A method for simulating and analyzing aerodynamic noise of a multi-perforated medium material multi-section airfoil

Abstract

This invention relates to the field of multi-segment airfoil analysis technology, specifically to a method for simulating and analyzing the aerodynamic noise of multi-segment airfoils using porous media materials. The method includes: establishing a multi-segment airfoil model; adding a porous media material to the multi-segment airfoil; setting the permeability of the porous media material and the operating conditions of the multi-segment airfoil; using the LBM-LES algorithm to numerically calculate the flow field and sound field of the multi-segment airfoil model after using the porous media material; comparing the changes in the flow field and sound field of the multi-segment airfoil under different permeabilities and operating conditions, and analyzing the influence of the porous media material on the aerodynamic noise generation of the multi-segment airfoil. This invention, based on the LBM-LES algorithm, is accurate and feasible for directly calculating the complex sound field of multi-segment airfoils, and has certain guiding significance for the analysis of aerodynamic noise control of multi-segment airfoils.

Description

Technical Field

[0001] This invention relates to the field of multi-segment airfoil analysis technology, specifically to a method for simulating and analyzing the aerodynamic noise of a multi-segment airfoil made of porous media materials. Background Technology

[0002] In recent years, research on reducing trailing-edge noise by using porous media materials on airfoils has made some progress both domestically and internationally. This research primarily employs experimental methods or numerical simulations using simplified porous media step surface models, achieving noise reduction over a wide frequency range. It has been shown that locally applying porous media materials at the trailing edge can reduce aerodynamic noise at the airfoil's trailing edge while maintaining or minimizing aerodynamic performance loss. However, current research lacks in-depth investigation of airfoil aerodynamic noise and porous media with different permeabilities, making it impossible to analyze the noise reduction mechanism of porous media at different permeabilities.

[0003] Therefore, it is necessary to design an aerodynamic noise simulation and analysis method for multi-segment airfoils made of porous media materials. Summary of the Invention

[0004] The purpose of this invention is to at least solve one of the technical problems existing in the prior art, and to provide a method for simulating and analyzing the aerodynamic noise of a multi-segment airfoil made of porous media material.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for aerodynamic noise simulation and analysis of multi-segment airfoils made of porous media materials, comprising the following steps:

[0006] Step 1: Establish a multi-segment airfoil model and add porous media material to the multi-segment airfoil;

[0007] Step 2: Set the permeability of the porous media material and the operating conditions of the multi-segment airfoil;

[0008] Step 3: The LBM-LES algorithm is used to numerically calculate the flow field and sound field of the multi-segment airfoil model after using porous media material;

[0009] Step 4: Compare the changes in flow field and sound field of multi-segment airfoils under different permeabilities and operating conditions, and analyze the influence of porous media materials on the aerodynamic noise of multi-segment airfoils.

[0010] Furthermore, in step 1, the multi-segment airfoil model adopts a high-lift configuration, which includes slats, main wings, and flaps.

[0011] Furthermore, in step 1, the porous medium material is disposed at the slits of the multi-segment airfoil.

[0012] Furthermore, step 3 specifically includes:

[0013] Quadtree meshes were used to divide the computational domain of the multi-segment airfoil model.

[0014] By coupling the LBM algorithm with the LES algorithm, we obtain the LBM-LES algorithm.

[0015] The LBM-LES algorithm is used to perform numerical calculations on the computational domain.

[0016] Furthermore, the LBM algorithm is coupled with the LES algorithm to obtain the LBM-LES algorithm; specifically, this includes:

[0017] The Navier-Stokes equations were solved using the LBM algorithm to obtain the original solution;

[0018] Turbulence effects below the lattice scale are modeled using a sub-lattice model;

[0019] Spatial or temporal filtering operations are performed on the original solution to remove small-scale turbulent structures and leave large-scale vortices.

[0020] By using a subgrid model, eddy viscosity is incorporated into the calculation of small-scale eddies, while keeping the original equations unchanged.

