sampling at equal time intervals to obtain unsteady flow field pressure distribution data, i.e., snapshot data. , Representing the coordinates and time of the snapshot point in three directions, the time-domain snapshot data is assembled based on the Welch periodogram as follows: ， Among them, superscript Indicates the first A snapshot of a data block. The number of overlapping data blocks in the division. If each data block contains a number of snapshots, then the individual snapshots within a data block are: ， in, This indicates the number of snapshots that overlap between adjacent data blocks, typically selected as... ; Each data block is windowed using a symmetric function, employing a Hamming window: ， The weighted snapshot data is transformed to the frequency domain using a discrete Fourier transform to obtain the first... The Fourier transform data of each data block is as follows: ， According to frequency The algorithm rearranges the snapshot data in the above formula to form a frequency-based algorithm. The following snapshot matrix: ， Cross-spectral density matrix at ... Build as: ， right Perform eigenvalue decomposition: ， in, These are the eigenvector matrix and eigenvalue matrix of the eigenvalue decomposition, respectively. Finally, construct the orthogonal modes of spectral features. , represented as: ， Spectral characteristic orthogonal modes at each frequency The orthogonality is maintained in both the spatiotemporal inner product and the spatial inner product. The eigenvalues ​​quantify the energy of each mode and reflect the contribution ratio of each mode in the flow field.

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