Flow sound mode decomposition method coupling local projection and Helmholtz decomposition

Abstract

The invention discloses a streaming sound mode decomposition method coupling local projection and Helmholtz decomposition, and relates to the streaming sound mode decomposition field, and the method comprises the steps: employing a local projection method to obtain turbulence coherent structure velocity field time series data and turbulence disordered structure velocity field time series data; respectively carrying out Helmholtz decomposition on the two to obtain a first decomposition result and a second decomposition result; performing divergence on the two decomposition results to obtain a first Poisson equation and a second Poisson equation respectively; carrying out numerical solution on the two Poisson equations to respectively obtain a first scalar potential and a second scalar potential; taking gradients from the two scalar potentials to respectively obtain a turbulent coherent structure acoustic mode velocity field and a turbulent disordered structure acoustic mode velocity field; obtaining a turbulence coherent structure dynamic modal velocity field based on the turbulence coherent structure acoustic modal velocity field; obtaining a turbulence disorder structure dynamic modal velocity field based on the turbulence disorder structure acoustic modal velocity field; according to the method, the flow sound mode decomposition of the nonlinear evolution flow velocity field can be realized.

Description

Technical Field

[0001] The present invention relates to the field of flow acoustic mode decomposition, and specifically, to a flow acoustic mode decomposition method that couples local projection and Helmholtz decomposition. Background Art

[0002] The unsteady motion of a fluid medium generates aerodynamic noise, which is widespread in many fields, such as advanced supersonic aircraft, large aircraft, helicopters, automobiles, high-speed rails, and wind energy utilization and development. The flow and noise together constitute a complex flow-acoustic coupling field. In the far-field region far from the sound source of the fluid medium, it is usually composed only of acoustic modes. However, in the near-field region of the flow that we are concerned about, the sound field is part of the flow field. However, compared with the dynamic modes, the amplitude of the acoustic modes is usually several orders of magnitude smaller, and the acoustic modes are almost submerged in the dynamic modes, posing great challenges to revealing the near-field sound generation mechanism and sound source localization. Therefore, it is necessary to develop an efficient and accurate flow acoustic mode decomposition method.

[0003] The existing flow acoustic mode decomposition methods are divided into three categories.

[0004] One is the filtering decomposition based on signal analysis. This method mainly separates according to the difference in propagation speed between the dynamic mode and the acoustic mode. The dynamic mode propagates downstream at the convection velocity, while the acoustic mode propagates at the speed of sound. When the convection velocity is close to the speed of sound, such as in transonic flow, it is difficult to perform effective separation.

[0005] The second is the decomposition based on the difference in physical properties. This method is based on the Helmholtz decomposition of the fluid and separates according to the rotational and divergence-free characteristics of the dynamic mode and the compressible characteristics of the acoustic mode for a specific moment of the flow field.

[0006] The third is the decomposition based on data-driven methods, including proper orthogonal decomposition (POD), spectral proper orthogonal decomposition (SPOD), and dynamic mode decomposition (DMD). These methods extract the flow modes by performing dimensionality reduction decomposition on the time-series flow field data. However, POD, DMD, and SPOD all extract the dynamic mode structures with specific characteristics and cannot accurately obtain the dynamic modes and acoustic modes separately.

[0007] Recently, the inventors have proposed a flow-acoustic mode decomposition method that combines the second method with the third method, such as a flow-acoustic mode decomposition and fast prediction method coupling physical properties and data-driven (Patent No.: ZL 202111500578.X) and a flow-acoustic mode decomposition method, device, and equipment applicable to broadband noise flow (Patent No.: ZL202410192705.1). Such methods can achieve the separation of dynamic modes and acoustic modes in single-frequency noise-dominated flows, as well as the efficient decomposition of hydrodynamic modes and acoustic modes at characteristic frequencies in broadband noise spectra. However, such methods are based on DMD and SPOD decompositions, both of which are linear methods and are not applicable to non-linear processes in time, such as the noise generation behavior during flow bursting and the noise generation behavior during flow intermittency.