[0021] The eddy viscosity obtained from the subgrid model is introduced into the LBM algorithm in the form of equivalent viscosity, and the coupling of the LBM algorithm and the LES algorithm is achieved by modifying the relaxation time.

[0022] Furthermore, the LBM algorithm is used to solve the Navier-Stokes equations to obtain the original solution; specifically, this includes:

[0023] The incompressible Navier-Stokes equations in the lattice Boltzmann method take the following form:

[0024] ;

[0025] in, Indicates the time interval Inside, the particle moves from position x with a velocity Move to position Probability changes; collision terms Describes the time interval The collisions between particles within the particle alter the distribution function;

[0026] The collision form of the multi-relaxation time model is represented as:

[0027] ;

[0028] In the single relaxation factor model or the BGK collision operator model, the collision form is as follows: ;

[0029] The D2Q9 discrete velocity model describes nine possible velocity directions in two-dimensional space:

[0030] ; in, This represents the macroscopic density of the fluid. Represents the macroscopic velocity vector of the fluid. Represents the speed of sound in a lattice. The first in the discrete velocity model A discrete velocity vector;

[0031] weighting coefficients This represents the weight of each velocity component. Corresponding to the discrete velocity direction:

[0032] ;

[0033] The matrix M of the D2Q9-MRT model has the following specific form:

[0034] ;

[0035] The relaxation matrix is ​​a diagonal matrix, and its diagonal elements represent the relaxation factors of each velocity component. The specific form obtained through linearization analysis is as follows:

[0036] ;

[0037] in, It is the relaxation factor for the i-th velocity component;

[0038] Finally, relaxation time With fluid shear viscosity The relationship between them can be expressed by the following formula:

[0039] ;

[0040] in, Indicates the speed of sound. Indicates the time step;

[0041] The volumetric viscosity needs to be increased for noise calculations. The relationship between it and the relaxation factor is as follows:

[0042] ;

[0043] in, This is the noise relaxation time.

[0044] Furthermore, the eddy viscosity obtained from the subgrid model is introduced into the LBM algorithm in the form of equivalent viscosity, and the coupling between the LBM and LES algorithms is achieved by modifying the relaxation time; specifically including:

[0045] Eddy viscosity can be expressed as:

[0046] ;

[0047] In the above formula, Represented as subgrid model coefficients, This is the grid filtering scale, typically taken as the grid size;

[0048] Represented as strain variable after filtration; total viscosity Represented as dynamic viscosity vorticity With fluid dynamic viscosity sum;

[0049] ;

[0050] At each time step, the equivalent viscosity and relaxation time are dynamically updated based on the instantaneous velocity field.

[0051] As can be seen from the above description of the present invention, compared with the prior art, the aerodynamic noise simulation and analysis method for porous dielectric material multi-segment airfoils of the present invention has at least one of the following beneficial effects:

[0052] 1. This invention designs the LBM-LES algorithm, which directly calculates the flow field and sound field of a multi-segment airfoil with added porous media material. The calculated surface pressure coefficient and the position of the discretized peak of the Strouhal number are in good agreement with the experimental values. This invention is accurate and feasible for direct numerical calculation of the complex sound field of a multi-segment airfoil based on the LBM-LES algorithm, and has certain guiding significance for the analysis of aerodynamic noise control of multi-segment airfoils.

[0053] 2. The commonly used Smagorinsky subgrid model has certain limitations in simulating multi-scale flows. This invention introduces eddy viscosity into the calculation of small-scale eddies while keeping the original equations unchanged. This allows the LBM-LES algorithm to better simulate flows at high Reynolds numbers, improving the accuracy and applicability of the simulation. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the steps of an aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous media material, according to a preferred embodiment of the present invention.

