A Fast Airfoil Grid Deformation Method Based on Principal Component Analysis

Abstract

A fast airfoil grid deformation method based on principal component analysis, which selects n different airfoils and generates corresponding flow field grids; extracts the grid point coordinates of each airfoil flow field grid, writes the mapping relationship between each grid cell and the grid coordinate points into matrix E, and writes the grid point coordinates into matrix P; uses the principal component analysis method to calculate the principal component coefficient matrix C, the principal component score matrix S, the interpretation degree vector e and the coordinate mean vector μ of matrix P; calculates the principal component dimension m; calculates the first m-dimensional principal component score vector Sm of the initial airfoil grid point coordinate vector N to generate a new principal component score vector Sm'; obtains the deformed airfoil grid coordinate vector Nt; writes the vector Nt and matrix E into a grid file according to a specific grid file format, and regenerates a new airfoil grid to realize airfoil grid deformation. In this method, the amount of calculation involved in grid deformation is very small, so it has very high computational efficiency and reduces the time consumption of grid deformation.

Description

Technical Field

[0001] The present invention relates to the technology of aircraft aerodynamic shape analysis, and further relates to the method of two-dimensional airfoil flow field grid deformation. Specifically, it is a fast airfoil grid deformation method based on principal component analysis. Background Art

[0002] Using the method of computational fluid dynamics (CFD) to conduct aerodynamic optimization analysis on the aerodynamic shape is a key technical means in aerodynamic design. In CFD calculations, it is necessary to mesh the flow field where the aerodynamic shape is located as the input of CFD calculations. The quality of the flow field grid directly determines the quality of the CFD calculation accuracy. In the calculation of airfoil aerodynamic optimization design, the quality of the airfoil flow field grid will directly determine the calculation accuracy of airfoil aerodynamic data. There are mainly two technical routes for traditional airfoil flow field grid deformation. Route one is grid reconstruction. For two-dimensional airfoil grids with simple geometric shapes, first change the airfoil surface coordinates, and then import the deformed airfoil coordinates into the grid generation software to regenerate a new airfoil grid. This method cannot guarantee the invariance of the airfoil grid spatial topological relationship. For a single two-dimensional airfoil, the calculation time of this method is within one minute. In airfoil optimization, thousands or even tens of thousands of CFD calculation iterations are often required, and new airfoil flow field grids need to be generated each time, which results in the cumulative calculation time of airfoil reconstruction being non-negligible. Route two is grid deformation. According to the deformed airfoil surface coordinates, calculate the position of each grid coordinate point again according to certain deformation rules, and then deform the grid. This method can guarantee the invariance of the spatial topological relationship of airfoil grid elements before and after deformation. However, its deformation algorithm has a large amount of calculation, and compared with route one, its calculation time has not been significantly reduced. In order to ensure the invariance of the spatial topological relationship of airfoil grid elements and improve the calculation efficiency of airfoil grid deformation, a new fast grid deformation method needs to be designed. Summary of the Invention

[0003] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a fast airfoil grid deformation method based on principal component analysis.

[0004] To achieve the above purpose, the present invention adopts the following technical solutions:

[0005] A fast airfoil grid deformation method based on principal component analysis, the specific steps include:

[0006] Step 1: Select n different airfoils and generate corresponding flow field grids;

[0007] Step 2: Extract the grid point coordinates of each airfoil flow field grid, write the mapping relationship between each grid cell and the grid point coordinates into matrix E, and write the grid point coordinates into matrix P;

[0008] Step 3: Calculate the principal component coefficient matrix C, the principal component score matrix S, the interpretability vector e, and the coordinate mean vector μ of matrix P using the principal component analysis method;

[0009] Step 4: Calculate the principal component dimension m corresponding to an interpretability greater than 99.9%;

[0010] Step 5: According to the principal component coefficient matrix C, calculate the first m - dimensional principal component score vector Sm of the initial airfoil grid point coordinate vector N, and use Sm as the shape parameter of the initial airfoil;

[0011] Step 6: Change the values of each dimension of Sm to generate a new principal component score vector Sm';

[0012] Step 7: Multiply Sm' by the transpose of the first m columns of matrix C, and then add the coordinate mean vector μ to obtain the deformed airfoil grid coordinate vector Nt;

[0013] Step 8: According to the vector Nt and matrix E, regenerate a new airfoil grid in a specific grid file format to achieve airfoil grid deformation.

[0014] Preferably, when generating the flow - field grids corresponding to n different airfoils in Step 1, the batch - processing method is adopted to ensure that the grid coordinate points of the n flow - field grids have the same topological structure.

[0015] Preferably, in Step 1, to ensure the accuracy of grid deformation, n should be not less than 200.

[0016] Preferably, in Step 2, the row vectors of matrix E store the grid node numbers corresponding to each grid cell.

[0017] Preferably, in Step 2, the grid point coordinates of each airfoil are reorganized into a one - dimensional row vector and stored in the row vectors of matrix P. Each row of matrix P stores all the grid point coordinate vectors of one airfoil.

[0018] Preferably, in Step 5, the specific calculation method of Sm is: Sm=(N - μ)·Cm.

[0019] The beneficial effect of this application is that: in the grid deformation, only the linear calculation between low - dimensional vectors and matrices is involved in Step 7, and the calculation time used can be almost ignored. Therefore, this method has high calculation efficiency and small time cost required for grid deformation. At the same time, it can ensure that the topological relationship of the airfoil flow - field grid remains consistent before and after deformation.

[0020] The following further describes this application in detail with reference to the accompanying drawings of the embodiments. Description of the Drawings

[0021] Figure 1 It is the initial airfoil flow - field grid diagram generated according to the method provided by the present invention.