[0008] Therefore, it is necessary to develop a suitable flow-acoustic mode decomposition method for the non-linear problems existing in time series. Summary of the Invention

[0009] Aiming at the shortcoming that the existing technology is difficult to handle the non-linearity of time series, the present invention proposes a flow-acoustic mode decomposition method that couples the local projection method and Helmholtz decomposition, which can achieve the flow-acoustic mode decomposition of the non-linearly evolving flow velocity field.

[0010] To achieve the above invention purpose, the present invention provides a flow-acoustic mode decomposition method that couples local projection and Helmholtz decomposition, and the method includes: Step 1: Obtain the time series data of the velocity field of the fluid, perform local projection processing on the time series data of the velocity field to obtain the time series data of the velocity field of the turbulent coherent structure; based on the time series data of the velocity field and the time series data of the velocity field of the turbulent coherent structure, obtain the time series data of the velocity field of the turbulent disordered structure; Step 2: Perform Helmholtz decomposition on the time series data of the velocity field of the turbulent coherent structure and the time series data of the velocity field of the turbulent disordered structure respectively, and obtain the first decomposition result and the second decomposition result respectively; Step 3: Take the divergence of the first decomposition result and the second decomposition result to obtain the first Poisson equation and the second Poisson equation respectively; Step 4: Numerically solve the first Poisson equation and the second Poisson equation to obtain the first scalar potential and the second scalar potential respectively; Step 5: Take the gradient of the first scalar potential and the second scalar potential to obtain the acoustic mode velocity field of the turbulent coherent structure and the acoustic mode velocity field of the turbulent disordered structure respectively; Step 6: Calculate the turbulent coherent structure dynamic mode velocity field based on the time series data of the turbulent coherent structure velocity field and the turbulent coherent structure acoustic mode velocity field; calculate the turbulent disordered structure dynamic mode velocity field based on the time series data of the turbulent disordered structure velocity field and the turbulent disordered structure acoustic mode velocity field.

[0011] Among them, the principle of this method is to reconstruct the original flow field time series data into a l dimensional phase space. In this phase space, there is a hyperplane, and the deviation part between the phase point and the hyperplane represents the velocity field of the turbulent disordered structure. Subtracting this deviation part from the original velocity field, the turbulent coherent structure velocity field is obtained, which is applicable not only to the linear process in time but also to the non-linear process in time. On this basis, using Helmholtz decomposition to decompose the turbulent coherent structure velocity field and the turbulent disordered structure velocity field, the turbulent coherent structure acoustic mode velocity field and dynamic mode velocity field, as well as the turbulent disordered structure acoustic mode velocity field and dynamic mode velocity field can be obtained. The most important difference from the original method is that when the original method decomposes the time series to obtain the turbulent coherent structure velocity field and the turbulent disordered structure velocity field, it can only handle the linear process in time, while this method can handle the non-linear process in time. Therefore, this method can be applied to the analysis of the flow noise generation process that is non-linear in time, such as the noise generation behavior during flow bursts and the noise generation behavior during flow intermittency.

[0012] Preferably, step 1 specifically includes: Obtain the time series data of the fluid velocity field through experiments or numerical simulations; Obtain the velocity components in the three spatial directions of each spatial point in the time series data of the velocity field; Reconstruct the phase space for the time series data of the velocity components in the three directions to obtain the reconstructed data; Localize the phase points in the reconstructed data to obtain the processed phase points; Construct a covariance matrix based on the processed phase points; Obtain the eigenvalues and corresponding eigenvectors of the covariance matrix; Obtain the time series data of the turbulent coherent structure velocity field based on the phase points in the reconstructed data and the eigenvectors; Obtain the time series data of the turbulent disordered structure velocity field based on the time series data of the velocity field and the time series data of the turbulent coherent structure velocity field.

[0013] Preferably, the time series data of the fluid velocity field is u, u = ( u 1 , u 2, u 3 ), u 1 , u 2 and u 3 are respectively u the velocity components in three directions of space; The velocity components of each spatial point in three directions of space are u j , j=1,2,3 , u j The time series data of: ; N is the time series number of the flow field segment, is the i th velocity field segment, i = 1, 2, …, N ; The n th phase point in the reconstructed data is Y n , Y n The calculation method of is: ; Among them, l is the embedding space dimension, and τ is the lag time.

