A 2D airfoil flow field grid generation method based on a neural network surrogate model

Abstract

A two-dimensional airfoil flow field grid generation method based on a neural network surrogate model. The method uses the free form deformation (FFD) method to generate N sets of airfoil profile point coordinates; generates the flow field grids corresponding to N airfoils in a batch processing manner; and writes the grid point coordinates into matrix P. The principal component analysis method is used to reduce the dimension of the grid point coordinate data matrix P to m dimensions, and the reduced matrix is Pr. Using matrix Y and matrix Pr as the input and output of the neural network, the neural network is trained to obtain the mapped surrogate model. The FFD parameter matrix Y1 of N1 target airfoils is input into the surrogate model to obtain the corresponding reduced-dimensional matrix Pr1 of grid point coordinates. The matrix Pr1 is re-dimensioned to obtain the flow field grid point coordinate data matrix P1 of N1 target airfoils, and then written back into the grid file, thus obtaining the flow field grid files of N1 target airfoils. The grid generation method of the present invention can quickly generate airfoil flow field grid files in batches for airfoil optimization. This method has high generation efficiency, low computational cost, and high grid quality. At the same time, it can ensure that the topological relationships of the flow field grids of different airfoils are consistent.

Description

Technical Field

[0001] The present invention relates to a method for generating a two-dimensional airfoil flow field grid. Specifically, it relates to a method for generating a two-dimensional airfoil flow field grid based on a neural network surrogate model. Background Art

[0002] Using the computational fluid dynamics (CFD) method to optimize the airfoil design is a key step in the aircraft aerodynamic design process. The main steps of the current airfoil optimization design based on the CFD method are as follows: (1) parameterize the airfoil geometric shape; (2) generate the flow field calculation grid of the initial airfoil; (3) the optimization program calls the CFD solver to calculate the aerodynamic data; (4) the optimization program determines whether the aerodynamic data meets the optimization goal within the constraint range. If it meets, the optimization ends; if not, a new airfoil is generated by changing the airfoil geometric shape parameters, and the airfoil flow field grid is deformed or regenerated based on the new airfoil. In step (4) above, the commonly used grid construction method is as follows: for the two-dimensional airfoil flow field grid, if the number of grids is small, the method of regeneration is used to obtain the flow field grid of the new airfoil; if the number of flow field grids is large, the method of grid deformation is used to generate the flow field grid of the new airfoil. Among them, grid regeneration is relatively costly in terms of computing, especially when hundreds or thousands of grid generations are required in the optimization calculation, and the computing time consumed is also very large. Using the method of grid deformation, the quality of the new grid after deformation depends on the degree of geometric deformation and the grid deformation method, and the efficiency of generating the new grid also depends on the grid deformation method.

[0003] The process from the airfoil geometric shape parameters to generating the airfoil flow field grid can be regarded as a time-consuming high-precision model. The input of this model is the airfoil geometric shape parameters, and the output is the coordinates and topological relationship of the airfoil flow field grid points. Using a surrogate model such as a neural network as an approximation of this model to generate the airfoil flow field grid can reduce the computing cost of grid generation and improve the computing efficiency while ensuring the invariance of the grid topological relationship. However, the training cost of the neural network increases with the increase in the dimension of the input and output data, and the number of grid points of the airfoil flow field grid is generally above the order of magnitude of 10 4 If the coordinates of the grid points of the airfoil flow field grid are directly used as the output of the neural network, it will lead to an excessive computing cost for training. Therefore, in order to reduce the computing cost of the neural network, it is necessary to reduce the dimension of the grid point data of the airfoil flow field grid and use it as the output of the neural network. Summary of the Invention

[0004] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a method for generating a two-dimensional airfoil flow field grid based on a neural network surrogate model.