[0022] Figure 2 The airfoil flow field grid diagram after deformation according to the method provided by the present invention.

[0023] Figure 3 The principle block diagram of the fast airfoil grid deformation method based on principal component analysis. Specific implementation mode

[0024] A fast airfoil grid deformation method based on principal component analysis provided by the present invention. The airfoil flow field grid deformation steps include:

[0025] Step 1: Select 1000 different airfoils, and use the batch processing method of ICEM software to generate the corresponding flow field grids. The flow field grid elements are quadrilateral, and the boundary grid elements are linear. Each airfoil grid has a total of 36720 grid elements;

[0026] Step 2: Extract the grid point coordinates of each airfoil flow field grid. Each airfoil has 36360 grid points, and write the grid point numbers corresponding to each grid cell into matrix E. Each row of matrix E corresponds to a grid cell, and the elements of matrix E are [3031 720 721; 721 720 722 723; 723 722 724 725;...]. Each row has four numbers, representing the four grid node numbers corresponding to each cell. There are a total of 36720 grid cells, so the size of matrix E is 36720 rows and 4 columns. Each airfoil has 36360 grid points. Rearrange the three-dimensional coordinates of the grid points of each airfoil grid into a one-dimensional vector and write it into matrix P. Each row of matrix P corresponds to an airfoil. Columns 1 to 36360 are the x coordinates of each grid point, columns 36361 to 72720 are the y coordinates of each grid point, and columns 72721 to 109080 are the z coordinates of each grid point. Therefore, the size of matrix P is 1000 rows and 109080 columns;

[0027] Step 3: Use the principal component analysis method to calculate the principal component coefficient matrix C, the principal component score matrix S, the interpretation degree vector e, and the coordinate mean vector μ of matrix P;

[0028] Step 4: Calculate the principal component dimension m corresponding to the interpretation degree greater than 99.9%, and calculate m = 8;

[0029] Step 5: Select the NACA 4412 airfoil as the initial airfoil. According to the principal component coefficient matrix C and the coordinate mean vector μ, calculate the first 8-dimensional principal component score vector Sm of the initial airfoil grid point coordinate vector N, and calculate Sm = [2.0416, 0.0216, 0.2510, 0.0249, 0.0133, -0.0149, -0.0030, -0.0366]. Take Sm as the shape parameter of the initial airfoil;

[0030] Step 6: Change the element values of vector Sm to generate new airfoil shape parameters. As an example, here the value of the first element of vector Sm is changed to 4 to generate a new principal component score vector Sm', Sm' = [4, 0.0216, 0.2510, 0.0249, 0.0133, -0.0149, -0.0030, -0.0366];

[0031] Step 7: Multiply Sm' by the transpose of the first 8 columns of matrix C, and then add the coordinate mean vector μ to obtain the deformed airfoil grid coordinate vector Nt;

[0032] Step 8: Re-generate a new airfoil grid in the su2 grid file format with vector Nt and matrix E to achieve airfoil grid deformation.

[0033] The initial airfoil flow field grid and the deformed airfoil flow field grid are obtained as Figure 1 and Figure 2 shown. It can be seen that the spatial topological structure of the airfoil grid cells remains consistent before and after deformation. At the same time, the first element of the principal component score vector determines the camber of the airfoil, and the change in its magnitude has an obvious impact on the airfoil grid. The larger the value, the greater the camber of the corresponding airfoil.

[0034] 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 be within the protection scope of the present invention.

Claims

1. A rapid airfoil grid deformation method based on principal component analysis, characterized in that, The specific steps are as follows: Step 1: Select n different airfoils and generate the corresponding flow field grids. In Step 1, when generating the flow field grids corresponding to n different airfoils, a batch processing method is adopted to ensure that the grid coordinate points of the n flow field grids have the same topological structure, that is, they have the same matrix E. Step 2: Extract the grid point coordinates of each airfoil flow field grid, write the mapping relationship between each grid cell and the grid coordinate points into matrix E, and write the grid point coordinates into matrix P. Step 3: Use the principal component analysis method to calculate the principal component coefficient matrix C, the principal component score matrix S, the interpretability vector e, and the coordinate mean vector μ of matrix P. Step 4: Calculate the principal component dimension m corresponding to an interpretability greater than 99.9%. Step 5: According to the principal component coefficient matrix C and the coordinate mean vector μ, calculate the first m-dimensional principal component score vector Sm of the initial airfoil grid point coordinate vector N, and use Sm as the shape parameter of the initial airfoil. Step 6: Change the values of each dimension of Sm to generate a new principal component score vector Sm'. Step 7: Multiply Sm' by the transpose of the first m columns of matrix C, and then add the coordinate mean vector μ to obtain the deformed airfoil grid coordinate vector Nt. Step 8: According to the vector Nt and matrix E, regenerate a new airfoil grid in a specific grid file format to achieve airfoil grid deformation.

2. The rapid airfoil grid deformation method based on principal component analysis according to claim 1, characterized in that, In Step 1, to ensure the accuracy of grid deformation, n should be not less than 200.

3. The rapid airfoil grid deformation method based on principal component analysis according to claim 1, characterized in that, In Step 2, the row vectors of matrix E store the grid node numbers corresponding to each grid cell.

4. The rapid airfoil grid deformation method based on principal component analysis according to claim 1, characterized in that, In Step 2, the grid point coordinates of each airfoil are reorganized into a one-dimensional row vector and stored in the row vectors of matrix P. Each row of matrix P stores all the grid point coordinate vectors of one airfoil.

5. The rapid airfoil grid deformation method based on principal component analysis according to claim 1, characterized in that, In Step 5, the specific calculation method of Sm is: Sm = (N - μ) · Cm.

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