[0014] Preferably, the following formula is used to localize the phase point Y n in the reconstructed data: ; Among them, R is the diagonal weight matrix, is Y n the centroid of the phase points in the neighborhood ζ n , Z n is Y n the local projection matrix of; ; Among them, q is Y n the serial number of the phase points included in the neighborhood ζ n , Y q is the q th phase point.

[0015] Preferably, the covariance matrix is C , C the component of C ij The expression is: ; wherein, Z q is Y q the local projection matrix of is the Z q th i row of the matrix is the Z q th j column of the matrix Subtract C the eigenvalues of λ q from smallest to largest, and obtain λ q the corresponding eigenvectors as a q , q = 1, …, m ; Subtract the eigenvectors corresponding to the C first λ q smallest eigenvalues of Q from Y n to obtain the processed phase points ; ; wherein, Q is the number of eigenvalues subtracted; wherein, ; Based on obtain the flow field time series after local projection processing; Based on the flow field time series after local projection processing, obtain the turbulent coherent structure velocity field time series data , , , and are respectively the velocity components in three directions of space; Based on the velocity field time series data u and the turbulent coherent structure velocity field time series data , obtain the turbulent incoherent structure velocity field time series data ; Among them, .

[0016] Preferably, the following formula is used for Helmholtz decomposition of the time series data of the turbulent coherent structure velocity field : ; Among them, is the first scalar potential, is the first vorticity mode vector potential, and ∇ is the gradient operator; The following formula is used for Helmholtz decomposition of the time series data of the turbulent disordered structure velocity field : ; Among them, is the second scalar potential, is the second vorticity mode vector potential.

[0017] Preferably, the first Poisson equation is: ; The second Poisson equation is: ; Among them, ∇ 2 is the divergence of the gradient.

[0018] Preferably, the acoustic mode velocity field of the turbulent coherent structure is , and the calculation method is: ; The acoustic mode velocity field of the turbulent disordered structure is , and the calculation method is: ; Among them, ∇ is the gradient operator, is the first scalar potential, is the second scalar potential.

[0019] Preferably, the dynamic mode velocity field of the turbulent coherent structure is , and the calculation method is: ; The dynamic mode velocity field of the turbulent disordered structure is , and the calculation method is: ; Among them, is the time series data of the turbulent coherent structure velocity field, is the acoustic mode velocity field of the turbulent coherent structure, is the time series data of the turbulent disordered structure velocity field, It is the sound mode velocity field of the turbulent disordered structure.

[0020] Preferably, the method further includes: Step 7: Perform target sound source localization based on the dynamic mode velocity field of the turbulent coherent structure and the dynamic mode velocity field of the turbulent disordered structure.

[0021] One or more technical solutions provided by the present invention have at least the following technical effects or advantages: The present invention is directed to the nonlinearly evolving flow velocity field, and adopts a coupling method of local projection and Helmholtz decomposition to perform flow-acoustic mode decomposition on the nonlinearly evolving flow velocity field. Since the local projection method adopted in Step 1 is applicable to nonlinear time series analysis, the velocity fields corresponding to the turbulent coherent structure and the turbulent disordered structure can be obtained respectively, and the Helmholtz decomposition can obtain the dynamic modes and sound modes of the velocity field at a specific moment. Therefore, based on the coupling method of local projection and Helmholtz decomposition, the flow-acoustic mode decomposition of the nonlinearly evolving flow velocity field can be performed. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, and constitute a part of the present invention, but do not limit the embodiments of the present invention; Figure 1 It is a schematic flow chart of a flow-acoustic mode decomposition method coupling local projection and Helmholtz decomposition. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] In order to more clearly understand the above objects, features and advantages of the present invention, the present invention will be further described in detail below with reference to the drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0024] Many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention may be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0025] Embodiment 1; Please refer to Figure 1 , Figure 1 It is a schematic flow chart of a flow-acoustic mode decomposition method coupling local projection and Helmholtz decomposition. The present invention provides a flow-acoustic mode decomposition method coupling local projection and Helmholtz decomposition. The present invention performs local projection method and Helmholtz coupling decomposition on the velocity field time series data obtained from experiments or numerical simulations to achieve the flow-acoustic mode decomposition of the nonlinearly evolving flow velocity field.