[0055] Figure 2 This is a comparison diagram of the pressure coefficient distribution on the surface of the solid airfoil in a preferred embodiment of the present invention;

[0056] Figure 3 This is a sound pressure spectrum diagram in a preferred embodiment of the present invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0058] Reference Figure 1 As shown in the preferred embodiment of the present invention, an aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous dielectric material includes the following steps:

[0059] Step 1: Establish a multi-segment airfoil model and add porous media material to the multi-segment airfoil;

[0060] Step 2: Set the permeability of the porous media material and the operating conditions of the multi-segment airfoil;

[0061] Step 3: The LBM-LES algorithm is used to numerically calculate the flow field and sound field of the multi-segment airfoil model after using porous media material;

[0062] Step 4: Compare the changes in flow field and sound field of multi-segment airfoils under different permeabilities and operating conditions, and analyze the influence of porous media materials on the aerodynamic noise of multi-segment airfoils.

[0063] As a preferred embodiment of the present invention, it may also have the following additional technical features:

[0064] In this embodiment, in step 1, the multi-segment airfoil model adopts a high-lift configuration, which includes slats, main wings, and flaps.

[0065] In this embodiment, in step 1, the porous medium material is disposed at the slits of the multi-segment airfoil.

[0066] To investigate the sound source at the slats, and to explore the influence of porous media materials with different permeabilities on the aerodynamic noise of multi-segment airfoils, six porous media materials with different permeabilities were used for analysis without changing their location and size. The permeabilities, from highest to lowest, were k=1.789e-7m. 2 k=1.789e-8m 2 k=8.947e-8m 2k=8.947e-9m 2 k=1.789e-9m 2 k = 1.789e-10m 2 In order to better study the noise reduction effect of porous media materials on multi-segment airfoils at different angles of attack, three different angles of attack, namely 0°, 4° and 8°, were selected.

[0067] In this embodiment, step 3 specifically includes:

[0068] Quadtree meshes were used to divide the computational domain of the multi-segment airfoil model.

[0069] By coupling the LBM algorithm with the LES algorithm, we obtain the LBM-LES algorithm.

[0070] The LBM-LES algorithm is used to perform numerical calculations on the computational domain.

[0071] In this embodiment, the coupling of the LBM algorithm and the LES algorithm to obtain the LBM-LES algorithm specifically includes:

[0072] The Navier-Stokes equations were solved using the LBM algorithm to obtain the original solution;

[0073] Turbulence effects below the lattice scale are modeled using a sub-lattice model;

[0074] Spatial or temporal filtering operations are performed on the original solution to remove small-scale turbulent structures and leave large-scale vortices.

[0075] By using a subgrid model, eddy viscosity is incorporated into the calculation of small-scale eddies, while keeping the original equations unchanged.

[0076] The eddy viscosity obtained from the subgrid model is introduced into the LBM algorithm in the form of equivalent viscosity, and the coupling of the LBM algorithm and the LES algorithm is achieved by modifying the relaxation time.

[0077] In this embodiment, the step of using the LBM algorithm to solve the Navier-Stokes equations to obtain the original solution specifically includes:

[0078] The incompressible Navier-Stokes equations in the lattice Boltzmann method take the following form:

[0079] ;

[0080] in, Indicates the time interval Inside, the particle moves from position x with a velocity Move to position Probability changes; collision terms Describes the time interval The collisions between particles within the particle alter the distribution function;

[0081] The collision form of the multi-relaxation time model is represented as:

[0082] ;

[0083] In the single relaxation factor model or the BGK collision operator model, the collision form is as follows: ;

[0084] The D2Q9 discrete velocity model describes nine possible velocity directions in two-dimensional space:

[0085] ; in, This represents the macroscopic density of the fluid. Represents the macroscopic velocity vector of the fluid. Represents the speed of sound in a lattice. The first in the discrete velocity model A discrete velocity vector;

[0086] weighting coefficients This represents the weight of each velocity component. Corresponding to the discrete velocity direction:

[0087] ;

[0088] The matrix M of the D2Q9-MRT model has the following specific form:

[0089] ;

[0090] The relaxation matrix is ​​a diagonal matrix, and its diagonal elements represent the relaxation factors of each velocity component. The specific form obtained through linearization analysis is as follows:

[0091] ;

[0092] in, It is the relaxation factor for the i-th velocity component;

[0093] Finally, relaxation time With fluid shear viscosity The relationship between them can be expressed by the following formula:

[0094] ;

[0095] in, Indicates the speed of sound. Indicates the time step;

[0096] The volumetric viscosity needs to be increased for noise calculations. The relationship between it and the relaxation factor is as follows:

[0097] ;

[0098] in, This is the noise relaxation time.

[0099] In this embodiment, the eddy viscosity obtained from the subgrid model is introduced into the LBM algorithm in the form of equivalent viscosity, and the coupling between the LBM algorithm and the LES algorithm is achieved by modifying the relaxation time; specifically including:

[0100] Eddy viscosity can be expressed as:

[0101] ;

[0102] In the above formula, Represented as subgrid model coefficients, This is the grid filtering scale, typically taken as the grid size;

[0103] Represented as strain variable after filtration; total viscosity Represented as dynamic viscosity vorticity With fluid dynamic viscosity sum;

[0104] ;

[0105] At each time step, the equivalent viscosity and relaxation time are dynamically updated based on the instantaneous velocity field.

[0106] The present invention has been verified by numerical calculations, as follows:

[0107] To verify the reliability of the numerical calculation method used, the LBM-LES algorithm was used to directly calculate the sound field of the 30P30N airfoil with a Reynolds number of 1.0e+6 (based on a chord length of C = 0.5 m), a sampling frequency of 3835.233 Hz, and an angle of attack of 4°. The specific calculation parameters are shown in the table below.

[0108] Operating conditions and calculation parameter table

[0109] parameter value Incoming flow velocity (m / s) 34 Dynamic viscosity coefficient 1.789e-5 Reynolds number 1.0e+6 Angle of attack (°) 4

[0110] The pressure coefficient of the solid airfoil surface obtained by numerical calculation under this working condition is compared with the surface pressure coefficient obtained by Pagani et al. using wind tunnel experiments. The results are as follows: Figure 2As shown, EXP represents the value obtained by Pagani et al. using wind tunnel experiments. The numerical calculation of the airfoil surface pressure coefficient obtained in this invention is in good agreement with the experimental value of the airfoil surface pressure coefficient.

[0111] To further verify the sound pressure spectrum characteristics of the multi-segment airfoil, sound pressure spectrum analysis was performed at the monitoring points (2C, 0.5C) on the trailing edge, and the resulting sound pressure spectrum diagram is shown below. Figure 3 As shown in the figure, a relatively obvious peak is observed at (St=1.85, 2.69, 3.48, 4.36). The discretized peak positions of the Strouhal number obtained by numerical calculation using the LBM-LES algorithm are compared with the results obtained by Pagani et al. using wind tunnel experiments and Souza et al. using the LBM-FW-H method under the same conditions. The results are shown in the table below:

[0112] Strouhal number discretization peak table

[0113] n 1 2 3 4 EXP 1.85 2.72 3.50 4.46 LBM-FW-H 1.88 2.76 3.53 4.41 LBM-LES 1.83 2.69 3.48 4.36

[0114] The peak positions of the Strouhal number discretization are basically consistent. This indicates that using the LBM-LES algorithm to calculate the aerodynamic noise of multi-segment airfoils has good reliability and accuracy.

[0115] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and its improved concept, should be covered within the scope of protection of the present invention.

Claims

1. A method for simulating and analyzing aerodynamic noise of a multi-segment airfoil made of porous media materials, characterized in that, Includes the following steps: Step 1: Establish a multi-segment airfoil model and add porous media material to the multi-segment airfoil; Step 2: Set the permeability of the porous media material and the operating conditions of the multi-segment airfoil; Step 3: The LBM-LES algorithm is used to numerically calculate the flow field and sound field of the multi-segment airfoil model after using porous media material; Step 4: Compare the changes in flow field and sound field of multi-segment airfoils under different permeabilities and operating conditions, and analyze the influence of porous media materials on the aerodynamic noise of multi-segment airfoils.