[0005] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0006] A two-dimensional airfoil flow field grid generation method based on a neural network surrogate model, the specific steps include:

[0007] Step 1: Adopt the free form deformation method, which is also called the FFD method. Generate N airfoils from N groups of F airfoil parameters in each group. The geometric shape of each airfoil is described by Nc pairs of discrete point coordinates. The FFD parameters of each airfoil are stored as a matrix Y. The matrix Y has N rows and F columns. Each row represents an airfoil, and the column elements of the matrix are the FFD parameters of each airfoil;

[0008] Step 2: Generate the flow field grids corresponding to N airfoils in a batch processing manner. The number of grids and the topological relationship of the N airfoil flow field grids are consistent, and the number of grid points of each airfoil flow field is Np;

[0009] Step 3: Extract the grid point coordinates and topological relationship M of the N airfoil flow field grids. The grid point coordinate data of the N airfoil flow field grids is represented by a matrix P. P is an N-row and Np×3-column matrix. Each row represents the flow field grid of an airfoil, and the x, y, and z coordinates of the grid points of each airfoil flow field are sequentially stored in the columns of the matrix P;

[0010] Step 4: Use the principal component analysis method to reduce the dimension of the grid point coordinate data matrix P to m dimensions. The reduced matrix is Pr. The matrix P has N rows and m columns. Each row represents the flow field grid of an airfoil, and each column represents the information after the dimensionality reduction of the grid point coordinates of each airfoil flow field;

[0011] Step 5: Use the row vectors of the matrix Y and the matrix Pr as the input and output of the neural network, train the neural network, and use the trained neural network as a surrogate model for mapping the matrix Y to the matrix Pr;

[0012] Step 6: Input the FFD parameters Y1 of N1 target airfoils into the surrogate model to obtain the corresponding matrix Pr1. Perform the inverse operation on the matrix Pr1 according to the dimensionality reduction method in Step 3 to re-increase the dimension and obtain the flow field grid coordinate matrix P1 of N1 target airfoils;

[0013] Step 7: Rewrite the matrix P1 obtained in Step 6 into the grid file according to the topological relationship M extracted in Step 3, and the flow field grid file of N1 target airfoils can be obtained.

[0014] Preferably, in Step 1, Latin hypercube sampling is used to select F FFD parameters for each airfoil, so that the FFD parameters of N groups of airfoils are evenly distributed in the design space.

[0015] Preferably, to ensure the generalization ability of the neural network, N in Step 1 should satisfy N≥100×F.

[0016] Preferably, in Step 4, 5≤m≤50.

[0017] Preferably, in step 5, the neural network is a forward neural network, the number of hidden layers is 3, and the number of neurons in each hidden layer is not less than 3×F.

[0018] The beneficial effects of the present application are as follows: The two-dimensional airfoil flow field grid generation method can quickly generate airfoil flow field grid files in batches for airfoil optimization. This method has high generation efficiency, low calculation cost, and high grid quality. At the same time, it can ensure that the topological relationships of different airfoil flow field grids are consistent. Description of the Drawings

[0019] Figure 1 It is a flow field grid diagram around a two-dimensional airfoil generated by the method provided according to the present invention.

[0020] Figure 2 It is a flow field grid diagram near the leading edge of the airfoil.

[0021] Explanation of the numbers in the figure: 1 airfoil, 2 grid, 3 leading edge of the airfoil Detailed Embodiments

[0022] A two-dimensional airfoil flow field grid generation method based on a neural network surrogate model provided according to the present invention. The steps of generating the airfoil flow field grid include:

[0023] Step 1: Generate using the free form deformation (FFD) method. 2000 airfoils are generated from 2000 groups of 6 airfoil parameters each, and the geometric shape of each airfoil is described by 100 pairs of discrete point coordinates. The FFD parameters of each airfoil are stored as a matrix Y. Matrix Y has 2000 rows and 6 columns. Each row represents an airfoil, and the column elements of the matrix are the FFD parameters of each airfoil;

[0024] Step 2: Use ICEM software to import the airfoil coordinates and generate the flow field grids corresponding to 2000 airfoils in a batch processing manner. The number of flow field grid points for each airfoil is 36360;

[0025] Step 3: Extract the grid point coordinates and topological relationship M of 2000 airfoil flow field grids. The grid point coordinate data of 2000 airfoil flow field grids is represented by a matrix P. P is a 2000-row and 36360×3-column matrix. Each row represents the flow field grid of an airfoil, and the x, y, and z coordinates of the grid points of each airfoil flow field are sequentially stored in the columns of matrix P;

