A U-Net transonic two-dimensional airfoil flow field prediction method fusing finite volume method geometric metric characteristics

Abstract

A U-Net transonic two-dimensional airfoil flow field prediction method, incorporating the geometric metric features of the finite volume method, belongs to the field of fluid dynamics computational technology. This invention addresses the problem of improving the efficiency and applicability of flow field simulation. The method includes sampling the transonic two-dimensional airfoil flow field to construct a two-dimensional airfoil flow field dataset, divided into training, testing, and validation sets; constructing a U-Net flow field prediction network; training the constructed U-Net flow field prediction network using the obtained training set to obtain a trained U-Net flow field prediction network; and using the testing set to rapidly predict the transonic two-dimensional airfoil flow field using the trained U-Net flow field prediction network. This invention significantly enhances the practical value of online aerodynamic optimization and digital wind tunnel applications.

Description

Technical Field

[0001] This invention belongs to the field of fluid dynamics computational technology, specifically relating to a U-Net transonic two-dimensional airfoil flow field prediction method that integrates the geometric metric features of the finite volume method. Background Technology

[0002] With the rapid development of aviation technology, the requirements for the aerodynamic performance of airfoils are becoming increasingly stringent. As a key aerodynamic component of aircraft, the accurate prediction of the flow field around the airfoil is crucial for the evaluation and optimization of aircraft performance. In the preliminary design phase, aerodynamic engineers typically need to rapidly iterate multiple design schemes to make initial decisions. Wind tunnel testing is the traditional method for obtaining the airfoil flow field and aerodynamic characteristics. Based on the test results, continuous optimization and iteration are performed until the designed airfoil meets the flow field and aerodynamic characteristic requirements. This entire process consumes a significant amount of resources. Later, computational fluid dynamics (CFD) methods became the mainstream for airfoil optimization design, reducing excessive reliance on wind tunnel testing. Although traditional CFD methods are mature in airfoil flow field simulation, they face problems such as high computational costs and long computation times, especially under complex flow conditions, such as high Reynolds numbers, large angles of attack, and high Mach numbers. In the airfoil optimization design process, the computational efficiency of aerodynamic characteristics is of utmost concern, which can sometimes lead to unacceptable computation time. These problems limit the application of CFD in rapid design iteration and optimization processes. In addressing the time-consuming nature of airfoil optimization design, both domestically and internationally, most methods employ simplified flow field solvers or approximation techniques, which are all indirect approaches. Research indicates that such optimization designs yield low accuracy and significant errors. Therefore, developing a method capable of rapidly and accurately reconstructing the flow field around an airfoil is of significant practical importance.

[0003] The rapid development of artificial intelligence technology in recent years has led to the application of deep learning methods, represented by convolutional neural networks, in the fields of flow field reconstruction and aerodynamic characteristic prediction. Internationally, deep learning technology has been widely used in fluid mechanics, particularly in flow field prediction and turbulence modeling. Although deep learning methods have achieved millisecond-level inference speeds in subsonic flow field reconstruction, their reliance on regular pixel grids as input makes them unable to effectively capture boundary layer flow characteristics, resulting in insufficient reconstruction accuracy for high-gradient regions such as shock waves and boundary layers. Furthermore, most research focuses on predicting low Reynolds number flows, while transonic flows exhibit different characteristics due to factors such as fluid compressibility. In addition, existing deep learning models still have limitations when processing flow field data with complex geometries and non-uniform grids. Summary of the Invention

[0004] The problem this invention aims to solve is to improve the efficiency and applicability of flow field simulation while maintaining physical accuracy. It proposes a U-Net transonic two-dimensional airfoil flow field prediction method that integrates the geometric metric features of the finite volume method.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A U-Net transonic two-dimensional airfoil flow field prediction method that integrates geometric metric features of the finite volume method includes the following steps:

[0007] S1. Sample the transonic two-dimensional airfoil flow field to construct a two-dimensional airfoil flow field dataset, which is divided into a training set, a test set, and a validation set;

[0008] S2. Construct the U-Net flow field prediction network;

[0009] S3. Use the training set obtained in step S1 to train the U-Net flow field prediction network constructed in step S2 to obtain the trained U-Net flow field prediction network.

[0010] S4. Use the test set to quickly predict the transonic two-dimensional airfoil flow field using the U-Net flow field prediction network trained in step S3.