2. The aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous dielectric material according to claim 1, characterized in that, In step 1, the multi-segment airfoil model adopts a high-lift configuration, which includes slats, main wings, and flaps.

3. The aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous media material according to claim 1, characterized in that, In step 1, the porous medium material is disposed at the slits of the multi-segment airfoil.

4. The aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous media material according to claim 1, characterized in that, Step 3 specifically includes: Quadtree meshes were used to divide the computational domain of the multi-segment airfoil model. By coupling the LBM algorithm with the LES algorithm, we obtain the LBM-LES algorithm. The LBM-LES algorithm is used to perform numerical calculations on the computational domain.

5. The aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous media material according to claim 1, characterized in that, The LBM algorithm is coupled with the LES algorithm to obtain the LBM-LES algorithm; specifically, this includes: The Navier-Stokes equations were solved using the LBM algorithm to obtain the original solution; Turbulence effects below the lattice scale are modeled using a sub-lattice model; Spatial or temporal filtering operations are performed on the original solution to remove small-scale turbulent structures and leave large-scale vortices. By using a subgrid model, eddy viscosity is incorporated into the calculation of small-scale eddies, while keeping the original equations unchanged. The eddy viscosity obtained from the subgrid model is introduced into the LBM algorithm in the form of equivalent viscosity, and the coupling of the LBM algorithm and the LES algorithm is achieved by modifying the relaxation time.

6. The aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous media material according to claim 5, characterized in that, The method of using the LBM algorithm to solve the Navier-Stokes equations to obtain the original solution includes: The incompressible Navier-Stokes equations in the lattice Boltzmann method take the following form: ； in, Indicates the time interval Inside, the particle moves from position x with a velocity Move to position Probability changes; collision terms Describes the time interval The collisions between particles within the particle alter the distribution function; The collision form of the multi-relaxation time model is represented as: ； In the single relaxation factor model or the BGK collision operator model, the collision form is as follows: ； The D2Q9 discrete velocity model describes nine possible velocity directions in two-dimensional space: ； in, This represents the macroscopic density of the fluid. Represents the macroscopic velocity vector of the fluid. Represents the speed of sound in a lattice. The first in the discrete velocity model A discrete velocity vector; weighting coefficients This represents the weight of each velocity component. Corresponding to the discrete velocity direction: ； The matrix M of the D2Q9-MRT model has the following specific form: ； The relaxation matrix is ​​a diagonal matrix, and its diagonal elements represent the relaxation factors of each velocity component. The specific form obtained through linearization analysis is as follows: ； in, It is the relaxation factor for the i-th velocity component; Finally, relaxation time With fluid shear viscosity The relationship between them can be expressed by the following formula: ； in, Indicates the speed of sound. Indicates the time step; The volumetric viscosity needs to be increased for noise calculations. The relationship between it and the relaxation factor is as follows: ； in, This is the noise relaxation time.

7. The aerodynamic noise simulation and analysis method for a multi-segment airfoil made of porous media material according to claim 6, characterized in that, The eddy viscosity obtained from the subgrid model is introduced into the LBM algorithm in the form of equivalent viscosity, and the coupling between the LBM and LES algorithms is achieved by modifying the relaxation time; specifically including: Eddy viscosity can be expressed as: ； In the above formula, Represented as subgrid model coefficients, This is the grid filtering scale, typically taken as the grid size; Represented as strain variable after filtration; total viscosity Represented as dynamic viscosity vorticity With fluid dynamic viscosity sum; ； At each time step, the equivalent viscosity and relaxation time are dynamically updated based on the instantaneous velocity field.

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