[0026] Step 4: Use the principal component analysis method to reduce the dimensionality of the grid point coordinate data matrix P to 15 dimensions. The reduced matrix is Pr. Matrix P has 2000 rows and 15 columns. Each row represents the flow field grid of an airfoil, and each column represents the information after dimensionality reduction of the grid point coordinates of each airfoil flow field;

[0027] Step 5: Using the row vectors of matrix Y and matrix Pr as the input and output of the neural network, train the neural network, and use the trained neural network as the surrogate model for mapping matrix Y to matrix Pr;

[0028] Step 6: Input the FFD parameters Y1 of one target airfoil into the surrogate model to obtain the corresponding matrix Pr1. Perform the inverse operation on matrix Pr1 according to the dimensionality reduction method in Step 3 to re-increase the dimension and obtain the flow field grid coordinate matrix P1 of one target airfoil;

[0029] Step 7: Rewrite the matrix P1 obtained in Step 6 into the grid file according to the topological relationship M extracted in Step 3, and the flow field grid file of one target airfoil can be obtained.

[0030] Obtain the flow field grid 2 of the final airfoil 1 and the grid 2 near the leading edge 3 of the airfoil, as Figure 1 and Figure 2 shown.

[0031] The specific embodiments of the present invention have been described above. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made. These improvements and refinements should also fall within the protection scope of the present invention.

Claims

1. A method for generating a two-dimensional airfoil flow field grid based on a neural network surrogate model, characterized in that, The specific steps include: Step 1: Using the FFD method, generate N airfoils from N groups of F FFD parameters for each airfoil. The geometric shape of each airfoil is described by Nc pairs of discrete point coordinates. The FFD parameters of each airfoil are stored as a matrix Y. Matrix Y has N rows and F columns. Each row represents an airfoil, and the column elements of the matrix are the FFD parameters of each airfoil. In the said Step 1, Latin hypercube sampling is used to select F FFD parameters for each airfoil, so that the FFD parameters of N groups of airfoils are evenly distributed in the design space. Step 2: In a batch processing manner, generate flow field grids corresponding to N airfoils. The number of grids and the topological relationship of the N airfoil flow field grids are the same. The number of grid points for each airfoil flow field is Np. Step 3: Extract the grid point coordinates and topological relationship M of the N airfoil flow field grids. The grid point coordinate data of the N airfoil flow field grids is represented by a matrix P. P is an N-row and Np×3-column matrix. Each row represents the flow field grid of an airfoil. The x, y, and z coordinates of the grid points of each airfoil flow field are sequentially stored in the columns of matrix P. Step 4: Use the principal component analysis method to reduce the dimensionality of the grid point coordinate data matrix P to m dimensions. The reduced matrix is Pr. Matrix P has N rows and m columns. Each row represents the flow field grid of an airfoil, and each column represents the information after dimensionality reduction of the grid point coordinates of each airfoil flow field. Step 5: Use the row vectors of matrix Y and matrix Pr as the input and output of the neural network, train the neural network, and use the trained neural network as a surrogate model for mapping matrix Y to matrix Pr. Step 6: Input the FFD parameters Y1 of N1 target airfoils into the surrogate model to obtain the corresponding matrix Pr1. Perform the inverse operation on matrix Pr1 according to the dimensionality reduction method in Step 3 to re-increase the dimensionality and obtain the flow field grid coordinate matrix P1 of N1 target airfoils. Step 7: Write the matrix P1 obtained in Step 6 back into the grid file according to the topological relationship M extracted in Step 3, and the flow field grid files of N1 target airfoils can be obtained.

2. The method for generating a two-dimensional airfoil flow field grid based on a neural network surrogate model according to claim 1, characterized in that, In the said Step 1, to ensure the generalization ability of the neural network, N should satisfy N≥100×F.

3. The method for generating a two-dimensional airfoil flow field grid based on a neural network surrogate model according to claim 1, characterized in that, In the said Step 4, 5≤m≤50.

4. The method for generating a two-dimensional airfoil flow field grid based on a neural network surrogate model according to claim 1, characterized in that, In the said Step 5, the neural network is a forward neural network, with 3 hidden layers, and the number of neurons in each hidden layer is not less than 3×F.

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