[0011] Furthermore, the specific implementation method of step S1 includes the following steps:

[0012] S1.1. Mesh generation: 900 sharp trailing edge airfoils were selected from the UIUC airfoil database published by the University of Illinois at Urbana-Champaign. C-type body-fitted meshes were generated using two-dimensional elliptic equations. The mesh generation parameters and topology of all airfoils were kept consistent, and the mesh dimensions were all 128×128.

[0013] S1.2. Numerical simulation method for flow field: Set the sampling range to Mach number. Angle of attack: 0.6~0.9 For -2° to +6°, Reynolds number 1×10 6 ~5×10 6 Random sampling is performed, and five operating conditions are randomly selected from the sampling range for each airfoil in step S1.1 as data samples. The flow field properties of each data sample are calculated, including the density field. Velocity field and the sound field ,in, for Directional velocity, for Directional velocity, and spliced ​​the flow field properties of each data sample into output features of 4 channels;

[0014] S1.3. Mesh coordinate transformation: Convert the geometric space information and corresponding flow field space information of each airfoil obtained in step S1.2 from the original Cartesian coordinates to curvilinear coordinates;

[0015] S1.4: Data Preprocessing: Set the input features for each training sample, including: airfoil surface grid coordinates. ,in The x-axis coordinates of the airfoil surface mesh are... The y-axis coordinates of the airfoil surface mesh are used to calculate the mesh geometric metric characteristics based on the finite volume method. ,in Represents the area of ​​the grid cell, express edge normal vector Quantity, express edge normal vector Quantity, express Side length, express edge normal vector Quantity, express edge normal vector Quantity, express Side length, incoming flow condition Mach number Angle of attack Reynolds number This yields multi-dimensional input features across 12 channels;

[0016] S1.5. After normalizing the input and output features, construct a two-dimensional airfoil flow field dataset, and divide it into training set, test set and validation set in a ratio of 7:2:1.

[0017] Furthermore, the specific implementation method of step S2 includes the following steps:

[0018] S2.1. Set the input of the U-Net flow field prediction network to a 12-channel multi-dimensional feature tensor, including 3 incoming flow conditional Mach numbers, angle of attack, Reynolds number, 7 grid geometric metric features, and 2 airfoil surface grid coordinates. The overall dimension of the input feature matrix is ​​( ,12,128,128), of which Represents the number of samples;

[0019] S2.2. Setting up the U-Net flow field prediction network: In the encoding part, the input feature matrix is ​​converted into 512-dimensional single-point data through 7 convolutional layers and downsampling layers. In the decoding part, it is converted into 512-dimensional single-point data through 7 convolutional layers and upsampling layers, and the residual structure is used to concatenate with the features of the encoding part to finally obtain the output flow field matrix.

[0020] S2.3. Set the output flow field matrix of the U-Net flow field prediction network, including density, Directional velocity, The four physical quantities—direction, velocity, and speed of sound—have the following data dimensions: ,4,128,128).

[0021] Furthermore, the specific method for training the U-Net flow field prediction network in step S3 is as follows: the training batch size is 8, the training period is 500 epochs, the optimizer is the Adam optimizer, and the initial learning rate is set to... The learning rate is gradually reduced to 10% of its initial value in the latter half of the training iterations. L1 loss is used during training, and the formula for calculating L1 loss is:

[0022]

[0023] in, For the true target value, These are the model's predicted values. Indicates the number of samples.

[0024] Furthermore, the fast prediction method for the two-dimensional airfoil flow field in step S4 is as follows: a 128×128 dimension C-shaped body-fitting mesh is generated through the two-dimensional elliptic equation, the Cartesian coordinates are converted into curvilinear coordinates, the airfoil surface mesh coordinates, the mesh geometric metric features calculated based on the finite volume method, and the flow field conditions are spliced ​​into 12 channel dimensions of input features, which are then normalized and input into the U-Net flow field prediction network trained in step S3. The output is then inversely normalized to obtain the predicted flow field.

[0025] The beneficial effects of this invention are:

[0026] The present invention discloses a U-Net transonic two-dimensional airfoil flow field prediction method that integrates geometric metric features of the finite volume method, extracting data through coordinate transformation. - The geometric features in the coordinate system are utilized, leveraging the element geometric metrics (such as element volume, surface normal vector, and boundary length) inherent in the structured mesh. This finite volume geometric information is systematically injected into the skip connections of the multi-scale U-Net, transforming it into a 128×128 feature tensor input to the convolutional neural network for model training. Flow field reconstruction results demonstrate that this method maintains physical consistency while controlling the transonic flow field reconstruction error to approximately 1%, and reduces the computation time by two orders of magnitude compared to directly solving the Navier–Stokes equations, significantly enhancing the practical value of online aerodynamic optimization and digital wind tunnel applications.