[0026] The method includes: Step 1: Obtain the time series data of the velocity field of the fluid, and perform local projection processing on the time series data of the velocity field to obtain the time series data of the velocity field of the turbulent coherent structure; based on the time series data of the velocity field and the time series data of the velocity field of the turbulent coherent structure, obtain the time series data of the velocity field of the turbulent disordered structure; Step 2: Perform Helmholtz decomposition on the time series data of the velocity field of the turbulent coherent structure and the time series data of the velocity field of the turbulent disordered structure respectively, and obtain the first decomposition result and the second decomposition result respectively; Step 3: Take the divergence of the first decomposition result and the second decomposition result to obtain the first Poisson equation and the second Poisson equation respectively; Step 4: Numerically solve the first Poisson equation and the second Poisson equation to obtain the first scalar potential and the second scalar potential respectively; Step 5: Take the gradient of the first scalar potential and the second scalar potential to obtain the acoustic mode velocity field of the turbulent coherent structure and the acoustic mode velocity field of the turbulent disordered structure respectively; Step 6: Calculate the dynamic mode velocity field of the turbulent coherent structure based on the time series data of the velocity field of the turbulent coherent structure and the acoustic mode velocity field of the turbulent coherent structure; calculate the dynamic mode velocity field of the turbulent disordered structure based on the time series data of the velocity field of the turbulent disordered structure and the acoustic mode velocity field of the turbulent disordered structure.

[0027] Among them, in the embodiment of the present invention, the specific content of the step 1 includes: Obtain the time series data of the velocity field of the fluid through experiments or numerical simulations; the time series data of the velocity field of the fluid is u ; Obtain the velocity components in the three directions of space at each spatial point in the time series data of the velocity field; u = ( u 1 , u 2 , u 3 ), u 1 , u 2 and u 3 are respectively u the velocity components in the three directions of space; For each component of each spatial point in the time series data of the velocity field u perform the following operations on u j （j=1,2,3） perform the following operations on u j the time series data of ( Nis the number of time series of the flow field segment, is the i th velocity field segment) to reconstruct the phase space. Let Y n be its n th phase point, Y n is calculated as follows: ; (1) where is the embedding space dimension and τ is the time delay. The Y n is localized as follows: ; (2) where R is the diagonal weight matrix, is Y n neighborhood ζ n the centroid of the phase points inside, that is, satisfying: ; (3) C is Z n the covariance matrix of, and the expressions of its components are: ; (4) Subtract the eigenvector corresponding to the smallest eigenvalue from the acoustic signal time series, that is: C the eigenvalues of λ q are arranged in ascending order to obtain the corresponding eigenvectors as a q , q = 1,..., m ; Subtract the eigenvector corresponding to the smallest eigenvalue from the acoustic signal time series, that is: ; (5) where .

[0028] Thus, the flow field time series after local projection processing is obtained. Each component u j （j= 1,2,3） After processing, the time series data of the velocity field of the turbulent coherent structure after local projection processing is obtained, corresponding to the part where the turbulent coherent structure of the flow dominates, while the time series data of the velocity field of the turbulent disordered structure is: . (6) Among them, in the embodiments of the present invention, the following formula is used for the time series data of the velocity field of the turbulent coherent structure and the time series data of the velocity field of the turbulent disordered structure to perform Helmholtz decomposition, which is characterized by the scalar potential gradient and the vector potential curl. The former represents the acoustic mode velocity, and the latter represents the kinetic mode velocity: ; (7) where is the first scalar potential, is the first vorticity mode vector potential, and ∇ is the gradient operator; ; (8) where is the second scalar potential, is the second vorticity mode vector potential.

[0029] Taking the divergence of both sides of the Helmholtz decomposition formulas (7) and (8) simultaneously gives the first and second Poisson equations. The first Poisson equation is: ; (9) The second Poisson equation is: ; (10) where ∇ 2 is the divergence of the gradient.

[0030] The numerical solutions of the Poisson equations (9) and (10) are obtained by using Gauss - Seidel iteration or successive over - relaxation iteration or SSOR iteration to obtain the first and second scalar potentials.

[0031] Taking the gradient of the first and second scalar potentials can respectively obtain the acoustic mode velocity field of the turbulent coherent structure as and the acoustic mode velocity field of the turbulent disordered structure as , and the calculation method is: ; (11) ; (12) where ∇ is the gradient operator, is the first scalar potential, is the second scalar potential.