[0027] The present invention discloses a U-Net transonic two-dimensional airfoil flow field prediction method that integrates the geometric metric features of the finite volume method. This method can achieve high-precision flow field reconstruction and improve the efficiency and applicability of flow field simulation. The present invention integrates the element geometric metrics contained in the structured grid into the U-Net network, which significantly shortens the calculation time for direct solution of the Navier-Stokes equations while maintaining physical consistency, and significantly enhances the practical value of online aerodynamic optimization and digital wind tunnel. Attached Figure Description

[0028] Figure 1 This is a flowchart of a U-Net transonic two-dimensional airfoil flow field prediction method that integrates geometric metric features of the finite volume method, as described in this invention.

[0029] Figure 2 This is a schematic diagram of the structure of the U-Net flow field prediction network described in this invention;

[0030] Figure 3 The images show the effect of the U-Net transonic two-dimensional airfoil flow field prediction method that integrates the geometric metric features of the finite volume method according to the present invention. (a) is the predicted density distribution map, (b) is the calculated density distribution map, (c) is the predicted velocity distribution map in the x direction, (d) is the calculated velocity distribution map in the x direction, (e) is the predicted velocity distribution map in the y direction, (f) is the calculated velocity distribution map in the y direction, (g) is the predicted sound speed distribution map, and (h) is the calculated sound speed distribution map.

[0031] Figure 4The diagrams show the distribution of surface pressure coefficients for the NACA airfoil. (a) shows the distribution of surface pressure coefficients for the NACA airfoil at Mach 0.69, angle of attack 5.57°, and Reynolds number 4824k; (b) shows the distribution of surface pressure coefficients for the NACA airfoil at Mach 0.64, angle of attack -1.12°, and Reynolds number 1583k; (c) shows the distribution of surface pressure coefficients for the NACA airfoil at Mach 0.63, angle of attack 2.4°, and Reynolds number 2428k; and (d) shows the distribution of surface pressure coefficients for the NACA airfoil at Mach 0.72, angle of attack 1.04°, and Reynolds number 3761k. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0033] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0034] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 -Appendix Figure 4 Detailed explanation is as follows:

[0035] Example 1:

[0036] A U-Net transonic two-dimensional airfoil flow field prediction method that integrates geometric metric features of the finite volume method includes the following steps:

[0037] S1. Sample the transonic two-dimensional airfoil flow field to construct a two-dimensional airfoil flow field dataset, which is divided into a training set, a test set, and a validation set;

[0038] Furthermore, the specific implementation method of step S1 includes the following steps:

[0039] S1.1. Mesh generation: 900 sharp trailing edge airfoils were selected from the UIUC airfoil database published by the University of Illinois at Urbana-Champaign. C-type body-fitted meshes were generated using two-dimensional elliptic equations. The mesh generation parameters and topology of all airfoils were kept consistent, and the mesh dimensions were all 128×128.

[0040] S1.2. Numerical simulation method for flow field: Set the sampling range to Mach number. Angle of attack: 0.6~0.9 For -2° to +6°, Reynolds number 1×10 6 ~5×10 6 Random sampling is performed, and five operating conditions are randomly selected from the sampling range for each airfoil in step S1.1 as data samples. The flow field properties of each data sample are calculated, including the density field. Velocity field and the sound field ,in, for Directional velocity, for Directional velocity, and spliced ​​the flow field properties of each data sample into output features of 4 channels;

[0041] S1.3. Mesh coordinate transformation: Convert the geometric space information and corresponding flow field space information of each airfoil obtained in step S1.2 from the original Cartesian coordinates to curvilinear coordinates;

[0042] Furthermore, the grid coordinate transformation formula is as follows:

[0043]

[0044] in, For a Jacobi determinant, it means ( )and( Transformation matrix between coordinate systems. , ; These are the indices of the CFD mesh nodes in different directions. and It is the maximum quantity in each direction. Because The orientation is based on the airfoil geometry. The orientation is based on the vertical airfoil geometry. It can represent the geometric curves of the airfoil surface.

[0045] S1.4: Data Preprocessing: Set the input features for each training sample, including: airfoil surface grid coordinates. ,in The x-axis coordinates of the airfoil surface mesh are... The y-axis coordinates of the airfoil surface mesh are used to calculate the mesh geometric metric characteristics based on the finite volume method. ,in Represents the area of ​​the grid cell, express edge normal vector Quantity, express edge normal vector Quantity, express Side length, express edge normal vector Quantity, express edge normal vector Quantity, express Side length, incoming flow condition Mach number Angle of attack Reynolds number This yields multi-dimensional input features across 12 channels;

[0046] S1.5. After normalizing the input and output features, construct a two-dimensional airfoil flow field dataset and divide it into a training set, a test set, and a validation set in a ratio of 7:2:1.