[0032] Subsequently, the kinetic mode velocity fields of the turbulent coherent structure and the turbulent disordered structure can be respectively obtained by simple subtraction. The kinetic mode velocity field of the turbulent coherent structure is , and the calculation method is: ; (13) The kinetic mode velocity field of the turbulent disordered structure is , the calculation method is as follows: ; (14) wherein, is the time series data of the velocity field of the turbulent coherent structure, is the acoustic mode velocity field of the turbulent coherent structure, is the time series data of the velocity field of the turbulent disordered structure, is the acoustic mode velocity field of the turbulent disordered structure.

[0033] Through the above steps, based on the original velocity field data, the flow-acoustic mode decomposition of the nonlinearly evolving flow velocity field is realized. The present invention is directed to the nonlinearly evolving flow velocity field, and adopts a coupling method of local projection and Helmholtz decomposition to perform flow-acoustic mode decomposition on the nonlinearly evolving flow velocity field.

[0034] The present invention performs local projection on the velocity field to obtain the velocity fields corresponding to the turbulent coherent structure and the turbulent disordered structure, and then performs Helmholtz decomposition on the two velocity fields to obtain the dynamic mode and the acoustic mode (corresponding to formulas (7)-(14)), realizing the flow-acoustic mode decomposition of the nonlinearly evolving flow velocity field.

[0035] Embodiment 2; Embodiment 2 of the present invention provides a sound source localization method, and the sound source localization method includes: On the basis of Embodiment 1, the acoustic mode velocity field of the turbulent coherent structure is obtained as and the acoustic mode velocity field of the turbulent disordered structure is . Taking the flow-induced problems caused by the high-speed jet ejected from the aircraft engine as an example, the noise therein includes the noise generated by the large-scale turbulent structure and the noise generated by the small-scale turbulent structure. The noise generated by the large-scale turbulent structure corresponds to the acoustic mode of the turbulent coherent structure, which is the velocity field corresponding to the acoustic mode of the large-scale turbulent structure. The noise generated by the small-scale turbulent structure corresponds to the acoustic mode of the turbulent disordered structure, which is the velocity field corresponding to the acoustic mode of the small-scale turbulent structure. In practical applications, usually more attention is paid to the sound source area of the turbulent coherent structure, and the area with a larger amplitude is the sound source position of the turbulent coherent structure. By setting a threshold , the smaller amount of is filtered out to obtain ; . (15) The corresponding spatial region is the sound source position of the turbulent coherent structure.

[0036] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once they learn of the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications that fall within the scope of the present invention.

[0037] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition, characterized in that, The method includes: Step 1: Obtain the time series data of the velocity field of the fluid, and perform local projection processing on the time series data of the velocity field to obtain the time series data of the velocity field of the turbulent coherent structure; based on the time series data of the velocity field and the time series data of the velocity field of the turbulent coherent structure, obtain the time series data of the velocity field of the turbulent disordered structure; Step 2: Perform Helmholtz decomposition on the time series data of the velocity field of the turbulent coherent structure and the time series data of the velocity field of the turbulent disordered structure respectively, and obtain the first decomposition result and the second decomposition result respectively; Step 3: Take the divergence of the first decomposition result and the second decomposition result to obtain the first Poisson equation and the second Poisson equation respectively; Step 4: Numerically solve the first Poisson equation and the second Poisson equation to obtain the first scalar potential and the second scalar potential respectively; Step 5: Take the gradient of the first scalar potential and the second scalar potential to obtain the acoustic mode velocity field of the turbulent coherent structure and the acoustic mode velocity field of the turbulent disordered structure respectively; Step 6: Calculate the dynamic mode velocity field of the turbulent coherent structure based on the time series data of the velocity field of the turbulent coherent structure and the acoustic mode velocity field of the turbulent coherent structure; calculate the dynamic mode velocity field of the turbulent disordered structure based on the time series data of the velocity field of the turbulent disordered structure and the acoustic mode velocity field of the turbulent disordered structure.