[0047] Furthermore, the normalization formula is:

[0048]

[0049]

[0050] in, The input values ​​are normalized. The output value is the normalized value. , These represent the maximum and minimum values ​​for the corresponding channels in the dataset input values, respectively. , These are the maximum and minimum values ​​for the corresponding channels in the dataset output, respectively.

[0051] S2. Construct the U-Net flow field prediction network;

[0052] Furthermore, the specific implementation method of step S2 includes the following steps:

[0053] S2.1. Set the input of the U-Net flow field prediction network to a 12-channel multi-dimensional feature tensor, including 3 incoming flow conditional Mach numbers, angle of attack, Reynolds number, 7 grid geometric metric features, and 2 airfoil surface grid coordinates. The overall dimension of the input feature matrix is ​​( ,12,128,128), of which Represents the number of samples;

[0054] S2.2. Setting up the U-Net flow field prediction network: In the encoding part, the input feature matrix is ​​converted into 512-dimensional single-point data through 7 convolutional layers and downsampling layers. In the decoding part, it is converted into 512-dimensional single-point data through 7 convolutional layers and upsampling layers, and the residual structure is used to concatenate with the features of the encoding part to finally obtain the output flow field matrix.

[0055] S2.3. Set the output flow field matrix of the U-Net flow field prediction network, including density, Directional velocity, The four physical quantities—direction, velocity, and speed of sound—have the following data dimensions: ,4,128,128).

[0056] S3. Use the training set obtained in step S1 to train the U-Net flow field prediction network constructed in step S2 to obtain the trained U-Net flow field prediction network.

[0057] Furthermore, the specific method for training the U-Net flow field prediction network in step S3 is as follows: the training batch size is 8, the training period is 500 epochs, the optimizer is the Adam optimizer, and the initial learning rate is set to... The learning rate is gradually reduced to 10% of its initial value in the latter half of the training iterations. L1 loss is used during training, and the formula for calculating L1 loss is:

[0058]

[0059] in, For the true target value, These are the model's predicted values. Indicates the number of samples.

[0060] Furthermore, Table 1 shows the L1 loss for the training set, test set, and validation set, and Table 2 shows the relative errors for the four key indicators of density, velocity, speed of sound, and pressure in the test set.

[0061] Table 1

[0062]

[0063] Table 2

[0064]

[0065] The formula for calculating the relative density error is: The formula for calculating the relative speed error is: ( + ) / ( + The formula for calculating the relative error of sound speed is: ,in, This is the density prediction value. This is the calculated density value. This is the predicted value of the velocity in the x-direction. The calculated value is the velocity in the x-direction. This is the predicted velocity value in the y-direction. The calculated value is the velocity in the y-direction. This is the predicted value for the speed of sound. This is the calculated value for the speed of sound;

[0066] S4. Use the test set to quickly predict the transonic two-dimensional airfoil flow field using the U-Net flow field prediction network trained in step S3.

[0067] Furthermore, the fast prediction method for the two-dimensional airfoil flow field in step S4 is as follows: a 128×128 dimension C-shaped body-fitting mesh is generated through the two-dimensional elliptic equation, the Cartesian coordinates are converted into curvilinear coordinates, the airfoil surface mesh coordinates, the mesh geometric metric features calculated based on the finite volume method, and the flow field conditions are spliced ​​into 12 channel dimensions of input features, which are then normalized and input into the U-Net flow field prediction network trained in step S3. The output is then inversely normalized to obtain the predicted flow field. Figure 3 This demonstrates the NACA airfoil at Mach number. Angle of attack Reynolds number A comparison between predicted and calculated values ​​of the flow field distribution under the given conditions. Figure 4 The diagram shows the variation of the pressure coefficient distribution on the airfoil surface.

[0068] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0069] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A U-Net transonic two-dimensional airfoil flow field prediction method integrating geometric metric features of the finite volume method, characterized in that, Includes the following steps: S1. Sample the transonic two-dimensional airfoil flow field to construct a two-dimensional airfoil flow field dataset, which is divided into a training set, a test set, and a validation set; S2. Construct the U-Net flow field prediction network; S3. Use the training set obtained in step S1 to train the U-Net flow field prediction network constructed in step S2 to obtain the trained U-Net flow field prediction network. S4. Use the test set to quickly predict the transonic two-dimensional airfoil flow field using the U-Net flow field prediction network trained in step S3.

2. The U-Net transonic two-dimensional airfoil flow field prediction method based on the finite volume method geometric metric features as described in claim 1, characterized in that, The specific implementation method of step S1 includes the following steps: S1.

1. Mesh generation: 900 sharp trailing edge airfoils were selected from the UIUC airfoil database published by the University of Illinois at Urbana-Champaign. C-type body-fitted meshes were generated using two-dimensional elliptic equations. The mesh generation parameters and topology of all airfoils were kept consistent, and the mesh dimensions were all 128×128. S1.

2. Numerical simulation method for flow field: Set the sampling range to Mach number. Angle of attack: 0.6~0.9 For -2° to +6°, Reynolds number 1×10 6 ~5×10 6 Random sampling is performed, and five operating conditions are randomly selected from the sampling range for each airfoil in step S1.1 as data samples. The flow field properties of each data sample are calculated, including the density field. Velocity field and the sound field ,in, for Directional velocity, for Directional velocity, and spliced ​​the flow field properties of each data sample into output features of 4 channels; S1.

3. Mesh coordinate transformation: Convert the geometric space information and corresponding flow field space information of each airfoil obtained in step S1.2 from the original Cartesian coordinates to curvilinear coordinates; S1.4: Data Preprocessing: Set the input features for each training sample, including: airfoil surface grid coordinates. ,in The x-axis coordinates of the airfoil surface mesh are... The y-axis coordinates of the airfoil surface mesh are used to calculate the mesh geometric metric characteristics based on the finite volume method. ,in Represents the area of ​​the grid cell, express edge normal vector Quantity, express edge normal vector Quantity, express Side length, express edge normal vector Quantity, express edge normal vector Quantity, express Side length, incoming flow condition Mach number Angle of attack Reynolds number This yields multi-dimensional input features across 12 channels; S1.

5. After normalizing the input and output features, construct a two-dimensional airfoil flow field dataset, and divide it into training set, test set and validation set in a ratio of 7:2:

1.

3. The U-Net transonic two-dimensional airfoil flow field prediction method based on the finite volume method geometric metric features as described in claim 2, characterized in that, The specific implementation method of step S2 includes the following steps: S2.

1. Set the input of the U-Net flow field prediction network to a 12-channel multi-dimensional feature tensor, including 3 incoming flow conditional Mach numbers, angle of attack, Reynolds number, 7 grid geometric metric features, and 2 airfoil surface grid coordinates. The overall dimension of the input feature matrix is ​​( ,12,128,128), of which Represents the number of samples; S2.

2. Setting up the U-Net flow field prediction network: In the encoding part, the input feature matrix is ​​converted into 512-dimensional single-point data through 7 convolutional layers and downsampling layers. In the decoding part, it is converted into 512-dimensional single-point data through 7 convolutional layers and upsampling layers, and the residual structure is used to concatenate with the features of the encoding part to finally obtain the output flow field matrix. S2.

3. Set the output flow field matrix of the U-Net flow field prediction network, including density, Directional velocity, The four physical quantities—direction, velocity, and speed of sound—have the following data dimensions: ,4,128,128).

4. The U-Net transonic two-dimensional airfoil flow field prediction method based on the finite volume method geometric metric features as described in claim 3, characterized in that, The specific method for training the U-Net flow field prediction network in step S3 is as follows: the training batch size is 8, the training period is 500 epochs, the optimizer is the Adam optimizer, and the initial learning rate is set to... The learning rate is gradually reduced to 10% of its initial value in the latter half of the training iterations. L1 loss is used during training, and the formula for calculating L1 loss is: ； in, For the true target value, These are the model's predicted values. Indicates the number of samples.

5. The U-Net transonic two-dimensional airfoil flow field prediction method based on the finite volume method geometric metric features as described in claim 4, characterized in that, The fast prediction method for the two-dimensional airfoil flow field in step S4 is as follows: a 128×128 dimension C-shaped body-fitting mesh is generated by the two-dimensional elliptic equation, the Cartesian coordinates are converted into curvilinear coordinates, the airfoil surface mesh coordinates, the mesh geometric metric features calculated based on the finite volume method, and the flow field conditions are spliced ​​into 12 channel dimensions of input features, which are then normalized and input into the U-Net flow field prediction network trained in step S3. The output is then inversely normalized to obtain the predicted flow field.

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