2. The flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 1, characterized in that, The specific content of Step 1 includes: Obtain the time series data of the velocity field of the fluid through experiments or numerical simulations; Obtain the velocity components in the three spatial directions of each spatial point in the time series data of the velocity field; Reconstruct the phase space of the time series data of the velocity components in the three directions to obtain the reconstructed data; Localize the phase points in the reconstructed data to obtain the processed phase points; Construct a covariance matrix based on the processed phase points; Obtain the eigenvalues of the covariance matrix and the corresponding eigenvectors; Obtain the time series data of the velocity field of the turbulent coherent structure based on the phase points in the reconstructed data and the eigenvectors; Based on the time series data of the velocity field and the time series data of the velocity field of the turbulent coherent structure, obtain the time series data of the velocity field of the turbulent disordered structure.

3. The flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 2, characterized in that: The time series data of the velocity field of the fluid is u, u = ( u 1 , u 2 , u 3 ), u 1 , u 2 and u 3 are respectively u the velocity components in the three directions of space; The velocity components of each spatial point in the three directions of space are u j , j=1,2,3 , u j . The time series data is: ; N is the time series number of the flow field segment, is the i th velocity field segment, i = 1, 2, …, N ; The n th phase point in the reconstructed data is Y n , Y n is calculated as follows: ； where l is the embedding space dimension and τ is the time delay.

4. The flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 3, characterized in that, The phase points in the reconstructed data are processed locally using the following formula Y n as follows: ； Among them, R is the diagonal weight matrix, is Y n the neighborhood ζ n the centroid of the inner phase points, Z n is Y n the local projection matrix of ； Among them, q is Y n the neighborhood ζ n the serial number of the included phase points, Y q is the q th phase point.

5. The flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 4, characterized in that, The covariance matrix is C , C components of C ij The expression is: ； Among them, Z q is Y q the local projection matrix of, is the matrix Z q the i th row of, is the matrix Z q the j th column of; Arrange the C eigenvalues λ q in ascending order to obtain λ q The corresponding eigenvectors are a q , q = 1, …, m ; Subtract C the eigenvalues of λ q the first smallest Q eigenvectors corresponding to the eigenvalues from Y n to obtain the processed phase points ; ； Among them, Q is the number of partial eigenvalues subtracted; Among them, ; Based on Obtain the time series of the flow field after local projection processing ; Based on the time series of the flow field after local projection processing , the time series data of the velocity field of the turbulent coherent structure is obtained , , , and are respectively the velocity components in three directions of space; Based on the time series data of the velocity field u and the time series data of the velocity field of the coherent structures in turbulence , the time series data of the velocity field of the disordered structures in turbulence is obtained ; Among them, 。 6. A flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 1, characterized in that, The time series data of the velocity field of the turbulent coherent structure is decomposed by Helmholtz decomposition using the following formula as follows: ； wherein, is the first scalar potential, is the first vorticity mode vector potential, and ∇ is the gradient operator; The time series data of the velocity field of the turbulent disordered structure is decomposed by Helmholtz decomposition using the following formula: Perform Helmholtz decomposition on it: ； Among them, is the second scalar potential, is the second vorticity mode vector potential.

7. A flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 6, characterized in that, The first Poisson equation is: ； The second Poisson equation is: ； where ∇ 2 is the divergence of the gradient.

8. A flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 1, characterized in that, The velocity field of the acoustic mode of the turbulent coherent structure is , and the calculation method is as follows: ； The acoustic mode velocity field of the turbulent disordered structure is , and the calculation method is as follows: ； where ∇ is the gradient operator, is the first scalar potential, is the second scalar potential.

9. A flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 1, characterized in that, The dynamic modal velocity field of the turbulent coherent structure is , and the calculation method is as follows: ； The dynamic modal velocity field of the turbulent disordered structure is , and the calculation method is as follows: ； Among them, is the time series data of the velocity field of the turbulent coherent structure, is the acoustic mode velocity field of the turbulent coherent structure, is the time series data of the velocity field of the turbulent disordered structure, is the acoustic mode velocity field of the turbulent disordered structure.

10. A flow-acoustic modal decomposition method coupling local projection and Helmholtz decomposition according to claim 1, characterized in that, The method further includes: Step 7: Perform target sound source localization based on the dynamic mode velocity field of the turbulent coherent structure and the dynamic mode velocity field of the turbulent disordered structure.

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